Abstract

Optically multiplexed imaging is the process by which multiple images are overlaid on a single image surface. Uniquely encoding the discrete images allows scene reconstruction from multiplexed images via post processing. We describe a class of optical systems that can achieve high density image multiplexing through a novel division of aperture technique. Fundamental design considerations and performance attributes for this sensor architecture are discussed. A number of spatial and temporal encoding methods are presented including point spread function engineering, amplitude modulation, and image shifting. Results from a prototype five-channel sensor are presented using three different encoding methods in sparse-scene star tracking demonstration. A six-channel optically multiplexed prototype sensor is used to reconstruct imagery from information rich dense scenes through dynamic image shifting.

© 2015 Optical Society of America

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References

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  1. M. D. Stenner, P. Shankar, and M. A. Neifeld, “Wide-Field Feature-Specific Imaging,” in Frontiers in Optics 2007, OSA Technical Digest (Optical Society of America, 2007), paper FMJ2.
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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2015 (2)

A. Daniels, “Infrared systems – technology & design,” SPIE Short Course SC835, 279 (2015).

Y. Rachlin, V. Shah, R. H. Shepard, and T. Shih, “Dynamic optically multiplexed imaging,” Proc. SPIE 9600, 96003 (2015).

2010 (2)

2009 (3)

2008 (2)

2006 (3)

J. Sasian, “Interpretation of pupil aberrations in imaging systems,” Proc. SPIE 6342, 634208 (2006).
[Crossref]

E. J. Candes and T. Tao, “Near-optimal signal recovery from random projections: universal encoding strategies?” IEEE Trans. Inf. Theory 52(12), 5406–5425 (2006).
[Crossref]

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
[Crossref]

1993 (1)

S. G. Mallat and Z. Zhang, “Matching pursuits with time-frequency dictionaries,” Signal Processing, IEEE Transactions on 41(12), 3397–3415 (1993).
[Crossref]

1986 (1)

D. Shafer, “Aberration Theory and the Meaning of Life,” Proc. SPIE 554, 25 (1986).
[Crossref]

1982 (1)

C. C. Paige and M. A. Saunders, “LSQR: An algorithm for sparse linear equations and sparse least squares,” TOMS 8(1), 43–71 (1982).
[Crossref]

Ashok, A.

Bhagavatula, V. K.

Brady, D.

Brady, D. J.

Candes, E. J.

E. J. Candes and T. Tao, “Near-optimal signal recovery from random projections: universal encoding strategies?” IEEE Trans. Inf. Theory 52(12), 5406–5425 (2006).
[Crossref]

Chen, C. Y.

Daniels, A.

A. Daniels, “Infrared systems – technology & design,” SPIE Short Course SC835, 279 (2015).

Donoho, D. L.

D. L. Donoho, A. Maleki, and A. Montanari, “Message-passing algorithms for compressed sensing,” Proc. Natl. Acad. Sci. U.S.A. 106(45), 18914–18919 (2009).
[Crossref] [PubMed]

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
[Crossref]

Eldeniz, C.

Goodman, N. A.

Gupta, R.

R. Gupta, P. Indyk, E. Price, and Y. Rachlin, “Compressive sensing with local geometric features,” Proc. of the 27th annual ACM symposium on computational geometry, 87–98, ACM (2011).
[Crossref]

Haberfelde, T.

Horisaki, R.

Indyk, P.

R. Gupta, P. Indyk, E. Price, and Y. Rachlin, “Compressive sensing with local geometric features,” Proc. of the 27th annual ACM symposium on computational geometry, 87–98, ACM (2011).
[Crossref]

John, R.

Kim, C.

Kim, J.

Mahalanobis, A.

Maleki, A.

D. L. Donoho, A. Maleki, and A. Montanari, “Message-passing algorithms for compressed sensing,” Proc. Natl. Acad. Sci. U.S.A. 106(45), 18914–18919 (2009).
[Crossref] [PubMed]

Mallat, S. G.

S. G. Mallat and Z. Zhang, “Matching pursuits with time-frequency dictionaries,” Signal Processing, IEEE Transactions on 41(12), 3397–3415 (1993).
[Crossref]

Marcia, R. F.

Montanari, A.

D. L. Donoho, A. Maleki, and A. Montanari, “Message-passing algorithms for compressed sensing,” Proc. Natl. Acad. Sci. U.S.A. 106(45), 18914–18919 (2009).
[Crossref] [PubMed]

Neifeld, M.

Neifeld, M. A.

Paige, C. C.

C. C. Paige and M. A. Saunders, “LSQR: An algorithm for sparse linear equations and sparse least squares,” TOMS 8(1), 43–71 (1982).
[Crossref]

Price, E.

R. Gupta, P. Indyk, E. Price, and Y. Rachlin, “Compressive sensing with local geometric features,” Proc. of the 27th annual ACM symposium on computational geometry, 87–98, ACM (2011).
[Crossref]

Rachlin, Y.

Y. Rachlin, V. Shah, R. H. Shepard, and T. Shih, “Dynamic optically multiplexed imaging,” Proc. SPIE 9600, 96003 (2015).

R. Gupta, P. Indyk, E. Price, and Y. Rachlin, “Compressive sensing with local geometric features,” Proc. of the 27th annual ACM symposium on computational geometry, 87–98, ACM (2011).
[Crossref]

Sasian, J.

J. Sasian, “Interpretation of pupil aberrations in imaging systems,” Proc. SPIE 6342, 634208 (2006).
[Crossref]

Saunders, M. A.

C. C. Paige and M. A. Saunders, “LSQR: An algorithm for sparse linear equations and sparse least squares,” TOMS 8(1), 43–71 (1982).
[Crossref]

Shafer, D.

D. Shafer, “Aberration Theory and the Meaning of Life,” Proc. SPIE 554, 25 (1986).
[Crossref]

Shah, V.

Y. Rachlin, V. Shah, R. H. Shepard, and T. Shih, “Dynamic optically multiplexed imaging,” Proc. SPIE 9600, 96003 (2015).

Shepard, R. H.

Y. Rachlin, V. Shah, R. H. Shepard, and T. Shih, “Dynamic optically multiplexed imaging,” Proc. SPIE 9600, 96003 (2015).

Shih, T.

Y. Rachlin, V. Shah, R. H. Shepard, and T. Shih, “Dynamic optically multiplexed imaging,” Proc. SPIE 9600, 96003 (2015).

Sun, W. S.

Tanida, J.

Tao, T.

E. J. Candes and T. Tao, “Near-optimal signal recovery from random projections: universal encoding strategies?” IEEE Trans. Inf. Theory 52(12), 5406–5425 (2006).
[Crossref]

Treeaporn, V.

Uttam, S.

Willett, R. M.

Yang, T. T.

Zhang, Z.

S. G. Mallat and Z. Zhang, “Matching pursuits with time-frequency dictionaries,” Signal Processing, IEEE Transactions on 41(12), 3397–3415 (1993).
[Crossref]

Appl. Opt. (1)

IEEE Trans. Inf. Theory (2)

E. J. Candes and T. Tao, “Near-optimal signal recovery from random projections: universal encoding strategies?” IEEE Trans. Inf. Theory 52(12), 5406–5425 (2006).
[Crossref]

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
[Crossref]

Opt. Express (5)

Proc. Natl. Acad. Sci. U.S.A. (1)

D. L. Donoho, A. Maleki, and A. Montanari, “Message-passing algorithms for compressed sensing,” Proc. Natl. Acad. Sci. U.S.A. 106(45), 18914–18919 (2009).
[Crossref] [PubMed]

Proc. SPIE (3)

J. Sasian, “Interpretation of pupil aberrations in imaging systems,” Proc. SPIE 6342, 634208 (2006).
[Crossref]

D. Shafer, “Aberration Theory and the Meaning of Life,” Proc. SPIE 554, 25 (1986).
[Crossref]

Y. Rachlin, V. Shah, R. H. Shepard, and T. Shih, “Dynamic optically multiplexed imaging,” Proc. SPIE 9600, 96003 (2015).

Signal Processing, IEEE Transactions on (1)

S. G. Mallat and Z. Zhang, “Matching pursuits with time-frequency dictionaries,” Signal Processing, IEEE Transactions on 41(12), 3397–3415 (1993).
[Crossref]

SPIE Short Course (1)

A. Daniels, “Infrared systems – technology & design,” SPIE Short Course SC835, 279 (2015).

TOMS (1)

C. C. Paige and M. A. Saunders, “LSQR: An algorithm for sparse linear equations and sparse least squares,” TOMS 8(1), 43–71 (1982).
[Crossref]

Other (3)

M. D. Stenner, P. Shankar, and M. A. Neifeld, “Wide-Field Feature-Specific Imaging,” in Frontiers in Optics 2007, OSA Technical Digest (Optical Society of America, 2007), paper FMJ2.

R. Gupta, P. Indyk, E. Price, and Y. Rachlin, “Compressive sensing with local geometric features,” Proc. of the 27th annual ACM symposium on computational geometry, 87–98, ACM (2011).
[Crossref]

Y. C. Pati, R. Rezaiifar, and P. S. Krishnaprasad, “Orthogonal matching pursuit: Recursive function approximation with applications to wavelet decomposition,” Proc. 27th Asilomar Conference on Signals, Systems and Computers. IEEE Computer Society Press, 40 (1993).
[Crossref]

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Figures (10)

Fig. 1
Fig. 1 Pupil division strategies. (a) division of amplitude using a cascade of beam splitters, (b) division of aperture using an array of prisms.
Fig. 2
Fig. 2 Configurations for division of aperture systems and their beam projections on the multiplexing assembly (MA). (a) the MA serves as the aperture stop, (b) a remotely located MA, and (c) a design that projects the entrance pupil to the MA with aberration of the pupil.
Fig. 3
Fig. 3 (a) a notional 2-element single-prism MA for a LWIR camera. Encoding is performed by a simple motor assembly that rotates the MA about the optical axis of the lens. (b) optical layout for a 4-channel multiplexing assembly based on achromatic prisms.
Fig. 4
Fig. 4 Beam deviation and dispersion. (a) a thin prism. (b) secondary dispersion in an achromatic prism pair.
Fig. 5
Fig. 5 Notional Reflective multiplexing assemblies. (a) a narrow FOV lens used with a single element MA acting as a remote tilted aperture stop, and (b) a multi-element MA shown with a reimaging lens that projects the pupil to the MA.
Fig. 6
Fig. 6 A five-channel optically multiplexed sensor and field of view projection.
Fig. 7
Fig. 7 SWIR five-channel prototypes. Left: SWIR prototype 2 with a wedged dichroic fold mirror for spatial encoding. Center: a visible witness camera. Right: SWIR prototype 1 with a metalized fold mirror and filter wheel.
Fig. 8
Fig. 8 Six-channel visible prototype.
Fig. 9
Fig. 9 Multiplexed images of the night sky and a disambiguated image. (a) multiplexed image from SWIR prototype 2, (b) a long integration multiplexed image from SWIR prototype 1 demonstrating passive temporal encoding via image rotation, and (c) a multiplexed image from SWIR prototype 1 demonstrating active temporal encoding. (d) a reconstruction of the night sky prototype 2.
Fig. 10
Fig. 10 Images collected with the visible waveband prototype. (a) a single four megapixel multiplexed image, (b) a 24 megapixel image reconstructed from a sequence of uniquely encoded multiplexed frames.

Tables (3)

Tables Icon

Table 1 A selection of low-dispersion materials.

Tables Icon

Table 2 Examples of achromatic prism pairs with small amounts of secondary dispersion.

Tables Icon

Table 3 Prototype system parameters

Equations (29)

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Φ=τLAΩ
Φ total =( τ N )LA(NΩ)
Φ total =τL( A N )(NΩ)
f l N =f l o .
A N = A o N ,
d N d o N ,
F # N N F # o .
θ xN,yN = θ x o , y o 2 Tan 1 ( n x,y d p 2f l o )
M pix,N =N n x n y .
M opt,N = N θ xo θ yo π ( 1.22 λ d N ) 2 M opt,o .
MT F cut,det = 1 d p ,
MT F cut,opt = 1 λF # N .
λ N 1/2 F # o d p 2, optically limited
D R N = D N o N ,
B N = B o lo g 2 N,
δ=ztanθ,
V= n λ mid 1 n λ low n λ high
δ( n λ mid 1)α
Δ δ V
φ d p f l o .
Δ max =kφ.
δ max =kVφ.
ε( P 2 P 1 V 2 V 1 )δ
P= n λ mid n λ high n λ low n λhigh .
δ max =| V 2 V 1 P 2 P 1 |kφ.
z=Ax+ε,
z= A multiplex A downsample A selection A encoding x+ε.
z ˜ = A ˜ x+ ε ˜
x ^ = A ˜ 1 z ˜ .

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