Abstract

A ray-based approach that models the geometric mapping properties of a flat optical detector based on a microlens array is presented. The investigated optical detector substitutes a single-aperture lens optic for planar and tomographic data acquisition in space-constrained small-animal imaging applications. The formalism implements forward mapping of a three-dimensional object volume onto a two-dimensional sensor surface as well as the backprojection (inverse mapping) of acquired sensor data sets. The object focus distance is the sole free parameter for the inverse mapping. By variation of the object focus distance, arbitrary object surface areas within the computed object images can be focused. The inverse mapping algorithm was applied to an experimentally acquired sensor data set from a three-dimensional phantom. The results are compared with focal point image formation.

© 2009 Optical Society of America

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References

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  1. A. H. Hielscher, “Optical tomographic imaging of small animals,” Curr. Opin. Biotechnol. 16, 79-88 (2005).
    [CrossRef] [PubMed]
  2. V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. 23, 313-320 (2005).
    [CrossRef] [PubMed]
  3. J. Peter, D. Unholtz, R. B. Schulz, J. Doll, and W. Semmler, “Development and initial results of a tomographic dual-modality positron/optical small animal imager,” IEEE Trans. Nucl. Sci. 54, 1553-1560 (2007).
    [CrossRef]
  4. J. Duparré, P. Dannberg, P. Schreiber, A. Bräuer, and A. Tünnermann, “Thin compound-eye camera,” Appl. Opt. 44, 2949-2956 (2005).
    [CrossRef] [PubMed]
  5. Advanced Microoptics Systems Gmbh, Saarbrücken, Germany.
  6. Rad-icon Imaging Corp., Santa Clara, Calif., USA.
  7. S. R. Cherry, Physics in Nuclear Medicine, 3rd ed. (Saunders, 2003).
  8. N. Lindlein, “Simulation of micro-optical systems including microlens arrays,” J. Opt. A 4, 1-9 (2002).
    [CrossRef]
  9. R. Ng, “Fourier slice photography,” ACM Trans. Graphics 24, 735-744 (2005).
    [CrossRef]
  10. R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Stanford University Computer Science Tech Report CSTR 2005-02 (20 April 2005).
  11. D. Unholtz, R. B. Schulz, W. Semmler, and J. Peter, “High-resolution image acquisition using a compact microlens-coupled detector,” Proc. SPIE 6631, 66311F (2007).
    [CrossRef]
  12. S.-H. Hong, J.-S. Jang, and B. Javidi, “Three-dimensional volumetric object reconstruction using computational integral imaging,” Opt. Express 12, 483-491 (2004).
    [CrossRef] [PubMed]
  13. C. P. McElhinney, B. M. Hennelly, and T. J. Naughton, “Extended focused imaging for digital holograms of macroscopic three-dimensional objects,” Appl. Opt. 47, D71-D79 (2008).
    [CrossRef] [PubMed]
  14. R. B. Schulz, J. Ripoll, and V. Ntziachristos, “Experimental fluorescence tomography of tissues with noncontact measurements,” IEEE Trans. Med. Imaging 23, 492-500 (2004).
    [CrossRef] [PubMed]

2008

2007

J. Peter, D. Unholtz, R. B. Schulz, J. Doll, and W. Semmler, “Development and initial results of a tomographic dual-modality positron/optical small animal imager,” IEEE Trans. Nucl. Sci. 54, 1553-1560 (2007).
[CrossRef]

D. Unholtz, R. B. Schulz, W. Semmler, and J. Peter, “High-resolution image acquisition using a compact microlens-coupled detector,” Proc. SPIE 6631, 66311F (2007).
[CrossRef]

2005

A. H. Hielscher, “Optical tomographic imaging of small animals,” Curr. Opin. Biotechnol. 16, 79-88 (2005).
[CrossRef] [PubMed]

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. 23, 313-320 (2005).
[CrossRef] [PubMed]

J. Duparré, P. Dannberg, P. Schreiber, A. Bräuer, and A. Tünnermann, “Thin compound-eye camera,” Appl. Opt. 44, 2949-2956 (2005).
[CrossRef] [PubMed]

R. Ng, “Fourier slice photography,” ACM Trans. Graphics 24, 735-744 (2005).
[CrossRef]

2004

R. B. Schulz, J. Ripoll, and V. Ntziachristos, “Experimental fluorescence tomography of tissues with noncontact measurements,” IEEE Trans. Med. Imaging 23, 492-500 (2004).
[CrossRef] [PubMed]

S.-H. Hong, J.-S. Jang, and B. Javidi, “Three-dimensional volumetric object reconstruction using computational integral imaging,” Opt. Express 12, 483-491 (2004).
[CrossRef] [PubMed]

2003

S. R. Cherry, Physics in Nuclear Medicine, 3rd ed. (Saunders, 2003).

2002

N. Lindlein, “Simulation of micro-optical systems including microlens arrays,” J. Opt. A 4, 1-9 (2002).
[CrossRef]

Bräuer, A.

Brédif, M.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Stanford University Computer Science Tech Report CSTR 2005-02 (20 April 2005).

Cherry, S. R.

S. R. Cherry, Physics in Nuclear Medicine, 3rd ed. (Saunders, 2003).

Dannberg, P.

Doll, J.

J. Peter, D. Unholtz, R. B. Schulz, J. Doll, and W. Semmler, “Development and initial results of a tomographic dual-modality positron/optical small animal imager,” IEEE Trans. Nucl. Sci. 54, 1553-1560 (2007).
[CrossRef]

Duparré, J.

Duval, G.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Stanford University Computer Science Tech Report CSTR 2005-02 (20 April 2005).

Hanrahan, P.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Stanford University Computer Science Tech Report CSTR 2005-02 (20 April 2005).

Hennelly, B. M.

Hielscher, A. H.

A. H. Hielscher, “Optical tomographic imaging of small animals,” Curr. Opin. Biotechnol. 16, 79-88 (2005).
[CrossRef] [PubMed]

Hong, S.-H.

Horowitz, M.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Stanford University Computer Science Tech Report CSTR 2005-02 (20 April 2005).

Jang, J.-S.

Javidi, B.

Levoy, M.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Stanford University Computer Science Tech Report CSTR 2005-02 (20 April 2005).

Lindlein, N.

N. Lindlein, “Simulation of micro-optical systems including microlens arrays,” J. Opt. A 4, 1-9 (2002).
[CrossRef]

McElhinney, C. P.

Naughton, T. J.

Ng, R.

R. Ng, “Fourier slice photography,” ACM Trans. Graphics 24, 735-744 (2005).
[CrossRef]

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Stanford University Computer Science Tech Report CSTR 2005-02 (20 April 2005).

Ntziachristos, V.

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. 23, 313-320 (2005).
[CrossRef] [PubMed]

R. B. Schulz, J. Ripoll, and V. Ntziachristos, “Experimental fluorescence tomography of tissues with noncontact measurements,” IEEE Trans. Med. Imaging 23, 492-500 (2004).
[CrossRef] [PubMed]

Peter, J.

J. Peter, D. Unholtz, R. B. Schulz, J. Doll, and W. Semmler, “Development and initial results of a tomographic dual-modality positron/optical small animal imager,” IEEE Trans. Nucl. Sci. 54, 1553-1560 (2007).
[CrossRef]

D. Unholtz, R. B. Schulz, W. Semmler, and J. Peter, “High-resolution image acquisition using a compact microlens-coupled detector,” Proc. SPIE 6631, 66311F (2007).
[CrossRef]

Ripoll, J.

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. 23, 313-320 (2005).
[CrossRef] [PubMed]

R. B. Schulz, J. Ripoll, and V. Ntziachristos, “Experimental fluorescence tomography of tissues with noncontact measurements,” IEEE Trans. Med. Imaging 23, 492-500 (2004).
[CrossRef] [PubMed]

Schreiber, P.

Schulz, R. B.

J. Peter, D. Unholtz, R. B. Schulz, J. Doll, and W. Semmler, “Development and initial results of a tomographic dual-modality positron/optical small animal imager,” IEEE Trans. Nucl. Sci. 54, 1553-1560 (2007).
[CrossRef]

D. Unholtz, R. B. Schulz, W. Semmler, and J. Peter, “High-resolution image acquisition using a compact microlens-coupled detector,” Proc. SPIE 6631, 66311F (2007).
[CrossRef]

R. B. Schulz, J. Ripoll, and V. Ntziachristos, “Experimental fluorescence tomography of tissues with noncontact measurements,” IEEE Trans. Med. Imaging 23, 492-500 (2004).
[CrossRef] [PubMed]

Semmler, W.

D. Unholtz, R. B. Schulz, W. Semmler, and J. Peter, “High-resolution image acquisition using a compact microlens-coupled detector,” Proc. SPIE 6631, 66311F (2007).
[CrossRef]

J. Peter, D. Unholtz, R. B. Schulz, J. Doll, and W. Semmler, “Development and initial results of a tomographic dual-modality positron/optical small animal imager,” IEEE Trans. Nucl. Sci. 54, 1553-1560 (2007).
[CrossRef]

Tünnermann, A.

Unholtz, D.

D. Unholtz, R. B. Schulz, W. Semmler, and J. Peter, “High-resolution image acquisition using a compact microlens-coupled detector,” Proc. SPIE 6631, 66311F (2007).
[CrossRef]

J. Peter, D. Unholtz, R. B. Schulz, J. Doll, and W. Semmler, “Development and initial results of a tomographic dual-modality positron/optical small animal imager,” IEEE Trans. Nucl. Sci. 54, 1553-1560 (2007).
[CrossRef]

Wang, L. V.

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. 23, 313-320 (2005).
[CrossRef] [PubMed]

Weissleder, R.

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. 23, 313-320 (2005).
[CrossRef] [PubMed]

ACM Trans. Graphics

R. Ng, “Fourier slice photography,” ACM Trans. Graphics 24, 735-744 (2005).
[CrossRef]

Appl. Opt.

Curr. Opin. Biotechnol.

A. H. Hielscher, “Optical tomographic imaging of small animals,” Curr. Opin. Biotechnol. 16, 79-88 (2005).
[CrossRef] [PubMed]

IEEE Trans. Med. Imaging

R. B. Schulz, J. Ripoll, and V. Ntziachristos, “Experimental fluorescence tomography of tissues with noncontact measurements,” IEEE Trans. Med. Imaging 23, 492-500 (2004).
[CrossRef] [PubMed]

IEEE Trans. Nucl. Sci.

J. Peter, D. Unholtz, R. B. Schulz, J. Doll, and W. Semmler, “Development and initial results of a tomographic dual-modality positron/optical small animal imager,” IEEE Trans. Nucl. Sci. 54, 1553-1560 (2007).
[CrossRef]

J. Opt. A

N. Lindlein, “Simulation of micro-optical systems including microlens arrays,” J. Opt. A 4, 1-9 (2002).
[CrossRef]

Nat. Biotechnol.

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. 23, 313-320 (2005).
[CrossRef] [PubMed]

Opt. Express

Proc. SPIE

D. Unholtz, R. B. Schulz, W. Semmler, and J. Peter, “High-resolution image acquisition using a compact microlens-coupled detector,” Proc. SPIE 6631, 66311F (2007).
[CrossRef]

Other

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Stanford University Computer Science Tech Report CSTR 2005-02 (20 April 2005).

Advanced Microoptics Systems Gmbh, Saarbrücken, Germany.

Rad-icon Imaging Corp., Santa Clara, Calif., USA.

S. R. Cherry, Physics in Nuclear Medicine, 3rd ed. (Saunders, 2003).

Supplementary Material (1)

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Figures (10)

Fig. 1
Fig. 1

Enlarged views of component sections in relative proportions: (a) MLA [5], (b) septum mask, and (c) CMOS sensor surface [6]. The overall detector active area covers 24.6 mm × 49.2 mm . The MLA focal length is 2.15 mm . Each microlens is optically isolated by the septum mask, yielding an allocated area of 10 × 10 pixels on the sensor surface. Several of these pixels, which are covered by the septum mask, are not available for light detection.

Fig. 2
Fig. 2

MLA mapping: (a) a focal point image is formed by sampling the center focal points of individual microlenses, into which perpendicular incident light is projected. (b) Focal point image formation from an angularly shifted FOV is achieved, if sensor pixels with an equidistant offset to the center focal point are used. (c) The mapping model simultaneously includes incident light from all accepted directions. This corresponds to the superposition of all angularly shifted focal point images.

Fig. 3
Fig. 3

Mapping model: positions of object voxels r, sensor pixels p, and pinholes o are defined in the same coordinate system; f is the microlens focal length; a sensor pixel pitch; d microlens pitch; D septum mask borehole diameter; and N, M, L are numbers of discrete elements in dimension x, y, z respectively.

Fig. 4
Fig. 4

Forward mapping: Intensities from the object space are projected onto the sensor surface. Sampled object voxels at a specific sensor–object distance t are located within a square-based pyramid that is defined by each sensor pixel with its associated pinhole.

Fig. 5
Fig. 5

Inverse mapping: a single object voxel at a specific sensor–object distance t is related to a certain number of sensor pixels through their associated pinholes. Based on these relations, the sensor pixel intensities are backprojected into the object space.

Fig. 6
Fig. 6

Sensor data as acquired from a homogeneous, planar, and diffuse light source. The individual pixel sensitivities influenced by the pixel position, microlens, and septum mask borehole transmission are used for the object image normalization. The nonuniformity is caused particularly by the sensor readout process.

Fig. 7
Fig. 7

Experimental setup for data acquisition: a mouse phantom is positioned close to the active area of the optical detector assembly. The object is illuminated with white-light sources.

Fig. 8
Fig. 8

Complete sensor readout resulting from the scene as shown in Fig. 7. This data set was used for both focal point image extraction and image formation utilizing inverse mapping, as shown in Figs. 9, 10. During the specific image formation process, weighting factors are considered based on sensor pixel sensitivities (Fig. 6).

Fig. 9
Fig. 9

Focal point image of the sensor data (Fig. 8) formed from the MLA center focal points. According to the number of microlenses, the image size is 51 × 102 pixels.

Fig. 10
Fig. 10

Object image formation employing the mapping model (Media 1): resulting images are computed with the inverse mapping at different object focus distances t: at the head (a), at the torso (b), and at the backside (c). The image size is equal to the number of sensor pixels ( 512 × 1024 ). The spatial resolution of computed object images decreases with increasing object focus distances owing to the mapping geometry.

Tables (1)

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Table 1 Element Specifications of Optical Detector Components

Equations (11)

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( x y t ) = ( n p a m p a 0 ) + t f [ ( n o d m o d f ) ( n p a m p a 0 ) ] ,
( x n o d ) 2 + ( y m o d ) 2 ( t f f D 2 ) 2 .
j v i j = ( t f f ) 2 .
g p 0 = U p V g r 0 ,
u i p = g i p 0 ( f t f ) 2 .
g i p = g i p 0 ( f t f ) 2 j v i j g j r .
( x y 0 ) = ( n r a m r a t ) + t t f [ ( n o d m o d f ) ( n r a m r a t ) ] ,
( x n o d ) 2 + ( y m o d ) 2 ( D / 2 ) 2 .
g r 0 = U r W U p g p 0 .
u i r = ( t f f ) 2 j w i j ( g j p 0 ) 2 .
g i r = 1 j w i j ( g j p 0 ) 2 j w i j g j p 0 g j p .

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