Asymptotic expressions are derived for the two-dimensional incoherent optical transfer function (OTF) of an optical system with defocus and spherical aberration. The two-dimensional stationary phase method is used to evaluate the aberrated OTF at large and moderately large defocus and spherical aberration. For small aberrations, the OTF is approximated by a power series in the aberration coefficients. An accurate approximation (in elementary functions) to the OTF is obtained for a defocused optical system with a circular pupil. We experimentally demonstrate the validity of the OTF approximations in sharp-focus image restoration from two defocused images. A digital focusing method is presented.
© 2010 Optical Society of America
Original Manuscript: June 1, 2010
Revised Manuscript: October 9, 2010
Manuscript Accepted: October 9, 2010
Published: November 10, 2010
Aleksey N. Simonov and Michiel C. Rombach, "Asymptotic behavior of the spatial frequency response of an optical system with defocus and spherical aberration," J. Opt. Soc. Am. A 27, 2563-2573 (2010)