Estimating distances between multiple point image sources with quantum imaging
Method for estimating separation distances between a plurality of image sources in a multi-point source imaging system includes: receiving a plurality of light beams, each from a respective image source and having a quantum state mode; constructing a point spread function (PSF) for light beams specific to a symmetry of the image sources; calculating a quantum Fourier transform on the quantum state mode of the plurality of light beams that achieves a quantum limit in a paraxial approximation regime to estimate separation of image sources at the quantum limit to transform the light beams; detecting the transformed light beams to generate electrical signals from respective transformed light beams; and performing signal processing on the electrical signals to estimate the separation distances between the plurality of image sources.
1 . A method for estimating separation distances between a plurality of image sources in a multi-point source imaging system, the method comprising:
receiving a plurality of light beams, each from a respective image source and having a quantum state mode;
constructing a point spread function (PSF) for light beams specific to a symmetry of the image sources;
calculating a quantum Fourier transform on the quantum state mode of the plurality of light beams that achieves a quantum limit in a paraxial approximation regime to estimate separation of image sources at the quantum limit to transform the light beams;
detecting the transformed light beams to generate electrical signals from respective transformed light beams; and
performing signal processing on the electrical signals to estimate the separation distances between the plurality of image sources.
2 . The method of claim 1 , wherein the quantum Fourier transform is an Abelian Fourier transform.
3 . The method of claim 1 , wherein the signal processing achieves the classical Cramer-Rao bound.
4 . The method of claim 1 , wherein the point spread function is a collection of delta functions in a Fourier space.
5 . The method of claim 1 , wherein the point spread function is a collection of delta functions in a momentum space.
6 . The method of claim 1 , wherein the image sources are arranged in a circle around a known centroid.
7 . The method of claim 1 , wherein the signal processing is performed using a maximum likelihood estimation (MLE) method.
8 . The method of claim 7 , wherein the MLE method maximizes a posterior probability of obtaining detected signals given a separation distance so that, under a prior probability distribution for the separation distances, observed data is most probable.
9 . The method of claim 8 , wherein a point in parameter space that maximizes the posterior probability is the separation distance.
10 . The method of claim 1 , wherein the signal processing is performed using a Minimum mean squared error estimation method.
11 . The method of claim 1 , wherein the signal processing is performed using a maximum a posteriori estimation method.