Re: How can I simulate expensive photograph lenses on my photograph at computer

Hi,

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).FT{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.

Best Wishes,