Calibration of the 9-Mythen detector at the Cristal beamline at Soleil¶
Mythen detectors are 1D-strip detector sold by Dectris. On the Cristal beamline at Soleil, 9 of them are mounted on the goniometer.
This notebook explains how to calibrate precisely their position (including the wavelength used) as function of the goniometer position.
All input data are provided in a Nexus file wich contrains both the (approximate) energy, the goniometer positions (500 points have been measured) and the measured signal.
As pyFAI is not made for 1D data, the Mythen detector will be considered as a 1x1280 image.
We start by importing a whole bunch of modules:
In [1]:
%matplotlib nbagg
In [2]:
from collections import OrderedDict
#import ipympl
from matplotlib import pyplot as plt
import numpy
import h5py
from pyFAI import goniometer
from pyFAI.detectors import Detector
from pyFAI.goniometer import ExtendedTransformation, GoniometerRefinement
from pyFAI.control_points import ControlPoints
from pyFAI.geometryRefinement import GeometryRefinement
from pyFAI.gui import jupyter
from pyFAI.units import hc
from pyFAI.calibrant import get_calibrant
from pyFAI.containers import Integrate1dResult
import ipywidgets as widgets
from scipy.signal import find_peaks_cwt
from scipy.interpolate import interp1d
from scipy.optimize import bisect, minimize
from scipy.spatial import distance_matrix
import time
start_time = time.time()
/mntdirect/_scisoft/users/jupyter/jupy35/lib/python3.5/site-packages/h5py/__init__.py:36: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.
from ._conv import register_converters as _register_converters
The data file can be downoaded from: http://www.silx.org/pub/pyFAI/gonio/LaB6_17keV_att3_tth2C_24_01_2018_19-43-20_1555.nxs
In [3]:
#Open the Nexus file and retrieve the actual positions:
h5 = h5py.File("LaB6_17keV_att3_tth2C_24_01_2018_19-43-20_1555.nxs", mode="r")
position = h5["/LaB6_17keV_att3_1555/scan_data/actuator_1_1"][:]
print("Positions: ", position[:5], "...")
Positions: [90.00000001 89.79994445 89.5998889 89.39994445 89.19994445] ...
In [4]:
#Read all data
data = {}
ds_names = []
for idx in range(1,13):
name = "data_%02i"%idx
ds = h5["/LaB6_17keV_att3_1555/scan_data/"+name][:]
print(name, ds.shape)
if ds.shape[1]<2000:
#Keep only the single modules
data[name] = ds
ds_names.append(name)
print(ds_names)
data_01 (501, 5120)
data_02 (501, 1280)
data_03 (501, 1280)
data_04 (501, 1280)
data_05 (501, 1280)
data_06 (501, 5120)
data_07 (501, 1280)
data_08 (501, 1280)
data_09 (501, 1280)
data_10 (501, 1280)
data_11 (501, 1280)
data_12 (501, 1280)
['data_02', 'data_03', 'data_04', 'data_05', 'data_07', 'data_08', 'data_09', 'data_10', 'data_11', 'data_12']
In [5]:
#Define a Mythen-detector mounted vertically:
class MythenV(Detector):
"Verical Mythen dtrip detector from Dectris"
aliases = ["MythenV 1280"]
force_pixel = True
MAX_SHAPE = (1280, 1)
def __init__(self,pixel1=50e-6, pixel2=8e-3):
super(MythenV, self).__init__(pixel1=pixel1, pixel2=pixel2)
In [6]:
#Define all modules as single detectors of class MythenV.
# Each one has a mask defined from dummy-values in the dataset
modules = {}
for name, ds in data.items():
one_module = MythenV()
mask = ds[0]<0
#discard the first 20 and last 20 pixels as their intensities are less reliable
mask[:20] = True
mask[-20:] = True
one_module.mask = mask.reshape(-1,1)
modules[name] = one_module
for k,v in modules.items():
print(k, v.name)
data_08 MythenV 1280
data_07 MythenV 1280
data_03 MythenV 1280
data_02 MythenV 1280
data_04 MythenV 1280
data_05 MythenV 1280
data_10 MythenV 1280
data_12 MythenV 1280
data_09 MythenV 1280
data_11 MythenV 1280
In [7]:
# Define a peak-picking function based on the dataset-name and the frame_id:
def peak_picking(module_name, frame_id,
threshold=500):
"""Peak-picking base on find_peaks_cwt from scipy plus
second-order tailor exapention refinement for sub-pixel resolution.
The half-pixel offset is accounted here, i.e pixel #0 has its center at 0.5
"""
module = modules[module_name]
msk = module.mask.ravel()
spectrum = data[module_name][frame_id]
guess = find_peaks_cwt(spectrum, [20])
valid = numpy.logical_and(numpy.logical_not(msk[guess]),
spectrum[guess]>threshold)
guess = guess[valid]
#Based on maximum is f'(x) = 0 ~ f'(x0) + (x-x0)*(f''(x0))
df = numpy.gradient(spectrum)
d2f = numpy.gradient(df)
bad = d2f==0
d2f[bad] = 1e-10 #prevent devision by zero. Discared later on
cor = df / d2f
cor[abs(cor)>1] = 0
cor[bad] = 0
ref = guess - cor[guess] + 0.5 #half a pixel offset
x = numpy.zeros_like(ref) + 0.5 #half a pixel offset
return numpy.vstack((ref,x)).T
%timeit peak_picking(ds_names[0], 93)
print(peak_picking(ds_names[0], 93))
18.8 ms ± 792 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)
[[287.06072343 0.5 ]]
In [8]:
nrj = h5["/LaB6_17keV_att3_1555/CRISTAL/Monochromator/energy"][0]
wl = hc / nrj *1e-10
print("Energy (keV): ",nrj, "\nWavelength (A): ",wl)
LaB6 = get_calibrant("LaB6")
LaB6.wavelength = wl
print(LaB6)
Energy (keV): 17.027082549190933
Wavelength (A): 7.281587849134994e-11
LaB6 Calibrant at wavelength 7.281587849134994e-11
In [9]:
#This cell defines the transformation of coordinates for a simple goniometer mounted vertically.
trans = ExtendedTransformation(dist_expr="dist",
poni1_expr="poni1",
poni2_expr="poni2",
rot1_expr="rot1",
rot2_expr="pi*(offset+scale*angle)/180.",
rot3_expr="0.0",
wavelength_expr="hc/nrj*1e-10",
param_names=["dist", "poni1", "poni2", "rot1", "offset", "scale", "nrj"],
pos_names=["angle"],
constants={"hc": hc})
In [10]:
def get_position(idx):
"Returns the postion of the goniometer for the given frame_id"
return position[idx]
#Approximate offset for the module #0 at 0°
print("Approximated offset for the first module: ",get_position(36))
Approximated offset for the first module: 82.79994445106844
In [11]:
#This interactive plot lets one visualize any spectra acquired by any module
fig, ax = plt.subplots()
line = ax.plot(data[ds_names[0]][250])[0]
ligne = plt.Line2D(xdata=[640,640], ydata=[-500, 1000], figure=fig, linestyle="--", color='red', axes=ax)
ax.add_line(ligne)
ax.set_title("spectrum")
fig.show()
def update(module_id, frame_id):
spectrum = data[ds_names[module_id]][frame_id]
line.set_data(numpy.arange(spectrum.size), spectrum)
ax.set_title("Module %i, Frame %i"%(module_id, frame_id))
fig.canvas.draw()
interactive_plot = widgets.interactive(update,
module_id=(0, len(data)-1),
frame_id=(0, data[ds_names[0]].shape[0]-1))
display(interactive_plot)
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In [12]:
#Work with the first module corresponding to:
name = ds_names[0]
print(name)
ds = data[name]
module = modules[name]
#Use the previous widget to select:
## the index where the beam-center is in the middle of the module
zero_pos = 36
## The frame index where the first LaB6 peak enters the right-hand side of the spectrum
peak_zero_start = 74
## The frame index where this first LaB6 leaves the spectrum or the second LaB6 peak appears:
peak_zero_end = 94
# The frames between peak_zero_start and peak_zero_end will be used to calibrate roughly the goniometer
# and used later for finer peak extraction
data_02
In [13]:
param0 = {"dist": 0.72,
"poni1": 640*50e-6,
"poni2": 4e-3,
"rot1":0,
"offset": -get_position(zero_pos),
"scale":1,
"nrj": nrj}
#Lock enegy for now and a couple of other parameters
bounds0 = {"nrj": (nrj, nrj),
"dist": (0.71, 0.73),
"poni2": (4e-3, 4e-3),
"rot1": (0,0),
"scale":(1,1),
}
gonioref0 = GoniometerRefinement(param0,
get_position,
trans,
detector=module,
wavelength=wl,
bounds=bounds0
)
goniometers = {name: gonioref0}
print(gonioref0)
GoniometerRefinement with 0 geometries labeled: .
In [14]:
# Extract the frames where only the peak zero from LaB6 is present.
for i in range(peak_zero_start, peak_zero_end):
cp = ControlPoints(calibrant=LaB6, wavelength=wl)
peak = peak_picking(name, i)
if len(peak)!=1:
continue
cp.append([peak[0]], ring=0)
img = ds[i].reshape((-1,1)) #Images are vertical ... transpose the spectrum
sg = gonioref0.new_geometry("%s_%04i"%(name,i),
image=img,
metadata=i,
control_points=cp,
calibrant=LaB6)
sg.geometry_refinement.data = numpy.array(cp.getList())
print(gonioref0)
print("Residual error before fit:")
print(gonioref0.chi2())
GoniometerRefinement with 20 geometries labeled: data_02_0074, data_02_0075, data_02_0076, data_02_0077, data_02_0078, data_02_0079, data_02_0080, data_02_0081, data_02_0082, data_02_0083, data_02_0084, data_02_0085, data_02_0086, data_02_0087, data_02_0088, data_02_0089, data_02_0090, data_02_0091, data_02_0092, data_02_0093.
Residual error before fit:
6.737384336276989e-07
In [15]:
#First refinement:
gonioref0.refine2()
Cost function before refinement: 6.737384336276989e-07
[ 7.20000000e-01 3.20000000e-02 4.00000000e-03 0.00000000e+00
-8.27999445e+01 1.00000000e+00 1.70270825e+01]
fun: 2.490988798391531e-11
jac: array([ 1.58414573e-07, 2.91897065e-08, 5.74391333e-11, -6.39962716e-10,
3.42479452e-11, 1.40698490e-07, -1.59997085e-11])
message: 'Optimization terminated successfully.'
nfev: 19
nit: 2
njev: 2
status: 0
success: True
x: array([ 7.19994724e-01, 3.14085784e-02, 4.00000000e-03, 0.00000000e+00,
-8.27999519e+01, 1.00000000e+00, 1.70270825e+01])
Cost function after refinement: 2.490988798391531e-11
GonioParam(dist=0.7199947243683663, poni1=0.03140857835160603, poni2=0.004, rot1=0.0, offset=-82.7999518865857, scale=1.0, nrj=17.027082549190933)
maxdelta on: poni1 (1) 0.032 --> 0.03140857835160603
Out[15]:
array([ 7.19994724e-01, 3.14085784e-02, 4.00000000e-03, 0.00000000e+00,
-8.27999519e+01, 1.00000000e+00, 1.70270825e+01])
In [16]:
#Here we extract all spectra for peaks,
# If there are as many peaks as expected from the theoritical LaB6. perform the assignment.
#Peaks from LaB6:
tths = LaB6.get_2th()
for i in range(peak_zero_end, ds.shape[0]):
peak = peak_picking(name, i)
ai=gonioref0.get_ai(get_position(i))
tth = ai.array_from_unit(unit="2th_rad", scale=False)
tth_low = tth[20]
tth_hi = tth[-20]
ttmin, ttmax = min(tth_low, tth_hi), max(tth_low, tth_hi)
valid_peaks = numpy.logical_and(ttmin<=tths, tths<ttmax)
cnt = valid_peaks.sum()
if (len(peak) == cnt):
cp = ControlPoints(calibrant=LaB6, wavelength=wl)
#revert the order of assignment if needed !!
if tth_hi < tth_low:
peak = peak[-1::-1]
for p, r in zip(peak, numpy.where(valid_peaks)[0]):
#print(p,r)
cp.append([p], ring=r)
img = ds[i].reshape((-1,1))
sg = gonioref0.new_geometry("%s_%04i"%(name,i),
image=img,
metadata=i,
control_points=cp,
calibrant=LaB6)
sg.geometry_refinement.data = numpy.array(cp.getList())
#print(sg.label, len(sg.geometry_refinement.data))
#print(gonioref0)
print(" Number of peaks found and used for refinement")
print(sum([len(sg.geometry_refinement.data) for sg in gonioref0.single_geometries.values()]))
print("Residual error before fitting: ", gonioref0.chi2())
Number of peaks found and used for refinement
1203
Residual error before fitting: 3.118672809442448e-06
In [17]:
gonioref0.refine2()
Cost function before refinement: 3.118672809442448e-06
[ 7.19994724e-01 3.14085784e-02 4.00000000e-03 0.00000000e+00
-8.27999519e+01 1.00000000e+00 1.70270825e+01]
fun: 2.734250432678472e-06
jac: array([-5.58224542e-08, -3.65304231e-10, 3.63058044e-06, -2.62495314e-06,
6.31729336e-10, 1.53969062e-04, 9.87797637e-06])
message: 'Optimization terminated successfully.'
nfev: 65
nit: 7
njev: 7
status: 0
success: True
x: array([ 7.23095347e-01, 3.18453768e-02, 4.00000000e-03, 0.00000000e+00,
-8.27999466e+01, 1.00000000e+00, 1.70270825e+01])
Cost function after refinement: 2.734250432678472e-06
GonioParam(dist=0.7230953467494027, poni1=0.03184537681912273, poni2=0.004, rot1=0.0, offset=-82.79994661694376, scale=1.0, nrj=17.027082549190933)
maxdelta on: dist (0) 0.7199947243683663 --> 0.7230953467494027
Out[17]:
array([ 7.23095347e-01, 3.18453768e-02, 4.00000000e-03, 0.00000000e+00,
-8.27999466e+01, 1.00000000e+00, 1.70270825e+01])
In [18]:
gonioref0.set_bounds("poni1", -1, 1)
gonioref0.set_bounds("poni2", -1, 1)
gonioref0.set_bounds("rot1", -1, 1)
gonioref0.set_bounds("scale", 0.9, 1.1)
gonioref0.refine2()
Cost function before refinement: 2.734250432678472e-06
[ 7.23095347e-01 3.18453768e-02 4.00000000e-03 0.00000000e+00
-8.27999466e+01 1.00000000e+00 1.70270825e+01]
fun: 2.6891723022540698e-06
jac: array([-5.14464347e-07, -1.24120874e-07, 5.95670514e-07, -4.28660144e-07,
-9.28110921e-10, -8.53860058e-08, -1.60467593e-06])
message: 'Optimization terminated successfully.'
nfev: 36
nit: 4
njev: 4
status: 0
success: True
x: array([ 7.23096248e-01, 3.20537111e-02, 3.98485468e-03, 1.09479202e-05,
-8.27999440e+01, 9.99415047e-01, 1.70270825e+01])
Cost function after refinement: 2.6891723022540698e-06
GonioParam(dist=0.7230962484347616, poni1=0.03205371109950758, poni2=0.003984854679408886, rot1=1.0947920188414968e-05, offset=-82.7999439896301, scale=0.9994150470263444, nrj=17.027082549190933)
maxdelta on: scale (5) 1.0 --> 0.9994150470263444
Out[18]:
array([ 7.23096248e-01, 3.20537111e-02, 3.98485468e-03, 1.09479202e-05,
-8.27999440e+01, 9.99415047e-01, 1.70270825e+01])
In [19]:
# Perform the azimuthal intgration of all data for the first module:
mg = gonioref0.get_mg(position)
mg.radial_range = (0, 95)
images = [i.reshape(-1, 1) for i in ds]
res_mg = mg.integrate1d(images, 50000)
results={name: res_mg}
print(results)
{'data_02': (array([9.50000113e-04, 2.85000011e-03, 4.75000011e-03, ...,
9.49952500e+01, 9.49971500e+01, 9.49990500e+01]), array([0.00000000e+00, 0.00000000e+00, 0.00000000e+00, ...,
1.27163417e+08, 1.30591594e+08, 1.33665235e+08]))}
In [20]:
# Plot the integrated pattern vs expected peak positions:
LaB6_new = get_calibrant("LaB6")
LaB6_new.wavelength = hc/gonioref0.param[-1]*1e-10
p = jupyter.plot1d(res_mg, calibrant=LaB6_new)
p.figure.show()
Data type cannot be displayed: application/javascript
In [21]:
#Peak profile function based on a bilinear interpolations:
def calc_fwhm(integrate_result, calibrant, tth_min=None, tth_max=None):
"calculate the tth position and FWHM for each peak"
delta = integrate_result.intensity[1:] - integrate_result.intensity[:-1]
maxima = numpy.where(numpy.logical_and(delta[:-1]>0, delta[1:]<0))[0]
minima = numpy.where(numpy.logical_and(delta[:-1]<0, delta[1:]>0))[0]
maxima += 1
minima += 1
tth = []
FWHM = []
if tth_min is None:
tth_min = integrate_result.radial[0]
if tth_max is None:
tth_max = integrate_result.radial[-1]
for tth_rad in calibrant.get_2th():
tth_deg = tth_rad*integrate_result.unit.scale
if (tth_deg<=tth_min) or (tth_deg>=tth_max):
continue
idx_theo = abs(integrate_result.radial-tth_deg).argmin()
id0_max = abs(maxima-idx_theo).argmin()
id0_min = abs(minima-idx_theo).argmin()
I_max = integrate_result.intensity[maxima[id0_max]]
I_min = integrate_result.intensity[minima[id0_min]]
tth_maxi = integrate_result.radial[maxima[id0_max]]
I_thres = (I_max + I_min)/2.0
if minima[id0_min]>maxima[id0_max]:
if id0_min == 0:
min_lo = integrate_result.radial[0]
else:
min_lo = integrate_result.radial[minima[id0_min-1]]
min_hi = integrate_result.radial[minima[id0_min]]
else:
if id0_min == len(minima) -1:
min_hi = integrate_result.radial[-1]
else:
min_hi = integrate_result.radial[minima[id0_min+1]]
min_lo = integrate_result.radial[minima[id0_min]]
f = interp1d(integrate_result.radial, integrate_result.intensity-I_thres)
try:
tth_lo = bisect(f, min_lo, tth_maxi)
tth_hi = bisect(f, tth_maxi, min_hi)
except:
pass
else:
FWHM.append(tth_hi-tth_lo)
tth.append(tth_deg)
return tth, FWHM
In [22]:
# Peak error:
def calc_peak_error(integrate_result, calibrant, tth_min=10, tth_max=95):
"calculate the tth position and FWHM for each peak"
peaks = find_peaks_cwt(integrate_result.intensity, [10])
df = numpy.gradient(integrate_result.intensity)
d2f = numpy.gradient(df)
bad = d2f==0
d2f[bad] = 1e-10
cor = df / d2f
print((abs(cor)>1).sum())
cor[abs(cor)>1] = 0
cor[bad] = 0
got = numpy.interp(peaks-cor[peaks],
numpy.arange(len(integrate_result.radial)),
integrate_result.radial)
mask = numpy.logical_and(got>=tth_min,
got<=tth_max)
got = got[mask]
target = numpy.array(calibrant.get_2th())*integrate_result.unit.scale
mask = numpy.logical_and(target>=tth_min,
target<=tth_max)
target = target[mask]
print(len(got), len(target))
d2 = distance_matrix(target.reshape(-1, 1 ),
got.reshape(-1, 1), p=1)
return target, target-got[d2.argmin(axis=-1)]
In [23]:
fig, ax = plt.subplots()
ax.plot(*calc_fwhm(res_mg, LaB6_new), "o", label="FWHM")
ax.plot(*calc_peak_error(res_mg, LaB6_new), "o", label="offset")
ax.set_title("Peak shape & error as function of the angle")
ax.set_xlabel(res_mg.unit.label)
ax.legend()
fig.show()
Data type cannot be displayed: application/javascript
29209
81 60
Module 1¶
We can apply the same procdure for the second module ... and try to rationalize the procedure.
In [24]:
module_id = 1
name = ds_names[module_id]
ds = data[name]
zero_pos = 64
frame_start = 103
frame_stop = 123
In [25]:
param1 = {"dist": 0.72,
"poni1": 640*50e-6,
"poni2": 4e-3,
"rot1":0,
"offset": -get_position(zero_pos),
"scale":1,
"nrj": nrj}
#Lock enegy for now and a couple of other parameters
bounds1 = {"nrj": (nrj, nrj),
"dist": (0.7, 0.8),
"poni2": (4e-3, 4e-3),
"rot1": (0,0),
"scale":(1,1), }
gonioref1 = GoniometerRefinement(param1,
get_position,
trans,
detector=modules[name],
wavelength=wl,
bounds=bounds1
)
print(gonioref1)
goniometers[name]=gonioref1
GoniometerRefinement with 0 geometries labeled: .
In [26]:
#Exctract frames with peak#0
for i in range(frame_start, frame_stop):
cp = ControlPoints(calibrant=LaB6, wavelength=wl)
peak = peak_picking(name, i)
if len(peak)!=1:
continue
cp.append([peak[0]], ring=0)
img = (ds[i]).reshape((-1,1))
sg = gonioref1.new_geometry("%s_%04i"%(name,i),
image=img,
metadata=i,
control_points=cp,
calibrant=LaB6)
sg.geometry_refinement.data = numpy.array(cp.getList())
print(gonioref1)
print(gonioref1.chi2())
GoniometerRefinement with 20 geometries labeled: data_03_0103, data_03_0104, data_03_0105, data_03_0106, data_03_0107, data_03_0108, data_03_0109, data_03_0110, data_03_0111, data_03_0112, data_03_0113, data_03_0114, data_03_0115, data_03_0116, data_03_0117, data_03_0118, data_03_0119, data_03_0120, data_03_0121, data_03_0122.
1.4524700202830549e-06
In [27]:
gonioref1.refine2()
Cost function before refinement: 1.4524700202830549e-06
[ 7.20000000e-01 3.20000000e-02 4.00000000e-03 0.00000000e+00
-7.72000000e+01 1.00000000e+00 1.70270825e+01]
fun: 2.3431861472723482e-11
jac: array([ 1.37377624e-07, 1.03462536e-07, 2.38592839e-09, -2.23238045e-09,
9.89688559e-10, 1.85837277e-07, -5.81633804e-10])
message: 'Optimization terminated successfully.'
nfev: 19
nit: 2
njev: 2
status: 0
success: True
x: array([ 7.20006378e-01, 3.28683965e-02, 4.00000000e-03, 0.00000000e+00,
-7.71999891e+01, 1.00000000e+00, 1.70270825e+01])
Cost function after refinement: 2.3431861472723482e-11
GonioParam(dist=0.7200063780313144, poni1=0.03286839651397956, poni2=0.004, rot1=0.0, offset=-77.19998908850266, scale=1.0, nrj=17.027082549190933)
maxdelta on: poni1 (1) 0.032 --> 0.03286839651397956
Out[27]:
array([ 7.20006378e-01, 3.28683965e-02, 4.00000000e-03, 0.00000000e+00,
-7.71999891e+01, 1.00000000e+00, 1.70270825e+01])
In [28]:
#Exctract all frames with peak>0
tths = LaB6.get_2th()
#print(tths)
for i in range(frame_stop, ds.shape[0]):
frame_name = "%s_%04i"%(name, i)
if frame_name in gonioref1.single_geometries:
continue
peak = peak_picking(name, i)
ai=gonioref1.get_ai(get_position(i))
tth = ai.array_from_unit(unit="2th_rad", scale=False)
tth_low = tth[20]
tth_hi = tth[-20]
ttmin, ttmax = min(tth_low, tth_hi), max(tth_low, tth_hi)
valid_peaks = numpy.logical_and(ttmin<=tths, tths<ttmax)
cnt = valid_peaks.sum()
if (len(peak) == cnt) and cnt>0:
cp = ControlPoints(calibrant=LaB6, wavelength=wl)
#revert the order of assignment if needed !!
if tth_hi < tth_low:
peak = peak[-1::-1]
for p, r in zip(peak, numpy.where(valid_peaks)[0]):
cp.append([p], ring=r)
img = ds[i].reshape((-1,1))
sg = gonioref1.new_geometry(frame_name,
image=img,
metadata=i,
control_points=cp,
calibrant=LaB6)
sg.geometry_refinement.data = numpy.array(cp.getList())
#print(frame_name, len(sg.geometry_refinement.data))
print(" Number of peaks found and used for refinement")
print(sum([len(sg.geometry_refinement.data) for sg in gonioref1.single_geometries.values()]))
print("Residual error before fitting: ", gonioref1.chi2())
Number of peaks found and used for refinement
1183
Residual error before fitting: 6.334769973618362e-07
In [29]:
gonioref1.refine2()
gonioref1.set_bounds("poni1", -1, 1)
gonioref1.set_bounds("poni2", -1, 1)
gonioref1.set_bounds("rot1", -1, 1)
gonioref1.set_bounds("scale", 0.9, 1.1)
gonioref1.refine2()
Cost function before refinement: 6.334769973618362e-07
[ 7.20006378e-01 3.28683965e-02 4.00000000e-03 0.00000000e+00
-7.71999891e+01 1.00000000e+00 1.70270825e+01]
fun: 1.3797542164386038e-07
jac: array([-4.62580205e-07, 2.40834463e-08, 5.10766142e-06, -3.67570741e-06,
1.35589318e-11, 2.65546301e-04, 1.99388955e-05])
message: 'Optimization terminated successfully.'
nfev: 19
nit: 2
njev: 2
status: 0
success: True
x: array([ 7.20006340e-01, 3.33754761e-02, 4.00000000e-03, 0.00000000e+00,
-7.71999827e+01, 1.00000000e+00, 1.70270825e+01])
Cost function after refinement: 1.3797542164386038e-07
GonioParam(dist=0.7200063395001164, poni1=0.033375476115602126, poni2=0.004, rot1=0.0, offset=-77.19998271232215, scale=1.0, nrj=17.027082549190933)
maxdelta on: poni1 (1) 0.03286839651397956 --> 0.033375476115602126
Cost function before refinement: 1.3797542164386038e-07
[ 7.20006340e-01 3.33754761e-02 4.00000000e-03 0.00000000e+00
-7.71999827e+01 1.00000000e+00 1.70270825e+01]
fun: 8.828686563664207e-10
jac: array([ 6.56076518e-08, 6.55451977e-07, -1.75522725e-07, 1.26240119e-07,
7.93555705e-09, 2.91447578e-07, 1.05708096e-07])
message: 'Optimization terminated successfully.'
nfev: 117
nit: 13
njev: 13
status: 0
success: True
x: array([ 7.20682081e-01, 3.36782425e-02, 4.05801126e-03, -4.44860018e-05,
-7.71999788e+01, 9.98967223e-01, 1.70270825e+01])
Cost function after refinement: 8.828686563664207e-10
GonioParam(dist=0.7206820809610033, poni1=0.033678242508301, poni2=0.00405801125545738, rot1=-4.448600179438364e-05, offset=-77.19997879310895, scale=0.9989672227193093, nrj=17.027082549190933)
maxdelta on: scale (5) 1.0 --> 0.9989672227193093
Out[29]:
array([ 7.20682081e-01, 3.36782425e-02, 4.05801126e-03, -4.44860018e-05,
-7.71999788e+01, 9.98967223e-01, 1.70270825e+01])
In [30]:
mg1 = gonioref1.get_mg(position)
mg1.radial_range = (0, 95)
images = [i.reshape(-1, 1) for i in data[name]]
res_mg1 = mg1.integrate1d(images, 50000)
results[name] = res_mg1
area_pixel=0.04011793214486481 area_sum=0.05472285778563535, Error= -0.3640498116411517
area_pixel=0.06755918226705582 area_sum=0.07017344439747103, Error= -0.038695881783785545
area_pixel=0.06470384723321665 area_sum=0.06854713835898787, Error= -0.05939818558112286
area_pixel=0.038258287348172715 area_sum=0.05426051394830549, Error= -0.4182682422373795
area_pixel=0.06290299608614092 area_sum=0.06750646087344028, Error= -0.07318355362589196
area_pixel=0.06866181632504009 area_sum=0.0710979827571788, Error= -0.03548065813764767
area_pixel=0.045481003274128184 area_sum=0.05690843539150094, Error= -0.2512572567604998
area_pixel=0.051372066242729275 area_sum=0.060437735665688296, Error= -0.17647079601829507
area_pixel=0.08412331180916155 area_sum=0.08447601010651973, Error= -0.004192634476377893
area_pixel=0.07467387290401106 area_sum=0.07603231757541912, Error= -0.018191699701370204
area_pixel=0.0624099895059711 area_sum=0.0673026438866445, Error= -0.07839537259023732
area_pixel=0.04195900037770173 area_sum=0.05573620360979919, Error= -0.32834917676968967
area_pixel=0.05715571439263911 area_sum=0.06402386234646332, Error= -0.12016555171793514
area_pixel=0.08038761552922224 area_sum=0.08112738452122062, Error= -0.009202524382993493
area_pixel=0.07843450940492147 area_sum=0.07937664635982263, Error= -0.012011765765465969
area_pixel=0.05907229451306506 area_sum=0.06522039353885213, Error= -0.10407753882706032
area_pixel=0.040121002784973214 area_sum=0.055076739171659624, Error= -0.3727657672676088
area_pixel=0.061909101662060095 area_sum=0.06698716844120342, Error= -0.08202455927825762
area_pixel=0.07486883011958412 area_sum=0.0762213872653684, Error= -0.01806569093738887
area_pixel=0.08390728427714045 area_sum=0.08427957645881265, Error= -0.004436947100355958
area_pixel=0.052353526345367385 area_sum=0.061054313175336744, Error= -0.16619294701510143
area_pixel=0.05061563353131504 area_sum=0.060016745022665983, Error= -0.18573533186213373
area_pixel=0.08664846785681313 area_sum=0.08667317488344674, Error= -0.000285140952225944
area_pixel=0.07201199510202194 area_sum=0.07377214053011852, Error= -0.024442392209838324
area_pixel=0.062293472479096224 area_sum=0.06710802538833513, Error= -0.07728824092852621
area_pixel=0.04161483391746934 area_sum=0.055387896893291044, Error= -0.3309652275228704
area_pixel=0.06664231871870818 area_sum=0.06966942981335798, Error= -0.045423255865795896
area_pixel=0.06246630299088629 area_sum=0.06709144439642731, Error= -0.07404218249022702
area_pixel=0.04218618802653751 area_sum=0.05535486043373737, Error= -0.312156016535934
In [31]:
LaB6_new = get_calibrant("LaB6")
LaB6_new.wavelength = hc/gonioref1.param[-1]*1e-10
p = jupyter.plot1d(res_mg1, calibrant=LaB6_new)
p.figure.show()
Data type cannot be displayed: application/javascript
In [32]:
fig, ax = plt.subplots()
ax.plot(*calc_fwhm(res_mg1, LaB6_new, 10, 88), "o", label="FWHM")
ax.plot(*calc_peak_error(res_mg1, LaB6_new, 10, 88), "o", label="error")
ax.set_title("Peak shape & error as function of the angle")
ax.set_xlabel(res_mg.unit.label)
ax.legend()
fig.show()
Data type cannot be displayed: application/javascript
27712
72 53
All other Modules¶
We define now an automatic procedure for any module. The detection used 3 parameter visually extracted from the Figure1:
- zero_pos: the frame where the beam-stop is in the center of the module
- frame_start: the frame where the first peak of LaB6 appears (positive)
- frame_stop: the frame where the second peak of LaB6 appears (positive)
This is enough for boot-strapping the goniometer configuration.
In [33]:
def add_module(name,
zero_pos,
frame_start,
frame_stop,
):
ds = data[name]
param = {"dist": 0.72,
"poni1": 640*50e-6,
"poni2": 4e-3,
"rot1":0,
"offset": -get_position(zero_pos),
"scale":1,
"nrj": nrj}
#Lock enegy for now and a couple of other parameters
bounds = {"nrj": (nrj, nrj),
"dist": (0.7, 0.8),
"poni2": (4e-3, 4e-3),
"rot1": (0,0),
"scale": (1,1)}
gonioref = GoniometerRefinement(param,
get_position,
trans,
detector=modules[name],
wavelength=wl,
bounds=bounds
)
goniometers[name] = gonioref
for i in range(frame_start, frame_stop):
cp = ControlPoints(calibrant=LaB6, wavelength=wl)
peak = peak_picking(name, i)
if len(peak)!=1:
continue
cp.append([peak[0]], ring=0)
img = (ds[i]).reshape((-1,1))
sg = gonioref.new_geometry("%s_%04i"%(name, i),
image=img,
metadata=i,
control_points=cp,
calibrant=LaB6)
sg.geometry_refinement.data = numpy.array(cp.getList())
print(gonioref.chi2())
gonioref.refine2()
tths = LaB6.get_2th()
#print(tths)
for i in range(frame_stop, ds.shape[0]):
frame_name = "%s_%04i"%(name, i)
if frame_name in gonioref.single_geometries:
continue
peak = peak_picking(name, i)
ai=gonioref.get_ai(get_position(i))
tth = ai.array_from_unit(unit="2th_rad", scale=False)
tth_low = tth[20]
tth_hi = tth[-20]
ttmin, ttmax = min(tth_low, tth_hi), max(tth_low, tth_hi)
valid_peaks = numpy.logical_and(ttmin<=tths, tths<ttmax)
cnt = valid_peaks.sum()
if (len(peak) == cnt) and cnt>0:
cp = ControlPoints(calibrant=LaB6, wavelength=wl)
#revert the order of assignment if needed !!
if tth_hi < tth_low:
peak = peak[-1::-1]
for p, r in zip(peak, numpy.where(valid_peaks)[0]):
cp.append([p], ring=r)
img = (ds[i]).reshape((-1,1))
sg = gonioref.new_geometry(frame_name,
image=img,
metadata=i,
control_points=cp,
calibrant=LaB6)
sg.geometry_refinement.data = numpy.array(cp.getList())
#print(frame_name, len(sg.geometry_refinement.data))
print(" Number of peaks found and used for refinement")
print(sum([len(sg.geometry_refinement.data) for sg in gonioref.single_geometries.values()]))
gonioref.refine2()
gonioref.set_bounds("poni1", -1, 1)
gonioref.set_bounds("poni2", -1, 1)
gonioref.set_bounds("rot1", -1, 1)
gonioref.set_bounds("scale", 0.9, 1.1)
gonioref.refine2()
mg = gonioref.get_mg(position)
mg.radial_range = (0, 95)
images = [i.reshape(-1, 1) for i in ds]
res_mg = mg.integrate1d(images, 50000)
results[name] = res_mg
LaB6_new = get_calibrant("LaB6")
LaB6_new.wavelength = hc/gonioref.param[-1]*1e-10
p = jupyter.plot1d(res_mg, calibrant=LaB6_new)
p.figure.show()
fig, ax = plt.subplots()
ax.plot(*calc_fwhm(res_mg, LaB6_new), "o", label="FWHM")
ax.plot(*calc_peak_error(res_mg, LaB6_new, 10, 89), "o", label="error")
ax.set_title("Peak shape & error as function of the angle")
ax.set_xlabel(res_mg.unit.label)
ax.legend()
fig.show()
In [34]:
add_module(ds_names[2],
92,
131,
151)
8.406338771704969e-06
Cost function before refinement: 8.406338771704969e-06
[ 7.20000000e-01 3.20000000e-02 4.00000000e-03 0.00000000e+00
-7.15999445e+01 1.00000000e+00 1.70270825e+01]
fun: 1.808572002652971e-11
jac: array([ 4.57424569e-08, 8.17041295e-07, 2.47626008e-08, -1.79775418e-08,
9.91633086e-09, 6.60392633e-07, -5.86643086e-09])
message: 'Optimization terminated successfully.'
nfev: 19
nit: 2
njev: 2
status: 0
success: True
x: array([ 7.20018961e-01, 3.40893083e-02, 4.00000000e-03, 0.00000000e+00,
-7.15999182e+01, 1.00000000e+00, 1.70270825e+01])
Cost function after refinement: 1.808572002652971e-11
GonioParam(dist=0.7200189605020697, poni1=0.03408930832642036, poni2=0.004, rot1=0.0, offset=-71.59991818229837, scale=1.0, nrj=17.027082549190933)
maxdelta on: poni1 (1) 0.032 --> 0.03408930832642036
Number of peaks found and used for refinement
1093
Cost function before refinement: 5.55731697942323e-07
[ 7.20018961e-01 3.40893083e-02 4.00000000e-03 0.00000000e+00
-7.15999182e+01 1.00000000e+00 1.70270825e+01]
fun: 1.1961227626432414e-07
jac: array([-9.44231683e-07, 2.30905108e-08, 4.88576803e-06, -3.51407454e-06,
-1.74829040e-11, 2.33600314e-04, 1.70705134e-05])
message: 'Optimization terminated successfully.'
nfev: 19
nit: 2
njev: 2
status: 0
success: True
x: array([ 7.20018345e-01, 3.45650482e-02, 4.00000000e-03, 0.00000000e+00,
-7.15999122e+01, 1.00000000e+00, 1.70270825e+01])
Cost function after refinement: 1.1961227626432414e-07
GonioParam(dist=0.7200183446976933, poni1=0.034565048153275144, poni2=0.004, rot1=0.0, offset=-71.59991220000985, scale=1.0, nrj=17.027082549190933)
maxdelta on: poni1 (1) 0.03408930832642036 --> 0.034565048153275144
Cost function before refinement: 1.1961227626432414e-07
[ 7.20018345e-01 3.45650482e-02 4.00000000e-03 0.00000000e+00
-7.15999122e+01 1.00000000e+00 1.70270825e+01]
fun: 6.570539910514945e-10
jac: array([ 2.18222064e-08, 1.73947572e-08, -1.60806027e-07, 1.15807314e-07,
-1.82359884e-10, 8.08015633e-09, 8.85008258e-08])
message: 'Optimization terminated successfully.'
nfev: 90
nit: 10
njev: 10
status: 0
success: True
x: array([ 7.20686437e-01, 3.48247495e-02, 4.04316666e-03, -3.37686772e-05,
-7.15999088e+01, 9.98982863e-01, 1.70270825e+01])
Cost function after refinement: 6.570539910514945e-10
GonioParam(dist=0.7206864370148651, poni1=0.03482474946152798, poni2=0.004043166657976692, rot1=-3.376867719168802e-05, offset=-71.5999088132962, scale=0.9989828627069963, nrj=17.027082549190933)
maxdelta on: scale (5) 1.0 --> 0.9989828627069963
area_pixel=0.04101321524826673 area_sum=0.04635522282228846, Error= -0.13025088478639793
area_pixel=0.04805074298699985 area_sum=0.050770187552341764, Error= -0.056595265677320754
area_pixel=0.05470148979267009 area_sum=0.056228786108716095, Error= -0.027920561612394357
area_pixel=0.062098761379894896 area_sum=0.062392206682634205, Error= -0.004725461445907599
area_pixel=0.040415219606433794 area_sum=0.046336505956633724, Error= -0.1465112996505234
area_pixel=0.06211637552982907 area_sum=0.062425234207049, Error= -0.004972258516139761
area_pixel=0.0545957431661801 area_sum=0.05610676727387377, Error= -0.027676591984367248
area_pixel=0.046408760633763535 area_sum=0.04924681820885727, Error= -0.06115348775396895
area_pixel=0.04985697246649501 area_sum=0.05218296613471554, Error= -0.04665332757185872
area_pixel=0.0522213978747601 area_sum=0.05417632538646705, Error= -0.03743537307054384
area_pixel=0.06152426635945751 area_sum=0.06185028694021803, Error= -0.005299056779575941
area_pixel=0.04466499326386497 area_sum=0.04810216511625828, Error= -0.07695449167735718
area_pixel=0.043420597173687625 area_sum=0.04734951311542082, Error= -0.09048507384679808
Data type cannot be displayed: application/javascript
Data type cannot be displayed: application/javascript
25667
180 54
In [35]:
add_module(ds_names[3],
121,
159,
179)
1.0825408441330163e-06
Cost function before refinement: 1.0825408441330163e-06
[ 7.20000000e-01 3.20000000e-02 4.00000000e-03 0.00000000e+00
-6.57999444e+01 1.00000000e+00 1.70270825e+01]
fun: 2.4921939380829473e-11
jac: array([-8.60015175e-08, 7.99451827e-08, 1.64794931e-09, -8.07493243e-10,
6.18853503e-10, -1.33401994e-08, -3.62117520e-10])
message: 'Optimization terminated successfully.'
nfev: 19
nit: 2
njev: 2
status: 0
success: True
x: array([ 7.20006745e-01, 3.27496622e-02, 4.00000000e-03, 0.00000000e+00,
-6.57999350e+01, 1.00000000e+00, 1.70270825e+01])
Cost function after refinement: 2.4921939380829473e-11
GonioParam(dist=0.7200067449851295, poni1=0.032749662244436796, poni2=0.004, rot1=0.0, offset=-65.79993502488618, scale=1.0, nrj=17.027082549190933)
maxdelta on: poni1 (1) 0.032 --> 0.032749662244436796
Number of peaks found and used for refinement
978
Cost function before refinement: 4.705197877733383e-07
[ 7.20006745e-01 3.27496622e-02 4.00000000e-03 0.00000000e+00
-6.57999350e+01 1.00000000e+00 1.70270825e+01]
fun: 9.924141633593764e-08
jac: array([-1.34035538e-09, -8.95816754e-12, 4.47653376e-06, -3.22526285e-06,
-3.95764310e-10, 1.97125028e-04, 1.39658085e-05])
message: 'Optimization terminated successfully.'
nfev: 64
nit: 7
njev: 7
status: 0
success: True
x: array([ 7.20481821e-01, 3.31886380e-02, 4.00000000e-03, 0.00000000e+00,
-6.57999293e+01, 1.00000000e+00, 1.70270825e+01])
Cost function after refinement: 9.924141633593764e-08
GonioParam(dist=0.7204818213178118, poni1=0.03318863803715359, poni2=0.004, rot1=0.0, offset=-65.7999293473278, scale=1.0, nrj=17.027082549190933)
maxdelta on: dist (0) 0.7200067449851295 --> 0.7204818213178118
Cost function before refinement: 9.924141633593764e-08
[ 7.20481821e-01 3.31886380e-02 4.00000000e-03 0.00000000e+00
-6.57999293e+01 1.00000000e+00 1.70270825e+01]
fun: 5.124963686571038e-10
jac: array([-5.05292020e-07, -5.37136276e-09, -1.29798578e-07, 9.55532346e-08,
-4.36381951e-10, 2.56600519e-09, 8.43817010e-08])
message: 'Optimization terminated successfully.'
nfev: 46
nit: 5
njev: 5
status: 0
success: True
x: array([ 7.20482931e-01, 3.34099564e-02, 3.97791142e-03, 1.59099880e-05,
-6.57999266e+01, 9.98999110e-01, 1.70270825e+01])
Cost function after refinement: 5.124963686571038e-10
GonioParam(dist=0.7204829305671493, poni1=0.033409956436720734, poni2=0.003977911420613329, rot1=1.5909988045817424e-05, offset=-65.79992655965417, scale=0.9989991098968561, nrj=17.027082549190933)
maxdelta on: scale (5) 1.0 --> 0.9989991098968561
Data type cannot be displayed: application/javascript
Data type cannot be displayed: application/javascript
24026
384 54
In [36]:
add_module(ds_names[4],
150,
188,
208)
2.3192859672732885e-07
Cost function before refinement: 2.3192859672732885e-07
[ 7.20000000e-01 3.20000000e-02 4.00000000e-03 0.00000000e+00
-6.00000556e+01 1.00000000e+00 1.70270825e+01]
fun: 2.0856624751999954e-10
jac: array([-2.72031959e-07, 2.34632462e-08, -3.13650477e-11, 1.14575097e-09,
-9.14368789e-11, -1.88744526e-07, 5.83778581e-11])
message: 'Optimization terminated successfully.'
nfev: 19
nit: 2
njev: 2
status: 0
success: True
x: array([ 7.19996884e-01, 3.16531473e-02, 4.00000000e-03, 0.00000000e+00,
-6.00000599e+01, 1.00000000e+00, 1.70270825e+01])
Cost function after refinement: 2.0856624751999954e-10
GonioParam(dist=0.719996884236354, poni1=0.031653147292955666, poni2=0.004, rot1=0.0, offset=-60.00005992106343, scale=1.0, nrj=17.027082549190933)
maxdelta on: poni1 (1) 0.032 --> 0.031653147292955666
Number of peaks found and used for refinement
864
Cost function before refinement: 3.883355149577502e-07
[ 7.19996884e-01 3.16531473e-02 4.00000000e-03 0.00000000e+00
-6.00000599e+01 1.00000000e+00 1.70270825e+01]
fun: 8.35586015918641e-08
jac: array([-2.49360177e-09, -2.03934647e-11, 4.26768070e-06, -3.07547620e-06,
-2.94530622e-10, 1.68280037e-04, 1.16002486e-05])
message: 'Optimization terminated successfully.'
nfev: 64
nit: 7
njev: 7
status: 0
success: True
x: array([ 7.20644233e-01, 3.20496137e-02, 4.00000000e-03, 0.00000000e+00,
-6.00000548e+01, 1.00000000e+00, 1.70270825e+01])
Cost function after refinement: 8.35586015918641e-08
GonioParam(dist=0.7206442326818199, poni1=0.032049613716226354, poni2=0.004, rot1=0.0, offset=-60.000054800019825, scale=1.0, nrj=17.027082549190933)
maxdelta on: dist (0) 0.719996884236354 --> 0.7206442326818199
Cost function before refinement: 8.35586015918641e-08
[ 7.20644233e-01 3.20496137e-02 4.00000000e-03 0.00000000e+00
-6.00000548e+01 1.00000000e+00 1.70270825e+01]
fun: 3.3388878229483034e-10
jac: array([-3.34948071e-07, -1.35145738e-09, -1.13491295e-07, 8.31385815e-08,
-3.43393425e-10, 3.68209766e-09, 5.32985622e-08])
message: 'Optimization terminated successfully.'
nfev: 46
nit: 5
njev: 5
status: 0
success: True
x: array([ 7.20645314e-01, 3.22371238e-02, 3.97565133e-03, 1.75424155e-05,
-6.00000524e+01, 9.99011856e-01, 1.70270825e+01])
Cost function after refinement: 3.3388878229483034e-10
GonioParam(dist=0.7206453140156728, poni1=0.03223712376780837, poni2=0.003975651331253134, rot1=1.7542415484114082e-05, offset=-60.000052437600765, scale=0.999011855791219, nrj=17.027082549190933)
maxdelta on: scale (5) 1.0 --> 0.999011855791219
Data type cannot be displayed: application/javascript
Data type cannot be displayed: application/javascript
22258
578 54
In [37]:
add_module(ds_names[5],
178,
216,
236)
1.496585538687667e-06
Cost function before refinement: 1.496585538687667e-06
[ 7.20000000e-01 3.20000000e-02 4.00000000e-03 0.00000000e+00
-5.43998333e+01 1.00000000e+00 1.70270825e+01]
fun: 2.0171535150920134e-10
jac: array([-2.79014458e-07, 1.12723053e-07, 2.76456642e-09, -8.39426390e-10,
1.01678678e-09, -1.46581687e-07, -5.97716569e-10])
message: 'Optimization terminated successfully.'
nfev: 19
nit: 2
njev: 2
status: 0
success: True
x: array([ 7.20008138e-01, 3.28813990e-02, 4.00000000e-03, 0.00000000e+00,
-5.43998223e+01, 1.00000000e+00, 1.70270825e+01])
Cost function after refinement: 2.0171535150920134e-10
GonioParam(dist=0.7200081378039512, poni1=0.03288139900481467, poni2=0.004, rot1=0.0, offset=-54.399822256631786, scale=1.0, nrj=17.027082549190933)
maxdelta on: poni1 (1) 0.032 --> 0.03288139900481467
Number of peaks found and used for refinement
754
Cost function before refinement: 3.084426464441637e-07
[ 7.20008138e-01 3.28813990e-02 4.00000000e-03 0.00000000e+00
-5.43998223e+01 1.00000000e+00 1.70270825e+01]
fun: 6.551090453612858e-08
jac: array([-1.59759495e-09, -1.69126935e-11, 3.81129886e-06, -2.74614198e-06,
-3.33598038e-10, 1.33732118e-04, 8.98242363e-06])
message: 'Optimization terminated successfully.'
nfev: 64
nit: 7
njev: 7
status: 0
success: True
x: array([ 7.20526837e-01, 3.32363709e-02, 4.00000000e-03, 0.00000000e+00,
-5.43998177e+01, 1.00000000e+00, 1.70270825e+01])
Cost function after refinement: 6.551090453612858e-08
GonioParam(dist=0.7205268365472406, poni1=0.03323637090038128, poni2=0.004, rot1=0.0, offset=-54.39981766227154, scale=1.0, nrj=17.027082549190933)
maxdelta on: dist (0) 0.7200081378039512 --> 0.7205268365472406
Cost function before refinement: 6.551090453612858e-08
[ 7.20526837e-01 3.32363709e-02 4.00000000e-03 0.00000000e+00
-5.43998177e+01 1.00000000e+00 1.70270825e+01]
fun: 2.9801782405594906e-10
jac: array([-6.28824819e-07, -6.16534335e-09, -8.41801711e-08, 6.31905195e-08,
-4.25490289e-10, 1.87107307e-09, 5.29587814e-08])
message: 'Optimization terminated successfully.'
nfev: 46
nit: 5
njev: 5
status: 0
success: True
x: array([ 7.20528271e-01, 3.33948197e-02, 3.97295090e-03, 1.94838596e-05,
-5.43998157e+01, 9.99025942e-01, 1.70270825e+01])
Cost function after refinement: 2.9801782405594906e-10
GonioParam(dist=0.7205282706408196, poni1=0.033394819722196205, poni2=0.003972950903091611, rot1=1.948385963684671e-05, offset=-54.399815665191156, scale=0.999025941539747, nrj=17.027082549190933)
maxdelta on: scale (5) 1.0 --> 0.999025941539747
Data type cannot be displayed: application/javascript
Data type cannot be displayed: application/javascript
20560
758 54
In [38]:
add_module(ds_names[6],
207,
245,
266)
7.414763745399852e-08
Cost function before refinement: 7.414763745399852e-08
[ 7.20000000e-01 3.20000000e-02 4.00000000e-03 0.00000000e+00
-4.85998889e+01 1.00000000e+00 1.70270825e+01]
fun: 5.6513401976066356e-11
jac: array([-2.81311437e-07, 1.90457697e-08, -2.47022619e-10, 1.33814411e-09,
-1.23389936e-10, -2.00557892e-07, 7.73080818e-11])
message: 'Optimization terminated successfully.'
nfev: 19
nit: 2
njev: 2
status: 0
success: True
x: array([ 7.19998572e-01, 3.18038587e-02, 4.00000000e-03, 0.00000000e+00,
-4.85998914e+01, 1.00000000e+00, 1.70270825e+01])
Cost function after refinement: 5.6513401976066356e-11
GonioParam(dist=0.719998571752675, poni1=0.031803858748058605, poni2=0.004, rot1=0.0, offset=-48.599891358709684, scale=1.0, nrj=17.027082549190933)
maxdelta on: poni1 (1) 0.032 --> 0.031803858748058605
Number of peaks found and used for refinement
626
Cost function before refinement: 2.383350348017308e-07
[ 7.19998572e-01 3.18038587e-02 4.00000000e-03 0.00000000e+00
-4.85998914e+01 1.00000000e+00 1.70270825e+01]
fun: 5.1984312387232055e-08
jac: array([-2.19915020e-09, -2.37196929e-11, 3.57712533e-06, -2.57769667e-06,
-2.59923194e-10, 1.07698151e-04, 7.05422505e-06])
message: 'Optimization terminated successfully.'
nfev: 64
nit: 7
njev: 7
status: 0
success: True
x: array([ 7.20606858e-01, 3.21138531e-02, 4.00000000e-03, 0.00000000e+00,
-4.85998873e+01, 1.00000000e+00, 1.70270825e+01])
Cost function after refinement: 5.1984312387232055e-08
GonioParam(dist=0.7206068584664383, poni1=0.03211385308050831, poni2=0.004, rot1=0.0, offset=-48.599887342357356, scale=1.0, nrj=17.027082549190933)
maxdelta on: dist (0) 0.719998571752675 --> 0.7206068584664383
Cost function before refinement: 5.1984312387232055e-08
[ 7.20606858e-01 3.21138531e-02 4.00000000e-03 0.00000000e+00
-4.85998873e+01 1.00000000e+00 1.70270825e+01]
fun: 2.5561187046317613e-10
jac: array([-6.63680455e-07, 8.68967625e-08, -6.74647493e-08, 5.12958215e-08,
7.87452992e-10, 2.88084273e-09, 4.15782562e-08])
message: 'Optimization terminated successfully.'
nfev: 54
nit: 6
njev: 6
status: 0
success: True
x: array([ 7.20609298e-01, 3.22472627e-02, 3.96893520e-03, 2.23757106e-05,
-4.85998857e+01, 9.99040899e-01, 1.70270825e+01])
Cost function after refinement: 2.5561187046317613e-10
GonioParam(dist=0.7206092976334295, poni1=0.03224726268736372, poni2=0.003968935202854616, rot1=2.237571059770315e-05, offset=-48.599885660072495, scale=0.9990408988314912, nrj=17.027082549190933)
maxdelta on: scale (5) 1.0 --> 0.9990408988314912
area_pixel=0.041071116230573246 area_sum=0.04123092083600752, Error= -0.0038909243307907342
area_pixel=0.0404747680993891 area_sum=0.04058389121931238, Error= -0.0026960777058762783
Data type cannot be displayed: application/javascript
Data type cannot be displayed: application/javascript
18647
952 54
In [39]:
add_module(ds_names[7],
236,
273,
293)
4.37748174147368e-06
Cost function before refinement: 4.37748174147368e-06
[ 7.20000000e-01 3.20000000e-02 4.00000000e-03 0.00000000e+00
-4.27998889e+01 1.00000000e+00 1.70270825e+01]
fun: 9.109058243486396e-11
jac: array([-3.53771074e-07, 3.50167703e-09, -7.17406458e-10, 1.96667227e-09,
-3.65232464e-10, -2.61708398e-07, 2.20481224e-10])
message: 'Optimization terminated successfully.'
nfev: 19
nit: 2
njev: 2
status: 0
success: True
x: array([ 7.19986034e-01, 3.04925065e-02, 4.00000000e-03, 0.00000000e+00,
-4.27999078e+01, 1.00000000e+00, 1.70270825e+01])
Cost function after refinement: 9.109058243486396e-11
GonioParam(dist=0.7199860338026991, poni1=0.030492506521307684, poni2=0.004, rot1=0.0, offset=-42.79990784447931, scale=1.0, nrj=17.027082549190933)
maxdelta on: poni1 (1) 0.032 --> 0.030492506521307684
Number of peaks found and used for refinement
543
Cost function before refinement: 1.9115723976987742e-07
[ 7.19986034e-01 3.04925065e-02 4.00000000e-03 0.00000000e+00
-4.27999078e+01 1.00000000e+00 1.70270825e+01]
fun: 4.1213792481813325e-08
jac: array([-3.06070636e-09, -2.41167086e-11, 3.21647439e-06, -2.31812136e-06,
-3.62528230e-10, 8.61096023e-05, 5.54324342e-06])
message: 'Optimization terminated successfully.'
nfev: 64
nit: 7
njev: 7
status: 0
success: True
x: array([ 7.20705559e-01, 3.07684347e-02, 4.00000000e-03, 0.00000000e+00,
-4.27999042e+01, 1.00000000e+00, 1.70270825e+01])
Cost function after refinement: 4.1213792481813325e-08
GonioParam(dist=0.7207055592224313, poni1=0.030768434748054685, poni2=0.004, rot1=0.0, offset=-42.79990417388946, scale=1.0, nrj=17.027082549190933)
maxdelta on: dist (0) 0.7199860338026991 --> 0.7207055592224313
Cost function before refinement: 4.1213792481813325e-08
[ 7.20705559e-01 3.07684347e-02 4.00000000e-03 0.00000000e+00
-4.27999042e+01 1.00000000e+00 1.70270825e+01]
fun: 1.9055962541521217e-10
jac: array([-5.20672544e-07, -3.45117956e-07, -5.78527760e-08, 4.38009067e-08,
-4.68311260e-09, 9.35212499e-08, 5.08197212e-08])
message: 'Optimization terminated successfully.'
nfev: 45
nit: 5
njev: 5
status: 0
success: True
x: array([ 7.20707163e-01, 3.08633971e-02, 3.96520588e-03, 2.50699030e-05,
-4.27999030e+01, 9.99050597e-01, 1.70270825e+01])
Cost function after refinement: 1.9055962541521217e-10
GonioParam(dist=0.7207071627511924, poni1=0.03086339714237221, poni2=0.003965205877861361, rot1=2.5069903048049418e-05, offset=-42.79990297383393, scale=0.99905059684665, nrj=17.027082549190933)
maxdelta on: scale (5) 1.0 --> 0.99905059684665
area_pixel=0.04131177354259297 area_sum=0.04228396460577287, Error= -0.023533026539699672
area_pixel=0.0435894947035802 area_sum=0.04387578172532226, Error= -0.006567798587455262
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Data type cannot be displayed: application/javascript
16809
1107 54
In [40]:
add_module(ds_names[8],
264,
302,
322)
9.734044802496035e-08
Cost function before refinement: 9.734044802496035e-08
[ 7.20000000e-01 3.20000000e-02 4.00000000e-03 0.00000000e+00
-3.72000000e+01 1.00000000e+00 1.70270825e+01]
fun: 1.3838347147363678e-10
jac: array([-5.98673543e-07, 2.23605236e-08, -1.03159942e-10, 2.50403027e-09,
-2.11195058e-10, -4.33428498e-07, 1.29258940e-10])
message: 'Optimization terminated successfully.'
nfev: 19
nit: 2
njev: 2
status: 0
success: True
x: array([ 7.19998053e-01, 3.17753501e-02, 4.00000000e-03, 0.00000000e+00,
-3.72000028e+01, 1.00000000e+00, 1.70270825e+01])
Cost function after refinement: 1.3838347147363678e-10
GonioParam(dist=0.7199980533232613, poni1=0.03177535006475983, poni2=0.004, rot1=0.0, offset=-37.20000282727144, scale=1.0, nrj=17.027082549190933)
maxdelta on: poni1 (1) 0.032 --> 0.03177535006475983
Number of peaks found and used for refinement
454
Cost function before refinement: 1.430842008138168e-07
[ 7.19998053e-01 3.17753501e-02 4.00000000e-03 0.00000000e+00
-3.72000028e+01 1.00000000e+00 1.70270825e+01]
fun: 3.226849481117596e-08
jac: array([-3.92485422e-09, -5.23527888e-11, 2.95969591e-06, -2.13336162e-06,
-3.04084313e-10, 6.79809093e-05, 4.29992953e-06])
message: 'Optimization terminated successfully.'
nfev: 64
nit: 7
njev: 7
status: 0
success: True
x: array([ 7.20809333e-01, 3.20129561e-02, 4.00000000e-03, 0.00000000e+00,
-3.71999997e+01, 1.00000000e+00, 1.70270825e+01])
Cost function after refinement: 3.226849481117596e-08
GonioParam(dist=0.7208093328161905, poni1=0.032012956081398876, poni2=0.004, rot1=0.0, offset=-37.19999969780997, scale=1.0, nrj=17.027082549190933)
maxdelta on: dist (0) 0.7199980533232613 --> 0.7208093328161905
Cost function before refinement: 3.226849481117596e-08
[ 7.20809333e-01 3.20129561e-02 4.00000000e-03 0.00000000e+00
-3.71999997e+01 1.00000000e+00 1.70270825e+01]
fun: 1.8511910126699818e-10
jac: array([-5.57402301e-07, 1.08439870e-09, -4.85885850e-08, 3.72815016e-08,
-3.49842101e-10, 3.44041984e-09, 3.16520936e-08])
message: 'Optimization terminated successfully.'
nfev: 45
nit: 5
njev: 5
status: 0
success: True
x: array([ 7.20810790e-01, 3.20817605e-02, 3.95963325e-03, 2.90908690e-05,
-3.71999988e+01, 9.99058845e-01, 1.70270825e+01])
Cost function after refinement: 1.8511910126699818e-10
GonioParam(dist=0.7208107904725951, poni1=0.03208176053609102, poni2=0.003959633245361843, rot1=2.9090869024017394e-05, offset=-37.1999988266373, scale=0.9990588449954669, nrj=17.027082549190933)
maxdelta on: scale (5) 1.0 --> 0.9990588449954669
area_pixel=0.04876436188373834 area_sum=0.050127698054059644, Error= -0.027957633764832325
area_pixel=0.057546003803974344 area_sum=0.05775905585124136, Error= -0.0037022909182844216
area_pixel=0.049658293833474865 area_sum=0.05076774880169413, Error= -0.022341785884543948
area_pixel=0.05525805937418937 area_sum=0.055742972286024095, Error= -0.00877542420646828
area_pixel=0.05413146279471537 area_sum=0.05471036770655596, Error= -0.010694425791447673
area_pixel=0.045739492253746405 area_sum=0.04707526635197212, Error= -0.029203955540549473
area_pixel=0.04829832444085547 area_sum=0.04934824839708468, Error= -0.021738310146036582
area_pixel=0.05408463708295397 area_sum=0.054632906002321624, Error= -0.010137239499762784
area_pixel=0.04180745340076797 area_sum=0.04491414146774922, Error= -0.0743094308376167
area_pixel=0.04855682651641935 area_sum=0.04971370658799365, Error= -0.023825281728061563
area_pixel=0.05821213808510883 area_sum=0.058390691277043244, Error= -0.0030672845528085186
area_pixel=0.053533284197945896 area_sum=0.0542348167245984, Error= -0.013104604680305085
area_pixel=0.05444126075367084 area_sum=0.055046238495225275, Error= -0.011112485882569193
area_pixel=0.05139325908436465 area_sum=0.052436334224842895, Error= -0.020295952408193915
Data type cannot be displayed: application/javascript
Data type cannot be displayed: application/javascript
16876
1111 54
In [41]:
len(goniometers)
Out[41]:
9
In [42]:
# print all the parameters to be able to compare them visually
goniometers["data_12"] = goniometers["data_11"]
for name in ds_names:
print(name, *["%8.4e"%i for i in goniometers[name].param])
data_02 7.2310e-01 3.2054e-02 3.9849e-03 1.0948e-05 -8.2800e+01 9.9942e-01 1.7027e+01
data_03 7.2068e-01 3.3678e-02 4.0580e-03 -4.4486e-05 -7.7200e+01 9.9897e-01 1.7027e+01
data_04 7.2069e-01 3.4825e-02 4.0432e-03 -3.3769e-05 -7.1600e+01 9.9898e-01 1.7027e+01
data_05 7.2048e-01 3.3410e-02 3.9779e-03 1.5910e-05 -6.5800e+01 9.9900e-01 1.7027e+01
data_07 7.2065e-01 3.2237e-02 3.9757e-03 1.7542e-05 -6.0000e+01 9.9901e-01 1.7027e+01
data_08 7.2053e-01 3.3395e-02 3.9730e-03 1.9484e-05 -5.4400e+01 9.9903e-01 1.7027e+01
data_09 7.2061e-01 3.2247e-02 3.9689e-03 2.2376e-05 -4.8600e+01 9.9904e-01 1.7027e+01
data_10 7.2071e-01 3.0863e-02 3.9652e-03 2.5070e-05 -4.2800e+01 9.9905e-01 1.7027e+01
data_11 7.2081e-01 3.2082e-02 3.9596e-03 2.9091e-05 -3.7200e+01 9.9906e-01 1.7027e+01
data_12 7.2081e-01 3.2082e-02 3.9596e-03 2.9091e-05 -3.7200e+01 9.9906e-01 1.7027e+01
Use the negative part of the spectum ...¶
Until now, we used only the data where 2th >0 For the last modules, this thows away half of the data.
We setup here a way to assign the peaks for the negative part of the spectrum.
In [43]:
def complete_gonio(module_id=None, name=None):
"Scan missing frames for un-indexed peaks"
if name is None:
name = ds_names[module_id]
gonioref = goniometers[name]
ds = data[name]
print("Number of peaks previously found:",
sum([len(sg.geometry_refinement.data) for sg in gonioref.single_geometries.values()]))
tths = LaB6.get_2th()
for i in range(ds.shape[0]):
frame_name = "%s_%04i"%(name, i)
if frame_name in gonioref.single_geometries:
continue
peak = peak_picking(name, i)
ai=gonioref.get_ai(get_position(i))
tth = ai.array_from_unit(unit="2th_rad", scale=False)
tth_low = tth[20]
tth_hi = tth[-20]
ttmin, ttmax = min(tth_low, tth_hi), max(tth_low, tth_hi)
valid_peaks = numpy.logical_and(ttmin<=tths, tths<ttmax)
cnt = valid_peaks.sum()
if (len(peak) == cnt) and cnt>0:
cp = ControlPoints(calibrant=LaB6, wavelength=wl)
#revert the order of assignment if needed !!
if tth_hi < tth_low:
peak = peak[-1::-1]
for p, r in zip(peak, numpy.where(valid_peaks)[0]):
cp.append([p], ring=r)
img = ds[i].reshape((-1,1))
sg = gonioref.new_geometry(frame_name,
image=img,
metadata=i,
control_points=cp,
calibrant=LaB6)
sg.geometry_refinement.data = numpy.array(cp.getList())
#print(frame_name, len(sg.geometry_refinement.data))
print("Number of peaks found after re-scan:",
sum([len(sg.geometry_refinement.data) for sg in gonioref.single_geometries.values()]))
return gonioref
In [44]:
gonio8 = complete_gonio(module_id=8)
gonio8.refine2()
Number of peaks previously found: 454
Number of peaks found after re-scan: 1006
Cost function before refinement: 4.70706125439368e-09
[ 7.20810790e-01 3.20817605e-02 3.95963325e-03 2.90908690e-05
-3.71999988e+01 9.99058845e-01 1.70270825e+01]
fun: 9.802737682604375e-10
jac: array([-8.29338917e-07, 1.79786978e-08, -2.22576465e-07, 1.63791395e-07,
-1.37361011e-10, -3.00380388e-08, 3.83178298e-08])
message: 'Optimization terminated successfully.'
nfev: 37
nit: 4
njev: 4
status: 0
success: True
x: array([ 7.20813440e-01, 3.20849228e-02, 3.96153953e-03, 2.77060750e-05,
-3.71999988e+01, 9.98991349e-01, 1.70270825e+01])
Cost function after refinement: 9.802737682604375e-10
GonioParam(dist=0.7208134400755615, poni1=0.03208492277691861, poni2=0.003961539527372513, rot1=2.770607503862905e-05, offset=-37.19999878574453, scale=0.9989913487191389, nrj=17.027082549190933)
maxdelta on: scale (5) 0.9990588449954669 --> 0.9989913487191389
Out[44]:
array([ 7.20813440e-01, 3.20849228e-02, 3.96153953e-03, 2.77060750e-05,
-3.71999988e+01, 9.98991349e-01, 1.70270825e+01])
In [45]:
gonio7 = complete_gonio(module_id=7)
Number of peaks previously found: 543
Number of peaks found after re-scan: 1004
In [46]:
gonio7.refine2()
Cost function before refinement: 2.049750654664114e-09
[ 7.20707163e-01 3.08633971e-02 3.96520588e-03 2.50699030e-05
-4.27999030e+01 9.99050597e-01 1.70270825e+01]
fun: 6.982178014396509e-10
jac: array([-6.61610503e-07, 1.82061135e-08, -2.31096076e-07, 1.69227578e-07,
-1.05927128e-10, -2.98934004e-08, 2.67495021e-08])
message: 'Optimization terminated successfully.'
nfev: 37
nit: 4
njev: 4
status: 0
success: True
x: array([ 7.20709219e-01, 3.08662496e-02, 3.96669042e-03, 2.39916666e-05,
-4.27999029e+01, 9.99006679e-01, 1.70270825e+01])
Cost function after refinement: 6.982178014396509e-10
GonioParam(dist=0.7207092190734912, poni1=0.030866249621701404, poni2=0.0039666904208374675, rot1=2.3991666571782472e-05, offset=-42.799902936952186, scale=0.9990066787571606, nrj=17.027082549190933)
maxdelta on: scale (5) 0.99905059684665 --> 0.9990066787571606
Out[46]:
array([ 7.20709219e-01, 3.08662496e-02, 3.96669042e-03, 2.39916666e-05,
-4.27999029e+01, 9.99006679e-01, 1.70270825e+01])
In [47]:
gonio6 = complete_gonio(module_id=6)
gonio6.refine2()
Number of peaks previously found: 626
Number of peaks found after re-scan: 990
Cost function before refinement: 9.054048566564434e-10
[ 7.20609298e-01 3.22472627e-02 3.96893520e-03 2.23757106e-05
-4.85998857e+01 9.99040899e-01 1.70270825e+01]
fun: 6.093728642246349e-10
jac: array([-8.02155920e-07, 3.63691515e-08, -2.33166253e-07, 1.71261021e-07,
1.53140861e-10, -6.90587253e-08, 3.30203031e-08])
message: 'Optimization terminated successfully.'
nfev: 37
nit: 4
njev: 4
status: 0
success: True
x: array([ 7.20611756e-01, 3.22490408e-02, 3.97006720e-03, 2.15500507e-05,
-4.85998856e+01, 9.99018033e-01, 1.70270825e+01])
Cost function after refinement: 6.093728642246349e-10
GonioParam(dist=0.7206117564391414, poni1=0.03224904075932756, poni2=0.003970067202282311, rot1=2.1550050733043843e-05, offset=-48.599885636781195, scale=0.9990180333619139, nrj=17.027082549190933)
maxdelta on: scale (5) 0.9990408988314912 --> 0.9990180333619139
Out[47]:
array([ 7.20611756e-01, 3.22490408e-02, 3.97006720e-03, 2.15500507e-05,
-4.85998856e+01, 9.99018033e-01, 1.70270825e+01])
In [48]:
gonio5 = complete_gonio(module_id=5)
gonio5.refine2()
Number of peaks previously found: 754
Number of peaks found after re-scan: 1038
Cost function before refinement: 5.322312447273672e-10
[ 7.20528271e-01 3.33948197e-02 3.97295090e-03 1.94838596e-05
-5.43998157e+01 9.99025942e-01 1.70270825e+01]
fun: 5.247814297615004e-10
jac: array([-6.54781369e-07, 1.29256630e-07, -1.62656541e-07, 1.19840950e-07,
1.28911966e-09, -2.77499652e-07, 2.46511989e-08])
message: 'Optimization terminated successfully.'
nfev: 37
nit: 4
njev: 4
status: 0
success: True
x: array([ 7.20530687e-01, 3.33953448e-02, 3.97363667e-03, 1.89799990e-05,
-5.43998157e+01, 9.99021890e-01, 1.70270825e+01])
Cost function after refinement: 5.247814297615004e-10
GonioParam(dist=0.7205306865337416, poni1=0.033395344810677706, poni2=0.0039736366657854355, rot1=1.8979998986411344e-05, offset=-54.39981565735447, scale=0.999021890228638, nrj=17.027082549190933)
maxdelta on: scale (5) 0.999025941539747 --> 0.999021890228638
Out[48]:
array([ 7.20530687e-01, 3.33953448e-02, 3.97363667e-03, 1.89799990e-05,
-5.43998157e+01, 9.99021890e-01, 1.70270825e+01])
In [49]:
gonio4 = complete_gonio(module_id=4)
gonio4.refine2()
Number of peaks previously found: 864
Number of peaks found after re-scan: 1081
Cost function before refinement: 4.522981580650044e-10
[ 7.20645314e-01 3.22371238e-02 3.97565133e-03 1.75424155e-05
-6.00000524e+01 9.99011856e-01 1.70270825e+01]
fun: 4.329968320302878e-10
jac: array([-3.23619143e-07, -1.33810126e-08, -8.07893403e-08, 5.95277891e-08,
-4.92710775e-10, 3.16598865e-08, 5.83323419e-08])
message: 'Optimization terminated successfully.'
nfev: 37
nit: 4
njev: 4
status: 0
success: True
x: array([ 7.20646423e-01, 3.22359951e-02, 3.97581932e-03, 1.74168753e-05,
-6.00000525e+01, 9.99019702e-01, 1.70270825e+01])
Cost function after refinement: 4.329968320302878e-10
GonioParam(dist=0.7206464234341815, poni1=0.032235995133433754, poni2=0.0039758193176266145, rot1=1.7416875286579755e-05, offset=-60.00005245067518, scale=0.9990197021796172, nrj=17.027082549190933)
maxdelta on: scale (5) 0.999011855791219 --> 0.9990197021796172
Out[49]:
array([ 7.20646423e-01, 3.22359951e-02, 3.97581932e-03, 1.74168753e-05,
-6.00000525e+01, 9.99019702e-01, 1.70270825e+01])
In [50]:
gonio3 = complete_gonio(module_id=3)
gonio3.refine2()
Number of peaks previously found: 978
Number of peaks found after re-scan: 1156
Cost function before refinement: 7.053238687700532e-10
[ 7.20482931e-01 3.34099564e-02 3.97791142e-03 1.59099880e-05
-6.57999266e+01 9.98999110e-01 1.70270825e+01]
fun: 6.316819601296489e-10
jac: array([-4.99814708e-07, -1.63155748e-08, 9.67096626e-09, -4.95315009e-09,
-5.75364555e-10, 3.90058487e-08, 1.04654441e-07])
message: 'Optimization terminated successfully.'
nfev: 37
nit: 4
njev: 4
status: 0
success: True
x: array([ 7.20484799e-01, 3.34074959e-02, 3.97770054e-03, 1.60543912e-05,
-6.57999266e+01, 9.99015617e-01, 1.70270825e+01])
Cost function after refinement: 6.316819601296489e-10
GonioParam(dist=0.7204847991260711, poni1=0.03340749593129299, poni2=0.003977700542249465, rot1=1.605439120863723e-05, offset=-65.79992658922357, scale=0.9990156171464057, nrj=17.027082549190933)
maxdelta on: scale (5) 0.9989991098968561 --> 0.9990156171464057
Out[50]:
array([ 7.20484799e-01, 3.34074959e-02, 3.97770054e-03, 1.60543912e-05,
-6.57999266e+01, 9.99015617e-01, 1.70270825e+01])
In [51]:
gonio2 = complete_gonio(module_id=2)
gonio2.refine2()
Number of peaks previously found: 1093
Number of peaks found after re-scan: 1229
Cost function before refinement: 8.306533586355894e-10
[ 7.20686437e-01 3.48247495e-02 4.04316666e-03 -3.37686772e-05
-7.15999088e+01 9.98982863e-01 1.70270825e+01]
fun: 7.771891010372871e-10
jac: array([ 9.15257278e-08, -1.05189468e-09, 5.61627546e-08, -4.08345480e-08,
-4.25668376e-10, 2.85157377e-09, 1.17395008e-07])
message: 'Optimization terminated successfully.'
nfev: 37
nit: 4
njev: 4
status: 0
success: True
x: array([ 7.20686041e-01, 3.48226304e-02, 4.04289725e-03, -3.35729680e-05,
-7.15999088e+01, 9.98998235e-01, 1.70270825e+01])
Cost function after refinement: 7.771891010372871e-10
GonioParam(dist=0.7206860412873665, poni1=0.0348226304357366, poni2=0.004042897251336869, rot1=-3.357296798617952e-05, offset=-71.59990883821092, scale=0.9989982349992665, nrj=17.027082549190933)
maxdelta on: scale (5) 0.9989828627069963 --> 0.9989982349992665
Out[51]:
array([ 7.20686041e-01, 3.48226304e-02, 4.04289725e-03, -3.35729680e-05,
-7.15999088e+01, 9.98998235e-01, 1.70270825e+01])
In [52]:
gonio1 = complete_gonio(module_id=1)
gonio1.refine2()
Number of peaks previously found: 1183
Number of peaks found after re-scan: 1285
Cost function before refinement: 9.822658405373417e-10
[ 7.20682081e-01 3.36782425e-02 4.05801126e-03 -4.44860018e-05
-7.71999788e+01 9.98967223e-01 1.70270825e+01]
fun: 9.683803822381625e-10
jac: array([ 1.05204414e-07, -1.40910812e-09, -2.64455137e-09, 1.49411766e-09,
-3.43193224e-10, 4.36284460e-09, 1.50605559e-07])
message: 'Optimization terminated successfully.'
nfev: 37
nit: 4
njev: 4
status: 0
success: True
x: array([ 7.20681597e-01, 3.36766788e-02, 4.05808287e-03, -4.45357208e-05,
-7.71999788e+01, 9.98975895e-01, 1.70270825e+01])
Cost function after refinement: 9.683803822381625e-10
GonioParam(dist=0.7206815966774245, poni1=0.03367667883450645, poni2=0.004058082874451283, rot1=-4.4535720801764846e-05, offset=-77.19997881123506, scale=0.9989758952763078, nrj=17.027082549190933)
maxdelta on: scale (5) 0.9989672227193093 --> 0.9989758952763078
Out[52]:
array([ 7.20681597e-01, 3.36766788e-02, 4.05808287e-03, -4.45357208e-05,
-7.71999788e+01, 9.98975895e-01, 1.70270825e+01])
In [53]:
gonio0 = complete_gonio(module_id=0)
gonio0.refine2()
Number of peaks previously found: 1203
Number of peaks found after re-scan: 1255
Cost function before refinement: 2.580092692155849e-06
[ 7.23096248e-01 3.20537111e-02 3.98485468e-03 1.09479202e-05
-8.27999440e+01 9.99415047e-01 1.70270825e+01]
fun: 2.5799877551962334e-06
jac: array([-1.43881863e-07, 3.61314392e-08, 5.52834337e-07, -3.99174581e-07,
1.01925934e-09, -1.14581923e-07, -1.57262758e-06])
message: 'Optimization terminated successfully.'
nfev: 37
nit: 4
njev: 4
status: 0
success: True
x: array([ 7.23096999e-01, 3.20658547e-02, 3.98130190e-03, 1.35139061e-05,
-8.27999438e+01, 9.99396229e-01, 1.70270825e+01])
Cost function after refinement: 2.5799877551962334e-06
GonioParam(dist=0.7230969991414224, poni1=0.03206585469442816, poni2=0.003981301898312368, rot1=1.351390607705048e-05, offset=-82.79994383949249, scale=0.9993962290572798, nrj=17.027082549190933)
maxdelta on: scale (5) 0.9994150470263444 --> 0.9993962290572798
Out[53]:
array([ 7.23096999e-01, 3.20658547e-02, 3.98130190e-03, 1.35139061e-05,
-8.27999438e+01, 9.99396229e-01, 1.70270825e+01])
In [54]:
#Rescan module0 which looks much different:
gonio0.single_geometries.clear()
gonio0 = complete_gonio(module_id=0)
gonio0.refine2()
Number of peaks previously found: 0
Number of peaks found after re-scan: 1250
Cost function before refinement: 9.454138761636617e-07
[ 7.23096999e-01 3.20658547e-02 3.98130190e-03 1.35139061e-05
-8.27999438e+01 9.99396229e-01 1.70270825e+01]
fun: 9.315197221462237e-07
jac: array([-1.20646249e-08, -1.14537357e-08, 1.03723337e-07, -7.48339701e-08,
1.34221523e-10, -9.52891099e-09, -5.30292098e-07])
message: 'Optimization terminated successfully.'
nfev: 82
nit: 9
njev: 9
status: 0
success: True
x: array([ 7.21973759e-01, 3.22003255e-02, 3.94381184e-03, 4.51413618e-05,
-8.27999423e+01, 9.99140776e-01, 1.70270825e+01])
Cost function after refinement: 9.315197221462237e-07
GonioParam(dist=0.7219737589812981, poni1=0.03220032545666352, poni2=0.003943811844450548, rot1=4.5141361782464955e-05, offset=-82.79994226310926, scale=0.9991407764529461, nrj=17.027082549190933)
maxdelta on: dist (0) 0.7230969991414224 --> 0.7219737589812981
Out[54]:
array([ 7.21973759e-01, 3.22003255e-02, 3.94381184e-03, 4.51413618e-05,
-8.27999423e+01, 9.99140776e-01, 1.70270825e+01])
Discard wronly assigned peaks¶
We have seen previously that some modules have a much higher residual error, while all have almost the same number of peaks recorded and fitted.
Some frames are contributing much more than all the other in those badly-fitted data. Let’s spot them and re-assign them
In [55]:
#search for mis-assigned peaks in module #0
labels = []
errors = []
for lbl,sg in gonio0.single_geometries.items():
labels.append(lbl)
errors.append(sg.geometry_refinement.chi2())
s = numpy.argsort(errors)
for i in s[-10:]:
print(labels[i], errors[i])
data_02_0455 6.313051349592421e-07
data_02_0464 6.523630272471416e-07
data_02_0465 6.891655641669719e-07
data_02_0457 7.370430556294668e-07
data_02_0456 7.376242032882277e-07
data_02_0460 7.45857621330519e-07
data_02_0466 7.67143438989774e-07
data_02_0461 7.935716411266278e-07
data_02_0462 7.971563845471846e-07
data_02_0480 0.001130766003993148
In [56]:
#remove wrongly assigned peak for frame 480
print(gonio0.single_geometries.pop("data_02_0480").control_points)
gonio0.refine2()
gonio0 = complete_gonio(module_id=0)
gonio0.refine2()
ControlPoints instance containing 4 group of point:
LaB6 Calibrant with 109 reflections at wavelength 7.281587849134994e-11
Containing 4 groups of points:
#psg ring 52: 1 points
#psh ring 53: 1 points
#psi ring 54: 1 points
#psj ring 55: 1 points
Cost function before refinement: 8.041228082228945e-09
[ 7.21973759e-01 3.22003255e-02 3.94381184e-03 4.51413618e-05
-8.27999423e+01 9.99140776e-01 1.70270825e+01]
fun: 9.214430277838577e-10
jac: array([-3.08678332e-08, -3.82866689e-08, -1.82877549e-07, 1.31905635e-07,
-8.44315805e-10, -1.61540448e-08, 1.38174042e-07])
message: 'Optimization terminated successfully.'
nfev: 82
nit: 9
njev: 9
status: 0
success: True
x: array([ 7.20595797e-01, 3.22844186e-02, 4.04252687e-03, -2.05352660e-05,
-8.27999410e+01, 9.98975164e-01, 1.70270825e+01])
Cost function after refinement: 9.214430277838577e-10
GonioParam(dist=0.720595797367119, poni1=0.03228441857336863, poni2=0.0040425268658778706, rot1=-2.0535266006967913e-05, offset=-82.79994103917592, scale=0.9989751641349021, nrj=17.027082549190933)
maxdelta on: dist (0) 0.7219737589812981 --> 0.720595797367119
Number of peaks previously found: 1246
Number of peaks found after re-scan: 1263
Cost function before refinement: 9.385263673786183e-10
[ 7.20595797e-01 3.22844186e-02 4.04252687e-03 -2.05352660e-05
-8.27999410e+01 9.98975164e-01 1.70270825e+01]
fun: 9.382286239666452e-10
jac: array([-2.66626459e-08, -1.46606972e-06, -1.81711541e-07, 1.31048747e-07,
-1.88137349e-08, -4.38931502e-08, 2.40047863e-07])
message: 'Optimization terminated successfully.'
nfev: 11
nit: 1
njev: 1
status: 0
success: True
x: array([ 7.20595804e-01, 3.22848040e-02, 4.04257464e-03, -2.05697223e-05,
-8.27999410e+01, 9.98975176e-01, 1.70270825e+01])
Cost function after refinement: 9.382286239666452e-10
GonioParam(dist=0.7205958043774563, poni1=0.032284804043109315, poni2=0.00404257464280098, rot1=-2.0569722299120257e-05, offset=-82.79994103422928, scale=0.9989751756756091, nrj=17.027082549190933)
maxdelta on: poni1 (1) 0.03228441857336863 --> 0.032284804043109315
Out[56]:
array([ 7.20595804e-01, 3.22848040e-02, 4.04257464e-03, -2.05697223e-05,
-8.27999410e+01, 9.98975176e-01, 1.70270825e+01])
In [57]:
def search_outliers(module_id=None, name=None, threshold=1.2):
"Search for wrongly assigned peaks"
if name is None:
name = ds_names[module_id]
gonioref = goniometers[name]
labels = []
errors = []
for lbl,sg in gonioref.single_geometries.items():
labels.append(lbl)
errors.append(sg.geometry_refinement.chi2())
s = numpy.argsort(errors)
last = errors[s[-1]]
to_remove = []
for i in s[-1::-1]:
lbl = labels[i]
current = errors[i]
print(lbl , current, last, last/current)
if threshold*current<last:
break
last=current
to_remove.append(lbl)
return to_remove
for lbl in search_outliers(8):
gonio8.single_geometries.pop(lbl)
gonio8.refine2()
gonio8 = complete_gonio(module_id=8)
gonio8.refine2()
data_11_0495 1.4653542984471542e-06 1.4653542984471542e-06 1.0
data_11_0496 1.4360982661347142e-06 1.4653542984471542e-06 1.0203718874970744
data_11_0499 1.4166548534532985e-06 1.4360982661347142e-06 1.0137248763409235
data_11_0497 1.4084572221561037e-06 1.4166548534532985e-06 1.0058202912862668
data_11_0498 1.3833016059917487e-06 1.4084572221561037e-06 1.0181851998547489
data_11_0500 1.3709107012975464e-06 1.3833016059917487e-06 1.0090384477139718
data_11_0492 1.3295890859461896e-06 1.3709107012975464e-06 1.0310784856675854
data_11_0489 1.3287700089647162e-06 1.3295890859461896e-06 1.0006164174205825
data_11_0491 1.3216144771699174e-06 1.3287700089647162e-06 1.0054142353298985
data_11_0490 1.301822888645974e-06 1.3216144771699174e-06 1.015202980909737
data_11_0494 1.2865582016523121e-06 1.301822888645974e-06 1.0118647465571768
data_11_0493 1.2861450147452866e-06 1.2865582016523121e-06 1.0003212599685793
data_11_0483 1.2244483499124188e-06 1.2861450147452866e-06 1.0503873151017604
data_11_0486 1.207372827265345e-06 1.2244483499124188e-06 1.0141427090799693
data_11_0485 1.201809830402108e-06 1.207372827265345e-06 1.0046288495255324
data_11_0484 1.1994812838848202e-06 1.201809830402108e-06 1.0019412945817263
data_11_0487 1.1764652443222126e-06 1.1994812838848202e-06 1.019563722493024
data_11_0477 1.1389594650443204e-06 1.1764652443222126e-06 1.0329298631153943
data_11_0478 1.1156745972945301e-06 1.1389594650443204e-06 1.0208706622936967
data_11_0481 1.1104824081112956e-06 1.1156745972945301e-06 1.0046756158812686
data_11_0479 1.1057757403752895e-06 1.1104824081112956e-06 1.0042564396777314
data_11_0480 1.1002412230846842e-06 1.1057757403752895e-06 1.0050302762471384
data_11_0482 8.673291356185134e-07 1.1002412230846842e-06 1.26853944817624
Cost function before refinement: 1.059476333549205e-09
[ 7.20813440e-01 3.20849228e-02 3.96153953e-03 2.77060750e-05
-3.71999988e+01 9.98991349e-01 1.70270825e+01]
fun: 1.0589449037804424e-09
jac: array([-8.45058784e-07, -1.25301789e-06, -2.51805109e-07, 1.84923760e-07,
-1.61392479e-08, 9.17399903e-08, 8.34009091e-08])
message: 'Optimization terminated successfully.'
nfev: 11
nit: 1
njev: 1
status: 0
success: True
x: array([ 7.20813810e-01, 3.20854710e-02, 3.96164970e-03, 2.76251683e-05,
-3.71999988e+01, 9.98991309e-01, 1.70270825e+01])
Cost function after refinement: 1.0589449037804424e-09
GonioParam(dist=0.7208138098008553, poni1=0.032085470990150605, poni2=0.00396164969570614, rot1=2.762516825116013e-05, offset=-37.19999877868338, scale=0.9989913085815821, nrj=17.027082549190933)
maxdelta on: poni1 (1) 0.03208492277691861 --> 0.032085470990150605
Number of peaks previously found: 918
Number of peaks found after re-scan: 1006
Cost function before refinement: 9.804599649789273e-10
[ 7.20813810e-01 3.20854710e-02 3.96164970e-03 2.76251683e-05
-3.71999988e+01 9.98991309e-01 1.70270825e+01]
fun: 9.798014434813442e-10
jac: array([-8.28830624e-07, 2.04374424e-06, -2.22646167e-07, 1.63839575e-07,
2.53636863e-08, 1.00410517e-06, 4.36574660e-08])
message: 'Optimization terminated successfully.'
nfev: 11
nit: 1
njev: 1
status: 0
success: True
x: array([ 7.20813997e-01, 3.20850099e-02, 3.96169993e-03, 2.75882029e-05,
-3.71999988e+01, 9.98991082e-01, 1.70270825e+01])
Cost function after refinement: 9.798014434813442e-10
GonioParam(dist=0.7208139968009581, poni1=0.032085009882209824, poni2=0.0039616999289563675, rot1=2.7588202897190342e-05, offset=-37.19999878440591, scale=0.9989910820361755, nrj=17.027082549190933)
maxdelta on: poni1 (1) 0.032085470990150605 --> 0.032085009882209824
Out[57]:
array([ 7.20813997e-01, 3.20850099e-02, 3.96169993e-03, 2.75882029e-05,
-3.71999988e+01, 9.98991082e-01, 1.70270825e+01])
In [58]:
print(gonio7.chi2())
for lbl in search_outliers(7):
gonio7.single_geometries.pop(lbl)
gonio7.refine2()
gonio7 = complete_gonio(module_id=7)
gonio7.refine2()
6.982178014396509e-10
data_10_0292 4.478307386585731e-06 4.478307386585731e-06 1.0
data_10_0291 4.441611877573707e-06 4.478307386585731e-06 1.0082617549717265
data_10_0288 4.42110785615644e-06 4.441611877573707e-06 1.0046377564367075
data_10_0285 4.41519072824658e-06 4.42110785615644e-06 1.0013401749265336
data_10_0290 4.411402144902852e-06 4.41519072824658e-06 1.0008588161358412
data_10_0289 4.40449960049467e-06 4.411402144902852e-06 1.001567157460386
data_10_0284 4.3863439763980785e-06 4.40449960049467e-06 1.004139124563482
data_10_0275 4.376867017048265e-06 4.3863439763980785e-06 1.0021652381287574
data_10_0286 4.374938577698873e-06 4.376867017048265e-06 1.0004407923254561
data_10_0283 4.360023596330053e-06 4.374938577698873e-06 1.0034208487727851
data_10_0281 4.358112634515273e-06 4.360023596330053e-06 1.000438483805959
data_10_0282 4.355265304875879e-06 4.358112634515273e-06 1.0006537672082128
data_10_0278 4.352327511323348e-06 4.355265304875879e-06 1.0006749936774948
data_10_0280 4.35154401569245e-06 4.352327511323348e-06 1.000180050030075
data_10_0277 4.349860479592271e-06 4.35154401569245e-06 1.0003870322066828
data_10_0276 4.339663932302855e-06 4.349860479592271e-06 1.0023496168017796
data_10_0279 4.33808469320417e-06 4.339663932302855e-06 1.0003640406332222
data_10_0274 4.337318248584353e-06 4.33808469320417e-06 1.000176709334176
data_10_0287 4.319683506474051e-06 4.337318248584353e-06 1.0040824153167407
data_10_0496 1.9508464721227965e-06 4.319683506474051e-06 2.2142611262349234
Cost function before refinement: 6.590257595658292e-10
[ 7.20709219e-01 3.08662496e-02 3.96669042e-03 2.39916666e-05
-4.27999029e+01 9.99006679e-01 1.70270825e+01]
fun: 6.580251686582122e-10
jac: array([-6.41067336e-07, 7.99913209e-09, -1.44533165e-07, 1.06757288e-07,
-2.37724944e-10, -3.75138453e-07, 6.15574400e-09])
message: 'Optimization terminated successfully.'
nfev: 19
nit: 2
njev: 2
status: 0
success: True
x: array([ 7.20709357e-01, 3.08656493e-02, 3.96672263e-03, 2.39678916e-05,
-4.27999029e+01, 9.99006434e-01, 1.70270825e+01])
Cost function after refinement: 6.580251686582122e-10
GonioParam(dist=0.720709357471267, poni1=0.030865649336609666, poni2=0.003966722633045513, rot1=2.3967891595469488e-05, offset=-42.79990294443424, scale=0.999006433638064, nrj=17.027082549190933)
maxdelta on: poni1 (1) 0.030866249621701404 --> 0.030865649336609666
Number of peaks previously found: 985
Number of peaks found after re-scan: 1004
Cost function before refinement: 6.991420234285395e-10
[ 7.20709357e-01 3.08656493e-02 3.96672263e-03 2.39678916e-05
-4.27999029e+01 9.99006434e-01 1.70270825e+01]
fun: 6.980031455333567e-10
jac: array([-6.60879262e-07, 1.52170131e-07, -2.32103327e-07, 1.69950571e-07,
1.58023172e-09, 9.61263490e-08, 3.00039453e-08])
message: 'Optimization terminated successfully.'
nfev: 19
nit: 2
njev: 2
status: 0
success: True
x: array([ 7.20709502e-01, 3.08662430e-02, 3.96677226e-03, 2.39315396e-05,
-4.27999029e+01, 9.99006765e-01, 1.70270825e+01])
Cost function after refinement: 6.980031455333567e-10
GonioParam(dist=0.7207095017700934, poni1=0.03086624296585714, poni2=0.003966772262865057, rot1=2.393153960923883e-05, offset=-42.79990293688988, scale=0.9990067647525397, nrj=17.027082549190933)
maxdelta on: poni1 (1) 0.030865649336609666 --> 0.03086624296585714
Out[58]:
array([ 7.20709502e-01, 3.08662430e-02, 3.96677226e-03, 2.39315396e-05,
-4.27999029e+01, 9.99006765e-01, 1.70270825e+01])
In [59]:
print(gonio0.chi2())
print(len(search_outliers(0)))
# for lbl in search_outliers(7):
# gonio7.single_geometries.pop(lbl)
# gonio7.refine2()
# gonio7 = complete_gonio(module_id=7)
# gonio7.refine2()
9.382286239666452e-10
data_02_0462 7.971563845471846e-07 7.971563845471846e-07 1.0
data_02_0461 7.935716411266278e-07 7.971563845471846e-07 1.004517227222822
data_02_0466 7.67143438989774e-07 7.935716411266278e-07 1.034450144254191
data_02_0460 7.45857621330519e-07 7.67143438989774e-07 1.0285387144282092
data_02_0456 7.376242032882277e-07 7.45857621330519e-07 1.0111620768483298
data_02_0457 7.370430556294668e-07 7.376242032882277e-07 1.000788485359603
data_02_0465 6.891655641669719e-07 7.370430556294668e-07 1.0694716827883974
data_02_0464 6.523630272471416e-07 6.891655641669719e-07 1.056414197897037
data_02_0455 6.313051349592421e-07 6.523630272471416e-07 1.0333561238801883
data_02_0463 6.240813179531244e-07 6.313051349592421e-07 1.0115751213797115
data_02_0459 6.163901121421231e-07 6.240813179531244e-07 1.0124778215281103
data_02_0448 6.082027920092041e-07 6.163901121421231e-07 1.013461497119854
data_02_0454 5.868929875551012e-07 6.082027920092041e-07 1.036309523040778
data_02_0439 5.868112798407111e-07 5.868929875551012e-07 1.0001392401904958
data_02_0435 5.859910233268107e-07 5.868112798407111e-07 1.0013997765857292
data_02_0426 5.755884184129568e-07 5.859910233268107e-07 1.0180729920566098
data_02_0458 5.724220421407079e-07 5.755884184129568e-07 1.0055315414836359
data_02_0453 5.590340754134061e-07 5.724220421407079e-07 1.0239483911913623
data_02_0434 5.570146124178882e-07 5.590340754134061e-07 1.0036255117020212
data_02_0444 5.524804844432388e-07 5.570146124178882e-07 1.0082068563547881
data_02_0430 5.489356696711307e-07 5.524804844432388e-07 1.0064576141940855
data_02_0443 5.459478619353463e-07 5.489356696711307e-07 1.005472697933449
data_02_0447 5.424219010224628e-07 5.459478619353463e-07 1.0065004029266464
data_02_0468 5.360729258271283e-07 5.424219010224628e-07 1.0118434916024501
data_02_0425 5.340453928849802e-07 5.360729258271283e-07 1.0037965554410928
data_02_0467 5.066740382282769e-07 5.340453928849802e-07 1.0540216245387561
data_02_0438 5.014377962589753e-07 5.066740382282769e-07 1.0104424556911487
data_02_0429 4.994042990677361e-07 5.014377962589753e-07 1.0040718455869027
data_02_0442 4.988918594371316e-07 4.994042990677361e-07 1.0010271557270602
data_02_0421 4.887207364704953e-07 4.988918594371316e-07 1.020811727859332
data_02_0452 4.818408313589759e-07 4.887207364704953e-07 1.0142783771398438
data_02_0441 4.708090789077316e-07 4.818408313589759e-07 1.0234314777379352
data_02_0433 4.6907543413049604e-07 4.708090789077316e-07 1.0036958762942876
data_02_0437 4.6744164098782785e-07 4.6907543413049604e-07 1.0034951810010242
data_02_0420 4.599765374239142e-07 4.6744164098782785e-07 1.0162293137943985
data_02_0451 4.5329173383081183e-07 4.599765374239142e-07 1.0147472435391849
data_02_0446 4.4537990827667195e-07 4.5329173383081183e-07 1.0177642174851431
data_02_0428 4.424570034888956e-07 4.4537990827667195e-07 1.006606076442973
data_02_0424 4.374993360555643e-07 4.424570034888956e-07 1.0113318284732244
data_02_0432 4.3734600098152413e-07 4.374993360555643e-07 1.0003506035809087
data_02_0436 4.331873497281146e-07 4.3734600098152413e-07 1.0096001216471804
data_02_0450 4.2621140965589126e-07 4.331873497281146e-07 1.0163673236196455
data_02_0445 4.1944505996655087e-07 4.2621140965589126e-07 1.016131670950851
data_02_0427 4.184060457298792e-07 4.1944505996655087e-07 1.0024832677426043
data_02_0423 4.1312003395546793e-07 4.184060457298792e-07 1.012795341159807
data_02_0419 3.876880857648326e-07 4.1312003395546793e-07 1.06559899342912
data_02_0408 3.542342460674882e-07 3.876880857648326e-07 1.0944398800193103
data_02_0418 3.436569950091102e-07 3.542342460674882e-07 1.0307785123305802
data_02_0412 3.4365083733233073e-07 3.436569950091102e-07 1.0000179184105218
data_02_0398 3.357907683844476e-07 3.4365083733233073e-07 1.0234076385890518
data_02_0389 3.271544614435567e-07 3.357907683844476e-07 1.0263982551324031
data_02_0394 3.2138316313793743e-07 3.271544614435567e-07 1.0179576871708809
data_02_0416 3.194683144152933e-07 3.2138316313793743e-07 1.0059938611631918
data_02_0403 3.071333103624269e-07 3.194683144152933e-07 1.0401617266401704
data_02_0411 3.0688042859822684e-07 3.071333103624269e-07 1.0008240400515445
data_02_0407 3.0628793103577707e-07 3.0688042859822684e-07 1.0019344463245616
data_02_0402 3.0490188744369036e-07 3.0628793103577707e-07 1.0045458675369554
data_02_0393 2.980904108777663e-07 3.0490188744369036e-07 1.022850371287915
data_02_0388 2.945092984652161e-07 2.980904108777663e-07 1.0121595903124707
data_02_0397 2.920821886183787e-07 2.945092984652161e-07 1.0083096811151624
data_02_0384 2.824639030221881e-07 2.920821886183787e-07 1.034051379639242
data_02_0406 2.8172340654452183e-07 2.824639030221881e-07 1.0026284520933098
data_02_0401 2.8153081654147476e-07 2.8172340654452183e-07 1.000684081428147
data_02_0417 2.810860465158435e-07 2.8153081654147476e-07 1.0015823269463011
data_02_0392 2.739808285543106e-07 2.810860465158435e-07 1.0259332669333994
data_02_0410 2.7025873527903e-07 2.739808285543106e-07 1.0137723329143744
data_02_0415 2.650180952687086e-07 2.7025873527903e-07 1.0197746497461155
data_02_0405 2.6433948563352065e-07 2.650180952687086e-07 1.002567189814876
data_02_0414 2.5775864796179354e-07 2.6433948563352065e-07 1.0255310063261294
data_02_0396 2.5700799922953914e-07 2.5775864796179354e-07 1.0029207212791225
data_02_0391 2.4851756352407427e-07 2.5700799922953914e-07 1.0341643286094844
data_02_0387 2.4757346323797714e-07 2.4851756352407427e-07 1.0038134147083027
data_02_0383 2.436319262841532e-07 2.4757346323797714e-07 1.016178244838186
data_02_0400 2.411208711876606e-07 2.436319262841532e-07 1.0104140926669858
data_02_0395 2.386282639357738e-07 2.411208711876606e-07 1.0104455658804845
data_02_0399 2.307240689353976e-07 2.386282639357738e-07 1.0342582160450255
data_02_0386 2.2832923413210657e-07 2.307240689353976e-07 1.0104885159028976
data_02_0409 2.2099257445959475e-07 2.2832923413210657e-07 1.033198670545617
data_02_0404 2.2006310772588735e-07 2.2099257445959475e-07 1.004223637225305
data_02_0390 2.185528631262913e-07 2.2006310772588735e-07 1.0069102027673889
data_02_0382 2.1738267272521252e-07 2.185528631262913e-07 1.0053830895830322
data_02_0381 2.0686178374626022e-07 2.1738267272521252e-07 1.0508595100961586
data_02_0413 2.0388171846465108e-07 2.0686178374626022e-07 1.014616638039206
data_02_0385 2.014026959293881e-07 2.0388171846465108e-07 1.0123087852614054
data_02_0360 1.9864831310383662e-07 2.014026959293881e-07 1.013865624039363
data_02_0375 1.9263499624078313e-07 1.9864831310383662e-07 1.0312161184644622
data_02_0370 1.9202965590739344e-07 1.9263499624078313e-07 1.003152327334699
data_02_0365 1.9112544339834668e-07 1.9202965590739344e-07 1.0047309897257488
data_02_0380 1.896068545228752e-07 1.9112544339834668e-07 1.0080091454462068
data_02_0369 1.7565509702989891e-07 1.896068545228752e-07 1.0794270005760294
data_02_0355 1.7104015084110744e-07 1.7565509702989891e-07 1.0269816541092662
data_02_0374 1.699946080760567e-07 1.7104015084110744e-07 1.006150446634066
data_02_0364 1.694066729270692e-07 1.699946080760567e-07 1.0034705548419607
data_02_0350 1.6598878773796802e-07 1.694066729270692e-07 1.0205910606112547
data_02_0363 1.5748085176203178e-07 1.6598878773796802e-07 1.0540252092920637
data_02_0373 1.5391498398723758e-07 1.5748085176203178e-07 1.0231677753680557
data_02_0354 1.5253285693309903e-07 1.5391498398723758e-07 1.0090611759454866
data_02_0358 1.511161110628414e-07 1.5253285693309903e-07 1.0093752139351209
data_02_0349 1.4524762167521378e-07 1.511161110628414e-07 1.0404033423745145
data_02_0368 1.4209107029916782e-07 1.4524762167521378e-07 1.0222149876793802
data_02_0359 1.3720480308760376e-07 1.4209107029916782e-07 1.0356129457687004
data_02_0379 1.37066156653446e-07 1.3720480308760376e-07 1.0010115293048474
data_02_0367 1.3261291173680126e-07 1.37066156653446e-07 1.033580779264414
data_02_0378 1.3251823783043865e-07 1.3261291173680126e-07 1.000714421712155
data_02_0362 1.282724946539807e-07 1.3251823783043865e-07 1.0330994044195598
data_02_0372 1.2748563415571346e-07 1.282724946539807e-07 1.0061721503248449
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data_02_0147 2.012235348938875e-08 2.0214746920241275e-08 1.0045915817402395
data_02_0122 2.0049202575832967e-08 2.012235348938875e-08 1.003648569726357
data_02_0107 1.938714534962891e-08 2.0049202575832967e-08 1.0341492888336308
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data_02_0175 1.9131945757118e-08 1.9242219372987482e-08 1.0057638474031558
data_02_0192 1.9060909360862577e-08 1.9131945757118e-08 1.0037268104532977
data_02_0214 1.8668523669383202e-08 1.9060909360862577e-08 1.0210185710679895
data_02_0246 1.8085116798197382e-08 1.8668523669383202e-08 1.0322589495935117
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data_02_0234 1.7743067624651617e-08 1.7783980521679194e-08 1.0023058525105735
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data_02_0247 1.4173933717675753e-08 1.503683121703211e-08 1.0608791826280568
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data_02_0088 1.387514072593158e-08 1.4169011127970798e-08 1.0211796339830987
data_02_0235 1.3468333617225374e-08 1.387514072593158e-08 1.030204709822893
data_02_0160 1.3120004952502951e-08 1.3468333617225374e-08 1.026549430886912
data_02_0161 1.2298582595302832e-08 1.3120004952502951e-08 1.0667900020864065
data_02_0260 1.216723491447803e-08 1.2298582595302832e-08 1.010795195600975
data_02_0159 1.199993752002408e-08 1.216723491447803e-08 1.0139415221266597
data_02_0294 1.1975844891213482e-08 1.199993752002408e-08 1.002011768608349
data_02_0273 1.1970496190147518e-08 1.1975844891213482e-08 1.0004468236722188
data_02_0241 1.180009018680682e-08 1.1970496190147518e-08 1.0144410763513674
data_02_0109 1.175617850876184e-08 1.180009018680682e-08 1.0037352000067243
data_02_0254 1.1681359586635138e-08 1.175617850876184e-08 1.0064049840749962
data_02_0089 1.0944685681180611e-08 1.1681359586635138e-08 1.0673088224654308
data_02_0319 1.071026016339414e-08 1.0944685681180611e-08 1.0218879386877733
data_02_0291 9.647626338630572e-09 1.071026016339414e-08 1.1101445876389946
data_02_0110 9.297424836505559e-09 9.647626338630572e-09 1.0376665053262895
data_02_0090 8.94600182435908e-09 9.297424836505559e-09 1.0392826895238931
data_02_0440 8.921549332760699e-09 8.94600182435908e-09 1.002740834656217
data_02_0292 8.845576776004658e-09 8.921549332760699e-09 1.008588762347542
data_02_0293 8.013141726493833e-09 8.845576776004658e-09 1.103883729743422
data_02_0091 5.400087708579987e-09 8.013141726493833e-09 1.4838910326886112
376
Overlay of the differents results¶
We are getting to an end. Here are the first actually integrated data
In [60]:
fig, ax = plt.subplots()
summed, counted, radial = None, None, None
for i in range(9):
name = ds_names[i]
ds = data[name]
gonioref = goniometers[name]
mg = gonioref.get_mg(position)
mg.radial_range = (0, 95)
images = [i.reshape(-1, 1) for i in ds]
res_mg = mg.integrate1d(images, 50000)
results[name] = res_mg
if summed is None:
summed = res_mg.sum
counted = res_mg.count
else:
summed += res_mg.sum
counted += res_mg.count
radial = res_mg.radial
jupyter.plot1d(res_mg, label="%i %s"%(i, name), calibrant=LaB6, ax=ax )
ax.plot(radial, summed/counted, label="Merged")
ax.legend()
fig.show()
Data type cannot be displayed: application/javascript
area_pixel=0.05054585816712631 area_sum=0.05084240089824814, Error= -0.005866805745810646
area_pixel=0.05448433978731071 area_sum=0.05460194376540826, Error= -0.002158491385903477
area_pixel=0.05706893234299759 area_sum=0.057097754167008734, Error= -0.0005050352762500703
area_pixel=0.04575136894640419 area_sum=0.046103520693760155, Error= -0.007697075638731046
area_pixel=0.0503875602291064 area_sum=0.05041948354020665, Error= -0.0006335554044510445
area_pixel=0.050887046288177196 area_sum=0.05090400923674137, Error= -0.0003333451202514585
area_pixel=0.047764037615231736 area_sum=0.047787742717740125, Error= -0.0004962960355099896
area_pixel=0.054600585079026764 area_sum=0.05461392295287675, Error= -0.00024428078619822223
area_pixel=0.04398098576245957 area_sum=0.0451093409852144, Error= -0.025655523704017393
area_pixel=0.05413585962925449 area_sum=0.054261047973434326, Error= -0.0023124846458000116
area_pixel=0.05074179597564754 area_sum=0.051022305153632666, Error= -0.005528168102677118
area_pixel=0.05670749981502521 area_sum=0.0567493721010123, Error= -0.0007383906207058524
area_pixel=0.0522725582237884 area_sum=0.052599157191360185, Error= -0.006248000455105984
area_pixel=0.04886833409786284 area_sum=0.05916004122953074, Error= -0.21060073607293242
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area_pixel=0.08582264210207136 area_sum=0.08598966627233767, Error= -0.0019461550725468225
area_pixel=0.07293769354366653 area_sum=0.07452580505574181, Error= -0.021773536218615323
area_pixel=0.06333498912628421 area_sum=0.06785807669315522, Error= -0.07141530501966896
area_pixel=0.03963769199827816 area_sum=0.054891531459535764, Error= -0.3848316764235472
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area_pixel=0.07314430360340829 area_sum=0.07481382789893049, Error= -0.022825076093067092
area_pixel=0.0854466193934389 area_sum=0.08560825287900438, Error= -0.0018916311343020336
area_pixel=0.04673599374915405 area_sum=0.057774642096181, Error= -0.23619158300719262
area_pixel=0.05583010601315941 area_sum=0.06324832936851839, Error= -0.13287138221823314
area_pixel=0.07322943409217153 area_sum=0.07499526481604342, Error= -0.02411367431365501
area_pixel=0.0852345027976682 area_sum=0.08533894045176349, Error= -0.0012252978625710697
area_pixel=0.04599237073951734 area_sum=0.05746828088313036, Error= -0.24951769084938125
area_pixel=0.06070260492291091 area_sum=0.061073736040080526, Error= -0.006113924067030317
area_pixel=0.044319725410217004 area_sum=0.047768636124481664, Error= -0.07781886467801953
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area_pixel=0.058320415107782964 area_sum=0.059174815319163986, Error= -0.014650105109882882
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area_pixel=0.06337332199284873 area_sum=0.06344873015210023, Error= -0.0011899038409255117
area_pixel=0.052121672519851 area_sum=0.05393823010119017, Error= -0.03485225038869034
area_pixel=0.0479534333591225 area_sum=0.05044117779204517, Error= -0.05187833818471332
area_pixel=0.04600451074681722 area_sum=0.048891635204346216, Error= -0.06275742118893726
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area_pixel=0.053340349058393244 area_sum=0.055062805328933664, Error= -0.03229180725185726
area_pixel=0.04918182529843129 area_sum=0.05170780411764328, Error= -0.051360005528151
area_pixel=0.0542987243748243 area_sum=0.05587411994858145, Error= -0.029013491419838604
area_pixel=0.048922568471164496 area_sum=0.05165291259833061, Error= -0.05580950086002555
area_pixel=0.041726822421832566 area_sum=0.042106909997024614, Error= -0.00910895086497591
area_pixel=0.039582151362063556 area_sum=0.04069836796135787, Error= -0.02819999825386246
area_pixel=0.05048661327088855 area_sum=0.051104638944560715, Error= -0.012241377142018202
area_pixel=0.05462653755615676 area_sum=0.054859630660605146, Error= -0.004267030547355515
area_pixel=0.052955102565457324 area_sum=0.053292036127629394, Error= -0.006362626939596422
area_pixel=0.05776491656818106 area_sum=0.05779778818874337, Error= -0.0005690585655657377
area_pixel=0.04640522109095535 area_sum=0.0470074553630645, Error= -0.012977726599529699
area_pixel=0.04660652023051526 area_sum=0.04708417266487089, Error= -0.010248618261847633
area_pixel=0.055970272141323996 area_sum=0.05607648098314985, Error= -0.0018975938076141565
area_pixel=0.04137995412261919 area_sum=0.04379345464441353, Error= -0.058325355186294676
area_pixel=0.04876562355702152 area_sum=0.04919111397280354, Error= -0.008725212244738255
area_pixel=0.052309101601506036 area_sum=0.05260266489758367, Error= -0.005612088280812288
area_pixel=0.043221450987522836 area_sum=0.044503584967261894, Error= -0.029664297482960136
area_pixel=0.042611371967804956 area_sum=0.04391185184599117, Error= -0.030519549550500034
/mntdirect/_scisoft/users/jupyter/jupy35/lib/python3.5/site-packages/ipykernel_launcher.py:22: RuntimeWarning: invalid value encountered in true_divide
Multi-Gonio fit¶
Can we fit everything togeather ? Just assume energy and scale parameter of the goniometer are the same for all modules and fit everything.
In [61]:
from scipy.optimize import minimize
class MultiGoniometer:
def __init__(self, list_of_goniometers,
param_name_split,
param_name_common):
self.nb_gonio = len(list_of_goniometers)
self.goniometers = list_of_goniometers
self.names_split = param_name_split
self.names_common = param_name_common
self.param = None
def init_param(self):
param = []
for gonio in self.goniometers:
param += list(gonio.param[:len(self.names_split)])
param += list(gonio.param[len(self.names_split):])
self.param = numpy.array(param)
def residu2(self, param):
"Actually performs the calulation of the average of the error squared"
sumsquare = 0.0
npt = 0
for idx, gonio in enumerate(self.goniometers):
gonio_param = numpy.concatenate((param[len(self.names_split)*idx:len(self.names_split)*(1+idx)],
param[len(self.names_split)*len(self.goniometers):]))
sumsquare += gonio.residu2(gonio_param)
return sumsquare
def chi2(self, param=None):
"""Calculate the average of the square of the error for a given parameter set
"""
if param is not None:
return self.residu2(param)
else:
if self.param is None:
self.init_param()
return self.residu2(self.param)
def refine2(self, method="slsqp", **options):
"""Geometry refinement tool
See https://docs.scipy.org/doc/scipy-0.18.1/reference/generated/scipy.optimize.minimize.html
:param method: name of the minimizer
:param options: options for the minimizer
"""
if method.lower() in ["simplex", "nelder-mead"]:
method = "Nelder-Mead"
former_error = self.chi2()
print("Cost function before refinement: %s" % former_error)
param = numpy.asarray(self.param, dtype=numpy.float64)
print(param)
res = minimize(self.residu2, param, method=method,
tol=1e-12,
options=options)
print(res)
newparam = res.x
new_error = res.fun
print("Cost function after refinement: %s" % new_error)
if new_error < former_error:
self.param = newparam
return self.param
def integrate(self, list_of_dataset, npt=50000, radial_range=(0,100)):
summed = None
counted = None
param = self.param
for idx, ds in enumerate(list_of_dataset):
gonio = self.goniometers[idx]
gonio_param = numpy.concatenate((param[len(self.names_split)*idx:len(self.names_split)*(1+idx)],
param[len(self.names_split)*len(self.goniometers):]))
print(gonio_param)
gonio.param = gonio_param
mg = gonio.get_mg(position)
mg.radial_range = radial_range
images = [i.reshape(-1, 1) for i in ds]
res_mg = mg.integrate1d(images, 50000)
if summed is None:
summed = res_mg.sum
counted = res_mg.count
else:
summed += res_mg.sum
counted += res_mg.count
radial = res_mg.radial
res = Integrate1dResult(radial, summed/numpy.maximum(counted, 1e-10))
res._set_unit(res_mg.unit)
res._set_count(counted)
res._set_sum(summed)
return res
In [62]:
multigonio = MultiGoniometer([goniometers[ds_names[i]] for i in range(9)],
["dist", "poni1", "poni2", "rot1", "offset"],
["scale", "nrj"])
In [63]:
%time print(multigonio.chi2())
multigonio.param = numpy.array([ 7.20594053e-01, 3.22408604e-02, 4.05228023e-03, -2.75578440e-05,
-8.27999414e+01, 7.20612302e-01, 3.36369797e-02, 4.02094516e-03,
-1.74996556e-05, -7.71999791e+01, 7.20636130e-01, 3.47920978e-02,
4.01341931e-03, -1.21330600e-05, -7.15999090e+01, 7.20757808e-01,
3.33850817e-02, 3.95036100e-03, 3.46517345e-05, -6.57999267e+01,
7.20813915e-01, 3.22167822e-02, 3.97128822e-03, 2.00055269e-05,
-6.00000525e+01, 7.20881596e-01, 3.33801850e-02, 3.97760147e-03,
1.47074593e-05, -5.43998157e+01, 7.21048510e-01, 3.22346939e-02,
4.02104962e-03, -1.69519259e-05, -4.85998856e+01, 7.21074630e-01,
3.08484557e-02, 4.09385968e-03, -6.91378973e-05, -4.27999030e+01,
7.21154891e-01, 3.20619921e-02, 4.24950906e-03, -1.81328256e-04,
-3.71999987e+01, 9.99038595e-01, 1.70266104e+01])
%time print(multigonio.chi2())
8.603112017040267e-09
CPU times: user 7.43 s, sys: 12 ms, total: 7.44 s
Wall time: 644 ms
6.1395983620232986e-09
CPU times: user 6.41 s, sys: 12 ms, total: 6.42 s
Wall time: 541 ms
In [64]:
%time multigonio.refine2()
Cost function before refinement: 6.1395983620232986e-09
[ 7.20594053e-01 3.22408604e-02 4.05228023e-03 -2.75578440e-05
-8.27999414e+01 7.20612302e-01 3.36369797e-02 4.02094516e-03
-1.74996556e-05 -7.71999791e+01 7.20636130e-01 3.47920978e-02
4.01341931e-03 -1.21330600e-05 -7.15999090e+01 7.20757808e-01
3.33850817e-02 3.95036100e-03 3.46517345e-05 -6.57999267e+01
7.20813915e-01 3.22167822e-02 3.97128822e-03 2.00055269e-05
-6.00000525e+01 7.20881596e-01 3.33801850e-02 3.97760147e-03
1.47074593e-05 -5.43998157e+01 7.21048510e-01 3.22346939e-02
4.02104962e-03 -1.69519259e-05 -4.85998856e+01 7.21074630e-01
3.08484557e-02 4.09385968e-03 -6.91378973e-05 -4.27999030e+01
7.21154891e-01 3.20619921e-02 4.24950906e-03 -1.81328256e-04
-3.71999987e+01 9.99038595e-01 1.70266104e+01]
fun: 6.1395983620232986e-09
jac: array([ 5.90883473e-08, -1.08561671e-07, -2.52646911e-08, 1.79747064e-08,
-1.72926662e-09, 1.79298213e-08, 9.69570013e-09, 4.03865801e-08,
-2.91714863e-08, -1.94683714e-10, 2.72323741e-08, -6.07769467e-08,
2.33525472e-08, -1.69337616e-08, -1.17130239e-09, 2.09023376e-07,
-5.80926751e-09, 1.58839289e-08, -1.22906173e-08, -4.71553241e-10,
1.47614749e-07, -1.33281402e-07, -1.82833877e-08, 1.25890469e-08,
-2.00339789e-09, 2.45125083e-07, -6.85051675e-08, -3.08888884e-08,
2.12864152e-08, -1.23765842e-09, 2.99788196e-07, -2.02647332e-08,
-7.85245061e-08, 5.54326079e-08, -5.67168867e-10, 2.54716680e-07,
1.39967174e-07, -1.44580129e-07, 1.03263413e-07, 1.46673401e-09,
1.30733052e-08, 8.84376917e-08, -1.94036564e-07, 1.39886310e-07,
7.47406914e-10, -3.89892417e-08, 6.53007231e-07])
message: 'Optimization terminated successfully.'
nfev: 49
nit: 1
njev: 1
status: 0
success: True
x: array([ 7.20594053e-01, 3.22408604e-02, 4.05228023e-03, -2.75578440e-05,
-8.27999414e+01, 7.20612302e-01, 3.36369797e-02, 4.02094516e-03,
-1.74996556e-05, -7.71999791e+01, 7.20636130e-01, 3.47920978e-02,
4.01341931e-03, -1.21330600e-05, -7.15999090e+01, 7.20757808e-01,
3.33850817e-02, 3.95036100e-03, 3.46517345e-05, -6.57999267e+01,
7.20813915e-01, 3.22167822e-02, 3.97128822e-03, 2.00055269e-05,
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1.47074593e-05, -5.43998157e+01, 7.21048510e-01, 3.22346939e-02,
4.02104962e-03, -1.69519259e-05, -4.85998856e+01, 7.21074630e-01,
3.08484557e-02, 4.09385968e-03, -6.91378973e-05, -4.27999030e+01,
7.21154891e-01, 3.20619921e-02, 4.24950906e-03, -1.81328256e-04,
-3.71999987e+01, 9.99038595e-01, 1.70266104e+01])
Cost function after refinement: 6.1395983620232986e-09
CPU times: user 1h 53min 26s, sys: 6.39 s, total: 1h 53min 32s
Wall time: 11min 2s
Out[64]:
array([ 7.20594053e-01, 3.22408604e-02, 4.05228023e-03, -2.75578440e-05,
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4.01341931e-03, -1.21330600e-05, -7.15999090e+01, 7.20757808e-01,
3.33850817e-02, 3.95036100e-03, 3.46517345e-05, -6.57999267e+01,
7.20813915e-01, 3.22167822e-02, 3.97128822e-03, 2.00055269e-05,
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1.47074593e-05, -5.43998157e+01, 7.21048510e-01, 3.22346939e-02,
4.02104962e-03, -1.69519259e-05, -4.85998856e+01, 7.21074630e-01,
3.08484557e-02, 4.09385968e-03, -6.91378973e-05, -4.27999030e+01,
7.21154891e-01, 3.20619921e-02, 4.24950906e-03, -1.81328256e-04,
-3.71999987e+01, 9.99038595e-01, 1.70266104e+01])
In [65]:
LaB6_new = get_calibrant("LaB6")
LaB6_new.wavelength = 1e-10*hc/multigonio.param[-1]
print(LaB6,"\n", LaB6_new)
LaB6 Calibrant with 109 reflections at wavelength 7.281789761742598e-11
LaB6 Calibrant at wavelength 7.281789768115395e-11
In [66]:
%time res = multigonio.integrate([data[ds_names[i]] for i in range(9)])
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area_pixel=0.053413862261281864 area_sum=0.055214882933248166, Error= -0.033718225863472326
area_pixel=0.045333067243413794 area_sum=0.04986384765291535, Error= -0.09994427213966664
area_pixel=0.03918749031126367 area_sum=0.04563241935519968, Error= -0.16446393970995232
area_pixel=0.04641997394066166 area_sum=0.05056017758649528, Error= -0.0891901329183427
area_pixel=0.04963019502342725 area_sum=0.052784706110374724, Error= -0.06356032019335069
area_pixel=0.041808779534353135 area_sum=0.04729034242949584, Error= -0.13111033032281305
area_pixel=0.053529818242976646 area_sum=0.05553764984245543, Error= -0.03750865714441734
area_pixel=0.05746249488342414 area_sum=0.05828939512131753, Error= -0.014390259935127214
area_pixel=0.03804626259786659 area_sum=0.04468957516491201, Error= -0.17461143653615904
area_pixel=0.0579645518625469 area_sum=0.05860457337617547, Error= -0.011041602031984604
area_pixel=0.0514530597536762 area_sum=0.05403218600224738, Error= -0.05012580905622247
area_pixel=0.04708587038231293 area_sum=0.05104328125237842, Error= -0.08404667552990643
area_pixel=0.0414210821500145 area_sum=0.04727614277194664, Error= -0.1413546029707022
area_pixel=0.057188034039880264 area_sum=0.05760891916847055, Error= -0.0073596712259208176
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area_pixel=0.06406776393820302 area_sum=0.06431614060731783, Error= -0.003876780674824036
area_pixel=0.036519974544861 area_sum=0.045063743745274665, Error= -0.23394784106211602
area_pixel=0.06022365655235262 area_sum=0.06045501049825683, Error= -0.0038415791924405825
area_pixel=0.06470520384919531 area_sum=0.06480584410676266, Error= -0.0015553657446454841
area_pixel=0.042761484590993604 area_sum=0.04894851144272455, Error= -0.14468690483758498
area_pixel=0.05556804666999149 area_sum=0.0572738285392099, Error= -0.030697171692011003
area_pixel=0.05157759645584292 area_sum=0.054703089692101546, Error= -0.06059788456669262
area_pixel=0.04628344743831292 area_sum=0.051193164385785, Error= -0.1060793268266329
area_pixel=0.04441767384784612 area_sum=0.04995426406033848, Error= -0.12464836027789516
area_pixel=0.05377034832596905 area_sum=0.05619131504982555, Error= -0.04502419640616803
area_pixel=0.05745532746690074 area_sum=0.0586344668434077, Error= -0.020522716143011228
area_pixel=0.04107664840957703 area_sum=0.047752702889470366, Error= -0.16252675761970906
area_pixel=0.05946818134114551 area_sum=0.05993335889343876, Error= -0.00782229322979813
area_pixel=0.07058082407797173 area_sum=0.07058105681613237, Error= -3.2974701512325326e-06
area_pixel=0.046987941054872806 area_sum=0.05167050922411581, Error= -0.09965467871372943
area_pixel=0.051123579128637076 area_sum=0.05437612755835594, Error= -0.063621297357425
area_pixel=0.05248017980128061 area_sum=0.055180053859511885, Error= -0.05144559466934963
area_pixel=0.047912061925078575 area_sum=0.05226569446005236, Error= -0.09086715035937463
area_pixel=0.04572012763952671 area_sum=0.05084193350468269, Error= -0.11202518736470006
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[ 7.20881596e-01 3.33801850e-02 3.97760147e-03 1.47074593e-05
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area_pixel=0.0991017473223863 area_sum=0.10463027384689139, Error= -0.05578636778744499
area_pixel=0.07069194828200054 area_sum=0.08784192624601114, Error= -0.24260157458946852
area_pixel=0.07363944575302739 area_sum=0.08917599048958212, Error= -0.21098128289369983
area_pixel=0.11866235123215318 area_sum=0.12004419996868715, Error= -0.011645216213780306
area_pixel=0.042113113396123225 area_sum=0.07678977886848182, Error= -0.8234172844497124
area_pixel=0.10206300321222628 area_sum=0.10662320384564644, Error= -0.044680251314355705
area_pixel=0.09032959255696227 area_sum=0.09890206075850298, Error= -0.09490210194554875
area_pixel=0.05405730719101953 area_sum=0.0803776405557316, Error= -0.4868968643167011
area_pixel=0.06486418102965885 area_sum=0.08504369583806178, Error= -0.3111041330989122
area_pixel=0.07961206312065627 area_sum=0.09217586427332167, Error= -0.15781278188487957
area_pixel=0.11567416847953638 area_sum=0.11751408489279526, Error= -0.015906026707979987
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area_pixel=0.08974770209027838 area_sum=0.09849411368900213, Error= -0.09745554922315022
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area_pixel=0.06644918714957981 area_sum=0.08579443366184009, Error= -0.29112841468945794
area_pixel=0.07815101996878226 area_sum=0.09155079246491357, Error= -0.17145998224314793
area_pixel=0.11811873530334793 area_sum=0.11959505854816217, Error= -0.012498637417872821
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area_pixel=0.10302869305435536 area_sum=0.10744525208257137, Error= -0.04286727218684554
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area_pixel=0.04968735428679949 area_sum=0.07918713886310795, Error= -0.5937080973567899
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area_pixel=0.09827120932201439 area_sum=0.10420386190981694, Error= -0.06037020027261983
area_pixel=0.09671215194481775 area_sum=0.10311234681820346, Error= -0.06617777336851678
area_pixel=0.04760569306460383 area_sum=0.07848600072570878, Error= -0.648668377103522
area_pixel=0.12413022185356226 area_sum=0.12469829377225909, Error= -0.004576419104180694
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CPU times: user 1min 23s, sys: 92 ms, total: 1min 23s
Wall time: 7.48 s
In [67]:
ax = jupyter.plot1d(res, calibrant=LaB6_new)
ax.figure.show()
/mntdirect/_scisoft/users/jupyter/jupy35/lib/python3.5/site-packages/matplotlib/pyplot.py:537: RuntimeWarning: More than 20 figures have been opened. Figures created through the pyplot interface (`matplotlib.pyplot.figure`) are retained until explicitly closed and may consume too much memory. (To control this warning, see the rcParam `figure.max_open_warning`).
max_open_warning, RuntimeWarning)
Data type cannot be displayed: application/javascript
In [68]:
fig, ax = plt.subplots()
ax.plot(*calc_fwhm(res, LaB6_new, 10, 95), "o", label="FWHM")
ax.plot(*calc_peak_error(res, LaB6_new, 10, 95), "o", label="error")
ax.set_title("Peak shape & error as function of the angle")
ax.set_xlabel(res.unit.label)
ax.legend()
fig.show()
/mntdirect/_scisoft/users/jupyter/jupy35/lib/python3.5/site-packages/matplotlib/pyplot.py:537: RuntimeWarning: More than 20 figures have been opened. Figures created through the pyplot interface (`matplotlib.pyplot.figure`) are retained until explicitly closed and may consume too much memory. (To control this warning, see the rcParam `figure.max_open_warning`).
max_open_warning, RuntimeWarning)
Data type cannot be displayed: application/javascript
28457
68 60
In [69]:
print("total run time: ", time.time()-start_time)
total run time: 1576.358293056488
Conclusion¶
The calibration works and the FWHM of every single peak is pretty small: 0.02°. The geometry has been refined with the wavelength: The goniometer scale parameter refines to 0.999 instead of 1 and the wavelength is fitted with a change at the 5th digit which is pretty precise.
In [ ]: