MicroscopePSFs

MicroscopePSFs provides a Microscope Point Spread Function (PSF) calculator.

Current implementaions provide widefield PSFs assuming an incoherent point source.

Features

• 2D Gaussian PSF
• 2D Airy PSF
• 2D/3D Scalar PSF
• Scalar PSF allows arbitrary Pupil Function modification
• Phase and Magnitude Aberrations via Zernike expansion
• Any PSF can be converted to an interpolated PSF for faster generation at new positions

Design

The high-level interface is designed to facilitate generation of synthetic data as would be seen by an Array Detector (e.g. Camera). The PSF is considered a probability distribution that is normalized across 2D sections. Calculating the PSF at a location follows the convention from Distributions.jl where a distribution is created, and the PDF is calculated at a location.

Unit Convention

Pixel and source locations are in pixels for $x,y$ and in physical unit (typically micron) for $z$. This was chosen as it is the most natural units for simulating and interpreting data because the camera is referenced in pixels and stage movements in the $z$ dimention are in micron.

Examples

Airy PSF

using MicroscopePSFs
PSF=MicroscopePSFs

# Create an Airy PSF
na=1.2
λ=.6 
pixelsize=.1
p=PSF.Airy2D(na,λ,pixelsize)

# calculate the PSF at a point
camera_pixel=(0,0)
source_position=(0,0)
PSF.pdf(p,camera_pixel,source_position)

# calculate the PSF in a region
sz=16
camera_pixels=[(x,y) for y=1:sz, x=1:sz]
source_position=(sz/2,sz/2)
im=PSF.pdf(p,camera_pixels,source_position)

3D Scalar PSF with Astigmatism

using MicroscopePSFs
PSF=MicroscopePSFs

# Zernike Magnitude and Phase Coefficients 
z_mag=[1.0]
z_phase=zeros(10)
z_phase[6]=1 # astigmatism
z=PSF.ZernikeCoefficients(z_mag,z_phase)

# Create a scalar PSF
na=1.2
n=1.3
λ=.6 
pixelsize=.1

p=PSF.Scalar3D(na,λ,n,pixelsize;z=z)

# calculate the PSF in a region
sz=32
camera_pixels=[(x,y,z) for y=-sz/2:(sz/2-1), x=-sz/2:(sz/2-1), z=-1:.5:1] # Note z in microns.  
source_position=(0.0,0.0,0)
im=PSF.pdf(p,camera_pixels,source_position)

Future Development

MicroscopePSFs should be considered under development and the interface may change as we build the JuliaSMLM ecosystem. Comments and Feature requests are welcome via an issue.

Future Features

• GPU calculations
• Vector PSFs
• Super-critical angle PSFs
• Integration across finite pixels sizes using sub-sampling.