Dispersive null-optics for aspheric surface and wavefront metrology

• US 20030128368A1
• Filed: 11/05/2002
• Published: 07/10/2003
• Est. Priority Date: 11/15/2001
• Status: Active Grant

• Current Assignee: Zygo Corporation (Ametek Incorporated)
• Original Assignee: Zygo Corporation (Ametek Incorporated)
• Inventors: Kuchel, Michael
• Granted Patent: US 6,717,679 B2
• Time in Patent Office: Days
• US Class Current: 356/512
• CPC Class Codes: G01B 11/2441 using interferometry
• CPC Class Codes: G01B 9/02039 by matching the wavefront with a particular object surface shape

Abstract

Interferometric method and apparatus for measuring aspheric surfaces and wavefronts by directing a spherical wavefront of known design at a wavelength λ₁ at a reference sphere with known measured surface properties to generate a first electronic signal containing information about the optical path differences between the reference and measurement wavefronts generated an interferometer and directing an aspherical wavefront of known design at a wavelength λ₂ at an aspherical surface or wavefront to be tested to generate a second electronic signal containing information about the optical path differences between the reference and measurement wavefronts generated by the interferometer. The first and second electronic signals are analyzed and calculated therefrom are wavefront error maps W₁=W₁(λ₁) and W₂=W₂(λ₂), both of which contain wavelength dependent known design and measured errors and unknown errors due to the manufacture, material composition of components in the interferometer, and systematic errors. Optical path length errors caused by shape errors in the aspherical surface or wavefront are determined while accounting for substantially all error sources present in the electronic signals to provide for enhanced precision.

Claims

1. A method for measuring aspheric surfaces and wavefronts with the use of an interferometer;

said method comprising the steps of;

directing a spherical wavefront of known design at a wavelength λ

₁ at a reference sphere with known measured surface properties to generate a first electronic signal containing information about the optical path differences between the reference and measurement wavefronts generated by the interferometer;

directing an apherical wavefront of known design at a wavelength λ

₂ at an aspherical surface or wavefront to be tested to generate a second electronic signal containing information about the optical path differences between the reference and measurement wavefronts generated by the interferometer

analyzing said first and second electronic signals and calculating therefrom wavefront error maps W₁=W₁(λ

₁) and W₂=W₂(λ

₂) both of which contain wavelength dependent known design and measured errors and unknown errors due to the manufacture, material composition of components in the interferometer, and systematic errors; and

determining the optical path error caused by shape errors in the aspherical surface or wavefront while accounting for substantially all error sources present in the electronic signals.

2. The method of claim 1 wherein the optical path length error caused by shape errors in the aspherical surface or wavefront is of the form:

3. The method of claim 2 further including the step of determining the Known Errors in the surface shapes and materials of the interferometer components by one of measurement and calculation procedures.

4. The method of claim 3 further including the step of reducing the Unknown Errors to the form:

opd_{manufacturingerror}(λ

₂−

λ

₁);

estimating opd_{manufacturingerror}; and

calculating the final error A using the determined values for [(Known Errors=f(λ

₁,λ

₂))+(Unknown Errors=f(λ

₁,λ

₂))]

5. The method of claim 2 wherein A is of the form:

6. The method of claim 5 wherein the manufacturing error at λ

₁ is given by;

7. The method of claim 6 further including the step of calculating the value of OPD_{manufacturingerror}(λ

₁) and refiguring components of the interferometer to compensate for errors due to manufacturing.

8. The method of claim 5 wherein [OPD_{manufacturingerror}(λ

₂)−

OPD_{manufacturingerror}(λ

₁)] is represented by a Taylor series expansion in which a first part is known and a second part which describes the change in manufacturing errors with wavelength.

9. The method of claim 8 wherein said second part is much smaller than said first part when multiplied by (λ

₂−

λ

₁) and is smaller by a factor between 30 and 100.

10. The method of claim 8 wherein OPD_{manufacturingerror}(λ

₂) expressed as a Taylor series expansion is represented by;

11. The method of claim 10 wherein the bracketed term, [OPD_{manufacturingerror}(λ

₂)−

OPD_{manufacturingerror}(λ

₁)], appearing in claim 5 reduces to opd_{manufacturingerror}(λ

₂−

λ

₁) when OPD_{manufacturingerror}(λ

₂) is replaced by said Taylor series expansion.

12. The method of claim 11 wherein opd_{manufacturingerror}(λ

₂−

λ

₁) is composed of surface errors on the lenses and inhomogenity errors in glass components of the interferometer.

13. The method of claim 12 wherein the surface and inhomogeniety errors of a compensating lens in the interferometer are estimated based on the indices of refraction and dispersion properties of its glass composition.

14. The method of claim 1 wherein the spherical and aspherical wavefronts are generated by directing a collimated beam through a compensating lens at λ

₁ and λ

₂ at different times.

15. The method of claim 14 wherein said aspherical wavefront is nominally identical to the aspheric surface or wavefront to be measured.

16. The method of claim 1 wherein the precision by which said aspheric surface or wavefront can be measured is a fraction of a nanometer.

17. The method of claim 1 carried out using a common path interferometer.

18. The method of claim 17 wherein said common path interferometer is a Fizeau in form.

23. The interferometric apparatus of claim 2 wherein A is of the form:

24. The interferometric apparatus of claim 23 wherein the manufacturing error at λ

₁ is given by;

25. The interferometric apparatus of claim 24 further including means for calculating the value of OPD_{manufacturingerror}(λ

₁) to compensate for errors due to manufacturing.

26. The interferometric apparatus of claim 23 wherein [OPD_{manufacturingerror}(λ

₂)−

OPD_{manufacturingerror}(λ

₁)] is represented by a Taylor series expansion in which a first part is known and a second part which describes the change in manufacturing errors with wavelength.

27. The interferometric apparatus of claim 26 wherein said second part is much smaller than said first part when multiplied by (λ

₂−

λ

₁) and is smaller by a factor between 30 and 100.

28. The interferometric apparatus of claim 26 wherein OPD_{manufacturingerror}(λ

₂) expressed as a Taylor series expansion is represented by;

29. The interferometric apparatus of claim 28 wherein the bracketed term, [OPD_{manufacturingerror}(λ

₂)−

OPD_{manufacturingerror}(λ

₁)], appearing in claim 23 reduces to opd_{manufacturingerror}(λ

₂−

λ

₁) when OPD_{manufacturingerror}(λ

₂) is replaced by said Taylor series expansion.

30. The interferometric apparatus of claim 24 wherein opd_{manufacturingerror}(λ

₂−

λ

₁) is composed of surface errors on the lenses and inhomogenity errors in glass components of said interferometer.

31. The interferometric apparatus of claim 30 wherein said surface and inhomogeniety errors are those of a compensating lens in the interferometer and are estimated based on the indices of refraction and dispersion properties of its glass composition.

19. Interferometric apparatus for measuring aspheric surfaces and wavefronts;

said apparatus comprising;

an interferometer having reference and measurement legs;

means positioned along said measurement leg for providing a support for alternately holding a reference sphere and an aspheric surface or means for generating an aspheric wavefront;

means for directing an aspherical wavefront of known design at a wavelength λ

₁ at a reference sphere with known measured surface properties to generate a first electronic signal containing information about the optical path differences between the reference and measurement wavefronts generated by said interferometer and for directing an apherical wavefront of known design at a wavelength λ

₂ at an aspherical surface or wavefront to be tested to generate a second electronic signal containing information about the optical path differences between the reference and measurement wavefronts generated by said interferometer; and

means for analyzing said first and second electronic signals and calculating therefrom wavefront error maps W₁=W₁(λ

₁) and W₂=W₂(λ

₂) both of which contain wavelength dependent known design and measured errors and unknown errors due to the manufacture, material composition of components in the interferometer, and systematic errors and determining the optical path error caused by shape errors in the aspherical surface or wavefront while accounting for substantially all error sources present in said electronic signals.

20. The interferometric apparatus of claim 19 wherein the optical path length error caused by shape errors in the aspherical surface or wavefront is of the form:

21. The interferometric apparatus of claim 20 further including means for determining the Known Errors in the surface shapes and materials of the interferometer components by measurement and calculation.

22. The interferometric apparatus of claim 21 further including means for reducing the Unknown Errors to the form:

opd_{manufacturingerror}(λ

₂−

λ

₁);

estimating opd_{manufacturingerror}; and

calculating the final error A using the determined values for [(Known Errors=f(λ

₁,λ

₂))+(Unknown Errors=f(λ

₁,λ

₂))].

32. The interferometric apparatus of claim 19 including means directing a collimated beam through a compensating lens at λ

₁ and λ

₂ at different times to generate the spherical and aspherical wavefronts.

33. The interferometric apparatus of claim 32 wherein said aspherical wavefront is nominally identical to the aspheric surface or wavefront to be measured.

34. The interferometric apparatus of claim 19 wherein the precision by which said aspheric surface or wavefront can be measured is a fraction of a nanometer.

35. The interferometric apparatus of claim 19 wherein said interferometer comprises a common path interferometer.

36. The interferometric apparatus of claim 35 wherein said common path interferometer is a Fizeau in form.