Modeling of coherence scanning interferometry using classical Fourier optics

Groot, Peter J. de; Lega, Xavier Colonna de; Su, Rong; Coupland, John N.; Leach, Richard

doi:10.1117/1.oe.60.10.104106

Cited by 11 publications

(11 citation statements)

References 53 publications

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“…It has also been shown that for continuous surfaces with modest slopes and for small discontinuities (steps), an approximate elementary Fourier optics (EFO) method provides comparable accuracy to more advanced models [13]. The applicability of EFO modeling is consistent with SFR and ITF prediction for interferometers that use phase analysis to determine the final measured topography [14].…”

mentioning

confidence: 69%

Modeling the topographic lateral resolution of interferometers

de Groot,

Kramer,

Sutherland

2023

Modeling Aspects in Optical Metrology IX

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Performance characteristics for interferometers that measure surface topography include the ability to resolve closely spaced surface features, referred to as topographic spatial resolution. Within well-defined limits, scalar diffraction theory and classical Fourier optics provide a software model for prediction of the resolution and spatial frequency response for interference phase-based measurements of surface topography. Analytical solutions and adaptive sampling allow for rapid simulation of both the nominal linear transfer function and an estimate of intrinsic residual nonlinearities.

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confidence: 69%

Modeling the topographic lateral resolution of interferometers

de Groot,

Kramer,

Sutherland

2023

Modeling Aspects in Optical Metrology IX

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“…However, if in addition the slope of the phase along the fringe frequency is considered, the 2π-ambiguity can be overcome enabling an unambiguous profile reconstruction. This is the basic idea of the FDA algorithm introduced 30 years ago by de Groot et al 21,22 However, the envelope position results from the slope of the phase with respect to the fringe frequency. According to Figure 1 this slope shows a linear behaviour.…”

Section: Extended Signal Analysis In Coherence Scanning Interferometrymentioning

confidence: 99%

Universal Fourier optics model for virtual coherence scanning interferometers

Lehmann,

Pahl,

Riebeling

2023

Modeling Aspects in Optical Metrology IX

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Optical surface topography measurements sometimes suffer from systematic errors. In order to predict such deviations, modeling of optical profilers is a substantial part of the European project TracOptic (Traceable Optics). Within the framework of this project, we recently developed the UFO (Universal Fourier Optics) model, which simulates virtual CSI measurements of surface topographies that fulfill the requirements of the scalar Kirchhoff approximation. The model enables a fast computation of 'measured' surface topographies as it is based on discrete Fourier transforms. It treats the surface under investigation as a two-dimensional phase object assuming a linear dependence of the interference phase on surface height and axial spatial frequency. The scattered light field is transferred to the Fourier domain and multiplied by a partial two-dimensional transfer function (TF) representing a horizontal cross section of the three-dimensional TF at a certain axial spatial frequency or evaluation wavelength, respectively. The TF includes parameters of the interference microscope and the reference field distribution. Inverse Fourier transform enables the reconstruction of the phase object. The coherence peak position of an interference signal results from numerical differentiation with respect to the axial spatial frequency and is generally used to overcome the 2π ambiguity of the phase profile. Parameters affecting final results of reconstructed surface topographies are the central wavelength and the spectral bandwidth of the illuminating light as well as the numerical aperture of the objective lens and the chosen evaluation wavelength. We discuss results of the UFO model with respect to the prediction of systematic deviations of measured surface topographies.

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“…The signal modeling requires tools such as rigorous coupled wave analysis (RCWA) to predict the scatterometry signals [247]. RCWA is an established calculation method for scatterometry of grating structures in semiconductor wafer process metrology and has been applied to interference microscopy to better understand the imaging properties of these tools [245,248,249].…”

Section: Interferometric Scatterometrymentioning

confidence: 99%

A review of selected topics in interferometric optical metrology

Groot

2019

Rep. Prog. Phys.

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This review gathers together 15 special topics in modern interferometric metrology representing a sampling of historical, current and future developments. The selected topics cover a wide range of applications, including distance and displacement measurement, the testing of optical components, interference microscopy for surface structure analysis, form and dimensional measurements of industrial parts, and recent applications in semiconductor manufacturing and consumer electronics. Techniques range from laser Fizeau systems to dynamic ellipsometry using polarized heterodyne interferometry.

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Modeling of coherence scanning interferometry using classical Fourier optics

Cited by 11 publications

References 53 publications

Modeling the topographic lateral resolution of interferometers

Modeling the topographic lateral resolution of interferometers

Universal Fourier optics model for virtual coherence scanning interferometers

A review of selected topics in interferometric optical metrology

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