Stochastic analysis of 1D and 2D surface topography of x-ray mirrors

摘要

The design and evaluation of the expected performance of new optical systems requires sophisticated and reliable information about the surface topography for planned optical elements before they are fabricated. The problem is especially complex in the case of x-ray optics, particularly for the X-ray Surveyor under development and other missions. Modern x-ray source facilities are reliant upon the availability of optics with unprecedented quality (surface slope accuracy < 0.1 μrad). The high angular resolution and throughput of future x-ray space observatories requires hundreds of square meters of high quality optics. The uniqueness of the optics and limited number of proficient vendors makes the fabrication extremely time consuming and expensive, mostly due to the limitations in accuracy and measurement rate of metrology used in fabrication. We discuss improvements in metrology efficiency via comprehensive statistical analysis of a compact volume of metrology data. The data is considered stochastic and a new statistical model called Invertible Time Invariant Linear Filter (InTILF) is developed now for 2D surface profiles to provide compact description of the 2D data additionally to 1D data treated so far. The model captures faint patterns in the data and serves as a quality metric and feedback to polishing processes, avoiding high resolution metrology measurements over the entire optical surface. The modeling, implemented in our Beatmark software, allows simulating metrology data for optics made by the same vendor and technology. The forecast data is vital for reliable specification for optical fabrication, to be exactly adequate for the required system performance.