Below letter came from a Turkish professor via madsci. I called her and she says she is ready for help.

I want to be independent from not yet commercial softwares and i want to make the otf psf calculating software also.

It is a very good question. The photograph lenses are simulated by a lens

optical system model, which is based upon a generalized imaging system

model and coordinate system. The significant properties of the imaging

system can be formed from a real physical optical system. The object

plane and optical system are assumed to be plane and rotationally

symmetric respectively. The image formation process in an optical system

with incoherent illumination can be described by a convolution operation

Iimage(x,y,wavelength)=Point Spread function(x,y,wavelength){Convolution}

Iideal(x,y,wavelength)

where

Iideal(x,y,wavelength)={pi.T.Lplane(x/m,y/m,wavelength).R

(x,y,wavelength)}/{4.(f/Aeff)^2}

Iideal is the ideal, geometric image irradiance distribution, unaberrated

m is the magnification of the optical system

T is the transmittance of the optics

Lplane is the Lambertian object plane radiance distribution

R is the relative illumination factor

f/Aeff=effectivef-Number=0.5/Numerical Aperture

The Point spread function is the image of a point object formed by the

optical system. It contains all optical aberrations and diffraction in

the optical system. Iideal gives an ideal optical system without

aberrations or diffraction.

In same time, Image formation can be viewed as a linear filtering process.

FT{Iimage(x,y,wavelength)}=FT{Point Spread function(x,y,wavelength)}.FT

{Iideal(x,y,wavelength)}

FT{Iimage(x,y,wavelength)}=OTF(fx,fy,wavelength).F T{Iideal

(x,y,wavelength)}

Iimage(x,y,wavelength)= FT^-1{OTF.FT{Iideal(x,y,wavelength)}

where FT is the Fourier Transform Operator

You say "But If I am not wrong we have to change psf for each pixel color

and position."

You are right PSF(point spread function) depends on position and each

wavelength in coherent illumination

That is mathematics of the process

After that, by thinking the optical system (lenses), the image formation

can be achieved by convolving each section with its associated PSF

followed by summation of the individual results to obtain the final image

irradiance distribution. Alternatively, the final image airradiance

distribution can be obtained by filtering the spatial frequency

components of each section with its associated OTF, followed by inverse

Fourier transforming the filtered section transforms and summing the

results to obtain the final image irradiance distribution. The optical

system data are generated by lens design program for a given lens with

specific object plane distance. Lastly, the filtering is realized to form

the final image without distortion. The process is achieved step by step.

I hope, the answer can help you.

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Best ,

Mustafa Umut Sarac