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Based on our results of the James Webb Space Telescope (JWST) center-of-curvature tests where we were able to measure dynamic amplitudes of Zernike terms to the order of a few picometers, we have applied the same approach to determine if it is possible to measure the accuracy of higher-order Zernike terms as a function of time rather than frequency, i.e., static measurements in place of measuring the amplitude of frequency components. We have applied this approach to data taken for the JWST backplane structure test article (BSTA) in 2006 and find that we can measure effects at the sub-nanometer level, as small as 50 pm for Zernike terms over 30. We conclude that these results show it will be possible to use these techniques to ensure that the optics and support structure for large space telescopes can meet the necessary stability requirements for detecting spectral signatures of life on Earth-like extra-solar planets.

Future space observatory missions are forecasting the need for sensing and controlling wavefront error and system alignment stability to picometer scale. Picometer stability performance demands precision knowledge of the mirror and metering structure materials to the same degree. A high-speed electronic speckle pattern interferometer was designed and built to demonstrate measurements of both static and dynamic responses of picometer amplitudes in materials of diffuse surface subjected to very low energy disturbances. This paper describes the details of a test to impart a dynamic disturbance of picometer scale and measure the response of a composite material. The results of the test are also reported and show conclusively that sub-picometer scale effects can be accurately measured in an open test environment outside a vacuum chamber.

A high-speed interferometer has been designed and built to measure the dynamics of the James Webb Space Telescope primary mirror system currently under testing. This interferometer is capable of tracking large absolute motion (i.e., piston) of the mirror's entire surface over orders of magnitudes of wavelengths displacement. Preliminary tests have shown it to be capable of measuring dynamic effects on the level of tens of picometers reliably. This paper reports the details of test setup to do so, the data system used to collect and process the data, and the algorithms to distill the dynamics motions detected. The results that were obtained are presented and followed by a discussion of the conclusions and potential applications of this measurement technique.

This feature issue of Applied Optics contains a series of selected papers reflecting recent progress of correlation optics and illustrating current trends in vector singular optics, internal energy flows at light fields, optical science of materials, and new biomedical applications of lasers.

Using a simultaneous phase sensor, the proposed instrument performs highly repeatable measurements over an extended range in the presence of vibration common to a laboratory setting. Measurement of a 4.5 μm step standard in the presence of vibration amplitudes of 40 nm produces a repeatability of 1.5 nm RMS with vertical scanning data acquired at 400 nm intervals. The outlined method demonstrates the potential to tolerate larger vibration amplitudes up to or beyond a quarter wavelength and to increase the data acquisition step size to that approaching the depth of field of standard microscope imaging systems.

The addition of electronics, computers, and software to interferometry has enabled enormous improvements in optical metrology. This paper discusses four areas in which computerized interferometric measurement improvements have been made in the measurement of surface shape and surface roughness: (a) The use of computer-generated holograms for the testing of aspheric optics, (b) phase-shifting interferometry for getting interferometric data into a computer so the data can be analyzed, (c) computerized interference microscopes, including multiple-wavelength and coherence scanning, for the precision measurement of surface microstructure, and (d) vibration-insensitive dynamic interferometers for enabling precise measurements in noncontrolled environments.

A new instrument, the polarization phase-shifting point-diffraction interferometer, has been developed by use of a birefringent pinhole plate. The interferometer uses polarization to separate the test and reference beams, interfering what begin as orthogonal polarization states. The instrument is compact, simple to align, and vibration insensitive and can phase shift without moving parts or separate reference optics. The theory of the interferometer is presented, along with properties and fabrication techniques for the birefringent pinhole plate and a new model used to determine the quality of the reference wavefront from the pinhole as a function of pinhole size and test optic aberrations. The performance of the interferometer is also presented, along with a detailed error analysis and experimental results.

We realized what we believe is a new phase-shifting scatterplate interferometer by exploiting the polarization characteristics of a birefringent scatterplate. The common-path design of the interferometer reduces its sensitivity to environmental effects, and phase shifting allows quick and accurate quantitative measurements of the test surface. A major feature of the birefringent scatterplate approach for phase shifting is that no high-quality optical components are required in the test setup. The theory of the interferometer is presented, the procedure for the fabrication of the birefringent scatterplate is described, and experimental results are shown.

Different materials with different phase changes on reflection affect the surface-height measurement when interferometric techniques are employed for testing objects constructed of different materials that are adjacent to one another. We test the influence of this phase change on reflection when vertical scanning interferometry with a broadband source is used. We show theoretically and experimentally that the strong linear dependence of the dispersion of the phase change on reflection preserves the shape of the coherence envelope of the fringes but shifts it along the optical axis by approximately 10-40 nm for metallic surfaces.

An interference fringe modulation skewing effect in white-light vertical scanning interferometry that can produce a batwings artifact in a step height measurement is described. The skewing occurs at a position on or close to the edge of a step in the sample under measurement when the step height is less than the coherence length of the light source used. A diffraction model is used to explain the effect.

We describe a method that combines phase-shifting and coherence-peak-sensing techniques to permit measurements with the height resolution of phase-shifting interferometry without the interval-slope limitation of lambda/4 per data sample of phase-shifting interferometry. A five-frame algorithm is used to determine both the best-focus frame position and the fractional phase from the best-focus frame of the correlogram acquired through vertical scanning. The two surface profiles retrieved from the phase and the modulation contrast of the correlograms are compared in the phase-unwrapping process to remove fringe-order ambiguity.

We describe a modified three-flat method. In a Cartesian coordinate system, a flat can be expressed as the sum of even-odd, odd-even, even-even, and odd-odd functions. The even-odd and the odd-even functions of each flat are obtained first, and then the even-even function is calculated. All three functions are exact. The odd-odd function is difficult to obtain. In theory, this function can be solved by rotating the flat 90°, 45°, 22.5°, etc. The components of the Fourier series of this odd-odd function are derived and extracted from each rotation of the flat. A flat is approximated by the sum of the first three functions and the known components of the odd-odd function. In the experiments, the flats are oriented in six configurations by rotating the flats 180°, 90°, and 45° with respect to one another, and six measurements are performed. The exact profiles along every 45° diameter are obtained, and the profile in the area between two adjacent diameters of these diameters is also obtained with some approximation. The theoretical derivation, experiment results, and error analysis are presented.

Multiple reflections between two surfaces of a window introduce a fixed pattern error in optical measurements. One way to remove these spurious reflections is to use a reasonably large wedge so that the interference fringes formed by the two surfaces are too dense for the detector to resolve. However, this method does not work if the wedge angle is small, e.g., several arcseconds. By tilting both the window and the return mirror properly, it is possible to remove the effect of multiple reflections of a window. Theory and experimental results are presented.

Phase errors in a Fizeau phase-shifting interferometer caused by multiple-reflected beams from a retroreflective optics, such as a corner cube and a right-angle prism, are studied. Single- and double-pass configurations are presented, and their measurement results are compared. An attenuator is not needed in a double-pass configuration because light is reflected by the retroreflective optics twice and the reference surface once and hence the intensities match. It is more accurate to test a corner cube or a right-angle prism in a double-pass configuration than in a single-pass configuration. Simulations and experimental results are presented.

A technique for measuring the quality of spherical surfaces that provides a quasi-absolute result is presented. It requires only two measurement positions rather than the traditional method of absolute sphere measurement that requires three measurement positions. A measurement is taken with a mirror at the focus of the interferometer diverger lens and is subtracted from a measurement of the sphere tested at its center of curvature. This test assumes that the test sphere does not contain any aberrations with odd symmetry so that these aberrations can be subtracted to provide a fast, quasi-absolute measurement. We describe the new technique and compare measurement results from testing a lambda/12 peak-to-valley sphere (numerical aperture = 0.4) by using a phase-measuring Fizeau interferometer with results from the three-position absolute sphere measurement technique. The repeatability of this measurement technique is +/-0.01 waves peak to valley.

In an interferometer which uses a reference surface, the measured surface heights correspond to the difference between the test and reference surfaces. To accurately determine the rms roughness of supersmooth surfaces, the effects of the reference surface roughness need to be removed. One technique for doing this involves averaging a number of uncorrelated measurements of a mirror to generate a reference surface profile which can then be subtracted from subsequent measurements so that they do not contain errors due to the reference surface. The other technique provides an accurate rms roughness of the surface by taking two uncorrelated measurements of the surface. These two techniques for measurement of supersmooth surfaces are described in detail, and results of the measurement of a 0.7-A rms roughness mirror are presented. The expected error in the rms roughness measurement of a supersmooth mirror due to instrument noise is 0.02 A.

A variable shear lateral shearing interferometer consisting of two holographically produced crossed diffraction gratings is used to test nonrotationally symmetric wavefronts having aberrations greater than 100 wavelengths and slope variations of more than 400 wavelengths/diameter. Comparisons are made with results of Twyman-Green interferometric tests for wavefront aberrations of up to thirty wavelengths. The results indicate that small wavefront aberrations can be measured as accurately with the lateral-shear interferometer as with the Twyman-Green interferometer and that aberrations that cannot be measured at all with a Twyman-Green interferometer can be measured to about 1% accuracy or better.

The use of a lateral shear interferometer in measuring the power variation of ophthalmic lenses is described and demonstrated. It is shown that an appropriate lateral shear interferometer directly measures the power variation of an ophthalmic lens. If the ophthalmic lens has a toric surface, the power for each axis can be measured separately. Individual surfaces can be tested, as well as the whole lens or the different segments of a multifocal lens. The sensitivity of the test can be selected by varying the amount of lateral shear. Because of the demonstrated simple relationship between fringe spacing and dioptric power, qualitative examination of the fringes has proved a useful adjunct to conventional quality control methods.

The use of a symbolic math system, muMATH-79, to solve polarized light problems is described. The problems are setup using Jones calculus, and muMATH running on a Z-80 microprocessor multiplies out the Jones matrices and simplifies the final algebraic expressions. Only a minimal amount of operator interaction with the microcomputer is required. Several examples are given.

The phase errors caused by spurious reflection in Twyman-Green and Fizeau interferometers are studied. A practical algorithm effectively eliminating the error is presented. Two other algorithms are reviewed, and the results obtained using the three algorithms are compared.

Increased performance requirements for modern optical systems have necessitated the development of more precise optical testing techniques. The need for accurate and rapid measurements is being met by the use of laser interferometers, microprocessors to gather test data, and computers to analyze the data and remove errors in the test equipment.

An analysis is performed to determine the accuracy with which an ac heterodyne lateral shear interferometer can measure wavefront aberrations if a white light extended source is used with the interferometer, and shot noise is the predominate noise source. The analysis shows that for uniform circular or square sources larger than a derived minimum size, the wavefront measurement accuracy depends only upon the radiance of the source and not upon the angular subtense of the source. For a 1-msec integration time, a 25-cm(2) collecting area, and a source radiance of 10 W/m(2)-sr the rms wavefront error is approximately 1/30 wave, assuming the signal is shot noise limited. It is shown that for both uniform circular and square sources an optimum shear distance is approximately (1/2) the aperture diameter required to resolve the light source. Comments are made on the optimum shear for nonuniform radiance distributions.

Interferometric techniques described in this paper permit real-time optical image subtraction of two input photograph transparencies without the necessity of intermediate processing steps (e.g., holograms or contact-print transparencies). These interferometric techniques allow the use of a white-light source as well as an extended light source, small input-collimator optics, and optical components with minimal requirements on wavefront quality. Experimental results with NASA LANDSAT (formerly ERTS) photographs are presented.

If the nonlinearity of the motion of a piezoelectric transducer (PZT) can be described as a quadratic function, the integrated intensity of one frame in phase shift interferometry can be calculated using the Fresnel integral. For a PZT with smaller nonlinearity, the rms phase error is almost linearly proportional to the quadratic coefficient The effects of PZT nonlinearity on the three- and the four-bucket algorithms are compared.

An IR Twyman-Green interferometer is described. It uses a cw CO(2) laser as a light source operating at a 10.6-microm wavelength. Theoretical analysis and experimental measurements of the relationship between the contrast of the interference fringes and the rms roughness of test surfaces are discussed. Interferometric testing results and special alignment methods are shown for rough surface optics.

The use of lateral shear interferometers for measuring the optical transfer function of an optical system for a white light source is investigated. It is shown that grating lateral shear interferometers fulfill the requirements necessary to perform measurements of both the optical transfer function and the optical coherence function for a white light source. Several possible grating lateral shear interferometers are described.

The extreme alignment sensitivity of nonlinear diamond-turned reflaxicons makes them difficult to test and analyze. To evaluate the wave front it is necessary to know what portion results from alignment errors. This paper describes the setup, alignment, and testing of a nonlinear diamond-turned independent-element reflaxicon manufactured at the Union Carbide, Oak Ridge Y-12 plant. Interferograms taken with the center cone misaligned a known amount are analyzed using the axicon preprocessing option in FRINGE [J. S. Loomis (ASTM Report STP 666 and Proc. Soc. Photo-Opt. Instrum. Eng. 171, 64 (1979)]. The results show that FRINGE correctly removes the cone and decenter errors introduced by the misalignments. It is also shown how the resulting interferograms are unfolded to give the OPD errors as seen on the outer cone.

It is shown that both single exposure and double exposure two-wavelength holography provide a good method of using visible light to obtain an interferogram identical to what would be obtained if a longer nonvisible wavelength were used. Both techniques provide for the real-time adjustment of defocus and tilt in the final interferogram. When both hologram exposures are made simultaneously, the sensitivity to air turbulence is essentially the same as if the longer nonvisible wavelength were used. Results are shown for testing both lenses and mirrors at equivalent wavelengths at 6.45 micro, 9.47 micro, 14.20 micro, 20.22 micro, and 28.50 micro obtained by using an argon laser for the visible light source.

A simple grating lateral shear interferometer is described that can be made to give simultaneously two interferograms having shear in two orthogonal directions. The shear for the two orthogonal directions is produced in one plane by one double frequency crossed diffraction grating that can easily be produced holographically. Translating the grating sideways causes the irradiance of the interferogram to vary sinusoidally with time enabling the interferometer to be used with real-time heterodyne phase detection.

Theory and experiment show that for a hologram object of two or more object points, the nonlinearity of the photographic process causes reconstructed images in addition to both the desired reconstructed image and the higher order reconstructed images. It is theoretically and experimentally shown that for a plane object parallel to the hologram plane, some of these undesired images may be focused in the plane of the desired reconstructed image.

The application of computer generated holograms to the interferometric testing of aspheric optical elements has been investigated, and it has been shown that they provide a convenient and practical method of producing an aspheric reference wavefront.

The use of computer generated holograms for the testing of aspheric wavefronts is described. An analysis of the errors produced by emulsion movement, incorrect hologram size and position, and distortion in hologram plotter and photoreduction lens is given, and it is shown that all the errors are proportional to the slope of the aspheric wavefront. Experimental results verifying the error analysis are shown for testing rotationally nonsymmetric wavefronts having slopes as large as 125 waves per radius and departures as large as sixty-five waves.

A grating lateral shear interferometer is described that can be used with a white light source. The use of the interferometer with certain types of extended sources is also demonstrated.