Abstract

Multichanneled imaging systems rely on nonredundant images recorded by an array of low-resolution imagers to enable construction of a high-resolution image. We show how the varying degree of redundancy associated with imaging throughout the imaged volume effects image quality. Using ray-traced image simulations and a metric used as a proxy for human perception, we show that robust recovery of high-resolution images can be obtained by avoiding excessive redundancy and that this is a felicitous consequence of typical manufacturing tolerances.

© 2012 Optical Society of America

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References

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    [CrossRef]
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  13. ZEMAX Corporation, “ZEMAX-EE(32bit),” Version: April 14 (2010).
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    [CrossRef]
  15. Z. Wang, A. Bovik, H. Sheikh, and E. Simoncelli, “Image quality assessment: From error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
    [CrossRef]
  16. S. Young, “Alias-free image subsampling using Fourier-based windowing methods,” Opt. Eng. 43, 843–855 (2004).
    [CrossRef]
  17. R. Horisaki, Y. Nakao, T. Toyoda, K. Kagawa, Y. Masaki, and J. Tanida, “A compound-eye imaging system with irregular lens-array arrangement,” Proc. SPIE 7072, 1–9 (2008).

2009

G. Muyo and A. Harvey, “The effect of detector sampling in wavefront-coded imaging systems,” J. Opt. A 11, 054002 (2009).
[CrossRef]

2008

2007

2006

2005

R. Driggers, K. Krapels, S. Murrill, S. Young, M. Thielke, and J. Schuler, “Superresolution performance for undersampled imagers,” Opt. Eng. 44, 014002 (2005).
[CrossRef]

2004

Z. Wang, A. Bovik, H. Sheikh, and E. Simoncelli, “Image quality assessment: From error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[CrossRef]

S. Young, “Alias-free image subsampling using Fourier-based windowing methods,” Opt. Eng. 43, 843–855 (2004).
[CrossRef]

2003

S. Park, M. Park, and M. Kang, “Super-resolution image reconstruction: a technical overview,” IEEE Signal Process. Mag. 20, 21–36 (2003).
[CrossRef]

2001

1982

W. Wittenstein, J. Fontanella, A. Newbery, and J. Baars, “The definition of the OTF and the measurement of aliasing for sampled imaging systems,” J. Mod. Opt. 29, 41–50 (1982).

Ackerman, J.

Ashok, A.

Baars, J.

W. Wittenstein, J. Fontanella, A. Newbery, and J. Baars, “The definition of the OTF and the measurement of aliasing for sampled imaging systems,” J. Mod. Opt. 29, 41–50 (1982).

Boreman, G.

G. Boreman, Modulation Transfer Function in Optical and Electro-Optical Systems (SPIE, 2001).

Bovik, A.

Z. Wang, A. Bovik, H. Sheikh, and E. Simoncelli, “Image quality assessment: From error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[CrossRef]

Brady, D.

Carriere, J.

Chen, C.

Choi, K.

Driggers, R.

R. Driggers, K. Krapels, S. Murrill, S. Young, M. Thielke, and J. Schuler, “Superresolution performance for undersampled imagers,” Opt. Eng. 44, 014002 (2005).
[CrossRef]

R. Vollmerhausen and R. Driggers, Analysis of Sampled Imaging Systems (SPIE, 2000).

Fleet, E.

Fontanella, J.

W. Wittenstein, J. Fontanella, A. Newbery, and J. Baars, “The definition of the OTF and the measurement of aliasing for sampled imaging systems,” J. Mod. Opt. 29, 41–50 (1982).

Gibbons, R.

Harvey, A.

G. Muyo and A. Harvey, “The effect of detector sampling in wavefront-coded imaging systems,” J. Opt. A 11, 054002 (2009).
[CrossRef]

Horisaki, R.

R. Horisaki, Y. Nakao, T. Toyoda, K. Kagawa, Y. Masaki, and J. Tanida, “A compound-eye imaging system with irregular lens-array arrangement,” Proc. SPIE 7072, 1–9 (2008).

Ichioka, Y.

Ishida, K.

Kagawa, K.

R. Horisaki, Y. Nakao, T. Toyoda, K. Kagawa, Y. Masaki, and J. Tanida, “A compound-eye imaging system with irregular lens-array arrangement,” Proc. SPIE 7072, 1–9 (2008).

Kanaev, A.

Kang, M.

S. Park, M. Park, and M. Kang, “Super-resolution image reconstruction: a technical overview,” IEEE Signal Process. Mag. 20, 21–36 (2003).
[CrossRef]

Kolste, R.

Kondou, N.

Krapels, K.

R. Driggers, K. Krapels, S. Murrill, S. Young, M. Thielke, and J. Schuler, “Superresolution performance for undersampled imagers,” Opt. Eng. 44, 014002 (2005).
[CrossRef]

Kumagai, T.

Masaki, Y.

R. Horisaki, Y. Nakao, T. Toyoda, K. Kagawa, Y. Masaki, and J. Tanida, “A compound-eye imaging system with irregular lens-array arrangement,” Proc. SPIE 7072, 1–9 (2008).

Miyatake, S.

Miyazaki, D.

Morimoto, T.

Murrill, S.

R. Driggers, K. Krapels, S. Murrill, S. Young, M. Thielke, and J. Schuler, “Superresolution performance for undersampled imagers,” Opt. Eng. 44, 014002 (2005).
[CrossRef]

Muyo, G.

G. Muyo and A. Harvey, “The effect of detector sampling in wavefront-coded imaging systems,” J. Opt. A 11, 054002 (2009).
[CrossRef]

Nakao, Y.

R. Horisaki, Y. Nakao, T. Toyoda, K. Kagawa, Y. Masaki, and J. Tanida, “A compound-eye imaging system with irregular lens-array arrangement,” Proc. SPIE 7072, 1–9 (2008).

Neifeld, M. A.

Newbery, A.

W. Wittenstein, J. Fontanella, A. Newbery, and J. Baars, “The definition of the OTF and the measurement of aliasing for sampled imaging systems,” J. Mod. Opt. 29, 41–50 (1982).

Nitta, K.

Park, M.

S. Park, M. Park, and M. Kang, “Super-resolution image reconstruction: a technical overview,” IEEE Signal Process. Mag. 20, 21–36 (2003).
[CrossRef]

Park, S.

S. Park, M. Park, and M. Kang, “Super-resolution image reconstruction: a technical overview,” IEEE Signal Process. Mag. 20, 21–36 (2003).
[CrossRef]

Pitsianis, N.

Portnoy, A.

Prather, D.

Schuler, J.

R. Driggers, K. Krapels, S. Murrill, S. Young, M. Thielke, and J. Schuler, “Superresolution performance for undersampled imagers,” Opt. Eng. 44, 014002 (2005).
[CrossRef]

Schulz, T.

Scribner, D.

Shankar, M.

Sheikh, H.

Z. Wang, A. Bovik, H. Sheikh, and E. Simoncelli, “Image quality assessment: From error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[CrossRef]

Shogenji, R.

Simoncelli, E.

Z. Wang, A. Bovik, H. Sheikh, and E. Simoncelli, “Image quality assessment: From error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[CrossRef]

Sun, X.

Tanida, J.

Thielke, M.

R. Driggers, K. Krapels, S. Murrill, S. Young, M. Thielke, and J. Schuler, “Superresolution performance for undersampled imagers,” Opt. Eng. 44, 014002 (2005).
[CrossRef]

Toyoda, T.

R. Horisaki, Y. Nakao, T. Toyoda, K. Kagawa, Y. Masaki, and J. Tanida, “A compound-eye imaging system with irregular lens-array arrangement,” Proc. SPIE 7072, 1–9 (2008).

Vollmerhausen, R.

R. Vollmerhausen and R. Driggers, Analysis of Sampled Imaging Systems (SPIE, 2000).

Wang, Z.

Z. Wang, A. Bovik, H. Sheikh, and E. Simoncelli, “Image quality assessment: From error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[CrossRef]

Willett, R.

Wittenstein, W.

W. Wittenstein, J. Fontanella, A. Newbery, and J. Baars, “The definition of the OTF and the measurement of aliasing for sampled imaging systems,” J. Mod. Opt. 29, 41–50 (1982).

Yamada, K.

Young, S.

R. Driggers, K. Krapels, S. Murrill, S. Young, M. Thielke, and J. Schuler, “Superresolution performance for undersampled imagers,” Opt. Eng. 44, 014002 (2005).
[CrossRef]

S. Young, “Alias-free image subsampling using Fourier-based windowing methods,” Opt. Eng. 43, 843–855 (2004).
[CrossRef]

Appl. Opt.

IEEE Signal Process. Mag.

S. Park, M. Park, and M. Kang, “Super-resolution image reconstruction: a technical overview,” IEEE Signal Process. Mag. 20, 21–36 (2003).
[CrossRef]

IEEE Trans. Image Process.

Z. Wang, A. Bovik, H. Sheikh, and E. Simoncelli, “Image quality assessment: From error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[CrossRef]

J. Mod. Opt.

W. Wittenstein, J. Fontanella, A. Newbery, and J. Baars, “The definition of the OTF and the measurement of aliasing for sampled imaging systems,” J. Mod. Opt. 29, 41–50 (1982).

J. Opt. A

G. Muyo and A. Harvey, “The effect of detector sampling in wavefront-coded imaging systems,” J. Opt. A 11, 054002 (2009).
[CrossRef]

Opt. Eng.

R. Driggers, K. Krapels, S. Murrill, S. Young, M. Thielke, and J. Schuler, “Superresolution performance for undersampled imagers,” Opt. Eng. 44, 014002 (2005).
[CrossRef]

S. Young, “Alias-free image subsampling using Fourier-based windowing methods,” Opt. Eng. 43, 843–855 (2004).
[CrossRef]

Opt. Lett.

Proc. SPIE

R. Horisaki, Y. Nakao, T. Toyoda, K. Kagawa, Y. Masaki, and J. Tanida, “A compound-eye imaging system with irregular lens-array arrangement,” Proc. SPIE 7072, 1–9 (2008).

Other

R. Vollmerhausen and R. Driggers, Analysis of Sampled Imaging Systems (SPIE, 2000).

G. Boreman, Modulation Transfer Function in Optical and Electro-Optical Systems (SPIE, 2001).

ZEMAX Corporation, “ZEMAX-EE(32bit),” Version: April 14 (2010).

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Figures (8)

Fig. 1.
Fig. 1.

(a) Optical, pixel, and combined components of an ideal imaging system modulation transfer function (MTF). Zeros in the pixel MTF occur at integer multiples of ν s (fill factor is unity), and ν c is 1 / F λ , where F is the system F -number. (b) The shaded region is the spurious response that the system (a) is sensitive to. Any portion of a recorded image that is within this region of frequency versus contrast space is considered as spurious, as it is not possible to differentiate between real and spurious recordings.

Fig. 2.
Fig. 2.

The multichanneled imaging concept [1,12]. This figure is adapted from [1].

Fig. 3.
Fig. 3.

Geometry for the sampling phase offset, Δ d = γ γ = f D / R , between images of a point source recorded by neighboring imagers under the small angle approximation.

Fig. 4.
Fig. 4.

(a) With ideal phase offset, a three-lenslet system (in one dimension) yields much lower levels of spurious signal due to thecancellationn of replicas in the summation of multiple channels. (b) Signal-replicas and spurious response of the multichanneled imager when subimages on either side of a central subimage are translated inwards by 0.1 pixel pitch. (c) When R , d k d k ± 1 0 k , resulting in full redundancy and a consequent ineffectiveness of super-resolution.

Fig. 5.
Fig. 5.

Reference and recovered images: (a) best possible result used as reference for MSSIM. (b), (c), and (d) Recovered images using back-projection. (e) Up-sampled LR image. (f), (g), and (h) Recovered images using pixel-rearrangement. For (b) and (f),  d k = 0 k ; for (c) and (g), the standard deviation of d k is 1 / 2 ν s ; and for (d) and (h),  d = d ideal .

Fig. 6.
Fig. 6.

A plot of the similarity of images reconstructed to an ideal image versus distance for a number of sampling phase scenarios using the (a) back-projection method and (b) pixel-rearrangement method.

Fig. 7.
Fig. 7.

Reconstruction of an HR signal through pixel-rearrangement of LR subsignals (a). (b) The subsignals are padded with N 1 zeros between recordings and shifted depending on the relative sampling position of the recorded signals in the image plane. (c) The signals are then summed to generate an HR reconstruction.

Fig. 8.
Fig. 8.

(a) In an aliased system, a signal ν 0 , where ν 0 > ν Ny (the sampling Nyquist frequency) is beat down onto the frequency ν = ν s ν 0 . (b) After reconstruction, the spurious signal is cancelled and only the component at ν = ν 0 persists.

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

f ( x ; d ) = m = [ h o ( x ) * h p ( x ) ] · δ ( x [ m ν s d ] ) ,
F ( ν ) = q = [ H o ( ν ) · H p ( ν ) ] * [ δ ( ν q ν s ) · e i 2 π ν d ] = q = H ( ν q ν s ) e i 2 π ν d ,
Δ d = f D R ,
F system ( ν ) = k = 0 N 1 [ q = H ( ν q ν s ) e i 2 π ν d k ] .
d ideal = ( d 0 , d N 1 ) , where d k = k N ν s + d , k = 0 , 1 , , N 1 ,
f k ( x ; d k ) = m = 0 n 1 cos ( 2 π x ν 0 ) * [ h o ( x ) * h p ( x ) ] · δ ( x [ m ν s d k ] ) ,
F k ( v ; v 0 ) = q = 1 1 H o ( v 0 ) H p ( v 0 ) exp [ i 2 π v 0 d k ] × 1 2 [ δ ( v q v s + v 0 ) + δ ( v q v s v 0 ) ] ,
G k ( ν ; ν 0 ) = { F k ( ν ; ν 0 ) if ν Ny ν ν Ny , 0 otherwise.
G k ( ν ; ν 0 ) = H o ( ν 0 ) H p ( ν 0 ) · 1 2 { δ ( ν ν s + ν 0 ) exp [ i 2 π ν 0 d k ] + δ ( ν + ν s ν 0 ) exp [ i 2 π ( ν 0 ) d k ] } .
U ( ν ) = a δ ( ν a ν s ) ,
P k ( ν ) = exp [ i 2 π ν k N ν s ] .
Y ( ν ; ν 0 ) = k a G k ( ν a ν s ) · P k ( ν ) ,
Y ( ν ; ν 0 ) = H o ( ν 0 ) H p ( ν 0 ) × 1 2 { δ ( ν s + ν s ν 0 ) exp [ i 2 π ( ν 0 ) d k ] + δ ( ν s ν s + ν 0 ) exp [ i 2 π ( ν 0 ) d k ] + δ ( ν s ν 0 ) exp [ i 2 π ( ν 0 ) d k ] + δ ( ν s + ν 0 ) exp [ i 2 π ( ν 0 ) d k ] + δ ( ν s + ν s ν 0 ) exp [ i 2 π ( ν 0 ) d k ] + δ ( ν s ν s + ν 0 ) exp [ i 2 π ( ν 0 ) d k ] } × exp [ i 2 π ν k N ν s ] .
k = 1 N exp [ i 2 π ( ν 0 d k + ( ν s ν 0 ) k N ν s ) ] .
k = 1 N exp [ i 2 π ( ν 0 d k + ν 0 k N ν s ) ] .

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