Optical Testing

Measurement of picometer-scale mirror dynamics

  • Babak Saif, David Chaney, Perry Greenfield, Marcel Bluth, Kyle Van Gorkom, Koby Smith, Josh Blush, Lee Feinberg, James C. Wyant, Michael North-Morris, and Ritva Keski-Kuha
  • APPLIED OPTICS, Vol. 56, page 6457, 10 August 2017
  • URL: https://doi.org/10.1364/AO.56.006457
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A high-speed interferometer has been designed and built to measure the dynamics of the James Webb Space┬áTelescope primary mirror system currently under testing. This interferometer is capable of tracking large absolute┬ámotion (i.e., piston) of the mirrorÔÇÖ s entire surface over orders of magnitudes of wavelengths displacement. Preliminary┬átests have shown it to be capable of measuring dynamic effects on the level of tens of picometers reliably. This paper┬áreports the details of test setup to do so, the data system used to collect and process the data, and the algorithms to┬ádistill the dynamics motions detected. The results that were obtained are presented and followed by a discussion of┬áthe conclusions and potential applications of this measurement technique.


Vibration insensitive extended range interference microscopy

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 ╬╝m step standard in the presence of vibration amplitudes of 40 nm produces a repeatability of 1.5nm RMSwith vertical scanning data acquired at 400 nmintervals. 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.


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.


Developments in optical testing technology during the last decade

Modern electronics, computers, and software have made it possible to greatly improve
the testing of optical components and optical systems and the resulting improvements in the new optical instruments and devices we use are evident. Until recently a major limitation of interferometry for precision metrology was the sensitivity to the environment. In recent years many techniques for performing high quality interferometric measurements in non-ideal environments have been developed and new techniques are being introduced all the time. This talk discusses one very powerful technique for reducing the effects of vibration and atmospheric turbulence on interferometric measurements. The application of this technique for the measurement of surface vibration, the testing of optical components including large astronomical optics, the phasing of segmented optical components, and the measurement of deformations of diffuse structures will be described.


Improved interferometric optical testing

While the basic principles of interferometry have been well known for more than 100 years, this powerful measurement tool is continually evolving. Indeed, modern electronics, computers and software are changing the ways that interferometry can be used and broadening its metrology applications in industrial and research labs.


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 sourceÔÇÖs 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 0.002ÔÇô0.005 . These errors are largely mitigated by high-rate data acquisition and consequent data averaging.


Advances in interferometric surface measurement

  • James C. Wyant
  • Proceedings of SPIE Vol. 6024, page 602401-1-11, 2005
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The addition of electronics, computers, and software to interferometry has provided tremendous improvements in the measurement of surface shape and roughness. This talk will describe three such improvements; use of computer generated holograms for testing aspheric surfaces, techniques for performing interferometric measurements more accurate than the reference surface, and two single-shot interferometric techniques for reducing the sensitivity of an optical test to vibration and measuring dynamically changing surface shapes.


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, 2005), 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, 2004), 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, 2004), 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-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, 2004), 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, 2004), 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.


Vibration insensitive interferometric optical testing

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 spatial carrier interferometry.


Dynamic interferometry

Interferometry is a powerful measurement tool. Efforts to reduce the sensitivity of interferometers to vibration could greatly expand the number of fields in which they are employed.


Polarization phase-shifting point-diffraction interferometer

A new point-diffraction interferometer has been developed utilizing a birefringent
pinhole plate, which allows for phase-shifting by changing the polarization state of the laser source. The interferometer is compact, simple to align, vibration insensitive and can phase-shift without moving parts or separate reference optics.


Instantaneous phase-shift, point-diffraction interferometer

We demonstrate a phase-shift, point diffraction interferometer that achieves high
accuracy and is capable of measuring a single pulse of light. Results of measuring transient phenomena and numerical apertures as high as NA 0.8 are presented. The operational limits and accuracies of the technique are discussed.


Instantaneous phase-shifted speckle interferometer for measurement of large optical structures

An instantaneous phase-shifting interferometer (PhaseCam, 4D Technology) was
modified to a speckle phase-shifted interferometer. This interferometer was used to measure ÔÇťdiffusedÔÇŁ objects such as a carbon fiber. Repeatability, accuracy, and dynamic range of the interferometer were measured. Different phase shifting algorithms were utilized to get rid of the high frequency speckle that modulates the low frequency fringes.


Advances in Interferometric Metrology

  • James C. Wyant
  • Proceedings of SPIE, Vol. 4927, pp. 154-162, September 2002
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Modern electronics, computers, and software have made interferometry an extremely powerful tool in many fields including the testing of optical components and optical systems. This paper will discuss some of the recent advances in reducing the sensitivity of phase-shifting interferometers to vibration.


White Light Interferometry

  • James C. Wyant
  • Proceedings of SPIE, Vol. 4737, pp. 98-107, July 2002
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White light interferometry is an extremely powerful tool for optical measurements. This paper discusses the advantages and disadvantages of white light interferometry compared to laser light interferometry. Three different white light interferometers are discussed; 1. diffraction grating interferometers, 2. vertical scanning or coherence probe interferometers, and 3. white light scatterplate interferometers.


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.


Phase-shifting scatterplate interferometer

  • Michael B. North-Morris and James C. Wyant
  • Proceedings of SPIE, Vol. 4231, pp. 59-66, 2000
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The advantages of common path interferometers for reducing effects of vibrations are well known. A scatterplate interferometer is one common-path interferometer that is well suited for the testing of large concave mirrors, however due to the common path characteristics it is difficult to perform phase-shifting. This paper describes a phase-shifting scatterplate interferometer where the phase-shifting is achieved by making use of the polarization characteristics of a birefringent scatterplate. The major advantage of this design is that it does not require any optical components to be placed near the surface under test. The theory of the interferometer is presented and experimental results are shown.


NGST OTA optical metrology instrumentation and conceptual approaches

  • R. Keski-Kuha, P. Bely, R. Burg, J. Burge, P. Davila, J. Geary, J. Hagopian, D. Jacobson, A. Lowman, S. Macenka, J. Mangus, C. Perrygo, D. Redding, B. saif, S. Smith, and J. Wyant
  • Proceedings of SPIE, Vol. 4013, pp. 826-835, 2000
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An Integrated Product Team (IPT) was formed to develop a detailed concept for optical test methodology for testing of the NGST individual primary, secondary and tertiary mirrors and the full telescope system on the ground. The large, lightweight, deployable primary mirror, and the cryogenic operating environment make optical testing of NGST OTA (Optical Telescope Assembly) extremely challenging. A telescope of the complexity of NGST has never been built and tested on the ground in 1-g environment. A brief summary of the preliminary metrology test plan at the mirror component and telescope system level is presented.


Birefringent scatterplate phase-shifting interferometer

  • Michael B. North-Morris, Jay VanDelden and James C. Wyant
  • Proceedings of SPIE, Vol. 3749, pp. 432-433, 1999
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A new phase shifting scatterplate interferometer is realized by exploiting the polarization characteristics of a birefringent scatterplate. The advantages of this design are that it does not require any optical components to be placed near the surface under test and the hot spot and background intensity, which are inherent to scatterplate interferometers, are eliminated. The theory of the interferometer is presented.


Transfer function characterization of laser Fizeau interferometer for high spatial frequency phase measurements

  • Erik Novak, Chiayu Ai, and, James C. Wyant
  • Proceedings of SPIE, Vol. 3134, pp. 114-121, 1997
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Large, high power laser systems such as that being constructed by Lawrence Livermore National Laboratories for the National Ignition Facility (NIF) require accurate measurement of spatial frequencies of up to 2.5lines/mm over a 100mm field of view. In order to ensure accurate measurements of the parts, the test apparatus must be well characterized. The system transfer function (SiT) of the interferometer under development to perform these measurements was calculated by comparing the power spectra of measurements of known phase objects to their theoretical power spectra. Several potential problem areas were identified and studied. Of primary concern was the effect on the STF of the rotating diffuser and incoherent relay system employed in most commercial laser Fizeau interferometers. It was determined that such an arrangement degraded the transfer function beyond acceptability. The other major concern was possible inability to measure certain frequencies due to propagation between the test piece and alignment of the system optics. Use of strictly coherent imaging and small propagation distances between the test piece and return flat, the system transfer function could be kept at acceptable levels within the range of interest.


Errors caused by nearly parallel optical elements in a laser Fizeau interferometer utilizing strictly coherent imaging

  • Erik Novak, Chiayu Ai, and, James C. Wyant
  • Proceedings of SPIE, Vol. 3134, pp. 456-460, 1997
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Most commercial laser Fizeau interferometers employ a rotating diffuser on an intermediate image plane. The image formed on this plane is relayed to the detector using incoherent imaging, eliminating potential interference effects from elements after the diffuser. Systems requiring high spatial frequency resolution cannot employ the diffuser or incoherent relay system to the degradation they cause to the system transfer function. With strictly coherent imaging, however, nearly parallel optical elements such as the CCD cover glass will produce interference fringes. Though these elements are common path, fringes will be visible in the phase measurement unless one of several specific conditions are met. This paper explores the theory behind the formation of these fringes and examines cases where this error may be eliminated. Theoretical calculations are compared with actual measurements taken on a laser Fizeau interferometer. The errors evident in the final phase measurement may be minimized with proper coating of the system optics, sufficient wedge in the elements, or removal of the nearly parallel elements from the system.


Optical and mechanical design considerations in the construction of a 24-inch phase shifting interferometer

  • Joe Lamb, James Semrad, James Wyant, Chiayu Ai, Robert Knowlden, Erik Novak, John Downie, and Robert Wolfe
  • Proceedings of SPIE, Vol. 3047, pp. 415-426, 1997
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WYKO Corporation is currently designing and manufacturing specialized phase shifting interferometers to aid in the qualification of large optics for the U.S. N.I.F. program. The interferometers will be used to qualify homogeneity of raw material and provide in-process inspection information and final inspection qualification data. The 24″ systemsw ill be the largest commercially available Fizeau phase shifting interferometers ever manufactured. Systems will be produced using traditional CCD cameras as well as a megapixel CCD camera for applications requiring higher lateral resolution. Mechanical and optical design considerations include vibration and distortion control of critical optical elements, polarization control of the laser source, imaging system design, and optical transfer function optimization. We also address effects in the test cavity arising from measuring transmitted and reflected wavefronts of optics mounted at Brewster’s angle


Optical resolution of phase measurements of laser Fizeau interferometer

  • Erik Novak, Chiayu Ai, and James C. Wyant
  • Proceedings of SPIE, Vol. 2870, pp. 545-552, 1996
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Accurate interferometric measurement of large laser slabs requires spatial frequencies of 1mm/cycle to 33mm/cycle over a 100mm field of view to be passed by the system with no more than 25% loss in modulation. To eliminate noise and artifacts due to strictly coherent imaging, many commercial interferometers employ a rotating diffuser on an intermediate image plane and relay this image incoherently onto a detector. Unfortunately, this process may adversely affect the resolution of the instrument. Through measurement of a sinusoidal phase grating an fused silica step, the transfer function a laser Fizeau interferometer was measured for both a system with and without the incoherent relay system. Results are compared to those predicted by diffraction theory. Studies of the effects of defocus and propagation on the measurement were also made. Using strictly coherent imaging dramatically increases the system’s ability to measure features of high spatial frequency and allows the measurement requirements for laser slabs to be met.


Testing an optical window of a small wedge angle

  • Chiayu Ai and James C. Wyant
  • Proceedings of SPIE, Vol. 1994, pp. 102-110, 1994
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Multiple reflections between two surfaces of a window introduce a fixed pattern error in the transmitted wavefront. In a Fizeau or Twyman-Green interferometer, this wavefront is reflected by a return flat and transmits through the window. The fixed pattern error is carried in the measurement result. This error is negligible, only if the wedge angle is so large that the interference fringes formed by the two surfaces are too dense for the detector to resolve. However, if the wedge angle is small (e.g. several arc-seconds), the phase error (pv) could be up to 0.025 fringes for most glass (n =1.5). By tilting both the window and the return flat properly, it is possible to cancel the effect of multiple reflections of a window.


Testing an optical window of a small wedge sample: effect of multiple reflections

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.


Absolute testing of flats by using even and odd functions

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 90o, 45o, 22.5o, 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 180o, 90o, and 45o with respect to one another, and six measurements are performed. The exact profiles along every 45o 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, experimental results, and error analysis are presented.


Effect of retroreflection on a Fizeau phase-shifting interferometer

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.


Testing spherical surfaces: a fast, quasi-absolute technique

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 l/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.


Absolute testing of flats decomposed to even and odd functions

  • Chiayu Ai and James C. Wyant
  • Proceedings of SPIE, Vol. 1776, pp. 73-83, 1992
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This paper describes a method for measuring the absolute flatness of flats. A function in a Cartesian coordinate system can be expressed as the sum of even-odd, odd-even, even-even, and odd-odd functions. Three flats are measured at eight orientations; one flat is rotated 180┬░, 90┬░, and 45┬░with respect to another flat. From the measured results the even-odd and the odd-even functions of each flat are obtained first, then the even-even function is calculated. All three functions are exact. The odd-odd function is difficult to obtain. For the points on a circle centered at the origin, the odd-odd function has a period of 180┬░ and can be expressed as a Fourier sine series. The sum of one half of the Fourier sine series is obtained from the 90o rotation group. The other half is further divided into two halves, and one of them is obtained from the 45┬░ rotation group. Thus, after each rotation, one half of the unknown components of the Fourier sine series of the odd-odd function is obtained. The flat is approximated by the sum of the first three functions and the known components of the odd-odd function. In the simulation, three flats (each is an OPD map obtained from a Fizeau interferometer) are reconstructed. The theoretical derivation and the simulating results are presented.


Measurement of the inhomogeneity of a window

  • Chiayu Ai and James C. Wyant
  • OPTICAL ENGINEERING, Vol. 30 No. 9, page 1399, September 1991
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We describe three methods to measure the inhomogeneity of a window material. The first method immerses the window in a liquid between two planes. However, this method is inconvenient for some applications. The second method measures the optical figure of the front surface and then measures the return wavefront that transmits through the window and reflects from the rear surface of the window. The advantage of this method is that it can remove the contributions of both the surface figures and the return fiat plus the system error of the interferometer. The disadvantage is that a small wedge must be fabricated between the two surfaces to eliminate spurious interference. The third method derives the inhomogeneity of the window material by measuring the optical figure of the front surface of the window and then flipping the mirror to measure the back surface. The advantage of this method is that it is not necessary to have a wedge between the two surfaces. The disadvantage of the window-flipping method is that the contribution of system error can increase.


Testing stress birefringence of an optical window

  • Chiayu Ai and James C. Wyant
  • Proceedings of SPIE, Vol. 1531, pp. 165-172, 1991
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This paper describes a method to measure the birefringence of an optical window. The transmitting wavefront includes the contributions from the two surfaces, the material inhomogeneity, and the birefringence. Because of the birefringence, the transmitting wavefront has different profiles for different orientations of polarization of linearly polarized beams. From this difference, the amount of phase difference for the fast and slow axes is obtained. Thus, the birefringence is calculated. With this method, the contributions from the two surfaces and the material inhomogeneity are removed. A laser rod was measured with different methods. The theoretical derivation, comparison of different methods, and experimental results are presented.


Absolute measurement of surface roughness

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 needs 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-├ů rms surface roughness mirror are presented. The expected error in the rms roughness measurement of a supersmooth mirror due to instrument noise is 0.02 ├ů.


Absolute measurement of spherical surfaces

  • Katherine Creath and James C. Wyant
  • Proceedings of SPIE, Vol. 1332, pages 2-7, 1990
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The testing of spherical surfaces using the three-measurement technique outlined by Jensen requires very precise alignment of the sphere relative to the interferometer. An easier technique for the absolute measurement of spherical surfaces has been developed which does not require the precise alignment of the Jensen technique and uses only two measurements. As long as the test surface does not contain any aberrations with odd symmetry, these aberrations can be subtracted from the measurement and an absolute measurement of the test surface can be obtained. This paper describes and compares these two techniques and shows results of testing a l/12 P-V (peak-to-valley) sphere (N.A.=0.4) using both techniques with a phase-measuring Fizeau interferometer. These measurement techniques are repeatable to ┬▒0.01waves P-V.


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.


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.


Direct phase measurement interferometer working at 3.8 ┬Ám

A direct phase measurement interferometer designed and constructed to operate at a 3.8-┬Ám 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.


Self-referencing wavefront sensor

  • K. Underwood, J.C. Wyant, and C.L. Koliopoulos
  • Proceedings of SPIE, Vol. 351, page 108, 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.


Testing of nonlinear diamond-turned reflaxicons

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.


Rough surface interferometry at 10.6 ┬Ám

An IR Twyman-Green interferometer is described. It uses a cw CO2 laser as a light source operating at a 10.6-┬Ám 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.


Precision Optical Testing

  • James C. Wyant
  • SCIENCE, Vol. 206, page 168, 12 October 1979
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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.


Energy distribution in a scatterplate interferometer

In this paper, a Fourier-optics approach to scatterplate interferometry is introduced. In particular, it is used to explain how energy is conserved for both “phase”- and “density”-type scatterplates.


Infrared point-diffraction interferometer

A point-diffraction interferometer (PDI) for use in the infrared is discussed. It is shown that the PDI is simple and easy to use and also yields fringes of constant optical path difference similar to those obtained with a Twyman-Green interferometer. The fabrication of the PDI is described, and typical results obtained using the interferometer at a wavelength of 10.6 ┬Ám are shown.


Optical figure inspection of diamond-turned metal mirrors

  • R. N. Shagam, R. E. Sladky, and J. C. Wyant
  • OPTICAL ENGINEERING, Vol. 16 No. 4, page 375, July-August 1977
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This paper demonstrates that the optical testing of diamond-turned surfaces is best accomplished by interferometry and not by tests which measure wavefront slope. Certain conditions regarding the interferometer configuration must be met in order to generate meaningful and accurate interferograms. A 40 cm diameter aperture modified Mach-Zehnder interferometer mounted directly on the diamond-turning lathe to facilitate rapid testing of figure between fabrication cuts is described. Results for a spherical surface tested in a Twyman-Green interferometer and an off-axis parabola tested in the Mach-Zehnder interferometer are illustrated.


Determination of the dihedral angle errors of a corner cube from its Twyman-Green interferogram

A technique is devised for calculating the magnitudes of the dihedral angle errors of a comer cube from a single Twyman-Green interferogram. Experimental examples are given in which the dihedral angles of two corner cubes are determined to within 2 arcsec by this procedure. These values are also shown to be in good agreement with independent goniometer measurements.


Interferometer for measuring power distribution of ophthalmic lenses

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.

 

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