Optical circuit for estimating distances between multiple point image sources with quantum imaging

1. An optical circuit for estimating separation distances between N image sources, where N is an integer greater than 2, in a multi-point source imaging system comprising:

an aperture for receiving N light beams with quantum state modes m 1 to m N , respectively and producing a point spread function (PSF) specific to a symmetry of the image sources from the plurality of light beams;

(N-1) first optical phase shifters to shift (N-1) of the quantum state modes of (N-1) light beams by N N , based on a quantum Fourier Transform, where N=e 2πi/N ;

a plurality of first beamsplitters, each for mixing respective pairs of quantum state modes of outputs of the (N-1) first optical phase shifters for a quantum superposition of the respective pairs of the quantum state modes by combining photons in each quantum state mode into a quantum superposition over both quantum state modes of the respective pairs;

a plurality of second beamsplitters, each for mixing respective outputs of the plurality of first beamsplitters alternatively

(N-1) second phase shifters to further shift outputs of the plurality of second beamsplitters by N N and produce N shifted output light beams representing the quantum Fourier Transform of the received N light beams;

N detectors for converting each of the received N light beams to an analog electrical signal, respectively; and

a signal processing circuit for performing signal processing on the analog electrical signals to estimate the separation distances between the plurality of image sources.

2. The optical circuit of claim 1 , wherein the quantum Fourier transform is an Abelian Fourier transform.

3. The optical circuit of claim 1 , wherein the signal processing achieves the classical Cramer-Rao bound.

4. The optical circuit of claim 1 , wherein the point spread function is a collection of delta functions in a Fourier space.

5. The optical circuit of claim 1 , wherein the point spread function is a collection of delta functions in a momentum space.

6. The optical circuit of claim 1 , wherein the image sources are arranged in a circle around a known centroid.

7. The optical circuit of claim 1 , wherein the signal processing is performed using a maximum likelihood estimation (MLE) method.

8. The optical circuit 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 optical circuit of claim 8 , wherein a point in parameter space that maximizes the posterior probability is the separation distance.

10. The optical circuit of claim 1 , wherein the signal processing is performed using a Minimum mean squared error estimation method.

11. The optical circuit of claim 1 , wherein the signal processing is performed using a maximum a posteriori estimation method.

12. The optical circuit of claim 1 , wherein the aperture is a high numerical aperture objective lens to produce a three-dimensional diffraction pattern of light as the PSF.

13. The optical circuit of claim 1 , wherein a number of the plurality of first beamsplitters and a number of the plurality of second beamsplitters is equal to or less than N*(N-1)/2.