As a method to extract information from optical systems,imaging can be viewed as a parameter estimation problem.The fundamental precision in locating one emitter or estimating the separation between two incoherent emi...As a method to extract information from optical systems,imaging can be viewed as a parameter estimation problem.The fundamental precision in locating one emitter or estimating the separation between two incoherent emitters is bounded below by the multiparameter quantum Cramér-Rao bound(QCRB).Multiparameter QCRB gives an intrinsic bound in parameter estimation.We determine the ultimate potential of quantum-limited imaging for improving the resolution of a far-field,diffraction-limited optical field within the paraxial approximation.We show that the quantum Fisher information matrix(QFIm)in about one emitter’s position is independent on its true value.We calculate the QFIm of two unequal-brightness emitters’relative positions and intensities;the results show that only when the relative intensity and centroids of two-point sources,including longitudinal and transverse directions,are known exactly,the separation in different directions can be estimated simultaneously with finite precision.Our results give the upper bounds on certain far-field imaging technology and will find wide use in applications from microscopy to astrometry.展开更多
基金National Key Research and Development Program of China(2017YFA0303703,2018YFA030602)National Natural Science Foundation of China(91836303,61975077,11690032)Fundamental Research Funds for the Central Universities(020214380068)。
文摘As a method to extract information from optical systems,imaging can be viewed as a parameter estimation problem.The fundamental precision in locating one emitter or estimating the separation between two incoherent emitters is bounded below by the multiparameter quantum Cramér-Rao bound(QCRB).Multiparameter QCRB gives an intrinsic bound in parameter estimation.We determine the ultimate potential of quantum-limited imaging for improving the resolution of a far-field,diffraction-limited optical field within the paraxial approximation.We show that the quantum Fisher information matrix(QFIm)in about one emitter’s position is independent on its true value.We calculate the QFIm of two unequal-brightness emitters’relative positions and intensities;the results show that only when the relative intensity and centroids of two-point sources,including longitudinal and transverse directions,are known exactly,the separation in different directions can be estimated simultaneously with finite precision.Our results give the upper bounds on certain far-field imaging technology and will find wide use in applications from microscopy to astrometry.
