nabu.preproc.phase module¶
- nabu.preproc.phase.lmicron_to_db(Lmicron, energy, distance)[source]¶
Utility to convert the “Lmicron” parameter of PyHST to a value of delta/beta.
- Parameters:
Lmicron (float) – Length in microns, values of the parameter “PAGANIN_Lmicron” in PyHST2 parameter file.
energy (float) – Energy in keV.
distance (float) – Sample-detector distance in microns
Notes
The conversion is done using the formula
\[L^2 = \pi \lambda D \frac{\delta}{\beta}\]
- class nabu.preproc.phase.PaganinPhaseRetrieval(shape, distance=0.5, energy=20, delta_beta=250.0, pixel_size=1e-06, padding='edge', margin=None, use_rfft=True, use_R2C=None, fftw_num_threads=None)[source]¶
Bases:
objectPaganin Phase Retrieval for an infinitely distant point source. Formula (10) in [1].
- Parameters:
shape (int or tuple) – Shape of each radio, in the format (num_rows, num_columns), i.e (size_vertical, size_horizontal). If an integer is provided, the shape is assumed to be square.
distance (float, optional) – Propagation distance in meters.
energy (float, optional) – Energy in keV.
delta_beta (float, optional) – delta/beta ratio, where n = (1 - delta) + i*beta is the complex refractive index of the sample.
pixel_size (float, optional) – Detector pixel size in meters. Default is 1e-6 (one micron)
padding (str, optional) – Padding method. Available are “zeros”, “mean”, “edge”, “sym”, “reflect”. Default is “edge”. Please refer to the “Padding” section below for more details.
margin (tuple, optional) –
The user may provide integers values U, D, L, R as a tuple under the form ((U, D), (L, R)) (same syntax as numpy.pad()). The resulting filtered radio will have a size equal to (size_vertic - U - D, size_horiz - L - R). These values serve to create a “margin” for the filtering process, where U, D, L R are the margin of the Up, Down, Left and Right part, respectively. The filtering is done on a subset of the input radio. The subset size is (Nrows - U - D, Ncols - R - L). The margins is used to do the padding for the rest of the padded array.
For example in one dimension, where
padding="edge":<------------------------------ padded_size ---------------------------> [padding=edge | padding=data | radio data | padding=data | padding=edge] <------ N2 ---><----- L -----><- (N-L-R)--><----- R -----><----- N2 --->
Some or all the values U, D, L, R can be 0. In this case, the padding of the parts related to the zero values will fall back to the one of “padding” parameter. For example, if padding=”edge” and L, R are 0, then the left and right parts will be padded with the edges, while the Up and Down parts will be padded using the the user-provided margins of the radio, and the final data will have shape (Nrows - U - D, Ncols). Some or all the values U, D, L, R can be the string “auto”. In this case, the values of U, D, L, R are automatically computed as a function of the Paganin filter width.
use_rfft (bool, optional) – Whether to use Real-to-Complex (R2C) transform instead of standard Complex-to-Complex transform, providing better performances
use_R2C (bool, optional) – DEPRECATED, use use_rfft instead
fftw_num_threads (bool or None or int, optional) – Whether to use FFTW for speeding up FFT. Default is to use all available threads. You can pass a negative number to use N - fftw_num_threads cores.
Important
Mind the units! Distance and pixel size are in meters, and energy is in keV.
Notes
Padding methods
The phase retrieval is a convolution done in Fourier domain using FFT, so the Fourier transform size has to be at least twice the size of the original data. Mathematically, the data should be padded with zeros before being Fourier transformed. However, in practice, this can lead to artefacts at the edges (Gibbs effect) if the data does not go to zero at the edges. Apart from applying an apodization (Hamming, Blackman, etc), a common strategy to avoid these artefacts is to pad the data. In tomography reconstruction, this is usually done by replicating the last(s) value(s) of the edges ; but one can think of other methods:
“zeros”: the data is simply padded with zeros.
“mean”: the upper side of extended data is padded with the mean of the first row, the lower side with the mean of the last row, etc.
“edge”: the data is padded by replicating the edges. This is the default mode.
“sym”: the data is padded by mirroring the data with respect to its edges. See
numpy.pad().“reflect”: the data is padded by reflecting the data with respect to its edges, including the edges. See
numpy.pad().
Formulas
The radio is divided, in the Fourier domain, by the original “Paganin filter” [1].
\[F = 1 + \frac{\delta}{\beta} \lambda D \pi |k|^2\]where k is the wave vector.
References
- [1] D. Paganin Et Al, “Simultaneous phase and amplitude extraction
from a single defocused image of a homogeneous object”, Journal of Microscopy, Vol 206, Part 1, 2002
- available_padding_modes = ['zeros', 'mean', 'edge', 'symmetric', 'reflect']¶
- powers¶
- pad_with_values(data, top_val=0, bottom_val=0, left_val=0, right_val=0)[source]¶
Pad the data into self.padded_data with values.
- Parameters:
data (numpy.ndarray) – data (radio)
top_val (float or numpy.ndarray, optional) – Value(s) to fill the top of the padded data with.
bottom_val (float or numpy.ndarray, optional) – Value(s) to fill the bottom of the padded data with.
left_val (float or numpy.ndarray, optional) – Value(s) to fill the left of the padded data with.
right_val (float or numpy.ndarray, optional) – Value(s) to fill the right of the padded data with.
- lmicron_to_db(Lmicron)[source]¶
Utility to convert the “Lmicron” parameter of PyHST to a value of delta/beta. Please see the doc of nabu.preproc.phase.lmicron_to_db()
- retrieve_phase(radio, padding_method=None, output=None)¶