Binary pseudorandom array test standard optimized for characterization of large field-of-view optical interferometers

Abstract

Recently, a technique for calibrating the modulation transfer function (MTF) of a broad variety of metrology instrumentation has been demonstrated. This technique is based on test samples structured as one-dimensional binary pseudo-random (BPR) sequences and two-dimensional BPR arrays (BPRAs). The inherent power spectral density of BPR gratings (sequences) and arrays has a deterministic white-noise-like character that allows direct determination of the MTF with uniform sensitivity over the entire spatial frequency range and field-of-view of an instrument. As such, the BPR samples satisfy the characteristics of a test standard: functionality, ease of specification and fabrication, reproducibility, and low sensitivity to manufacturing error. Here we discuss our recent developments directed to the optimization of the sample design, fabrication, application, and data processing procedures, suitable for thorough characterization of large aperture optical interferometers. Compared with the previous coded-aperture based design, the improved, 'highly randomized' BPRA pattern of the new test standard provides better accuracy and reliability of instrument MTF and aberration characterization, and enables operation optimization of large aperture optical interferometers. We describe the pattern generation algorithm and tests to verify the compliance to desired BPRA topography. The data acquisition and analysis procedures for different applications of the technique are also discussed.

Reliability investigation of the instrument transfer function calibration technique based on binary pseudo-random array standards

“…Indeed, the inherent PSD of a particular BPRA pattern as designed and fabricated is perfectly constant being evaluated applying the discrete Fourier transform methods to the BPR array with the pixilation determined by the elementary size of the pattern (see, for example, Refs. [7,8,32,33] and references therein).…”

“…2) are designed according to the prescription for a uniformly redundant array (URA) [30,31]; whereas, the patterns A2, B2, C2 and D2 with the elementary sizes of 2.501 µm, 1.201 µm, 801 nm, and 401 nm are designed according to the highly randomized (HR) BPR arrays described in Ref. [32]. The step-function pattern E1 that is also etched to the standard is used for cross-comparison investigations in the scope of the analytical modeling of the ITF of the interferometric microscope (see the corresponding discussion in Ref.…”

“…URA-based BPRA patterns generated by sophisticated prescription algorithms [30,31] have PSD distributions that are perfectly constant when evaluated over the entire array. However, the PSDs of the URA-based BPRA pattern subareas, shortened (cropped) and resampled in the course of the ITF measurements, have excess variance [14,32]. Subsequently, the accuracy of the ITF calibration is reduced.…”

“…The HR BPRAs have been specially designed [32] to eliminate the limitation of the URA-based BPRA patterns mentioned above. Consequently, the measurements discussed in this paper are mostly performed over the HR BPRA patterns.…”

“…From that time, a broad variety of BPR test standards with the elementary sizes from 1.5 nanometers and up to the dozens of microns have been developed and successfully applied for resolution calibration of the electron, x-ray, and optical microscopes, optical scatterometers, and large-aperture Fizeau interferometers (see, for example, Refs. [9][10][11][12][13][14][15][16][17] and references therein).…”