Linearizing the vertical scale of an interferometric microscope and its effect on step-height measurement.

The vertical scale calibration of an interferometric microscope is important for establishing traceability of surface topography measurements to the International System of Units (SI) unit of length, the meter. Building on the calibration procedure for the amplification coefficient developed by de Groot and Beverage [Proc. SPIE 9526, 952610 (2015)], this paper describes a calibration procedure that yields the response curve for the entire vertical scan motion of a coherent scanning interferometric microscope. The method requires only a flat mirror as an artifact, a narrow band spectral filter, an aperture to reduce the effective numerical aperture, and the ability to raise and lower the microscope head so that the center of the interferogram can be varied within the scan range. The local frequency of the interferogram is determined by fitting sections of the interferogram to a sinusoidal function. The nonlinearity determined from the local frequency data can be used to estimate the uncertainty in uncorrected vertical height measurements. We describe how optical profile data can be corrected for nonlinearity due to dynamic effects in the scan motion and show that the correction improves the reproducibility of step height measurements by at least a factor of three and close to that of the repeatability.

Sensing fabrication errors in diffraction gratings using high dynamic range imaging.

We describe the design of a simple instrument for the identification and characterization of fabrication errors in diffraction gratings. The instrument uses an uncooled charge-coupled device (CCD) camera and a high dynamic range imaging process to detect the light scattered off a grating under test in the focal plane of a lens. We demonstrate that the instrument can achieve a dynamic range around nine orders of magnitude and we show that we are able to clearly identify small, periodic fabrication errors in two test gratings that could not be detected with microscopic techniques.

Holographic radius test plates for spherical surfaces with large radius of curvature.

We describe a novel interferometric method, based on nested Fresnel zone lenses or photon sieves, for testing and measuring the radius of curvature of precision spherical surfaces that have radii in a range between several meters and a few hundred meters. We illustrate the measurement concept with radius measurements of a spherical mirror with a radius of about 10 m. The measured radius is 9877 mm±10 mm for a coverage factor k=2. Our measurements also demonstrate, for the first time to the best of our knowledge, the utility of photon sieves for precision surface metrology because they diffuse higher diffraction orders of computer generated holograms, which reduces coherent noise.

Modified Roberts-Langenbeck test for measuring thickness and refractive index variation of silicon wafers.

We describe a method to simultaneously measure thickness variation and refractive index homogeneity of 300 mm diameter silicon wafers using a wavelength-shifting Fizeau interferometer operating at 1550 nm. Only three measurements are required, corresponding to three different cavity configurations. A customized phase shifting algorithm is used to suppress several high order harmonics and minimize intensity sampling errors. The new method was tested with both silicon and fused silica wafers and measurement results proved to be highly repeatable. The reliability of the method was further verified by comparing the measured thickness variation of a 150 mm diameter wafer to a measurement of the wafer flatness after bonding the wafer to an optical flat.

Binary amplitude holograms made from dyed photoresist.

A method for fabricating binary amplitude holograms from a dyed photoresist is described. It is of particular interest for holograms that are used as null optics in the form metrology of aspheric surfaces and wavefronts. A pigment that strongly absorbs light near 633 nm was dissolved in a positive photoresist and the dyed resist was spun onto silica glass substrates. Stable resist layers were obtained that were essentially opaque at 633 nm with little effect on the transmittance of the resist in the UV. A Fresnel zone plate was fabricated from the dyed resist layer using contact lithography, and its performance was demonstrated at 633 nm.

Deformation-free form error measurement of thin, plane-parallel optics floated on a heavy liquid.

We describe a novel method for measuring the unconstrained flatness error of thin, plane-parallel precision optics. Test parts are floated on high-density aqueous metatungstate solutions while measuring the flatness error with an interferometer. The support of the flat optics by the uniform hydrostatic pressure at the submerged face of the flat optic eliminates flatness errors caused by mounting forces. A small, well characterized flatness error results from the bending of the floating flat by the hydrostatic pressure gradient at the edges. An equation describing the bending of thin, flat plates floating on a liquid is derived, which can be used to correct the flatness measurements of arbitrarily shaped plates. The method can be used to measure flatness errors of both nontransparent and transparent parts, and it is illustrated with flatness measurements of photomask blanks and substrates for extreme ultraviolet lithography. The refractive index of a saturated aqueous lithium metatungstate solution was measured at 632.8 nm and was found to be close to the refractive indices of several low thermal expansion optical materials.

Three-flat test solutions based on simple mirror symmetry.

In interferometric surface and wavefront metrology, three-flat tests are the archetypes of measurement procedures to separate errors in the interferometer reference wavefront from errors due to the test part surface, so-called absolute tests. What is believed to be a new class of solutions of the three-flat problem for circular flats is described in terms of functions that are symmetric or antisymmetric with respect to reflections at a single line passing through the center of the flat surfaces. The new solutions are simpler and easier to calculate than the known solutions based on twofold mirror symmetry or rotation symmetry. Strategies for effective azimuthal averaging and a method for determining the averaging error are also discussed.

Form-Profiling of Optics Using the Geometry Measuring Machine and the M-48 CMM at NIST.

We are developing an instrument, the Geometry Measuring Machine (GEMM), to measure the profile errors of aspheric and free form optical surfaces, with measurement uncertainties near 1 nm. Using GEMM, an optical profile is reconstructed from local curvatures of a surface, which are measured at points on the optic's surface. We will describe a prototype version of GEMM, its repeatability with time, a measurements registry practice, and the calibration practice needed to make nanometer resolution comparisons with other instruments. Over three months, the repeatability of GEMM is 3 nm rms, and is based on the constancy of the measured profile of an elliptical mirror with a radius of curvature of about 83 m. As a demonstration of GEMM's capabilities for curvature measurement, profiles of that same mirror were measured with GEMM and the NIST Moore M-48 coordinate measuring machine. Although the methods are far different, two reconstructed profiles differ by 22 nm peak-to-valley, or 6 nm rms. This comparability clearly demonstrates that with appropriate calibration, our prototype of the GEMM can measure complex-shaped optics.

Absolute refractive indices and thermal coefficients of CaF2, SrF2, BaF2, and LiF near 157 nm.

We present high-accuracy measurements for wavelengths near 157 nm of the absolute index of refraction, the index dispersion, and the temperature dependence of the index for the ultraviolet optical materials with cubic symmetry: CaF2, SrF2, BaF2, and LiF. Accurate values of these quantities for these materials are needed for designs of the lens systems for F2 excimer-laser-based exposure tools for 157-nm photolithography. These tools are expected to use CaF2 as the primary optical material and possibly one of the others to correct for chromatic aberrations. These optical properties were measured by the minimum deviation method. Absolute refractive indices were obtained with an absolute accuracy of 5 x 10(-6) to 6 x 10(-6).