Abstract

Plenoptic imaging is a 3D imaging technique that has been applied for quantification of 3D particle locations and sizes. This work experimentally evaluates the accuracy and precision of such measurements by investigating a static particle field translated to known displacements. Measured 3D displacement values are determined from sharpness metrics applied to volumetric representations of the particle field created using refocused plenoptic images, corrected using a recently developed calibration technique. Comparison of measured and known displacements for many thousands of particles allows for evaluation of measurement uncertainty. Mean displacement error, as a measure of accuracy, is shown to agree with predicted spatial resolution over the entire measurement domain, indicating robustness of the calibration methods. On the other hand, variation in the error, as a measure of precision, fluctuates as a function of particle depth in the optical direction. Error shows the smallest variation within the predicted depth of field of the plenoptic camera, with a gradual increase outside this range. The quantitative uncertainty values provided here can guide future measurement optimization and will serve as useful metrics for design of improved processing algorithms.

© 2017 Optical Society of America

Full Article  |  PDF Article
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References

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2017 (6)

H. Chen, V. Sick, M. A. Woodward, and D. Burke, “Human iris 3D imaging using a micro-plenoptic camera,” Opt. Life Sci. 2017, 8–10 (2017).

K. C. Johnson, B. S. Thurow, T. Kim, G. Blois, and K. T. Christiansen, “Volumetric velocity measurements in the wake of a hemispherical roughness element,” AIAA J. 55(7), 2158–2173 (2017).
[Crossref]

P. Drap, J. P. Royer, M. M. Nawaf, M. Saccone, D. Merad, À. López-Sanz, J. B. Ledoux, and J. Garrabou, “Underwater photogrammetry, coded target and plenoptic technology: a set of tools for monitoring red coral in mediterranean sea in the framework of the ”Perfect” project,” in ISPRS - Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci XLII-2(W3), 275–282 (2017).
[Crossref]

T. T. Truscott, J. Belden, R. Ni, J. Pendlebury, and B. McEwen, “Three-dimensional microscopic light field particle image velocimetry,” Exp. Fluids 58(3), 16 (2017).
[Crossref]

X. Jin, L. Liu, Y. Chen, and Q. Dai, “Point spread function and depth-invariant focal sweep point spread function for plenoptic camera 20,” Opt. Express 25(9), 9947–9962 (2017).
[Crossref] [PubMed]

H. Chen and V. Sick, “Three-dimensional three-component air flow visualization in a steady-state engine flow bench using a plenoptic camera,” SAE Int. J. Engines 10(2), 625–635 (2017).
[Crossref]

2016 (4)

E. M. Hall, B. S. Thurow, and D. R. Guildenbecher, “Comparison of three-dimensional particle tracking and sizing using plenoptic imaging and digital in-line holography,” Appl. Opt. 55(23), 6410–6420 (2016).
[Crossref] [PubMed]

N. Zeller, F. Quint, and U. Stilla, “Depth estimation and camera calibration of a focused plenoptic camera for visual odometry,” ISPRS J. Photogramm. Remote Sens. 118, 83–100 (2016).
[Crossref]

E. A. Deem, L. N. Cattafesta, T. W. Fahringer, and B. S. Thurow, “On the resolution of plenoptic PIV,” Meas. Sci. Technol. 27(8), 084003 (2016).
[Crossref]

M. Jambor, V. Nosenko, S. K. Zhdanov, and H. M. Thomas, “Plasma crystal dynamics measured with a three-dimensional plenoptic camera,” Rev. Sci. Instrum. 87(3), 033505 (2016).
[Crossref] [PubMed]

2015 (2)

H.-Y. Liu, E. Jonas, L. Tian, J. Zhong, B. Recht, and L. Waller, “3D imaging in volumetric scattering media using phase-space measurements,” Opt. Express 23(11), 14461–14471 (2015).
[Crossref] [PubMed]

T. W. Fahringer, K. P. Lynch, and B. S. Thurow, “Volumetric particle image velocimetry with a single plenoptic camera,” Meas. Sci. Technol. 26(11), 115201 (2015).
[Crossref]

2014 (1)

S. Wanner and B. Goldluecke, “Variational light field analysis for disparity estimation and super-resolution,” IEEE Trans. Pattern Anal. Mach. Intell. 36(3), 606–619 (2014).
[Crossref] [PubMed]

2013 (2)

2011 (1)

T. Khanam, M. Nurur Rahman, A. Rajendran, V. Kariwala, and A. K. Asundi, “Accurate size measurement of needle-shaped particles using digital holography,” Chem. Eng. Sci. 66(12), 2699–2706 (2011).
[Crossref]

2010 (1)

J. Katz and J. Sheng, “Applications of holography in fluid mechanics and particle dynamics,” Annu. Rev. Fluid Mech. 42(1), 531–555 (2010).
[Crossref]

Agentis, D.

E. A. Deem, D. Agentis, F. Nicolas, L. N. Cattafesta, T. Fahringer, and B. Thurow, “A canonical experiment comparing tomographic and plenoptic PIV,” in 10th Pacific Symp. Flow Visulaization Image Process. (2015), pp. 15–18.

Asundi, A. K.

T. Khanam, M. Nurur Rahman, A. Rajendran, V. Kariwala, and A. K. Asundi, “Accurate size measurement of needle-shaped particles using digital holography,” Chem. Eng. Sci. 66(12), 2699–2706 (2011).
[Crossref]

Belden, J.

T. T. Truscott, J. Belden, R. Ni, J. Pendlebury, and B. McEwen, “Three-dimensional microscopic light field particle image velocimetry,” Exp. Fluids 58(3), 16 (2017).
[Crossref]

Blois, G.

K. C. Johnson, B. S. Thurow, T. Kim, G. Blois, and K. T. Christiansen, “Volumetric velocity measurements in the wake of a hemispherical roughness element,” AIAA J. 55(7), 2158–2173 (2017).
[Crossref]

Burke, D.

H. Chen, V. Sick, M. A. Woodward, and D. Burke, “Human iris 3D imaging using a micro-plenoptic camera,” Opt. Life Sci. 2017, 8–10 (2017).

Cattafesta, L. N.

E. A. Deem, L. N. Cattafesta, T. W. Fahringer, and B. S. Thurow, “On the resolution of plenoptic PIV,” Meas. Sci. Technol. 27(8), 084003 (2016).
[Crossref]

E. A. Deem, D. Agentis, F. Nicolas, L. N. Cattafesta, T. Fahringer, and B. Thurow, “A canonical experiment comparing tomographic and plenoptic PIV,” in 10th Pacific Symp. Flow Visulaization Image Process. (2015), pp. 15–18.

Chen, H.

H. Chen, V. Sick, M. A. Woodward, and D. Burke, “Human iris 3D imaging using a micro-plenoptic camera,” Opt. Life Sci. 2017, 8–10 (2017).

H. Chen and V. Sick, “Three-dimensional three-component air flow visualization in a steady-state engine flow bench using a plenoptic camera,” SAE Int. J. Engines 10(2), 625–635 (2017).
[Crossref]

Chen, J.

Chen, Y.

Christiansen, K. T.

K. C. Johnson, B. S. Thurow, T. Kim, G. Blois, and K. T. Christiansen, “Volumetric velocity measurements in the wake of a hemispherical roughness element,” AIAA J. 55(7), 2158–2173 (2017).
[Crossref]

Dai, Q.

Deem, E. A.

E. A. Deem, L. N. Cattafesta, T. W. Fahringer, and B. S. Thurow, “On the resolution of plenoptic PIV,” Meas. Sci. Technol. 27(8), 084003 (2016).
[Crossref]

E. A. Deem, D. Agentis, F. Nicolas, L. N. Cattafesta, T. Fahringer, and B. Thurow, “A canonical experiment comparing tomographic and plenoptic PIV,” in 10th Pacific Symp. Flow Visulaization Image Process. (2015), pp. 15–18.

Drap, P.

P. Drap, J. P. Royer, M. M. Nawaf, M. Saccone, D. Merad, À. López-Sanz, J. B. Ledoux, and J. Garrabou, “Underwater photogrammetry, coded target and plenoptic technology: a set of tools for monitoring red coral in mediterranean sea in the framework of the ”Perfect” project,” in ISPRS - Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci XLII-2(W3), 275–282 (2017).
[Crossref]

Fahringer, T.

E. A. Deem, D. Agentis, F. Nicolas, L. N. Cattafesta, T. Fahringer, and B. Thurow, “A canonical experiment comparing tomographic and plenoptic PIV,” in 10th Pacific Symp. Flow Visulaization Image Process. (2015), pp. 15–18.

Fahringer, T. W.

E. A. Deem, L. N. Cattafesta, T. W. Fahringer, and B. S. Thurow, “On the resolution of plenoptic PIV,” Meas. Sci. Technol. 27(8), 084003 (2016).
[Crossref]

T. W. Fahringer, K. P. Lynch, and B. S. Thurow, “Volumetric particle image velocimetry with a single plenoptic camera,” Meas. Sci. Technol. 26(11), 115201 (2015).
[Crossref]

Gao, J.

Garrabou, J.

P. Drap, J. P. Royer, M. M. Nawaf, M. Saccone, D. Merad, À. López-Sanz, J. B. Ledoux, and J. Garrabou, “Underwater photogrammetry, coded target and plenoptic technology: a set of tools for monitoring red coral in mediterranean sea in the framework of the ”Perfect” project,” in ISPRS - Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci XLII-2(W3), 275–282 (2017).
[Crossref]

Goldluecke, B.

S. Wanner and B. Goldluecke, “Variational light field analysis for disparity estimation and super-resolution,” IEEE Trans. Pattern Anal. Mach. Intell. 36(3), 606–619 (2014).
[Crossref] [PubMed]

Guildenbecher, D. R.

Hall, E. M.

Jambor, M.

M. Jambor, V. Nosenko, S. K. Zhdanov, and H. M. Thomas, “Plasma crystal dynamics measured with a three-dimensional plenoptic camera,” Rev. Sci. Instrum. 87(3), 033505 (2016).
[Crossref] [PubMed]

Jin, X.

Johnson, K. C.

K. C. Johnson, B. S. Thurow, T. Kim, G. Blois, and K. T. Christiansen, “Volumetric velocity measurements in the wake of a hemispherical roughness element,” AIAA J. 55(7), 2158–2173 (2017).
[Crossref]

Jonas, E.

Kariwala, V.

T. Khanam, M. Nurur Rahman, A. Rajendran, V. Kariwala, and A. K. Asundi, “Accurate size measurement of needle-shaped particles using digital holography,” Chem. Eng. Sci. 66(12), 2699–2706 (2011).
[Crossref]

Katz, J.

J. Katz and J. Sheng, “Applications of holography in fluid mechanics and particle dynamics,” Annu. Rev. Fluid Mech. 42(1), 531–555 (2010).
[Crossref]

Khanam, T.

T. Khanam, M. Nurur Rahman, A. Rajendran, V. Kariwala, and A. K. Asundi, “Accurate size measurement of needle-shaped particles using digital holography,” Chem. Eng. Sci. 66(12), 2699–2706 (2011).
[Crossref]

Kim, T.

K. C. Johnson, B. S. Thurow, T. Kim, G. Blois, and K. T. Christiansen, “Volumetric velocity measurements in the wake of a hemispherical roughness element,” AIAA J. 55(7), 2158–2173 (2017).
[Crossref]

Ledoux, J. B.

P. Drap, J. P. Royer, M. M. Nawaf, M. Saccone, D. Merad, À. López-Sanz, J. B. Ledoux, and J. Garrabou, “Underwater photogrammetry, coded target and plenoptic technology: a set of tools for monitoring red coral in mediterranean sea in the framework of the ”Perfect” project,” in ISPRS - Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci XLII-2(W3), 275–282 (2017).
[Crossref]

Levoy, M.

M. Levoy, “Light field photography, microscopy, and illumination,” in International Optical Design Conference (2010), pp. 6–8.

Liu, H.-Y.

Liu, L.

López-Sanz, À.

P. Drap, J. P. Royer, M. M. Nawaf, M. Saccone, D. Merad, À. López-Sanz, J. B. Ledoux, and J. Garrabou, “Underwater photogrammetry, coded target and plenoptic technology: a set of tools for monitoring red coral in mediterranean sea in the framework of the ”Perfect” project,” in ISPRS - Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci XLII-2(W3), 275–282 (2017).
[Crossref]

Lynch, K. P.

T. W. Fahringer, K. P. Lynch, and B. S. Thurow, “Volumetric particle image velocimetry with a single plenoptic camera,” Meas. Sci. Technol. 26(11), 115201 (2015).
[Crossref]

McEwen, B.

T. T. Truscott, J. Belden, R. Ni, J. Pendlebury, and B. McEwen, “Three-dimensional microscopic light field particle image velocimetry,” Exp. Fluids 58(3), 16 (2017).
[Crossref]

Merad, D.

P. Drap, J. P. Royer, M. M. Nawaf, M. Saccone, D. Merad, À. López-Sanz, J. B. Ledoux, and J. Garrabou, “Underwater photogrammetry, coded target and plenoptic technology: a set of tools for monitoring red coral in mediterranean sea in the framework of the ”Perfect” project,” in ISPRS - Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci XLII-2(W3), 275–282 (2017).
[Crossref]

Nawaf, M. M.

P. Drap, J. P. Royer, M. M. Nawaf, M. Saccone, D. Merad, À. López-Sanz, J. B. Ledoux, and J. Garrabou, “Underwater photogrammetry, coded target and plenoptic technology: a set of tools for monitoring red coral in mediterranean sea in the framework of the ”Perfect” project,” in ISPRS - Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci XLII-2(W3), 275–282 (2017).
[Crossref]

Ni, R.

T. T. Truscott, J. Belden, R. Ni, J. Pendlebury, and B. McEwen, “Three-dimensional microscopic light field particle image velocimetry,” Exp. Fluids 58(3), 16 (2017).
[Crossref]

Nicolas, F.

E. A. Deem, D. Agentis, F. Nicolas, L. N. Cattafesta, T. Fahringer, and B. Thurow, “A canonical experiment comparing tomographic and plenoptic PIV,” in 10th Pacific Symp. Flow Visulaization Image Process. (2015), pp. 15–18.

Nosenko, V.

M. Jambor, V. Nosenko, S. K. Zhdanov, and H. M. Thomas, “Plasma crystal dynamics measured with a three-dimensional plenoptic camera,” Rev. Sci. Instrum. 87(3), 033505 (2016).
[Crossref] [PubMed]

Nurur Rahman, M.

T. Khanam, M. Nurur Rahman, A. Rajendran, V. Kariwala, and A. K. Asundi, “Accurate size measurement of needle-shaped particles using digital holography,” Chem. Eng. Sci. 66(12), 2699–2706 (2011).
[Crossref]

Pendlebury, J.

T. T. Truscott, J. Belden, R. Ni, J. Pendlebury, and B. McEwen, “Three-dimensional microscopic light field particle image velocimetry,” Exp. Fluids 58(3), 16 (2017).
[Crossref]

Quint, F.

N. Zeller, F. Quint, and U. Stilla, “Depth estimation and camera calibration of a focused plenoptic camera for visual odometry,” ISPRS J. Photogramm. Remote Sens. 118, 83–100 (2016).
[Crossref]

Rajendran, A.

T. Khanam, M. Nurur Rahman, A. Rajendran, V. Kariwala, and A. K. Asundi, “Accurate size measurement of needle-shaped particles using digital holography,” Chem. Eng. Sci. 66(12), 2699–2706 (2011).
[Crossref]

Recht, B.

Reu, P. L.

Royer, J. P.

P. Drap, J. P. Royer, M. M. Nawaf, M. Saccone, D. Merad, À. López-Sanz, J. B. Ledoux, and J. Garrabou, “Underwater photogrammetry, coded target and plenoptic technology: a set of tools for monitoring red coral in mediterranean sea in the framework of the ”Perfect” project,” in ISPRS - Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci XLII-2(W3), 275–282 (2017).
[Crossref]

Saccone, M.

P. Drap, J. P. Royer, M. M. Nawaf, M. Saccone, D. Merad, À. López-Sanz, J. B. Ledoux, and J. Garrabou, “Underwater photogrammetry, coded target and plenoptic technology: a set of tools for monitoring red coral in mediterranean sea in the framework of the ”Perfect” project,” in ISPRS - Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci XLII-2(W3), 275–282 (2017).
[Crossref]

Sheng, J.

J. Katz and J. Sheng, “Applications of holography in fluid mechanics and particle dynamics,” Annu. Rev. Fluid Mech. 42(1), 531–555 (2010).
[Crossref]

Sick, V.

H. Chen and V. Sick, “Three-dimensional three-component air flow visualization in a steady-state engine flow bench using a plenoptic camera,” SAE Int. J. Engines 10(2), 625–635 (2017).
[Crossref]

H. Chen, V. Sick, M. A. Woodward, and D. Burke, “Human iris 3D imaging using a micro-plenoptic camera,” Opt. Life Sci. 2017, 8–10 (2017).

Stilla, U.

N. Zeller, F. Quint, and U. Stilla, “Depth estimation and camera calibration of a focused plenoptic camera for visual odometry,” ISPRS J. Photogramm. Remote Sens. 118, 83–100 (2016).
[Crossref]

Thomas, H. M.

M. Jambor, V. Nosenko, S. K. Zhdanov, and H. M. Thomas, “Plasma crystal dynamics measured with a three-dimensional plenoptic camera,” Rev. Sci. Instrum. 87(3), 033505 (2016).
[Crossref] [PubMed]

Thurow, B.

E. A. Deem, D. Agentis, F. Nicolas, L. N. Cattafesta, T. Fahringer, and B. Thurow, “A canonical experiment comparing tomographic and plenoptic PIV,” in 10th Pacific Symp. Flow Visulaization Image Process. (2015), pp. 15–18.

Thurow, B. S.

K. C. Johnson, B. S. Thurow, T. Kim, G. Blois, and K. T. Christiansen, “Volumetric velocity measurements in the wake of a hemispherical roughness element,” AIAA J. 55(7), 2158–2173 (2017).
[Crossref]

E. A. Deem, L. N. Cattafesta, T. W. Fahringer, and B. S. Thurow, “On the resolution of plenoptic PIV,” Meas. Sci. Technol. 27(8), 084003 (2016).
[Crossref]

E. M. Hall, B. S. Thurow, and D. R. Guildenbecher, “Comparison of three-dimensional particle tracking and sizing using plenoptic imaging and digital in-line holography,” Appl. Opt. 55(23), 6410–6420 (2016).
[Crossref] [PubMed]

T. W. Fahringer, K. P. Lynch, and B. S. Thurow, “Volumetric particle image velocimetry with a single plenoptic camera,” Meas. Sci. Technol. 26(11), 115201 (2015).
[Crossref]

Tian, L.

Truscott, T. T.

T. T. Truscott, J. Belden, R. Ni, J. Pendlebury, and B. McEwen, “Three-dimensional microscopic light field particle image velocimetry,” Exp. Fluids 58(3), 16 (2017).
[Crossref]

Waller, L.

Wanner, S.

S. Wanner and B. Goldluecke, “Variational light field analysis for disparity estimation and super-resolution,” IEEE Trans. Pattern Anal. Mach. Intell. 36(3), 606–619 (2014).
[Crossref] [PubMed]

Woodward, M. A.

H. Chen, V. Sick, M. A. Woodward, and D. Burke, “Human iris 3D imaging using a micro-plenoptic camera,” Opt. Life Sci. 2017, 8–10 (2017).

Zeller, N.

N. Zeller, F. Quint, and U. Stilla, “Depth estimation and camera calibration of a focused plenoptic camera for visual odometry,” ISPRS J. Photogramm. Remote Sens. 118, 83–100 (2016).
[Crossref]

Zhdanov, S. K.

M. Jambor, V. Nosenko, S. K. Zhdanov, and H. M. Thomas, “Plasma crystal dynamics measured with a three-dimensional plenoptic camera,” Rev. Sci. Instrum. 87(3), 033505 (2016).
[Crossref] [PubMed]

Zhong, J.

AIAA J. (1)

K. C. Johnson, B. S. Thurow, T. Kim, G. Blois, and K. T. Christiansen, “Volumetric velocity measurements in the wake of a hemispherical roughness element,” AIAA J. 55(7), 2158–2173 (2017).
[Crossref]

Annu. Rev. Fluid Mech. (1)

J. Katz and J. Sheng, “Applications of holography in fluid mechanics and particle dynamics,” Annu. Rev. Fluid Mech. 42(1), 531–555 (2010).
[Crossref]

Appl. Opt. (2)

Chem. Eng. Sci. (1)

T. Khanam, M. Nurur Rahman, A. Rajendran, V. Kariwala, and A. K. Asundi, “Accurate size measurement of needle-shaped particles using digital holography,” Chem. Eng. Sci. 66(12), 2699–2706 (2011).
[Crossref]

Exp. Fluids (1)

T. T. Truscott, J. Belden, R. Ni, J. Pendlebury, and B. McEwen, “Three-dimensional microscopic light field particle image velocimetry,” Exp. Fluids 58(3), 16 (2017).
[Crossref]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

S. Wanner and B. Goldluecke, “Variational light field analysis for disparity estimation and super-resolution,” IEEE Trans. Pattern Anal. Mach. Intell. 36(3), 606–619 (2014).
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in ISPRS - Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci (1)

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[Crossref]

ISPRS J. Photogramm. Remote Sens. (1)

N. Zeller, F. Quint, and U. Stilla, “Depth estimation and camera calibration of a focused plenoptic camera for visual odometry,” ISPRS J. Photogramm. Remote Sens. 118, 83–100 (2016).
[Crossref]

Meas. Sci. Technol. (2)

E. A. Deem, L. N. Cattafesta, T. W. Fahringer, and B. S. Thurow, “On the resolution of plenoptic PIV,” Meas. Sci. Technol. 27(8), 084003 (2016).
[Crossref]

T. W. Fahringer, K. P. Lynch, and B. S. Thurow, “Volumetric particle image velocimetry with a single plenoptic camera,” Meas. Sci. Technol. 26(11), 115201 (2015).
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Opt. Express (3)

Opt. Life Sci. (1)

H. Chen, V. Sick, M. A. Woodward, and D. Burke, “Human iris 3D imaging using a micro-plenoptic camera,” Opt. Life Sci. 2017, 8–10 (2017).

Rev. Sci. Instrum. (1)

M. Jambor, V. Nosenko, S. K. Zhdanov, and H. M. Thomas, “Plasma crystal dynamics measured with a three-dimensional plenoptic camera,” Rev. Sci. Instrum. 87(3), 033505 (2016).
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H. Chen and V. Sick, “Three-dimensional three-component air flow visualization in a steady-state engine flow bench using a plenoptic camera,” SAE Int. J. Engines 10(2), 625–635 (2017).
[Crossref]

Other (8)

J. Klemkowsky, T. Fahringer, C. Clifford, B. Bathel, and B. Thurow, “Plenoptic background oriented schlieren imaging,” Meas. Sci. Technol., in-press (2017).

F. V Pepe, F. Di Lena, A. Mazzilli, G. Scarcelli, M. D. Angelo, M. Storico, R. Enrico, I.- Roma, S. Bari, and I.- Bari, “Diffraction-limited plenoptic imaging with correlated light,” Cornell Univ. Libr. 1–8 (2017).

E. A. Deem, D. Agentis, F. Nicolas, L. N. Cattafesta, T. Fahringer, and B. Thurow, “A canonical experiment comparing tomographic and plenoptic PIV,” in 10th Pacific Symp. Flow Visulaization Image Process. (2015), pp. 15–18.

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M. Levoy, “Light field photography, microscopy, and illumination,” in International Optical Design Conference (2010), pp. 6–8.

J. T. Bolan, “Enhancing Image Resolvability in Obscured Environments Using 3D Deconvolution and a Plenoptic Camera,” Auburn University, MS Thesis (2015).

E. M. Hall, T. W. Fahringer, and B. S. Thurow, “Volumetric calibration of a plenoptic camera,” AIAA SciTech Forum, 55th Annu. Aerosp. Sci. Meet. 1–13 (2017).
[Crossref]

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Figures (13)

Fig. 1
Fig. 1 Three-dimensional particle measurements using a single plenoptic camera. (a) The raw image shows a crown splash from a droplet impact with insert highlighting the sub-images from the microlens array; (b) computationally refocused results from this one instantaneous realization; and (c) the measured 3D particle positions and sizes showing an in-plane view (top) and reconstructed top-down view (bottom) [4].
Fig. 2
Fig. 2 Illustration of the theoretical depth resolution, Δz, (top) and the total depth range (bottom). A numerically refocused image (top) is determined by integrating the intensity of all light rays which pass through the main lens aperture and has a relatively narrow depth of field. In contrast, the narrow aperture of a single pixel (bottom) determines the effective depth range over which numerically refocused images remain sharp.
Fig. 3
Fig. 3 Photo showing the static particle apparatus and plenoptic camera experimental configuration.
Fig. 4
Fig. 4 Experimental configuration depicting the three measurement distances used to extend the translation range.
Fig. 5
Fig. 5 Example refocused images from the middle depth configuration with a magnification of 0.5. Relative to the nominal focal plane, these images are focused at −25 mm (left), 0 mm (middle), and 25 mm (right).
Fig. 6
Fig. 6 Example refocused images from the middle depth configuration with a magnification of 0.25. Relative to the nominal focal plane, these images are focused at −25 mm (left), 0 mm (middle), and 25 mm (right).
Fig. 7
Fig. 7 Example of measured particle locations, diameter indicated by color.
Fig. 8
Fig. 8 Isometric (top) and planar (bottom) views of measured particles and displacements from the middle configuration with a magnification of 0.25.
Fig. 9
Fig. 9 Depth error determination for the middle depth configuration with a magnification of 0.5.
Fig. 10
Fig. 10 Histogram of depth error measurements for the middle depth configuration with a magnification of 0.5.
Fig. 11
Fig. 11 Average depth error as a function of particle depth, z, in (a) physical dimension and (b) normalized.
Fig. 12
Fig. 12 Standard deviation of depth error for each magnification as a function of particle depth, z, in (a) physical dimensions, and (b) normalized.
Fig. 13
Fig. 13 Standard deviation of in-plane error for each magnification as a function of particle depth, z, in (a) physical dimensions, and (b) normalized.

Tables (2)

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Table 1 Experimental configurations and theoretical measurement performance.

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Table 2 Comparison of theoretical and measured depth precision.

Equations (4)

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Δz= f (M1) 2 M(M1) f μ N/ f( N2 ) f (M1) 2 M(M1)+ f μ /f ,
Δx= p μ / M .
DOF=[ D l o DΔx l o ][ D l o D+Δx l o ],
z N =[ D l o D+Δx l o ] and z F =[ D l o DΔx l o ].

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