Quandou Wang

A simple ball averager for reference sphere calibrations

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.

Three-flat tests including mounting-induced deformations

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.

Measuring Form and Radius of Spheres with Interferometry

Abstract The geometry of a nearly spherical surface, for example that of a precision optic, is completely determined by the radius-of-curvature at one point and the deviation from the perfect spherical form at all other points of the sphere. Measurements of radius and form error can now be made with interferometers to remarkable accuracy. We describe measurements of radius and form error of a precision silicon sphere, having a nominal radius of 46.8 mm, with the “extremely accurate CALIBration InterferometeR” (XCALIBIR) at the National Institute of Standards and Technology (NIST). For these measurements XCALIBIR is configured as a spherical Fizeau interferometer providing a field of view of 44°. To measure the radius, a variant of the well known interferometric radius bench method is used. Careful alignment of phase measuring and displacement measuring interferometers enables us to achieve a standard measurement uncertainty for the sphere radius of about 5 parts in 10 7 . The measurement of the form error is complicated because the entire sphere surface cannot be imaged in one measurement. Instead, 138 overlapping areas of the sphere surface are measured. A “stitching” algorithm is then employed to assemble these measurements into a form error map for the entire surface. We show that form errors can lead to considerable uncertainty in the radius of a sphere obtained through a radius-of-curvature measurement with the radius bench method.

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.

Measuring the phase transfer function of a phase-shifting interferometer

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.

Spatially resolved height response of phase-shifting interferometers measured using a patterned mirror with varying spatial frequency

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 interferometers 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.

Uncertainties in aspheric profile measurements with the geometry measuring machine at NIST

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.

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.

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.

Versatile bilayer resist for laser lithography at 405 nm on glass substrates

Abstract. 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.