The effect of fourth-, sixth-, and eighth-order balanced spherical aberrations on the incoherent point-spread function of an optical imaging system with a circular pupil is considered. It is shown that the location of the first minimum remains practically unchanged and its value remains close to zero as aberrations are introduced into the system. Thus, the central Airy disk maintains its size and distinction. Moreover, the aberrations reduce the irradiance distribution inside the Airy disk quite uniformly. The central irradiance, i.e., the Strehl ratio, can be determined quite accurately from the phase aberration variance according to S ≃ exp(-σ2Φ). Thus, the aberrated spread functions and encircled energy for a given aberration can be determined very quickly from the aberration-free results by multiplying them with the Strehl ratio. For further simplicity, the spread functions are approximated by a Gaussian function appropriately scaled by the Strehl ratio. The approximation is quite good for points lying within a circle of radius roughly half that of the Airy disk. Defocused but otherwise aberration-free spread functions are also considered. It is shown that results similar to those for spherical aberrations are obtained but over a narrower range of Strehl ratio as well as distance from the center of the spread functions.
© 1983 Optical Society of America
Virendra N. Mahajan, "Aberrated point-spread functions for rotationally symmetric aberrations," Appl. Opt. 22, 3035-3041 (1983)