WYKO Corporation is currently designing and manufacturing specialized phase shifting interferometers to aid in the qualification of large optics for the U.S. NIF 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' systems will be the largest commercially available Fizeau phase shifting interferometers ever manufactured. Systems will be produced using traditional CCD cameras as well as 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.
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 measurements 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 measurements 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.
Large, high power laser systems such as that being constructed by Lawrence Livermore National Laboratories for the National Ignition Facility require accurate measurements of spatial frequencies of up to 2.5 lines/mm over a 100mm field of view.In order to ensure accurate measurements of the parts, the test apparatus must be well characterized. The systems transfer function (STF) 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 distance between the test piece and return flat, the system transfer function could be kept at acceptable levels within the range of interest.
The goal of this 24 inch phase shifting Fizeau interferometer design is to measure the wavefront of an optical window at Brewster's angle. There are two important requirements: a small wavefront slope error and a high optical resolution. To test the sample in transmission, each pencil of light returned from the RF must go back through the window from which it was previously transmitted. Therefore, the slope of the wavefront transmitted through the TF has to be less than a few arc seconds, especially for a long cavity length. For example, for a 2 meter round trip, a 5 arc second slope causes the beam to deviate 0.05 mm. For a 431-mm sample imaged onto a 1000 pixel array, a 0.05 mm displacement corresponds to a 0.116 pixel, which is negligible. However, when a 100 mm sub-aperture is imaged, a 0.05 mm displacement is significant. A shorter round-trip distance can effectively reduce the displacement. The deviations due to a 5-arc second wavefront slope is 0.12 pixel for 2-meter round trip in the full aperture and 0.10 pixel for 0.4-meter round trip in the sub-aperture imaging. Because the phase of the optical window is to be measured and not the amplitude or intensity, the MTF is ont suitable for evaluating the interferometer's resolution. A phase object was measured to determine the system transfer function. The fidelity of the measurement is required to be within 60 percent amplitude for a specified spatial frequency range. For example,for a sinusoidal phase object with a phase undulation of 0.01 wave p-v, the measured result should not be less than 0.006 wave. From theory, a phase object with a smaller phase undulation can be imaged with good fidelity. Because the wavefront slope and optical resolution requirements are very tight, to ensure the interferometer meets these requirements, theoretical errors were thoroughly analyzed and the design implementation was carefully studied.
Laser interferometers have been used widely in the optics and disk drive industries. Often the surface of the sample is either too curved to resolve the fringes or too rough to reflect the incident beam back into the interferometer. Illuminating at a graze incident angle effectively increases the equivalent wavelength, and hence the reflectivity, but the image of a circular aperture becomes elliptical. Lasers with a long IR wavelength seem to be the solution. However,the spatial resolution of the vidicon cameras is usually poor, and the image lag is often too long. These limit the accuracy of an IR phase-shifting interferometer. Recently, we have designed tow types of interferometers for 3.39 micrometers and 10.6 micrometers using an InSb array and a micro- bolometer array, respectively. These modern cameras have a high resolution and hence greatly extend the range of measurable material from a blank to a finished optics. Because the refractive index of the optical material at the IR wavelength is usually very high, the anti-reflection coating of the optics at IR is more critical than that at a visible wavelength. The interferometer's design, the resolution, the dependence of the fringe contrast on the sample roughness, and the measurement results of various samples are presented.
Accurate interferometric measurement of large laser slabs requires spatial frequencies of 1 mm/cycle to 33 mm/cycle over a 100 mm 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 and 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.
WYKO Corporation is designing and building 24' (61 cm) aperture phase shifting interferometers to aid in the manufacture and qualification of optics for the NIF (U.S. National Ignition Facility). The first interferometer is scheduled for delivery in early 1997. The 24' systems will be the largest commercially available phase shifting interferometers, and will use a megapixel CCD camera to give high lateral resolution. Some of the NIF optics will be tested at Brewster's angle, and that condition places unusual design requirements on the interferometer. The main effect of testing a planar optical element in transmission at Brewster's angle is that there is a large separation between areas of the element and the return flat, so that optical propagation effects become important. We describe our design of a large aperture phase shifting interferometer, and how it will be used to test the NIF optics.
This interferometer is designed to measure 75x40 cm laser glass. The entire surface is measured
at a Brewsters angle, 56.57°, with an s-polarization beam. The reflected beam is retro-reflected
by a highly reflective mirror. Thus, a 75x40 cm surface can be tested with a 60-cm aperture.
The most troublesome problem is the ghost reflection from the rear surface of a flat while the
front surface is being measured. After the second surface is polished, both surfaces are reflective
and their beams can interfere. However, the second surface of a flat is to be polished to ensure
the transmitted wavefront quality, not the quality of the surface itself. Therefore, the second
surface does not need to be measured directly. To avoid reflection from both surfaces, the laser
is switched to a p-polarization after the first surface is measured while the flat is still at a
Brewster's angle. Thus, the transmitted wavefront is not affected by the reflection.
We believe that a 60-cm clear aperture, Fizeau phase-shifting interferometer is the most practical
and accurate instrument for testing 75x40 cm optical flats. In this paper, we briefly summarize
the important design factors, and show in theory that the design can meet the required
performance.
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 equals 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.
This paper describes a simple and effective phase unwrapping technique that prevents the propagation of errors introduced at some locations on a surface from being included in or propagating to all subsequent calculations for the remaining area of the surface. Unlike conventional phase unwrapping methods that use only the principal phase value, the proposed technique utilizes the modulation information about the fringe pattern to divide the principal phase map into regions, performs mathematical morphology operations to generate a labeled unwrapping sequence mask, and carries out multi-stage phase unwrapping procedures.
We have developed a new realistic 3-D microsurface visualization technique utilizing optical phase-shifting interferometry (PSI). First, we measure the surface topography directly by determining the phase of the wavefront reflected from the surface of the object. The phase information is obtained by shifting the phase of one beam of the interferometer by a known amount and measuring the intensity of the interferometer for many different phase shifts. A phase difference map between the reference and object wavefronts is then calculated from the measured intensities. The vertical resolution is on the order of a few Angstroms. Second, we extend phase-shifting interferometry to a measurement of surface reflectivity. The measured reflectivity is not affected by any variations associated with the light source across the entire illumination field. Third, both the measured surface height data and the reflectivity images are fed into a workstation where advanced computer graphics algorithms are applied. The surface height data are used to generate the 3-D surface profile, which is then shaded by the reflectivity image, resulting in a realistic 3-D image. We will present the theoretical analysis, system setup, experimental measurements, and examples of realistic 3-D microscopic surface images.
Recent interest in using optical systems at shorter and shorter wavelengths for applications like UV photolithography and synchrotron focussing mirrors has put increasing pressure on optical metrologists to improve absolute methods of testing. Because optical metrologist do not have the luxury of possessing measuring instruments that are many times more accurate than what they want to measure, they are forced to make differential measurements between "reference" surfaces and the surface under test. However, even the (often) flat reference surface figure is not known to the accuracy now required by these new applications. This need for a more accurate knowledge of the reference surfaces has created a wide interest in the absolute calibration of flats.
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 degree(s), 90 degree(s), and 45 degree(s) 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 degree(s) and can be expressed as a Fourier sine series. The sum of one half of the Fourier sine series is obtained from the 90 degree(s) rotation group. The other half is further divided into two halves, and one of them is obtained from the 45 degree(s) 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.
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.
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 flat 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.
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