Abstract

Computed tomographic imaging spectrometers measure the spectrally resolved image of an object scene in an entirely different manner from traditional whisk-broom or push-broom systems, and thus their noise behavior and data artifacts are unfamiliar. We review computed tomographic imaging spectrometry (CTIS) measurement systems and analyze their performance, with the aim of providing a vocabulary for discussing resolution in CTIS instruments, by illustrating the artifacts present in their reconstructed data and contributing a rule-of-thumb measure of their spectral resolution. We also show how the data reconstruction speed can be improved, at no cost in reconstruction quality, by ignoring redundant projections within the measured raw images.

© 2008 Optical Society of America

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References

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2002 (1)

D. Sabatke, A. Locke, E. L. Dereniak, M. Descour, J. Garcia, T. Hamilton, and R. W. McMillan, “Snapshot imaging spectropolarimeter,” Opt. Eng. 41, 1048-1054 (2002).
[CrossRef]

1999 (1)

1997 (2)

1995 (1)

1993 (1)

1981 (1)

An, M.

Barrett, H. H.

H. H. Barrett and K. Myers, Foundations of Image Science (Wiley, 2004).

H. H. Barrett and K. Myers, Foundations of Image Science (Wiley, 2004), p. 311.

Brodzik, A. K.

Dereniak, E.

Dereniak, E. L.

Descour, M.

D. Sabatke, A. Locke, E. L. Dereniak, M. Descour, J. Garcia, T. Hamilton, and R. W. McMillan, “Snapshot imaging spectropolarimeter,” Opt. Eng. 41, 1048-1054 (2002).
[CrossRef]

M. Descour and E. Dereniak, “Computed-tomography imaging spectrometer: experimental calibration and reconstruction results,” Appl. Opt. 34, 4817-4826 (1995).
[CrossRef] [PubMed]

Descour, M. R.

Garcia, J.

D. Sabatke, A. Locke, E. L. Dereniak, M. Descour, J. Garcia, T. Hamilton, and R. W. McMillan, “Snapshot imaging spectropolarimeter,” Opt. Eng. 41, 1048-1054 (2002).
[CrossRef]

George, J. D.

J. D. George, “Designing a non-scanning imaging spectrometer,” Ph.D. dissertation (University of Arizona, 2001).

Gleeson, T. M.

Hamilton, T.

D. Sabatke, A. Locke, E. L. Dereniak, M. Descour, J. Garcia, T. Hamilton, and R. W. McMillan, “Snapshot imaging spectropolarimeter,” Opt. Eng. 41, 1048-1054 (2002).
[CrossRef]

Hopkins, M. F.

Locke, A.

D. Sabatke, A. Locke, E. L. Dereniak, M. Descour, J. Garcia, T. Hamilton, and R. W. McMillan, “Snapshot imaging spectropolarimeter,” Opt. Eng. 41, 1048-1054 (2002).
[CrossRef]

Maker, P. D.

McMillan, R. W.

D. Sabatke, A. Locke, E. L. Dereniak, M. Descour, J. Garcia, T. Hamilton, and R. W. McMillan, “Snapshot imaging spectropolarimeter,” Opt. Eng. 41, 1048-1054 (2002).
[CrossRef]

Mooney, J. M.

Myers, K.

H. H. Barrett and K. Myers, Foundations of Image Science (Wiley, 2004).

H. H. Barrett and K. Myers, Foundations of Image Science (Wiley, 2004), p. 311.

Okamoto, T.

Perez-Mendez, V.

Sabatke, D.

D. Sabatke, A. Locke, E. L. Dereniak, M. Descour, J. Garcia, T. Hamilton, and R. W. McMillan, “Snapshot imaging spectropolarimeter,” Opt. Eng. 41, 1048-1054 (2002).
[CrossRef]

Takahashi, A.

Tam, K. C.

Vickers, V. E.

Volin, C. E.

Wilson, D. W.

Yamaguchi, I.

Appl. Opt. (2)

Appl. Spectrosc. (1)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Opt. Eng. (1)

D. Sabatke, A. Locke, E. L. Dereniak, M. Descour, J. Garcia, T. Hamilton, and R. W. McMillan, “Snapshot imaging spectropolarimeter,” Opt. Eng. 41, 1048-1054 (2002).
[CrossRef]

Other (3)

H. H. Barrett and K. Myers, Foundations of Image Science (Wiley, 2004).

H. H. Barrett and K. Myers, Foundations of Image Science (Wiley, 2004), p. 311.

J. D. George, “Designing a non-scanning imaging spectrometer,” Ph.D. dissertation (University of Arizona, 2001).

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Figures (15)

Fig. 1
Fig. 1

CTIS instrument views the target scene through a 2D grating. The field stop limits the field of view, such that the dispersed diffraction orders are spatially separated.

Fig. 2
Fig. 2

Nondescript scene taken with an RGB camera and a pair of crossed gratings inserted in front of the lens.

Fig. 3
Fig. 3

The 5 × 5 CTIS design produces a pattern of 25 projections onto the detector array, each of which is a prismatic version of the zero-order image. Each of these prismatic images produces a footprint on the detector array that is a tomographic projection through the object scene’s 3D data cube.

Fig. 4
Fig. 4

Past CTIS dispersion patterns: from left to right, 3 × 3 pattern produced by a pair of crossed cosine gratings, 3XCos pattern produced by three cosine gratings oriented at 60 ° to one another, 5 × 5 pattern, 7 × 7 pattern.

Fig. 5
Fig. 5

Illustration of the spatial–spectral sampling trade-off in a given CTIS design. For a focal plane array of dimension Z and a data cube dimension of D (this latter giving the spatial sampling), the longest wavelength is diffracted to the edge of the array: a distance of ( Z / 2 ) ( D / 2 ) in pixel units. If we assume a spectral range of 400 700 nm , then the shortest wavelength image is diffracted by 4 / 7 of the same distance. The spectral dispersion distance is therefore ( 3 / 7 ) [ ( Z D ) / 2 ] . Along an outer diagonal order, this distance is increased by 2.

Fig. 6
Fig. 6

Left, various CTIS dispersion patterns and, right, their corresponding Fourier slice diagrams.

Fig. 7
Fig. 7

(a) For a CTHIS instrument taking a large number of projections, the missing cone becomes a true right-circular double cone. (b) In the corresponding Fourier cube, any planar slice containing the h axis will have the form shown. (Black indicates the missing cone region; white indicates the sampled regions.) (c) Corresponding VSF. Here ( ρ , h ) and ( x , λ ) are Fourier conjugate coordinates.

Fig. 8
Fig. 8

Spectra from different spatial positions in the reconstructed 25 × 25 × 145 data cube for a point source with λ = 557 nm . The locations sampled in the data cube are indicated. Note that each of the spectra shares the same abscissa, ranging from 400 to 700 nm , and that the vertical axes (in arbitrary irradiance units) have a different scale in each plot: as we move further out from the center of the data cube, the peaks show a drop in amplitude by about a factor of 10 from one plot to the next.

Fig. 9
Fig. 9

Several planes shown from the reconstructed data cube for a point source at λ = 557 nm . The gray-scale mapping on these figures is logarithmic to accentuate the low-irradiance pixels. Each image is also scaled to have its brightest pixel map to white.

Fig. 10
Fig. 10

Several planes shown from the backprojected data cube for a point source at λ = 557 nm . The gray-scale mapping on these figures is linear. Each image is also scaled to have its brightest pixel map to white.

Fig. 11
Fig. 11

Best RMSE for the 16 data cube models. Left, comparing the corner patterns with the symmetric full patterns; right, comparing the outer patterns with the full patterns. The data cube models are numbered according to: (1) uniform, (2) point, (3) blob, (4) column, (5) wide column, (6) column_Mod10, (7) column_Mod20, (8) Mod0-0-10, (9) Mod5-5-0, (10) Mod8-8-0, (11) Mod5-5-5, (12) Mod8-8-8, (13) point + Bkgd , (14) UA_Logo, (15) starfield, (16) checkerboard. In the plots above, the most important feature to notice is where the curves diverge from one another at a given data cube model, showing that one pattern performs substantially better than the others. (Note that higher values in the plots indicate poorer reconstruction performance.)

Fig. 12
Fig. 12

Left, panchromatic images of three example input data cubes. Right, panchromatic images of the corresponding reconstructed data cubes, for the models (top) Mod5-5-5, (middle) UA_Logo, and (bottom) uniform.

Fig. 13
Fig. 13

Outer dispersion patterns from (left) 5 × 5 and (right) 7 × 7 patterns.

Fig. 14
Fig. 14

Sections of the vectorized Mod0-0-10 data cube (of dimensions 25 × 25 × 145 ), where every 145 voxel section (containing 10 periods of modulation) represents the spectrum at a single spatial location in the data cube. (a) Snapshot from the ( x , y ) = ( 0 , 0 ) corner of the data cube, moving to increasing values of x from left to right; (b) snapshot from the middle ( x , y ) = ( 12 , 12 ) region in the data cube. Note that the flat region of the red (central) curve of (b) is the exact middle spatial location in the data cube, and that the reconstructed voxels on the left-hand side show reverse contrast.

Fig. 15
Fig. 15

Section from the middle region of the vectorized Column_Mod10 data cube, where every 145 voxel section (containing 10 periods of modulation) represents the spectrum at a single spatial location.

Tables (3)

Tables Icon

Table 1 Comparison of Linear CTIS Patterns a

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Table 2 Data Cube Models Used in the CTIS Simulation a

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Table 3 Comparing MTF Values with the RMSE Measure for the Two Spectrally Modulated Data Cube Models

Equations (2)

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L 3 2 14 ( Z D ) ,
ϵ = ( 1 m = 1 M f m m = 1 M ( f m f ^ m ) 2 ) 1 / 2 ,

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