prysm.propagation¶

Numerical optical propagation.

prysm.propagation.focus(wavefunction, Q)¶

Propagate a pupil plane to a PSF plane.

Parameters

wavefunction (numpy.ndarray) – the pupil wavefunction
Q (float) – oversampling / padding factor

Returns

psf – point spread function

Return type

numpy.ndarray

prysm.propagation.unfocus(wavefunction, Q)¶

Propagate a PSF plane to a pupil plane.

Parameters

wavefunction (numpy.ndarray) – the pupil wavefunction
Q (float) – oversampling / padding factor

Returns

pupil – field in the pupil plane

Return type

numpy.ndarray

prysm.propagation.focus_fixed_sampling(wavefunction, input_dx, prop_dist, wavelength, output_dx, output_samples)¶

Propagate a pupil function to the PSF plane with fixed sampling.

Parameters

wavefunction (numpy.ndarray) – the pupil wavefunction
input_dx (float) – spacing between samples in the pupil plane, millimeters
prop_dist (float) – propagation distance along the z distance
wavelength (float) – wavelength of light
output_dx (float) – sample spacing in the output plane, microns
output_samples (int) – number of samples in the square output array

Returns

data – 2D array of data

Return type

numpy.ndarray

prysm.propagation.unfocus_fixed_sampling(wavefunction, input_dx, prop_dist, wavelength, output_dx, output_samples)¶

Propagate an image plane field to the pupil plane with fixed sampling.

Parameters

wavefunction (numpy.ndarray) – the image plane wavefunction
input_dx (float) – spacing between samples in the pupil plane, millimeters
prop_dist (float) – propagation distance along the z distance
wavelength (float) – wavelength of light
output_dx (float) – sample spacing in the output plane, microns
output_samples (int) – number of samples in the square output array

Returns

x (numpy.ndarray) – x axis unit, 1D ndarray
y (numpy.ndarray) – y axis unit, 1D ndarray
data (numpy.ndarray) – 2D array of data

prysm.propagation.Q_for_sampling(input_diameter, prop_dist, wavelength, output_dx)¶

Value of Q for a given output sampling, given input sampling.

Parameters

input_diameter (float) – diameter of the input array in millimeters
prop_dist (float) – propagation distance along the z distance, millimeters
wavelength (float) – wavelength of light, microns
output_dx (float) – sampling in the output plane, microns

Returns

requesite Q

Return type

float

prysm.propagation.pupil_sample_to_psf_sample(pupil_sample, samples, wavelength, efl)¶

Convert pupil sample spacing to PSF sample spacing. fλ/D or Q.

Parameters

pupil_sample (float) – sample spacing in the pupil plane
samples (int) – number of samples present in both planes (must be equal)
wavelength (float) – wavelength of light, in microns
efl (float) – effective focal length of the optical system in mm

Returns

the sample spacing in the PSF plane

Return type

float

prysm.propagation.psf_sample_to_pupil_sample(psf_sample, samples, wavelength, efl)¶

Convert PSF sample spacing to pupil sample spacing.

Parameters

psf_sample (float) – sample spacing in the PSF plane
samples (int) – number of samples present in both planes (must be equal)
wavelength (float) – wavelength of light, in microns
efl (float) – effective focal length of the optical system in mm

Returns

the sample spacing in the pupil plane

Return type

float

prysm.propagation.fresnel_number(a, L, lambda_)¶

Compute the Fresnel number.

Notes

if the fresnel number is << 1, paraxial assumptions hold for propagation

Parameters

a (float) – characteristic size (“radius”) of an aperture
L (float) – distance of observation
lambda (float) – wavelength of light, same units as a

Returns

the fresnel number for these parameters

Return type

float

prysm.propagation.talbot_distance(a, lambda_)¶

Compute the talbot distance.

Parameters

a (float) – period of the grating, units of microns
lambda (float) – wavleength of light, units of microns

Returns

talbot distance, units of microns

Return type

float

prysm.propagation.angular_spectrum(field, wvl, dx, z, Q=2, tf=None)¶

Propagate a field via the angular spectrum method.

Parameters

field (numpy.ndarray) – 2D array of complex electric field values
wvl (float) – wavelength of light, microns
z (float) – propagation distance, units of millimeters
dx (float) – cartesian sample spacing, units of millimeters
Q (float) – sampling factor used. Q>=2 for Nyquist sampling of incoherent fields
tf (numpy.ndarray) – if not None, clobbers all other arguments transfer function for the propagation

Returns

2D ndarray of the output field, complex

Return type

numpy.ndarray

prysm.propagation.angular_spectrum_transfer_function(samples, wvl, dx, z)¶

Precompute the transfer function of free space.

Parameters

samples (int or tuple) – (y,x) or (r,c) samples in the output array
wvl (float) – wavelength of light, microns
dx (float) – intersample spacing, mm
z (float) – propagation distance, mm

Returns

ndarray of shape samples containing the complex valued transfer function such that X = fft2(x); xhat = ifft2(X*tf) is signal x after free space propagation

Return type

numpy.ndarray

class prysm.propagation.Wavefront(cmplx_field, wavelength, dx, space='pupil')¶

Bases: object

(Complex) representation of a wavefront.

classmethod from_amp_and_phase(amplitude, phase, wavelength, dx)¶

Create a Wavefront from amplitude and phase.

Parameters

amplitude (numpy.ndarray) – array containing the amplitude
phase (numpy.ndarray, optional) – array containing the optical path error with units of nm if None, assumed zero
wavelength (float) – wavelength of light with units of microns
dx (float) – sample spacing with units of mm

intensity¶: Intensity, abs(w)^2.

phase¶: Phase, angle(w). Possibly wrapped for large OPD.

free_space(dz=nan, Q=1, tf=None)¶

Perform a plane-to-plane free space propagation.

Uses angular spectrum and the free space kernel.

Parameters

dz (float) – inter-plane distance, millimeters
Q (float) – padding factor. Q=1 does no padding, Q=2 pads 1024 to 2048.
tf (numpy.ndarray) – if not None, clobbers all other arguments transfer function for the propagation

Returns

the wavefront at the new plane

Return type

Wavefront

focus(efl, Q=2)¶

Perform a “pupil” to “psf” plane propgation.

Uses an FFT with no quadratic phase.

Parameters

efl (float) – focusing distance, millimeters
Q (float) – padding factor. Q=1 does no padding, Q=2 pads 1024 to 2048. To avoid aliasng, the array must be padded such that Q is at least 2 this may happen organically if your data does not span the array.

Returns

the wavefront at the focal plane

Return type

Wavefront

unfocus(efl, Q=2)¶

Perform a “psf” to “pupil” plane propagation.

uses an FFT with no quadratic phase.

Parameters

efl (float) – un-focusing distance, millimeters
Q (float) – padding factor. Q=1 does no padding, Q=2 pads 1024 to 2048. To avoid aliasng, the array must be padded such that Q is at least 2 this may happen organically if your data does not span the array.

Returns

the wavefront at the pupil plane

Return type

Wavefront

focus_fixed_sampling(efl, dx, samples)¶

Perform a “pupil” to “psf” propagation with fixed output sampling.

Uses matrix triple product DFTs to specify the grid directly.

Parameters

efl (float) – focusing distance, millimeters
dx (float) – output sample spacing, microns
samples (int) – number of samples in the output plane. If int, interpreted as square else interpreted as (x,y), which is the reverse of numpy’s (y, x) row major ordering

Returns

the wavefront at the psf plane

Return type

Wavefront

unfocus_fixed_sampling(efl, dx, samples)¶

Perform a “psf” to “pupil” propagation with fixed output sampling.

Uses matrix triple product DFTs to specify the grid directly.

Parameters

efl (float) – un-focusing distance, millimeters
dx (float) – output sample spacing, millimeters
samples (int) – number of samples in the output plane. If int, interpreted as square else interpreted as (x,y), which is the reverse of numpy’s (y, x) row major ordering

Returns

wavefront at the pupil plane

Return type

Wavefront

prysm.propagation¶

prysm

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