Motion compensation for dynamic imaging

1. A method for forming an image of a target with a laser detection and ranging system comprising a laser transmitter and an array detector, the method comprising: transmitting a sequence of laser pulses; forming a plurality of point clouds, each point cloud corresponding to a respective transmitted laser pulse, each point in the point cloud corresponding to a point on a surface of the target; grouping the plurality of point clouds into a plurality of point cloud groups according to a contiguous subset of the sequence of laser pulses, each of the point clouds of each group having an index; forming a plurality of average point clouds, each of the average point clouds being the average of a respective group of the plurality of point cloud groups; forming a first estimate of a six-dimensional velocity of the target, comprising three translational velocity components and three angular velocity components, from the plurality of average point clouds; transforming each of the point clouds of a first group of the plurality of point cloud groups by a transformation proportional to the product of: the first estimate of the six-dimensional velocity, and the index of the point cloud within the first group of point clouds; forming the image of the target from the transformed point clouds; and displaying the image of the target on a display.

2. The method of claim 1 , wherein forming of each point cloud comprises: detecting, with an array detector, a plurality of ladar return photons from the corresponding laser pulse, each detection producing an electrical pulse; and

identifying, for each of the electrical pulses, a bin, of a plurality of time bins corresponding to the laser pulse, within which the electrical pulse was produced.

3. The method of claim 1 , wherein forming a first estimate of a six-dimensional velocity of the target comprises:

estimating a six dimensional transformation for approximately transforming a first average point cloud corresponding to a first group of point clouds to a second average point cloud, of the plurality of average point clouds, corresponding to a second group of point clouds;

calculating the first estimate of the six-dimensional velocity as the ratio of:

the six dimensional transformation and

a difference between:

an average time for the second group of point clouds; and

an average time for the first group of point clouds.

4. The method of claim 3 , wherein estimating a six dimensional transformation comprises estimating the six dimensional transformation with an iterative closest point (ICP) algorithm.

5. The method of claim 1 , wherein forming an average point cloud of the plurality of average point clouds comprises discarding data using coincidence processing.

6. The method of claim 5 , wherein discarding data using coincidence processing comprises:

defining a plurality of three-dimensional voxels; and

discarding data from each voxel, from among the plurality of voxels, within which a number of detected ladar return photons is less than a threshold value.

7. The method of claim 6 , wherein the threshold value is 10.

8. The method of claim 1 , further comprising,

forming a plurality of average transformed point clouds from the transformed point clouds;

forming a second estimate of the six-dimensional velocity of the target, from the plurality of average transformed point clouds; and

transforming each of the point clouds, of a second group of point clouds, of the plurality of groups of point clouds, by a transformation proportional to the product of:

the second estimate of the six-dimensional velocity, and

the index of the point cloud within the first group of point clouds.

9. A ladar system for forming an image of a target, the system comprising: a pulsed laser transmitter configured to transmit a sequence of laser pulses; a camera comprising an array detector; a processing circuit; and a display, the camera and the processing circuit being together configured to form a plurality of point clouds, each point cloud corresponding to a respective transmitted laser pulse, each point in the point cloud corresponding to a point on a surface of the target, the processing circuit being configured to: group the plurality of point clouds into a plurality of point cloud groups according to a contiguous subset of the sequence of laser pulses, each of the point clouds of each group having an index; form a plurality of average point clouds, each of the average point clouds being the average of a respective group of the plurality of point cloud groups; form a first estimate of a six-dimensional velocity of the target, comprising three translational velocity components and three angular velocity components, from the plurality of average point clouds; and transform each of the point clouds of a first group of the plurality of point cloud groups, by a transformation proportional to the product of: the first estimate of the six-dimensional velocity, and the index of the point cloud within the first group of point clouds; form the image of the target from the transformed point clouds; and display the image of the target on the display.

10. The system of claim 9 , wherein forming each point cloud comprises: detecting, with an array detector, a plurality of ladar return photons from the corresponding laser pulse, each detection producing an electrical pulse; and

identifying, for each of the electrical pulses, a bin, of a plurality of time bins corresponding to the laser pulse, within which the electrical pulse was produced.

11. The system of claim 9 , wherein forming the first estimate of the six-dimensional velocity of the target comprises:

estimating a six dimensional transformation for approximately transforming a first average point cloud corresponding to a first group of point clouds to a second average point cloud, of the plurality of average point clouds, corresponding to a second group of point clouds;

calculating the first estimate of the six-dimensional velocity as the ratio of:

the six dimensional transformation and

a difference between:

an average time for the second group of point clouds; and

an average time for the first group of point clouds.

12. The system of claim 11 , wherein estimating a six dimensional transformation comprises estimating the six dimensional transformation with an iterative closest point (ICP) algorithm.

13. The system of claim 9 , wherein forming an average point cloud of the plurality of average point clouds comprises discarding data using coincidence processing.

14. The system of claim 13 , wherein discarding data using coincidence processing comprises:

defining a plurality of three-dimensional voxels; and

discarding data from each voxel, from among the plurality of voxels, within which a number of detected ladar return photons is less than a threshold value.

15. The system of claim 14 , wherein the threshold value is 10.

16. The system of claim 9 , wherein the processing circuit is further configured to:

form a plurality of average transformed point clouds from the transformed point clouds;

form a second estimate of the six-dimensional velocity of the target, from the plurality of average transformed point clouds; and

transform each of the point clouds, of a second group of point clouds, of the plurality of groups of point clouds, by a transformation proportional to the product of:

the second estimate of the six-dimensional velocity, and

the index of the point cloud within the first group of point clouds.