Abstract

Infrared spectral features have proved useful in the identification of threat objects. Dual-band focal-plane arrays (FPAs) have been developed in which each pixel consists of superimposed midwave and long-wave photodetectors [Dyer and Tidrow, Conference on Infrared Detectors and Focal Plane Arrays (SPIE, Bellingham, Wash., 1999), pp. 434–440]. Combining dual-band FPAs with imaging spectrometers capable of interband hyperspectral resolution greatly improves spatial target discrimination. The computed-tomography imaging spectrometer (CTIS) [Descour and Dereniak, Appl. Opt. 34, 4817–4826 (1995)] has proved effective in producing hyperspectral images in a single spectral region. Coupling the CTIS with a dual-band detector can produce two hyperspectral data cubes simultaneously. We describe the design of two-dimensional, surface-relief, computer-generated hologram dispersers that permit image information in these two bands simultaneously.

© 2003 Optical Society of America

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References

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  1. M. R. Descour, E. L. Dereniak, “Computed-tomography imaging spectrometer: experimental calibration and reconstruction results,” Appl. Opt. 34, 4817–4826 (1995).
    [CrossRef] [PubMed]
  2. C. E. Volin, J. P. Garcia, E. L. Dereniak, M. R. Descour, T. Hamilton, R. McMillan, “Midwave-infrared snapshot imaging spectrometer,” Appl. Opt. 40, 4501–4506 (2001).
    [CrossRef]
  3. B. Ford, M. R. Descour, R. M. Lynch, “Large-image-format computed tomography imaging spectrometer for fluorescence microscopy,” Opt. Express 9, 444–453 (2001).
    [CrossRef] [PubMed]
  4. W. R. Dyer, M. Z. Tidrow, “Applications of MCT and QWIP to ballistic missile defense,” in Infrared Detectors and Focal Plane Arrays V, E. L. Derniak, R. E. Sampson, eds., Proc. SPIE3379, 434–440 (1999).
  5. A number of spectral libraries can be accessed from the Internet from the USGS. The main web address is http://speclab.cr.usgs.gov/spectral-lib.html .
  6. C. L. Coleman, “Computer generated holograms for free-space optical interconnects,” Ph.D. dissertation (Optical Sciences Center, University of Arizona, Tucson, Ariz., 1998), Chap. 3.
  7. G. H. Golub, C. F. Van Loan, Matrix Computations, 3rd ed. (Johns Hopkins University Press, Baltimore, Md., 1996).
  8. H. H. Barrett, K. M. Myers, Foundations of Image Science: Mathematical and Statistical Foundations, (Wiley, Hoboken, N. J., 2003), (to be published).
  9. M. R. Descour, C. E. Volin, E. L. Dereniak, T. M. Gleeson, M. F. Hopkins, D. W. Wilson, P. D. Maker, “Demonstration of a computed-tomography imaging spectrometer using a computer-generated hologram disperser,” Appl. Opt. 36, 3694–3698 (1997).
    [CrossRef] [PubMed]

2001 (2)

1997 (1)

1995 (1)

Barrett, H. H.

H. H. Barrett, K. M. Myers, Foundations of Image Science: Mathematical and Statistical Foundations, (Wiley, Hoboken, N. J., 2003), (to be published).

Coleman, C. L.

C. L. Coleman, “Computer generated holograms for free-space optical interconnects,” Ph.D. dissertation (Optical Sciences Center, University of Arizona, Tucson, Ariz., 1998), Chap. 3.

Dereniak, E. L.

Descour, M. R.

Dyer, W. R.

W. R. Dyer, M. Z. Tidrow, “Applications of MCT and QWIP to ballistic missile defense,” in Infrared Detectors and Focal Plane Arrays V, E. L. Derniak, R. E. Sampson, eds., Proc. SPIE3379, 434–440 (1999).

Ford, B.

Garcia, J. P.

Gleeson, T. M.

Golub, G. H.

G. H. Golub, C. F. Van Loan, Matrix Computations, 3rd ed. (Johns Hopkins University Press, Baltimore, Md., 1996).

Hamilton, T.

Hopkins, M. F.

Lynch, R. M.

Maker, P. D.

McMillan, R.

Myers, K. M.

H. H. Barrett, K. M. Myers, Foundations of Image Science: Mathematical and Statistical Foundations, (Wiley, Hoboken, N. J., 2003), (to be published).

Tidrow, M. Z.

W. R. Dyer, M. Z. Tidrow, “Applications of MCT and QWIP to ballistic missile defense,” in Infrared Detectors and Focal Plane Arrays V, E. L. Derniak, R. E. Sampson, eds., Proc. SPIE3379, 434–440 (1999).

Van Loan, C. F.

G. H. Golub, C. F. Van Loan, Matrix Computations, 3rd ed. (Johns Hopkins University Press, Baltimore, Md., 1996).

Volin, C. E.

Wilson, D. W.

Appl. Opt. (3)

Opt. Express (1)

Other (5)

W. R. Dyer, M. Z. Tidrow, “Applications of MCT and QWIP to ballistic missile defense,” in Infrared Detectors and Focal Plane Arrays V, E. L. Derniak, R. E. Sampson, eds., Proc. SPIE3379, 434–440 (1999).

A number of spectral libraries can be accessed from the Internet from the USGS. The main web address is http://speclab.cr.usgs.gov/spectral-lib.html .

C. L. Coleman, “Computer generated holograms for free-space optical interconnects,” Ph.D. dissertation (Optical Sciences Center, University of Arizona, Tucson, Ariz., 1998), Chap. 3.

G. H. Golub, C. F. Van Loan, Matrix Computations, 3rd ed. (Johns Hopkins University Press, Baltimore, Md., 1996).

H. H. Barrett, K. M. Myers, Foundations of Image Science: Mathematical and Statistical Foundations, (Wiley, Hoboken, N. J., 2003), (to be published).

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Figures (24)

Fig. 1
Fig. 1

Object-cube collection methods. (a) Conventional methods. (b) Result of object-cube collection with a CTIS instrument.

Fig. 2
Fig. 2

Soil spectral signatures for (a) dark, reddish-brown, organic-rich, silty loam and (b) brown-to-dark brown sand. Note the spectral features in the sand in the LWIR (8– 12 µm) band that are absent from the loam signature. Also note that the spectral features in the MWIR (3–5 µm) band for both soils are very similar.

Fig. 3
Fig. 3

Projections of the object cube. Spectral information along the vertical axis of the object cube is projected along the radial coordinate of the focal plane and multiplexed with spatial information.

Fig. 4
Fig. 4

Optical schematic of the basic CTIS instrument. The CTIS consists of four optics groups: an objective lens (shown here as a three-lens zoom lens), a collimator lens (shown here as a three-lens zoom lens), a dispersive element (shown here as a rectangular block), and a reimaging lens (shown here as a biconvex single lens). The final plane, shown on the far right, represents the focal-plane array.

Fig. 5
Fig. 5

MWIR CTIS instrument indicating where the optical components diagrammed in Fig. 4 are placed. The FPA in the MWIR instrument is cooled with liquid nitrogen.

Fig. 6
Fig. 6

Example of a CGH disperser. This disperser consists of 2 × 2 unit cells. Each unit cell consists of 10 × 10 pixels. Each pixel has a uniform depth. The cell size is the fundamental period of the CGH, which determines the diffraction angles.

Fig. 7
Fig. 7

Schematic similar to that shown in Fig. 2 of how a dual-band disperser projects the object cube for the MWIR and the LWIR bands onto a two-layer FPA. Note that for a fixed size of the FPA, the dual-band disperser can project the MWIR hyperspectral object-cube data at most onto the central 5 × 5 diffraction orders and project the LWIR hyperspectral object-cube data at most onto the central 3 × 3 orders.

Fig. 8
Fig. 8

CGH-disperser profile of the 8 × 8 pixel unit cell for design 1 at 7.5 µm on an IR transmissive material.

Fig. 9
Fig. 9

Representative diffraction-efficiency patterns corresponding to the design 1 in the MWIR wavelength band. All figures are far-field diffraction patterns of a unit cell of a CGH phase grating. The top set of figures illustrate the desired prespecified diffraction-efficiency pattern of the central 5 × 5 diffraction orders all with equal intensity. The bottom set of figures are the corresponding actual diffraction-efficiency patterns from that design.

Fig. 10
Fig. 10

Representative desired and actual diffraction-efficiency patterns for design 1 as in Fig. 9 but for the LWIR wavelength range of 8–12 µm. The desired diffraction-efficiency pattern in the top set of figures has equal intensity in the 3 × 3 central diffraction orders.

Fig. 11
Fig. 11

Summed diffraction efficiency for the zeroth, intermediate, and outer diffraction orders as a function of wavelength for the design-1, phase-only CGH disperser. Note that the second-order curve representing the sum of diffraction efficiencies into the outermost diffraction orders in the 5 × 5 set diminishes in the LWIR band. This effect is in agreement with the constraint that only a 3 × 3 diffraction-order set be emphasized in the LWIR performance of the dual-band CGH disperser.

Fig. 12
Fig. 12

Average diffraction efficiency per diffraction order for the central 5 × 5 diffraction orders as a function of wavelength for the phase grating of design 1. The group labeled first order consists of the eight diffraction orders surrounding the zeroth diffraction order. The group labeled second order consists of the outermost diffraction orders in the 5 × 5 diffraction-order set.

Fig. 13
Fig. 13

MSE between the desired and the predicted FPA irradiance patterns associated with the design-1, phase-only CGH disperser.

Fig. 14
Fig. 14

Total diffraction efficiency ηtotal(λ) of the desired diffraction orders versus the wavelength for the designs 1 and 2 dual-band CGH dispersers. This number is also the same as the fraction of desired energy onto the FPA. For an ideal design these values should be unity at each wavelength. Note the discontinuity at 9 µm for the design-1 disperser.

Fig. 15
Fig. 15

CGH-disperser profile of the 8 × 8 pixel unit cell for design 2 at 7.5 µm on an IR transmissive material.

Fig. 16
Fig. 16

Representative diffraction-efficiency patterns corresponding to the design 2 in the MWIR wavelength band. All figures are far-field diffraction patterns of a unit cell of a CGH phase grating. The top set of figures illustrate the desired prespecified diffraction-efficiency pattern of the central 3 × 3 diffraction orders all with equal intensity. The bottom set of figures are the corresponding actual diffraction-efficiency patterns from that design.

Fig. 17
Fig. 17

Representative desired and actual diffraction-efficiency patterns for design 2 as in Fig. 16 but for the LWIR wavelength range of 8–12 µm. The desired diffraction-efficiency pattern in the top set of figures has equal intensity in the 3 × 3 central diffraction orders.

Fig. 18
Fig. 18

Summed diffraction efficiency for the zeroth and outer diffraction orders as a function of wavelength for the design-2, phase-only CGH disperser. The diffraction orders in the group labeled first order are the eight diffraction orders surrounding the zeroth diffraction order. Note that in this design, the total diffraction efficiency in the first-order group is approximately eight times greater than the diffraction efficiency in the zeroth diffraction order. This is in good agreement with the design constraint of equal diffraction efficiency among all diffraction orders in the 3 × 3 set.

Fig. 19
Fig. 19

Average diffraction efficiency per diffraction order for the central 3 × 3 diffraction orders as a function of wavelength for the phase grating of design 2. The group labeled first order consists of the eight diffraction orders surrounding the zeroth diffraction order. Note that with the exception of the problem at 3.6 µm, the average diffraction efficiencies in the zeroth- and the first-order groups remain nearly the same and invariant with wavelength.

Fig. 20
Fig. 20

MSE between the desired and the predicted FPA irradiance patterns associated with the design-2, phase-only CGH disperser.

Fig. 21
Fig. 21

Distribution of the normalized, wavelength-integrated energy onto the central 5 × 5 diffraction orders on the FPA due to design 1. Diffraction-efficiency integration is performed over the MWIR range of 3–5 µm. After normalization, the average wavelength-integrated diffraction efficiency is unity. The IEFOM is the standard deviation of the values that make up the 2D bar chart in this figure. In the case of our ideal design, all values plotted in this figure would equal unity.

Fig. 22
Fig. 22

Distribution of the normalized, integrated energy onto the central 3 × 3 diffraction orders on the FPA due to design 1. Diffraction-efficiency integration is performed over the LWIR range of 8–12 µm.

Fig. 23
Fig. 23

Distribution of the normalized, wavelength-integrated energy onto the central 3 × 3 diffraction orders on the FPA due to design 2. Diffraction-efficiency integration is performed over the MWIR range of 3–5 µm.

Fig. 24
Fig. 24

Distribution of the normalized, integrated energy onto the central 3 × 3 diffraction orders on the FPA due to design 2. Diffraction-efficiency integration is performed over the LWIR range of 8–12 µm.

Tables (1)

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Table 1 IEFOM Values for the Two Dual-Band CGH-Disperser Designs Presented in This Paper

Equations (8)

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ϕpixelλ=2πλnλ-1dpixel,
t0r, s, λ=n=-N/2N/2-1m=-M/2M/2-1expiΦmnλδr-nd×δs-md **rectrd, sd,
tr, s, λ=t0r, s, λ**1NMdcombrNd, sMd×rectrRNd, sSMd,
combx=n=- δx-n.
Ux, y, λ  RSMNd2 sinc RNdxλf, SMdyλf**×n=-N/2N/2-1m=M/2M/2-1expiΦmnλexp×-i2πdnx+myλf×d2 sincdxλf, dyλf×combNdxλf, Mdyλf,
MSEλ=1256m=-87n=-87ηmndλ-ηmnaλ2,
ηtotalλ=m,ndesired ηm,naλ.
IEFOMMWIR=λ=3μm5 μm1K-1×specifiedm,nηmnaλ-η¯MWIR2, IEFOMLWIR=λ=8μm12μm1K-1×specifiedm,nηmnaλ-η¯LWIR2,

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