Takacs, PZ | Search NASA

DOE OSTI2023

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.

Takacs, PZ↗

DOE OSTI2022

Calibration, modeling, parameterization, and verification of the instrument transfer function of an interferometric microscope

Interferometric microscopes are used to measure surface roughness, from which the computed power spectral density function can be used to extract bandwidth-limited values of the various surface properties, such as root-mean-square (rms) height and slope errors. Measurements with a microscope equipped with different objectives that have an overlapping spatial frequency range usually give different rms results over the common frequency bandwidth. This is a result of different instrument transfer functions (ITFs) that attenuate spatial frequencies by different amounts over the overlapping range. We report on the use of binary pseudo-random array (BPRA) standards to characterize the ITF of an interferometric microscope with the various objectives. We use a simple model of a 1D binary Results show that the spectrum for an undersampled array is a cosine function, rather than a straight line, constant white noise spectrum. We have an analytical model of the ITF that includes the effects of an obscured aperture and defocus, in addition to the usual parameters of numerical aperture, wavelength, and sampling period. In addition, the model includes the effect of aliasing of spatial frequency components beyond the Nyquist back into the sub-Nyquist region. We compare the model PSD predictions to the measurements performed with different objectives. Departures of the measured PSDs from the model predictions indicate that there are higher-order ITF corrections yet to be identified and included in the model.

Takacs, PZ↗