# Point Spread Function with Gaussian (radial direction) and exponential (axial direction)

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poptrop459 on 5 Aug 2019
Commented: poptrop459 on 6 Aug 2019
A paper I'm reading had the following statement: "we can approximate the point-spread function by a Gaussian in the radial direction and an exponential with average height,d, in the axial direction."
Does anyone have any idea how this could translate into MATLAB code? I was thinking of generating random numbers from distributions and making a histogram, but the translation of the Gaussian/exponential combo to code itself is confusing me.

Image Analyst on 5 Aug 2019
I don't know. You can use fspecial() to get a Gaussian image/pattern/matrix. Of course the values of that Gaussian are determined by the amplitude and standard deviation. I don't see how you can have it do that in the radial direction and have some other function in the axial direction. I don't even know what the axial direction is. Is that the distance along the optic axis from scene to lens/sensor/camera? Maybe the amplitude of the Gaussian changes along the optic axis according to an exponential. So your Gaussian close to the lens would be different than the Gaussian close to the scene. I've never heard of this though. Usually there is just one PSF for the whole system that takes everything into account no matter what caused it.

poptrop459 on 5 Aug 2019
Hi Image Analyst,
I did some digging around and found this in one the sections. It gets a bit technical, so I don't know how helpful it'll be.
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The program updates the positions of particles randomly distributed in two dimensions with a Gaussian random number generator with standard deviation sqrt(2DT) where T is the period of the simulation and D is the diffusion coefficient. For each frame, a Gaussian intensity distribution was superimposed on the position of each particle with amplitude corresponding to the average intensity/frame. A Poisson random number generator was then used to calculate the photon counts corresponding to each intensity
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So that gives some insight on the standard deviation. Still can't figure out what its saying about the radial and axial directions though.
Image Analyst on 5 Aug 2019
Try contacting the authors.
poptrop459 on 6 Aug 2019
Yep, I shot them an email. Hopefully I'll hear from them soon. Thanks for your help.