Optical system invariant to second-order aberrations

An approximate analytical expression is derived for the two-dimensional incoherent optical transfer function (OTF) of an imaging system invariant to second-order aberrations. The system broadband behavior resulting from a third-order phase mask in its pupil plane is analyzed by using the two-dimensional stationary phase method. This approach does not require mathematical separability of the pupil function and can be applied to any pupil shape. The OTF is found to be a well-defined and smooth function at all nonzero spatial frequencies when the phase mask function includes third-order mixed terms in the pupil coordinates. (C) 2009 Optical Society of America