Abstract

Single-pixel imaging (SPI) is an innovative technique that images an object from non-pixelated detection. To do so, SPI has to conduct structured illumination that functions as a way to scan the object. The illumination basis and corresponding scanned intensities are then used for correlation measurement to reconstruct an image. In this process, the illumination structure, or scanning basis plays an important role on the scanning efficiency and therefore reconstruction quality. In this work we discuss the efficiency of different scanning basis in iterative SPI. A comparison between raster scan (RS) and multi-pixel structured scan (MS) in SPI is carried out under the criterions of signal to noise ratio and structural similarity index. Theoretical analysis is followed with demonstration from both experiment and simulation. Our conclusion is believed to be useful guidelines for choosing the right illumination basis depending on the iterative SPI application situation.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (2)

2017 (7)

2016 (5)

Z. Zhang and J. Zhong, “Three-dimensional single-pixel imaging with far fewer measurements than effective image pixels,” Opt. Lett. 41, 2497–2500 (2016).
[Crossref] [PubMed]

H. Yu, R. Lu, S. Han, H. Xie, G. Du, T. Xiao, and D. Zhu, “Fourier-transform ghost imaging with hard X rays,” Phys. Rev. Lett. 117, 113901 (2016).
[Crossref] [PubMed]

D. Pelliccia, A. Rack, M. Scheel, V. Cantelli, and D. M. Paganin, “Experimental X-ray ghost imaging,” Phys. Rev. Lett. 117, 113902 (2016).
[Crossref] [PubMed]

N. Huynh, E. Zhang, M. Betcke, S. Arridge, P. Beard, and B. Cox, “Single-pixel optical camera for video rate ultrasonic imaging,” Optica 3, 26–29 (2016).
[Crossref]

D. Shin, J. H. Shapiro, and V. K. Goyal, “Performance analysis of low-flux least-squares single-pixel imaging,” IEEE Signal Process. Lett. 23, 1756–1760 (2016).
[Crossref]

2015 (3)

M. P. Edgar, G. M. Gibson, R. W. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. S. Welsh, and M. J. Padgett, “Simultaneous real-time visible and infrared video with single-pixel detectors,” Sci. Rep. 5, 10669 (2015).
[Crossref] [PubMed]

Z. Zhang, X. Ma, and J. Zhong, “Single-pixel imaging by means of Fourier spectrum acquisition,” Nat. Commun. 6, 6225 (2015).
[Crossref] [PubMed]

K. Shibuya, K. Nakae, Y. Mizutani, and T. Iwata, “Comparison of reconstructed images between ghost imaging and hadamard transform imaging,” Opt. Rev. 22, 897–902 (2015).
[Crossref]

2014 (1)

E. Li, Z. Bo, M. Chen, W. Gong, and S. Han, “Ghost imaging of a moving target with an unknown constant speed,” Appl. Phys. Lett. 104, 251120 (2014).
[Crossref]

2013 (2)

S. S. Welsh, M. P. Edgar, R. Bowman, P. Jonathan, B. Sun, and M. J. Padgett, “Fast full-color computational imaging with single-pixel detectors,” Opt. Express 21, 23068–23074 (2013).
[Crossref] [PubMed]

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340, 844–847 (2013).
[Crossref] [PubMed]

2012 (2)

C. Zhao, W. Gong, M. Chen, E. Li, H. Wang, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints,” Appl. Phys. Lett. 101, 141123 (2012).
[Crossref]

B. Sun, S. S. Welsh, M. P. Edgar, J. H. Shapiro, and M. J. Padgett, “Normalized ghost imaging,” Opt. Express 20, 16892–16901 (2012).
[Crossref]

2010 (1)

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104, 253603 (2010).
[Crossref] [PubMed]

2008 (3)

E. J. Candes and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25, 21–30 (2008).
[Crossref]

J. Romberg, “Imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 14–20 (2008).
[Crossref]

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 83–91 (2008).
[Crossref]

1976 (1)

Altmann, Y.

R. Tobin, Y. Altmann, X. Ren, A. McCarthy, R. A. Lamb, S. McLaughlin, and G. S. Buller, “Comparative study of sampling strategies for sparse photon multispectral lidar imaging: towards mosaic filter arrays,” J. Opt. 19, 094006 (2017).
[Crossref]

Arridge, S.

Baraniuk, R. G.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 83–91 (2008).
[Crossref]

Beard, P.

Betcke, M.

Bian, L.

Bo, Z.

E. Li, Z. Bo, M. Chen, W. Gong, and S. Han, “Ghost imaging of a moving target with an unknown constant speed,” Appl. Phys. Lett. 104, 251120 (2014).
[Crossref]

Bowman, A.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340, 844–847 (2013).
[Crossref] [PubMed]

Bowman, R.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340, 844–847 (2013).
[Crossref] [PubMed]

S. S. Welsh, M. P. Edgar, R. Bowman, P. Jonathan, B. Sun, and M. J. Padgett, “Fast full-color computational imaging with single-pixel detectors,” Opt. Express 21, 23068–23074 (2013).
[Crossref] [PubMed]

Bowman, R. W.

M. P. Edgar, G. M. Gibson, R. W. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. S. Welsh, and M. J. Padgett, “Simultaneous real-time visible and infrared video with single-pixel detectors,” Sci. Rep. 5, 10669 (2015).
[Crossref] [PubMed]

Buller, G. S.

R. Tobin, Y. Altmann, X. Ren, A. McCarthy, R. A. Lamb, S. McLaughlin, and G. S. Buller, “Comparative study of sampling strategies for sparse photon multispectral lidar imaging: towards mosaic filter arrays,” J. Opt. 19, 094006 (2017).
[Crossref]

A. M. Pawlikowska, A. Halimi, R. A. Lamb, and G. S. Buller, “Single-photon three-dimensional imaging at up to 10 kilometers range,” Opt. Express 25, 11919–11931 (2017).
[Crossref] [PubMed]

Candes, E. J.

E. J. Candes and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25, 21–30 (2008).
[Crossref]

Cantelli, V.

D. Pelliccia, A. Rack, M. Scheel, V. Cantelli, and D. M. Paganin, “Experimental X-ray ghost imaging,” Phys. Rev. Lett. 117, 113902 (2016).
[Crossref] [PubMed]

Chen, F.

Chen, L.

Chen, M.

E. Li, Z. Bo, M. Chen, W. Gong, and S. Han, “Ghost imaging of a moving target with an unknown constant speed,” Appl. Phys. Lett. 104, 251120 (2014).
[Crossref]

C. Zhao, W. Gong, M. Chen, E. Li, H. Wang, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints,” Appl. Phys. Lett. 101, 141123 (2012).
[Crossref]

Cox, B.

Dai, Q.

L. Bian, J. Suo, Q. Dai, and F. Chen, “Experimental comparison of single-pixel imaging algorithms,” J. Opt. Soc. Am. A 35, 78–87 (2018).
[Crossref]

Y. Wang, Y. Liu, J. Suo, G. Situ, C. Qiao, and Q. Dai, “High speed computational ghost imaging via spatial sweeping,” Sci. Rep. 7, 45325 (2017).
[Crossref] [PubMed]

Davenport, M. A.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 83–91 (2008).
[Crossref]

Du, G.

H. Yu, R. Lu, S. Han, H. Xie, G. Du, T. Xiao, and D. Zhu, “Fourier-transform ghost imaging with hard X rays,” Phys. Rev. Lett. 117, 113901 (2016).
[Crossref] [PubMed]

Duarte, M. F.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 83–91 (2008).
[Crossref]

Edgar, M. P.

Ferri, F.

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104, 253603 (2010).
[Crossref] [PubMed]

Gatti, A.

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104, 253603 (2010).
[Crossref] [PubMed]

Gibson, G. M.

G. M. Gibson, B. Sun, M. P. Edgar, D. B. Phillips, N. Hempler, G. T. Maker, G. P. A. Malcolm, and M. J. Padgett, “Real-time imaging of methane gas leaks using a single-pixel camera,” Opt. Express 25, 2998–3005 (2017).
[Crossref] [PubMed]

M. P. Edgar, G. M. Gibson, R. W. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. S. Welsh, and M. J. Padgett, “Simultaneous real-time visible and infrared video with single-pixel detectors,” Sci. Rep. 5, 10669 (2015).
[Crossref] [PubMed]

Gong, W.

E. Li, Z. Bo, M. Chen, W. Gong, and S. Han, “Ghost imaging of a moving target with an unknown constant speed,” Appl. Phys. Lett. 104, 251120 (2014).
[Crossref]

C. Zhao, W. Gong, M. Chen, E. Li, H. Wang, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints,” Appl. Phys. Lett. 101, 141123 (2012).
[Crossref]

Goyal, V. K.

D. Shin, J. H. Shapiro, and V. K. Goyal, “Performance analysis of low-flux least-squares single-pixel imaging,” IEEE Signal Process. Lett. 23, 1756–1760 (2016).
[Crossref]

Guo, H.

Halimi, A.

Han, S.

H. Yu, R. Lu, S. Han, H. Xie, G. Du, T. Xiao, and D. Zhu, “Fourier-transform ghost imaging with hard X rays,” Phys. Rev. Lett. 117, 113901 (2016).
[Crossref] [PubMed]

E. Li, Z. Bo, M. Chen, W. Gong, and S. Han, “Ghost imaging of a moving target with an unknown constant speed,” Appl. Phys. Lett. 104, 251120 (2014).
[Crossref]

C. Zhao, W. Gong, M. Chen, E. Li, H. Wang, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints,” Appl. Phys. Lett. 101, 141123 (2012).
[Crossref]

Harwit, M.

He, Y.

Hempler, N.

Hendry, E.

Hobson, P.

Hornett, S. M.

Huynh, N.

Iwata, T.

K. Shibuya, K. Nakae, Y. Mizutani, and T. Iwata, “Comparison of reconstructed images between ghost imaging and hadamard transform imaging,” Opt. Rev. 22, 897–902 (2015).
[Crossref]

Jonathan, P.

Kelly, K. F.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 83–91 (2008).
[Crossref]

Lamb, R. A.

R. Tobin, Y. Altmann, X. Ren, A. McCarthy, R. A. Lamb, S. McLaughlin, and G. S. Buller, “Comparative study of sampling strategies for sparse photon multispectral lidar imaging: towards mosaic filter arrays,” J. Opt. 19, 094006 (2017).
[Crossref]

A. M. Pawlikowska, A. Halimi, R. A. Lamb, and G. S. Buller, “Single-photon three-dimensional imaging at up to 10 kilometers range,” Opt. Express 25, 11919–11931 (2017).
[Crossref] [PubMed]

Laska, J. N.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 83–91 (2008).
[Crossref]

Li, E.

E. Li, Z. Bo, M. Chen, W. Gong, and S. Han, “Ghost imaging of a moving target with an unknown constant speed,” Appl. Phys. Lett. 104, 251120 (2014).
[Crossref]

C. Zhao, W. Gong, M. Chen, E. Li, H. Wang, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints,” Appl. Phys. Lett. 101, 141123 (2012).
[Crossref]

Li, J.

Liu, Y.

Y. Wang, Y. Liu, J. Suo, G. Situ, C. Qiao, and Q. Dai, “High speed computational ghost imaging via spatial sweeping,” Sci. Rep. 7, 45325 (2017).
[Crossref] [PubMed]

Lu, R.

H. Yu, R. Lu, S. Han, H. Xie, G. Du, T. Xiao, and D. Zhu, “Fourier-transform ghost imaging with hard X rays,” Phys. Rev. Lett. 117, 113901 (2016).
[Crossref] [PubMed]

Lugiato, L. A.

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104, 253603 (2010).
[Crossref] [PubMed]

Luo, B.

Ma, X.

Z. Zhang, X. Ma, and J. Zhong, “Single-pixel imaging by means of Fourier spectrum acquisition,” Nat. Commun. 6, 6225 (2015).
[Crossref] [PubMed]

Magatti, D.

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104, 253603 (2010).
[Crossref] [PubMed]

Maker, G. T.

Malcolm, G. P. A.

McCarthy, A.

R. Tobin, Y. Altmann, X. Ren, A. McCarthy, R. A. Lamb, S. McLaughlin, and G. S. Buller, “Comparative study of sampling strategies for sparse photon multispectral lidar imaging: towards mosaic filter arrays,” J. Opt. 19, 094006 (2017).
[Crossref]

McLaughlin, S.

R. Tobin, Y. Altmann, X. Ren, A. McCarthy, R. A. Lamb, S. McLaughlin, and G. S. Buller, “Comparative study of sampling strategies for sparse photon multispectral lidar imaging: towards mosaic filter arrays,” J. Opt. 19, 094006 (2017).
[Crossref]

Mitchell, K. J.

M. P. Edgar, G. M. Gibson, R. W. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. S. Welsh, and M. J. Padgett, “Simultaneous real-time visible and infrared video with single-pixel detectors,” Sci. Rep. 5, 10669 (2015).
[Crossref] [PubMed]

Mizutani, Y.

K. Shibuya, K. Nakae, Y. Mizutani, and T. Iwata, “Comparison of reconstructed images between ghost imaging and hadamard transform imaging,” Opt. Rev. 22, 897–902 (2015).
[Crossref]

Nakae, K.

K. Shibuya, K. Nakae, Y. Mizutani, and T. Iwata, “Comparison of reconstructed images between ghost imaging and hadamard transform imaging,” Opt. Rev. 22, 897–902 (2015).
[Crossref]

Padgett, M. J.

Paganin, D. M.

D. Pelliccia, A. Rack, M. Scheel, V. Cantelli, and D. M. Paganin, “Experimental X-ray ghost imaging,” Phys. Rev. Lett. 117, 113902 (2016).
[Crossref] [PubMed]

Pawlikowska, A. M.

Pelliccia, D.

D. Pelliccia, A. Rack, M. Scheel, V. Cantelli, and D. M. Paganin, “Experimental X-ray ghost imaging,” Phys. Rev. Lett. 117, 113902 (2016).
[Crossref] [PubMed]

Phillips, D. B.

Qiao, C.

Y. Wang, Y. Liu, J. Suo, G. Situ, C. Qiao, and Q. Dai, “High speed computational ghost imaging via spatial sweeping,” Sci. Rep. 7, 45325 (2017).
[Crossref] [PubMed]

Rack, A.

D. Pelliccia, A. Rack, M. Scheel, V. Cantelli, and D. M. Paganin, “Experimental X-ray ghost imaging,” Phys. Rev. Lett. 117, 113902 (2016).
[Crossref] [PubMed]

Radwell, N.

M. P. Edgar, G. M. Gibson, R. W. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. S. Welsh, and M. J. Padgett, “Simultaneous real-time visible and infrared video with single-pixel detectors,” Sci. Rep. 5, 10669 (2015).
[Crossref] [PubMed]

Ren, X.

R. Tobin, Y. Altmann, X. Ren, A. McCarthy, R. A. Lamb, S. McLaughlin, and G. S. Buller, “Comparative study of sampling strategies for sparse photon multispectral lidar imaging: towards mosaic filter arrays,” J. Opt. 19, 094006 (2017).
[Crossref]

Romberg, J.

J. Romberg, “Imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 14–20 (2008).
[Crossref]

Scheel, M.

D. Pelliccia, A. Rack, M. Scheel, V. Cantelli, and D. M. Paganin, “Experimental X-ray ghost imaging,” Phys. Rev. Lett. 117, 113902 (2016).
[Crossref] [PubMed]

Shapiro, J. H.

D. Shin, J. H. Shapiro, and V. K. Goyal, “Performance analysis of low-flux least-squares single-pixel imaging,” IEEE Signal Process. Lett. 23, 1756–1760 (2016).
[Crossref]

B. Sun, S. S. Welsh, M. P. Edgar, J. H. Shapiro, and M. J. Padgett, “Normalized ghost imaging,” Opt. Express 20, 16892–16901 (2012).
[Crossref]

Shibuya, K.

K. Shibuya, K. Nakae, Y. Mizutani, and T. Iwata, “Comparison of reconstructed images between ghost imaging and hadamard transform imaging,” Opt. Rev. 22, 897–902 (2015).
[Crossref]

Shin, D.

D. Shin, J. H. Shapiro, and V. K. Goyal, “Performance analysis of low-flux least-squares single-pixel imaging,” IEEE Signal Process. Lett. 23, 1756–1760 (2016).
[Crossref]

Situ, G.

Y. Wang, Y. Liu, J. Suo, G. Situ, C. Qiao, and Q. Dai, “High speed computational ghost imaging via spatial sweeping,” Sci. Rep. 7, 45325 (2017).
[Crossref] [PubMed]

Sloane, N. J. A.

Stantchev, R. I.

Sun, B.

Sun, T.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 83–91 (2008).
[Crossref]

Suo, J.

L. Bian, J. Suo, Q. Dai, and F. Chen, “Experimental comparison of single-pixel imaging algorithms,” J. Opt. Soc. Am. A 35, 78–87 (2018).
[Crossref]

Y. Wang, Y. Liu, J. Suo, G. Situ, C. Qiao, and Q. Dai, “High speed computational ghost imaging via spatial sweeping,” Sci. Rep. 7, 45325 (2017).
[Crossref] [PubMed]

Takhar, D.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 83–91 (2008).
[Crossref]

Tobin, R.

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Vittert, L. E.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340, 844–847 (2013).
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Y. Wang, Y. Liu, J. Suo, G. Situ, C. Qiao, and Q. Dai, “High speed computational ghost imaging via spatial sweeping,” Sci. Rep. 7, 45325 (2017).
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H. Yu, R. Lu, S. Han, H. Xie, G. Du, T. Xiao, and D. Zhu, “Fourier-transform ghost imaging with hard X rays,” Phys. Rev. Lett. 117, 113901 (2016).
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Appl. Opt. (1)

Appl. Phys. Lett. (2)

C. Zhao, W. Gong, M. Chen, E. Li, H. Wang, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints,” Appl. Phys. Lett. 101, 141123 (2012).
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R. Tobin, Y. Altmann, X. Ren, A. McCarthy, R. A. Lamb, S. McLaughlin, and G. S. Buller, “Comparative study of sampling strategies for sparse photon multispectral lidar imaging: towards mosaic filter arrays,” J. Opt. 19, 094006 (2017).
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Phys. Rev. Lett. (3)

H. Yu, R. Lu, S. Han, H. Xie, G. Du, T. Xiao, and D. Zhu, “Fourier-transform ghost imaging with hard X rays,” Phys. Rev. Lett. 117, 113901 (2016).
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Y. Wang, Y. Liu, J. Suo, G. Situ, C. Qiao, and Q. Dai, “High speed computational ghost imaging via spatial sweeping,” Sci. Rep. 7, 45325 (2017).
[Crossref] [PubMed]

M. P. Edgar, G. M. Gibson, R. W. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. S. Welsh, and M. J. Padgett, “Simultaneous real-time visible and infrared video with single-pixel detectors,” Sci. Rep. 5, 10669 (2015).
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Science (1)

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340, 844–847 (2013).
[Crossref] [PubMed]

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Figures (4)

Fig. 1
Fig. 1 (a) Schematic diagram of experimental setup. SPI is conducted under either active (green dash box) or passive (purple dash box) illumination. Two modulation modules, a DMD modulation module (blue solid box) and a 2D Galvanometer Scanner (red solid box) are employed. In active mode, laser beam (green arrow) is incident on either of the modulation apparatuses. The modulated light illuminates on the target and then collected by a bucket detector. In passive mode (indicated in purple arrow), the target is illuminated by a LED source directly and imaged on the DMD that works as a coded aperture. After being modulated the reflected signal is collected into a SPD. (b) and (c) are the optical setup of SPI using DMD and 2D-Galvo, respectively. In (b) the parameters l1, l2 and f1 are subject to the imaging formula of the thin lens. The object is in the image plane of the DMD window in respect to Lens-1.
Fig. 2
Fig. 2 (a) Experiment reconstruction of a half black and half white board under three different imaging conditions. All RSD and MS reconstructions are done under the same illuminance. While RSG is done with a scanning beam that generates the same power as that covers the whole DMD active area in the other two situations. In each resolution, SNR of the two reconstructions are well related by a factor pixel number. This relation is also well kept between RSG and MS. SSIM is also presented. (b) An object with reasonable complicity is used for simulation. Illumination is set according to the experiment. Only detector noise is considered and set in a Poisson distribution. Noise level is independent to that in the experiment.
Fig. 3
Fig. 3 Experimental and simulation results under (a) sinusoidal illumination and (b) Gaussian illumination fluctuation. The sinusoidal fluctuation is in a frequency of 100 Hz, with a peak-to-peak amplitude of 10% of the average illumination. Reconstruction is done in two pattern frequencies, 20 kHz and 10 kHz respectively. Gaussian noise is set in the relative (to the average illuminance) variance of 2.8% and 5.6%, respectively.
Fig. 4
Fig. 4 Reconstructions of MS and RS at four different patterns frequencies under passive illumination. Both illumination fluctuation and detector noise are considered. MS at 20 kHz pattern frequency generates the best image, which indicates that the dominant noise in MS is from illumination, especially at low pattern frequencies. On the other hand, RS is limited by both illumination and detector noise. AS pattern frequency increases, dominant noise in RS changes from illumination to detector noise. Generally, under this ambient light illumination, MS is able to provide much better results than RS.

Equations (7)

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Y = A X
O ( X ) = A T Y
O ( X ) = A T ( α Y + n )
SNR = O ( x ) ( O ( x ) O ( x ) ) 2
O ( X ) = E α X + A T α Δ A X
O ( X i ) = E α X i + m = 1 M ( α Δ m A im T Y m )
Δ O ( X i ) = m = 1 M ( α Δ m A i m T Y m ) = α Δ 1 X i 1 + α Δ 2 X i 2 + + α Δ M X i M = m = 1 M α Δ m X im

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