Abstract

We have previously reported on coded aperture snapshot spectral imagers (CASSI) that can capture a full frame spectral image in a snapshot. Here we describe the use of CASSI for spectral imaging of a dynamic scene at video rate. We describe significant advances in the design of the optical system, system calibration procedures and reconstruction method. The new optical system uses a double Amici prism to achieve an in-line, direct view configuration, resulting in a substantial improvement in image quality. We describe NeAREst, an algorithm for estimating the instantaneous three-dimensional spatio-spectral data cube from CASSI’s two-dimensional array of encoded and compressed measurements. We utilize CASSI’s snapshot ability to demonstrate a spectral image video of multi-colored candles with live flames captured at 30 frames per second.

© 2009 Optical Society of America

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References

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  1. J. Mooney, V. Vickers, and A. Brodzik, "High throughput hyperspectral infrared camera," J. Opt. Soc. Am. A 14, 2951-2961 (1997).
    [CrossRef]
  2. C. Volin, B. Ford, M. Descour, J. Garcia, D. Wilson, P. Maker, and G. Bearman, "High-speed spectral imager for imaging transient fluorescent phenomena," Appl. Opt. 37, 8112-8119 (1998).
    [CrossRef]
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    [CrossRef]
  4. W. Johnson, D. Wilson, W. Fink, M. Humayun, and G. Bearman, "Snapshot hyperspectral imaging in ophthalmology," J. Biomed. Opt.  12, 0140,361-0140,367 (2007).
    [CrossRef]
  5. M. Descour, C. Volin, E. Dereniak, K. Thorne, A. Schumacher, D. Wilson, and P. Maker, "Demonstration of a high-speed nonscanning imaging spectrometer," Opt. Lett. 22, 1271-1273 (1997).
    [CrossRef] [PubMed]
  6. N. Gat, G. Scriven, J. Garman, M. D. Li, and J. Zhang, "Development of four-dimensional imaging spectrometers (4D-IS)," Proc. SPIE 6302, 63020M (2006).
    [CrossRef]
  7. A. Wagadarikar, R. John, R. Willett, and D. J. Brady, "Single disperser design for coded aperture snapshot spectral imaging," Appl. Opt. 47, B44-B51 (2008).
    [CrossRef]
  8. M. Gehm, R. John, D. J. Brady, R. Willett, and T. Schulz, "Single-shot compressive spectral imaging with a dual-disperser architecture," Opt. Express 15, 14,013-14,027 (2007).
    [CrossRef]
  9. A. Wagadarikar, N. Pitsianis, X. Sun, and D. Brady, "Spectral Image Estimation for Coded Aperture Snapshot Spectral Imagers," Proc. SPIE 7076, 707602 (2008).
    [CrossRef]
  10. X. Sun and N. Pitsianis, "Solving non-negative linear inverse problems with the NeAREst method," Proc. SPIE 7074, 7074E (2008).

2008 (3)

A. Wagadarikar, R. John, R. Willett, and D. J. Brady, "Single disperser design for coded aperture snapshot spectral imaging," Appl. Opt. 47, B44-B51 (2008).
[CrossRef]

A. Wagadarikar, N. Pitsianis, X. Sun, and D. Brady, "Spectral Image Estimation for Coded Aperture Snapshot Spectral Imagers," Proc. SPIE 7076, 707602 (2008).
[CrossRef]

X. Sun and N. Pitsianis, "Solving non-negative linear inverse problems with the NeAREst method," Proc. SPIE 7074, 7074E (2008).

2007 (1)

M. Gehm, R. John, D. J. Brady, R. Willett, and T. Schulz, "Single-shot compressive spectral imaging with a dual-disperser architecture," Opt. Express 15, 14,013-14,027 (2007).
[CrossRef]

2006 (1)

N. Gat, G. Scriven, J. Garman, M. D. Li, and J. Zhang, "Development of four-dimensional imaging spectrometers (4D-IS)," Proc. SPIE 6302, 63020M (2006).
[CrossRef]

2003 (1)

K. Hege, D. O’Connell, W. Johnson, S. Basty, and E. Dereniak, "Hyperspectral imaging for astronomy and space surveillance," Proc. SPIE 5159, 380-391 (2003).
[CrossRef]

1998 (1)

1997 (2)

Basty, S.

K. Hege, D. O’Connell, W. Johnson, S. Basty, and E. Dereniak, "Hyperspectral imaging for astronomy and space surveillance," Proc. SPIE 5159, 380-391 (2003).
[CrossRef]

Bearman, G.

Brady, D.

A. Wagadarikar, N. Pitsianis, X. Sun, and D. Brady, "Spectral Image Estimation for Coded Aperture Snapshot Spectral Imagers," Proc. SPIE 7076, 707602 (2008).
[CrossRef]

Brady, D. J.

A. Wagadarikar, R. John, R. Willett, and D. J. Brady, "Single disperser design for coded aperture snapshot spectral imaging," Appl. Opt. 47, B44-B51 (2008).
[CrossRef]

M. Gehm, R. John, D. J. Brady, R. Willett, and T. Schulz, "Single-shot compressive spectral imaging with a dual-disperser architecture," Opt. Express 15, 14,013-14,027 (2007).
[CrossRef]

Brodzik, A.

Dereniak, E.

K. Hege, D. O’Connell, W. Johnson, S. Basty, and E. Dereniak, "Hyperspectral imaging for astronomy and space surveillance," Proc. SPIE 5159, 380-391 (2003).
[CrossRef]

M. Descour, C. Volin, E. Dereniak, K. Thorne, A. Schumacher, D. Wilson, and P. Maker, "Demonstration of a high-speed nonscanning imaging spectrometer," Opt. Lett. 22, 1271-1273 (1997).
[CrossRef] [PubMed]

Descour, M.

Ford, B.

Garcia, J.

Garman, J.

N. Gat, G. Scriven, J. Garman, M. D. Li, and J. Zhang, "Development of four-dimensional imaging spectrometers (4D-IS)," Proc. SPIE 6302, 63020M (2006).
[CrossRef]

Gat, N.

N. Gat, G. Scriven, J. Garman, M. D. Li, and J. Zhang, "Development of four-dimensional imaging spectrometers (4D-IS)," Proc. SPIE 6302, 63020M (2006).
[CrossRef]

Gehm, M.

M. Gehm, R. John, D. J. Brady, R. Willett, and T. Schulz, "Single-shot compressive spectral imaging with a dual-disperser architecture," Opt. Express 15, 14,013-14,027 (2007).
[CrossRef]

Hege, K.

K. Hege, D. O’Connell, W. Johnson, S. Basty, and E. Dereniak, "Hyperspectral imaging for astronomy and space surveillance," Proc. SPIE 5159, 380-391 (2003).
[CrossRef]

John, R.

A. Wagadarikar, R. John, R. Willett, and D. J. Brady, "Single disperser design for coded aperture snapshot spectral imaging," Appl. Opt. 47, B44-B51 (2008).
[CrossRef]

M. Gehm, R. John, D. J. Brady, R. Willett, and T. Schulz, "Single-shot compressive spectral imaging with a dual-disperser architecture," Opt. Express 15, 14,013-14,027 (2007).
[CrossRef]

Johnson, W.

K. Hege, D. O’Connell, W. Johnson, S. Basty, and E. Dereniak, "Hyperspectral imaging for astronomy and space surveillance," Proc. SPIE 5159, 380-391 (2003).
[CrossRef]

Li, M. D.

N. Gat, G. Scriven, J. Garman, M. D. Li, and J. Zhang, "Development of four-dimensional imaging spectrometers (4D-IS)," Proc. SPIE 6302, 63020M (2006).
[CrossRef]

Maker, P.

Mooney, J.

O’Connell, D.

K. Hege, D. O’Connell, W. Johnson, S. Basty, and E. Dereniak, "Hyperspectral imaging for astronomy and space surveillance," Proc. SPIE 5159, 380-391 (2003).
[CrossRef]

Pitsianis, N.

A. Wagadarikar, N. Pitsianis, X. Sun, and D. Brady, "Spectral Image Estimation for Coded Aperture Snapshot Spectral Imagers," Proc. SPIE 7076, 707602 (2008).
[CrossRef]

X. Sun and N. Pitsianis, "Solving non-negative linear inverse problems with the NeAREst method," Proc. SPIE 7074, 7074E (2008).

Schulz, T.

M. Gehm, R. John, D. J. Brady, R. Willett, and T. Schulz, "Single-shot compressive spectral imaging with a dual-disperser architecture," Opt. Express 15, 14,013-14,027 (2007).
[CrossRef]

Schumacher, A.

Scriven, G.

N. Gat, G. Scriven, J. Garman, M. D. Li, and J. Zhang, "Development of four-dimensional imaging spectrometers (4D-IS)," Proc. SPIE 6302, 63020M (2006).
[CrossRef]

Sun, X.

A. Wagadarikar, N. Pitsianis, X. Sun, and D. Brady, "Spectral Image Estimation for Coded Aperture Snapshot Spectral Imagers," Proc. SPIE 7076, 707602 (2008).
[CrossRef]

X. Sun and N. Pitsianis, "Solving non-negative linear inverse problems with the NeAREst method," Proc. SPIE 7074, 7074E (2008).

Thorne, K.

Vickers, V.

Volin, C.

Wagadarikar, A.

A. Wagadarikar, N. Pitsianis, X. Sun, and D. Brady, "Spectral Image Estimation for Coded Aperture Snapshot Spectral Imagers," Proc. SPIE 7076, 707602 (2008).
[CrossRef]

A. Wagadarikar, R. John, R. Willett, and D. J. Brady, "Single disperser design for coded aperture snapshot spectral imaging," Appl. Opt. 47, B44-B51 (2008).
[CrossRef]

Willett, R.

A. Wagadarikar, R. John, R. Willett, and D. J. Brady, "Single disperser design for coded aperture snapshot spectral imaging," Appl. Opt. 47, B44-B51 (2008).
[CrossRef]

M. Gehm, R. John, D. J. Brady, R. Willett, and T. Schulz, "Single-shot compressive spectral imaging with a dual-disperser architecture," Opt. Express 15, 14,013-14,027 (2007).
[CrossRef]

Wilson, D.

Zhang, J.

N. Gat, G. Scriven, J. Garman, M. D. Li, and J. Zhang, "Development of four-dimensional imaging spectrometers (4D-IS)," Proc. SPIE 6302, 63020M (2006).
[CrossRef]

Appl. Opt. (2)

J. Opt. Soc. Am. A (1)

Opt. Express (1)

M. Gehm, R. John, D. J. Brady, R. Willett, and T. Schulz, "Single-shot compressive spectral imaging with a dual-disperser architecture," Opt. Express 15, 14,013-14,027 (2007).
[CrossRef]

Opt. Lett. (1)

Proc. SPIE (4)

N. Gat, G. Scriven, J. Garman, M. D. Li, and J. Zhang, "Development of four-dimensional imaging spectrometers (4D-IS)," Proc. SPIE 6302, 63020M (2006).
[CrossRef]

K. Hege, D. O’Connell, W. Johnson, S. Basty, and E. Dereniak, "Hyperspectral imaging for astronomy and space surveillance," Proc. SPIE 5159, 380-391 (2003).
[CrossRef]

A. Wagadarikar, N. Pitsianis, X. Sun, and D. Brady, "Spectral Image Estimation for Coded Aperture Snapshot Spectral Imagers," Proc. SPIE 7076, 707602 (2008).
[CrossRef]

X. Sun and N. Pitsianis, "Solving non-negative linear inverse problems with the NeAREst method," Proc. SPIE 7074, 7074E (2008).

Other (1)

W. Johnson, D. Wilson, W. Fink, M. Humayun, and G. Bearman, "Snapshot hyperspectral imaging in ophthalmology," J. Biomed. Opt.  12, 0140,361-0140,367 (2007).
[CrossRef]

Supplementary Material (2)

» Media 1: MOV (3055 KB)     
» Media 2: MOV (3942 KB)     

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Figures (12)

Fig. 1.
Fig. 1.

(a) Schematic of the direct view CASSI. (b) Ray bundles passing through the double Amici prism and being dispersed differently at different wavelengths.

Fig. 2.
Fig. 2.

The aperture code: a random 256 × 248 binary element pattern, with the smallest element being 2×2 CCD pixels (19.8 μm on each side). The cross on the top helps to align the aperture code with the detector pixels during the calibration process.

Fig. 3.
Fig. 3.

Spot diagrams of 450 nm rays at 9 different field points at the detector.

Fig. 4.
Fig. 4.

Spot diagrams of 550 nm rays at 9 different field points at the detector.

Fig. 5.
Fig. 5.

Spot diagrams of 650 nm rays at 9 different field points at the detector.

Fig. 6.
Fig. 6.

Demonstrating CASSI’s response to uniform illumination at 33 different monochromatic wavelengths. These wavelengths define the centers of CASSI’s 33 spectral channels.

Fig. 7.
Fig. 7.

The purple dots track the location of the cross on the top of the aperture code as a function of wavelength and demonstrate the non-linear dispersion by the double Amici prism. The black crosshairs identify the 33 wavelengths that define the centers of CASSI’s 33 spectral channels.

Fig. 8.
Fig. 8.

Single frame excerpts of birthday candles with colored flames as viewed by (a) a Canon SD300 digital camera, and (b) from the CASSI CCD detector array. (Media 1)

Fig. 9.
Fig. 9.

Spectral image estimate of CASSI frame 107 generated using the NeAREst algorithm. The spatial content in each of 33 spectral channels between 455 and 650 nm is shown. (Media 2)

Fig. 10.
Fig. 10.

Enlarged versions of spectral channels 11, 22, 27, and 30.

Fig. 11.
Fig. 11.

Spectra of the bodies of the five candles at equally spaced 1 nm wavelengths, as measured by a non-imaging, reference spectrometer.

Fig. 12.
Fig. 12.

Channel-wise spectra of the bodies of the five candles. The purple dots are the spectral signatures measured at points on the candle bodies by CASSI. The dashed blue curves are the spectral signatures measured by the reference spectrometer after being integrated into the 33 spectral channels with equivalent bandwidths to the CASSI spectral channels.

Equations (43)

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f 1 ( x , y , λ ) = T ( x , y ) f 0 ( x , y , λ )
T ( x , y ) = i , j t i , j τ ( i , j ; x , y ) ,
τ ( i , j ; x , y ) = rect ( x Δ i , y Δ j ) .
f 2 ( x , y , λ ) = f 1 ( x , y , λ ) h ( x ϕ ( λ ) x , y y , λ ) dx dy
= T ( x , y ) f 0 ( x , y , λ ) h ( x ϕ ( λ ) x , y y , λ ) dx dy .
p ( m , n ; x , y ) = rect ( x Δ m , y Δ n ) ,
g n , m = Λ f 2 ( x , y , λ ) p ( m , n ; x , y ) dxdydλ
= Λ T ( x , y ) f 0 ( x , y , λ ) h ( x ϕ ( λ ) , x , y , y , λ ) p ( m , n ; x , y ) dx dy dxdydλ
= Λ ij t i , j rect ( x′ Δ i , y′ Δ j ) f 0 ( x , y , λ ) h ( x ϕ ( λ ) x , y y , λ )
× rect ( x Δ m , y Δ n ) d x d y dxdydλ
= i , j t i , j Ω i , j , m , n .
g n , m = i , j t i , j Ω i , j , m , n
= i t i , n Ω i , m , n .
Ω i , n , m = Λ rect ( x′ Δ i , y′ Δ n ) rect ( x Δ m , y Δ n )
× f 0 ( x , y , λ ) h ( x ϕ ( λ ) x , y y , λ ) dx dy dxdydλ .
Ω i , n , m = Λ rect ( x′′ Δ , y′′ Δ ) rect ( x Δ m , y Δ n )
× f 0 ( x ′′ + i Δ , y ′′ + n Δ , λ ) h ( x ′′ + i Δ ϕ ( λ ) x , y ′′ + n Δ y , λ )
× dx ′′ dy ′′ dxdydλ .
Ω i , n , m = Λ rect ( x′′ Δ , y′′ Δ ) rect ( x ′′′ Δ , y ′′′ Δ )
× f 0 ( x ′′ + i Δ , y ′′ + n Δ , λ ) h ( x ′′ + i Δ ϕ ( λ ) x ′′′ + m Δ , y ′′ y ′′′ , λ )
× dx ′′ dy ′′ dx ′′′ dy ′′′ .
Ω i , n , m = Λ rect ( x′′ Δ , y′′ Δ ) rect ( x ′′′ Δ , y ′′′ Δ )
× f 0 ( x ′′ + i Δ , y ′′ + n Δ , λ′ + m Δ + i Δ α ) h ( x ′′ x ′′′ αλ′ , y ′′ y ′′′ , λ + m Δ + i Δ α )
× dx ′′ dy ′′ dx ′′′ dy ′′′ dλ′ .
f i , n , m = Λ rect ( x′′ Δ , y′′ Δ ) rect ( x ′′′ Δ , y ′′′ Δ )
× f 0 ( x ′′ + i Δ , y ′′ + n Δ , λ′ + m Δ α ) h ( x ′′ x ′′′ αλ′ , y ′′ y ′′′ , λ + m Δ + i Δ α )
× dx ′′ dy ′′ dx ′′′ dy ′′′ dλ′ .
g n , m = i t i , n f i , n , m + i
= k t k m , n f k m , n , k .
g n , m = k t m k , n f′ m , n , k
g = Hf .
g ( x , y , λ ) = ( i , j ) A i , j G i , j ( x , y ; x , y , λ ) dx dy
G i , j ( x , y ; x , y , λ ) = T i , j ( x , y ) f ( x , y , λ ) h ( x ϕ ( λ ) x , y y , λ ) ,
g n , m = k Λ k p n , m g ( x , y , λ ) dxdydλ .
g n , m = i , j , k Q ( m , n ; i , j , k ) f ( x i , y j , λ k ) ,
Q ( m , n ; i , j , k ) = p n , m Λ k A i , j T i , j ( x , y ) h ( x ϕ ( λ ) x , y y , λ ) dx dy dλdxdy
Q ( m , n ; i , j , k ) w m , n w i , j w k T i , j ( x i , y j ) h ( x i ϕ ( λ k ) x m , y j y n , λ k )
ϕ ( λ k ) = α λ k .
Q ( m + α λ k , n ; i , j , k ) c k h ( x i x m , y j y n , λ k ) T i , j ( x i , y j ) ,
Q ( m + α λ k , n ; i , j , k ) c k h [ k ] ( x i x , y j y n ) T i , j [ k ] ( x i , y j ) .
g = Qf = k Q k f k ,
arg min f 0 m , n g n , m [ log ( g n , m ) log ( ( Qf ) n , m ) ] [ ( g n , m sgn ( g n , m ) ( Qf ) n , m ) ] ,
Q k f k ( m , n ) = ( i , j ) Q ( m , n ; i , j , k ) f ( x i , y j , λ k ) .

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