Binary pseudo-random array (BPRA) “white noise” artifacts are highly effective for characterizing the instrument transfer function (ITF) of surface topography metrology tools and wavefront measurement instruments. These BPRA artifacts feature all spatial frequencies within the instrument bandpass equally, resulting in a power spectral density with a white-noise-like character. This characteristic allows for direct ITF determination with uniform sensitivity across the entire spatial frequency range. We have developed a novel BPRA calibration standard that combines the diffractive pattern of a reflection computer-generated hologram (CGH) with the white noise generating BPRA pattern. By integrating these technologies using the same lithographic techniques, the resulting calibration sample enables ITF characterization of a Fizeau interferometer with a transmission sphere, or any nulling optic.
Binary pseudo-random array (BPRA) artifacts are useful devices for calibrating the instrument transfer function (ITF) of interferometric microscopes and other optical and non-optical surface and wavefront measurement instruments. The intrinsic white noise character of the power spectral density function of the artifact simplifies the deconvolution of the ITF from the measured power spectral density (PSD). However, resampling of the BPRA intrinsic artifact features with the measurement tool’s specific sampling pattern modifies the white noise character of the intrinsic spectrum and needs to be accounted for in the ITF-based data deconvolution process. We have developed an analytic solution to the spectrum of a resampled one- and two- dimensional BPRA. The resultant nominal PSD function is a simple two-parameter cosine function with a period equal to the resampled pixel width. A transfer function model for interferometric microscopes that incorporates this function, along with an ITF that includes aliasing effects and variable numerical aperture (NA), wavelength, and obscuration factor, is used to fit to the BPRA PSDs measured by an interference microscope for a range of objective and zoom lens magnification combinations.
We summarize our development of a low-cost instrument for the detection of fabrication errors in diffraction gratings. Our instrument applies a low-cost digital camera and high dynamic range (HDR) imaging in the focal plane of a lens to analyze light reflected by a diffraction grating. A dynamic range close to 1010 is achieved for a spatial frequency range that is relevant for types of errors that occur in the lithographic fabrication of gratings. We also describe a modification of the instrument in which a spatial filter is used to block the large fraction of light that does not carry information on fabrication errors. This “coronagraph” modification reduces measurement times by about an order of magnitude. A unique pseudologarithmic transformation is described for the visualization of wide range data that include zero or negative values, such as HDR images.
Accurate topography measurements of engineered surfaces over a wide range of spatial frequencies are required in many applications. The instrument transfer function (ITF) of the microscope used to characterize the surface topography must be taken into consideration to ensure that the height, or depth, of features with higher spatial frequency content is not underestimated. This applies especially when comparing surface topography measurements made by different types of microscopes. We discuss ITF measurements of a confocal microscope and an interferometric microscope using a binary pseudo-random array (BPRA) standard. BPRA standards are surfaces designed to have constant inherent power spectral density (PSD) over the spatial frequency passband of a microscope. The ITF of a microscope can thus be derived from a PSD measurement of a BPRA standard in a straight-forward manner. We further show how BPRA standards can be used as efficient diagnostic tools to characterize aspects of the imaging performance of topography-measuring microscopes.
Recently, a technique for calibrating the modulation transfer function (MTF) of a broad variety of metrology instrumentation has been demonstrated. This technique is based on test samples structured as one-dimensional binary pseudo-random (BPR) sequences and two-dimensional BPR arrays (BPRAs). The inherent power spectral density of BPR gratings (sequences) and arrays has a deterministic white-noise-like character that allows direct determination of the MTF with uniform sensitivity over the entire spatial frequency range and field-of-view of an instrument. As such, the BPR samples satisfy the characteristics of a test standard: functionality, ease of specification and fabrication, reproducibility, and low sensitivity to manufacturing error. Here we discuss our recent developments directed to the optimization of the sample design, fabrication, application, and data processing procedures, suitable for thorough characterization of large aperture optical interferometers. Compared with the previous coded-aperture based design, the improved, ‘highly randomized’ BPRA pattern of the new test standard provides better accuracy and reliability of instrument MTF and aberration characterization, and enables operation optimization of large aperture optical interferometers. We describe the pattern generation algorithm and tests to verify the compliance to desired BPRA topography. The data acquisition and analysis procedures for different applications of the technique are also discussed.
We describe a coronagraph-like instrument for the characterization of fabrication errors in diffraction gratings and diffractive optics. A diffraction grating under test is illuminated with collimated laser light, and a reflected diffraction order is focused by a lens. A beam stop placed at the focal plane of the lens blocks the primary diffracted beam, passing only the small fraction of light scattered into nearby angles due to fabrication errors. The transmitted light fraction is focused by a second lens onto a digital camera and the light distribution is measured with a sensitive high dynamic range imaging method. Preliminary measurements with the coronagraph setup are compared to focal-plane images made without beam stop.
We report on recent progress in the development of our focal plane imaging system for the detection and characterization of small fabrication errors in diffraction gratings. The instrument uses a purpose-designed high dynamic range imaging method in conjunction with a low-cost digital camera to acquire images with a dynamic range that can now exceed eight orders of magnitude. The sensitivity and utility of the instrument is demonstrated with measurements of three different diffraction gratings. Avenues for further possible improvements of the instrument are discussed.
Recently, a technique for calibration of the Modulation Transfer Function (MTF) of a broad variety of metrology instrumentation has been established. The technique is based on test samples structured according to binary pseudorandom (BPR) one-dimensional sequences and two-dimensional arrays. The inherent power spectral density of BPR gratings and arrays, has a deterministic white-noise-like character that allows a direct determination of the MTF with a uniform sensitivity over the entire spatial frequency range and field-of-view of an instrument. As such, the BPR samples satisfy the characteristics of a test standard: functionality, ease of specification and fabrication, reproducibility, and low sensitivity to manufacturing error. Here we discuss our recent developments working with support of the U.S. Department of Energy on industrialization of the technique. The goal is to develop affordable BPR test samples, application procedures, and data processing software, suitable for thorough characterization of optical interferometers and microscopes, as well as x-ray, electron (scanning and transmission), and atomic force microscopes. We report on the development of BPR array test samples optimized for advanced characterization (including the instrumental MTF and aberrations) and operation optimization of large aperture optical interferometers. We describe the sample fabrication process and tests to verify the compliance to desired surface topography. The data acquisition and analysis procedures for application of the technique for precise focusing of Fizeau interferometer are discussed in detail.
Interferometers using computer-generated holograms (CGHs) have become the industry standard to accurately measure aspheric optics. The CGH is a diffractive optical element that can create a phase or amplitude distribution and can be manufactured with low uncertainty using modern lithographic techniques. However, these CGHs have conventionally been used with visible light and piezo-shifting interferometers. Testing the performance of transmissive optics in the infrared requires infrared CGHs and an infrared interferometer. Such an instrument is used in this investigation, which introduces its phase shift via wavelength-tuning. A procedure on how to design and manufacture infrared CGHs and how these were successfully used to model and measure the Wide-Field Infrared Survey Telescope grism elements is provided. Additionally, the paper provides a parametric model, simulation results, and calculations of the errors and measurements that come about when interferometers introduce a phase variation via wavelength-tuning interferometry to measure precision aspheres.
The slitless spectrometer plays an important role in the WFIRST mission for the survey of emission-line galaxies. This
will be an unprecedented very wide field, HST quality 3D survey of emission line galaxies1. The concept of the
compound grism as a slitless spectrometer has been presented previously. The presentation briefly discusses the
challenges and solutions of the optical design, and recent specification updates, as well as a brief comparison between
the prototype and the latest design. However, the emphasis of this paper is the progress of the grism prototype: the
fabrication and test of the complicated diffractive optical elements and powered prism, as well as grism assembly
alignment and testing. Especially how to use different tools and methods, such as IR phase shift and wavelength shift
interferometry, to complete the element and assembly tests. The paper also presents very encouraging results from
recent element tests to assembly tests. Finally we briefly touch the path forward plan to test the spectral characteristic,
such as spectral resolution and response.
We have explored a number of lithographic techniques and improvements to produce the resist lines that then define the grating groove edges of silicon immersion gratings. In addition to our lithographic process using contact printing with photomasks, which is our primary technique for the production of immersion gratings, we explored two alternative fabrication methods, direct-write electron beam and photo-lithography. We have investigated the application of antireflection (AR) coatings during our contact printing lithography method to reduce the effect of Fizeau fringes produced by the contact of the photomask on the photoresist surface. This AR coating reduces the amplitude of the periodic errors by a factor of 1.5. Electron beam (e-beam) patterning allows us to manufacture gratings that can be used in first order, with groove spacing down to 0.5 micrometer or smaller (2,000 grooves/mm), but could require significant e-beam write times of up to one week to pattern a full-sized grating. The University of Texas at Austin silicon diffractive optics group is working with Jet Propulsion Laboratory to develop an alternate e-beam method that employs chromium liftoff to reduce the write time by a factor of 10. We are working with the National Institute of Standards and Technology using laser writing to explore the possibility of creating very high quality gratings without the errors introduced during the contact-printing step. Both e-beam and laser patterning bypass the contact photolithography step and directly write the lines in photoresist on our silicon substrates, but require increased cost, time, and process complexity.
We describe a simple bilayer photoresist that is particularly well suited for laser lithography at an exposure wavelength of 405 nm on glass substrates, which are often used for the fabrication of binary diffractive optics and computer-generated holograms. The resist consists of a poly-dimethyl glutarimide (PMGI) bottom layer that is used as an antireflection coating between a glass substrate and a positive or negative photoresist. The optical properties of the PMGI layer at 405 nm result in excellent suppression of reflections into the photoresist and good process latitude.
We evaluate a method for testing the radius of a spherical surface with a hologram that consists of a pair of nested Fresnel
zone lenses. The hologram is positioned in the collimated test beam of a Fizeau interferometer. The inner zone lens
generates a focus at the test part surface, whereas the wavefront of the first diffraction order of the outer zone lens is
confocal with the test part. When the test part radius is equal to the nominal radius, the fringes in both zone lens areas are
nulled at the same distance of the test sphere from the zone lens. The radius error of the spherical surface can be calculated
from the test sphere displacement between interferometer null positions for the inner and outer zone lenses, or from the
defocus term of the outer (confocal) lens at the position of zero defocus of the inner (cat’s-eye) zone lens. The primary
benefits of the nested zone lens method are its ease of use, and that it enables radius measurements of spherical surfaces
with large radii. We describe the radius measurement of a precise convex sphere with a nominal radius of 80mm.
We describe a method for measuring the deflection due to gravity (sag) of horizontally mounted reference flats of phase
shifting interferometers. The planarity of a test flat can be measured sag-free while supporting it iso-statically on a suitable
visco-elastic polymer foam. A sag map is obtained when the sag-free flatness error is subtracted from the flatness error of
the same flat held at its edge.
Traceability of interferometric form measurements requires characterization of the reference wavefront. We
investigate absolute tests for spherical surfaces where the form errors of both reference and test surface are
estimated by minimizing the difference in measurements obtained at various positions and orientations of the
test surface. This approach yields an estimate for the test surface errors without changing experimental settings,
such as cavity length, that may affect the apparent reference errors. The method requires at least one translation
of the test surface in the field of view and one rotation. Additional measurements provide redundancies to improve
and characterize measurement uncertainties.
The errors of the reference and test surface are estimated with pixel-level spatial resolution without assuming
an underlying error model, such as a representation based on Zernike polynomials. The estimation algorithm
consists of an iterative sequence of stitching steps, with the role of reference and test surface reversed for each
step. Measurement uncertainties are evaluated using Monte-Carlo procedures and analysis of residual errors for
experiments with redundant measurements. Key sources of measurement uncertainty are spatially correlated
measurement errors resulting from errors in test surface location, image distortion, and environmental effects.
Experimental results are presented comparing the method to a random ball test.
In the performance evaluation of phase-shifting interferometers for figure metrology, the height response, or height transfer function, is rarely taken into consideration, because in most applications smooth surfaces are measured and only the lowest spatial frequencies are of interest. For measurements with low uncertainty it is important to understand the height response as a function of the spatial-frequency content of a surface under test, in particular when it contains form-error components with frequencies at the high end of an interferometer's spatial-frequency passband. A mirror with a patterned area of 140-mm diameter, consisting of several subpatterns with varying spatial frequency, was used to evaluate the spectral response. Our goal was to develop a method for efficient mapping of the spectral response over the circular field of view of a phase-shifting interferometer. A new way of representing the dependence of the spectral response on the field of view of an interferometer is described.
We describe a glancing-incidence interferometric double-pass test, based on a pair of computer-generated holograms
(CGHs), for mandrels used to fabricate x-ray mirrors for space-based x-ray telescopes. The design of the test and its
realization are described. The application illustrates the advantage of dual-CGH tests for the complete metrology of precise
optical surfaces.
A glancing-incidence interferometric test for large x-ray mirror mandrels, using two computer-generated holograms (CGHs), is described. The two CGHs are used to form a double-pass glancing-incidence system. One layout of the CGH-cavity glancing-incidence interferometer is studied and factors relating to its design are analyzed. A semianalytical expression for the phase function is derived that avoids high-order ripple errors and improves the efficiency of the CGH pattern generation. A system of coarse and fine fiducials for establishing the CGH-cavity and aligning the tested mandrel is discussed. Compared with traditional measurement devices, such as coordinate measuring machines (CMMs) or other scanning metrology systems, the CGH-cavity glancing-incidence interferometer can measure a mandrel surface without mechanical contact, at a high spatial sampling frequency, with lower uncertainty, and at high speed.
In characterizing the performance of a phase-shifting interferometer, the dependence of the measured height on the
spatial frequency is rarely considered. We describe a test mirror with a special height relief that can be used to measure
the height transfer function for the interferometer in a fashion analogous to the measurement of the modulation transfer
function for the optical imaging system. We fabricated the test mirror at the National Institute of Standards and
Technology (NIST) using a lithography-based process. The test mirror has several patterns (reminiscent of moth
antennae) with variable spacing in radial direction. We describe the fabrication of the test mirror and its application to
test the performance of the interferometer.
We investigate three-flat calibration methods based on rotational symmetry and mirror symmetry for absolute interferometric flatness measurements of circular flats in the presence of deformations caused by the support mechanism for the flats, which are a significant problem for large, heavy flats. We show that the mirror-symmetric component of the mounting-induced deformation can be determined by comparing flat test solutions based on mirror symmetry and on rotational symmetry, when the flats have identical deformations. We also describe a novel solution to the three-flat problem for three flats with identical mounting-induced deformations. In the new three-flat solution, the flat deformation is calculated along with the wavefront flatness errors for the three flats. Formulas for the uncertainty of three-flat test solutions are derived.
The "Improved Infrared Interferometer" (IR3) at the National Institute of Standards and Technology (NIST)
is a phase-measuring interferometer, operating at a wavelength of 1550 nm, which is being developed for measuring
the thickness and thickness variation of low-doped silicon wafers with diameters up to 300 mm. The purpose of the
interferometer is to produce calibrated silicon wafers, with a certified measurement uncertainty, which can be used as
reference wafers by wafer manufacturers and metrology tool manufacturers. We give an overview of the design of the
interferometer and discuss its application to wafer thickness measurements. The conversion of optical thickness, as
measured by the interferometer, to the wafer thickness requires knowledge of the refractive index of the material of
the wafer. We describe a method for measuring the refractive index which is then used to establish absolute
thickness and thickness variation maps for the wafer.
When measuring the form errors of precision optics with an interferometer, calibration of the reference wavefront is of central importance. In recent years, ball averaging, or random ball testing, has emerged as a robust method for calibrating spherical reference wavefronts in converging beams. We describe a simple instrument, consisting of an air bearing and two electric motors, that can rotate the test ball around three axes as required for a ball averaging test. The performance of the instrument is demonstrated by using it to calibrate a concave transmission sphere. Further we discuss the effects of image sampling at random locations or on uniform grids, and the effect of correlated measurements. Finally, we describe a method to determine the number of measurements which are sufficient for a ball averaging calibration.
The Geometry Measuring Machine (GEMM) of the National Institute of Standards and Technology (NIST) is a profilometer for free-form surfaces. A profile is reconstructed from local curvature of a test part surface, measured at several locations along a line. For profile measurements of free-form surfaces, methods based on local part curvature sensing have strong appeal. Unlike full-aperture interferometry they do not require customized null optics. The uncertainty of a reconstructed profile is critically dependent upon the uncertainty of the curvature measurement and on curvature sensor positioning. For an instrument of the GEMM type, we evaluate the measurement uncertainties for a curvature sensor based on a small aperture interferometer and then estimate the uncertainty in the reconstructed profile that can be achieved. In addition, profile
measurements of a free-form mirror, made with GEMM, are compared with measurements using a long-trace profiler, a coordinate measuring machine, and subaperture-stitching interferometry.
We have adapted a Shack-Hartmann wavefront sensor (SHWFS) to the measurement of highly aberrated large optics. The experiment uses a concave mirror operating at the radius point with a small lens to re-collimate the light onto the wavefront sensor. It is used to test large (300 mm) fused silica wafers in double pass transmission. The optic under test is placed in the intermediate path near the large return mirror. The aberrations of the large mirror, beam splitter and other optics are subtracted by recording a reference set of focal spot on the SHWFS without the wafer. The wavefront error for some of these wafers is nearly 100 waves, yet we are able to make accurate measurements with the wavefront sensor by selecting a sensor with the appropriate combination of focal length and lenslet diameter. The special sensor that we developed uses a megapixel camera with an arrangement of 100 X 100 lenslets. This sensor could achieve several hundred waves of dynamic range with better than λ/20 accuracy. Additional wafer thickness measurements that were made at NIST with the XCALIBIR interferometer corroborate the SHWFS results.
We have made accurate measurements near 157 nm of the absolute index of refraction, the index of refraction, the index dispersion, and the temperature dependence of the index, for the cubic-symmetry, group-II fluorides: calcium fluoride, strontium fluoride, and barium fluoride. Accurate measurements of these quantities for calcium fluoride are needed for designs of lens systems for 157 nm excimer-laser- based exposure tools for photolithography. Measurements of these isotropic materials high ly transmissive near 157 nm, such as strontium fluoride and barium fluoride, are needed for designs which include secondary materials in addition to calcium fluoride to correct for chromatic aberrations. These optical properties were measured with precision gonimeters on prisms of the materials in a nitrogen atmosphere using the minimum deviation method. The relative refractive indices were converted to absolute indices by using values of the index of nitrogen obtained by independent interferometric measurement near 157 nm. Values of the absolute refractive indices for these materials were obtained with an accuracy of 6 X 10-6. A key result is that the dispersion of barium fluoride near 157 nm is approximately 68 percent larger than that of calcium fluoride, which makes barium fluoride a potentially useful material for combination with calcium fluoride for chromatic aberration correction near 157 nm.
In the minds of many, Fourier transform spectrometry is restricted to applications in the infrared. In the ultraviolet, the increasingly severe demands on optical, data acquisition, and motion control systems of the interferometer diminish the effectiveness of the technique. However, with recent advances in ultraviolet optics, data acquisition and sampling techniques for Fourier transform spectrometers, these stringent demands are easier to meet at vacuum ultraviolet wavelengths and significantly reduce the cost of Fourier transform spectrometers. The FT700 spectrometer at NIST can operate at wavelengths as low as 140 nm, limited by the short wavelength cut-off of the calcium fluoride optics. We illustrate the capabilities of the FT700 spectrometer in the ultraviolet with several recent results in atomic emission spectrometry, plasma diagnostics, and refractometry.
We have made accurate measurement near 157 nm of the relative index of refraction, its dispersion, and its temperature dependence for two grades of calcium fluoride in N2 gas. Accurate measurements of these quantities are needed for the design of lens system for 157 nm F2 excimer-laser-based exposure tools for photolithography. These optical properties were measured with precision goniometer on prisms of the materials in a N2 atmosphere using the minimum deviation method. The dispersion was determined using line emission radiation from a deuterium lamp at several wavelengths near 157 nm. Values of the relative refractive index for two grades of calcium fluoride in N2 gas corrected to a temperature of 20 degrees C and a pressure of one standard atmosphere are well within our 7 ppm estimated uncertainty forth measurements. The temperature of the samples and the surrounding medium were controlled to 0.05 degrees C, which enabled accurate measurements of the temperature dependencies of the indices around room temperature near 157 nm.
We discuss a procedure for making accurate measurement of the index of refraction, its dispersion, and its temperature dependence, in the deep ultraviolet (near 193 nm), using precision goniometric spectrometers and the minimum deviation method. Measurements of the indices of fused silica and calcium fluoride near 193 nm, with a fractional accuracy of 7 ppm, are discussed. These measurements revealed differences in the indices between different grades of fused silica. Accurate values of the temperature dependencies were determined from measurements of the indices at several temperatures in a 20 degree Celsius range about 20 degrees Celsius. A procedure to measure the index of calcium fluoride in the vacuum ultraviolet region (157 nm) using a N2 purge housing is discussed.
We describe instrumentation that has been constructed at the National Institute of Standards and Technology (NIST) for measurement of the index of refraction of solid materials in the spectral region from 0.5 micrometer to 1000 micrometer using Fourier-transform based spectrophotometers and etalon samples. Preliminary index of refraction measurements have been performed on fused silica and arsenic trisulfide glass samples from 0.5 micrometer to 12 micrometer, and the results are compared to tabulated values on these materials.
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