Incoherent Point Source Resolution Based on Quantum Measurement Optimization

Shudong Xue; Yanan Li; Jun Xin; Xiao-Ming Lu

doi:10.3788/LOP202158.1011015

[1] den Dekker A J, van den Bos A. Resolution: a survey[J]. Journal of the Optical Society of America A, 14, 547(1997).

[2] de Villiers G, Pike E R[M](2016).

[3] Lord Rayleigh F R S. Investigations in optics, with special reference to the spectroscope[J]. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 8, 261-274(1879).

[4] Feynman R, Leighton R, Sands M. The Feynman lectures on physics: volume I[M]. New Jersey: Addison-Wesley(1963).

[5] Ronchi V. Resolving power of calculated and detected images[J]. Journal of the Optical Society of America, 51, 458-460(1961).

[6] di Francia T G. Resolving power and information[J]. Journal of the Optical Society of America, 45, 497-501(1955).

[7] Jaynes E T. Probability theory: the logic of science[M](2003).

[8] Casella G, Berger R L. Statistical inference[M]. 2nd ed(2002).

[9] Harris J L. Resolving power and decision theory[J]. Journal of the Optical Society of America, 54, 606-611(1964).

[10] Harris J L. Diffraction and resolving power[J]. Journal of the Optical Society of America, 54, 931-936(1964).

[11] Farrell E J. Information content of photoelectric star images[J]. Journal of the Optical Society of America, 56, 578-587(1966).

[12] Falconi O. Limits to which double lines, double stars, and disks can be resolved and measured[J]. Journal of the Optical Society of America, 57, 987-993(1967).

[13] Tsai M J, Dunn K P. Performance limitations on parameter estimation of closely spaced optical targets using shot-noise detectormodel[EB/OL]. [2021-01-28]. https://www.researchgate.net/publication/235055716_Performance_Limitations_on_Parameter_Estimation_of_Closely_Spaced_Optical_Targets_Using_Shot-Noise_Detector_Model

[14] Bettens E, van Dyck D, den Dekker A J et al. Model-based two-object resolution from observations having counting statistics[J]. Ultramicroscopy, 77, 37-48(1999).

[15] van Aert S, den Dekker A J, van Dyck D et al. High-resolution electron microscopy and electron tomography: resolution versus precision[J]. Journal of Structural Biology, 138, 21-33(2002).

[16] Ram S, Ward E S, Ober R J. Beyond Rayleigh's criterion: a resolution measure with application to single-molecule microscopy[J]. National Academy of Sciences, 103, 4457-4462(2006).

[17] Kolobov M I. Quantum imaging[M](2007).

[18] Moreau P A, Toninelli E, Gregory T et al. Imaging with quantum states of light[J]. Nature Reviews Physics, 1, 367-380(2019).

[19] Genovese M. Real applications of quantum imaging[J]. Journal of Optics, 18, 073002(2016).

[20] Han S S, Yu H, Shen X et al. A review of ghost imaging via sparsity constraints[J]. Applied Sciences, 8, 1379(2018).

[21] Helstrom C W. Quantum detection and estimation theory[M](1976).

[22] Helstrom C W. Resolution of point sources of light as analyzed by quantum detection theory[J]. IEEE Transactions on Information Theory, 19, 389-398(1973).

[23] Tsang M, Nair R, Lu X M. Quantum theory of superresolution for two incoherent optical point sources[J]. Physical Review X, 6, 031033(2016).

[24] Kay S M. Fundamentals of statistical signal process: estimation theory and detection theory[M]. Luo P F, Zhang W M, Liu Z, et al, Transl(2014).

[25] Fabre C, Treps N. Modes and states in quantum optics[J]. Reviews of Modern Physics, 92, 035005(2020).

[26] Paúr M, Stoklasa B, Hradil Z et al. Achieving the ultimate optical resolution[J]. Optica, 3, 1144-1147(2016).

[27] Tsang M. Resolving starlight: a quantum perspective[J]. Contemporary Physics, 60, 279-298(2019).

[28] Rehacek J, Paúr M, Stoklasa B et al. Optimal measurements for resolution beyond the Rayleigh limit[J]. Optics Letters, 42, 231-234(2017).

[29] Nair R, Tsang M. Interferometric superlocalization of two incoherent optical point sources[J]. Optics Express, 24, 3684-3701(2016).

[30] Tang Z S, Durak K, Ling A. Fault-tolerant and finite-error localization for point emitters within the diffraction limit[J]. Optics Express, 24, 22004-22012(2016).

[31] Nair R, Tsang M. Far-field superresolution of thermal electromagnetic sources at the quantum limit[J]. Physical Review Letters, 117, 190801(2016).

[32] Tham W K, Ferretti H, Steinberg A M. Beating Rayleigh's curse by imaging using phase information[J]. Physical Review Letters, 118, 070801(2017).

[33] Yang F, Tashchilina A, Moiseev E S et al. Far-field linear optical superresolution via heterodyne detection in a higher-order local oscillator mode[J]. Optica, 3, 1148-1152(2016).

[34] Yang F, Nair R, Tsang M et al. Fisher information for far-field linear optical superresolution via homodyne or heterodyne detection in a higher-order local oscillator mode[J]. Physical Review A, 96, 063829(2017).

[35] Boucher P, Fabre C, Labroille G et al. Spatial optical mode demultiplexing as a practical tool for optimal transverse distance estimation[J]. Optica, 7, 1621-1626(2020).

[36] Gessner M, Fabre C, Treps N. Superresolution limits from measurement crosstalk[J]. Physical Review Letters, 125, 100501(2020).

[37] Lu X M, Krovi H, Nair R et al. Quantum-optimal detection of one-versus-two incoherent optical sources with arbitrary separation[J]. Npj Quantum Information, 4, 64(2018).

[38] Lupo C, Pirandola S. Ultimate precision bound of quantum and subwavelength imaging[J]. Physical Review Letters, 117, 190802(2016).

[39] Grace M R, Dutton Z, Ashok A et al. Approaching quantum-limited imaging resolution without prior knowledge of the object location[J]. Journal of the Optical Society of America A, Optics, Image Science, and Vision, 37, 1288-1299(2020).

[40] Řehaček J, Hradil Z, Stoklasa B et al. Multiparameter quantum metrology of incoherent point sources: towards realistic superresolution[J]. Physical Review A, 96, 062107(2017).

[41] Řehaček J, Hradil Z, Koutný D et al. Optimal measurements for quantum spatial superresolution[J]. Physical Review A, 98, 012103(2018).

[42] Bonsma-Fisher K A G, Tham W K, Ferretti H et al. Realistic sub-Rayleigh imaging with phase-sensitive measurements[J]. New Journal of Physics, 21, 093010(2019).

[43] Ang S Z, Nair R, Tsang M. Quantum limit for two-dimensional resolution of two incoherent optical point sources[C]. //CLEO: Applications and Technology 2016, June 5-10, 2016, San Jose, California, JTu5A, 21(2016).

[44] Marar A, Kner P. Fundamental precision bounds for three-dimensional optical localization microscopy using self-interference digital holography[J]. Biomedical Optics Express, 12, 20-40(2021).

[45] Zhou Y Y, Yang J, Hassett J D et al. Quantum-limited estimation of the axial separation of two incoherent point sources[J]. Optica, 6, 534-541(2019).

[46] Yu Z X, Prasad S. Quantum limited superresolution of an incoherent source pair in three dimensions[J]. Physical Review Letters, 121, 180504(2018).

[47] Prasad S, Yu Z X. Quantum-limited superlocalization and superresolution of a source pair in three dimensions[J]. Physical Review A, 99, 022116(2019).

[48] Prasad S. Quantum limited super-resolution of an unequal-brightness source pair in three dimensions[J]. Physica Scripta, 95, 054004(2020).

[49] Napoli C, Piano S, Leach R et al. Towards superresolution surface metrology: quantum estimation of angular and axial separations[J]. Physical Review Letters, 122, 140505(2019).

[50] Wang B, Xu L, Zhang L. Quantum-limited localisation and resolution in three dimensions[EB/OL]. (2020-12-09)[2021-01-25]. https://arxiv.org/abs/2012.05089

[51] Bisketzi E, Branford D, Datta A. Quantum limits of localisation microscopy[J]. New Journal of Physics, 21, 123032(2019).

[52] Lupo C, Huang Z X, Kok P. Quantum limits to incoherent imaging are achieved by linear interferometry[J]. Physical Review Letters, 124, 080503(2020).

[53] Peng L, Lu X M. Generalization of Rayleigh's curse on parameter estimation with incoherent sources[EB/OL]. (2020-11-25)[2021-01-25]. https://arxiv.org/abs/2011.07897

[54] Dutton Z, Kerviche R, Ashok A et al. Attaining the quantum limit of superresolution in imaging an object's length via predetection spatial-mode sorting[J]. Physical Review A, 99, 033847(2019).

[55] Tsang M. Subdiffraction incoherent optical imaging via spatial-mode demultiplexing[J]. New Journal of Physics, 19, 023054(2017).

[56] Tsang M. Quantum limit to subdiffraction incoherent optical imaging[J]. Physical Review A, 99, 012305(2019).

[57] Zhou S S, Jiang L. Modern description of Rayleigh's criterion[J]. Physical Review A, 99, 013808(2019).

[58] Wu Z W, Qiu X D, Chen L X. Current status and prospect for correlated imaging technique[J]. Laser & Optoelectronics Progress, 57, 060001(2020).

[59] Shao X P, Liu F, Li W et al. Latest progress in computational imaging technology and application[J]. Laser & Optoelectronics Progress, 57, 020001(2020).

[60] Chen Y C, Li C K, Hao X et al. Progress of point scanning super-resolution microscopy based on frequency shifting[J]. Laser & Optoelectronics Progress, 57, 180001(2020).