Positioning errors of pencil-beam interferometers for long trace profilers

We analyze the random noise and the systematic errors of the positioning of the interference patterns in the long trace profilers (LTP). The analysis, based on linear regression methods, allows the estimation of the contributions to the positioning error of a number of effects, including non-uniformity of the detector photo-response and pixel pitch, read-out and dark signal noise, ADC resolution, as well as signal shot noise. The dependence of the contributions on pixel size and on total number of pixels involved in positioning is derived analytically. The analysis, when applied to the LTP II available at the ALS optical metrology laboratory, has shown that the main source for the random positioning error of the interference pattern is the read-out noise estimated to be {approx}0.2 rad. The photo-diode-array photo-response and pixel pitch non-uniformity determine the magnitude of the systematic positioning error and are found to be {approx}0.3 rad for each of the effects. Recommendations for an optimal fitting strategy, detector selection and calibration are provided. Following these recommendations will allow the reduction of the error of LTP interference pattern positioning to a level adequate for the slope measurement with 0.1-rad accuracy

Variable Free Spectral Range Spherical Mirror Fabry-Perot Interferometer

A spherical Fabry-Perot interferometer with adjustable mirror spacing is used to produce interference fringes with frequency separation (c/2L)/N, N=2-15. The conditions for observation of these fringes are derived from the consideration of the eigenmodes of the cavity with high transverse indices.Comment: 11 pages, 7 figures, accepted to Siberian Journal of Physic

Binary Pseudo-random Grating Standard for Calibration of Surface Profilometers

We suggest and describe the use of a binary pseudo-random (BPR) grating as a standard test surface for measurement of the modulation transfer function (MTF) of interferometric microscopes. Knowledge of the MTF of a microscope is absolutely necessary to convert the measured height distribution of a surface undergoing metrology into an accurate power spectral density (PSD) distribution. For an'ideal' microscope with an MTF function independent of spatial frequency out to the Nyquist frequency of the detector array with zero response at higher spatial frequencies, a BPR grating would produce a flat 1D PSD spectrum, independent of spatial frequency. For a'real' instrument, the MTF is found as the square root of the ratio of the PSD spectrum measured with the BPR grating to the'ideal,' spatial frequency independent, PSD spectrum. We present the results from a measurement of the MTF of MicromapTM-570 interferometric microscope demonstrating a high efficiency for the calibration method

Performance of the upgraded LTP-II at the ALS Optical Metrology Laboratory

The next generation of synchrotrons and free electron laser facilities requires x-ray optical systems with extremely high performance, generally of diffraction limited quality. Fabrication and use of such optics requires adequate, highly accurate metrology and dedicated instrumentation. Previously, we suggested ways to improve the performance of the Long Trace Profiler (LTP), a slope measuring instrument widely used to characterize x-ray optics at long spatial wavelengths. The main way is use of a CCD detector and corresponding technique for calibration of photo-response non-uniformity [J. L. Kirschman, et al., Proceedings of SPIE 6704, 67040J (2007)]. The present work focuses on the performance and characteristics of the upgraded LTP-II at the ALS Optical Metrology Laboratory. This includes a review of the overall aspects of the design, control system, the movement and measurement regimes for the stage, and analysis of the performance by a slope measurement of a highly curved super-quality substrate with less than 0.3 microradian (rms)slope variation

Progress of Multi-Beam Long Trace-Profiler Development

The multi-beam long trace profiler (LTP) under development at NASA s Marshall Space Flight Center[1] is designed to increase the efficiency of metrology of replicated X-ray optics. The traditional LTP operates on a single laser beam that scans along the test surface to detect the slope errors. While capable of exceptional surface slope accuracy, the LTP single beam scanning has slow measuring speed. As metrology constitutes a significant fraction of the time spent in optics production, an increase in the efficiency of metrology helps in decreasing the cost of fabrication of the x-ray optics and in improving their quality. Metrology efficiency can be increased by replacing the single laser beam with multiple beams that can scan a section of the test surface at a single instance. The increase in speed with such a system would be almost proportional to the number of laser beams. A collaborative feasibility study has been made and specifications were fixed for a multi-beam long trace profiler. The progress made in the development of this metrology system is presented

Development of a new generation of optical slope measuring profiler

A collaboration, including all DOE synchrotron labs, industrial vendors of x-ray optics, and with active participation of the HBZ-BESSY-II optics group has been established to work together on a new slope measuring profiler -- the optical slope measuring system (OSMS). The slope measurement accuracy of the instrument is expected to be<50 nrad for the current and future metrology of x-ray optics for the next generation of light sources. The goals were to solidify a design that meets the needs of mirror specifications and also be affordable; and to create a common specification for fabrication of a multi-functional translation/scanning (MFTS) system for the OSMS. This was accomplished by two collaborative meetings at the ALS (March 26, 2010) and at the APS (May 6, 2010)

Status of Multi-beam Long Trace-profiler Development

The multi-beam long trace profiler (MB-LTP) is under development at NASA's Marshall Space Flight Center. The traditional LTPs scans the surface under the test by a single laser beam directly measuring the surface figure slope errors. While capable of exceptional surface slope accuracy, the LTP single beam scanning has slow measuring speed. Metrology efficiency can be increased by replacing the single laser beam with multiple beams that can scan a section of the test surface at a single instance. The increase in speed with such a system would be almost proportional to the number of laser beams. The progress for a multi-beam long trace profiler development is presented

Development of pseudorandom binary arrays for calibration of surface profile metrology tools

Optical Metrology tools, especially for short wavelength (EUV and X-Ray), must cover a wide range of spatial frequencies from the very low, which affects figure, to the important mid-spatial frequencies and the high spatial frequency range, which produces undesirable scattering. A major difficulty in using surface profilometers arises due to the unknown Point-Spread Function (PSF) of the instruments [1] that is responsible for distortion of the measured surface profile. Generally, the distortion due to the PSF is difficult to account because the PSF is a complex function that comes to the measurement via the convolution operation, while the measured profile is described with a real function. Accounting for instrumental PSF becomes significantly simpler if the result of measurement of a profile is presented in a spatial frequency domain as a Power Spectral Density (PSD) distribution [2]. For example, the measured PSD distributions provide a closed set of data necessary for three-dimensional calculations of scattering of light by the optical surfaces [3], [4]. The distortion of the surface PSD distribution due to the PSF can be modeled with the Modulation Transfer Function (MTF), which is defined over the spatial frequency bandwidth of the instrument [1], [2]. The measured PSD distribution can be presented as a product of the squared MTF and the ideal PSD distribution inherent for the System Under Test (SUT). Therefore, the instrumental MTF can be evaluated by comparing a measured PSD distribution of a known test surface with the corresponding ideal numerically simulated PSD. The square root of the ratio of the measured and simulated PSD distributions gives the MTF of the instrument. In previous work [5], [6] the instrumental MTF of a surface profiler was precisely measured using reference test surfaces based on Binary Pseudo-Random (BPR) gratings. Here, we present results of fabricating and using two-dimensional (2D) BPR arrays that allow for a direct 2D calibration of the instrumental MTF. BPR sequences are widely used in engineering and communication applications such as Global Position System, and wireless communication protocols. The ideal BPR pattern has a flat 'white noise' response over the entire range of spatial frequencies of interest. The BPR array used here is based on the Uniformly Redundant Array prescription [7] initially used for x-ray and gamma ray astronomy applications. The URA's superior imaging capability originates from the fact that its cyclical autocorrelation function very closely approximates a delta function, which produces a flat PSD. Three different size BPR array patterns were fabricated by electron beam lithography and ICP etching of silicon. The basic size unit was 200 nm, 400 nm, and 600 nm. Two different etch processes were used, CF{sub 4}/Ar and HBr, which resulted in undercut and vertical sidewall profiles, respectively. The 2D BPR arrays were used as standard test surfaces for MTF calibration of the MicroMap{trademark}-570 interferometric microscope using all available objectives. The HBr etched two-dimensional BPR arrays have proven to be a very effective calibration standard making possible direct calibration corrections without the need of additional calculation considerations, while departures from the ideal vertical sidewall require an additional correction term for the CF{sub 4}/Ar etched samples. [8] Initial surface roughness of low cost 'prime' wafers limits low magnification calibration but should not be a limitation if better polished samples are used