Sinusoidal phase shifting interferometry
First Claim
1. A method comprising:
- combining a first light beam and at least a second light beam to form a combined light beam;
introducing a sinusoidal phase shift with a frequency f between a phase of the first light beam and a phase of the second light beam;
recording at least one interference signal based on a modulation of the combined light beam in response to the sinusoidal phase shift, the interference signal comprising at least three different frequency components, wherein each of the at least three different frequency components has a frequency which is an integer multiple of f;
for each interference signal, determining information related to the difference in optical path lengths of the first and second light beam by comparing the intensity of the at least three different frequency components of the interference signal; and
outputting the information,wherein the comparing comprises assigning a respective weight to the intensity of each of the at least three different frequency components to provide a corresponding weighted intensity; and
comparing the weighted intensities, the respective weights being selected to compensate an error, where the respective weights are selected so that the effect of the error on the weighted intensity corresponding to a first frequency component is compensated by the effect of the error on the weighted intensity corresponding to a second frequency component.
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Abstract
Disclosed is a method that includes combining a first light beam and at least a second light beam to form a combined light beam, introducing a sinusoidal phase shift with a frequency f between a phase of the first light beam and a phase of the second light beam, recording at least one interference signal based on a modulation of the combined light beam in response to the sinusoidal phase shift, where the interference signal includes at least three different frequency components, and outputting the information. For each interference signal, information related to the difference in optical path lengths of the first and second light beam is determined by comparing the intensity of the at least three different frequency components of the interference signal.
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Citations
82 Claims
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1. A method comprising:
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combining a first light beam and at least a second light beam to form a combined light beam; introducing a sinusoidal phase shift with a frequency f between a phase of the first light beam and a phase of the second light beam; recording at least one interference signal based on a modulation of the combined light beam in response to the sinusoidal phase shift, the interference signal comprising at least three different frequency components, wherein each of the at least three different frequency components has a frequency which is an integer multiple of f; for each interference signal, determining information related to the difference in optical path lengths of the first and second light beam by comparing the intensity of the at least three different frequency components of the interference signal; and outputting the information, wherein the comparing comprises assigning a respective weight to the intensity of each of the at least three different frequency components to provide a corresponding weighted intensity; and
comparing the weighted intensities, the respective weights being selected to compensate an error, where the respective weights are selected so that the effect of the error on the weighted intensity corresponding to a first frequency component is compensated by the effect of the error on the weighted intensity corresponding to a second frequency component. - 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, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69)
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28. A method comprising:
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combining a first light beam and at least a second light beam to form a combined light beam; introducing a sinusoidal phase shift with a frequency f between a phase of the first light beam and a phase of the second light beam; recording at least one interference signal based on a modulation of the combined light beam in response to the sinusoidal phase shift, the interference signal comprising at least three different frequency components; for each interference signal, determining information related to the difference in optical path lengths of the first and second light beam by comparing the intensity of the at least three different frequency components of the interference signal; and outputting the information, wherein the sinusoidal phase shift φ
(t) is of the form
φ
(t)=u cos [α
(t)+φ
]where u is the excursion of the sinusoidal phase shift, φ
is a timing offset, and
α
(t)=2π
ftis the scaled time dependence with f equal to the frequency of the sinusoidal phase shift, the recording comprises, during a cycle of the sinusoidal phase shift, acquiring intensity data g j for N successive sample positions each corresponding to a time tj, where j=0, 1, 2, . . . N−
1, andthe determining comprises; assigning a first respective weight wj(1) to each of the intensity data g j to provide a corresponding first weighted intensity;assigning a second respective weight wj(2) to each of the intensity data g j to provide a corresponding second weighted intensity;calculating the ratio of the sum of first weighted intensities to the sum of the second weighted intensities; and determining information related to the difference in optical path lengths based on the ratio. - View Dependent Claims (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, 55, 56, 57)
and
wj(2)=Γ
odd×
(heven)jwhere (hodd) is the jth element of a sampling vector hodd, (heven)j is the jth element of a sampling vector heven and Γ
even and Γ
odd are normalization coefficients based on a model of the interference signal.
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33. The method of claim 32, wherein the sampling vectors hodd, heven are selected subject to the constraints
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34. The method of claim 33, wherein the error comprises a variation in the excursion of the sinusoidal phase shift from the nominal value.
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35. The method of claim 34, wherein the sampling vectors hodd, heven are selected such that the ratio of the normalization coefficients remains stable in response to the variation of the excursion from the nominal value.
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36. The method of claim 33, wherein the error comprises additive random noise.
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37. The method of claim 36, wherein the additive random noise comprises mean noise.
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38. The method of claim 37, wherein the sampling vectors hodd, heven are selected subject to the constraint
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39. The method of claim 36, wherein the additive random noise comprises root mean square noise.
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40. The method of claim 39, wherein the sampling vectors hodd, heven are selected subject to the constraint that the magnitude of the quantities Γ
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odd/podd and Γ
even/peven be maximized where
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odd/podd and Γ
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41. The method of claim 33, wherein the error comprises additive synchronous noise.
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42. The method of claim 41, wherein the additive synchronous noise comprises noise at frequency ν
- ″
, and the sampling vectors hodd, heven are selected subject to the constraint that the magnitude of the quantities
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43. The method of claim 33, wherein the error comprises multiplicative synchronous noise.
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44. The method of claim 43, wherein the multiplicative synchronous noise comprises noise at frequency ν
- ″
, and the sampling vectors hodd, heven are selected to minimize a predicted sensitivity of the determined information to the noise at frequency ν
″
, based on the model of the interference signal.
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45. The method of claim 43, wherein the multiplicative synchronous noise comprises a sinusoid with frequency f oscillating in phase with the sinusoidal phase shift;
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the sampling vectors hodd, heven are selected subject to the constraint that the magnitude of the quantities
- and
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46. The method of claim 45, wherein:
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the common source comprises a laser diode; the providing a sinusoidal phase shift comprises sinusoidally varying the wavelength of a diode laser light source; and the multiplicative synchronous noise is diode laser intensity noise.
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47. The method of claim 33, wherein the error comprises synchronous vibration noise.
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48. The method of claim 47, wherein the synchronous vibration noise comprises noise at frequency ν
- ″
, and sampling vectors hodd, heven are selected to minimize a predicted sensitivity of the determined information to the noise at frequency ν
″
, based on the model of the interference signal.
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49. The method of claim 33, wherein the error comprises nonlinearity of the sinusoidal phase shift.
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50. The method of claim 49, wherein the nonlinearity is a quadratic nonlinearity, and the sampling vectors hodd, heven are selected subject to the constraint that the magnitude of the quantities
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51. The method of claim 33, wherein the error comprises phase shift timing offset error.
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52. The method of claim 51, wherein sampling vectors hodd, heven are selected subject to the constraint that the magnitude of the quantity
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53. The method of claim 28, wherein the determining comprises calculating the inverse tangent of the ratio.
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54. The method of claim 28, wherein:
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the recording comprises acquiring intensity data g j for N=8 successive measurement frames each corresponding to a time tj such that α
(tj)=jπ
/4+π
/8 for j=0, 1, 2, . . . 7; andthe determining comprises calculating a value for the phase difference θ
between the phase of first light beam and the phase of the second light beam based on the expression;
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55. The method of claim 54, where in the sinusoidal phase shift excursion u is set to a nominal value of 2.93 radians and the timing offset φ
- is set to a nominal value of 0.
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56. The method of claim 28, wherein:
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the recording comprises acquiring intensity data g i for N=16 successive measurement frames each corresponding to a time tj such that α
(tj)=jπ
/8+π
/16 for j=0, 1, 2, . . . 7; andthe determining comprises calculating a value for the phase difference θ
between the phase of first light beam and the phase of the second light beam based on the expression;
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57. The method of claim 56, where in the sinusoidal phase shift excursion u is set to a nominal value of 5.9 radians and the timing offset φ
- is set to a nominal value of 0.
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70. A system comprising:
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an interferometer which during operation combines a first light beam and a second light beam derived from a common source to form combined light beam; a phase shifting component which during operation introduces a sinusoidal phase shift between a phase of the first light beam and a phase of the second light beam; a camera positioned to detect the combined light beam and simultaneously provide at least one interference signal for each of multiple spatial locations on the camera based on the modulation of the combined light beam in response to the phase shift; and an electronic controller coupled to the phase shifting component and the camera, wherein the controller is configured to;
determine information related to the difference in optical path lengths of the first and second light beam by comparing the intensity of at least three frequency components of the interference signals. - View Dependent Claims (71, 72, 73, 74, 75, 76, 77, 78)
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79. A method comprising:
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combining a first light beam and at least a second light beam to form a combined light beam; introducing a sinusoidal phase shift with a frequency f between a phase of the first light beam and a phase of the second light beam; recording at least one interference signal based on a modulation of the combined light beam in response to the sinusoidal phase shift, the interference signal comprising at least three different frequency components; for each interference signal, determining information related to the difference in optical path lengths of the first and second light beam by comparing the intensity of the at least three different frequency components of the interference signal, wherein each of the at least three different frequency components has a frequency which is an integer multiple of f; and outputting the information, wherein the comparing comprises assigning a respective weight to the intensity of each of the at least three different frequency components to provide a corresponding weighted intensity and comparing a sum of the weighted intensities corresponding to the at least three different frequency components at even multiples off to a sum of the weighted intensities corresponding to the at least three different frequency components at odd multiples of f.
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80. A method comprising:
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combining a first light beam and at least a second light beam to form a combined light beam; introducing a sinusoidal phase shift with a frequency f between a phase of the first light beam and a phase of the second light beam; simultaneously recording an interference signal for each of multiple spatial locations on a camera based on a modulation of the combined light beam in response to the sinusoidal phase shift, the interference signals comprising at least three different frequency components; for each interference signal, determining information related to the difference in optical path lengths of the first and second light beam by comparing the intensity of the at least three different frequency components of the respective interference signal; and outputting the information.
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81. A system comprising:
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an interferometer which during operation combines a first light beam and a second light beam derived from a common source to form combined light beam; a phase shifting component which during operation introduces a sinusoidal phase shift between a phase of the first light beam and a phase of the second light beam; a photo detector positioned to detect the combined light beam and provide at least one interference signal based on the modulation of the combined light beam in response to the phase shift; and an electronic controller coupled to the phase shifting component and the photo detector, wherein the controller is configured to;
determine information related to the difference in optical path lengths of the first and second light beam by comparing the intensity of at least three frequency components of the interference signal,wherein the interferometer is an unequal path interferometer, and the phase-shifting component is a wavelength tunable diode laser configured to vary the wavelength at least one of the light beams.
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82. A system comprising:
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an interferometer which during operation combines a first light beam and a second light beam derived from a common source to form combined light beam; a phase shifting component which during operation introduces a sinusoidal phase shift between a phase of the first light beam and a phase of the second light beam; a photo detector positioned to detect the combined light beam and provide at least one interference signal based on the modulation of the combined light beam in response to the phase shift; and an electronic controller coupled to the phase shifting component and the photo detector, wherein the controller is configured to;
determine information related to the difference in optical path lengths of the first and second light beam by comparing the intensity of at least three frequency components of the interference signal,wherein the phase-shifting component is an acousto-optic modulator, an electro-optic modulator, or a transducer coupled to a surface to which the first light beam is directed.
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Specification