Practical considerations in using a binary pseudorandom array for instrument transfer function calibration

Published

October 2, 2023

Author(s)

Peter Takacs, Simon Rochester, Ian Lacey, Keiko Munechika, Ulf Griesmann, Valeriy Yashchuk

Abstract

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 two-parameter 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.

Proceedings Title

Proceedings of SPIE 12672

Conference Dates

August 20-24, 2023

Conference Location

San Diego, CA, US

Conference Title

SPIE Optical Engineering + Applications

Pub Type

Conferences

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Keywords

optical microscope, instrument transfer function, binary pseuo-random arrays

Citation

Takacs, P. , Rochester, S. , Lacey, I. , Munechika, K. , Griesmann, U. and Yashchuk, V. (2023), Practical considerations in using a binary pseudorandom array for instrument transfer function calibration, Proceedings of SPIE 12672, San Diego, CA, US, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=956305 (Accessed October 11, 2025)