Methods for compensating for crystal structure differential material removal rates in sub-aperture figuring processes

1 . A method comprising:

receiving, at a computing machine comprising processing circuitry and memory, an input related to a substrate crystal wherein the computing machine generates a first data set based on the input, wherein the input comprises imagery from at least two sensor positions, and wherein a surface map data structure comprises a three-dimensional model of the substrate crystal generated based on information representing the at least two sensor positions, the information representing the at least two sensor positions being stored in the memory;

generating with the computing machine, based on the input, the surface map data structure for the substrate crystal and a second data set based on the surface map data structure, wherein generating the surface map data structure comprises:

identifying, with the computing machine, at least two different crystal planes of the substrate crystal;

identifying, with the computing machine, an optical surface prescription in the input; and

determining one or more local tilt angles based on the optical surface prescription;

generating with the computing machine, based on the surface map data structure, a figuring route data structure for a figuring tool to figure the substrate crystal, wherein the figuring route data structure comprises a third data set, wherein the figuring route data structure compensates for crystal structure differential material removal rate due to the presence of the at least two different crystal planes of the substrate crystal; and

controlling, using the processing circuitry and based on the figuring route data structure, the figuring tool to figure the substrate crystal.

2 . The method of claim 1 , wherein generating the figuring route data structure further comprises:

performing a figuring run on a reference substrate, made of a same material as the substrate crystal, using the surface map data structure to calculate one or more compensation factors or a predicted figure error to generate the third data set, wherein the figuring route data structure compensates for the crystal structure differential material removal rates due to the presence of the at least two different crystal planes of the substrate crystal.

3 . The method of claim 1 , further comprising:

computing, based on at least the surface map data structure or the figuring route data structure, a differential rate of removal for the figuring tool to figure the substrate crystal, wherein the figuring tool is controlled based on the differential rate of removal.

4 . The method of claim 1 , wherein the substrate crystal comprises CaF 2 or MgF 2 .

5 . The method of claim 1 , further comprising:

storing, in the memory, the surface map data structure, wherein the surface map data structure is a three-dimensional mapping data structure; and

storing, in the memory, the figuring route data structure, wherein the figuring route data structure is a data structure for representing a path on a map.

6 . A system comprising:

processing circuitry; and

memory storing instructions which, when executed by the processing circuitry, cause the processing circuitry to perform operations comprising:

receiving an input related to a substrate crystal that comprises at least two different crystal planes, each of the at least two different crystal planes having a different rate of material removal, wherein the input comprises imagery from at least two sensor positions;

generating, based on the input, a surface map data structure for the substrate crystal, wherein the surface map data structure comprises a three-dimensional model of the substrate crystal generated based on information representing the at least two sensor positions, wherein generating the surface map data structure comprises:

identifying the at least two different crystal planes;

identifying an optical surface prescription in the input; and

determining one or more local tilt angles based on the optical surface prescription;

generating, based on the surface map data structure, a figuring route data structure for a figuring tool to figure the substrate crystal; and

controlling, based on the figuring route data structure, the figuring tool to figure the substrate crystal;

wherein the figuring route data structure compensates for crystal structure differential material removal rates due to the presence of the at least two different crystal planes of the substrate crystal.

7 . The system of claim 6 , further comprising:

two or more sensors, wherein the input is received from the two or more sensors.

8 . The system of claim 4 , wherein the information representing the at least two sensor positions is stored in the memory.

9 . A system comprising:

processing circuitry; and

memory storing instructions which, when executed by the processing circuitry, cause the processing circuitry to perform operations comprising:

receiving an input related to a substrate crystal that comprises at least two different crystal planes, wherein the input comprises imagery from at least two sensor positions;

generating, based on the input, a surface map data structure for the substrate crystal, wherein the surface map data structure comprises a three-dimensional model of the substrate crystal generated based on information representing the at least two sensor positions, wherein generating the surface map data structure comprises:

identifying the at least two different crystal planes;

identifying an optical surface prescription in the input; and

determining one or more local tilt angles based on the optical surface prescription;

generating, based on the surface map data structure, a figuring route data structure for a figuring tool to figure the substrate crystal;

controlling, based on the figuring route data structure, the figuring tool to figure the substrate crystal; and

computing, based on at least the surface map data structure or the figuring route data structure, a differential rate of removal for the figuring tool to figure the substrate crystal, wherein the figuring tool is controlled based on the differential rate of removal.