Aberrations

MicroscopePSFs includes a class of PSFs that are generated via integration over a complex pupil function, $P(k_x,k_y)$. Aberrations can be included in this calculation by modification of the pupil function. This can be done by direct modification of the pupil or by expansion into Zernike modes.

The Pupil Function

Zernike Expansion

Pupil function based PSFs can be created with a pupil magnitude and phase that are each given by a sum of Zernike polynomials. These are specified by a MicroscopePSFs.ZernikeCoefficients structure that is passed to the consructor:

The fields of this structure hold the coefficients of Zernike expansion using the OSA/ANSI linear index. These vectors are one based where e.g. mag[1] holds the coefficient for the j = 0 linear index.

Zernike polynomials are normalized such that coefficients are equal to the root-mean-square error across the unit disk. This normalization is:

\[\int_0^{2\pi}\int_0^1 Z^2 \rho d\rho d\phi = \pi\]

Example

A Tetrapod type PSF using a mixture of 1st and 2nd order astigmatism.

using Plots
using MicroscopePSFs

mag=[1.0]
phase=zeros(14)
phase[6]=.5 #osa index 5
phase[14]=-.5 #osa index 13
z=MicroscopePSFs.ZernikeCoefficients(mag,phase)

na=1.2
n=1.3
λ=.6
pixelsize=.1

p=MicroscopePSFs.Scalar3D(na,λ,n,pixelsize;z=z)