We present experimental, analytical, and numerical methods developed for reconstruction (deconvolution) of one-dimensional (1D) surface slope profiles over the spatial frequency range where the raw data are significantly perturbed due to the limited resolution of the measurement instrument. We characterize the spatial resolution properties of a profiler with the instrument's transfer function (ITF). To precisely measure the ITF, we apply a recently developed method utilizing test surfaces with 1D linear chirped height profiles of constant slope amplitude. Based on the results of the ITF calibration, we determine parameters of an analytical model for the ITF that is used in the original reconstruction software. Here, we treat surface slope metrology data obtained with the Optical Surface Measuring System (OSMS), using as a sensor an electronic autocollimator (AC) ELCOMAT-3000. The spatial resolution of the OSMS is limited by the size of the AC light-beam-collimating aperture. For the purposes of this investigation, the OSMS is equipped with a circular aperture with a diameter of 2.5 mm. This is a typical arrangement of most AC-based slope profilers developed for surface slope metrology of state-of-the-art x-ray mirrors. Using the example of surface slope metrology of two state-of-the-art elliptically shaped x-ray focusing mirrors, we demonstrate that the developed data reconstruction procedure allows us to significantly improve the accuracy of surface slope metrology with the OSMS over the spatial wavelength range from ∼1.6 mm to 7 mm. Thus, the amplitude of the quasi-periodic error characteristic of the deterministic polishing process used appears to be higher by a factor of ∼2 than is apparent from the rough metrology data. Underestimation of the surface slope errors in this spatial wavelength range can lead to serious errors in the expected performance of x-ray mirrors in synchrotron beamlines, especially at modern light sources utilizing coherent x rays, where the perturbations can lead to increased speckle-like intensity variation.

Improvements in the quality of synchrotron beamline x-ray optics required for next-generation light sources (e.g. the ALS Upgrade project) drive the need to improve the performance of the metrology instrumentation used to measure these components. The Long Trace Profiler (LTP) that is in use at many synchrotron metrology laboratories around the world has some known issues that affect the accuracy of its measurements. The main error source is optical path difference (OPD) phase error introduced into the probe beam by inhomogeneities in the glass components used in the optical head. We have developed a new optical head design, LTP-2020, that replaces the cube polarizing beamsplitter (PBS) with a thin wedge plate polarizing beamsplitter (WPBS) and replaces the cemented doublet lens with an aspheric singlet. Both of these components significantly reduce the glass volume traversed by the laser probe beam. Careful attention to ghost ray interference produced by back reflection from optical surfaces is necessary to minimize distortion in the primary image that translates into systematic error in the slope angle measurement. We make extensive use of a commercial raytracing program to model the back reflections and adjust component parameters as necessary to minimize distortion. Deliberate misalignment of components is necessary to make the system perform correctly. Stringent requirements are placed on the 45◦ incidence coatings on the WPBS and on the normal incidence coatings on the lens and camera window elements. We encourage our colleagues who wish to upgrade their current LTP systems to join us in the procurement of these custom optical components.

The advent of fully coherent free-electron laser and diffraction-limited synchrotron radiation storage ring sources of x-rays is catalyzing the development of new ultrahigh accuracy metrology methods. To fully exploit these sources, metrology needs to be capable of determining the figure of an optical element with subnanometer height accuracy. The major limiting factors of the current absolute accuracy of ex situ metrology are drift errors due to temporal instabilities of the lab's environmental conditions and systematic errors inherent to the metrology instruments. Here, we discuss in detail work at the Advanced Light Source X-Ray Optics Laboratory on building of advanced environmental control that is a key component in the development of ultrahigh accuracy ex situ metrology for x-ray optics. By a few examples, we show how the improvement of the environmental conditions in the lab allows us to significantly gain efficiency in performing ex situ metrology with high-quality x-ray mirrors. The developed concepts and approaches, included in the design of the new X-Ray Optics Laboratory, are described in detail. These data are essential for construction and successful operation of a modern metrology facility for x-ray optics, as well as high-precision measurements in many fields of experimental physics.

Super high quality aspherical x-ray mirrors with a residual slope error of ∼100 nrad (root-mean-square) and a height error of ∼1-2 nm (peak-to-valley), and even lower, are now available from a number of the most advanced vendors utilizing deterministic polishing techniques. The mirror specification for the fabrication is based on the simulations of the desired performance of the mirror in the beamline optical system and is normally given with the acceptable level of deviation of the mirror figure and finish from the desired ideal shape. For example, in the case of aspherical x-ray mirrors designed for the Advanced Light Source (ALS) QERLIN beamline, the ideal shape is defined with the beamline application (conjugate) parameters and their tolerances. In this paper, we first discuss an original procedure and dedicated software developed at the ALS X-Ray Optics Laboratory (XROL) for optimization of beamline performance of pre-shaped hyperbolic and elliptical mirrors. The optimization is based on results of ex situ surface slope metrology and consists in minimization of the mirror shape error by determining the conjugate parameters of the best-fit ideal shape within the specified tolerances. We describe novel optical metrology instrumentation, measuring techniques, and analytical methods used at the XROL for acquisition of surface slope data and optimization of the optic's beamline performance. The high efficacy of the developed experimental methods and data analysis procedures is demonstrated in results of measurements with and performance optimization of hyperbolic and elliptical cylinder mirrors designed and fabricated for the ALS QERLIN beamline.

The development of fully coherent free electron lasers and diffraction limited storage ring x-ray sources has brought to focus the need for higher performing x-ray optics with unprecedented tolerances for surface slope and height errors and roughness. For example, the proposed beamlines for the future upgraded Advance Light Source, ALS-U, require optical elements characterized by a residual slope error of <100 nrad (root-mean-square) and height error of <1-2 nm (peak-tovalley). These are for optics with a length of up to one meter. However, the current performance of x-ray optical fabrication and metrology generally falls short of these requirements. The major limitation comes from the lack of reliable and efficient surface metrology with required accuracy and with reasonably high measurement rate, suitable for integration into the modern deterministic surface figuring processes. The major problems of current surface metrology relate to the inherent instrumental temporal drifts, systematic errors, and/or an unacceptably high cost, as in the case of interferometry with computer-generated holograms as a reference. In this paper, we discuss the experimental methods and approaches based on correlation analysis to the acquisition and processing of metrology data developed at the ALS X-Ray Optical Laboratory (XROL). Using an example of surface topography measurements of a state-of-the-art x-ray mirror performed at the XROL, we demonstrate the efficiency of combining the developed experimental correlation methods to the advanced optimal scanning strategy (AOSS) technique. This allows a significant improvement in the accuracy and capacity of the measurements via suppression of the instrumental low frequency noise, temporal drift, and systematic error in a single measurement run. Practically speaking, implementation of the AOSS technique leads to an increase of the measurement accuracy, as well as the capacity of ex situ metrology by a factor of about four. The developed method is general and applicable to a broad spectrum of high accuracy measurements.

A new type of optical element that can focus a cylindrical wave to a point focus (or vice versa) is analytically described. Such waves are, for example, produced in a beamline where light is collimated in one direction and then doubly focused by a single optic. A classical example in X-ray optics is the collimated two-crystal monochromator, with toroidal mirror refocusing. The element here replaces the toroid, and in such a system provides completely aberration free, point-to-point imaging of rays from the on-axis source point. We present an analytic solution for the mirror shape in its laboratory coordinate system with zero slope at the centre, and approximate solutions, based on bending an oblique circular cone and a bent right circular cylinder, that may facilitate fabrication and metrology.

Modern deterministic polishing processes allow fabrication of x-ray optics with almost any arbitrary aspherical surface shape. Among these optics, the so called "diaboloid"mirror is of special interest. The diaboloid mirror that converts a cylindrical wave to a spherical wave would improve focusing in x-ray beamlines implementing a diffraction element between a parabolic cylinder and a toroidal mirror. The replacement of the toroidal mirror in existing beamlines by the diaboloid mirror would mitigate aberrations. The shape of the diaboloid mirror is usually calculated numerically based on a truncated polynomial solution of the optical path problem. Here, we present an exact analytical solution for the shape of a diaboloid mirror as a function of the conjugate parameters of the mirror placed in a beamline. The derived analytical expressions for the diaboloid mirror in both the canonical and mirror-based coordinate systems are implemented in ray-tracing simulations to verify the beamline performances.

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.

We discuss experimental, analytical, and numerical methods recently developed at the Advanced Light Source (ALS) X?Ray Optics Laboratory (XROL) for calibration and precision shaping of bendable x-ray mirrors. The methods are based on ex situ measurements with the mirrors using surface slope profilers available at the ALS XROL. The first realization of methods and dedicated software has allowed the optimization of the beamline performance of bendable mirrors by adjustment of the mirror shape to minimize the root-mean-square variation of residual (after subtraction of the ideal desired shape) slope deviations from ideal (specified) surface figure. Here, we further develop the methods that in application to elliptically bent mirrors adapt as a figure of merit the minimum of the rms size of the focused beam. The efficacy of the developed methods is demonstrated with examples of optimal tuning of an elliptically bendable cylindrical mirror designed for the ALS beamline 10.3.2.