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.
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.
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.
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.
In this paper, the manufacturing and testing procedures to make large off-axis aspherical mirrors are presented. The difficulties in polishing and testing for both circular aperture and rectangular aperture mirrors are previewed, and a possible solution is given. The two mirrors have been polished by means of CCOS, the final accuracy is 25-nm rms for 770-mm x 210-mm rectangular mirror and 20-nm rms for (phi) 600-mm circular mirror. These results just meet the optical tolerances specified by the designer, and the manufacturing and testing procedures presented here show good ability to make large off-axis aspherical mirrors.
The manufacturing procedure of a 500 mm in diameter, f/2 hyperbolic primary mirror based on Computer-Controlled Polishing is introduced in detail. The mirror was finally polished to the shape accuracy of 13 nm rms and the surface roughness of 2 nm Ra. Testing methods and data analysis for different stages ranging from grinding to polishing are discussed. Some critical factors affecting the efficiency and accuracy of the grinding/polishing procedure are summarized. In addition, the preliminary work to make large off-axis asphere mirrors is presented. The difficulties in polishing and testing for both circular aperture and rectangular aperture mirrors are previewed, and a possible solution is given. To control the geometrical parameters such as radius of curvature and conic constant, a new profiler has been built, and it has proven very useful to improve the grinding efficiency. Finally, the manufacturing of small aspheres using deterministic grinding tool is also introduced. The fine grinding procedure of LOH's asphere grinding machine is presented.
Three-dimensional or x-y-z profilometer is a well-established method for measuring non-symmetric aspherical surface. In this paper, the design of three-dimensional, x-θ -z profilometer called dual gauge profilometer (DGP), which uses a granite straight edge with high precision linearity as reference to reduce the linearity error of ball slide, is presented. The benefits of using this reference structure, data processing and error surface reconstruction are also discussed. Through the use of the novel profilometer, a non- symmetric off-axis mirror with 600 millimeter in diameter can be measured with accuracy of 4 microns Peak to Valley (PV) within 40 minutes, including data processing time.
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