Minimizing Artifacts in Analysis of Surface Statistics

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Accuracy Limitations in Long Trace Profilometry

As requirements for surface slope error quality of grazing incidence optics approach the 100 nanoradian level, it is necessary to improve the performance of the measuring instruments to achieve accurate and repeatable results at this level. We have identified a number of internal error sources in the Long Trace Profiler (LTP) that affect measurement quality at this level. The LTP is sensitive to phase shifts produced within the millimeter diameter of the pencil beam probe by optical path irregularities with scale lengths of a fraction of a millimeter. We examine the effects of mirror surface ''macroroughness'' and internal glass homogeneity on the accuracy of the LTP through experiment and theoretical modeling. We will place limits on the allowable surface ''macroroughness'' and glass homogeneity required to achieve accurate measurements in the nanoradian range

Significant improvements in long trace profiler measurement performance

A Modifications made to the Long Trace Profiler (LTP II) system at the Advanced Photon Source at Argonne National Laboratory have significantly improved the accuracy and repeatability of the instrument The use of a Dove prism in the reference beam path corrects for phasing problems between mechanical efforts and thermally-induced system errors. A single reference correction now completely removes both error signals from the measured surface profile. The addition of a precision air conditioner keeps the temperature in the metrology enclosure constant to within {+-}0.1{degrees}C over a 24 hour period and has significantly improved the stability and repeatability of the system. We illustrate the performance improvements with several sets of measurements. The improved environmental control has reduced thermal drift error to about 0.75 microradian RMS over a 7.5 hour time period. Measurements made in the forward scan direction and the reverse scan direction differ by only about 0.5 microradian RMS over a 500mm, trace length. We are now able to put 1-sigma error bar of 0.3 microradian on an average of 10 slope profile measurements over a 500mm long trace length, and we are now able to put a 0.2 microradian error bar on an average of 10 measurements over a 200mm trace length. The corresponding 1-sigma height error bar for this measurement is 1.1 run

Exact Maximal Height Distribution of Fluctuating Interfaces

We present an exact solution for the distribution P(h_m,L) of the maximal height h_m (measured with respect to the average spatial height) in the steady state of a fluctuating Edwards-Wilkinson interface in a one dimensional system of size L with both periodic and free boundary conditions. For the periodic case, we show that P(h_m,L)=L^{-1/2}f(h_m L^{-1/2}) for all L where the function f(x) is the Airy distribution function that describes the probability density of the area under a Brownian excursion over a unit interval. For the free boundary case, the same scaling holds but the scaling function is different from that of the periodic case. Numerical simulations are in excellent agreement with our analytical results. Our results provide an exactly solvable case for the distribution of extremum of a set of strongly correlated random variables.Comment: 4 pages revtex (two-column), 1 .eps figure include

Penta-prism long trace profiler (PPLTP) for measurement of grazing incidence space optics

The Long Trace Profiler (LTP) is in use at a number of locations throughout the world for the measurement of the figure and mid- frequency roughness of x-ray mirrors. The standard configuration requires that the surface tested lie in a horizontal plane as the optical head is scanned along a horizontal line. For applications where gravity-induced sag of the surface cannot be tolerated, such as in x-ray telescope mirror metrology, it is desirable to measure the mirror as it is mounted in a vertical configuration. By making simple modifications to the standard LTP system, we have demonstrated that it is possible to use the LTP principle to measure the surface of x- ray mirrors and mandrels mounted in the vertical orientation. The major change in the LTP system is the use of a penta prism on a vertical translation stage to direct the probe beam onto the surface and the addition of a precision rotation stage to hold the test object. A 3-D map of the surface topography of the complete cylindrical asphere can be generated quite easily with this technique. Measurements with a prototype system indicate a slope error accuracy of better than 1 microradian is possible, with a figure error repeatability of better than 50 nm. 19 refs., 4 figs

Synchrotron radiation and precision mirror metrology with a long trace profiler

The Long Trace Profiler (LTP) is in use at several synchrotron radiation (SR) laboratories throughout the world and by a number of manufacturers who specialize in making grazing incidence mirrors for SR customers. Recent improvements in the design and operation of the LTP system have reduced the slope profile error bar to the level of 0.3 microradians RMS over measurement lengths of 0.5 meter. This corresponds to a height error bar on the order of 20 nanometers. This level of performance allows one to measure with confidence the shape of large cylinders and spheres that have kilometer radii of curvature in the axial direction. The LTP is versatile enough to make measurements of a mirror in the face up, sideways, and face down configurations. The authors will illustrate the versatility of the current version of the instrument, the LTP II, and present results from two new versions of the instrument: the in-situ LTP (ISLTP) and the Vertical Scan LTP (VSLTP). Both of them are based on the penta-prism LTP (ppLTP) principle with a stationary optical head and moving penta-prism. The ISLTP is designed to measure the distortion of high heat load mirrors during actual operation in SR beam lines. The VSLTP is designed to measure the complete 3-dimensional shape of x-ray telescope cylinder mirrors and mandrels in a vertical configuration. Scans are done both in the axial direction and in the azimuthal direction

Towards Precision LSST Weak-Lensing Measurement - I: Impacts of Atmospheric Turbulence and Optical Aberration

The weak-lensing science of the LSST project drives the need to carefully model and separate the instrumental artifacts from the intrinsic lensing signal. The dominant source of the systematics for all ground based telescopes is the spatial correlation of the PSF modulated by both atmospheric turbulence and optical aberrations. In this paper, we present a full FOV simulation of the LSST images by modeling both the atmosphere and the telescope optics with the most current data for the telescope specifications and the environment. To simulate the effects of atmospheric turbulence, we generated six-layer phase screens with the parameters estimated from the on-site measurements. For the optics, we combined the ray-tracing tool ZEMAX and our simulated focal plane data to introduce realistic aberrations and focal plane height fluctuations. Although this expected flatness deviation for LSST is small compared with that of other existing cameras, the fast f-ratio of the LSST optics makes this focal plane flatness variation and the resulting PSF discontinuities across the CCD boundaries significant challenges in our removal of the systematics. We resolve this complication by performing PCA CCD-by-CCD, and interpolating the basis functions using conventional polynomials. We demonstrate that this PSF correction scheme reduces the residual PSF ellipticity correlation below 10^-7 over the cosmologically interesting scale. From a null test using HST/UDF galaxy images without input shear, we verify that the amplitude of the galaxy ellipticity correlation function, after the PSF correction, is consistent with the shot noise set by the finite number of objects. Therefore, we conclude that the current optical design and specification for the accuracy in the focal plane assembly are sufficient to enable the control of the PSF systematics required for weak-lensing science with the LSST.Comment: Accepted to PASP. High-resolution version is available at http://dls.physics.ucdavis.edu/~mkjee/LSST_weak_lensing_simulation.pd