Terrain elevation measurement by interferometric synthetic aperture radar (IFSAR)

• US 6,011,505 A
• Filed: 07/09/1997
• Issued: 01/04/2000
• Est. Priority Date: 07/11/1996
• Status: Expired due to Term

• Current Assignee: Leidos, Inc. (Leidos Holdings, Inc.)
• Original Assignee: Science Applications International Corporation
• Inventors: Mansfield, Arthur W., Poehler, Paul L.
• Primary Examiner(s): Lobo, Ian J.
• Application Number:
  US08/890,596
• Time in Patent Office: 909 Days
• Field of Search: 342/25, 342/191
• US Class Current: 342/25.00C
• CPC Class Codes: G01S 13/86 Combinations of radar systems with non-radar systems, e.g. sonar, direction finder
• CPC Class Codes: G01S 13/9019 Auto-focussing of the SAR signals
• CPC Class Codes: G01S 13/9023 combined with interferometric techniques
• CPC Class Codes: G01S 13/904 SAR modes

Abstract

An interferometric synthetic aperture radar (IFSAR) elevation measurement processor computes an elevation array by processing a first image array to generate an elevation corrected first image array, processing a second image array to generate an elevation corrected second image array, generating a phase interferogram from the elevation corrected first and second image arrays, and processing the phase interferogram to generate the computed elevation array. The layover correction is based on either (1) a predetermined elevation array, (2) an elevation array computed by radargrammetry, (3) an initial computed elevation array developed in an initial iteration by initial interferometry of uncorrected images followed by the layover correction in a subsequent iteration based on the initial computed elevation array, or (4) a combination of the above. The layover correction process removes range and Doppler distortion inherent in pixel data due to elevations variations in the imaged terrain.

Claims

1. A method of computing an elevation array comprising steps of:

processing a first image array to substantially remove layover effects and generate an elevation corrected first image array;

processing a second image array to substantially remove layover effects and generate an elevation corrected second image array;

generating a phase interferogram from the elevation corrected first and second image arrays; and

processing the phase interferogram to generate the computed elevation array.

2. The method of claim 1, wherein the step of processing a first:

image array includes a step of focussing an unfocussed first image array based on a hyperbolic phase gradient formed from a plurality of bright spots located within the unfocussed first image array to generate a focussed image array.

3. The method of claim 2, wherein the step of focussing comprises steps of:

selecting a first azimuth uncorrected segment from the unfocussed first image, the first azimuth uncorrected segment corresponding to a first bright spot of the plurality of bright spots;

forming an uncorrected spectrum vector from the first azimuth uncorrected segment;

determining an average phase slope from the uncorrected spectrum vector;

correcting the uncorrected spectrum vector based on the average phase slope to form a corrected spectrum vector;

forming a corrected segment from the corrected spectrum vector; and

packing the corrected segment into the focussed image array.

4. The method of claim 3, wherein the step of determining an average phase slope comprises steps of:

computing a phase gradient at each frequency in the uncorrected spectrum vector; and

computing the average phase slope by averaging the phase gradient determined at each frequency in the uncorrected spectrum vector.

5. The method of claim 1, wherein:

the step of processing a first image array includes a step of connecting image layover effects based on an elevation data array; and

the step of processing a second image array includes a step of correcting image layover effects based on the elevation data array.

6. The method of claim 5, wherein the elevation data array is a predetermined data array.

7. The method of claim 5, wherein the elevation data array is prepared by photogrammetry.

8. The method of claim 5, wherein a resolution of the first image array is unequal to a resolution of the elevation data array.

9. The method of claim 1, wherein the step of processing a first image array comprises steps of:

computing an elevation data array by stereoscopicly processing the first image array and a third image array; and

correcting image layover effects in the first image array based on the elevation data array.

10. The method of claim 9, wherein the step of computing includes radargrammetricly processing the first and third image arrays.

11. The method of claim 9, wherein:

the steps of processing first and second image arrays process synthetic aperture radar image arrays corresponding to a region of earth based on data collected at respective first and second positions, the first and second positions forming an angle with respect to the region of earth that is less than one half of a milliradian; and

the third image array is a synthetic aperture radar image array based on data collected at a third position, the first and third positions forming an angle with respect to the region of earth that is in a range between 10 and 60 degrees.

12. The method of claim 1, wherein the step of processing a first image array comprises steps of:

generating a first elevation data array by radargrammetry between the first image array and a third image array;

generating a second elevation data array by radargrammetry between the first image array and a fourth image array;

correcting image layover effects in the first image array based on the first elevation data array to generate a first partially corrected array;

correcting image layover effects in the first image array based on the second elevation data array to generate a second partially corrected array; and

computing a weighted average of the first and second partially corrected arrays to form the elevation corrected first image array.

13. The method of claim 1, wherein the step of processing a first image array comprises steps of:

generating a first elevation data array by radargrammetry between the first image array and a third image array;

generating a second elevation data array by radargrammetry between the second image array and a fourth image array;

correcting image layover effects in the first image array based on the first elevation data array to generate a first partially corrected array;

correcting image layover effects in the first image array based on the second elevation data array to generate a second partially corrected array; and

computing a weighted average of the first and second partially corrected arrays to form the elevation corrected first image array.

14. The method of claim 1, wherein the step of processing a first image array comprises steps of:

generating a first elevation data array by radargrammetry between the first image array and a third image array;

generating a second elevation data array by radargrammetry between the first image array and a fourth image array;

computing a weighted average of the first and second elevation data arrays to form an averaged elevation data array; and

correcting image layover effects in the first image array based on the averaged elevation data array to generate the elevation corrected first image array.

15. The method of claim 1, wherein the step of processing a first image array comprises steps of:

generating a first elevation data array by radargrammetry between the first image array and a third image array;

generating a second elevation data array by radargrammetry between the second image array and a fourth image array;

computing a weighted average of the first and second elevation data arrays to form an averaged elevation data array; and

correcting image layover effects in the first image array based on the averaged elevation data array to generate the elevation corrected first image array.

16. The method of claim 1, wherein the step of processing a first image array comprises steps of:

generating a first elevation data array by radargrammetry between the first image array and a third image array;

correcting image layover effects in the first image array based on the first elevation data array to generate a partially corrected first image array;

correcting image layover effects in a fourth image array based on the first elevation data array to generate a partially corrected fourth image array;

generating a second elevation data array by radargrammetry between the partially corrected first image array and the partially corrected fourth image array; and

correcting image layover effects in the partially corrected first image array based on the second elevation data array to generate the corrected first image array.

17. The method of claim 1, wherein the step of processing a first image array comprises steps of:

generating a first elevation data array by radargrammetry between the second image array and a third image array;

correcting image layover effects in the first image array based on the first elevation data array to generate a partially corrected first image array;

correcting image layover effects in a fourth image array based on the first elevation data array to generate a partially corrected fourth image array;

generating a second elevation data array by radargrammetry between the partially corrected first image array and the partially corrected fourth image array; and

correcting image layover effects in the partially corrected first image array based on the second elevation data array to generate the corrected first image array.

18. The method of claim 1, wherein the step of generating a phase interferogram comprises steps of:

forming a wrapped phase array; and

forming a twice unfolded array from the wrapped phase array and unwrapping the twice unfolded array into an unwrapped phase array.

19. The method of claim 18, wherein the step of unwrapping the twice unfolded array forms an array periodic in two dimensions.

20. The method of claim 18, wherein the step of unwrapping the twice unfolded array comprises steps of:

computing a first array from the twice unfolded array, each element of the first array being based on a discrete Poisson difference equation;

processing the first array through a two dimensional FFT to form a second array;

scaling the second array by a scaling function to form a third array; and

processing the third array through an inverse two dimensional FFT to form the unwrapped phase array.

21. The method of claim 1, wherein the step of processing the phase interferogram computes the elevation array from first and second image arrays acquired from a radar that operates at any frequency within a range from 0.4 GHz to 12 GHz.

22. The method of claim 1, wherein:

the step of processing a first image array processes the first image array acquired from a radar operating at an altitude greater than 100 nautical miles; and

the step of processing the phase interferogram computes the computed elevation array to have a one sigma vertical error of less than 30 meters averaged over the pixels in the computed elevation array, the computed elevation array characterizing the elevation of a swath of the earth'"'"'s surface, the swath being greater than 30 kilometers wide in an across track direction.

23. The method of claim 22, wherein the swath is greater than 50 kilometers wide in the across track direction.

24. The method of claim 22, wherein:

the radar from which the first image array is acquired is characterized by a first wavelength; and

the step of processing the phase interferogram computes the computed elevation array to have the one sigma vertical error of less than a smaller of 30 meters and 100 times the first wavelength averaged over the pixels in the computed elevation array.

25. The method of claim 22, wherein:

the radar from which the first image array is acquired is regarded as a first radar, the first radar being characterized by a first wavelength; and

the step of processing a second image array processes the second image array acquired from a second radar characterized by a second wavelength, the second wavelength being unequal to the first wavelength.

26. The method of claim 22, wherein:

the radar from which the first image array is acquired is regarded as a first radar; and

the step of processing a second image array processes the second image array acquired from a second radar operating at an altitude greater than 25,000 feet but less than 100 nautical miles.

27. The method of claim 22, wherein the step of processing a first image array includes a step of focussing an unfocussed first image array based on a hyperbolic phase gradient approximation formed from a plurality of bright spots located within the unfocussed first image array to generate a focussed image array.

28. The method of claim 22, wherein the step of generating a phase interferogram includes steps of:

forming a wrapped phase array; and

unwrapping the wrapped phase array into an unwrapped phase array.

29. The method of claim 22, wherein the step of generating a phase interferogram includes steps of:

forming a wrapped phase array; and

unwrapping the wrapped phase array using an inverse two dimensional FFT to form an unwrapped phase array.

30. The method of claim 22, wherein the elevation array is computed to have an elevation value for each of a plurality of pixels extending across the swath, the pixels being separated by less than 120 meters.

31. The method of claim 22, wherein the elevation array is computed to have an elevation value for each of a plurality of pixels extending across the swath, the pixels being separated by a range resolution, the range resolution being defined to be less than a smaller of 120 meters and twice the speed of light multipled by an inverse of the system range bandwidth multiplied by a secant of a slant plane angle of the first image array.

32. The method of claim 22, wherein the step of processing the first image array processes the first image array acquired from the radar, the radar operating at any frequency within a range from 0.4 GHz to 12 GHz.

33. The method of claim 22, wherein the step of processing the second image array processes the second image array acquired from a radar operating at any frequency within a range from 0.4 GHz to 12 GHz.

34. The method of claim 1, wherein:

the step of processing a first image array processes the first image array acquired from a radar operating at an altitude greater than 25,000 feet; and

the step of processing the phase interferogram computes the computed elevation array to have a one sigma vertical error of less than 30 meters averaged over the pixels in the computed elevation array, the computed elevation array characterizing the elevation of a swath of the earth'"'"'s surface, the swath being greater than 20 kilometers wide in an across track direction.

35. The method of claim 34 wherein the swath is greater than 50 kilometers wide in the across track direction.

36. The method of claim 34, wherein:

the radar from which the first image array is acquired is characterized by a first wavelength; and

the step of processing the phase interferogram computes the computed elevation array to have the one sigma vertical error of less than a smaller of 30 meters and 100 times the first wavelength averaged over the pixels in the computed elevation array.

37. The method of claim 34, wherein:

the radar from which the first image array is acquired is regarded as a first radar, the first radar being characterized by a first wavelength; and

the step of processing a second image array processes the second image array acquired from a second radar characterized by a second wavelength, the second wavelength being unequal to the first wavelength.

38. The method of claim 34, wherein:

the radar from which the first image array is acquired is regarded as a first radar; and

the step of processing a second image array processes the second image array acquired from a second radar operating at an altitude greater than 80 nautical miles.

39. The method of claim 34, wherein the step of processing a first image array includes a step of focussing an unfocussed first image array based on a hyperbolic phase gradient approximation formed from a plurality of bright spots located within the unfocussed first image array to generate a focussed image array.

40. The method of claim 34, wherein the step of generating a phase interferogram includes steps of:

forming a wrapped phase array; and

unwrapping the wrapped phase array into an unwrapped phase array.

41. The method of claim 34, wherein the step of generating a phase interferogram includes steps of:

forming a wrapped phase array; and

unwrapping the wrapped phase array using an inverse two dimensional FFT to form an unwrapped phase array.

42. The method of claim 34, wherein the elevation array is computed to have an elevation value for each of a plurality of pixels extending across the swath, the pixels being separated by less than 120 meters.

43. The method of claim 34, wherein the elevation array is computed to have an elevation value for each of a plurality of pixels extending across the swath, the pixels being separated by a range resolution, the range resolution being defined to be less than a smaller of 120 meters and twice the speed of light multipled by an inverse of the system range bandwidth multiplied by a secant of a slant plane angle of the first image array.

44. The method of claim 34, wherein the step of processing the first image array proses the first image array acquired from the radar, the radar operating at any frequency within a range from 0.4 GHz to 12 GHz.

45. The method of claim 34, wherein the step of processing the second image array processes the second image array acquired from a radar, the radar operating at any frequency within a range from 0.4 GHz to 12 GHz.

46. The method of claim 1, wherein:

the step of processing a first image array processes the first image array acquired from a radar operating at an altitude greater than 25,000 feet, the radar being characterized by a first wavelength; and

the step of processing the phase interferogram computes the computed elevation array to have a one sigma vertical error of less than a smaller of 30 meters and 100 times the first wavelength averaged over the pixels in the computed elevation array, the computed elevation array characterizing the elevation of a swath of the earth'"'"'s surface, the swath being greater than 2 kilometers wide in an across track direction.

47. The method of claim 46, wherein the swath is greater than 20 kilometers wide in the across track direction.

48. The method of claim 46, wherein the swath is greater than 30 kilometers wide in the across track direction.

49. The method of claim 46, wherein:

the radar from which the first image array is acquired is regarded as a first radar; and

the step of processing a second image array processes the second image array acquired from a second radar characterized by a second wavelength, the second wavelength being unequal to the first wavelength.

50. The method of claim 46, wherein:

the radar from which the first image array is acquired is regarded as a first radar; and

the step of processing a second image array processes the second image array acquired from a second radar operating at an altitude greater than 80 nautical miles.

51. The method of claim 46, wherein the step of processing a first image array includes a step of focussing an unfocussed first image array based on a hyperbolic phase gradient approximation formed from a plurality of bright spots located within the unfocussed first image array to generate a focussed image array.

52. The method of claim 46, wherein the step of generating a phase interferogram includes steps of:

forming a wrapped phase array; and

unwrapping the wrapped phase array into an unwrapped phase array.

53. The method of claim 46, wherein the step of generating a phase interferogram includes steps of:

forming a wrapped phase array; and

unwrapping the wrapped phase array using an inverse two dimensional FFT to form an unwrapped phase array.

54. The method of claim 46, wherein the elevation array is computed to have an elevation value for each of a plurality of pixels extending across the swath, the pixels being separated by less than 120 meters.

55. The method of claim 46, wherein the elevation array is computed to have an elevation value for each of a plurality of pixels extending across the swath, the pixels being separated by a range resolution, the range resolution being defined to be less than a smaller of 120 meters and twice the speed of light multipled by an inverse of the system range bandwidth multiplied by a secant of a slant plane angle of the first image array.

56. The method of claim 46, wherein the step of processing the first image array processes the first image array acquired from the radar, the radar operating at any frequency within a range from 0.4 GHz to 12 GHz.

57. The method of claim 46, wherein the step of processing the second image array processes the second image array acquired from a radar, the radar operating at any frequency within a range from 0.4 GHz to 12 GHz.

58. The method of claim 1, wherein the steps of processing first and second image arrays include a common step that processes synthetic aperture radar image arrays corresponding to a region of earth based on data collected at respective first and second positions, the first and second positions forming an angle with respect to the region of earth that is less than one half of a milliradian.

59. The method of claim 1, wherein the step of generating a phase interferogram includes a step of registering the elevation corrected first image array to the elevation corrected second image array.

60. The method of claim 59, wherein the step of registering comprises steps of:

culling a first sub-array from the elevation corrected first image array;

forming a sub-interferogram between the first sub-array at a pixel offset and the elevation corrected second image array;

processing the sub-interferogram through a two dimensional FFT to form a spectral array; and

determining a spectral peak from the spectral array.

61. The method of claim 60, wherein the step of registering further comprises steps of:

repeating with different pixel offsets the steps of culling a first sub-array, forming a sub-interferogram, processing the sub-interferogram and determining a spectral peak so that the spectral peaks determined at the different pixel offsets fill a correlation array; and

determining a registered pixel offset at a pixel offset where the corresponding spectral peak is greater than all other spectral peaks in the correlation array.

62. The method of claim 1, wherein the step of generating a phase interferogram includes a step of filtering the elevation corrected first image array.

63. The method of claim 62, wherein the step of filtering comprises a step of averaging a first pixel at a first range with at least one pixel at a greater range and at least one pixel at a lesser range.

64. The method of claim 62, wherein the step of filtering comprises a step of averaging a first pixel at a first azimuth with at least one pixel at a greater azimuth and at least one pixel at a lesser azimuth.

65. The method of claim 62, wherein the step of filtering comprises steps of:

averaging a first pixel at a first range with at least one pixel at a greater range and at least one pixel at a lesser range; and

averaging the first pixel at a first azimuth with at least one pixel at a greater azimuth and at least one pixel at a lesser azimuth.

66. The method of claim 62, wherein the step of filtering comprises steps of:

averaging a first pixel at a first range with one adjacent pixel at a greater range and one adjacent pixel at a lesser range; and

averaging the first pixel at a first azimuth with three adjacent pixels at a greater azimuth and three adjacent pixels at a lesser azimuth.

67. A method of computing an elevation array comprising steps of:

generating elevation corrected first, second and third image arrays so as to substantially remove layover effects;

generating a first phase interferogram from the elevation corrected first and second image arrays;

generating a second phase interferogram from the elevation corrected third image array;

computing a weighted average phase interferogram from the first and second phase interferograms; and

processing the weighted average phase interferogram to generate the computed elevation array.

68. The method of claim 67, wherein the step of generating a second phase interferogram generates the second phase interferogram from the elevation corrected first and third image arrays.

69. The method of claim 67, further comprising a step of generating an elevation corrected fourth image array, the step of generating a second phase interferogram generating the second phase interferogram from the elevation corrected third and fourth image arrays.

70. A method of computing an elevation array comprising steps of:

pre-processing first and second image arrays to generate an initial elevation array;

processing the first image array to substantially remove layover effects and generate an elevation corrected first image array based on the initial elevation array;

processing the second image array to substantially remove layover effects and generate an elevation corrected second image array based on the initial elevation array;

generating a phase interferogram from the elevation corrected first and second image arrays; and

processing the phase interferogram to generate the computed elevation array.

71. The method of claim 70, wherein the step of pre-processing comprises steps of:

warping the second image array onto a grid of the first image array;

generating an initial phase interferogram from the warped second image array and the first image array; and

processing the initial phase interferogram to generate the initial elevation array.

72. The method of claim 70, wherein the computed elevation array is regarded as the initial elevation array, the method further comprising a step of repeating the steps of processing the first image array, processing the second image array, generating a phase interferogram and processing the phase interferogram to generate a new computed elevation array.

73. The method of claim 72, wherein the step of repeating repeats it least three times the steps.

74. A computing machine comprising:

a processor;

a first module to substantially remove layover effects and generate an elevation corrected first image array from a first image array;

a second module to substantially remove layover effects and generate an elevation corrected second image array from a second image array;

a third module to generate a phase interferogram from the elevation corrected first and second image arrays; and

a fourth module to generate a computed elevation array from the phase interferogram.

75. The machine of claim 74, wherein the first module includes a fifth module to focus an unfocussed first image array based on a hyperbolic phase gradient formed from a plurality of bright spots located within the unfocussed first image array and to generate a focussed image array.

76. The machine of claim 75, wherein the fifth module includes:

a sub-module to select a first azimuth uncorrected segment from the unfocussed first image, the first azimuth uncorrected segment corresponding to a first bright spot of the plurality of bright spots;

a sub-module to form an uncorrected spectrum vector from the first azimuth uncorrected segment;

a sub-module to determine an average phase slope from the uncorrected spectrum vector;

a sub-module to correct the uncorrected spectrum vector based on the average phase slope to form a corrected spectrum vector;

a sub-module to form a corrected segment from the corrected spectrum vector; and

a sub-module to pack the corrected segment into the focussed image array.

77. The machine of claim 76, wherein the the sub-module to determine an average phase slope comprises:

a module element to compute a phase gradient at each frequency in the uncorrected spectrum vector; and

a module element to compute the average phase slope by averaging the phase gradient determined at each frequency in the uncorrected spectrum vector.

78. The machine of claim 74, wherein:

the first module includes a sub-module to correct image layover effects based on an elevation data array; and

the second module includes a sub-module to correct image layover effects based on the elevation data array.

79. The machine of claim 78, wherein the elevation data array is a predetermined data array.

80. The machine of claim 78, wherein the elevation data array is prepared by photogrammetry.

81. The machine of claim 78, wherein a resolution of the first image array is unequal to a resolution of the elevation data array.

82. The machine of claim 74, wherein the first module comprises:

a sub-module to compute an elevation data array by stereoscopicly processing the first image array and a third image array; and

a sub-module to correct image layover effects in the first image array based on the elevation data array.

83. The machine of claim 82, wherein the sub-module to compute an elevation data array includes a radargrammetry module to process the first and third image arrays.

84. The machine of claim 82, wherein:

the first and second modules process synthetic aperture radar image arrays corresponding to a region of earth based on data collected at respective first and second positions, the first and second positions forming an angle with respect to the region of earth that is less than one half of a milliradian; and

the third image array is a synthetic aperture radar image array based on data collected at a third position, the first and third positions forming an angle with respect to the region of earth that is in a range between 10 and 60 degrees.

85. The machine of claim 74, wherein the first module comprises:

a first sub-module to generate a first elevation data array by radargrammetry between the first image array and a third image array;

a second sub-module to generate a second elevation data array by radargrammetry between the first image array and a fourth image array;

a third sub-module to correct image layover effects in the first image array based on the first elevation data array to generate a first partially corrected array;

a fourth sub-module to correct image layover effects in the first image array based on the second elevation data array to generate a second partially corrected array; and

a fifth sub-module to compute a weighted average of the first and second partially corrected arrays to form the elevation corrected first image array.

86. The machine of claim 74, wherein the first module comprises:

a first sub-module to generate a first elevation data array by radargrammetry between the first image array and a third image array;

a second sub-module to generate a second elevation data array by radargrammetry between the second image array and a fourth image array;

a third sub-module to correct image layover effects in the first image array based on the first elevation data array to generate a first partially corrected array;

a fourth sub-module to correct image layover effects in the first image array based on the second elevation data array to generate a second partially corrected array; and

a fifth sub-module to compute a weighted average of the first and second partially corrected arrays to form the elevation corrected first image array.

87. The machine of claim 74, wherein the first module comprises:

a first sub-module to generate a first elevation data array by radargrammetry between the first image array and a third image array;

a second sub-module to generate a second elevation data array by radargrammetry between the first image array and a fourth image array;

a third sub-module to compute a weighted average of the first and second elevation data arrays to form an averaged elevation data array; and

a fourth sub-module to correct image layover effects in the first image array based on the averaged elevation data array to generate the elevation corrected first image array.

88. The machine of claim 74, wherein the first module comprises:

a first sub-module to generate a first elevation data array by radargrammetry between the first image array and a third image array;

a second sub-module to generate a second elevation data array by radargrammetry between the second image array and a fourth image array;

a third sub-module to compute a weighted average of the first and second elevation data arrays to form an averaged elevation data array; and

a fourth sub-module to correct image layover effects in the first image array based on the averaged elevation data array to generate the elevation corrected first image array.

89. The machine of claim 74, wherein the first module comprises:

a first sub-module to generate a first elevation data array by radargrammetry between the first image array and a third image array;

a second sub-module to correct image layover effects in the first image array based on the first elevation data array to generate a partially corrected first image array;

a third sub-module to correct image layover effects in a fourth image array based on the first elevation data array to generate a partially corrected fourth image array;

a fourth sub-module to generate a second elevation data array by radargrammetry between the partially corrected first image array and the partially corrected fourth image array; and

a fifth sub-module to correct image layover effects in the partially corrected first image array based on the second elevation data array to generate the corrected first image array.

90. The machine of claim 74, wherein the first module comprises:

a first sub-module to generate a first elevation data array by radargrammetry between the second image array and a third image array;

a second sub-module to correct image layover effects in the first image array based on the first elevation data array to generate a partially corrected first image array;

a third sub-module to correct image layover effects in a fourth image array based on the first elevation data array to generate a partially corrected fourth image array;

a fourth sub-module to generate a second elevation data array by radargrammetry between the partially corrected first image array and the partially corrected fourth image array; and

a fifth sub-module to correct image layover effects in the partially corrected first image array based on the second elevation data array to generate the corrected first image array.

91. The machine of claim 74, wherein the third module comprises:

a first sub-module to form a wrapped phase array; and

a second sub-module to unwrap the wrapped phase array into an unwrapped phase array.

92. The machine of claim 91, wherein the second sub-module comprises a third sub-module to form a twice unfolded array from the wrapped phase array.

93. The machine of claim 91, wherein the second sub-module comprises:

a third sub-module to compute a first array from the wrapped phase array, each element of the first array being based on a discrete Poisson difference equation;

a fourth sub-module to process the first array through a two dimensional FFT to form a second array;

a fifth sub-module to scale the second array by a scaling function to form a third array; and

a fourth sub-module to process the third array through an inverse two dimensional FFT to form the unwrapped phase array.

94. The machine of claim 74, wherein the fourth module computes the elevation array from first and second image arrays acquired from a radar that operates at any frequency within a range from 0.4 GHz to 12 GHz.

95. The machine of claim 74, wherein:

the first module includes a sub-module to process the first image array as an array acquired from a radar operating at an altitude greater than 100 nautical miles; and

the fourth module includes a sub-module to compute the computed elevation array to have a one sigma vertical error of less than 30 meters averaged over the pixels in the computed elevation array, the computed elevation array characterizing the elevation of a swath of the earth'"'"'s surface, the swath being greater than 30 kilometers wide in an across track direction.

96. The machine of claim 74, wherein:

the first module includes a sub-module to process the first image array acquired from a radar operating at an altitude greater than 25,000 feet; and

the fourth module includes a sub-module to compute the computed elevation array to have a one sigma vertical error of less than 30 meters averaged over the pixels in the computed elevation array, the computed elevation array characterizing the elevation of a swath of the earth'"'"'s surface, the swath being greater than 20 kilometers wide in an across track direction.

97. The machine of claim 74, wherein:

the first module includes a sub-module to process the first image array acquired from a radar operating at an altitude greater than 25,000 feet, the radar being characterized by a first wavelength; and

the fourth module includes a sub-module to compute the computed elevation array to have a one sigma vertical error of less than a smaller of 30 meters and 100 times the first wavelength averaged over the pixels in the computed elevation array, the computed elevation array characterizing the elevation of a swath of the earth'"'"'s surface, the swath being greater than 2 kilometers wide in an across;

track direction.

98. The machine of claim 74, wherein the first and second modules link to a common sub-module to process synthetic aperture radar image arrays corresponding to a region of earth based on data collected at respective first and second positions, the first and second positions forming an angle with respect to the region of earth that is less than one half of a milliradian.

99. The machine of claim 74, wherein the third module includes a registration module to register the elevation corrected first image array to the elevation corrected second image array.

100. The machine of claim 99, wherein the registration module comprises:

a first sub-module to cull a first sub-array from the elevation corrected first image array;

a second sub-module to form a sub-interferogram between the first sub-array at a pixel offset and the elevation corrected second image array;

a third sub-module to process the sub-interferogram through a two dimensional FFT to form a spectral array; and

a fourth sub-module to determine a spectral peak from the spectral array.

101. The machine of claim 100, wherein the registration module further comprises:

a fifth sub-module to control the first, second, third and fourth sub-modules to repeat with different pixel offsets so that the spectral peaks determined at the different pixel offsets fill a correlation array; and

a sixth sub-module to determine a registered pixel offset at a pixel offset where the corresponding spectral peak is greater than all other spectral peaks in the correlation array.

102. The machine of claim 74, wherein the third module includes a filter module to filter the elevation corrected first image array.

103. The machine of claim 102, wherein the filter module comprises a sub-module to average a first pixel at a first range with at least one pixel at a greater range and at least one pixel at a lesser range.

104. The machine of claim 102, wherein the filter module comprises a sub-module to average a first pixel at a first azimuth with at least one pixel at a greater azimuth and at least one pixel at a lesser azimuth.

105. The machine of claim 102, wherein the filter module comprises:

a first sub-module to average a first pixel at a first range with at least one pixel at a greater range and at least one pixel at a lesser range; and

a second sub-module to average the first pixel at a first azimuth with at least one pixel at a greater azimuth and at least one pixel at a lesser azimuth.

106. The machine of claim 102, wherein the filter module comprises:

a first sub-module to average a first pixel at a first range with one adjacent pixel at a greater range and one adjacent pixel at a lesser range; and

a second sub-module to average the first pixel at a first azimuth with three adjacent pixels at a greater azimuth and three adjacent pixels at a lesser azimuth.

107. A computing machine comprising:

a processor;

a first module to substantially remove layover effects and generate elevation corrected first, second and third image arrays;

a second module to generate a first phase interferogram from the elevation corrected first and second image arrays;

a third module to generate a second phase interferogram from the elevation corrected third image array;

a fourth module to compute a weighted average phase interferogram from the first and second phase interferograms; and

a fifth module to generate a computed elevation array from the weighted average phase interferogram.

108. The machine of claim 107, wherein the third module generates the second phase interferogram from the elevation corrected first and third image arrays.

109. The machine of claim 107, further comprising a sixth module to generate an elevation corrected fourth image array, the third module generating the second phase interferogram from the elevation corrected third and fourth image arrays.

110. A computing machine comprising:

a processor;

a first module to preprocess first and second image arrays to generate an initial elevation array;

a second module to process the first image array to substantially remove layover effects and generate an elevation corrected first image array based on the initial elevation array;

a third module to process the second image array to substantially remove layover effects and generate an elevation corrected second image array based on the initial elevation array;

a fourth module to generate a phase interferogram from the elevation corrected first and second image arrays; and

a fifth module to process the phase interferogram to generate the computed elevation array.

111. The machine of claim 110, wherein the first module comprises:

a first sub-module to warp the second image array onto a grid of the first image array;

a second sub-module to generate an initial phase interferogram from the warped second image array and the first image array; and

a third sub-module to process the initial phase interferogram to generate the initial elevation array.

112. The machine of claim 110, wherein the computed elevation array is regarded as the initial elevation array, the processor further comprising a sixth module to control the second, third, fourth and fifth modules to repeat the generation of the computed elevation array.

113. The machine of claim 112, wherein the sixth module controls the second, third, fourth and fifth modules to repeat the generation of the computed elevation array at least three times.

114. A computer readable medium having stored thereon a plurality of modules for controlling a processor, the plurality of modules comprising:

a first module to control the processor to substantially remove layover effects and generate an elevation corrected first image array from a first image array;

a second module to control the processor to substantially remove layover effects and generate an elevation corrected second image array from a second image array;

a third module to control the processor to generate a phase interferogram from the elevation corrected first and second image arrays; and

a fourth module to control the processor to generate a computed elevation array from the phase interferogram.

115. The medium of claim 114, wherein the first module includes a fifth module to control the processor to focus an unfocussed first image array based on a hyperbolic phase gradient formed from a plurality of bright spots located within the unfocussed first image array and to generate a focussed image array.

116. The medium of claim 115, wherein the fit module includes:

a sub-module to control the processor to select a first azimuth uncorrected segment from the unfocussed first image, the first azimuth uncorrected segment corresponding to a first bright spot of the plurality of bright spots;

a sub-module to control the processor to form an uncorrected spectrum vector from the first azimuth uncorrected segment;

a sub-module to control the processor to determine an average phase slope from the uncorrected spectrum vector;

a sub-module to control the processor to correct the uncorrected spectrum vector based on the average phase slope to form a corrected spectrum vector;

a sub-module to control the processor to form a corrected segment from the corrected spectrum vector; and

a sub-module to control the processor to pack the corrected segment into the focussed image array.

117. The medium of claim 116, wherein the the sub-module to determine an average phase slope comprises:

a module portion to control the processor to compute a phase gradient at each frequency in the uncorrected spectrum vector; and

a module portion to control the processor to compute the average phase slope by averaging the phase gradient determined at each frequency in the uncorrected spectrum vector.

118. The medium of claim 114, wherein:

the first module includes a sub-module to control the processor to correct image layover effects based on an elevation data array; and

the second module includes a sub-module to control the processor to correct image layover effects based on the elevation data array.

119. The medium of claim 118, wherein the elevation data array is a predetermined data array.

120. The medium of claim 118, wherein the elevation data array is prepared by photogrammetry.

121. The medium of claim 118, wherein a resolution of the first image array is unequal to a resolution of the elevation data array.

122. The medium of claim 114, wherein the first module comprises:

a first sub-module to control the processor to compute an elevation data array by stereoscopicly processing the first image array and a third image array; and

a second sub-module to control the processor to correct image layover effects in the first image array based on the elevation data array.

123. The medium of claim 122, wherein the first sub-module includes a radargrammetry module to control the processor to process the first and third image arrays.

124. The medium of claim 122, wherein:

the first and second modules control the processor to process synthetic aperture radar image arrays corresponding to a region of earth based on data collected at respective first and second positions, the first and second positions forming an angle with respect to the region of earth that is less than one half of a milliradian; and

the third image array is a synthetic aperture radar image array based on data collected at a third position, the first and third positions forming an angle with respect to the region of earth that is in a range between 10 and 60 degrees.

125. The medium of claim 114, wherein the first module comprises:

a first sub-module to control the processor to generate a first elevation data array by radargrammetry between the first image array and a third image array;

a second sub-module to control the processor to generate a second elevation data array by radargrammetry between the first image array and a fourth image array;

a third sub-module to control the processor to correct image layover effects in the first image array based on the first elevation data array to generate a first partially corrected array;

a fourth sub-module to control the processor to correct image layover effects in the first image array based on the second elevation data array to generate a second partially corrected array; and

a fifth sub-module to control the processor to compute a weighted average of the first and second partially corrected arrays to form the elevation corrected first image array.

126. The medium of claim 114, wherein the first module comprises:

a first sub-module to control the processor to generate a first elevation data array by radargrammetry between the first image array and a third image array;

a second sub-module to control the processor to generate a second elevation data array by radargrammetry between the second image array and a fourth image array;

a third sub-module to control the processor to correct image layover effects in the first image array based on the first elevation data array to generate a first partially corrected array;

a fourth sub-module to control the processor to correct image layover effects in the first image array based on the second elevation data array to generate a second partially corrected array; and

a fifth sub-module to control the processor to compute a weighted average of the first and second partially corrected arrays to form the elevation corrected first image array.

127. The medium of claim 114, wherein the first module comprises:

a first sub-module to control the processor to generate a first elevation data array by radargrammetry between the first image array and a third image array;

a second sub-module to control the processor to generate a second elevation data array by radargrammetry between the first image array and a fourth image array;

a third sub-module to control the processor to compute a weighted average of the first and second elevation data arrays to form an averaged elevation data array; and

a fourth sub-module to control the processor to correct image layover effects in the first image array based on the averaged elevation data array to generate the elevation corrected first image array.

128. The medium of claim 114, wherein the first module comprises:

a first sub-module to control the processor to generate a first elevation data array by radargrammetry between the first image array and a third image array;

a second sub-module to control the processor to generate a second elevation data array by radargrammetry between the second image array and a fourth image array;

a third sub-module to control the processor to compute a weighted average of the first and second elevation data arrays to form an averaged elevation data array; and

a fourth sub-module to control the processor to correct image layover effects in the first image array based on the averaged elevation data array to generate the elevation corrected first image array.

129. The medium of claim 114, wherein the first module comprises:

a first sub-module to control the processor to generate a first elevation data array by radargrammetry between the first image array and a third image array;

a second sub-module to control the processor to correct image layover effects in the first image array based on the first elevation data array to generate a partially corrected first image array;

a third sub-module to control the processor to correct image layover effects in a fourth image array based on the first elevation data array to generate a partially corrected fourth image array;

a fourth sub-module to control the processor to generate a second elevation data array by radargrammetry between the partially corrected first image array and the partially corrected fourth image array; and

a fifth sub-module to control the processor to correct image layover effects in the partially corrected first image array based on the second elevation data array to generate the corrected first image array.

130. The medium of claim 114, wherein the first module comprises:

a first sub-module to control the processor to generate a first elevation data array by radargrammetry between the second image array and a third image array;

a second sub-module to control the processor to correct image layover effects in the first image array based on the first elevation data array to generate a partially corrected first image array;

a third sub-module to control the processor to correct image layover effects in a fourth image array based on the first elevation data array to generate a partially corrected fourth image array;

a fourth sub-module to control the processor to generate a second elevation data array by radargrammetry between the partially corrected first image array and the partially corrected fourth image array; and

a fifth sub-module to control the processor to correct image layover effects in the partially corrected first image array based on the second elevation data array to generate the corrected first image array.

131. The medium of claim 114, wherein the third module comprises:

a first sub-module to control the processor to form a wrapped phase array; and

a second sub-module to control the processor to unwrap the wrapped phase array into an unwrapped phase array.

132. The medium of claim 131, wherein the second sub-module comprises a third sub-module to control the processor to form a twice unfolded array from the wrapped phase array.

133. The medium of claim 131, wherein the second sub-module comprises:

a third sub-module to control the processor to compute a first array from the wrapped phase array, each element of the first array being based on a discrete Poisson difference equation;

a fourth sub-module to control the processor to process the first array through a two dimensional FFT to form a second array;

a fifth sub-module to control the processor to scale the second array by a scaling function to form a third array; and

a fourth sub-module to control the processor to process the third array through an inverse two dimensional FFT to form the unwrapped phase array.

134. The medium of claim 114, wherein the fourth module controls the processor to compute the elevation array from first and second image arrays acquired from a radar that operates at any frequency within a range from 0.4 GHz to 12 GHz.

135. The medium of claim 114, wherein:

the first module includes a sub-module to control the processor to process the first image array as an array acquired from a radar operating at an altitude greater than 100 nautical miles; and

the fourth module includes a sub-module to control the processor to compute the computed elevation array to have a one sigma vertical error of less than 30 meters averaged over the pixels in the computed elevation array, the computed elevation array characterizing the elevation of a swath of the earth'"'"'s surface, the swath being greater than 30 kilometers wide in an across track direction.

136. The medium of claim 114, wherein:

the first module includes a sub-module to control the processor to process the first image array acquired from a radar operating at an altitude greater than 25,000 feet; and

the fourth module includes a sub-module to control the processor to compute the computed elevation array to have a one sigma vertical error of less than 30 meters averaged over the pixels in the computed elevation array, the computed elevation array characterizing the elevation of a swath of the earth'"'"'s surface, the swath being greater than 20 kilometers wide in an across track direction.

137. The medium of claim 114, wherein:

the first module includes a sub-module to control the processor to process the first image array acquired from a radar operating at an altitude greater than 25,000 feet, the radar being characterized by a first wavelength; and

the fourth module includes a sub-module to control the processor to compute the computed elevation array to have a one sigma vertical error of less than a smaller of 30 meters and 100 times the first wavelength averaged over the pixels in the computed elevation array, the computed elevation array characterizing the elevation of a swath of the earth'"'"'s surface, the swath being greater than 2 kilometers wide in an across track direction.

138. The medium of claim 114, wherein the first and second modules include links to a common sub-module to control the processor to process synthetic aperture radar image arrays corresponding to a region of earth based on data collected at respective first and second positions, the first and second positions forming an angle with respect to the region of earth that is less than one half of a milliradian.

139. The medium of claim 114, wherein the third module includes a registration module control the processor to register the elevation corrected first image array to the elevation corrected second image array.

140. The medium of claim 139, wherein the registration module comprises:

a first sub-module to control the processor to cull a first sub-array from the elevation corrected first image array;

a second sub-module to control the processor to form a sub-interferogram between the first sub-array at a pixel offset and the elevation corrected second image array;

a third sub-module to control the processor to process the sub-interferogram through a two dimensional FFT to form a spectral array; and

a fourth sub-module to control the processor to determine a spectral peak from the spectral array.

141. The medium of claim 140, wherein the registration module further comprises:

a fifth sub-module to control the processor to control the first, second, third and fourth sub-modules to repeat with different pixel offsets so that the spectral peaks determined at the different pixel offsets fill a correlation array; and

a sixth sub-module to control the processor to determine a registered pixel offset at a pixel offset where the corresponding spectral peak is greater than all other spectral peaks in the correlation array.

142. The medium of claim 114, wherein the third module includes a filler module to control the processor to filter the elevation corrected first image array.

143. The medium of claim 142, wherein the filter module comprises a sub-module to control the processor to average a first pixel at a first range with at least one pixel at a greater range and at least one pixel at a lesser range.

144. The medium of claim 142, wherein the filter module comprises a sub-module to control the processor to average a first pixel at a first azimuth with at least one pixel at a greater azimuth and at least one pixel at a lesser azimuth.

145. The medium of claim 142, wherein the filter module comprises:

a first sub-module to control the processor to average a first pixel at a first range with at least one pixel at a greater range and at least one pixel at a lesser range; and

a second sub-module to control the processor to average the first pixel at a first azimuth with at least one pixel at a greater azimuth and at least one pixel at a lesser azimuth.

146. The medium of claim 142, wherein the filter module comprises:

a first sub-module to control the processor to average a first pixel at a first range with one adjacent pixel at a greater range and one adjacent pixel at a lesser range; and

a second sub-module to control the processor to average the first pixel at a first azimuth with three adjacent pixels at a greater azimuth and three adjacent pixels at a lesser azimuth.

147. A computer readable medium having stored thereon a plurality of modules for controlling a processor, the plurality of modules comprising:

a first module to control the processor to substantially remove layover effects and generate elevation corrected first, second and third image arrays;

a second module to control the processor to generate a first phase interferogram from the elevation corrected first and second image arrays;

a third module to control the processor to generate a second phase interferogram from the elevation corrected third image array;

a fourth module to control the processor to compute a weighted average phase interferogram from the first and second phase interferograms; and

a fifth module to control the processor to generate a computed elevation array from the weighted average phase interferogram.

148. The medium of claim 147, wherein the third module controls the processor to generate the second phase interferogram from the elevation corrected first and third image arrays.

149. The medium of claim 147, further comprising a sixth module to control the processor to generate an elevation corrected fourth image array, the third module controlling the processor to generate the second phase interferogram from the elevation corrected third and fourth image arrays.

150. A computer readable medium having stored thereon a plurality of modules for controlling a processor, the plurality of modules comprising:

a first module to control the processor to pre-process first and second image arrays to generate an initial elevation array;

a second module to control the processor to process the first image array to substantially remove layover effects and generate an elevation corrected first image array based on the initial elevation array;

a third module to control the processor to process the second image array to substantially remove layover effects and generate an elevation corrected second image array based on the initial elevation array;

a fourth module to control the processor to generate a phase interferogram from the elevation corrected first and second image arrays; and

a fifth module to control the processor to process the phase interferogram to generate the computed elevation array.

151. The medium of claim 150, wherein the first module comprises:

a first sub-module to control the processor to warp the second image array onto a grid of the first image array;

a second sub-module to control the processor to generate an initial phase interferogram from the warped second image array and the first image array; and

a third sub-module to control the processor to process the initial phase interferogram to generate the initial elevation array.

152. The medium of claim 150, wherein the computed elevation array is regarded as the initial elevation array, the medium further comprising a sixth module to control the processor and cause the second, third, fourth and fifth modules to repeat the generation of the computed elevation array.

153. The medium of claim 152, wherein the sixth module controls the processor and causes the second, third, fourth and fifth modules to repeat the generation of the computed elevation array at least three times.