Sub-nanometre double shearing heterodyne interferometry for profiling large scale planar surfaces
TL;DR: In this paper, a double shearing interferometric method was proposed for profiling large-scale quasi-planar surfaces, such as semiconductor wafers, optical flats and x-ray mirrors.
Abstract: A novel interferometric method, called double shearing interferometry, is presented for profiling large-scale quasi-planar surfaces, such as semiconductor wafers, optical flats and x-ray mirrors. The surface profile is measured even if there is an inclination in the scanning stage. By adopting the common-path optical configuration and heterodyne detection, the proposed method achieves excellent resolution at the subnanometre scale and allows a robust measurement in the presence of unwanted disturbances in the measurement environment. A height resolution of 0.1 nm was achieved experimentally. The standard deviation of the analytical surface profiles was found to be 1.3 nm, even when using a conventional screw-lead scanning stage. The measured results show that the surface profile and stage inclination are determined separately. We confirmed that the resultant profile was quite consistent with that measured with a Fizeau interferometer.
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TL;DR: In this article, a fast Fourier transform method of topography and interferometry is proposed to discriminate between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour generation techniques.
Abstract: A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.
3,742 citations
Journal Article•
TL;DR: In this article, a self-scanned 1024 element photodiode array and a minicomputer are used to measure the phase (wavefront) in the interference pattern of an interferometer to lambda/100.
Abstract: A self-scanned 1024 element photodiode array and minicomputer are used to measure the phase (wavefront) in the interference pattern of an interferometer to lambda/100. The photodiode array samples intensities over a 32 x 32 matrix in the interference pattern as the length of the reference arm is varied piezoelectrically. Using these data the minicomputer synchronously detects the phase at each of the 1024 points by a Fourier series method and displays the wavefront in contour and perspective plot on a storage oscilloscope in less than 1 min (Bruning et al. Paper WE16, OSA Annual Meeting, Oct. 1972). The array of intensities is sampled and averaged many times in a random fashion so that the effects of air turbulence, vibrations, and thermal drifts are minimized. Very significant is the fact that wavefront errors in the interferometer are easily determined and may be automatically subtracted from current or subsequent wavefrots. Various programs supporting the measurement system include software for determining the aperture boundary, sum and difference of wavefronts, removal or insertion of tilt and focus errors, and routines for spatial manipulation of wavefronts. FFT programs transform wavefront data into point spread function and modulus and phase of the optical transfer function of lenses. Display programs plot these functions in contour and perspective. The system has been designed to optimize the collection of data to give higher than usual accuracy in measuring the individual elements and final performance of assembled diffraction limited optical systems, and furthermore, the short loop time of a few minutes makes the system an attractive alternative to constraints imposed by test glasses in the optical shop.
1,300 citations
Journal Article•
TL;DR: A comparison study between two- and three-longitudinal-mode laser interferometers confirms that the performance of the designed system is considerably improved.
Abstract: A new heterodyne nano-displacement with error reduction is presented. The main errors affecting the displacement accuracy of the nano-displacement measurement system including intermodulation distortion error, cross-talk error, cross-polarization error and phase detection error are calculated. In the designed system, a He-Ne laser having three-longitudinal-mode is considered as the stabilized source. The free spectral range of the 35cm laser cavity is about 435-MHz at 632.8-nm wavelength, which a secondary beat frequency equal to 300-kHz is produced by combining the reference and measurement beams. The resolution of the displacement measurement resulting from intermodulation distortion, cross-talk and cross-polarization errors is limited to 18-pm. Also, the phase detection uncertainty causes an error of only 5.9-pm in the displacement measurement. Furthermore, frequency-path models of two- and three-longitudinal-mode laser interferometers are modeled as the ac interference, ac reference, dc interference and optical power terms. A comparison study between two- and three-longitudinal-mode laser interferometers confirms that the performance of the designed system is considerably improved.
10 citations
Cites methods from "Sub-nanometre double shearing heter..."
...1 Introduction1 Distance or displacement measurement systems based on the coherent methods provide a high accuracy measurement in different axes [1-7]....
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TL;DR: In this article, an interferometric profile scanning system is proposed to measure straightness of a planar mirror surface, which stitches multiple sub-aperture profiles obtained by analyzing the single-interferogram.
9 citations
TL;DR: In this article, a differential interferometer setup with a moving hollow pentaprism was used to measure large optical flats/mirrors (more than 500 mm in diameter) with target uncertainty within the nm order.
Abstract: This paper describes a new simple and precise method for flatness measurement using a differential interferometer setup with a moving hollow pentaprism. This method is capable of measuring large optical flats/mirrors (more than 500 mm in diameter) with target uncertainty within the nm order. This device is also relatively easy to transport and is cheap. The first measurements of stability and repeatability are presented.
7 citations
References
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Journal Article•
TL;DR: In this article, a fast Fourier transform method of topography and interferometry is proposed to discriminate between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour generation techniques.
Abstract: A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.
3,742 citations
TL;DR: In this paper, a fast Fourier transform method of topography and interferometry is proposed to discriminate between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour generation techniques.
Abstract: A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.
3,650 citations
Journal Article•
TL;DR: In this article, a self-scanned 1024 element photodiode array and a minicomputer are used to measure the phase (wavefront) in the interference pattern of an interferometer to lambda/100.
Abstract: A self-scanned 1024 element photodiode array and minicomputer are used to measure the phase (wavefront) in the interference pattern of an interferometer to lambda/100. The photodiode array samples intensities over a 32 x 32 matrix in the interference pattern as the length of the reference arm is varied piezoelectrically. Using these data the minicomputer synchronously detects the phase at each of the 1024 points by a Fourier series method and displays the wavefront in contour and perspective plot on a storage oscilloscope in less than 1 min (Bruning et al. Paper WE16, OSA Annual Meeting, Oct. 1972). The array of intensities is sampled and averaged many times in a random fashion so that the effects of air turbulence, vibrations, and thermal drifts are minimized. Very significant is the fact that wavefront errors in the interferometer are easily determined and may be automatically subtracted from current or subsequent wavefrots. Various programs supporting the measurement system include software for determining the aperture boundary, sum and difference of wavefronts, removal or insertion of tilt and focus errors, and routines for spatial manipulation of wavefronts. FFT programs transform wavefront data into point spread function and modulus and phase of the optical transfer function of lenses. Display programs plot these functions in contour and perspective. The system has been designed to optimize the collection of data to give higher than usual accuracy in measuring the individual elements and final performance of assembled diffraction limited optical systems, and furthermore, the short loop time of a few minutes makes the system an attractive alternative to constraints imposed by test glasses in the optical shop.
1,300 citations
TL;DR: The system has been designed to optimize the collection of data to give higher than usual accuracy in measuring the individual elements and final performance of assembled diffraction limited optical systems, and furthermore, the short loop time of a few minutes makes the system an attractive alternative to constraints imposed by test glasses in the optical shop.
Abstract: A self-scanned 1024 element photodiode array and minicomputer are used to measure the phase (wavefront) in the interference pattern of an interferometer to lambda/100. The photodiode array samples intensities over a 32 x 32 matrix in the interference pattern as the length of the reference arm is varied piezoelectrically. Using these data the minicomputer synchronously detects the phase at each of the 1024 points by a Fourier series method and displays the wavefront in contour and perspective plot on a storage oscilloscope in less than 1 min (Bruning et al. Paper WE16, OSA Annual Meeting, Oct. 1972). The array of intensities is sampled and averaged many times in a random fashion so that the effects of air turbulence, vibrations, and thermal drifts are minimized. Very significant is the fact that wavefront errors in the interferometer are easily determined and may be automatically subtracted from current or subsequent wavefrots. Various programs supporting the measurement system include software for determining the aperture boundary, sum and difference of wavefronts, removal or insertion of tilt and focus errors, and routines for spatial manipulation of wavefronts. FFT programs transform wavefront data into point spread function and modulus and phase of the optical transfer function of lenses. Display programs plot these functions in contour and perspective. The system has been designed to optimize the collection of data to give higher than usual accuracy in measuring the individual elements and final performance of assembled diffraction limited optical systems, and furthermore, the short loop time of a few minutes makes the system an attractive alternative to constraints imposed by test glasses in the optical shop.
1,206 citations
TL;DR: In this article, a noncontact optical technique for the measurement of surface profile is described, which has a height sensitivity of the order of 1 A. The results of a surface measurement include graphical displays of the surface profile, autocovariance function, spectral density function, stability, and repeatability.
Abstract: A noncontact optical technique for the measurement of surface profile is described, which has a height sensitivity of the order of 1 A. It is based on a common path heterodyne interferometer in which two orthogonally polarized beams of slightly different frequency are focused on the surface to be measured. One focal point acts as a reference as the other point circularly scans the surface. The phase of the beat frequency of the interfering return beams is directly proportional to the surface height. The results of a surface measurement include graphical displays of the surface profile, autocovariance function, spectral density function, stability, and repeatability. Comparison with other instruments is also discussed.
234 citations