SBIR-STTR Award

Numerical simulation of the performance of new x-ray mirror performed by NASA and those under upgrade requires sophisticated and reliable information about the expected surface slope and height distributions of prospective x-ray optics before the optics are fabricated. Ideally, such information has to be based on the metrology data obtained from existing optics fabricated by the same vendor and technology, but, generally, with different sizes and slope and height rms variations. It has been demonstrated that an optical surface can be thought of as a stationary uniform random process. It was further shown that an autoregressive moving average (ARMA) modeling of one-dimensional (1D) slope measurements allows highly confident fitting of the metrology x-ray mirrors data with a limited number of parameters. With the parameters of the ARMA model, the surface slope profile of an optic with the newly desired specification can be forecast reliably. However, ARMA models are causal and do not allow for generalization from one dimension to two. We propose to generalize the method from processing of one dimensional profile data to two dimensional surface data with invertible time-invariant linear filter (InTILF). This approach will also allow to parameterize surface metrology of high quality x-ray optics optimally. Our preliminary studies indicate that the InTILF approximation has all advantages of one-sided AR and ARMA modeling, but it additionally gains in terms of fewer filter parameters and better spectral accuracy. The envisioned software can also be used to analyze a polishing process and as a feedback for polishing tools.

For X-Ray optics, polishing the mirrors is one of the most costly steps in the fabrication of the system. BeatMark software will significantly decrease the cost of X-Ray mirror production. BeatMark will allow for parametrization of surface metrology data, which will be used as feedback for polishing parameter optimization and metrology experiment planning. By providing the parametrized optical surface description, BeatMark will optimize the costly polishing-and metrology cycle and enable numerical simulation of the performance of new X-Ray mirrors performed by NASA. BeatMark will help fulfill the requirements for sophisticated and reliable information about the expected surface slope and height distributions of prospective X-Ray optics before the optics are fabricated. As we demonstrated in Phase I, an optical surface can be thought of as a stationary uniform stochastic process and modeled with optimal Invertible Time Invariant Filters (InTILF). It was further shown that the modeling of one-dimensional (1D) slope measurements allows highly confident fitting of the X-Ray mirror metrology data with a limited number of parameters and a 10-15% reduction of required length of metrology profiles. Theoretically, a reduction of 50% is possible. In Phase II, we will conduct field tests to assess what reduction in metrology is practical and implementable. With the parameters of the InTILF model developed in Phase I, the surface slope profile of optics with a new specification can be forecast reliably. BeatMark will also process 2-D metrology data and provide a polishing optimization method, based on analysis of the mirror quality response to the polishing parameters. Our Phase I studies indicated that the optimal InTILF modeling describes the mirror surfaces with very few filter parameters and high spectral accuracy.