Optical interferometry

• US 20030053079A1
• Filed: 08/23/2002
• Published: 03/20/2003
• Est. Priority Date: 08/23/2001
• Status: Active Grant

• Current Assignee: Zygo Corporation (Ametek Incorporated)
• Original Assignee: Zygo Corporation (Ametek Incorporated)
• Inventors: Hill, Henry A.
• Granted Patent: US 7,193,726 B2
• Time in Patent Office: Days
• US Class Current: 356/520
• CPC Class Codes: G01B 2290/70 Using polarization in the interferometer
• CPC Class Codes: G01B 9/02018 Multipass interferometers, e.g. double-pass
• CPC Class Codes: G01B 9/02061 Reduction or prevention of effects of tilts or misalignment
• CPC Class Codes: G03F 7/70775 Position control, e.g. interferometers or encoders for determining the stage position

Abstract

An interferometry system includes an interferometer to split an input beam into a measurement beam and at least one other beam. The interferometer directs the measurement beam along a measurement path that includes at least two passes to a measurement object, and overlaps the measurement beam with the other beam after the measurement beam completes the at least two passes. The path of the measurement beam is sheared during the first and second passes when the measurement object moves along a direction orthogonal to a portion of the measurement path that contacts the measurement object. The interferometry system includes optics to redirect the measurement beam after the first pass and before the second pass so that shear imparted during the second pass cancels shear imparted during the first pass. The optics also redirect the measurement beam after the second pass and before overlapping with the other beam so that the measurement beam propagates in a direction that is constant relative to the propagation direction of the other beam independent of changes in the orientation of the optics

Claims

1. An apparatus comprising:

an interferometer to split an input beam into a measurement beam and at least one other beam, to direct the measurement beam along a measurement path that includes at least two passes to a measurement object, to direct the other beam along a reference path that includes at least two passes to a reference object, and to overlap the measurement beam with the other beam after the measurement beam completes the at least two passes,

the path of the measurement beam being sheared during the first and second passes when the measurement object moves; and

optics to redirect the measurement beam after the first pass and before the second pass so that the shear imparted during the second pass cancels the shear imparted during the first pass..

2. The apparatus of claim 1 in which the shear of the measurement beam path is caused by a movement of the measurement object along a direction orthogonal to a portion of the measurement path that is incident on the measurement object during the first pass.

3. The apparatus of claim 1 in which the optics comprise a first reflection surface to redirect the measurement beam.

4. The apparatus of claim 3 in which the first reflection surface comprise a plane reflection surface.

5. The apparatus of claim 3 in which the optics further comprise a second reflection surface to redirect the measurement beam after the second pass and before overlapping with the other beam.

6. The apparatus of claim 5 in which the first reflection surface remains parallel relative to the second reflection surface when the first and the second reflection surfaces move.

7. The apparatus of claim 1 in which the optics comprise a mirror having a front reflection surface and a rear reflection surface, the front reflection surface to redirect the measurement beam after the first pass and before the second pass, the rear reflection surface to redirect the measurement beam after the second pass and before overlapping with the other beam.

8. The apparatus of claim 7 in which the front and rear reflection surfaces are parallel.

9. The apparatus of claim 5 in which the first reflection surface, the second reflection surface, and the interferometer are arranged so that after the measurement beam and the other beam overlaps, the measurement beam propagates in a direction parallel to the propagation direction of the other beam independent of movements of the first and second reflection surfaces relative to the interferometer.

10. The apparatus of claim 5 in which the first reflection surface, the second reflection surface, and the interferometer are arranged so that after the measurement beam and the other beam overlaps, the relative beam shear between the measurement beam and the other beam remains constant independent of a movement of the measurement object.

11. The apparatus of claim 1 in which the measurement object comprises a retroreflector.

12. The apparatus of claim 11 in which a first portion of the measurement beam propagating toward the retroreflector during the first pass contacts the retroreflector at a first location, a second portion of the measurement beam propagating away from the retroreflector during the first pass contacts the retroreflector at a second location, and the first and second locations are separated by a first distance.

13. The apparatus of claim 12 in which the measurement beam and the other beam overlaps to form an output beam that is separated from the input beam by a second distance.

14. The apparatus of claim 13 in which the second distance is smaller than the first distance.

15. The apparatus of claim 1 in which the reference object comprises a retroreflector or a plane reflection surface.

16. The apparatus of claim 1 in which the reference path is sheared during the first and second passes when the reference object moves.

17. The apparatus of claim 16 in which the shear in the reference path is caused by a movement of the reference object in a direction orthogonal to the direction of the path of a portion of the reference beam that is incident on the reference object during the first pass.

18. The apparatus of claim 16 further comprising second optics to redirect the other beam after the first pass and before the second pass so that the shear imparted during the second pass cancels the shear imparted during the first pass.

19. The apparatus of claim 18 in which the second optics further redirect the other beam after the second pass and before overlapping with the measurement beam.

20. The apparatus of claim 1 in which the optics further redirects the measurement beam after the second pass and before overlapping with the other beam so that the measurement beam propagates in a direction that remains constant relative to a propagation direction of the other beam independent of a change in the orientation of the optics.

21. The apparatus of claim 1 in which the optics further redirects the measurement beam after the second pass and before overlapping with the other beam so that a relative beam shear between the measurement beam and the other beam remains constant independent of a movement of the measurement object.

22. The apparatus of claim 1 in which the optics comprise an odd number of reflection surfaces to receive a first portion of the measurement beam traveling away from the measurement object after the first pass and to redirect a second portion of the measurement beam toward the measurement object during the second pass such that the first and second portions of the measurement beam are substantially parallel.

23. The apparatus of claim 1 in which the measurement beam and the other beam have different frequencies.

24. The apparatus of claim 1 in which the measurement object comprises a constant deviation reflector.

25. The apparatus of claim 24 in which the optics comprise a first reflection surface and a second reflection surface that is oriented at an angle relative to the first reflection surface.

26. The apparatus of claim 24 in which the optics comprise a truncated prism.

27. The apparatus of claim 24 in which the optics comprise a first reflection surface to redirect the measurement beam after the measurement beam travels the first pass but before the second pass.

28. The apparatus of claim 27 in which the optics comprise a second reflection surface to redirect the measurement beam after the measurement beam completes the first and second passes but before overlapping with the other beam.

29. The apparatus of claim 28 in which the constant deviation reflector reflects an input beam into an output beam such that the paths of the input and output beams form a first angle that remains constant independent of a propagation direction of the input beam.

30. The apparatus of claim 29 in which the first and second reflection surfaces form a second angle that is equal to the first angle.

31. The apparatus of claim 24 in which the constant deviation reflector and the optics are arranged so that after the measurement beam and the other beam overlaps, the measurement beam propagates in a direction parallel to the propagation direction of the other beam independent of a rotation of the optics relative to the interferometer.

32. The apparatus of claim 24 in which the constant deviation reflector and the optics are arranged so that after the measurement beam and the other beam overlaps, the relative beam shear between the measurement beam and the other beam remains constant independent of a movement of the constant deviation reflector.

33. The apparatus of claim 1 in which during the first pass, the measurement beam travels away from the interferometer and toward the measurement object, and is directed by the measurement object so that the measurement beam travels away from the measurement object and toward the optics.

34. The apparatus of claim 1 in which during the second pass, the measurement beam travels away from the optics and toward the measurement object, and is directed by the measurement object so that the measurement beam travels away from the measurement object and toward the interferometer.

35. The apparatus of claim 1 further comprising a detector that responds to optical interference between the overlapping beams and produces an interference signal indicative of an optical path length difference between the paths of the beams.

36. The apparatus of claim 35 in which the detector comprises a photodetector, an amplifier, and an analog-to-digital converter.

37. The apparatus of claim 35 further comprising an analyzer coupled to the detector to estimate a change in an optical path length difference of the beams based on the interference signal.

38. The apparatus of claim 1 further comprising a source to provide the beams.

39. The apparatus of claim 1 further comprising:

a stage to support a wafer for fabricating integrated circuits thereon;

an illumination system to image spatially patterned radiation onto the wafer; and

a positioning system to adjust the position of the stage relative to the imaged radiation, in which the interferometer is used to measure the position of the stage.

40. The apparatus of claim 1 further comprising:

a stage to support a wafer for fabricating integrated circuits thereon; and

an illumination system including a radiation source, a mask, a positioning system, and a lens assembly in which during operation the source directs radiation through the mask to produce spatially patterned radiation, the positioning system adjusts the position of the mask relative to wafer, the lens assembly images the spatially patterned radiation onto the wafer, and the interferometer is used to measure the position of the mask relative to the wafer.

41. The apparatus of claim 1 further comprising:

a source to provide a write beam to pattern a substrate,

a stage to support the substrate,

a beam directing assembly to deliver the write beam to the substrate, and

a positioning system to position the stage and beam directing assembly relative to one another, in which the interferometer and the optics are used to measure the position of the stage relative to the beam directing assembly.

77. A lithography system for use in fabricating integrated circuits on a wafer, comprising:

a stage to support the wafer;

an illumination system to image spatially patterned radiation onto the wafer;

a positioning system to adjust the position of the stage relative to the imaged radiation; and

the apparatus of claim 1 to measure the position of the stage along a first degree of freedom.

78. The lithography system of claim 77 further comprising a second one of the apparatus of claim 1 to measure the position of the stage along a second degree of freedom.

79. A lithography system for use in fabricating integrated circuits on a wafer, comprising:

a stage to support the wafer;

an illumination system including a radiation source, a mask, a positioning system, a lens assembly, and the apparatus of claim 1 in which during operation the source directs radiation through the mask to produce spatially patterned radiation, the positioning system adjusts the position of the mask relative to wafer, the lens assembly images the spatially patterned radiation onto the wafer, and the apparatus of claim 1 measures the position of the mask along a first degree of freedom relative to the wafer.

80. The lithography system of claim 79 further comprising a second one of the apparatus of claim 1 to measure the position of the mask along a second degree of freedom.

81. A lithography system for use in fabricating a lithography mask, comprising:

a source to provide a write beam to pattern the substrate,

a stage to support the substrate,

a beam directing assembly to deliver the write beam to the substrate;

a positioning system to position the stage and beam directing assembly relative to one another; and

the apparatus of claim 1 to measure the position of the stage along a first degree of freedom relative to the beam directing assembly.

82. The lithography system of claim 81 further comprising a second one of the apparatus of claim 1 to measure the position of the stage along a second degree of freedom.

42. An apparatus comprising:

an interferometer to split an input beam into a measurement beam and at least one other beam, to direct the measurement beam along a measurement path that includes at least two passes to a measurement object, and to overlap the measurement beam with the other beam after the measurement beam completes the at least two passes; and

optics to redirect the measurement beam after the first pass and before the second pass so that during the second pass, a portion of the measurement path traversed by the measurement beam propagating from the measurement object toward the interferometer remains the same independent of a movement of the measurement object,

the optics also to redirect the measurement beam after the second pass and before overlapping with the other beam.

43. The apparatus of claim 42 in which the optics is designed so that during the second pass, the portion of the measurement path traversed by the measurement beam propagating from the measurement object toward the interferometer remains the same independent of a movement of the measurement object along a direction that is orthogonal to a portion of the measurement path that is incident on the measurement object during the first pass.

44. The apparatus of claim 42 in which the measurement object comprises a retroreflector.

45. The apparatus of claim 42 in which the optics comprise a first reflection surface and a second reflection surface, the first reflection surface to redirect the measurement beam after the first pass and before the second pass, the second reflection surface to redirect the measurement beam after the second pass and before overlapping with the other beam.

46. The apparatus of claim 42 in which the optics are arranged so that when the measurement beam overlaps with the other beam, the measurement beam propagates in a direction that remains constant relative to a propagation direction of the other beam independent of a change in the orientation of the optics.

47. The apparatus of claim 45 in which the optics comprise a mirror having a front reflection surface and a rear reflection surface.

48. The apparatus of claim 47 in which the front and rear reflection surfaces are parallel to each other.

49. The apparatus of claim 47 in which the measurement beam contacts each of the front and rear reflection surfaces of the mirror at least once before overlapping with the other beam.

50. The apparatus of claim 42 in which the interferometer directs the other beam along a reference path.

51. The apparatus of claim 50 in which the measurement path and the reference path define an optical path length difference, and changes in the optical path length difference are indicative of changes in the relative positions of the measurement and reference objects.

52. The apparatus of claim 42 in which the measurement object comprises a constant deviation reflector.

53. The apparatus of claim 42 in which the optics comprise two reflection surfaces oriented at an angle relative to one another.

54. An apparatus comprising:

an interferometer to split an input beam into a measurement beam and at least one other beam, to direct the measurement beam along a measurement path that includes at least two passes to a measurement object, and to overlap the measurement beam with the other beam after the measurement beam completes the at least two passes;

a first optic to redirect the measurement beam after the first pass and before the second pass; and

a second optic to redirect the measurement beam after the second pass and before the measurement beam combines with the other beam, the first and second optics are designed such that when the orientations of the first and second optics are determined, relative beam shear between the measurement beam and the other beam remains the same independent of a movement of the measurement object along a direction that is orthogonal to a portion of the measurement path that is incident on the measurement object during the first pass.

55. The apparatus of claim 54 in which the first optic comprises a reflection surface or an odd number of reflection surfaces.

56. The apparatus of claim 55 in which the second optic comprises a reflection surface or an odd number of reflection surfaces.

57. The apparatus of claim 54 in which the first and second optics move in a fixed relationship relative to one another.

58. The apparatus of claim 57 in which the measurement beam and the other beam propagate in the same directions independent of movements of the first and second optics.

59. An apparatus comprising:

an interferometer to split an input beam into a measurement beam and at least one other beam, to direct the measurement beam along a measurement path that includes at least two passes to a cube corner retroreflector having reflection surfaces, and to overlap the measurement beam with the other beam after the measurement beam completes the at least two passes;

an odd number of reflection surfaces to redirect the measurement beam traveling away from the retroreflector after the first pass and before the second pass so that during the second pass, the measurement beam travels toward a reflection surface of the retroreflector that was the last in sequence to be contacted by the measurement beam during the first pass; and

a reflection surface to redirect the measurement beam after the second pass and before overlapping with the other beam.

60. An apparatus comprising:

an interferometer to split an input beam into at least a first beam and a second beam, to direct the first beam along a first path that reflects from a first object, to direct the second beam along a second path that reflects from a second object, and to overlap the first and second beams after being reflected by the first and second objects, respectively, and

portions of the second beam traveling through a region in a direction non-parallel to the direction of the portion of the first beam that is incident on the first object; and

optics to direct portions of the first beam through the region such that a change in the environmental conditions of the region causes equal amounts of change in the optical path lengths of the first and second beams.

61. The apparatus of claim 60 in which the region comprises air or inert gas.

62. The apparatus of claim 60 in which the environmental conditions include temperature.

63. The apparatus of claim 60 in which the first object comprises a retroreflector.

64. The apparatus of claim 60 in which the first path includes at least two passes to the first object.

65. The apparatus of claim 64 in which the optics include a first reflection surface that redirects the first beam after the first pass and before the second pass so that shear imparted to the first beam during the second pass cancels shear imparted to the first beam during the first pass.

66. The apparatus of claim 65 in which the shear is caused by a movement of the first object along a direction orthogonal to a portion of the first beam that is incident on the first object during the first pass.

67. The apparatus of claim 65 in which the optics include a second reflection surface that directs the first beam from a direction parallel to the direction of the portion of the first beam that is incident on the first object to a direction that is parallel to the portions of the second path passing through the region.

68. The apparatus of claim 67 in which the optics include a third reflection surface that redirects the first beam after the first beam completes the at least two passes and before overlapping with the second beam.

69. The apparatus of claim 68 in which the first reflection surface has an orientation that remains constant relative to an orientation of the third reflection surface.

70. The apparatus of claim 69 in which the first and third reflection surfaces are oriented so that when the first beam overlaps with the second beam, the first beam propagates in a direction that is constant relative to a propagation direction of the second beam independent of a change in the orientation of the first reflection and third reflection surfaces.

71. An apparatus comprising:

an interferometer to split an input beam into at least a first beam and a second beam, to direct the first beam along a first path that reflects from a first object, to direct the second beam along a second path that reflects from a second object, and to overlap the first and second beams after being reflected by the first and second objects, respectively,

the first path including two passes to the first object, the first path during the first pass including two portions that contact the first object, the two portions lying along a first plane, the second path including two passes to the second object, the second path during the first pass including two portions that contact the second object, the two portions lying along a second plane,

the first path being sheared during the first and second passes when the first object moves along a direction orthogonal to one of the two portions of the first path that contacts the first object; and

optics to redirect the first beam after the first pass and before the second pass so that shear imparted during the second pass cancels shear imparted during the first pass.

72. The apparatus of claim 71 in which the first plane is parallel to the second plane and spaced apart from the second plane.

73. The apparatus of claim 71 in which the second path is sheared during the first and second passes when the second object moves along a direction orthogonal to a portion of the second path that contacts the second object.

74. The apparatus of claim 71 in which the interferometer comprises a beam splitter to split the input beam.

75. The apparatus of claim 74 in which the first object comprises retroreflector.

76. The apparatus of claim 75 in which a usable clear aperture of the retroreflector is larger than a clear aperture of the beam splitter.

83. An interferometry system for measuring changes in a position of a measurement object, comprising:

an interferometer to split an input beam into a measurement beam and at least a reference beam, to direct the measurement beam along a measurement path that includes at least two passes to the measurement object, and to overlap the measurement beam with the reference beam after the measurement beam completes the at least two passes,

the path of the measurement beam being sheared during the first and second passes when the measurement object moves along a first direction or laterally along a second direction that is orthogonal to the first direction; and

optics to redirect the measurement beam after the first pass and before the second pass so that shear imparted during the second pass due to a movement if the measurement object cancels shear imparted during the first pass due to the movement.

84. The apparatus of claim 83 in which the measurement object comprises a constant deviation reflector.

85. The apparatus of claim 83 in which the optics comprise a first reflection surface and a second reflection surface that is oriented at an angle relative to the first reflection surface.

86. A method comprising;

directing a measurement beam along a measurement path through an interferometer, the measurement path including at least two passes to a measurement object, the path of the measurement beam being sheared during the first and second passes when the measurement object moves;

directing at least one other beam through the interferometer;

redirecting the measurement beam after the first pass and before the second pass so that shear imparted during the second pass cancels shear imparted during the first pass; and

overlapping the measurement beam with the other beam after the measurement beam completes the at least two passes.

87. The method of claim 86 in which the path of the measurement beam is sheared during the first and second passes when the measurement object moves along a direction orthogonal to a portion of the measurement path that is incident on the measurement object during the first pass.

88. The method of claim 86 further comprising redirecting the measurement beam after the measurement beam completes the at least two passes and before overlapping with the other beam so that when the measurement beam overlaps with the other beam, the measurement beam propagates in a direction that remains constant relative to a propagation direction of the other beam.

89. The method of claim 86 further comprising separating an input beam into the measurement beam and the at least one other beam.

90. The method of claim 86 further comprising directing the other beam along a reference path that includes at least two passes to a reference object.

91. The method of claim 90 in which the reference object comprises a retroreflector or a plane reflection surface.

92. The method of claim 90 in which the measurement object comprises a retroreflector or a constant deviation reflector.

93. The method of claim 90 further comprising determining an optical path length difference between the measurement and reference paths.

94. The method of claim 93 further comprising determining changes in the position of the measurement object relative to the reference object based on changes in the optical path length difference.

95. The method of claim 86 in which the measurement beam and the other beam have different frequencies.

96. The method of claim 86 further comprising detecting an interference signal from the overlapping beams.

97. The method of claim 96 further comprising determining changes in the position of the measurement object based on the interference signal.

98. The method of claim 86 further comprising:

supporting a wafer on a stage;

imaging spatially patterned radiation onto the wafer;

adjusting the position of the stage relative to the imaged radiation; and

measuring the relative position of the stage using the overlapping beams.

99. The method of claim 86 further comprising:

supporting a wafer on a stage;

directing radiation from a source through a mask to produce spatially patterned radiation;

positioning the mask relative to the wafer;

measuring the position of the mask relative to the wafer using the overlapping beams; and

imaging the spatially patterned radiation onto the wafer.

100. The method of claim 86 further comprising:

providing a write beam to pattern a substrate;

supporting the substrate on a stage;

delivering the write beam to the substrate;

positioning the stage relative to the write beam; and

measuring the relative position of the stage using the overlapping beams.

118. A lithography method for fabricating integrated circuits on a wafer, comprising:

supporting the wafer on a stage;

imaging spatially patterned radiation onto the wafer;

adjusting the position of the stage relative to the imaged radiation; and

measuring the relative position of the stage along a first degree of freedom using the method of claim 86.

119. The lithography method of claim 118 further comprising using the method of claim 86 to measure the relative position of the stage along a second degree of freedom.

120. A lithography method for fabricating integrated circuits on a wafer, comprising:

supporting the wafer on a stage;

directing radiation from a source through a mask to produce spatially patterned radiation;

positioning the mask relative to the wafer;

measuring the position of the mask along a first degree of freedom relative to the wafer using the method of claim 86;

and

imaging the spatially patterned radiation onto the wafer.

121. The lithography method of claim 120 further comprising using the method of claim 86 to measure the relative position of the mask along a second degree of freedom.

122. A beam writing method comprising:

providing a write beam to pattern a substrate;

supporting the substrate on a stage;

delivering the write beam to the substrate;

positioning the stage relative to the write beam; and

measuring the relative position of the stage along a first degree of freedom using the method of claim 86.

123. The beam writing method of claim 122 further comprising using the method of claim 86 to measure the relative position of the stage along a second degree of freedom.

101. A method comprising:

directing a measurement beam along a measurement path through an interferometer, the measurement path including at least two passes to a measurement object;

directing at least one other beam through the interferometer;

redirecting the measurement beam after the first pass and before the second pass so that during the second pass, a portion of the measurement path traversed by the measurement beam propagating from the measurement object toward the interferometer remains the same independent of a movement of the measurement object; and

overlapping the measurement beam and the other beam after the measurement beam completes the at least two passes.

102. The method of claim 101 in which the measurement beam is redirected so that during the second pass, a portion of the measurement path traversed by the measurement beam propagating from the measurement object toward the interferometer remains the same independent of a movement of the measurement object along a direction that is orthogonal to a portion of the measurement path that is incident on the measurement object.

103. The method of claim 101 further comprising redirecting the measurement beam after the measurement beam completes the at least two passes and before overlapping with the other beam so that when the measurement beam overlaps with the other beam, the measurement beam propagates in a direction that remains constant relative to a propagation direction of the other beam.

104. The method of claim 101 in which the measurement object comprises a retroreflector or a constant deviation reflector.

105. A method comprising:

directing a measurement beam along a measurement path through an interferometer, the measurement path including at least two passes to a measurement object;

directing at least one other beam through the interferometer;

redirecting the measurement beam after the first pass and before the second pass so that relative beam shear between the measurement path and the other path remains the same independent of a movement of the measurement object; and

overlapping the measurement beam and the other beam after the measurement beam completes the at least two passes.

106. The method of claim 105 in which redirecting the measurement beam after the first pass and before the second pass comprises redirecting the measurement beam so that relative beam shear between the measurement path and the other path remains the same independent of a movement of the measurement object along a direction that is orthogonal to a portion of the measurement path that is incident on the measurement object.

107. The method of claim 105 further comprising redirecting the measurement beam after the measurement beam completes the at least two passes and before overlapping with the other beam so that when the measurement beam overlaps with the other beam, the measurement beam propagates in a direction that remains constant relative to a propagation direction of the other beam.

108. The method of claim 105 in which the measurement object comprises a retroreflector or a constant deviation reflector.

109. A method comprising:

separating an input beam into a measurement beam and at least one other beam;

directing the measurement beam along a measurement path that includes at least two passes to a cube corner retroreflector having reflection surfaces;

redirecting the measurement beam traveling away from the retroreflector after the first pass and before the second pass so that during the second pass, the measurement beam travels toward a reflection surface of the retroreflector that was the last in sequence to be contacted by the measurement beam during the first pass; and

overlapping the measurement beam with the other beam after the measurement beam completes the at least two passes.

110. A method comprising:

directing a first beam along a first path through an interferometer, the first path contacting a first object;

directing a second beam along a second path through the interferometer, the second path contacting a second object, portions of the second path traveling through a region in a direction non-parallel to the direction of the portion of the first beam contacting the first object;

directing portions of the first beam through the region such that a change in the environmental conditions of the region causes equal amounts of change in the optical path lengths of the first and second beams; and

overlapping the first and second beams after being reflected by the first and second objects, respectively.

111. The method of claim 110 in which the environmental conditions include temperature.

112. The method of claim 110 in which the first path includes at least two passes to the first object.

113. The method of claim 112 further comprising redirecting the first beam after the first pass and before the second pass so that shear imparted to the first beam during the first pass is canceled by shear imparted to the first beam during the second pass.

114. The method of claim 113 in which the shear is caused by a shift in the position of the first object in a direction orthogonal to the direction of a portion of the first beam contacting the first object.

115. The method of claim 114 further comprising directing the first beam from a direction parallel to the direction of the portion of the first beam contacting the first object to a direction that is parallel to the portions of the second path passing through the region.

116. The method of claim 112 further comprising redirecting the first beam after the first beam completes the at least two passes and before overlapping with the second beam so that when the first beam overlaps with the second beam, the first beam propagates in a direction that is constant relative to a propagation direction of the second beam.

117. The method of claim 112 further comprising redirecting the first beam after the first pass and before the second pass so that when the first and second beams overlap, a relative shear between the first and second beams remains constant independent of a movement of the first object in a direction orthogonal to the direction of a portion of the first beam that is incident on the first object.