Cyclic error compensation in interferometry systems
First Claim
1. A method comprising:
- providing an interference signal S(t) from two beams directed along different paths, wherein the signal S(t) is indicative of changes in an optical path difference n{tilde over (L)}(t) between the different paths, where n is an average refractive index along the different paths, {tilde over (L)}(t) is a total physical path difference between the different paths, and t is time;
providing one or more coefficients representative of one or more errors that cause the signal S(t) to deviate from an ideal expression of the form A1 cos(ω
Rt+φ
(t)+ζ
1), where A1 and ζ
1 are constants, ω
R is an angular frequency difference between the two beams, and φ
(t)=n/k{tilde over (L)}(t), with k=2π
/λ and
λ
equal to a wavelength for the beams;
calculating a function of values of the signal S(t); and
reducing the deviation of S(t) from the ideal expression using an error signal Sψ
(t) generated from the coefficients and one or more error basis functions derived at least in part from the function of values of the signal S(t).
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Abstract
The invention features a method including: (i) providing an interference signal S(t) from two beams derived from a common source and directed along different paths, wherein the signal S(t) is indicative of changes in an optical path difference n{tilde over (L)}(t) between the different paths, where n is an average refractive index along the different paths, {tilde over (L)}(t) is a total physical path difference between the different paths, and t is time; (ii) providing coefficients representative of one or more errors that cause the signal S(t) to deviate from an ideal expression of the form A1 cos(ωRt+φ(t)+ζ1), where A1 and ζ1 are constants, ωR is an angular frequency difference between the two beams, and φ(t)=nk{tilde over (L)}(t), with k=2π/λ and λ equal to a wavelength for the beams; (iii) calculating a quadrature signal {tilde over (S)}(t) based on the signal S(t); and (iv) reducing the deviation of S(t) from the ideal expression using an error signal Sψ(t) generated from the coefficients and error basis functions derived from the signals S(t) and {tilde over (S)}(t).
57 Citations
67 Claims
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1. A method comprising:
-
providing an interference signal S(t) from two beams directed along different paths, wherein the signal S(t) is indicative of changes in an optical path difference n{tilde over (L)}(t) between the different paths, where n is an average refractive index along the different paths, {tilde over (L)}(t) is a total physical path difference between the different paths, and t is time;
providing one or more coefficients representative of one or more errors that cause the signal S(t) to deviate from an ideal expression of the form A1 cos(ω
Rt+φ
(t)+ζ
1), where A1 and ζ
1 are constants, ω
R is an angular frequency difference between the two beams, and φ
(t)=n/k{tilde over (L)}(t), with k=2π
/λ and
λ
equal to a wavelength for the beams;
calculating a function of values of the signal S(t); and
reducing the deviation of S(t) from the ideal expression using an error signal Sψ
(t) generated from the coefficients and one or more error basis functions derived at least in part from the function of values of the signal S(t). - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 53, 54, 55, 56, 57, 58, 59)
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35. A method comprising:
-
providing an interference signal S(t) from two beams derived from a common source and directed along different paths, wherein the signal S(t) is indicative of changes in an optical path difference n{tilde over (L)}(t) between the different paths, where n is an average refractive index along the different paths, {tilde over (L)}(t) is a total physical path difference between the different paths, and t is time;
providing coefficients representative of one or more errors that cause the signal S(t) to deviate from an ideal expression of the form A1 cos(ω
Rt+φ
(t)+ζ
1), where A1 and ζ
1 are constants, ω
R is an angular frequency difference between the two beams, and φ
(t)=nk{tilde over (L)}(t), with k=2π
/λ and
λ
equal to a wavelength for the beams; and
reducing the deviation of S(t) from the ideal expression using an error signal Sψ
(t) generated from the coefficients and error basis functions derived from the interference signal S(t) based on prior values of S(t) according to the approximation S(t)≈
S(t−
2π
N/ω
R), where N is a positive integer. - View Dependent Claims (36, 37, 38, 39)
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40. A method for estimating coefficients representative of one or more errors that cause an interference signal S(t) from two beams derived from a common source and directed along different paths to deviate from an ideal expression of the form A1 cos(ω
-
Rt+φ
(t)+ζ
1), wherein the signal S(t) is indicative of changes in an optical path difference n{tilde over (L)}(t) between the different paths,where n is an average refractive index along the different paths, {tilde over (L)}(t) is a total physical path difference between the different paths, t is time, A1 and ζ
1 are constants, ω
R is an angular frequency difference between the two beams, and φ
(t)=nk{tilde over (L)}(t), with k=2π
/λ and
λ
equal to a wavelength for the beams,the method comprising;
calculating a quadrature signal {tilde over (S)}(t) based on the signal S(t); and
calculating an estimate for the coefficients based on the signals S(t) and {tilde over (S)}(t). - View Dependent Claims (41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52)
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Rt+φ
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50. The method of claim wherein 48, the low-pass filtering comprises using a Butterworth filter.
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60. An apparatus comprising:
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an interferometry system which during operation directs two beams along different paths and provides an interference signal S(t) from the two beams, wherein the signal S(t) is indicative of changes in an optical path difference n{tilde over (L)}(t) between the different paths, where n is an average refractive index along the different paths, {tilde over (L)}(t) is a total physical path difference between the different paths, and t is time, wherein imperfections in the interferometry system produce one or more errors that cause the signal S(t) to deviate from an ideal expression of the form A1 cos(ω
Rt+φ
(t)+ζ
1), where A1 and ζ
1 are constants, ω
R is an angular frequency difference between the two beams, and φ
(t)=nk{tilde over (L)}(t), with k=2π
/λ and
λ
equal to a wavelength for the beams; and
an electronic processor which during operation receives the interference signal S(t) from the interferometry system, receives one or more coefficients representative of the one or more errors, calculates a function of values of the signal S(t), and reduces the deviation of S(t) from the ideal expression using an error signal Sψ
(t) generated from the coefficients and one or more error basis functions derived at least in part from the function of values of the signal S(t). - View Dependent Claims (63, 64, 65, 66, 67)
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61. An apparatus comprising:
-
an interferometry system which during operation directs two beams derived from a common source along different paths and provides an interference signal S(t) from the two beams, wherein the signal S(t) is indicative of changes in an optical path difference n{tilde over (L)}(t) between the different paths, where n is an average refractive index along the different paths, {tilde over (L)}(t) is a total physical path difference between the different paths, and t is time, wherein imperfections in the interferometry system produce one or more errors that cause the signal S(t) to deviate from an ideal expression of the form A1 cos(ω
Rt+φ
(t)+ζ
1), where A1 and ζ
1 are constants, ω
R is an angular frequency difference between the two beams, and φ
(t)=nk{tilde over (L)}(t), with k=2π
/λ and
λ
equal to a wavelength for the beams; and
an electronic processor which during operation receives the interference signal S(t) from the interferometry system, receives coefficients representative of the one or more errors, and reduces the deviation of S(t) from the ideal expression using an error signal Sψ
(t) generated from the coefficients and error basis functions derived from the interference signal S(t) based on prior values of S(t) according to the approximation S(t)≈
S(t−
2π
N/ω
R), where N is a positive integer.
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-
62. An apparatus comprising:
-
an interferometry system which during operation directs two beams derived from a common source along different paths and provides an interference signal S(t) from the two beams, wherein the signal S(t) is indicative of changes in an optical path difference n{tilde over (L)}(t) between the different paths, where n is an average refractive index along the different paths, {tilde over (L)}(t) is a total physical path difference between the different paths, and t is time, wherein imperfections in the interferometry system produce one or more errors that cause the signal S(t) to deviate from an ideal expression of the form A1 cos(ω
Rt+φ
(t)+ζ
1), where A1 and ζ
1 are constants, ω
R is an angular frequency difference between the two beams, and φ
(t)=nk{tilde over (L)}(t), with k=2π
/λ and
λ
equal to a wavelength for the beams; and
an electronic processor which during operation receives the interference signal S(t) from the interferometry system, calculates a quadrature signal {tilde over (S)}(t) based on the signal S(t), and calculates an estimate for the coefficients representative of the one or more errors based on the signals S(t) and {tilde over (S)}(t).
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Specification