Off-Axis Holography Using Lower-Level Functions

As an alternative to using the Holo Class as described in Off-Axis Holography Using the Holo Class , low-level functions can be called directly.

Getting Started Using Lower-Level Functions

Begin by importing the library:

import pyholoscope as pyh

We will assume we have a hologram hologram and a background image background_img which are both square 2D numpy arrays of the same size. If we do not know the modulation frequency in advance we can use:

crop_centre = pyh.off_axis_find_mod(background_img)
crop_radius = pyh.off_axis_find_crop_radius(background_img)

We can then demodulate using:

recon_field = pyh.off_axis_demod(hologram, crop_centre, crop_radius)

To remove the background, recover the background field using:

background_field = pyh.off_axis_demod(background_img, crop_centre, crop_radius)

Remove the background phase (for example due to aberrations in the imaging system) using:

corrected_field = pyh.relative_phase(recon_field, background_field)

The numpy array corrected_field is complex, to obtain the amplitude and phase, use:

amplitude = pyh.amp(recon_field)
phase = pyh.phase(recon_field)

If we would like to numerically refocus, we first define a propagator for use with the angular spectrum method. This requires specification of the hologram size, wavelength, pixel size and the depth we wish to refocus to:

grid_size = crop_radius * 2
wavelength = 0.5e-6
pixel_size = 2e-6
depth = 1e-3
prop = pyh.propagator(grid_size, wavelength, pixel_size, depth)

Note here that the grid_size is the size of the reconstructed field following demodulation which is smaller than the original image. The pixel size must also be specified as the pixel size in the reconstructed field, not the pixel size in the original hologram. Pixel size, wavelength and depth must be in the same units.

We can then refocus using:

refocused_field = pyh.refocus(corrected_field, prop)

The numpy array refocused_field is a 2D complex numpy array, to obtain the amplitude and phase as 2D numpy arrays, use:

amplitude = pyh.amp(refocused_field)
phase = pyh.phase(refocused_field)

As when using the Holo class, for cases when you know the reference beam is tilted in the both the x and y planes, it is possible to improve speed by using only a real FFT by passing real_fft = True to the off_axis_demod function, e.g.:

recon_field = pyh.off_axis_demod(hologram, crop_centre, crop_radius, real_fft=True)

real_fft = True must also be passed to the off_axis_find_mod and off_axis_find_crop_radius functions to correctly find the peak location in the real FFT.