Calculation of Diffraction Image Quality Using Apodized Wavefront Data

The point spread function (PSF) of an optical system is a function of both the amplitude and phase of the electric field in the exit pupil. Interferometric testing of optics yields information regarding variations in phase, but not in amplitude. Typically the PSF, encircled energy function (EEF) and Strehl ratio are calculated from the phase information alone, implicitly assuming that the amplitude is uniform across the pupil. For incoherent, unvignetted imaging systems this assumption is generally valid. Coherent optical systems are a different case due to the Gaussian irradiance profile of lasers. The optics in such systems are non-uniformly illuminated, the amplitude function in the pupil being characterized by a Gaussian or truncated Gaussian profile. This effect of apodization is examined for aberrated and unaberrated beams. Analytic forms and numerical results are presented, as are measurements of laser diode based optical systems. In general, little effect from apodization is seen on parameters which are typically of interest (e.g., Strehl, FWHM of PSF, 80% encircled energy) except for cases of pupil irradiance decrease of greater than half from center to edge.