Precision estimation of source dimensions from higher-order intensity correlations

Abstract

An important topic of interest in imaging is the construction of protocols that are not diffraction limited. This can be achieved in a variety of ways, including classical superresolution techniques or quantum entanglement-based protocols. Here, we consider superresolving imaging in the far field using higher-order intensity correlations. We show that third and fourth order correlations can improve upon the first and second order correlations that are traditionally used in classical optics and Hanbury Brown and Twiss type experiments. The improvement is achieved entirely by post-processing of the data. As a demonstrator, we simulate the far field intensity distribution of a circular aperture that emits thermal light and use maximum likelihood estimation to determine the radius of the aperture. We compare the achieved precision to the Cramér-Rao lower bound and find that the variance of measurements for the third and fourth order correlation functions are indeed closer to the Cramér-Rao bound than that of the second order correlation function. The method presented here is general, and can be used for all kinds of incoherent emitters, geometries, and types of noise.

Quantum metrology of spatial deformation using arrays of classical and quantum light emitters

“…We choose to work in the near-field regime over the far field. These define different regions of the electromagnetic field around the sources and allow the use of intensity measurements in the near field to estimate d as opposed to higher-order correlation measurements in the far field [21,22]. For complete state detection, the QFI remains invariant of the regime considered.…”

“…It is well known that quantum resources provide improvements to the estimation sensitivities of * jsidhu1@sheffield.ac.uk † p.kok@sheffield.ac.uk physical parameters, and this has been demonstrated for phase estimations in interferometers [15][16][17][18]. Such resources are exploited in quantum imaging to drive resolution capabilities past the Abbe-Rayleigh criterion [19][20][21][22][23][24][25][26][27][28].…”

Multipath correlation interference and controlled-NOT gate simulation with a thermal source

“…The Hanbury Brown and Twiss (HBT) effect [1,2] discovered in 1956 was at the heart of the development of the field of quantum optics. Indeed, this discovery led to numerous remarkable multiphoton experiments which have not only deepened our fundamental understanding of multiphoton interference [3][4][5][6][7][8][9] but have also led to numerous applications in information processing [10][11][12][13][14][15] and imaging [16][17][18][19][20][21][22].…”

Superresolving Imaging of Arbitrary One-Dimensional Arrays of Thermal Light Sources Using Multiphoton Interference

“…Here, we generalize the scheme to reconstruct any number of independent thermal light sources at arbitrary separations in one dimension exploiting intensity correlation functions of order m ≥ 3. We present experimental results confirming the imaging protocol and provide a rigorous mathematical proof for the obtained subclassical resolution.Higher order interferences with photons emitted by statistically independent light sources are an active field of research with the potential to increase the resolution in spectroscopy, lithography and interferometry [1][2][3][4][5][6], as well as in imaging and microscopy [7][8][9][10][11][12][13][14][15][16][17]. So far, subclassical resolution has been achieved by using entangled photons [3,8], but it was also shown that initially uncorrelated light fields -non-classical as well as classical -can be employed for that purpose [13][14][15][16][17].…”

“…So far, subclassical resolution has been achieved by using entangled photons [3,8], but it was also shown that initially uncorrelated light fields -non-classical as well as classical -can be employed for that purpose [13][14][15][16][17]. Recently, Oppel et al presented a detection scheme that allows to determine the source distance d for an array of N equidistant thermal light sources (TLS) with subclassical resolution by measuring the N th-order spatial intensity correlation function [14].…”