Interferometric imager and method

1 . An interferometric imaging method comprising:

simultaneously illuminating a scene with:

(i) a first diverging wave originating from a first source location and modulated with a first shift-and-add qualifying-code (first SAA-code), the scene including a scatterer that scatters the first diverging wave as a first expanding speckle field propagating from the scatterer toward a receiver, and

(ii) a second diverging wave originating from a second source location, modulated with a second SAA-code, the second source location being displaced from the first source location in a first displacement direction, the scatterer scattering the second diverging wave as a second expanding speckle field propagating from the scatterer toward the receiver;

detecting, at the receiver, an interference signal produced from spatially-integrated interference between the first expanding speckle field and the second expanding speckle field, the interference signal yielding a code temporally shifted with respect to the first SAA-code by a large-scale time-shift determined at least in part by (i) shift-and-add properties of the first and second SAA-codes, and (ii) a time-difference-of-arrival at the receiver proportional to (R 1 −R 2 )/c, where R 1 and R 2 are distances between (i) the scatterer and the first source location, and (ii) the scatterer and the second source location, respectively;

circulantly correlating the interference signal with a reference SAA-code to generate a correlation signal that includes a plurality of non-overlapping segments each associated with a respective one of a plurality of angularly-resolved bins as determined by the time difference of arrival;

determining the time-difference-of-arrival from the large-scale time-shift; and

determining a location of the scatterer by:

determining, from the time-difference-of-arrival, a hyperbolic contour that locates the scatterer angularly with respect to a depth direction perpendicular to the first displacement direction, (R 1 −R 2 )/2c being constant for each point on the hyperbolic contour and denoting an angular coordinate; and

determining, from one of (i) a small-scale time-shift of a correlation peak of the correlation signal and (ii) a ranging delay, an elliptical contour that locates a range of the scatterer with respect to the receiver, (R 1 +R 2 )/2c being constant for each point on the elliptical contour and denoting a bistatic range coordinate,

the location of the scatterer being the intersection of the hyperbolic contour and the elliptical contour.

2 . The method of claim 1 , the scene including an additional point scatterer, the interference signal including an additional SAA code temporally shifted with respect to the first SAA-code by a large-scale time-shift magnitude determined at least in part by (i) the first shift-and-add properties of the first and second SAA-codes, and (ii) an additional time-difference-of-arrival at the receiver equal to (R′ 1 −R′ 2 )/c, where R′ 1 and R′ 2 are distances between (i) the additional point scatterer and the first source location, and (ii) the additional point scatterer and the second source location, respectively; and further comprising

determining the additional time-difference-of-arrival from the large-scale time-shift;

determining an additional location of the additional scatterer by:

determining, from the additional time-difference-of-arrival, an additional hyperbolic contour that locates the additional point scatterer angularly with respect to the depth direction, (R′ 1 −R′ 2 )/2c being constant for each point on the additional hyperbolic contour and denoting an additional angular coordinate;

determining, from one of (i) a shift of a correlation peak of the correlation signal and (ii) a ranging delay, an additional elliptical contour that that locates an additional range of the additional scatterer with respect to the receiver, (R′ 1 +R′ 2 )/c being constant for each point on the additional elliptical contour,

the additional location of the additional scatterer being the intersection of the additional hyperbolic contour and the additional elliptical contour.

3 . The method of claim 1 , the second SAA-code being equal to the first SAA-code with a temporal offset, and further comprising determining the temporal offset such that the correlation signal includes the plurality of non-overlapping segments.

4 . The method of claim 3 , determining the temporal offset comprising executing a random search of a correlation surface generated by correlating the interference signal with the reference SAA for a plurality of trial ranges of temporal offsets.

5 . The method of claim 1 , at least one of the first SAA-code and the second SAA-code being one of maximal-length pseudo-noise codes, a preferred pseudo-noise sequence pair that produces a set of Gold codes with minimized cross-correlations.

6 . The method of claim 1 , the first SAA-code being a maximal length pseudonoise sequence and, in the step of correlating, the reference SAA-code being one of (i) the first SAA-code, (ii) the second SAA-code, (iii) a SAA code that is circulant delay offset of either the first SAA-code or the second SAA-code, and (iv) any combination thereof.

7 . The method of claim 1 , the first SAA-code being a maximal length pseudonoise sequence, the second SAA-code being a preferred pseudo-noise sequence pair that produces a set of Gold codes with minimized cross-correlations, the reference SAA-code being a bank of reference Gold codes each being a product of a first input SAA code and a second input SAA code time-shifted relative thereto to produce different Gold codes as different interferometric products for different TDOAs, said correlating comprising:

generating the correlation signal at least in part by correlating the interference signal against the bank of Gold reference codes to produce multiple correlation outputs.

8 . The method of claim 1 , the first diverging wave and the second diverging wave having a same carrier frequency.

9 . The method of claim 1 , the ranging delay being equal to (R 1 +R 2 +2R 0 )/c, where R 0 is the distance between the scatterer and the receiver.

10 . The method of claim 1 , each of the first and second SAA-codes being modulated onto the first and second diverging waves respectively via a binary-phase-shift-key scheme.

11 . The method of claim 1 , simultaneously illuminating a scene including:

illuminating the scene with a third diverging wave originating from a third source location, modulated with a third SAA-code with a shift-and-add property, the third source location being displaced from each of the first source location in a second displacement direction differing from the first displacement direction, the scatterer scattering the third diverging wave as a third expanding speckle field propagating from the scatterer toward an additional receiver;

and further comprising:

detecting, at the additional receiver, a second interference signal produced from spatially-integrated interference between the first expanding speckle field and the third expanding speckle field, the second interference signal yielding a second code temporally shifted with respect to the first SAA-code by a second large-scale time-shift determined at least in part by (i) the shift-and-add properties of the first and third SAA-codes, and (ii) a second time-difference-of-arrival at the receiver equal to (R 1 −R 3 )/c, where R 1 and R 3 are distances between (i) the scatterer and the first source location, and (ii) the scatterer and the third source location, respectively;

correlating the second interference signal with a second reference SAA-code to generate a second correlation signal;

circulantly correlating the second interference signal with a second reference SAA-code to generate a second correlation signal that includes a second plurality of non-overlapping segments each associated with a respective one of a second plurality of angularly-resolved bins as determined by the second time-difference-of-arrival;

determining the second time-difference-of-arrival from the second large-scale time-shift;

determining a second location of the scatterer by:

determining, from the second time-difference-of-arrival, a second hyperbolic contour that locates the scatterer angularly with respect to a second depth direction perpendicular to the second displacement direction, (R 1 −R 3 )/2c being constant for each point on the second hyperbolic contour and denoting a second angular coordinate; and

determining, from one of (i) a small-scale time-shift of a correlation peak of the second correlation signal and (ii) a second ranging delay, a second elliptical contour that locates a range of the scatterer with respect to the receiver, (R 1 +R 3 )/2c being constant for each point on the second elliptical contour and denoting a bistatic range coordinate,

the second location of the scatterer being the intersection of the second hyperbolic contour and the second elliptical contour.

12 . The method of claim 11 , the second displacement direction being perpendicular to the first displacement direction.

13 . An interferometric imager comprising:

a first transmitter configured to emit electromagnetic radiation in a first direction;

a second transmitter laterally displaced from the first transmitter in a displacement direction perpendicular to the first direction, and configured to emit electromagnetic radiation in the first direction;

a detector having an electromagnetic radiation-receiving surface facing the first direction;

a processor communicatively coupled to the detector; and

a memory storing machine readable instructions that when executed by a processor, control the processor to execute the method of claim 1 .