Hybrid diversity method utilizing adaptive diversity function for recovering unknown aberrations in an optical system

• US 7,635,832 B2
• Filed: 08/31/2006
• Issued: 12/22/2009
• Est. Priority Date: 08/31/2005
• Status: Active Grant

• Current Assignee: United States Of America As Represented By The Administrator Of The National Aeronautics And Space Administration
• Original Assignee: United States Of America As Represented By The Administrator Of The National Aeronautics And Space Administration
• Inventors: Dean, Bruce H.
• Primary Examiner(s): LE, QUE TAN
• Application Number:
  US11/469,105
• Publication Number:
  US 20080040077A1
• Time in Patent Office: 1,209 Days
• Field of Search: 250/216, 2502012-2017, 250/208.1, 382/103, 382/167, 382254-275, 359/618, 359/626, 359/639, 359707-722, 359/749, 359/775
• US Class Current: 250/208.1
• CPC Class Codes: G01M 11/005 Testing of reflective surfaces, e.g. mirrors
• CPC Class Codes: G03F 7/705 Modelling or simulating from physical phenomena up to complete wafer processes or whole workflow in wafer productions
• CPC Class Codes: G03F 7/706 Aberration measurement

Abstract

A method of recovering unknown aberrations in an optical system includes collecting intensity data produced by the optical system, generating an initial estimate of a phase of the optical system, iteratively performing a phase retrieval on the intensity data to generate a phase estimate using an initial diversity function corresponding to the intensity data, generating a phase map from the phase retrieval phase estimate, decomposing the phase map to generate a decomposition vector, generating an updated diversity function by combining the initial diversity function with the decomposition vector, generating an updated estimate of the phase of the optical system by removing the initial diversity function from the phase map. The method may further include repeating the process beginning with iteratively performing a phase retrieval on the intensity data using the updated estimate of the phase of the optical system in place of the initial estimate of the phase of the optical system, and using the updated diversity function in place of the initial diversity function, until a predetermined convergence is achieved.

Claims

1. A method of recovering unknown aberrations in an optical system, comprising:

collecting intensity data produced by the optical system;

generating an initial estimate of a phase of the optical system;

iteratively performing a phase retrieval on the intensity data to generate a phase estimate using an initial diversity function corresponding to the intensity data;

generating a phase map from the phase retrieval phase estimate;

decomposing the phase map to generate a decomposition vector;

generating an updated diversity function by combining the initial diversity function with the decomposition vector;

generating an updated estimate of the phase of the optical system by removing the initial diversity function from the phase map; and

repeating the process beginning with iteratively performing a phase retrieval on the intensity data using the updated estimate of the phase of the optical system in place of the initial estimate of the phase of the optical system, and using the updated diversity function in place of the initial diversity function, until a predetermined convergence is achieved.

2. The method of claim 1, wherein the intensity data is generated in response to a source selected from the group consisting of a point source, an extended known source, and an extended unknown source.

3. The method of claim 1, wherein the intensity data comprises broadband data.

4. The method of claim 1, further comprising introducing a known aberration into the optical system prior to collecting intensity data.

5. The method of claim 4, wherein the known aberration comprises at least one of piston, tip, tilt, defocus, astigmatism, coma, spherical, and trefoil.

6. The method of claim 4, wherein the known aberration is at least an order of magnitude greater than a largest expected unknown aberration.

7. The method of claim 1, wherein generating an initial estimate of a phase of the optical system comprises presuming the phase to have a predetermined value.

8. The method of claim 1, wherein decomposing the phase map comprises decomposing the phase map into a basis set suitable for a given sampling and aperture shape of the optical system.

9. The method of claim 1, wherein the predetermined convergence is a residual RMS wavefront error of less than a wavelength of the intensity data.

10. A method of recovering unknown aberrations in an optical system, comprising:

introducing one or more known aberrations into the optical system;

for each known aberration, collecting a set of intensity data produced by the optical system;

generating an initial estimate of a phase of the optical system;

iteratively performing a phase retrieval on each set of the intensity data to generate a phase estimate using an initial diversity function corresponding to the sets of the intensity data;

combining each of the phase retrieval phase estimates to generate a phase map;

decomposing the phase map to generate a decomposition vector;

generating an updated diversity function by combining the initial diversity function with the decomposition vector;

generating an updated estimate of the phase of the optical system by removing the initial diversity function from the phase map; and

repeating the process beginning with iteratively performing a phase retrieval on each set of the intensity data using the updated estimate of the phase of the optical system in place of the initial estimate of the phase of the optical system, and using the updated diversity function in place of the initial diversity function, until a predetermined convergence is achieved.

11. The method of claim 10, wherein the intensity data is generated in response to a source selected from the group consisting of a point source, an extended known source, and an extended unknown source.

12. The method of claim 10, wherein the intensity data comprises broadband data.

13. The method of claim 10, wherein the one or more known aberrations are chosen from piston, tip, tilt, defocus, astigmatism, coma, spherical, and trefoil.

14. The method of claim 10, wherein the one or more known aberrations comprise defocus.

15. The method of claim 10, wherein combining each of the phase retrieval phase estimates comprises generating a weighted average of the individual phase retrieval phase estimates.

16. The method of claim 10, wherein combining each of the phase retrieval phase estimates further comprises filtering the phase retrieval phase estimates prior to generating the phase map.

17. The method of claim 10, wherein generating an initial estimate of a phase of the optical system comprises presuming the phase to have a predetermined value.

18. The method of claim 10, wherein decomposing the phase map comprises decomposing the phase map into a basis set suitable for a given sampling and aperture shape of the optical system.

19. The method of claim 10, wherein the predetermined convergence is a residual RMS wavefront error of less than a wavelength of the intensity data.

20. The method of claim 10, further comprising:

generating updated intensity data using at least some components of the updated diversity function; and

comparing the updated intensity data with the collected intensity data to validate convergence.