Phase-Shifting Interferometry

Computerized interferometric surface measurements [invited]

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.

Low coherence vibration insensitive Fizeau interferometer

  • Brad Kimbrough, James Millerd, James Wyant, and John Hayes
  • Proceedings of SPIE Vol. 6292, page 62920F-1-12, 2006
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An on-axis, vibration insensitive, polarization Fizeau interferometer is realized through the use of a novel pixelated mask spatial carrier phase shifting technique in conjunction with a low coherence source and a polarization delay-line. In this arrangement, coherence is used to effectively separate out the orthogonally polarized test and reference beam components for interference. With both the test and the reference beams on-axis, the common path cancellation advantages of the Fizeau interferometer are maintained. The interferometer has the unique ability to isolate and measure any surface that is substantially normal to the optical axis of the cavity. Additionally, stray light interference is substantially reduced due to the source’s short coherence. An expression for the fringe visibility on-axis is derived and compared with that of a standard Fizeau. Using a 15 mW source, the maximum camera shutter speed, used when measuring a 4% reflector, was 150 usec, resulting in very robust vibration insensitivity. We experimentally demonstrate the measurement of both sides of a thin glass plate without the need to modify the plate between measurements. Experimental results show the performance of this new interferometer to be within the specifications of commercial phase shifting interferometers.

Polarization phase-shifting point-diffraction interferometer

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.

Analysis of a micropolarizer array-based simultaneous phase-shifting interferometer

Recent technological innovations have enabled the development of a new class of dynamic (vibration-insensitive) interferometer based on a CCD pixel-level phase-shifting approach. We present theoretical and experimental results for an interferometer based on this pixelated phase-shifting technique. Analyses of component errors and instrument functionality are presented. We show that the majority of error sources cause relatively small magnitude peak-to-valley errors in measurement of the order of 0.002–0.005 . These errors are largely mitigated by high-rate data acquisition and consequent data averaging.

Dynamic Interferometry

  • Neal Brock, John Hayes, Brad Kimbrough, James Millerd, Michael North-Morris, Matt Novak and James C. Wyant
  • Proceedings of SPIE Vol. 5875 (SPIE, Bellingham, WA), page 58750F-1, 2005
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The largest limitation of phase-shifting interferometry for optical testing is the sensitivity to the environment, both vibration and air turbulence. In many situations the measurement accuracy is limited by the environment and sometimes the environment is sufficiently bad that the measurement cannot be performed. Recently there have been several advances in dynamic interferometry techniques for reducing effects of vibration. This talk will describe and compare two dynamic interferometry techniques; simultaneous phase-shifting interferometry and a special form of spatial carrier interferometry utilizing a micropolarizer phase-shifting array.

Modern Approaches in Phase Measuring Metrology

  • James Millerd, Neal Brock, John Hayes, Brad Kimbrough, Matt Novak, Michael North-Morris and James C. Wyant
  • Proceedings of SPIE Vol. 5856 (SPIE, Bellingham, WA), page 14, 2004
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The measurement accuracy of an interferometric optical test is generally limited by the environment. This paper discusses two single-shot interferometric techniques for reducing the sensitivity of an optical test to vibration; simultaneous phase-shifting interferometry and a special form of spatial carrier interferometry utilizing a micropolarizer phase-shifting array. In both techniques averaging can be used to reduce the effects of turbulence and the normal double frequency errors generally associated with phase-shifting interferometry.

Instantaneous phase-shift, point-diffraction interferometer

  • James E. Millerd, Stephen J. Martinek, Neal J. Brock, John B. Hayes and James C. Wyant
  • Proceedings of SPIE Vol. 5380 (SPIE, Bellingham, WA), page 422, 2004
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We demonstrate an instantaneous phase-shift, point diffraction interferometer that achieves high accuracy and is capable of measuring a single pulse of light at NA greater than 0.8.

Instantaneous phase-shifted speckle interferometer for measurement of large structures

  • Babak N. Saif, James Millerd, Ritva Keski-Kuha, Lee Feinberg, and J. C. Wyant
  • Proceedings of SPIE Vol. 5494 (SPIE, Bellingham, WA), page 152, 2004
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Digital Speckle Pattern Interferometry (DSPI) is a well-established method for the measurement of diffuse objects in experimental mechanics. DSPIs are phase shifting interferometers. Three or four bucket temporal phase shifting algorithms are commonly used to provide phase shifting. These algorithms are sensitive to vibrations and can not be used to measure large optical structures far away from the interferometer. In this research a simultaneous phase shifted interferometer, PhaseCam product of 4D Technology Corporation in Tucson Arizona, is modified to be a Simultaneous phase shifted Digital Speckle Pattern Interferometer (SDSPI). Repeatability, dynamic range, and accuracy of the SDSPI are characterized by measuring a 5 cm x 5 cm carbon fiber coupon.

Instantaneous phase-shift, point-diffraction interferometer

  • James E. Millerd, Neal J. Brock, John B. Hayes and James C. Wyant
  • Proceedings of SPIE Vol. 5531 (SPIE, Bellingham, WA), page 264, 2004
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We demonstrate a phase-shifting, point diffraction interferometer that achieves high accuracy and is capable of measuring a single pulse of light. The measurement system utilizes a polarizing point diffraction plate to generate a synthetic reference beam that is orthogonally polarized to the transmitted test beam. The plate has very high polarization contrast, works over an extremely broad angular and spectral range, and is only 100 nanometers thick. The unique features of the polarizing element make the system amenable to measuring strongly convergent light from high numerical aperture optics without the need to use a point reference source to calibrate the system. Results of measuring optics with numerical apertures as high as NA 0.8 are presented.

Pixelated Phase-Mask Dynamic Interferometer

  • James Millerd, Neal Brock, John Hayes, Michael North-Morris, Matt Novak and James Wyant
  • Proceedings of SPIE Vol. 5531 (SPIE, Bellingham, WA), page 304, 2004
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We demonstrate a new type of spatial phase-shifting, dynamic interferometer that can acquire phase-shifted interferograms in a single camera frame. The interferometer is constructed with a pixelated phase-mask aligned to a detector array. The phase-mask encodes a high-frequency spatial interference pattern on two collinear and orthogonally polarized reference and test beams. The phase-difference between the two beams can be calculated using conventional N-bucket algorithms or by spatial convolution. The wide spectral response of the mask and true common path design permits operation with a wide variety of interferometer front ends, and with virtually any light source including white-light.

Dynamic interferometry

  • James C. Wyant
  • Optics and Photonics News, Vol. 14, pages 36-41, April 2003
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Phase-shifting birefringent scatterplate interferometer

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.

Fringe modulation characterization for a phase shifting ellipsometer

  • Conrad Wells and James C. Wyant
  • Proceedings of SPIE Vol. 3134 (SPIE, Bellingham, WA), page 466, 1997
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An imaging ellipsometer has been developed which employs phase shifting interferometry to characterize the ellipsometeric parameters. A modified Michelson interferometer is used in conjunction with a Wollaston prism to generate two interferograms with orthogonal polarization states. Subtraction of the phases in the two interferograms yields the ellipsometeric parameter D. The fringe modulation of the two interferograms is used to calculate the ellipsometeric parameter Y. The characterization of the average intensity of the interferogram is the largest contributor to the errors in the modulation. New algorithms for reducing the errors in modulation calculations for phase shifting interferometry are presented. The design of the instrument, results of measurements and algorithms for modulation characterization will be presented.

A phase shifting interferometric imaging ellipsometer

  • Conrad Wells and James C. Wyant
  • Proceedings of SPIE Vol. 3121 (SPIE, Bellingham, WA), page 13, 1997
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An imaging ellipsometer has been developed which employs phase shifting interferometry to characterize the ellipsometeric parameters. Polarized light from a laser or incoherent source is collimated and reflected off of the surface under test. A modified Michelson interferometer is used in conjunction with a Wollaston prism to generate two interferograms with orthogonal polarization states. Subtraction of the phases in the two interferograms yields the ellipsometeric parameter D .The fringe modulation of the two interferograms is used to calculate the ellipsometeric parameter Y. The instrument uses imaging optics to image the surface under test to a CCD, yielding a truly two dimensional ellipsometeric measurement. The design of the instrument and results of measurements will be presented.

Effect of spurious reflection on phase shift interferometry

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.

Effect of piezoelectric transducer nonlinearity on phase shift interferometry

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 four-bucket algorithms are compared.

Direct phase measurement of aspheric surface contours

  • Katherine Creath and James C. Wyant
  • Proceedings of SPIE, Vol. 645, page 101, 1986
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Two-wavelength holography and phase-shifting interferometry are combined to measure aspheric surface contours with variable sensitivity. In this technique, the surface is effectively tested at a synthesized longer equivalent wavelength leq=la lb/Abs[la – lb] using measurements made at wavelengths la and lb where the difference of the phases measured for la and lb yields modulo 2p phase at leq. A mask of point apertures is placed over the detector array in order to resolve closely spaced fringes. This technique has an rms repeatability of leq/100. Limits to this technique are discussed and results are shown.

Maximal fraction of acceptable measurements in phase-shifting speckle interferometry: a theoretical study

The interference between a uniform reference wave and a speckle object wave results in variable fringe contrast and background level. Taking these variations into account, we optimize system parameters of phase-shifting speckle interferometry. The results show that the optimal reference intensity should always be equal to one fourth of the detector’s saturation level. The optimal reference to the object-intensity shows an increase from one up to, in most practical cases, six as a chosen interference dynamic range increases from its minimum value. The dependence of a maximal fraction of acceptable measurements on the dynamic range is calculated. Numerical examples indicate that we may hope for a readout accuracy in the range of 1/50th to 1/100th of a fringe period and still cover more than half of the image area with acceptable data. These data are taken without spatial averaging and have maximum resolution.

Contouring aspheric surfaces using two-wavelength phase-shifting interferometry

  • Katherine Creath, Yeou-Yen Cheng, and James C. Wyant
  • Optica Acta, Vol. 32, page 1455, 1985
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Two-wavelength holography and phase-shifting interferometry are combined to measure the phase contours of deep wavefronts and surfaces, such as those produced by aspherics, with a variable sensitivity. When interference fringes are very closely spaced, the phase data contain high frequencies where 2p ambiguities cannot be resolved. In this technique, the surface is tested at a synthesized longer equivalent wavelength. The phase of the wavefront is calculated modulo 2p using phase-shifting techniques at each of two visible wavelengths. The difference between these two phase sets is the phase of the wavefront as it would be measured at leq =l1l2/|l1-l2|, assuming that 2p ambiguities can be removed at leq. This technique enables surfaces to be contoured to an accuracy of leq/l00.

High precision deformation measurement by digital phase shifting holographic interferometry

A digital phase shifting technique capable of quantitatively determining the phase of holographic interferometric displacement fringes is presented. This technique uses computer control to take data and calculate surface deformation. The phase value at each detector point can be calculated by taking four successive intensity data frames with the reference phase shifted between each frame. The displacement fringe order number can be assigned by adding or subtracting 2p from a data pont until the phase difference between adjacent data points is less than p. Experimental results show that this technique can precisely determine a fraction of a fringe with an accuracy of ±1o.

Phase shifter calibration in phase-shifting interferometry

This paper describes some practical methods to calibrate the phase shifter in phase-shifting interferometry (PSI). The phase shifter used in the experiment is a piezoelectric transducer (PZT) that has a nonlinearity of <l%. Using the quantitative method described in this paper, the repeatability in the measurement of the phase-shifting angle is ˜9.046 deg rms, and the 3s value is 0.139 deg. A calibration-insensitive phase calculation algorithm is discussed and compared with other synchronous detection equations (e.g., the three-bucket or the four-bucket method). Experimental results verify the calibration-insensitive mechanism of the self-calibrating algorithm.

Direct phase measurement interferometer working at 3.8 µm

A direct phase measurement interferometer designed and constructed to operate at a 3.8-µm wavelength is described. The interferometer uses a deuterium fluoride laser as the light source, zinc selenide transmitting optics, and a 32- X 64-element PtSi infrared CCD detector array with digital processing electronics and a graphics display on a desktop microcomputer. The instrument, which is useful for measuring a figure error caused by thickness variations in dielectric coatings applied to infrared optics, gives a wave front measurement repeatability of <l/50 rms.

Multiple-wavelength phase-shifting interferometry

This paper describes a method to enhance the capability of two-wavelength phase-shifting interferometry. By introducing the phase data of a third wavelength, one can measure the phase of a very steep wave front. Experiments have been performed using a linear detector array to measure surface height of an off-axis parabola. For the wave front being measured the optical path difference between adjacent detector pixels was as large as 3.3 waves. After temporal averaging of five sets of data, the repeatability of the measurement is better than 25-Å rms (l = 6328 Å).

Two-wavelength phase-shifting interferometry (560 KB)

This paper describes a technique that combines ideas of phase shifting interferometry (PSI) and two-wavelength interferometry (TWLI) to extend the phase measurement range of conventional single-wavelength PSI. To verify theoretical predictions, experiments have been performed using a solid-state linear detector array to measure 1-D surface heights. Problems associated with TWLPSI and the experimental setup are discussed. To test the capability of the TWLPSI, a very fine fringe pattern was used to illuminate 1024 element detector array. Without temporal averaging, the repeatability of measuring a surface having a sag of ~100mm is better than 25-Å (0.0025%) rms.

Testing aspherics using two-wavelength holography: use of digital electronic techniques

Two-wavelength holography has been shown to be quite useful for testing aspheric surfaces since it can produce interferograms with a wide range of sensitivities. However, TWH has the drawback that the accuracy attainable from measurements on photographs of the fringes is limited. It is shown how this limitation can be overcome by using electronic techniques to evaluate the phase distribution in the interference pattern.

Self-referencing wavefront sensor

  • K. Underwood, J.C. Wyant, and C.L. Koliopoulos
  • Proc. SPIE, Vol. 351, 1983
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A modified Smartt point-diffraction interferometer employing phase-shifting electronic phase measurement techniques is described. Special techniques making it possible for the interferometer to give good visibility interference fringes for a large range of input tilts are discussed. A trade-off between acceptable values of wavefront tilt and light efficiency is presented.

Optical frequency shifter for heterodyne interferometers using multiple rotating polarization retarders

  • R. N. Shagam and J. C. Wyant
  • APPLIED OPTICS, Vol. 17, page 3034, October 1, 1978
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Use of an ac heterodyne lateral shear interferometer with real-time wavefront correction systems

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-cm2 collecting area, and a source radiance of 10 W/m2-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.

Collimated Light Acoustooptic Lateral Shearing Interferometer (90 KB)

  • J. F. Ebersole and J. C. Wyant
  • APPLIED OPTICS, Vol. 13, page 1904, May, 1974
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White Light Extended Source Shearing Interferometer (105 KB)

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.

 

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