二阶和高阶关联成像研究
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摘要
关联成像实验首先是利用纠缠双光子对实现的,并且量子纠缠被认为是实现关联成像的必备条件。然而近几年的理论和实验研究表明热光源同样可以实现关联成像。由于热光容易获得,因此与纠缠光源相比,热光源关联成像具有更为广阔的应用前景。因此,热光关联成像引起了人们极大的兴趣,成为近年来受到广泛关注的热点问题之一。
本文主要对热光关联成像的性质进行了研究。主要内容包括:
1.阐述了关联成像的由来和研究历史,理论分析了热光的统计模型,介绍了赝热光源,分析了热光的相干性理论。
2.研究了热光二阶关联成像的两种方案:无透镜鬼成像和无透镜傅里叶变换关联成像方案,得出了光源、光学系统、待测物体和测量次数对成像可见度、信噪比等成像效果的影响,而且利用数值模拟的方法对其进行了验证。
3.研究了光的偏振对热光关联成像的影响。根据完全偏振光的不同偏振态和部分偏振光的不同偏振度对二阶关联函数的影响,利用统计光学理论研究了光的不同偏振性质对热光关联成像的可见度和信噪比的影响。研究结果表明,光的偏振对热光关联成像的影响体现在部分偏振光的不同偏振度上,并且得出了部分偏振光的偏振度对热光关联成像的可见度和信噪比的影响。
4.利用高阶关联函数对热光高阶无透镜傅里叶变换关联成像进行了研究。分析了高阶无透镜傅里叶变换关联成像的基本原理,并且对高阶无透镜傅里叶变换关联成像的可见度和信噪比进行了研究。研究结果表明,高阶无透镜傅里叶变换关联成像的可见度随阶数的增大而有所提高,但同时其信噪比降低了。
The first correlated imaging experiment was observed by using entangled photon pairs,and entanglement was thought as a prerequisite for achieving correlated imaging. However, it has been proved both theoretically and experimentally in recent years that correlated imaging can also be performed with a thermal source. Thermal source is easily obtainable, so compared with correlated imaging with an entangled source, correlated imaging with a thermal source has more potential in practice. So correlated imaging with thermal light attracts much attention in recent years as a hot topic.
In this dissertation, we work on the properties of correlated imaging with thermal light. The main content includes:
1. We briefly review the origin and the history of correlated imaging. Then, we analyze the statistic model of thermal light theoretically, and we introduce pseudo-thermal light. Finally we analyze the theory of the coherent property of thermal light.
2. We research on two schemes of second-order correlated imaging with thermal light: lensless ghost imaging and lensless Fourier-transform correlated imaging. It is shown that the light source, the optical system, the object imaged and the number of measurement have effects on the imaging quality such as the visibility and signal-to-noise (SNR), which are discussed in detail by numerical simulations.
3. The effect of light polarization on thermal correlated imaging is studied. Based on the effect of the polarization state of polarized light and the degree of polarization on the second-order correlation function, the influence of light polarization on the visibility and SNR of correlated imaging with thermal light is investigated by use of statistical optics theory. It is shown that only the degree of polarization has effect on thermal correlated imaging, and the influence of the degree of polarization on the visibility and SNR of thermal correlated imaging is obtained.
4. High-order lensless Fourier-transform correlated imaging with thermal light is investigated based on high-order correlated function. The detailed theory of high-order lensless Fourier-transform correlated imaging is analyzed, and the visibility and SNR of high-order lensless Fourier-transform correlated imaging are investigated. It is shown that although increasing the order of intensity correlation leads to the growth of the visibility of high-order lensless Fourier-transform correlated imaging, it also results in the decrease of the SNR.
本文主要对热光关联成像的性质进行了研究。主要内容包括:
1.阐述了关联成像的由来和研究历史,理论分析了热光的统计模型,介绍了赝热光源,分析了热光的相干性理论。
2.研究了热光二阶关联成像的两种方案:无透镜鬼成像和无透镜傅里叶变换关联成像方案,得出了光源、光学系统、待测物体和测量次数对成像可见度、信噪比等成像效果的影响,而且利用数值模拟的方法对其进行了验证。
3.研究了光的偏振对热光关联成像的影响。根据完全偏振光的不同偏振态和部分偏振光的不同偏振度对二阶关联函数的影响,利用统计光学理论研究了光的不同偏振性质对热光关联成像的可见度和信噪比的影响。研究结果表明,光的偏振对热光关联成像的影响体现在部分偏振光的不同偏振度上,并且得出了部分偏振光的偏振度对热光关联成像的可见度和信噪比的影响。
4.利用高阶关联函数对热光高阶无透镜傅里叶变换关联成像进行了研究。分析了高阶无透镜傅里叶变换关联成像的基本原理,并且对高阶无透镜傅里叶变换关联成像的可见度和信噪比进行了研究。研究结果表明,高阶无透镜傅里叶变换关联成像的可见度随阶数的增大而有所提高,但同时其信噪比降低了。
The first correlated imaging experiment was observed by using entangled photon pairs,and entanglement was thought as a prerequisite for achieving correlated imaging. However, it has been proved both theoretically and experimentally in recent years that correlated imaging can also be performed with a thermal source. Thermal source is easily obtainable, so compared with correlated imaging with an entangled source, correlated imaging with a thermal source has more potential in practice. So correlated imaging with thermal light attracts much attention in recent years as a hot topic.
In this dissertation, we work on the properties of correlated imaging with thermal light. The main content includes:
1. We briefly review the origin and the history of correlated imaging. Then, we analyze the statistic model of thermal light theoretically, and we introduce pseudo-thermal light. Finally we analyze the theory of the coherent property of thermal light.
2. We research on two schemes of second-order correlated imaging with thermal light: lensless ghost imaging and lensless Fourier-transform correlated imaging. It is shown that the light source, the optical system, the object imaged and the number of measurement have effects on the imaging quality such as the visibility and signal-to-noise (SNR), which are discussed in detail by numerical simulations.
3. The effect of light polarization on thermal correlated imaging is studied. Based on the effect of the polarization state of polarized light and the degree of polarization on the second-order correlation function, the influence of light polarization on the visibility and SNR of correlated imaging with thermal light is investigated by use of statistical optics theory. It is shown that only the degree of polarization has effect on thermal correlated imaging, and the influence of the degree of polarization on the visibility and SNR of thermal correlated imaging is obtained.
4. High-order lensless Fourier-transform correlated imaging with thermal light is investigated based on high-order correlated function. The detailed theory of high-order lensless Fourier-transform correlated imaging is analyzed, and the visibility and SNR of high-order lensless Fourier-transform correlated imaging are investigated. It is shown that although increasing the order of intensity correlation leads to the growth of the visibility of high-order lensless Fourier-transform correlated imaging, it also results in the decrease of the SNR.
引文
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[2] Klyshko D N. Photon and Nonlinear Optics. New York: Gordon and Breach Science, 1988
[3] Pittman T B, Shih Y H, Strekalov D V, Sergienko A V. Optical imaging by means of two-photon quantum entanglement. Phys. Rev. A, 1995, 52: R3429
[4] Strekalov D V, Sergienko A V, Klyshko D N, Shih Y H. Observation of two-photon“ghost”interference and diffraction. Phys. Rev. Lett., 1995, 74: 3600
[5] Pittlnan T B, Strekalov D V, Klyshko D N, et al. Two-photon geometric optics. Phys. Rev. A, 1996, 53: 2804
[6] Barbosa G A. Quantum images in double-slit experiments with spontaneous down-conversion light. Phys. Rev. A, 1996, 54: 4473
[7] Souto Ribeiro P H, Barbosa G A. Direct and ghost interference in double-slit experiments with coincidence measurements. Phys. Rev. A, 1996, 54: 3489
[8] Monken C H, Souto Ribeiro P H, Padua S. Transfer of angular spectrum and image formation in spontaneous parametric down-conversion. Phys. Rev. A, 1998, 57: 3123
[9] Fonseca E J S, Souto Ribeiro P H, Padua S, Monken C H. Quantum interference by a nonlocal double slit. Phys. Rev. A, 1999, 60: 1530
[10] Gatti A, Brambilla E, Lugiato L A, Kolobov M I. Quantum entangled images. Phys. Rev. Lett., 1999, 83: 1763
[11] Abouraddy A F, Nasr M B, Saleh B E A, et al. Demonstration of the complementarity of one- and two-photon interference. Phys. Rev. A, 2001, 63: 063803
[12] Saleh B E A, Abouraddy A F, Sergienko A V, Teich M C. Duality between partial coherence and partial entanglement. Phys. Rev. A, 2000, 62: 043816
[13] Abouraddy A F, Saleh B E A, Sergienko A V, Teich M C. Entangled-photon Fourier optics. J. Opt. Soc. Am. B, 2002, 19: 1174
[14] Gatti A, Brambilla E, Lugiato L A. Entangled imaging and wave-particle duality: from the microscopic to the macroscopic realm. Phys. Rev. Lett., 2003, 90: 133603
[15] D’Angelo M, Kim Y H, Kulik S P, Shih Y H. Identifying entanglement using quantum ghost interference and imaging. Phys. Rev. Lett., 2004, 92: 233601
[16] Abouraddy A F, Saleh B E A, Sergienko A V, Teich M C. Role of entanglement in two-photon imaging. Phys. Rev. Lett., 2001, 87: 123602
[17] Bennink R S, Benley S J, Boyd R W. ''Two-photon'' coincidence imaging with a classical source. Phys. Rev. Lett., 2002, 89: 113601
[18] Gatti A, Brambilla E, Bache M, Lugiato L A. Correlated imaging, quantum and classical. Phys. Rev. A., 2004, 70: 013802
[19] Cheng J, Han S S, Incoherent coincidence imaging and its applicability in X-ray diffraction. Phys. Rev. Lett., 2004, 92: 093903
[20] Cao D Z, Xiong J, Wang K G. Geometrical optics in correlated imaging systems. Phys. Rev. A, 2005, 71: 031801
[21] Valencia A, Scarcelli G, D’Angelo M, Shih Y H. Two-photon imaging with thermal light. Phys. Rev. Lett., 2005, 94: 063601
[22] Ferri F, Magatti D, Gatti A, et al. High-resolution ghost image and ghost diffraction experiments with thermal light. Phys. Rev. Lett., 2005, 94: 183602
[23] Zhai Y H, Chen X H, Zhang D, Wu L A. Two-photon interference with true thermal light. Phys. Rev. A, 2005, 72: 043805
[24] Zhang D, Zhai Y H, Wu L A. Correlated two-photon imaging with true thermal light. Opt. Lett., 2005, 30: 2354
[25] Chen X H, Liu Q, Luo K H, Wu L A. Lensless ghost imaging with true thermal light. Opt. Lett., 2009, 34: 695
[26] Cai Y J, Zhu S Y. Ghost interference with partially coherent radiation. Opt. Lett., 2004, 29: 2716
[27] Cai Y J, Wang F. Lensless imaging with partially coherent light. Opt. Lett., 2007, 32: 205
[28] Zhai Y H, Chen X H, Wu L A. Two-photon interference with two independent pseudothermal sources. Phys. Rev. A, 2006, 74: 053807
[29] Wang K G, Cao D Z. Subwavelength coincidence interference with classical thermal light. Phys. Rev. A, 2004, 70: 041801R
[30] Xiong J, Cao D Z, Huang F, Li H G, Sun X J, Wang K G. Experimental observation of classical subwavelength interference with a pseudothermal light source. Phys. Rev. Lett., 2005, 94: 173601
[31] Chan K W C, O’Sullivan M N, Boyd R W. Two-color ghost imaging. Phys. Rev. A, 2009, 79: 033808
[32] Vidal I, Caetano D P, Olindo C, et al. Second-order interference with orthogonally polarized pseudothermal beams. Phys. Rev. A, 2008, 78: 053815
[33] Vidal I, Caetano D P, Fonseca E J S, Hickmann J M. Effects of pseudothermal light source’s transverse size and coherence width in ghost-interference experiments. Opt. Lett., 2009, 34: 1450
[34] Scarcelli G, Berardi V, Shih Y H. Can Two-photon correlation of chaotic light be considered as correlation of intensity fluctuations? Phys. Rev. Lett., 2006, 96: 063602
[35] Meyers R, Deacon K, Shih Y H. A new two-photon ghost imaging experiment with distortion study. J. Mod. Opt., 2007, 54: 2381
[36] Scarcelli G, Valencia A, Shih Y H. Experimental study of the momentum correlation of a pseudothermal field in the photon-counting regime. Phys. Rev. A, 2004, 70: 051802R
[37]汪凯戈,曹德忠,熊俊.关联光学新进展.物理, 2008, 37: 223
[38] Gatti A, Bache M, Magatti D, et al. Coherent imaging with pseudo-thermal incoherent light. J. Mod. Opt., 2006, 53: 739
[39] Zhang M H, Wei Q, Shen X, Liu Y F, Liu H L, Cheng J, Han S S. Lensless Fourier-transform ghost imaging with classical incoherent light. Phys. Rev. A, 2006, 75: 021803R
[40] Bai Y F, Liu H L, Han S S. Transmission area and correlated imaging. Opt. Express, 2007, 15: 6062
[41] Ou L H, Kuang L M. Ghost imaging with third-order correlated thermal light. J. Phys. B: At. Mol. Opt. Phys., 2007, 40: 1833
[42] Bai Y F, Han S S. Ghost imaging with thermal light by third-order correlation. Phys. Rev. A, 2007, 76: 043828
[43] Chan K W C, O’Sullivan M N, Boyd R W. High-order thermal ghost imaging. Opt. Lett., 2009, 34: 3343
[44] Liu J B, Shih Y H. Nth-order coherence of thermal light. Phys. Rev. A, 2004, 79: 023819
[45] Cao D Z, Xiong J, Zhang S H, Lin L F, Gao L, Wang K G. Enhancing visibility and resolution in Nth-order intensity correlation of thermal light. Appl. Phys. Lett., 2008, 92: 201102
[46] Liu Q, Chen X H, Luo K H, Wu W, Wu L A. Role of multiphoton bunching in high-order ghost imaging with thermal light sources. Phys. Rev. A, 2009, 79: 053844
[47] Chen X H, Agafonov I N, Luo K H, Liu Q, Xian R, Chekhova M V, Wu L A. High-visibility, high-order lensless ghost imaging with thermal light. Opt. Lett., 2010, 35: 1166
[48] Chan K W C, O’Sullivan M N, Boyd R W. Optimization of thermal ghost imaging: high-order correlations vs. background subtraction. Opt. Express, 2010, 18: 5562
[49] Zhang P L, Gong W L, Shen X, Huang D J, Han S S. Improving resolution by the second-order correlation of light fields. Opt. Lett., 2009, 34: 1222
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