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As a novel imaging method, single-pixel imaging based on spectrum reconstruction is interesting. To date, however, there has not yet been a theory that can analyze the method in detail. In order to obtain a comprehensive understanding of the single-pixel imaging technique, a detailed theoretical analysis is proposed. Firstly, in the presented imaging theory, we analyze the effects of several factors involved in the imaging process on imaging reconstruction, including the direct detection, namely, the back scattering light from the imaged object is received by a detector; indirect detection, namely, the back scattering light is received after undergoing the diffuse reflections by multiple diffusing surfaces in proper sequence; multi-channel detection, namely, the scattering light is together detected after experiencing multiple diffuse reflections in proper sequence along multiple different paths; the size and location of the single-pixel detector. The theoretical results show that whether it is direct detection or indirect detection and whether it is single-channel detection or multi-channel detection, the above imaging method is valid as long as the scattering light can be received by the detector, and the obtained results are also in accord with the existing experimental results. Since the single-pixel detector is treated as a component of many point detectors due to its practical size, the effect of the single-pixel detector size on image reconstruction is equivalent to the integration of reconstructed images from multiple point detectors at different locations. Secondly, the spectrum reconstruction based on a three-step phase shift technique is also derived to increase the image reconstruction speed. Finally, the experimental results of the imaging reconstruction of an object, whose surface reflectivity is uniform, are demonstrated.
[1] Valencia A, Scarcelli G, D'Angelo M, Shih Y 2005 Phys. Rev. Lett. 94 063601
[2] Ferri F, Magatti D, Gatti A, Bache M, Brambilla E, Lugiato L A 2005 Phys. Rev. Lett. 94 183602
[3] Scarcelli G, Berardi V, Shih Y 2006 Phys. Rev. Lett. 96 063602
[4] Meyers R, Deacon K S, Shih Y 2008 Phys. Rev. A 77 041801
[5] Shapiro J H 2008 Phys. Rev. A 78 061802
[6] Bromberg Y, Katz O, Silberberg Y 2009 Phys. Rev. A 79 053840
[7] Jack B, Leach J, Romero J, Franke-Arnold S, Ritsch-Marte M, Barnett S M, Padgett M J 2009 Phys. Rev. Lett. 103 083602
[8] Ferri F, Magatti D, Lugiato L A, Gatti A 2010 Phys. Rev. Lett. 104 253603
[9] Zhong Y J, Liu J L, Wen Q, Zhao S M 2015 Acta Phys. Sin. 64 014202 (in Chinese)[仲亚军, 刘娇梁, 文强, 赵生妹2015物理学报64 014202]
[10] Li L Z, Yao X R, Liu X F, Yu W K, Zhai G J 2014 Acta Phys. Sin. 63 224201 (in Chinese)[李龙珍, 姚旭日, 刘雪峰, 俞文凯, 翟光杰2014物理学报63 224201]
[11] Liu X F, Yao X R, Li M F, Yu W K, Chen X H, Sun Z B, Wu L A, Zhai G J 2013 Acta Phys. Sin. 62 184205 (in Chinese)[刘雪峰, 姚旭日, 李明飞, 俞文凯, 陈希浩, 孙志斌, 吴令安, 翟光杰2013物理学报62 184205]
[12] Sun B Q, Welsh S S, Edgar M P, Shapiro J H, Padgett M J 2012 Opt. Express 20 16892
[13] Sun B, Edgar M P, Bowman R, Vittert L E, Welsh S, Bowman A, Padgett M J 2013 Science 340 844
[14] Zhang Z, Ma X, Zhong J 2015 Nat. Commun. 6 6225
[15] Edgar M P, Gibson G M, Bowman R W, Sun B, Radwell N, Mitchell K J, Welsh S S, Padgett M J 2015 Sci. Rep. 5 10669
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[1] Valencia A, Scarcelli G, D'Angelo M, Shih Y 2005 Phys. Rev. Lett. 94 063601
[2] Ferri F, Magatti D, Gatti A, Bache M, Brambilla E, Lugiato L A 2005 Phys. Rev. Lett. 94 183602
[3] Scarcelli G, Berardi V, Shih Y 2006 Phys. Rev. Lett. 96 063602
[4] Meyers R, Deacon K S, Shih Y 2008 Phys. Rev. A 77 041801
[5] Shapiro J H 2008 Phys. Rev. A 78 061802
[6] Bromberg Y, Katz O, Silberberg Y 2009 Phys. Rev. A 79 053840
[7] Jack B, Leach J, Romero J, Franke-Arnold S, Ritsch-Marte M, Barnett S M, Padgett M J 2009 Phys. Rev. Lett. 103 083602
[8] Ferri F, Magatti D, Lugiato L A, Gatti A 2010 Phys. Rev. Lett. 104 253603
[9] Zhong Y J, Liu J L, Wen Q, Zhao S M 2015 Acta Phys. Sin. 64 014202 (in Chinese)[仲亚军, 刘娇梁, 文强, 赵生妹2015物理学报64 014202]
[10] Li L Z, Yao X R, Liu X F, Yu W K, Zhai G J 2014 Acta Phys. Sin. 63 224201 (in Chinese)[李龙珍, 姚旭日, 刘雪峰, 俞文凯, 翟光杰2014物理学报63 224201]
[11] Liu X F, Yao X R, Li M F, Yu W K, Chen X H, Sun Z B, Wu L A, Zhai G J 2013 Acta Phys. Sin. 62 184205 (in Chinese)[刘雪峰, 姚旭日, 李明飞, 俞文凯, 陈希浩, 孙志斌, 吴令安, 翟光杰2013物理学报62 184205]
[12] Sun B Q, Welsh S S, Edgar M P, Shapiro J H, Padgett M J 2012 Opt. Express 20 16892
[13] Sun B, Edgar M P, Bowman R, Vittert L E, Welsh S, Bowman A, Padgett M J 2013 Science 340 844
[14] Zhang Z, Ma X, Zhong J 2015 Nat. Commun. 6 6225
[15] Edgar M P, Gibson G M, Bowman R W, Sun B, Radwell N, Mitchell K J, Welsh S S, Padgett M J 2015 Sci. Rep. 5 10669
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