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 before being directed along the different paths, and φ
(t)=nk{tilde over (L)}(t), with k=π
/λ and
λ
equal to a wavelength for the beams;
calculating a linear combination of values of the signal S(t); and
reducing the effect of the deviation of S(t) from the ideal expression on an estimate of {tilde over (L)}(t) using an error signal generated from the coefficients and one or more error basis functions derived at least in part from the linear combination 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 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 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(ωRt+φ(t)+ζ1), where A1 and ζ1 are constants, ωR is an angular frequency difference between the two beams before being directed along the different paths, and φ(t)=nk{tilde over (L)}(t), with k=2π/λ and λ equal to a wavelength for the beams; (iii) calculating a linear combination of values of the signal S(t); and (iv) reducing the effect of the deviation of S(t) from the ideal expression on an estimate of {tilde over (L)}(t) using an error signal generated from the coefficients and one or more error basis functions derived at least in part from the linear combination of values of the signal S(t).
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Citations
83 Claims
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1. A method comprising:
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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 before being directed along the different paths, and φ
(t)=nk{tilde over (L)}(t), with k=π
/λ and
λ
equal to a wavelength for the beams;calculating a linear combination of values of the signal S(t); and reducing the effect of the deviation of S(t) from the ideal expression on an estimate of {tilde over (L)}(t) using an error signal generated from the coefficients and one or more error basis functions derived at least in part from the linear combination 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, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 75, 76, 77, 78, 79, 80, 83)
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55. A computer readable medium storing instructions which during operation cause a processor to
receive 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; -
provide 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 before being directed along the different paths, and φ
(t)=nk{tilde over (L)}(t), with k=2π
/λ and
λ
equal to a wavelength for the beams;calculate a linear combination of values of the signal S(t); and reduce the effect of the deviation of S(t) from the ideal expression on an estimate of {tilde over (L)}(t) using an error signal generated from the coefficients and one or more error basis functions derived at least in part from the linear combination of values of the signal S(t).
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56. 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 before being directed along the different paths, and φ
(t)=nk{tilde over (L)}(t), with k=2π
/λ and
λ
equal to a wavelength for the beams; andan 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 linear combination of values of the signal S(t), and reduces the effect of the deviation of S(t) from the ideal expression on an estimate of {tilde over (L)}(t) using an error signal Sψ
(t) generated from the coefficients and one or more error basis functions derived at least in part from the linear combination of values of the signal S(t). - View Dependent Claims (57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 81, 82)
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67. 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 before being directed along the different paths, and φ
(t)=nk{tilde over (L)}(t), with k=2π
/λ and
λ
equal to a wavelength for the beams; andan electronic processor which during operation receives the interference signal S(t) from the interferometry system, calculates a linear combination of values of the signal S(t), and calculates an estimate for one or more coefficients representative of the one or more errors based on filtering a signal derived at least in part from the linear combination of values of the signal S(t). - View Dependent Claims (68, 69, 70, 71, 72, 73, 74)
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Specification