Binary pseudo-random grating as a standard test surface for measurement of modulation transfer function of interferometric microscopes

Abstract

TitleBinary pseudo-random grating as a standard test surface for measurement of modulation transfer function of interferometric microscopes ABSTRACTThe task of designing high performance X-ray optical systems requires the development of sophisticated X-ray scattering calculations based on rigorous information about the optics. One of the most insightful approaches to these calculations is based on the power spectral density (PSD) distribution of the surface height. The major problem of measurement of a PSD distribution with an interferometric and/or atomic force microscope arises due to the unknown Modulation Transfer Function (MTF) of the instruments. The MTF characterizes the perturbation of the PSD distribution at higher spatial frequencies. Here, we describe a new method and dedicated test surfaces for calibration of the MTF of a microscope. The method is based on use of a specially designed Binary Pseudo-random (BPR) grating. Comparison of a theoretically calculated PSD spectrum of a BPR grating with a spectrum measured with the grating provides the desired calibration of the instrumental MTF. The theoretical background of the method, as well as results of experimental investigations are presented.

Optically interrogated MEMS pressure sensor array

“…As can be shown the power spectral density spectrum of such a grid is independent of spatial frequency, i.e. white-noise-like (Yashchuk et al 2007). We intend to develop fabrication processes for a rough, diffusive surface and for the two above mentioned (partially) retro-reflective groove patterns and compare them regarding their capability to be detected by coherent illumination from different observation points.…”

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.…”

“…For more details on the URA generation algorithm see Refs. 42,43 1D and 2D BPR gratings and arrays which we use for MTF calibration of surface profilometers (such as interferometric microscopes, [21][22][23][24] scatterometers, 23 and, now, large area interferometers) are sets of rectangular grooves pseudo-randomly distributed over a uniform 1D and 2D grid, respectively. Figure 1a h , determines the amplitude of the array's inherent PSD spectrum.…”

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.…”