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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 13, Iss. 11 — Nov. 1, 1974
  • pp: 2669–2674

Two Asymmetric Hadamard Transform Spectrometers

Martin Harwit, Perry G. Phillips, Leon W. King, and Daniel A. Briotta, Jr.  »View Author Affiliations


Applied Optics, Vol. 13, Issue 11, pp. 2669-2674 (1974)
http://dx.doi.org/10.1364/AO.13.002669


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Abstract

We develop the theory of operation for dispersive spectrometers that modulate radiation at both the entrance and exit apertures by means of Hadamard codes. Specifically, we examine the operation of instruments illuminated by a beam of radiation known to be homogeneous. In this case, all spatial information obtained in the operation of the instrument can be effectively suppressed at no loss of spectral performance and at a considerable reduction in the number of measurements that need to be made. A particularly interesting instrument which mocks a monochromator is described. The spectrum is directly obtained from the data by simply subtracting a constant intensity value from all readings. This instrument bears a resemblance to the Girard grill spectrometer. We describe the construction and operation of an instrument that has been tested in both modes of operation and show some of the spectra obtained.

© 1974 Optical Society of America

History
Original Manuscript: April 9, 1973
Published: November 1, 1974

Citation
Martin Harwit, Perry G. Phillips, Leon W. King, and Daniel A. Briotta, "Two Asymmetric Hadamard Transform Spectrometers," Appl. Opt. 13, 2669-2674 (1974)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-13-11-2669


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References

  1. N. J. A. Sloane, T. Fine, P. G. Phillips, M. Harwit, Appl. Opt. 8, 2103 (1969). [CrossRef] [PubMed]
  2. J. A. Decker, M. Harwit, Appl. Opt. 8, 2552 (1969). [CrossRef] [PubMed]
  3. J. A. Decker, Appl. Opt. 10, 510 (1971). [CrossRef] [PubMed]
  4. M. Harwit, P. G. Phillips, T. Fine, N. J. A. Sloane, Appl. Opt. 9, 1149 (1970). [CrossRef] [PubMed]
  5. P. G. Phillips, M. Harwit, Appl. Opt. 10, 2780 (1971). [CrossRef] [PubMed]
  6. M. Harwit, Appl. Opt. 10, 1415 (1971). [CrossRef] [PubMed]
  7. We deliberately use the word encode throughout this paper to denote the modulation in the signal produced at the entrance and exit apertures. In an earlier paper4 we talked about doubly multiplexing since two separate encoding processes were involved, one at the entrance aperture, the other at the exit of the grating instrument. But the word multiplexing frequently has the connotation of color encoding, and several readers found this awkward.
  8. We use the figure of merit ∊/σ2 throughout this paper. It is proportional to the mean square noise of the final spectrum and provides a measure of the advantage to be gained by any given encoding procedure. For a single entrance, single exit slit instrument, this figure of merit is n, where n is the number of spectral elements in the spectrum. The same spectrum viewed with a single entrance, multiexit slit spectrometer would be 4. The lower the figure of merit, the better is the performance of the instrument.
  9. A. Girard, Appl Opt. 2, 79 (1963). [CrossRef]
  10. The fact that we do not obtain the full advantage indicates that we are not yet encoding optimally. A weakness of our current theoretical approach is that it permits an evaluation of a figure of merit once an encoding scheme is proposed. However, it does not provide basic rules that would permit us to construct improved codes. We are currently investigating codes that could provide further improvement.
  11. L. Mertz, Transformations in Optics (Wiley, New York, 1965), p. 68.
  12. P. Hansen, J. Strong, Appl. Opt. 11, 502 (1972). [CrossRef] [PubMed]
  13. E. D. Nelson, M. L. Fredman, J. Opt. Soc. Am. 60, 1664 (1970). [CrossRef]

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