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.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

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.

Digital wavefront measuring interferometer for testing optical surfaces and lenses

A review of interferometry for geometric measurement

Studies in the field of laser science and technology have resulted in the creation of a unique passively mode-locked laser generating a continuous regular train of ultrashort pulses. The unique feature of this laser is that it combines the properties of a radiation source with the output spectrum consisting of numerous extremely narrow strictly equidistant spectral lines with the properties of a radiation source emitting ultrashort high-power laser pulses. This feature has permitted a wide range of remarkable results. The basic properties of continuous-wave passively mode-locked lasers are discussed and their main applications are considered.

Continuous-wave femtosecond lasers

A synthetic-wavelength interferometry of optical frequency combs is proposed for the pulse-to-pulse alignment in absolute distance measurement. The synthetic wavelength derived from the virtual second harmonic and the real second harmonic is used to bridge the interference intensity peak-finding method and the heterodyne interferometric phase measurement, so that the pulse-to-pulse alignment can be linked directly to single-wavelength heterodyne interferometry. The experimental results demonstrate that the distance measured by the peak-finding method with micrometer accuracy can be improved to the nanometer level by applying the method proposed.

Pulse-to-pulse alignment technique based on synthetic-wavelength interferometry of optical frequency combs for distance measurement

A heterodyne interference system was developed for position measurement. A stabilized optical-frequency comb is used as the laser source. The preliminary experiment to measure a distance of 22.478 m shows a drift of 1.6 μm in 20 minutes after the temperature compensation. Comparison and frequency shift experiments have been done for a distance of about 7.493 m. The experimental results show that the drift is mainly caused by environmental condition changes and the vibration of the table and floor also has some effects. It was verified that the absolute distance measurement can be realized by fringe scanning and frequency-shifting methods.

http://www.nanolab.t.u-tokyo.ac.jp/pdffiles/2011-1R04.pdf

Space position measurement using long-path heterodyne interferometer with optical frequency comb.

a b s t r a c t A heterodyne interference system using an optical frequency comb has been developed for spatial positioning measurements and applied to long distances up to 152.85 m. The laser source is a Rb-stabilized optical-frequency comb, and temporal coherence interference occurs at discrete spatial positions, where two optical comb pulse trains in the different arms overlap. A piezoelectric transducer scans to find the peak of the interference fringe envelope corresponding to the position. The measurement of the absolute position is accomplished by shifting the frequencies of the optical comb by 100.1 MHz. The experimental results show that the measurement reproducibility is no more than 1.4 m for distances up to 152.85 m and that the accuracy is 1.1 m for a distance of 50.951 m. © 2013 Published by Elsevier Inc.

/pdf/spatial-positioning-measurements-up-to-150-m-using-temporal-39ve9ql6ou.pdf

Spatial positioning measurements up to 150 m using temporal coherence of optical frequency comb

a b s t r a c t The possibility of using an adjacent pulse repetition interval length (APRIL) as a scale is investigated. Theoretical analysis showed that an APRIL can be used as a standard for a high-accuracy distant evaluation. In an experiment, an APRIL was measured by using a Helium-Neon interferometer, and the measurement was compared with the result of a direct frequency count. The difference was a few hundred nanometers, and thus the APRIL's effectiveness as a length scale was confirmed. The present concept and analysis pave the way for the development of the remote transfer of APRIL as a length standard via fiber networks.

/pdf/a-study-of-the-possibility-of-using-an-adjacent-pulse-39px5x3abo.pdf

A study of the possibility of using an adjacent pulse repetition interval length as a scale using a Helium–Neon interferometer

This paper describes a novel approach for realizing femtosecond optical frequency comb (FOFC)-based length measurement. This approach is based on the analogy between the phase unwrapping problem and the integer ambiguity problem. Because the conventional synthetic wavelength method can solve the former, we investigated the possibility of using a synthetic adjacent pulse repetition interval length method to solve the latter. The results of theoretical analyses and numerical investigations show the feasibility of the proposed method. Our results should contribute toward the further development of FOFC-based length measurement methods.

/pdf/synthetic-adjacent-pulse-repetition-interval-length-method-47g6n1ox1w.pdf

Synthetic adjacent pulse repetition interval length method to solve integer ambiguity problem: theoretical analysis

A novel method of gauge block measurement without wringing onto a glass platen is proposed. By using tandem low-coherence interferometry to perform remote measurements, wringing is rendered unnecessary. To measure its length, a gauge block for measurement without wringing is set several millimeters above a glass platen that is positioned on a triangle interferometer such that the distances between the surfaces of the block and the reflection surface of the platen can be measured from opposite directions. By using tandem low-coherence interferometry with a He‐Ne laser as a reference length standard, gauge blocks with nominal lengths of 5, 10 and 75 mm have been measured remotely with an expanded uncertainty of about 86 nm.

/pdf/absolute-measurement-of-gauge-block-without-wringing-using-5c5pu7j663.pdf

Hirokazu Matsumoto

Papers

Space position measurement using long-path heterodyne interferometer with optical frequency comb.

Spatial positioning measurements up to 150 m using temporal coherence of optical frequency comb

A study of the possibility of using an adjacent pulse repetition interval length as a scale using a Helium–Neon interferometer

Synthetic adjacent pulse repetition interval length method to solve integer ambiguity problem: theoretical analysis

Absolute measurement of gauge block without wringing using tandem low-coherence interferometry