Spherical aberration and modulation transfer function

Abstract

The fundamental problem of the modulation transfer function(MTF) from the viewpoint of the lens designer is to find relation between the MTF and the geometrical aberrations. Let it be required to develop the spherical aberration into a polynomial expansion. The incoherent point spread function(PSF) of the optical imaging system is derived from the diffraction integral in the presence of aberrations. The optical transfer function(OTF) is the Fourier transform of the PSF, and the modulus of the OTF is the MTF. The relation between the spherical aberration and the MTF is denoted by numerical integration method. The normalized MTF is numerically calculated for various amounts of spherical aberration. A comparison is made between the MTF of the corrected spherical aberration using the optimum design for the minimum root mean square(RMS) wavefront aberration and those for the minimum peak-to-valley(P-V) wave front aberration.