Abstract

We show that computer-generated diffractive optical elements can be used to synthesize the infrared spectra of important compounds, and we describe a modified phase-retrieval algorithm useful for the design of elements of this type. In particular, we present the results of calculations of diffractive elements that are capable of synthesizing portions of the infrared spectra of gaseous hydrogen fluoride (HF) and trichloroethylene (TCE). Further, we propose a new type of correlation spectrometer that uses these diffractive elements rather than reference cells for the production of reference spectra. Storage of a large number of diffractive elements, each producing a synthetic spectrum corresponding to a different target compound, in compact-disk-like format will allow a spectrometer of this type to rapidly determine the composition of unknown samples. Other advantages of the proposed correlation spectrometer are also discussed.

© 1997 Optical Society of America

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References

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  1. R. Goody, “Cross-correlating spectrometer,” J. Opt. Soc. Am. 58, 900–908 (1968).
    [CrossRef]
  2. H. O. Edwards, J. P. Daikin, “Gas sensors using correlation spectroscopy compatible with fibre-optic operation,” Sensors Actuators B 11, 9–19 (1993).
    [CrossRef]
  3. F. W. Taylor, J. T. Houghton, G. D. Peskett, C. D. Rodgers, E. J. Williamson, “Radiometer for remote sounding of the upper atmosphere,” Appl. Opt. 11, 135–141 (1972).
    [CrossRef] [PubMed]
  4. J. Strong, “Balloon telescope optics,” Appl. Opt. 6, 179–189 (1967).
    [CrossRef] [PubMed]
  5. J. de Frutos, J. M. Rodríguez, F. López, A. J. de Castro, J. Meléndez, J. Meneses, “Electrooptical infrared compact gas sensor,” Sensors Actuators B 18–19, 682–686 (1994).
    [CrossRef]
  6. T. Chen, “Wavelength-modulated optical gas sensors,” Sensors Actuators B 13–14, 284–287 (1993).
    [CrossRef]
  7. The adjective holographic is used, not because holography is used to produce the diffractive elements, but because like white-light holograms, the diffractive elements are designed to simultaneously diffract several wavelengths of light at a common diffraction angle.
  8. D. M. Rider, J. T. Schofield, J. S. Margolis, D. J. McCleese, “Electrooptic phase modulation gas correlation spectroscopy: laboratory demonstration,” Appl. Opt. 25, 2860–2862 (1986).
    [CrossRef] [PubMed]
  9. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 4, pp. 57–74.
  10. R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).
  11. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982).
    [CrossRef] [PubMed]
  12. F. Wyrowski, O. Bryngdahl, “Iterative Fourier-transform algorithm applied to computer holography,” J. Opt. Soc. Am. A 5, 1058–1065 (1988).
    [CrossRef]
  13. F. Wyrowski, “Diffractive optical elements: iterative calculation of quantized blazed phase structures,” J. Opt. Soc. Am. A 7, 961–969 (1990).
    [CrossRef]
  14. T. Peter, F. Wyrowski, O. Bryngdahl, “Comparison of iterative methods to calculate quantized digital holograms,” in Workshop on Digital Holography, F. Wyrowski, ed., Proc. SPIE1718, 55–62 (1992).
    [CrossRef]
  15. The infrared spectra were obtained from Infrared Analysis, Inc., 1334 North Knollwood Circle, Anaheim, Calif., 92801.
  16. O. Solgaard, F. S. A. Sandejas, D. M. Bloom, “Deformable grating optical modulator,” Opt. Lett. 17, 688–690 (1992).
    [CrossRef] [PubMed]
  17. The pull-in voltage is the voltage necessary to cause a flexure-supported, micromachined element to snap down into contact with the underlying substrate.

1994

J. de Frutos, J. M. Rodríguez, F. López, A. J. de Castro, J. Meléndez, J. Meneses, “Electrooptical infrared compact gas sensor,” Sensors Actuators B 18–19, 682–686 (1994).
[CrossRef]

1993

T. Chen, “Wavelength-modulated optical gas sensors,” Sensors Actuators B 13–14, 284–287 (1993).
[CrossRef]

H. O. Edwards, J. P. Daikin, “Gas sensors using correlation spectroscopy compatible with fibre-optic operation,” Sensors Actuators B 11, 9–19 (1993).
[CrossRef]

1992

1990

1988

1986

1982

1972

F. W. Taylor, J. T. Houghton, G. D. Peskett, C. D. Rodgers, E. J. Williamson, “Radiometer for remote sounding of the upper atmosphere,” Appl. Opt. 11, 135–141 (1972).
[CrossRef] [PubMed]

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

1968

1967

Bloom, D. M.

Bryngdahl, O.

F. Wyrowski, O. Bryngdahl, “Iterative Fourier-transform algorithm applied to computer holography,” J. Opt. Soc. Am. A 5, 1058–1065 (1988).
[CrossRef]

T. Peter, F. Wyrowski, O. Bryngdahl, “Comparison of iterative methods to calculate quantized digital holograms,” in Workshop on Digital Holography, F. Wyrowski, ed., Proc. SPIE1718, 55–62 (1992).
[CrossRef]

Chen, T.

T. Chen, “Wavelength-modulated optical gas sensors,” Sensors Actuators B 13–14, 284–287 (1993).
[CrossRef]

Daikin, J. P.

H. O. Edwards, J. P. Daikin, “Gas sensors using correlation spectroscopy compatible with fibre-optic operation,” Sensors Actuators B 11, 9–19 (1993).
[CrossRef]

de Castro, A. J.

J. de Frutos, J. M. Rodríguez, F. López, A. J. de Castro, J. Meléndez, J. Meneses, “Electrooptical infrared compact gas sensor,” Sensors Actuators B 18–19, 682–686 (1994).
[CrossRef]

de Frutos, J.

J. de Frutos, J. M. Rodríguez, F. López, A. J. de Castro, J. Meléndez, J. Meneses, “Electrooptical infrared compact gas sensor,” Sensors Actuators B 18–19, 682–686 (1994).
[CrossRef]

Edwards, H. O.

H. O. Edwards, J. P. Daikin, “Gas sensors using correlation spectroscopy compatible with fibre-optic operation,” Sensors Actuators B 11, 9–19 (1993).
[CrossRef]

Fienup, J. R.

Gerchberg, R. W.

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 4, pp. 57–74.

Goody, R.

Houghton, J. T.

López, F.

J. de Frutos, J. M. Rodríguez, F. López, A. J. de Castro, J. Meléndez, J. Meneses, “Electrooptical infrared compact gas sensor,” Sensors Actuators B 18–19, 682–686 (1994).
[CrossRef]

Margolis, J. S.

McCleese, D. J.

Meléndez, J.

J. de Frutos, J. M. Rodríguez, F. López, A. J. de Castro, J. Meléndez, J. Meneses, “Electrooptical infrared compact gas sensor,” Sensors Actuators B 18–19, 682–686 (1994).
[CrossRef]

Meneses, J.

J. de Frutos, J. M. Rodríguez, F. López, A. J. de Castro, J. Meléndez, J. Meneses, “Electrooptical infrared compact gas sensor,” Sensors Actuators B 18–19, 682–686 (1994).
[CrossRef]

Peskett, G. D.

Peter, T.

T. Peter, F. Wyrowski, O. Bryngdahl, “Comparison of iterative methods to calculate quantized digital holograms,” in Workshop on Digital Holography, F. Wyrowski, ed., Proc. SPIE1718, 55–62 (1992).
[CrossRef]

Rider, D. M.

Rodgers, C. D.

Rodríguez, J. M.

J. de Frutos, J. M. Rodríguez, F. López, A. J. de Castro, J. Meléndez, J. Meneses, “Electrooptical infrared compact gas sensor,” Sensors Actuators B 18–19, 682–686 (1994).
[CrossRef]

Sandejas, F. S. A.

Saxton, W. O.

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Schofield, J. T.

Solgaard, O.

Strong, J.

Taylor, F. W.

Williamson, E. J.

Wyrowski, F.

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Lett.

Optik

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Sensors Actuators B

H. O. Edwards, J. P. Daikin, “Gas sensors using correlation spectroscopy compatible with fibre-optic operation,” Sensors Actuators B 11, 9–19 (1993).
[CrossRef]

J. de Frutos, J. M. Rodríguez, F. López, A. J. de Castro, J. Meléndez, J. Meneses, “Electrooptical infrared compact gas sensor,” Sensors Actuators B 18–19, 682–686 (1994).
[CrossRef]

T. Chen, “Wavelength-modulated optical gas sensors,” Sensors Actuators B 13–14, 284–287 (1993).
[CrossRef]

Other

The adjective holographic is used, not because holography is used to produce the diffractive elements, but because like white-light holograms, the diffractive elements are designed to simultaneously diffract several wavelengths of light at a common diffraction angle.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 4, pp. 57–74.

The pull-in voltage is the voltage necessary to cause a flexure-supported, micromachined element to snap down into contact with the underlying substrate.

T. Peter, F. Wyrowski, O. Bryngdahl, “Comparison of iterative methods to calculate quantized digital holograms,” in Workshop on Digital Holography, F. Wyrowski, ed., Proc. SPIE1718, 55–62 (1992).
[CrossRef]

The infrared spectra were obtained from Infrared Analysis, Inc., 1334 North Knollwood Circle, Anaheim, Calif., 92801.

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Figures (5)

Fig. 1
Fig. 1

Schematic representations of (a) a traditional correlation spectrometer and (b) a holographic correlation spectrometer.

Fig. 2
Fig. 2

Block diagram of the iterative Fourier transform phase-retrieval algorithm used to design diffractive elements for the production of synthetic spectra.

Fig. 3
Fig. 3

A schematic representation of part of the diffractive element designed for the synthesis of the HF spectrum shown in Fig. 4(b). Only the first 64 of the 4096 lines of the element are shown. Note that the aspect ratio used for this diagram exaggerates the relative amplitude of the surface relief profile.

Fig. 4
Fig. 4

(a) Spectrum (1 - T) of gaseous HF. (b) Calculated synthetic spectrum from a diffractive element designed to detect HF. (c) Calculated spectrum of the same element as in (b) observed at a slightly different diffraction angle (14.9° versus 15°).

Fig. 5
Fig. 5

(a) Spectrum (1 - T) of TCE. (b) Calculated synthetic spectrum of a diffractive element designed for the detection of TCE. (c) The calculated synthetic spectrum of a diffractive element designed to produce the spectrum of TCE with the 850 cm-1 absorption line intentionally omitted.

Equations (6)

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δPP0δλ=λ1λ2dλTSλTRλ+δλ-TRλ12λ1λ2dλTSλTRλ+δλ+TRλ,
δPP0δλ=-λ1λ2dλTSλTRλ+δλ-TRλ12λ1λ2dλTSλTRλ+δλ+TRλ-2.
auexpi·χu=C1λA  dx×expiϕλxexp-i2πux,
u=sinθλ=ν sinθ,
um=m/NΔ,  -N/2mN/2,
umax=um=N/2=12Δ=νmax sinθ,

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