ERROR COMPENSATION IN PHASE SHIFTING INTERFEROMETRY

• US 20100238455A1
• Filed: 03/20/2009
• Published: 09/23/2010
• Est. Priority Date: 03/20/2009
• Status: Active Grant

• Current Assignee: Zygo Corporation (Ametek Incorporated)
• Original Assignee: Zygo Corporation (Ametek Incorporated)
• Inventors: de Groot, Peter
• Granted Patent: US 7,948,637 B2
• Time in Patent Office: Days
• US Class Current: 356/512
• CPC Class Codes: G01B 2290/35 Mechanical variable delay line
• CPC Class Codes: G01B 9/02004 using frequency scans
• CPC Class Codes: G01B 9/0201 using temporal phase variation
• CPC Class Codes: G01B 9/02057 by using common path configuration, i.e. reference and object path almost entirely overlapping
• CPC Class Codes: G01B 9/02059 Reducing effect of parasitic reflections, e.g. cyclic errors
• CPC Class Codes: G01B 9/02069 Synchronization of light source or manipulator and detector
• CPC Class Codes: G01B 9/02083 characterised by particular signal processing and presentation

Abstract

In certain aspects, disclosed methods include combining reference light reflected from a reference surface with test light reflected from a test surface to form combined light, the test and reference light being derived from a common source, sinusoidally varying a phase between the test light and reference light, where the sinusoidal phase variation has an amplitude u, recording at least one interference signal related to changes in an intensity of the combined light in response to the sinusoidal variation of the phase, determining information related to the phase using a phase shifting algorithm that has a sensitivity that varies as a function of the sinusoidal phase shift amplitude, where the sensitivity of the algorithm at 2 u is 10% or less of the sensitivity of the algorithm at u.

Claims

29-1. The method of claim 1, wherein the test surface is a surface of an optical element.

31. A method, comprising:

combining reference light reflected from a reference surface with test light reflected from a test surface to form combined light, the test and reference light being derived from a common source;

sinusoidally varying a phase between the test light and reference light;

recording at least one interference signal based on a modulation of the combined light in response to varying the phase;

determining information related to the phase using a phase shifting algorithm that has a sensitivity to contributions to the combined light from test light that makes a double pass between the test and reference surfaces that is 10% or less of the sensitivity of the algorithm to contributions to the combined light from test light that makes a single pass between the test and reference surfaces.

32. A system, comprising:

an interferometer which during operation combines test light from a test surface with reference light from a reference surface to form combined light, where the test and reference light are derived from a common source;

a phase shifting component which during operation introduces a sinusoidal phase shift between the test light and reference light, where the sinusoidal phase variation has an amplitude u;

a detector positioned to detect the combined light and provide at least one interference signal based on the modulation of the combined light beam in response to varying the phase; and

an electronic controller coupled to the phase shifting component and the detector, wherein the electronic controller is configured to determine information related to the phase during operation of the system, where the electronic controller determined the information using a phase shifting algorithm that has a sensitivity that varies as a function of the sinusoidal phase shift amplitude, where the sensitivity of the algorithm at 2u is 10% or less of the sensitivity of the algorithm at u.

33. The system of claim 32, wherein the interferometer is a Fizeau interferometer.

34. The system of claim 32, wherein the phase shifting component is the common source, the common source being a wavelength tunable light source.

35. The system of claim 32, wherein the phase shifting component is a transducer coupled to the test surface or the reference surface.

36. A method, comprising:

combining reference light reflected from a reference surface with test light reflected from a test surface to form combined light, the test and reference light being derived from a common source;

sinusoidally varying a phase between the test light and reference light;

recording at least one interference signal related to changes in an intensity of the combined light in response to the sinusoidal variation of the phase;

determining information related to the phase by analyzing the at least one interference signal using a phase shifting algorithm, wherein the phase shifting algorithm is configured to determine a phase value, θ

, of the interference signal based on twenty intensity samples I_j of the combined light composing the interference signal according to the equation

37. The method of claim 36, wherein the sinusoidal phase variation has an amplitude u=4.18.

38. The method of claim 36, wherein the intensity samples I_j are acquired for phase shifts Δ

α

=π

/10.

39. A method, comprising:

combining reference light reflected from a reference surface with test light reflected from a test surface to form combined light, the test and reference light being derived from a common source;

sinusoidally varying a phase between the test light and reference light;

recording at least one interference signal related to changes in an intensity of the combined light in response to the sinusoidal variation of the phase;

determining information related to the phase by analyzing the at least one interference signal using a phase shifting algorithm, wherein the phase shifting algorithm is configured to determine a phase value, θ

, of the interference signal based on twenty intensity samples I_j of the combined light composing the interference signal according to the equation

40. The method of claim 39, wherein the sinusoidal phase variation has an amplitude u=3.384.

41. The method of claim 39, wherein the intensity samples I_j are acquired for phase shifts Δ

α

=π

/6.

42. A method, comprising:

combining reference light reflected from a reference surface with test light reflected from a test surface to form combined light, the test and reference light being derived from a common source;

sinusoidally varying a phase between the test light and reference light, where the sinusoidal phase variation has an amplitude u and a phase-offset;

recording an interference signal, while varying the phase-offset in a predetermined way; and

determining information related to the phase by analyzing the interference signal using a phase shifting algorithm.

43. The method of claim 42, wherein the interference signal comprises a sequence of intensity values and the phase shifting algorithm is configured to derive a phase from a subset of intensity values.

44. The method of claim 43, wherein the subset of intensity values corresponds to an oscillation of the sinusoidal variation of the phase.

45. The method of claim 43, wherein analyzing the interference signal includes deriving a phase for at least two subsets for different phase-offsets and determining information related to the phase includes averaging the phases of the at least two subsets.

46. The method of claim 43, wherein analyzing the interference signal includes averaging intensity values of the interference signal and determining information deriving a phase from the averaged intensity values.

47. The method of claim 43, wherein the interference signal comprises a sequence of N recorded subsets and the phase-offset varies between two subsets over a phase of 4π

/N.

48. The method of claim 42, wherein the phase shifting algorithm has a sensitivity that varies as a function of the sinusoidal phase shift amplitude, where the sensitivity of the algorithm at 2 u is 10% or less of the sensitivity of the algorithm at u.

49. The method of claim 42, wherein the phase-offset varies at a frequency that is lower than the frequency of the sinusoidal variation of the phase.

50. The method of claim 42, wherein the phase-offset varies at least one of continuously, stepwise, or randomly.

51. The method of claim 42, wherein the phase-offset varies according to a triangular function.

52. The method of claim 42, wherein the phase-offset varies over a phase range of 2π

.

53. The method of claim 42, wherein the phase-offset is varied according to a non-constant function ƒ

(t).

54. A method, comprising:

combining reference light reflected from a reference surface with test light reflected from a test surface to form combined light, the test and reference light being derived from a common source;

sinusoidally varying a phase between the test light and reference light, where the sinusoidal phase variation has an amplitude u;

recording at least one interference signal related to changes in an intensity of the combined light in response to the sinusoidal variation of the phase;

determining information related to the phase using a phase shifting algorithm that has a sensitivity that varies as a function of the sinusoidal phase shift amplitude, wherein the sensitivity of the algorithm has a minimum close to 2 u and in a range from 2 u±

0.2 u, the sensitivity is 10% or less of the sensitivity of the algorithm at u to suppress calibration errors in u.