# Phase Retrieval¶

Phase Retrieval is the process of extracting the phase shift, induced by the sample on the beam, acquired on the detector. This phase shift is then used to reconstruct a map of the (deviation from unity of the real part of) refractive index through tomographic reconstruction.

Nabu implements the following non-iterative phase retrieval methods.

## Paganin phase retrieval¶

This phase retrieval method was first described in [1].

The implementation PaganinPhaseRetrieval follows the normalization of [2].

The nabu implementation of Paganin phase retrieval should be compatible with the one of tomopy. More precisely, given a delta_beta value, the result should be the same as the one provided by tomopy with

extracted_phase_tomopy = retrieve_phase(
data,
pixel_size=pixel_size_meters*1e2,
dist=distance_m * 1e2,
energy=energy_kev,
alpha=1./(4*3.141592**2 * delta_beta),
)


there is notably a factor of 1/(4*pi**2) between the conventions.

Warning

Since version 2021.1.0, lengths in PaganinPhaseRetrieval are expressed in meters (distance and pixel size).

## Single-Distance CTF phase retrieval¶

This method, although based on Contrast Transfer Function (CTF) rather than Transport of Intensity (TIE), can also be expressed as a single step “filtering” processing. See for example [2].

This method is implemented in CTFPhaseRetrieval.

Note

Lengths are expressed in meters

To build a CTFPhaseRetrieval, one first needs to describe the setup geometry. This is done with the GeoPars class:

geo_pars = GeoPars(
z1_vh=None,
z2=z2,
pix_size_det=pix_size_det,
length_scale=length_scale,
wavelength=wavelength,
)


once this GeoPars object is built, the CTFPhaseRetrieval object can be created and called:

ctf_filter = CTFPhaseRetrieval(
geo_pars,
delta_beta,
lim1=1.0e-5,
lim2=0.2,
)

phase_image = ctf_filter.retrieve_phase(projection, normalize_by_mean=True)


## Unsharp masking¶

Single-distance phase retrieval tend to blur the images. To recover sharp features, a common method is to use a unsharp mask image processing step.

This feature is implemented in nabu.misc.unsharp, and in the Cuda/Opencl back-ends nabu.preproc.unsharp_cuda and nabu.preproc.unsharp_opencl respectively.

## Enable phase retrieval from the configuration file¶

To enable the phase retrieval processing step, modify the section [phase] of nabu config file:

[phase]
method = Paganin # possible values: none, Paganin, CTF


additional parameters can be specified:

# delta/beta ratio for the Paganin method
paganin_delta_beta = 100.0
# Padding type for the filtering step. Available are: mirror, edges, zeros
paganin_padding_type = mirror


To enable unsharp masking, the value of unsharp_coeff must be greater than zero.

# Unsharp mask strength. The unsharped image is equal to
#   UnsharpedImage =  (1 + coeff)*originalPaganinImage - coeff * ConvolutedImage. Setting this coefficient to zero means that no unsharp mask will be applied.
unsharp_coeff = 0
# Standard deviation of the Gaussian filter when applying an unsharp mask
# after the Paganin filtering. Disabled if set to 0.
unsharp_sigma = 0


## 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

[2] Boliang Yu Et Al, “Evaluation of phase retrieval approaches in magnified X-ray phase nano computerized tomography applied to bone tissue,” Opt. Express 26, 11110-11124 (2018)