Recovering spectral shape from spatial output
First Claim
1. A method of estimating the optical spectrum of a light beam, the method comprising:
- creating a two-dimensional matrix by interacting a test beam that is distinct from the light beam with a spectrometer, wherein the two-dimensional matrix represents the input-output relationship of the spectrometer and each entry of the two-dimensional matrix provides a relationship between one or more spatial areas of the spectrometer and a spectral feature;
projecting the light beam onto distinct spatial areas of the spectrometer, wherein each spatial area receives a different filtered version of the optical spectrum of the light beam;
detecting a characteristic of the projected light beam at each of the distinct spatial areas of the spectrometer; and
estimating the optical spectrum of the light beam based on an analysis that uses both the detected light beam characteristics and the created two-dimensional matrix.
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Accused Products
Abstract
A method is performed for estimating the optical spectrum of a light beam. The method includes: projecting the light beam onto distinct spatial areas of a spectrometer, wherein each spatial area receives a different filtered version of the optical spectrum; detecting a characteristic of the projected light beam at each of the distinct spatial areas of the spectrometer; receiving a two-dimensional matrix in which each entry of the matrix provides a relationship between one or more spatial areas and each spectral feature, wherein the two-dimensional matrix is related to the input-output relationship of the spectrometer; and estimating the optical spectrum of the light beam based on an analysis that uses both the detected light beam characteristics and the received two-dimensional matrix.
15 Citations
28 Claims
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1. A method of estimating the optical spectrum of a light beam, the method comprising:
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creating a two-dimensional matrix by interacting a test beam that is distinct from the light beam with a spectrometer, wherein the two-dimensional matrix represents the input-output relationship of the spectrometer and each entry of the two-dimensional matrix provides a relationship between one or more spatial areas of the spectrometer and a spectral feature; projecting the light beam onto distinct spatial areas of the spectrometer, wherein each spatial area receives a different filtered version of the optical spectrum of the light beam; detecting a characteristic of the projected light beam at each of the distinct spatial areas of the spectrometer; and estimating the optical spectrum of the light beam based on an analysis that uses both the detected light beam characteristics and the created two-dimensional matrix. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10)
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11. A method of estimating the optical spectrum of a light beam, the method comprising:
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creating a two-dimensional matrix that represents an input-output relationship of a spectrometer, wherein creating comprises; interacting a test beam with the spectrometer, the test beam being distinct from the light beam; changing a spectral feature of the test beam across a range of N distinct spectral features; and for each spectral feature in the range, detecting a characteristic of the test beam at each spatial area; and storing the detected characteristic of the test beam at each of M spatial areas of the spectrometer as a column of a preliminary two-dimensional matrix, wherein the column is assigned based on the spectral feature and wherein the preliminary two-dimensional matrix captures the input-output relationship of the spectrometer; and calculating a two-dimensional matrix based on the preliminary two-dimensional matrix; wherein the number of rows of the two-dimensional matrix and the number of columns of the preliminary two-dimensional matrix equals N, and the number of columns of the two-dimensional matrix and the number of rows of the preliminary two-dimensional matrix equals M; and projecting the light beam onto distinct spatial areas of the spectrometer and detecting a characteristic of the projected light beam at each distinct spatial area of the spectrometer; and estimating the optical spectrum of the light beam including performing matrix multiplication between the two-dimensional matrix and the detected light beam characteristics. - View Dependent Claims (12)
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13. A method of estimating the optical spectrum of a light beam, the method comprising:
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creating a two-dimensional matrix relating to an input-output relationship of a spectrometer by calculating a pseudoinverse of a preliminary two-dimensional matrix, wherein the preliminary two-dimensional matrix captures the input-output relationship of the spectrometer; storing the two-dimensional matrix; projecting the light beam onto distinct spatial areas of the spectrometer and detecting a characteristic of the projected light beam at each distinct spatial area of the spectrometer; and estimating the optical spectrum of the light beam comprising performing matrix multiplication between the stored two-dimensional matrix and the detected light beam characteristics. - View Dependent Claims (14, 15)
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16. A metrology apparatus comprising:
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a spectrometer comprising; a spectrum dispersing device configured to separate a light beam into different filtered versions of the optical spectrum of the light beam; and a detector defining distinct spatial areas, the detector being configured to receive a different filtered version of the optical spectrum at each spatial area and to detect a characteristic of the projected light beam at each distinct spatial area; a test apparatus configured to create a two-dimensional matrix that represents the input-output relationship of the spectrometer in which each entry of the two-dimensional matrix provides a relationship between one or more spatial areas of the detector and each spectral feature, the test apparatus including a test beam configured to interact with the spectrometer; a control system connected to the spectrometer and configured to; receive detected light beam characteristics produced from a light beam that interacts with the spectrometer and is distinct from the test beam; and estimate the optical spectrum of the light beam based on an analysis that uses the received detected light beam characteristics and the two-dimensional matrix. - View Dependent Claims (17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27)
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28. A metrology apparatus comprising:
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a spectrometer in the path of a light beam, the spectrometer comprising; a spectrum dispersing device configured to separate the light beam into different filtered versions of the optical spectrum of the light beam; and a detector in the path of the projected light beam and defining distinct spatial areas, the detector being configured to receive a different filtered version of the optical spectrum at each spatial area and to detect a characteristic of the projected light beam at each distinct spatial area; a control system connected to the spectrometer and configured to; receive a two-dimensional matrix in which each entry of the matrix provides a relationship between one or more spatial areas and each spectral feature, wherein the two-dimensional matrix is related to the input-output relationship of the spectrometer; analyze the detected light beam characteristics and the received two-dimensional matrix; and estimate an optical spectrum of the light beam based on the analysis; a test light source configured to produce a test beam, wherein the spectrometer interacts with the test beam; and a spectral feature actuation apparatus configured to control a spectral feature of the test beam; the spectral feature actuation apparatus is configured to change a spectral feature of the test beam across a range of N distinct spectral features while the test beam interacts with the spectrometer; the detector is configured to detect a characteristic of the test beam at each spatial area; and the control system is connected to the test light source and the spectral feature actuation apparatus, and is configured to create the two-dimensional matrix by;
for each spectral feature in the range, storing the detected characteristic of the test beam at each of M spatial areas of the spectrometer as a column of the preliminary two-dimensional matrix, wherein the column is assigned based on the spectral feature and wherein the preliminary two-dimensional matrix captures the input-output relationship of the spectrometer.
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Specification