Optimal measurements for resolution beyond the Rayleigh limit.

We establish the conditions to attain the ultimate resolution predicted by quantum estimation theory for the case of two incoherent point sources using a linear imaging system. The solution is closely related to the spatial symmetries of the detection scheme. In particular, for real symmetric point spread functions, any complete set of projections with definite parity achieves the goal.

[1]  Rory A. Fisher,et al.  Theory of Statistical Estimation , 1925, Mathematical Proceedings of the Cambridge Philosophical Society.

[2]  Yu-Ping Ho.  Pattern Transformation And Holographic Optical Systems , 1980, Other Conferences.

[3]  E. Abbe,et al.  Ueber einen neuen Beleuchtungsapparat am Mikroskop , 1873 .

[4]  M. Lavery,et al.  Efficient sorting of orbital angular momentum states of light. , 2010, Physical review letters.

[5]  Christoph Simon,et al.  Far-field linear optical superresolution via heterodyne detection in a higher-order local oscillator mode , 2016, 1606.02662.

[6]  M. Paris.  Quantum estimation for quantum technology , 2008, 0804.2981.

[7]  S. Hell.  Microscopy and its focal switch , 2008, Nature Methods.

[8]  Barry R. Masters,et al.  Resolution enhancement techniques in microscopy , 2013 .

[9]  Mankei Tsang,et al.  Far-Field Superresolution of Thermal Electromagnetic Sources at the Quantum Limit. , 2016, Physical review letters.

[10]  S. Braunstein,et al.  Statistical distance and the geometry of quantum states. , 1994, Physical review letters.

[11]  Stefano Pirandola,et al.  Ultimate Precision Bound of Quantum and Subwavelength Imaging. , 2016, Physical review letters.

[12]  Adriaan van den Bos,et al.  Resolution: a survey , 1997 .

[13]  Alexander Ling,et al.  Fault-tolerant and finite-error localization for point emitters within the diffraction limit. , 2016, Optics express.

[14]  Jaroslav Rehacek,et al.  Achieving the ultimate optical resolution , 2016, EPJ Web of Conferences.

[15]  S. Hell.  Far-Field Optical Nanoscopy , 2007, Science.

[16]  Radek Čelechovský,et al.  Optical implementation of the vortex information channel , 2007 .

[17]  Suliana Manley,et al.  Superresolution imaging using single-molecule localization. , 2010, Annual review of physical chemistry.