Sub-nyquist interferometry
AssigneeEastman Kodak Company
InventorJohn E. Greivenkamp, Jr.
Life of this patent
Estimating the term…
Abstract
A technique is described for extending the measurement range of interferometry past the Nyquist limit of the sampling frequency of the interferogram. The absolute phase values measured by an interferometer are reconstructed by applying constraints based upon a priori knowledge of the absolute phase values. The constraints include the knowledge that one or more derivatives of the spatial distribution of phase values is a continuous function, and the knowledge of step heights to within .lambda./2.
Claims24
A method of surface measurement interferometry, comprising the steps of:
- a. generating a first beam of coherent light;
- b. generating a second beam of coherent light;
- c. combining the first and second beams to form a interferogram;
- d. measuring the phase of the interferogram at a plurality of sampling locations to form samples of the interferogram, said samples representing phase values modulo 2.pi.;
- and
- e. reconstructing (i.e. removing 2.pi. phase discontinuities to produce) absolute phase values from said samples by adding to or subtracting from said samples multiples of 2.pi., including the step of applying a constraint based upon a priori knowledge of the absolute phase values to correctly reconstruct the absolute phase values when the absolute phase changes by more than .pi. per sample.
Apparatus for performing surface measurement interferometry, comprising:
- a. means for forming an interferogram;
- b. means for sampling phase values modulo 2.pi. of the interferogram at an array of sampling locations;
- c. means for reconstructing (i.e. removing 2.pi. phase discontinuities to produce) absolute phase values from said phase values modulo 2.pi. by adding or subtracting multiples of 2.pi., including means for constraining the reconstruction of said absolute phase values based upon a priori knowledge of the absolute phase values such that the absolute phase values are correctly reconstructed when the absolute phase changes by more than .pi. per sample location.
Apparatus for measuring the spatial distribution of phase differences between a test beam and a reference beam of coherent monochromatic light by phase-shifting interferometry, comprising:
- a. means for superposing the test beam and reference beam to form an interference pattern;
- b. means for detecting the intensity of the interference pattern and for generating signals representing the intensity of the interference pattern at a sparse array of sampling locations;
- c. means for displacing the relative phase of the reference beam and the test beam by fractions of a wavelength of the light;
- d. means for providing a starting location signal indicating a neighborhood of sampling locations where the phase between the test beam and the reference beam does not change by more than .pi. between adjacent sampling locations in the neighborhood;
- and
- e. signal processing means connected to said detecting means and said starting location signal providing means and responsive to the starting location signal and the signals representing the intensity of the interference pattern detected at three or more relative phase displacements to produce a signal representing the absolute phase values of said interference pattern at each of said sampling locations, said signal processing means including,
- (1) means responsive to the signals representing the intensity of the interference pattern detected at three or more relative phase displacements for generating signals representing phase values modulo 2.pi. at each sampling location, and
- (2) means connected to said means for generating signals representing phase values modulo 2.pi. responsive to the signals representing phase values modulo 2.pi. for reconstructing (i.e. removing 2.pi. phase discontinuities to produce) an absolute phase value at each of said sampling locations, said reconstructing means starting said reconstruction at said starting location, and reconstructing said absolute phase values according to the constraints that the spatial distribution and one or more derivatives of the spatial distribution of the phase values are continuous functions.
A method of measuring the spatial distribution of phase differences between a test beam and a reference beam of coherent monnochromatic light by phase-shifting interferometry, comprising:
- a. superposing the test beam and the reference beam to form an interference pattern;
- b. detecting the intensity of the interference pattern at a sparse array of sampling locations for three or more relative phase displacements between the reference beam and the test beam;
- c. determining a neighborhood of sampling locations where the phase difference between the test beam and the reference beam does not change by more than .pi. between adjacent sampling locations in the neighborhood;
- processing the intensity values to generate a phase value modulo 2.pi. at each sampling location;
- and
- d. reconstructing (i.e. removing 2.pi. phase discontinuities to produce) absolute phase values from said phase values modulo 2.pi. starting at said starting location and reconstructing said absolute phase values according to the constraint that the spatial distribution and one or more derivatives of the spatial distribution of the phase values are continuous functions.
Apparatus for performing phase-shifting interferometry wherein an array of phase values modulo 2.pi. are processed to reconstruct an array of absolute phase values by removing 2.pi. phase discontinuities from the phase values modulo 2.pi. according to the constraint that the phase values represent a continuous function, characterized by:
- the array of phase values being generated from a sparsely sampled interference fringe intensity pattern, and said absolute phase values being reconstructed according to the further constraint that the first and/or higher derivatives of the array of phase values represent a continuous functions, and said reconstruction originating at a location in a neighborhood of the array where the difference in phase from one sampling location to the next is less than .pi..
Dependencies are inferred from the claim text.