The optical design of the Long Trace Profiler optical system is explored with a commercial raytrace program, Zemax OpticStudio™ (ZOS)1, with the intent of finding and correcting sources of systematic error. ZOS provides both geometric raytracing tools and physical optics Gaussian beam propagation and diffraction image calculation tools, and two design modes, sequential component (SC) and non-sequential component (NSC) that are optimized for different aspects of the design process. The original LTP-II system employs a singlet lens with a 1250 mm focal length. It is optimized to provide minimum distortion over a surface slope angle range of ±5 mrad. Using the ZOS tools, we are able to simulate ghost rays that produce distortion in the beam spot image and can minimize the distortion by deliberate misalignment of the beamsplitter (BS) components. Unfortunately, the reference beam is compromised because of the component tilts. The most recent LTP500 system design simplifies the optical system and makes the reference beam usable again, even with misalignment of the polarizing beamsplitter (PBS). Two lenses are designed for the LTP500 - a cemented doublet that has been fabricated, and a singlet with one aspheric surface. Both have focal distances of 500 mm with an expanded angular measurement range of ±10 mrad. The aspheric singlet provides superior performance. ZOS allows the import of wavefront measurement data produced by commercial interferometer software. We apply the wavefront error measurement from the cemented doublet to the model to show that the 19nm RMS wavefront error needs to be improved by at least a factor of ten in order to reduce the systematic error to a level that will allow the LTP to approach its design limit of a few tens of nanoradians.

As early as 1989 [1,2], E. Church and P. Takacs presented a systematic theoretical foundation for characterization of X-ray optics in terms of imaging system performance, accounting for surface figure and finish errors. Physically, the distinction between figure and finish errors reflects two regimes of scattering, specular and diffuse scattering. In Refs. [1,2], both figure and finish of a mirror surface were treated statistically based on the power spectral density (PSD) distribution for the surface profile. Such an approach naturally leads to specification and characterization of figure and finish of X-ray optics in the terms of slope variation (rms) and roughness (rms), respectively. In the present work, we demonstrate the limitations of specification, characterization, and performance evaluation based on the totally statistical approach. The limitations arise due to the fundamentally deterministic character of the surface profile data at lower spatial frequency measured for a specific mirror. Due to the deterministic character of the mirror figure, detrending and windowing procedures usually applied to the measured profile before estimating the PSD distributions, can significantly effect the estimated PSD distributions. This in turn gives rise to uncertainty while evaluating system performance based on the PSD distribution. An example of a figure leading to a fatal performance violation is a two-facetted mirror surface. For such a surface the image intensity distribution consists of two peaks. To overcome these problems, we suggest an extension of the approach developed in Refs. [1,2]. The deterministic character of the surface finish is accounted for by a direct specular scattering calculation. In the simplest case, such a calculation can be performed with a ray-tracing code. For each ray-trace, image variation due to the finish errors are still treated statistically based on the PSD distribution measured at higher special frequencies. As a result, the image intensity distribution is estimated and compared with the parameters specified for the system. The effectiveness of the approach is demonstrated with a number of examples. We also propose a systematic method for the integration of our ideas into the development of a new level of 0.1 rad optics for 3rd and 4th generation sources, including new and more accurate Long Trace Profilers, and the establishment of International standards for evaluation of the PSD at specific frequencies. This work was supported by the U. S. Department of Energy under contract number DE- AC02-05CH11231. Keywords: X-ray optics metrology, power spectral density, X-ray optics specification [1] E. L. Church and P. Z. Takacs, Specification of surface figure and finish in terms of system performance, Applied Optics 32(19), 3344-53 (1993).[2] E. L. Church and P. Z. Takacs, Specification of glancing- and normal-incidence X-ray mirrors, Optical Engineering 34(2), 353-60 (1995).

The major problem of measurement of a power spectral density (PSD) distribution of the surface heights with surface profilometers arises due to the unknown Modulation Transfer Function (MTF) of the instruments. The MTF tends to distort the PSD at higher spatial frequencies. It has been suggested (Proc. SPIE 7077-7, 2007) that the instrumental MTF of a surface profiler can be precisely measured using standard test surfaces based on binary pseudo random (BPR) patterns. In the cited work, a one dimensional (1D) realization of the suggested method based on use of BPR gratings has been demonstrated. Here, we present recent achievements made in fabricating and using two-dimensional (2D) BPR arrays that allow for a direct 2D calibration of the instrumental MTF. The 2D BPRAs were used as standard test surfaces for MTF calibration of the MicroMapTM-570 interferometric microscope with all available objectives. The effects of fabrication imperfections on efficiency of calibration are also discussed.

The thorough realization of the advantages of the new generation x-ray light sources, such as the Upgraded Advanced Light Source (ALS-U) under construction, requires near-perfect x-ray optics, capable of delivering light without significant degradation of brightness and coherence. The stringent requirements of beamline optics drive the state of the art in ex situ optical metrology. Here, we present the results of the ongoing efforts at the ALS X-Ray Optics Laboratory to develop a new generation long trace profiler, LTP-2020. We discuss the system design that incorporates different types of surface slope sensors. In addition to the classical pencil beam interferometry (PBI) sensor with an improved optical design, we develop a deflectometry sensor based on a customized electronic autocollimator (AC). By applying a new data processing algorithm to the AC raw image data available from the customized AC, we significantly reduce the quasi-periodic systematic error of the AC equipped with a small size aperture. We also treat the possibility to use the AC as a PBI sensor with external light beam sources based on super-luminescent emitting diode (SLED) and single-mode laser diode (SMLD). Operation modes with stationary and/or translated sensors are possible due to the two-carriage gantry system with adjustable vertical position. The variety of the available operation modes allows optimization of the LTP-2020 experimental arrangement for providing the best possible performance in measurements with state-of-the-art aspherical x-ray optics, variable-line-spacing diffraction gratings, and multi-element optical systems.

To fully exploit the advantages of fourth-generation synchrotron light sources, diffraction-limited-storage-rings (DLSR) and fully coherent free electron lasers (FELs), beamline mirrors and diffraction grating must be of exceptional quality. To achieve the required mirror and grating quality, the metrology instrumentation and methods used to characterize these challenging optics and, even more so, optical assemblies must also offer exceptional functionality and performance. One of the most widely used slope measuring instruments for characterizing x-ray optics is the long trace profiler (LTP). The easily reconfigurable mechanical design of the LTP allows optimization of the profiler arrangement to the specifics of a particular metrology task. Here, we discuss the optical schematic, design, and performance of an original multifunctional light beam source that provides functional flexibility of the LTP optical sensor. With this source, the LTP can be easily reconfigured for measurements of x-ray mirrors or diffraction gratings that have widely different source coherence requirements. Usage of a source with a low degree of coherence for mirror metrology helps to suppress the LTP systematic errors due to spurious interference effects in the LTP optical elements. A high-coherence narrow-band source is used for groove-density-distribution characterization of x-ray diffraction gratings. The systematic error and spatial resolution of the LTP with the different sources is also measured and analyzed.

The advents of fully coherent free electron lasers and diffraction limited synchrotron storage ring sources of x-rays are catalyzing the development of new, ultra-high accuracy metrology methods. To fully exploit the potential of these sources, metrology needs to be capable of determining the figure of an optical element with sub-nanometer height accuracy. Currently, the two most prevalent slope measuring instruments used for characterization of x-ray optics are the auto-collimator based nanometer optical measuring device (NOM) and the long trace profiler (LTP) using pencil beam interferometry (PBI). These devices have been consistently improved upon by the x-ray optics metrology community, but appear to be approaching their metrological limits. Here, we revise the traditional optical schematic of the LTP. We experimentally show that, for the level of accuracy desired for metrology with state-of-the-art x-ray optics, the Dove prism in the LTP reference channel appears to be one of the major sources of instrumental error. Therefore, we suggest returning back to the original PBI LTP schematics with no Dove prism in the reference channel. In this case, the optimal scanning strategies [Yashchuk, Rev. Sci. Instrum. 80, 115101 (2009)] used to suppress the instrumental drift error have to be used to suppress a possible drift error associated with laser beam pointing instability. We experimentally and by numerical simulation demonstrate the usefulness of the suggested approach for measurements with x-ray optics with both face up and face down orientations.

The reliability of the instrument transfer function (ITF) calibration technique based on binary pseudo-random array (BPRA) standards is investigated and demonstrated in application to interferometric microscopes. We demonstrate the linearity of the calibration (that is, independence of the ITF calibration on the standards root-mean-square roughness) via comparison of the ITF measurements with a number of artifacts with the etched depth varying from 30 nm to 120 nm. We also show that the calibration does not depend on the surface reflectivity, at least in the range between ∼36% and ∼80%. The criteria for selection of the geometrical parameters of the BPRA standard design appropriate for a particular interferometric microscope arrangement (including optical magnification), as well as the data acquisition and analysis procedures for different applications are also discussed.

We investigate and compare the spatial (lateral) resolution, or more generally, the optical/instrumental transfer function (OTF/ITF) of surface slope measuring profilometers of two different types that are commonly used for high accuracy characterization of x-ray optics at the long-spatial-wavelength range. These are an autocollimator based profiler, Optical Surface Measuring System (OSMS), and a long trace profiler, LTP-II, both available at the Advanced Light Source (ALS) XË-Ray Optics Lab (XROL). In the OSMS, an ELCOMAT-3000 electronic auto-collimator, vertically mounted to the translation carriage and equipped with an aperture of 2.5 mm diameter, is scanned along the surface under test. The LTPË-II OTF has been measured for two different configurations, a classical two-beam pencil-beam-interferometry and a single-Gaussian-beam deflectometry. For the ITF calibration, we apply a recently developed method based on test surfaces with one-dimensional (1D) linear chirped height profiles of constant slope amplitude. Analytical expressions for the OTFs, empirically deduced based on the experimental results, are presented. We also discuss the application of the results of the ITF measurements and modeling to improve the surface slope metrology with state-of-The-Art x-ray mirrors. This work was supported by the U. S. Department of Energy under contract number DE-AC02-05CH11231.