Measuring the phase transfer function of a phase-shifting interferometer

Chu, Jiyoung; Wang, Quandou; Lehan, John P.; Gao, Ge; Griesmann, Ulf

doi:10.1117/12.795243

Cited by 10 publications

(10 citation statements)

References 4 publications

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“…45,46 Reliability of the PSD data for these and other applications depends on experimental methods available for comprehensive characterization and calibration of the spatial frequency response of the metrology instruments in use. [47][48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63][64][65] There are also problems inherent in the statistical description of surface metrology data that we discuss in the next section.…”

Section: Introductionmentioning

confidence: 99%

Reliable before-fabrication forecasting of expected surface slope distributions for x-ray optics

Yashchuk

2012

Opt. Eng

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Numerical simulation of the performance of new beamlines and those under upgrade requires sophisticated and reliable information about the expected surface slope and height distributions of planned x-ray optics before they are fabricated. Obtaining such information should be based on the metrology data measured from existing mirrors that are made by the same vendor and technology; but, generally, with different sizes, slope and height rms variations. In this work, we demonstrate a method for highly reliable forecasting of the expected surface slope distributions of the prospective x-ray optics. The method is based on an autoregressive moving average (ARMA) modeling of the slope measurements with a limited number of parameters. With the found parameters of the ARMA model, the surface slope profile of an optic with the newly desired specification can reliably be forecast. We demonstrate the high accuracy of this type of forecasting by comparing the power spectral density distributions of the measured and forecast slope profiles.

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Section: Introductionmentioning

confidence: 99%

Reliable before-fabrication forecasting of expected surface slope distributions for x-ray optics

Yashchuk

2012

Opt. Eng

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“…The MTF of an OCT system has also been reported in [180,181], as determined through measurements of nanoparticles. Grid patterns have also been used to establish the PTF of a phase-shifting interferometer [182]. Novak et al have used both phase steps and sine wave structures for characterizing a Fizeau interferometer [121].…”

Section: Interferometric Systemsmentioning

confidence: 99%

Determination of the transfer function for optical surface topography measuring instruments—a review

Foreman

Giusca

Coupland

et al. 2013

Meas. Sci. Technol.

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A significant number of areal surface topography measuring instruments, largely based on optical techniques, are commercially available. However, implementation of optical instrumentation into production is currently difficult due to the lack of understanding of the complex interaction between the light and the component surface. Studying the optical transfer function of the instrument can help address this issue. Here a review is given of techniques for the measurement of optical transfer functions. Starting from the basis of a spatially coherent, monochromatic confocal scanning imaging system, the theory of optical transfer functions in three-dimensional (3D) imaging is presented. Further generalizations are reviewed allowing the extension of the theory to the description of conventional and interferometric 3D imaging systems. Polychromatic transfer functions and surface topography measurements are also discussed. Following presentation of theoretical results, experimental methods to measure the optical transfer function of each class of system are presented, with a focus on suitable methods for the establishment of calibration standards in 3D imaging and surface topography measurements.

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“…[7][8][9][10][11][12][13][14][15][16][17][18][19] The effectiveness of a given method critically hinges on the appropriate choice of test surface. A successful test surface should be suitable for calibration over the entire instrumental field of view with a uniform sensitivity to the MTF over the entire spatial frequency range up to the Nyquist frequency of the instrument.…”

Section: Measured Psdmentioning

confidence: 99%

“…Additionally, in order to be used as a certified standard, the MTF test surface should satisfy the conditions of ease of specification, reproducibility, and repeatability; and the accuracy of the MTF calibration should have a reasonably low sensitivity to possible fabrication imperfections of the surface. Most of the common test patterns used in MTF measurements, including knife-edge sources (step height standards), [7][8][9][10][11] bar targets, 12 sinusoidal surfaces, 13 periodic and quasiperiodic patterns, [14][15][16] white noise patterns 17 and random reference specimens 15,18 fail to meet all of these requirements. For a comprehensive review of standard reference specimens, see Ref.…”

Section: Measured Psdmentioning

confidence: 99%

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

et al. 2010

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A modulation transfer function (MTF) calibration method based on binary pseudo-random (BPR) gratings and arrays [Proc. SPIE 7077-7 (2007), Opt. Eng. 47(7), 073602-1-5 (2008)] has been proven to be an effective MTF calibration method for a number of interferometric microscopes and a scatterometer [Nucl. Instr. and Meth. A 616, 172-82 (2010]. Here we report on a significant expansion of the application range of the method. We describe the MTF calibration of a 6 inch phase shifting Fizeau interferometer. Beyond providing a direct measurement of the interferometer's MTF, tests with a BPR array surface have revealed an asymmetry in the instrument's data processing algorithm that fundamentally limits its bandwidth. Moreover, the tests have illustrated the effects of the instrument's detrending and filtering procedures on power spectral density measurements. The details of the development of a BPR test sample suitable for calibration of scanning and transmission electron microscopes are also presented. Such a test sample is realized as a multilayer structure with the layer thicknesses of two materials corresponding to BPR sequence. The investigations confirm the universal character of the method that makes it applicable to a large variety of metrology instrumentation with spatial wavelength bandwidths from a few nanometers to hundreds of millimeters.

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Measuring the phase transfer function of a phase-shifting interferometer

Cited by 10 publications

References 4 publications

Reliable before-fabrication forecasting of expected surface slope distributions for x-ray optics

Reliable before-fabrication forecasting of expected surface slope distributions for x-ray optics

Determination of the transfer function for optical surface topography measuring instruments—a review

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

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