Practical considerations in using a binary pseudorandom array for instrument transfer function calibration
Binary pseudo-random array (BPRA) artifacts are useful devices for calibrating the instrument transfer function (ITF) of interferometric microscopes and other optical and non-optical surface and wavefront measurement instruments. The intrinsic white noise character of the power spectral density function of the artifact simplifies the deconvolution of the ITF from the measured power spectral density (PSD). However, resampling of the BPRA intrinsic artifact features with the measurement tool's specific sampling pattern modifies the white noise character of the intrinsic spectrum and needs to be accounted for in the ITF-based data deconvolution process. We have developed an analytic solution to the spectrum of a resampled one- and two- dimensional BPRA. The resultant nominal PSD function is a simple twoparameter cosine function with a period equal to the resampled pixel width. A transfer function model for interferometric microscopes that incorporates this function, along with an ITF that includes aliasing effects and variable numerical aperture (NA), wavelength, and obscuration factor, is used to fit to the BPRA PSDs measured by an interference microscope for a range of objective and zoom lens magnification combinations.