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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 develop

The development of deterministic polishing techniques has given rise to vendors that manufacture high quality threedimensional x-ray optics. The surface metrology on these optics remains a difficult task. For the fabrication, vendors usually use unique surface metrology tools, generally developed on site, that are not available in the optical metrology labs at x-ray facilities. At the Advanced Light Source X-Ray Optics Laboratory, we have developed a rather straightforward interferometric-microscopy-based procedure capable of sub microradian characterization of sagittal slope variation of x-ray optics for two-dimensionally focusing and collimating (such as ellipsoids, paraboloids, etc.). In the paper, we provide the mathematical foundation of the procedure and describe the related instrument calibration. We also present analytical expression describing the ideal surface shape in the sagittal direction of a spheroid specified by the conjugate parameters of the optic's beamline application. The expression is useful when analyzing data obtained with such optics. The high efficiency of the developed measurement and data analysis procedures is demonstrated in results of measurements with a number of x-ray optics with sagittal radius of curvature between 56 mm and 480 mm. We also discuss potential areas of further improvement.