Scanning interferometer for aspheric surfaces and wavefronts

• US 6,781,700 B2
• Filed: 06/03/2002
• Issued: 08/24/2004
• Est. Priority Date: 06/20/2001
• Status: Active Grant

• Current Assignee: Zygo Corporation (Ametek Incorporated)
• Original Assignee: Küchel, Michael
• Inventors: Küchel, Michael
• Primary Examiner(s): Font, Frank G.
• Assistant Examiner(s): Brown, Khaled
• Application Number:
  US10/160,672
• Publication Number:
  US 20030002049A1
• Time in Patent Office: 813 Days
• Field of Search: 356/511, 356/512, 356/513, 356/450
• US Class Current: 356/513
• CPC Class Codes: G01B 11/2441 using interferometry
• CPC Class Codes: G01B 2290/65 Spatial scanning object beam
• CPC Class Codes: G01B 9/02039 by matching the wavefront with a particular object surface shape
• CPC Class Codes: G01B 9/02057 by using common path configuration, i.e. reference and object path almost entirely overlapping
• CPC Class Codes: G01B 9/02072 by calibration or testing of interferometer
• CPC Class Codes: G01M 11/025 by determining the shape of the object to be tested measuring contours or curvatures by optical means G01B11/24
• CPC Class Codes: G01M 11/0271 by using interferometric methods

Abstract

Interferometric scanning method(s) and apparatus for measuring rotationally and non-rotationally symmetric test optics either having aspherical surfaces or that produce aspherical wavefronts by comparing known and unknown spherical and aspherical shapes. Preferably, a spherical or partial spherical wavefront or reflecting surface is defined with respect to a known origin along a scanning axis. The test optic is aligned with respect the scanning axis and selectively moved along it relative to the known origin so that the spherical shape intersects the test optic at the apex of the aspherical shape and at radial positions where the spherical shape and the aspheric shape intersect at points of common tangency. An axial distance, v, and optical path length, p, are interferometrically measured as the test optic is axially scanned by the spherical shape where v is the distance by which the test optic is moved with respect to the origin and p is the optical path length difference between the apex of an aspherical shape associated with the test optic and the apex of the circles of curvature that intersect the aspherical shape at the common points of tangency. Coordinates of the aspherical surface are calculated wherever the circles of curvature have intersected the aspherical shape and in correspondence with the interferometrically measured distances, v and p. Afterwards, the aspheric shape is calculated. Where the test optic comprises a refracting optic a known spherical reflecting surface is provided upstream of the refracting optic for movement along the optical axis and a known wavefront is made to transit the refracting optic, reflects from the known spherical surface, again transits the refracting optic traveling towards the known origin after which the interferogram is formed.

Claims

1. A scanning method for measuring rotationally and non-rotationally symmetric shapes of aspherical wavefronts and surfaces, said method comprising the steps of:

providing a scanning axis;

defining at least one known shape of known origin along said scanning axis;

selectively moving an unknown aspherical shape along said scanning axis relative to said known origin so that said known shape intersects said unknown aspherical shape at its apex and at radial positions where the known shape and the aspherical surface intersect at points of common tangency to generate an interference signal whose intensity varies with scan position and in accordance with the optical path length difference, p, between said apex and radial positions;

interferometrically measuring the axial distance, v, by which said aspherical shape is moved with respect to said origin and the optical path length difference, p, between the apex of said aspherical shape and the apex of the circles of curvature that intersect the aspherical shape at said common points of tangency as said aspherical shape and said known shape axially scan one another;

calculating the coordinates of the aspherical shape wherever said circles of curvature have intersected the aspherical shape at common points of tangency and in correspondence with the interferometrically measured distances, v and p; and

determining the unknown shape of said aspheric shape in accordance with said coordinate values and surface slopes at said common points of tangency.

2. The scanning method of claim 1 wherein said known shape is a spherical shape.

3. The scanning method of claim 2 wherein said spherical shape comprises a real surface that is at least partially reflective and wherein said aspherical shape comprises a wavefront emerging from an optical system that is at least in part refractive.

4. The scanning method of claim 2 wherein said known spherical shape is a spherical wavefront generated substantially from a point source located at said known origin.

5. The scanning method of claim 2 wherein said known spherical shape is a spherical wavefront generated by a ring source located at said known origin.

6. The method of claim 2 wherein said spherical shape is a wavefront generated from a source of radiation having at least two points located off said scanning axis from which radiation is simultaneously directed toward a test optic.

7. The scanning method of claim 1 wherein said spherical shape comprises a spherical wavefront of known origin along the optical axis and wherein said aspherical shape comprises a surface that is at least partially reflective.

8. The scanning method of claim 1 wherein said known shape comprises an aspherical shape.

9. The scanning method of claim 8 wherein said known aspherical shape is a conic section.

10. The method of claim 1 wherein said step of interferometrically measuring the optical path length difference p includes interfering light retroreflected from the apex of the aspheric surface with light retroreflected from the points of common tangency between the spherical wavefront and the aspherical surface from the test optic to generate an interferogram containing information indicative of p.

11. The method of claim 10 further including the step of performing phase shifting interferometric analysis on said interferogram.

12. The method of claim 10 further including the step of spatially filtering other than retroreflected light contributing to the interferogram.

13. The method of claim 10 wherein further including the step of polarization encoding said retroreflections on and off said scanning axis.

14. The method of claim 1 wherein z and h are said coordinates of the aspherical shape and are given by:

$\begin{array}{c}z=p+\left(R_0+v-p\right)<br><br>\frac{<br><br>p}{<br><br>v}<br><br><br><br>\text{and}\\ h=\left(R_0+v-p\right)<br><br>\sqrt{\frac{<br><br>p}{<br><br>v}<br><br>\left(2-\frac{<br><br>p}{<br><br>v}\right)}\end{array}$

where

R=R₀+v−

p, with R₀ equal to the reciprocal apical curvature of the aspherical shape.

15. The method of claim 1 wherein said aspheric shape is selected from the group comprising aspherical reflecting surfaces of generally positive and negative curvature.

16. The method of claim 1 wherein said aspheric shape is provided by a refracting optic and further including the step of providing a known reflecting surface fixed upstream of said refracting optic so that a spherical wavefront transits said refracting optic, reflects from said known aspheric surface, again transits said refracting optic traveling towards said known origin to produce said aspherical wavefront.

17. A scanning method for measuring rotationally and non-rotationally symmetric test optics having aspherical surfaces, said method comprising the steps of:

generating at least a partial spherical wavefront from a known origin along a scanning axis;

aligning a test optic with respect to the scanning axis and selectively moving said test optic along said scanning axis relative to said known origin so that said spherical wavefront intersects the test optic at the apex of the aspherical surface and at radial positions where the spherical wavefront and the aspheric surface intersect at points of common tangency to generate an interference signal whose intensity varies with scan position and in accordance with the optical path length difference, p, between said apex and radial positions;

interferometrically measuring the axial distance, v, by which said test optic is moved with respect to said origin and the optical path length difference, p, between the apex of an aspherical surface of said test optic and the apex of the circles of curvature that intersect the aspherical surface at common points of tangency as the test optic is axially scanned by the spherical wavefront;

calculating the coordinates of the aspherical surface wherever said circles of curvature have intersected the aspherical surface at common points of tangency and in correspondence with the interferometrically measured distances, v and p; and

determining the shape of said aspheric surface based on said coordinate values.

18. The method of claim 17 wherein said step of interferometrically measuring the optical path length difference p includes interfering light retroreflected from the apex of the aspheric surface with light retroreflected from the points of common tangency between the spherical wavefront and the aspherical surface from the test optic to generate an interferogram containing information indicative of p.

19. The method of claim 18 further including the step of spatially filtering other than retroreflected light contributing to the interferogram.

20. The method of claim 18 wherein further including the step of polarization encoding said retroreflections on and off said optical axis.

21. The method of claim 18 further including the step of performing phase shifting interferometric analysis on said interferogram.

22. The method of claim 17 wherein z and h are said coordinates of the aspherical surface and are given by:

$\begin{array}{c}z=p+\left(R_0+v-p\right)<br><br>\frac{<br><br>p}{<br><br>v}<br><br><br><br>\text{and}\\ h=\left(R_0+v-p\right)<br><br>\sqrt{\frac{<br><br>p}{<br><br>v}<br><br>\left(2-\frac{<br><br>p}{<br><br>v}\right)}\end{array}$

where

R=R₀+v−

p, with R₀ equal to the reciprocal apical curvature of the aspherical surface.

23. The method of claim 17 wherein said spherical wavefront is generated from a source of radiation having at least two points located off said scanning axis from which radiation is simultaneously directed toward a test optic.

24. The method of claim 17 wherein said test optic is selected from the group comprising aspherical reflecting surfaces of generally positive and negative curvature.

25. The method of claim 17 wherein said test optic comprises a refracting optic and further including the step of providing a known reflecting surface fixed upstream of said refracting optic so that the spherical wavefront transits said refracting optic, reflects from said known aspheric surface, again transits said refracting optic traveling towards said known origin to produce said aspherical wavefront.

26. A scanning method for measuring rotationally and non-rotationally symmetric test optics that produce aspherical wavefronts, said method comprising the steps of:

mounting at least a partial spherical mirror with a known origin along a scanning axis for movement therealong;

aligning a test optic with respect to the scanning axis and transmitting a wavefront through said test optic so that said test optic produces an aspherical wavefront and selectively moving said spherical mirror along said scanning axis relative to said known origin so that said aspherical wavefront from said test optic intersects the spherical mirror at the apex of its spherical surface and at radial positions where the aspherical wavefront and the spherical mirror intersect at points of common tangency to generate an interference signal whose intensity varies with scan position and in accordance with the optical path length difference, p, between said apex and radial positions;

interferometrically measuring the axial distance, v, by which said spherical mirror is moved with respect to said origin and the optical path length difference, p, between the apex of an aspherical surface associated with said test optic and the apex of the circles of curvature that intersect the spherical mirror at common points of tangency as the aspherical wavefront is axially scanned by the spherical mirror;

calculating the coordinates of the aspherical wavefront wherever said circles of curvature have intersected the aspherical surface at common points of tangency and in correspondence with the interferometrically measured distances, v and p; and

determining the shape of said aspherical surface based on said coordinate values.

27. The method of claim 26 wherein said step of interferometrically measuring the optical path length difference, p, includes interfering light reflected from the apex the spherical surface with light from the points of common tangency between the aspherical wavefront from the test optic and the spherical surface to generate an interferogram containing information indicative of p.

28. The method of claim 27 further including the step of spatially filtering other than light contributing to the interferogram.

29. The method of claim 26 wherein z and h are said coordinates of the aspherical wavefront and are given by:

$\begin{array}{c}z=p+\left(R_0+v-p\right)<br><br>\frac{<br><br>p}{<br><br>v}<br><br><br><br>\text{and}\\ h=\left(R_0+v-p\right)<br><br>\sqrt{\frac{<br><br>p}{<br><br>v}<br><br>\left(2-\frac{<br><br>p}{<br><br>v}\right)}\end{array}$

where

R=R₀+v−

p, with R₀ equal to the reciprocal apical curvature of the aspherical surface.

30. The method of claim 26 wherein said aspherical wavefront is generated from a source of radiation having at least two points located off said scanning axis from which radiation simultaneously emanates.

31. The method of claim 27 wherein including the step of polarization encoding said reflections on and off said scanning axis.

32. The method of claim 27 further including the step of performing phase shifting interferometric analysis on said interferogram.

33. The method of claim 26 wherein said test optic is selected from the group comprising aspherical refracting elements of generally positive and negative curvature.

34. The method of claim 26 wherein said test optic comprises a refracting optic and further including the step of providing a known reflecting surface fixed upstream of said refracting optic so that the spherical wavefront transits said refracting optic, reflects from said known aspheric surface, again transits said refracting optic traveling towards said known origin to produce said aspherical wavefront.

35. Interferometric apparatus for measuring rotationally and non-rotationally symmetric shapes of aspherical wavefronts and surfaces, said apparatus comprising:

means for providing a scanning axis;

means for defining at least one known shape of known origin along said scanning axis;

means for selectively moving an unknown aspherical shape along said scanning axis relative to said known origin so that said known shape intersects said unknown aspherical shape at its apex and at radial positions where the known shape and the aspherical surface intersect at points of common tangency to generate an interference signal whose intensity varies with scan position and in accordance with the optical path length difference, p, between said apex and radial positions;

means for interferometrically measuring the axial distance, v, by which said aspherical shape is moved with respect to said origin and the optical path length difference, p, between the apex of said aspherical shape and the apex of the circles of curvature that intersect the aspherical shape at said common points of tangency as said aspherical shape and said known shape axially scan one another;

means for calculating the coordinates of the aspherical shape wherever said circles of curvature have intersected the aspherical shape at common points of tangency and in correspondence with the interferometrically measured distances, v and p; and

means for determining the unknown shape of said aspheric shape in accordance with said coordinate values and surface slopes at said common points of tangency.

36. The apparatus of claim 35 wherein said known shape is a spherical shape.

37. The apparatus of claim 36 wherein said means for defining said spherical shape comprises a real spherical surface that is at least partially reflective and wherein said aspherical shape comprises a wavefront emerging from an optical system that is at least in part refractive.

38. The apparatus of claim 36 wherein said means for defining said known shape comprises a point source located at said known origin to generate a spherical wavefront.

39. The apparatus of claim 36 wherein said means for defining said known shape spherical shape is a ring source for generating at least a portion of a spherical wavefront.

40. The apparatus of claim 36 wherein said means for defining said known shape comprises a source of radiation having at least two points located off said scanning axis from which radiation is simultaneously generated.

41. The apparatus of claim 35 wherein said means for defining a known shape comprises a point source located at said known origin along the optical axis for generating a spherical wavefront and wherein said aspherical shape comprises a surface that is at least partially reflective.

42. The apparatus of claim 35 wherein said known shape comprises an aspherical shape.

43. The apparatus of claim 35 wherein said known aspherical shape is a conic section.

44. The apparatus of claim 35 wherein said means for interferometrically measuring the optical path length difference, p, is structured to interfere light retroreflected from the apex of the aspheric surface with light retroreflected from the points of common tangency between the known shape and the aspherical surface to generate an interferogram containing information indicative of p.

45. The apparatus of claim 44 further including means for performing phase shifting interferometric analysis on said interferogram.

46. The apparatus of claim 44 further including means for spatially filtering other than retroreflected light contributing to said interferogram.

47. The apparatus of claim 44 further including means for polarization encoding said retroreflections on and off said scanning axis.

48. The apparatus of claim 35 wherein z and h are said coordinates of the aspherical shape and are given by:

$\begin{array}{c}z=p+\left(R_0+v-p\right)<br><br>\frac{<br><br>p}{<br><br>v}<br><br><br><br>\text{and}\\ h=\left(R_0+v-p\right)<br><br>\sqrt{\frac{<br><br>p}{<br><br>v}<br><br>\left(2-\frac{<br><br>p}{<br><br>v}\right)}\end{array}$

where

R=R₀+v−

p, with R₀ equal to the reciprocal apical curvature of the aspherical shape.

49. The apparatus of claim 35 wherein said aspheric shape is selected from the group comprising aspherical reflecting surfaces of generally positive and negative curvature.

50. The apparatus of claim 35 wherein said aspheric shape is provided by a refracting optic and further including means for providing a known reflecting surface fixed upstream of said refracting optic so that a spherical wavefront transits said refracting optic, reflects from said known aspheric surface, again transits said refracting optic traveling towards said known origin to produce said aspherical wavefront.