Characterizing lateral resolution of interferometers: the Height Transfer Function (HTF)

Doerband, Bernd; Hetzler, Jochen

doi:10.1117/12.614311

Cited by 16 publications

(4 citation statements)

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“…The function T ( f ) is a linear filter for the mutually-independent Fourier components P ( f ). The ITF is sometimes referred to as the system transfer function [127] or the height transfer function [128]. The ITF is a more complete description of an instrument than a simple statement of the Rayleigh or Sparrow resolution limit [129].…”

Section: Lateral Resolution and The Instrument Transfer Functionmentioning

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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Section: Lateral Resolution and The Instrument Transfer Functionmentioning

confidence: 99%

A review of selected topics in interferometric optical metrology

Groot

2019

Rep. Prog. Phys.

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“…where P is the PSD, given by the square magnitude of the Fourier components of the known surface structure, and P is the corresponding measured value [17,[23][24][25]. More generally, it can be defined as the ratio of Fourier components for the measured and true topography; in which case   T  may include a complex phase.…”

Section:  mentioning

confidence: 99%

Does interferometry work? A critical look at the foundations of interferometric surface topography measurement

Groot

Lega

et al. 2019

Applied Optical Metrology III

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Interferometers for the measurement of surface form and texture have a reputation for high performance. However, the results for many types of surface features can deviate from the expectation of one cycle of phase shift per half wavelength of surface height. Here we review the fundamentals of imaging interferometry and describe ways of defining instrument response, including the linear instrument transfer function. These considerations define practical regimes of linear behavior that are usually satisfied for traditional uses of interferometers; but that are increasingly challenged by applications involving complex textures and high surface slopes. We conclude by proposing pathways for further improving performance on difficult surface structures using advanced modeling techniques.

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“…At high levels of precision, the data acquisition and analysis technique comes under scrutiny, including crosscoupling of errors related to mechanical phase shifting interferometry and multiple reflections in the Fizeau cavity [10]. It is equally important to consider the instrument transfer function, including the effects of imaging errors and phase distortions at high spatial frequencies [11,12]. Although it is beyond the scope of this paper, a full accounting of these errors is essential for a complete uncertainty analysis of high-precision interferometric measurements of steeply curved spheres.…”

Section: Advanced Fitting Algorithmsmentioning

confidence: 99%

Axial alignment for high-precision interferometric measurements of steeply-curved spheres

Groot¹,

Dresel²,

Truax³

2015

Surf. Topogr.: Metrol. Prop.

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Incorrect positioning of a steeply-curved sphere along the optical axis of a laser Fizeau interferometer introduces a measurement error that is proportional to the cosine of the inclination angle of the ray trace within the cavity, and directly proportional to the misalignment. The standard metrology solution is to subtract a fitted parabola from the 3D image, which corrects for most of the error, but neglects higher terms. As a consequence, measurements of steeply curved parts may have residual errors resembling spherical aberration. Here we calculate the magnitude of the error and present it in a graphical format that allows for straightforward quantification of the residual error as a function of the measured quadratic or power term in the measured 3D surface form. While our recommendation is to employ automated alignment for best results, we also consider options for higher-order software corrections for geometric misalignments.

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Characterizing lateral resolution of interferometers: the Height Transfer Function (HTF)

Cited by 16 publications

References 0 publications

A review of selected topics in interferometric optical metrology

A review of selected topics in interferometric optical metrology

Does interferometry work? A critical look at the foundations of interferometric surface topography measurement

Axial alignment for high-precision interferometric measurements of steeply-curved spheres

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