Angular calibration of surface slope measuring profilers with a bendable mirror

Performance of state-of-the-art surface slope measuring profilers, such as the Advanced Light Source's (ALS) long trace profiler (LTP-II) and developmental LTP (DLTP) is limited by the instrument's systematic error. The systematic error is specific for a particular measurement arrangement and, in general, depends on both the measured surface slope value and the position along a surface under test. Here we present an original method to characterize or measure the instrument's systematic error using a bendable X-ray mirror as a test surface. The idea of the method consists of extracting the systematic error from multiple measurements performed at different mirror bendings. An optimal measurement strategy for the optic, under different settings of the benders, and the method of accurate fitting of the measured slope variations with characteristic functions are discussed. We describe the procedure of separation of the systematic error of an actual profiler from surface slope variation inherent to the optic. The obtained systematic error, expressed as a function of the angle of measurement, is useful as a calibration of the instrument arranged to measure an optic with a close curvature and length. We show that accounting for the systematic error enables the optimal setting of bendable optics to the desired ideal shape with accuracy limited only by the experimental noise. Application of the method in the everyday metrology practice increases the accuracy of the measurements and allows measurements of highly curved optics with accuracy similar to those achieved with flat optics. This work was supported by the U. S. Department of Energy under Contract No. DE-AC02-05CH11231.