Binary pseudorandom grating standard for calibration of surface profilometers

Abstract

We suggest and describe the use of a binary pseudo-random (BPR) grating as a standard test surface for measurement of the modulation transfer function (MTF) of interferometric microscopes. Knowledge of the MTF of a microscope is absolutely necessary to convert the measured height distribution of a surface undergoing metrology into an accurate power spectral density (PSD) distribution. For an 'ideal' microscope with an MTF function independent of spatial frequency out to the Nyquist frequency of the detector array with zero response at higher spatial frequencies, a BPR grating would produce a flat 1D PSD spectrum, independent of spatial frequency. For a 'real' instrument, the MTF is found as the square root of the ratio of the PSD spectrum measured with the BPR grating to the 'ideal', spatial frequency independent, PSD spectrum. We present the results from a measurement of the MTF of Micromap TM -570 interferometric microscope demonstrating a high efficiency for the calibration method.

Calibration of the modulation transfer function of surface profilometers with binary pseudo-random test standards: expanding the application range

“…The success of applying this method to different interferometric microscopes and a scatterometer has been experimentally demonstrated. [20][21][22][23][24] In the present work, we present results of extending the BPRA method to large field-of-view interferometers, a class of instruments that are, and will continue to be, a standard for making high precision surface height measurements over relatively low spatial frequency ranges from approximately 10 -2 mm -1 to 10 mm -1 . An extension of the method to the micro-and nano-scale measurements with scanning and transmission electron microscopes (SEM and TEM, respectively) is also presented.…”

“…The technique is based on the use of binary pseudo-random gratings (BPRG) and arrays. 20,21 Unlike most conventional test surfaces, the inherent PSD of the BPR gratings and arrays has a deterministic white-noise-like character. This allows the direct determination of the one-(1D) and two-dimensional (2D) MTF, respectively, with a sensitivity uniform over the entire spatial frequency range of a profiler.…”

Binary pseudo-random gratings and arrays for calibration of the modulation transfer function of surface profilometers: recent developments

“…The BPR surfaces have numerous advantages over other surfaces. The major distinguishing properties are equal sensitivity to the entire spatial frequency range of an instrument and deterministic character of the inherent PSD 16,17 .…”

“…15 In Refs. [16,17] a new type of test surface based on binary pseudo random (BPR) patterns, gratings and arrays that are specifically designed for MTF measurement of surface profilers, has been suggested as use as a calibration standard. The effectiveness of the method was demonstrated experimentally with a BPR grating which is a 1D realization of the method.…”

Calibration of Modulation Transfer Function of Surface Profilometers with 1-D and 2-D Binary Pseudo-Random Array Standards

“…We suggest and describe the use of a binary pseudo-random (BPR) grating as a standard test surface for measurement of the MTF of microscopes [1][2][3]. For an 'ideal' microscope with an MTF function independent of spatial frequency out to the Nyquist frequency of the detector array with zero response at higher spatial frequencies, a BPR grating would produce a flat 1D PSD spectrum, independent of spatial frequency.…”