Ulf Griesmann

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.

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.

Absolute refractive indices and thermal coefficients of fused silica and calcium fluoride near 193 nm

The refractive indices of several fused silica and calcium fluoride samples from different suppliers were measured with the minimum deviation method in the deep UV between 191 and 196 nm with a standard uncertainty of 7 ppm. For both materials the dispersion dn/dlambda near 193 nm and 20 degrees C was determined. In addition, we measured the thermal coefficients of the refractive index near 193 nm and between 15 and 25 degrees C.

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).

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.

Refractivity of nitrogen gas in the vacuum ultraviolet

We have measured the refractivity of nitrogen gas in the ultraviolet and the vacuum ultraviolet, using a Fourier-transform spectrometer. A new two-term Sellmeier formula for the standard refractivity between 145 and 270 nm is derived.

Accurate Lifetimes and Absolute Transition Rates for Ultraviolet Transitions from 3d5(4G) 4p and 3d5(4P) 4p levels in Mn II

A recently developed, laser-induced fluorescence technique was used to measure the lifetimes of 14 3d5(4G)4p and 3d5(4P)4p levels in the Mn+ ion. Branching fractions for electric dipole transitions from these levels were measured with a vacuum ultraviolet Fourier transform spectrometer, using a hollow-cathode lamp and a Penning discharge source. Based on these new measurements, absolute electric dipole transition rates for about 170 spectral lines in the ultraviolet and vacuum ultraviolet were determined. The uncertainty of the transition rates is less than 5% for the strong transitions.

NIST FT700 Vacuum Ultraviolet Fourier Transform Spectrometer: applications in ultraviolet spectrometry and radiometry

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.

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.