David I. Farrant

Phase-shifting algorithms for nonlinear and spatially nonuniform phase shifts

In phase-shifting interferometry spatial nonuniformity of the phase shift gives a significant error in the evaluated phase when the phase shift is nonlinear. However, current error-compensating algorithms can counteract the spatial nonuniformity only in linear miscalibrations of the phase shift. We describe an error-expansion method to construct phase-shifting algorithms that can compensate for nonlinear and spatially nonuniform phase shifts. The condition for eliminating the effect of nonlinear and spatially nonuniform phase shifts is given as a set of linear equations of the sampling amplitudes. As examples, three new algorithms (six-sample, eight-sample, and nine-sample algorithms) are given to show the method of compensation for a quadratic and spatially nonuniform phase shift.

300-mm-aperture phase-shifting Fizeau interferometer

A 300-mm-aperture digital phase-shifting Fizeau interferometer (LADI) has been developed in house for precision metrology of optical components fabricated by the Optical Workshop at CSIRO Division of Telecommunications and Industrial Physics. This paper describes the optical and mechanical configuration of the instrument as well as its calibration and performance characteristics. Recent measurements on 250-mm-diam uncoated optical surfaces have consistently shown shortterm repeatability of 0.3 nm rms from measurement to measurement and allowed absolute characterization of these surfaces to an accuracy of a few nanometers.

Simultaneous measurement of three orthogonal components of displacement by electronic speckle-pattern interferometry and the Fourier transform method

The measurement of three-dimensional displacement by electronic speckle-pattern interferometry with three object beams and one reference beam is presented. Multiple interference fringes corresponding to different sensitivity vectors are recorded in a single interferogram and separated by means of the Fourier transform method to give three components of displacement. The relationship between the ratio of the speckle size to the pixel size of a TV camera and the measurement error is investigated experimentally and compared with the research of others. The optimum condition leading to a minimum measurement error occurs when the speckle size is approximately equal to the pixel size. With this condition satisfied, the measurement error varies from 1.5% to 6.0%.

Calibration of a 300-mm-aperture phase-shifting Fizeau interferometer

A 300-mm-aperture digital phase-shifting Fizeau interferometer has been developed in-house for precision metrology of optical components fabricated by the optical workshop at Telecommunications and Industrial Physics, Commonwealth Scientific and Industrial Research Organization. We describe the procedures used in the calibration of the instrument. A reference data file representing the deviations from flatness of the reference surface is generated, measurement uncertainty estimated, and aberrations in the instrument assessed. Measurements on 250-mm-diameter uncoated optical surfaces have consistently shown short-term repeatability of 0.3-nm rms from measurement to measurement and allowed for absolute characterization of these surfaces to within a few nanometers.

Measurement of transient deformations with dual-pulse addition electronic speckle-pattern interferometry

We describe an electronic speckle-pattern interferometry system for analyzing addition fringes generated by the transient deformation of a test object. The system is based on a frequency-doubled twin Nd:YAG laser emitting dual pulses at a TV camera field rate (50 Hz). The main advance has been the automatic, quantitative analysis of dual-pulse addition electronic speckle-pattern interferometry data by the introduction of carrier fringes and the application of Fourier methods. The carrier fringes are introduced between dual pulses by a rotating mirror that tilts the reference beam. The resulting deformation-modulated addition fringes are enhanced with a deviation filter, giving fringe visibility close to that of subtraction fringes. The phase distribution is evaluated with a Fourier-transform method with bandpass filtering. From the wrapped phase distribution, a continuous phase map is reconstructed with an iterative weighted least-squares unwrapper. Preliminary results for a thin plate excited by an acoustic shock show the suitability of the system for the quantitative evaluation of transient deformation fields.

Sensitivity errors in interferometric deformation metrology

Interferometric measurement techniques such as holographic interferometry and electronic speckle-pattern interferometry are valuable for measuring the deformation of objects. Conventional theoretical models of deformation measurement assume collimated illumination and telecentric imaging, which are usually only practical for small objects. Large objects often require divergent illumination, for which the models are valid only when the object is planar, and then only in the paraxial region. We present an analysis and discussion of the three-dimensional systematic sensitivity errors for both in-plane and out-of-plane interferometer configurations, where it is shown that the errors can be significant. A dimensionless approach is adopted to make the analysis generic and hence scalable to a system of any size.

Dynamic range of Ronchi test with a phase-shifted sinusoidal grating

The dynamic range of a Ronchi test with a phase-shifted sinusoidal grating was investigated theoretically and experimentally. As the number of fringes in a Ronchi interferogram increases, the fringe visibility decreases, which results in a decrease of phase-measurement resolution. It is shown that in order to optimize the dynamic range the effective wavelength of the interferogram should be tuned to the characteristic wavelength of the object wave front. The maximum dynamic range achievable is estimated to be 16 times larger than that of a Fizeau interferometer. Suppressing higher-order diffraction components has achieved sheared interferograms with a signal-to-noise ratio in excess of 60:1. The effects of nonsinusoidal transmittance of the grating and the phase-shift errors were minimized by a seven-sample phase-shifting algorithm, and a phase measurement uncertainty of less than 1/700 has been achieved.

Fabrication and measurement of optics for the Laser Interferometer Gravitational Wave Observatory

The manufacture and testing of high-precision optical surfaces for the Laser Interferometer Gravitational Wave Observatory is described. Through the use of carefully shaped polishing laps made of a nondeformable polymer material coated on a rigid base, surfaces 250 mm in diameter with radii of curvature between 7 and 15 km were polished to an accuracy of several hundred meters in the curvature and with low values of waviness and microroughness. Metrology instrumentation used to measure the optical finish included a large-aperture digital interferometer calibrated to nanometer-level accuracy for measurements of curvature, astigmatism, and waviness and an interference microscope for measurements of microroughness. The power spectra of the data from both instruments were in good agreement.

The design and construction of a prototype lateral-transfer retro-reflector for inter-satellite laser ranging

The Gravity Recovery and Climate Experiment (GRACE) mission, launched in 2002, is nearing an end, and a continuation mission (GRACE Followon) is on a fast-tracked development. GRACE Follow-on will include a laser ranging interferometer technology demonstrator, which will perform the first laser interferometric ranging measurement between separate spacecraft. This necessitates the development of lightweight precision optics that can operate in this demanding environment. In particular, this beam routing system, called the triple mirror assembly, for the GRACE Follow-on mission presents a significant manufacturing challenge. Here we report on the design and construction of a prototype triple mirror assembly for the GRACE Follow-on mission. Our constructed prototype has a co-alignment error between the incoming and

Sub-nanometer metrology of optical wafers using an angle-scanned Fabry-Perot interferometer.

An rms measurement repeatability of </=0.07 nm and a reproducibility of </=0.16 are reported from a series of thickness measurements made on a 280 microm thick, 37.5 mm diameter lithium niobate wafer. The measurements were taken on a custom made metrology rig based on accurate rotation of a Fabry-Perot etalon structure in a collimated beam from a wavelength stabilized Helium Neon laser. The measurements were made on different days with the wafer in three different orientations.