Nonuniform sampling for spectral and related applications

• US 6,005,664 A
• Filed: 10/06/1998
• Issued: 12/21/1999
• Est. Priority Date: 10/07/1997
• Status: Expired due to Fees

• Current Assignee: Massachusetts Institute of Technology
• Original Assignee: Massachusetts Institute of Technology
• Inventors: Korenberg, Michael J., Hunter, Ian W., Brenan, Colin J. H.
• Primary Examiner(s): Kim, Robert H.
• Application Number:
  US09/167,086
• Time in Patent Office: 441 Days
• Field of Search: 356/345, 356/346
• US Class Current: 356/451
• CPC Class Codes: G01J 3/453 by correlation of the amplitudes
• CPC Class Codes: G01J 9/02 by interferometric methods using interferometers for measuring optically the linear dimensions of objects G01B9/02

Abstract

A method for deriving a spectrum of a substance in such a manner as to enhance a specified characteristic of the spectrum. Irregular intervals are chosen in the signal domain for sampling the signal. The irregular intervals may be randomly spaced. The signal is sampled at the irregular intervals and transformed into the transform domain through application of a transform algorithm, such as a fast orthogonal search, capable of accommodating an irregularly sampled signal. Interferometric spectrometers having parallel optical paths with irregularly spaced phase delays are provided for the practice of the claimed method.

Claims

1. A method for enhancing a specified characteristic of a transform of a signal in a signal domain, the transform of the signal being in a transform domain, the method comprising:

a. choosing irregular intervals in the signal domain for sampling the signal;

b. sampling the signal at the irregular intervals; and

c. transforming the signal into the transform domain without interpolating regularly spaced values in the signal domain.

2. A method according to claim 1, wherein the specified characteristic is a spectral characteristic.

3. A method according to claim 1, wherein the transform domain and the signal domain are identical.

4. A method for obtaining a spectrum of a substance, the method comprising:

a. sampling an interferogram of the substance at irregular intervals for obtaining an irregularly sampled interferogram; and

b. transforming the irregularly sampled interferogram into a spectral domain without interpolating regularly spaced values in the signal domain.

5. A method according to claim 4, wherein the step of transforming the irregularly sampled interferogram into a spectral domain includes searching through a set of candidate frequencies for obtaining a sinusoidal series model.

6. A method according to claim 4, wherein the step of transforming is performed by means of a fast orthogonal search.

7. A method for deriving specified characteristics of a desired transform of a correlation function of a specified moment with respect to at least one random variable, the method comprising:

a. determining an optimized sampling strategy based on the specific characteristics to be determined;

b. sampling of the random variable according to the optimized sampling strategy for obtaining discrete and irregularly spaced samples of the random variable; and

c. transforming the samples of the random variable into a transform domain for obtaining the desired transform of the correlation function without interpolating regularly spaced values in the signal domain.

8. A spectrometer for obtaining an electromagnetic spectrum of a substance, the spectrometer comprising:

a. an input for receiving electromagnetic radiation;

b. a beamsplitter for splitting the electromagnetic radiation into a first and a second beam, the first and second beams having irregularly spaced spatial components;

c. a phase retarder for introducing an phase delay in the first beam relative to the second beam in such a manner that the phase delay is a function of the irregularly spaced spatial component of the first and the second beam; and

d. an array of detectors, such that each detector receives a spatial component of the first beam and a spatial component of the second beam.

9. A spectrometer according to claim 8, further including a waveguide for transmitting at least one spatial component of the first beam.

10. A spectrometer according to claim 9, wherein the waveguide is an optical fiber.

11. A spectrometer according to claim 8, wherein each detector is a photodetector.

12. A spectrometer according to claim 8, wherein the phase retarder is a step optical retarder.

13. A spectrometer according to claim 8, wherein the phase delay is based upon an irregular sampling strategy.

14. A spectrometer according to claim 8, further including a processor for searching through a set of candidate frequencies for obtaining a sinusoidal series model.

15. A spectrometer for obtaining an electromagnetic spectrum of a substance, the spectrometer comprising:

a. an input for receiving electromagnetic radiation;

b. a beamsplitter for splitting the electromagnetic radiation into a first set of beams and a second set of beams;

c. a plurality of phase retarders for introducing irregularly spaced phase delays in the first set of beams relative to the second set of beams in such a manner that the phase delays differ among the first set of beams and among the second set of beams; and

d. an array of detectors, such that each detector receives a spatial component of the first beam and a spatial component of the second beam.