MadSci Network: Physics |

Posted By:

Area of science:

ID:

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,

Try the links in the MadSci Library for more information on Physics.

MadSci Network, webadmin@madsci.org

© 1995-2006. All rights reserved.