Optical systems employing stepped diffractive surfaces

• US 6,462,874 B1
• Filed: 08/27/1999
• Issued: 10/08/2002
• Est. Priority Date: 08/28/1998
• Status: Expired due to Fees

• Current Assignee: KSM Associates, Inc.
• Original Assignee: KSM Associates, Inc.
• Inventors: Soskind, Yakov G.
• Primary Examiner(s): Spyrou, Cassandra
• Assistant Examiner(s): Juba, Jr., John
• Application Number:
  US09/384,746
• Publication Number:
  US 20020027712A1
• Time in Patent Office: 1,138 Days
• Field of Search: 359/565, 359/569, 359/570, 359/900
• US Class Current: 359/565
• CPC Class Codes: G02B 27/0037 with diffracting elements G02B27/0056 takes precedence; holographic optical elements G02B5/32; zone systems G02B5/1876
• CPC Class Codes: G02B 27/4205 having a diffractive optical element [DOE] contributing to image formation, e.g. whereby modulation transfer function MTF or optical aberrations are relevant
• CPC Class Codes: G02B 27/4211 correcting chromatic aberrations G02B27/0056, G02B27/4222, G02B27/4227 take precedence
• CPC Class Codes: G02B 27/4216 correcting geometrical aberrations
• CPC Class Codes: G02B 27/4222 in projection exposure systems, e.g. photolithographic systems
• CPC Class Codes: G02B 27/4266 Diffraction theory; Mathematical models
• CPC Class Codes: G02B 27/4283 having a diffractive element with major temperature dependent properties
• CPC Class Codes: G02B 5/1814 structurally combined with one or more further optical elements, e.g. lenses, mirrors, prisms or other diffraction gratings G02B5/189 takes precedence
• CPC Class Codes: G02B 5/1876 Diffractive Fresnel lenses; Zone plates; Kinoforms G02B5/1842, G02B5/1847 take precedence; optical systems having diffractive correction means G02B27/0037; Fresnel lenses operating by refraction G02B3/08
• CPC Class Codes: G02B 5/1895 such optical elements having dioptric power
• CPC Class Codes: Y10S 359/90 Methods

Abstract

Optical systems employing stepped diffractive surfaces (13) are provided. Ray tracing through such systems is performed using the grating equation to represent the stepped diffractive surface (SDS). In this way, the SDS can be used to correct a variety of monochromatic and chromatic aberrations by balancing the aberrations of the SDS against the aberrations of non-stepped optical surfaces in the system.

Claims

1. A method for reducing at least one aberration of an optical system which comprises:

(i) a stepped diffractive surface (SDS) which comprises a plurality of steps; and

(ii) an optical surface which has optical power and is not a stepped diffractive surface (non-SDS),

said method comprising;

(a) tracing rays through the system by representing the SDS by an equation which describes diffraction by a grating; and

(b) using the rays traced in step (a) to select one or more parameters of the system which reduce said at least one aberration;

wherein in step (a), rays are traced through individual steps of the SDS using the equation which describes diffraction by a grating.

2. The method of claim 1 wherein the at least one aberration is a monochromatic aberration.

3. The method of claim 2 wherein the at least one aberration is spherical aberration.

4. The method of claim 2 wherein the at least one aberration is field curvature.

5. The method of claim 2 wherein the at least one aberration is coma.

6. The method of claim 2 wherein the at least one aberration is astigmatism.

7. The method of claim 1 wherein the at least one aberration is a chromatic aberration.

8. The method of claim 7 wherein the at least one aberration is longitudinal chromatic aberration.

9. The method of claim 7 wherein the at least one aberration is lateral chromatic aberration.

10. The method of claim 1 wherein the optical system has a field of view of at least five degrees.

11. The method of claim 1 wherein the rays at the SDS correspond to a planar wavefront.

12. The method of claim 11 wherein the optical system has an optical axis and the rays at the SDS are parallel to that axis.

13. The method of claim 11 wherein the optical system has an optical axis and the rays at the SDS are at an angle to that axis.

14. The method of claim 1 wherein the rays at the SDS correspond to a non-planar wavefront.

15. The method of claim 1 wherein the rays at the SDS correspond to a converging beam.

16. The method of claim 1 wherein the rays at the SDS correspond to a diverging beam.

17. The method of claim 1 wherein the SDS'"'"'s contribution to the at least one aberration is substantially balanced against the non-SDS'"'"'s contribution to the at least one aberration.

18. The method of claim 1 wherein the optical system comprises a plurality of non-SDSs and the SDS'"'"'s contribution to the at least one aberration is substantially balanced against the combined contributions of the non-SDSs to the at least one aberration.

19. The method of claim 1 wherein the optical system comprises a plurality of SDSs each of which comprises a plurality of steps and the combined contributions of the SDSs to the at least one aberration is substantially balanced against the contribution of the non-SDS to the at least one aberration.

20. The method of claim 1 wherein the optical system comprises a plurality of SDSs each of which comprises a plurality of steps and a plurality of non-SDSs and the combined contributions of the SDSs to the at least one aberration is substantially balanced against the combined contributions of the non-SDSs to the at least one aberration.

21. The method of claim 1 wherein the at least one aberration is a chromatic aberration, the SDS contributes to reduction of the aberration, and the system comprises at least two optical materials with different dispersive properties which contribute to the reduction of the aberration.

22. The method of claim 1 wherein the at least one aberration comprises at least one monochromatic aberration and at least one chromatic aberration.

23. The method of claim 1 wherein the at least one aberration comprises two monochromatic aberrations.

24. The method of claim 1 wherein the at least one aberration comprises two chromatic aberrations.

25. The method of claim 1 wherein the SDS has a base curve which is an asphere.

26. The method of claim 1 wherein the SDS has a non-constant step height within a diffraction order.

27. The method of claim 1 wherein the SDS has a base curve which is an asphere and a non-constant step height within a diffraction order.

28. The method of claim 1 wherein:

(1) the optical system has a field of view and a nominal wavelength λ

₀; and

(2) the SDS has a constant step height selected to increase the SDS'"'"'s average diffraction efficiency over the field of view at λ

₀.

29. The method of claim 1 wherein:

(1) the optical system has a field of view and a nominal wavelength λ

₀; and

(2) the SDS has a constant step height selected so that the maximum diffraction efficiency at λ

₀ occurs at an intermediate field point within the field of view.

30. The method of claim 1 comprising the additional step of displaying the optical system having the one or more parameters selected in step (b).

31. The method of claim 1 comprising the additional step of producing the optical system having the one or more parameters selected in step (b).

36. The method of claim 1 or 32 wherein the SDS has:

(1) a base curve defined by the equation φ

(R,z)=0, where R is a radial coordinate and z is an axial coordinate,

(2) step depths d_i, and

(3) step widths λ

_i(R,d_i) given by the equation;

$w_i<br><br>\left(R,d_i\right)=d_i<br><br><br><br>\frac{\frac{\partial <br><br>\mathrm{\varphi <br><br>}<br><br>\left(R,z\right)}{\partial <br><br>z}}{\frac{\partial <br><br>\left(R,z\right)}{\partial <br><br>R}}<br><br>.$

37. The method of claim 36 wherein the step depths are constant.

38. The method of claim 36 wherein the step depths are variable.

32. A method for reducing at least one aberration of an optical system which comprises at least one optical element, said method comprising:

(a) incorporating an additional optical element in the system which comprises a stepped diffractive surface (SDS) which comprises a plurality of steps; and

(b) selecting the spacing between the SDS and the at least one optical element;

wherein step (b) is performed by tracing rays through the system by representing the SDS by an equation which describes diffraction by a grating, said equation being used to trace rays through individual steps of the SDS.

33. The method of claim 32 wherein the at least one aberration is a monochromatic aberration.

34. The method of claim 32 wherein the at least one aberration is a chromatic aberration.

35. The method of claim 34 wherein the at least one aberration is lateral chromatic aberration.

39. An optical system having an optical axis and comprising:

(a) a stepped diffractive surface (SDS) which has a clear aperture and within said clear aperture comprises N concentric planar steps orthogonal to the system'"'"'s optical axis which define a non-planar base curve, said steps satisfying the relationship;

40. The optical system of claim 39 wherein the SDS has a vertex and removal of the SDS and its replacement with a planar surface at the vertex results in an optically significant increase in the optical system'"'"'s lateral color.

41. The optical system of claim 39 wherein the SDS'"'"'s contribution to lateral color is substantially balanced against the non-SDS'"'"'s contribution to lateral color.

42. The optical system of claim 39 wherein the system comprises a plurality of non-SDSs and the SDS'"'"'s contribution to lateral color is substantially balanced against the combined contributions of the non-SDSs to lateral color.

43. The optical system of claim 39 wherein:

(i) the system comprises a plurality of SDSs;

(ii) the combined contributions of the SDSs to lateral color is substantially balanced against the contribution of the non-SDS to lateral color; and

(iii) each of the SDSs has a clear aperture and within said clear aperture comprises N concentric planar steps orthogonal to the system'"'"'s optical axis which define a non-planar base curve, said steps satisfy the relationship;

44. The optical system of claim 39 wherein:

the system comprises a plurality of SDSs and a plurality of non-SDSs;

(ii) the combined contributions of the SDSs to lateral color is substantially balanced against the combined contributions of the non-SDSs to lateral color; and

(iii) each of the SDSs has a clear aperture and within said clear aperture comprises N concentric planar steps orthogonal to the system'"'"'s optical axis which define a non-planar base curve, said steps satisfying the relationship;

45. The optical system of claim 39 wherein the system comprises at least two optical materials with different dispersive properties which contribute to the correction of lateral color.

46. The optical system of claim 39 wherein the SDS'"'"'s contribution to lateral color is determined using an equation which describes diffraction by a grating, said equation being used to trace rays through individual steps of the SDS.

47. An optical system having an optical axis and comprising:

(a) a stepped diffractive surface (SDS) which has a clear aperture and within said clear aperture comprises N concentric planar steps orthogonal to the systems'"'"'s optical axis which define a non-planar base curve, said steps satisfying the relationship;

48. The optical system of claim 47 wherein the SDS has a vertex and removal of the SDS and its replacement with a planar surface at the vertex results in an optically significant increase in the optical system'"'"'s astigmatism.

49. The optical system of claim 47 wherein the SDS'"'"'s contribution to astigmatism is substantially balanced against the non-SDS'"'"'s contribution to astigmatism.

50. The optical system of claim 47 wherein the system comprises a plurality of non-SDSs and the SDS'"'"'s contribution to astigmatism is substantially balanced against the combined contributions of the non-SDSs to astigmatism.

51. The optical system of claim 47 wherein:

(i) the system comprises a plurality of SDSs;

(ii) the combined contributions of the SDSs to astigmatism is substantially balanced against the contribution of the non-SDS to astigmatism; and

(iii) each of the SDSs has a clear aperture and within said clear aperture comprises N concentric planar steps orthogonal to the system'"'"'s optical axis which define a non-planar base curve, said steps satisfying the relationship;

52. The optical system of claim 47 wherein:

(i) the system comprises a plurality of SDSs and a plurality of non-SDSs;

(ii) the combined contributions of the SDSs to astigmatism is substantially balanced against the combined contribution of the non-SDS to astigmatism; and

(iii) each of the SDSs has a clear aperture and within said clear aperture comprises N concentric planar steps orthogonal to the system'"'"'s optical axis which define a non-planar base curve, said steps satisfying the relationship;

53. The optical system of claim 47 wherein the SDS'"'"'s contribution to astigmatism is determined using an equation which describes diffraction by a grating, said equation being used to trace rays through individual steps of the SDS.

54. An optical system having an optical axis and comprising:

(a) a stepped diffractive surface (SDS) which has a clear aperture and within said clear aperture comprises N concentric planar steps orthogonal to the system'"'"'s optical axis which define a non-planar base curve, said steps satisfying the relationship;

55. The optical system of claim 54 wherein the SDS has a vertex and removal of the SDS and its replacement with a planar surface at the vertex results in an optically significant increase in the optical system'"'"'s coma.

56. The optical system of claim 54 wherein the SDS'"'"'s contribution to coma is substantially balanced against the non-SDS'"'"'s contribution to coma.

57. The optical system of claim 54 wherein the system comprises a plurality of non-SDSs and the SDS'"'"'s contribution to coma is substantially balanced against the combined contributions of the non-SDSs to coma.

58. An optical system of claim 54 wherein:

(i) the system comprises a plurality of SDSs;

(ii) the combined contributions of the SDSs to coma is substantially balanced against the contributions of the non-SDS to coma; and

(iii) each of the SDSs has a clear aperture and within said clear aperture comprises N concentric planar steps orthogonal to the system'"'"'s optical axis which define a non-planar base curve, said steps satisfying the relationship;

59. The optical system of claim 54 wherein:

(i) the system comprises a plurality of SDSs and a plurality of non-SDSs;

(ii) the combined contributions of the SDSs to coma is substantially balanced against the combined contribution of the non-SDS to coma; and

(iii) each of the SDSs has a clear aperture and within said clear aperture comprises N concentric planar steps orthogonal to the system'"'"'s optical axis which define a non-planar base curve, said steps satisfying the relationship;

60. The optical system of claim 54 wherein the SDS'"'"'s contribution to coma is determined using an equation which describes diffraction by a grating, said equation being used to trace rays through individual steps of the SDS.

61. An optical system having an optical axis and comprising:

(a) a stepped diffractive surface (SDS) which has a clear aperture and within said clear aperture comprises N concentric planar steps orthogonal to the system'"'"'s optical axis which define a non-planar base curve, said steps satisfying the relationship;

62. The optical system of claim 61 wherein the SDS has a vertex and removal of the SDS and its replacement with a planar surface at the vertex results in an optically significant increase in the optical system'"'"'s distortion.

63. The optical system of claim 61 wherein the SDS'"'"'s contribution to distortion is substantially balanced against the non-SDS'"'"'s contribution to distortion.

64. The optical system of claim 61 wherein the system comprises a plurality of non-SDSs and the SDS'"'"'s contribution to distortion is substantially balanced against the combined contributions of the non-SDSs to distortion.

65. The optical system of claim 61 wherein:

(i) the system comprises a plurality of SDSs;

(ii) the combined contributions of the SDSs to distortion is substantially balanced against the contribution of the non-SDS to distortion; and

(iii) each of the SDSs has a clear aperture and within said clear aperture comprises N concentric planar steps orthogonal to the system'"'"'s optical axis which define a non-planar base curve, said steps satisfying the relationship;

66. The optical system of claim 61 wherein:

(a) the system comprises a plurality of SDSs and a plurality of non-SDSs;

(ii) the combined contributions of the SDSs to distortion is substantially balanced against the combined contribution of the non-SDSs to distortion; and

(iii) each of the SDSs has a clear aperture and within said clear aperture comprises N concentric planar steps orthogonal to the system'"'"'s optical axis which define a non-planar base curve, said steps satisfying the relationship;

67. The optical system of claim 61, wherein the SDS'"'"'s contribution to distortion is determined using an equation which describes diffraction by a grating, said equation being used to trace rays through individual steps of the SDS.

68. An optical system having an optical axis and comprising:

(a) a stepped diffractive surface (SDS) which has a clear aperture and within said clear aperture comprises N concentric planar steps orthogonal to the system'"'"'s optical axis which define a non-planar base curve, said steps satisfying the relationship;

69. The optical system of claim 68 wherein the SDS has a vertex and removal of the SDS and its replacement with a planar surface at the vertex results in an optically significant increase in the optical system'"'"'s spherical aberration.

70. The optical system of claim 68 wherein the SDS'"'"'s contribution to spherical aberration is substantially balanced against the non-SDS'"'"'s contribution to spherical aberration.

71. The optical system of claim 68 wherein the system comprises a plurality of non-SDSs and the SDS'"'"'s contribution to spherical aberration is substantially balanced against the combined contributions of the non-SDSs to spherical aberration.

72. The optical system of claim 68 wherein:

(i) the system comprises a plurality of SDSs;

(ii) the combined contributions of the SDSs to spherical aberration is substantially balanced against the contribution of the non-SDS to spherical aberration; and

(iii) each of the SDSs has a clear aperture and within said clear aperture comprises N concentric planar steps orthogonal to the system'"'"'s optical axis which define a non-planar base curve, said steps satisfying the relationship;

73. The optical system of claim 68 wherein:

(i) the system comprises a plurality of SDSs and a plurality of non-SDSs;

(ii) the combined contributions of the SDSs to spherically aberration is substantially balanced against the combined contribution of the non-SDSs to spherical aberration; and

(iii) each of the SDSs has a clear aperture and within said clear aperture comprises N concentric planar steps orthogonal to the system'"'"'s optical axis which define a non-planar base curve, said steps satisfying the relationship;

74. The optical system of claim 68, wherein the SDS'"'"'s contribution to spherical aberration is determined using an equation which describes diffraction by a grating, said equation being used to trace rays through individual steps of the SDS.

75. An optical system having an optical axis and comprising:

(a) a stepped diffractive surface (SDS) which has a clear aperture and within said clear aperture comprises N concentric planar steps orthogonal to the system'"'"'s optical axis which define a non-planar base curve, said steps satisfying the relationship;

76. The optical system of claim 75 wherein the two aberrations are primary aberrations.

77. The optical system of claim 75 wherein the two aberrations are chromatic aberrations.

78. The optical system of claim 77 wherein the two chromatic aberrations are primary chromatic aberrations.

79. The optical system of claim 75 wherein the two aberrations are monochromatic aberrations.

80. The optical system of claim 75 wherein one of the aberrations is a chromatic aberration and the other is a monochromatic aberration.

81. The optical system of claim 75 wherein the SDS has a vertex and removal of the SDS and its replacement with a planar surface at the vertex results in an optically significant increase in both of the aberrations.

82. The optical system of claim 75 wherein the SDS'"'"'s contribution to each of the aberrations is substantially balanced against the non-SDS'"'"'s contribution to each of the aberrations.

83. The optical system of claim 75 wherein the system comprises a plurality of non-SDSs and the SDS'"'"'s contribution to each of the aberrations is substantially balanced against the combined contributions of the non-SDSs to each of the aberrations.

84. The optical system of claim 75 wherein:

(i) the system comprises a plurality of SDSs;

(ii) the combined contributions of the SDSs to each of the aberrations is substantially balanced against the contribution of the non-SDS to each of the aberrations; and

(iii) each of the SDSs has a clear aperture and within said clear aperture comprises N concentric planar steps orthogonal to the system'"'"'s optical axis which define a non-planar base curve, said steps satisfying the relationship;

85. The optical system of claim 75 wherein:

(i) the system comprises a plurality of SDSs and a plurality of non-SDSs;

(ii) the combined contributions of the SDSs to each of the aberrations is substantially balanced against the combined contributions of the non-SDS to each of the aberrations; and

(iii) each of the SDSs has a clear aperture and within said clear aperture comprises N concentric planar steps orthogonal to the system'"'"'s optical axis which define a non-planar base curve, said steps satisfying the relationship;

86. The optical system of claim 75 wherein at least one of the aberrations is a chromatic aberration and the system comprises at least two optical materials with different dispersive properties which contribute to the correction of that aberration.

87. The optical system of claim 75 wherein the SDS'"'"'s contributions to the aberrations are determined using an equation which describes diffraction by a grating, said equation being used to trace rays through individual steps of the SDS.

88. The optical system of claim 75 wherein a planar wavefront is incident on the SDS.

89. The optical system of claim 88 wherein the direction of propagation of the planar wavefront is along the optical axis.

90. The optical system of claim 88 wherein the direction of propagation of the planar wavefront is oriented at a non-zero angle to the optical axis.

91. The optical system of claim 75 wherein a non-planar wavefront is incident on the SDS.

92. The optical system of claim 75 wherein a converging beam is incident on the SDS.

93. The optical system of claim 75 wherein a diverging beam is incident on the SDS.

94. The optical system of claim 75 wherein the system has a field of view of at least five degrees.

95. The optical system of claim 75 wherein the SDS has a base curve which is an asphere.

96. The optical system of claim 75 wherein the SDS has a non-constant step height within a diffraction order.

97. The optical system of claim 75 wherein the SDS has a base curve which is an asphere and a non-constant step height within a diffraction order.

98. The optical system of claim 75 wherein the step depths are constant.

99. The optical system of claim 75 wherein the step depths are variable.

100. An optical system having an optical axis and comprising:

(a) a stepped diffractive surface (SDS) which has a clear aperture and within said clear aperture comprises N concentric planar steps orthogonal to the system'"'"'s optical axis which define a non-planar base curve, said steps satisfying the relationship;

102. The optical system of claim 100 or 101 wherein:

(1) the non-planar base curve is defined by the equation φ

(R,z)=0, where R is a radial coordinate and z is an axial coordinate, and

(2) the SDS has step widths λ

_i(R,d_i) given by the equation;

$w_i<br><br>\left(R,d_i\right)=d_i<br><br><br><br>\frac{\frac{\partial <br><br>\mathrm{\varphi <br><br>}<br><br>\left(R,z\right)}{\partial <br><br>z}}{\frac{\partial <br><br>\left(R,z\right)}{\partial <br><br>R}}<br><br>.$

101. An optical system having an optical axis and comprising:

(a) a stepped diffractive surface (SDS) which has a clear aperture and within said clear aperture comprises N concentric planar steps orthogonal to the system'"'"'s optical axis which define a non-planar base curve, said steps satisfying the relationship;

103. An optical system having an optical axis and comprising:

(a) a stepped diffractive surface (SDS) which has a clear aperture and within said clear aperture comprises N concentric planar steps orthogonal to the system'"'"'s optical axis which define a non-planar base curve, said steps satisfying the relationship;

104. The optical system of claim 103 wherein the wavefront is converging or diverging.

105. The optical system of claim 103 wherein the diffraction efficiency is optimized over a spectral range.

106. The optical system of claim 103 wherein the optical system has a finite field and the diffraction efficiency is optimized over that field.

107. The optical system of claim 106 wherein the diffraction efficiency is optimized over a spectral range.

113. The optical system of claim 39, 47, 54, 61, 68, 103, 108, or 112 wherein:

(1) the non-planar base curve is defined by the equation φ

(R,z)=0, where R is a radial coordinate and z is an axial coordinate, and

(2) the SDS has step widths λ

_i(R,d_i) given by the equation;

$w_i<br><br>\left(R,d_i\right)=d_i<br><br><br><br>\frac{\frac{\partial <br><br>\mathrm{\varphi <br><br>}<br><br>\left(R,z\right)}{\partial <br><br>z}}{\frac{\partial <br><br>\left(R,z\right)}{\partial <br><br>R}}<br><br>.$

114. The optical system of claim 113 wherein the step depths are constant.

115. The optical system of claim 114 wherein the step depths are variable.

108. An optical system having an optical axis and comprising:

a stepped diffractive surface (SDS) which has a clear aperture and within said clear aperture comprises N concentric planar steps orthogonal to the system'"'"'s optical axis which define a non-planar base curve, said steps satisfying the relationship;

109. The optical system of claim 108 wherein the diffraction efficiency is optimized over a spectral range.

110. The optical system of claim 108 wherein the optical system has a finite field and the diffraction efficiency is optimized over that field.

111. The optical system of claim 110 wherein the diffraction efficiency is optimized over a spectral range.

112. An optical system having an optical axis and comprising:

(a) stepped diffractive surface (SDS) which has a clear aperture and within said clear aperture comprises N concentric planar steps orthogonal to the system'"'"'s optical axis which define a non-planar base curve, said steps satisfying the relationship;

116. A stepped diffractive surface having an optical axis and a clear aperture, said surface comprising, within said clear aperture, N concentric planar steps orthogonal to the optical axis which define a non-planar base curve defined by the equation φ

(R,z)=0, where R is a radial coordinate and z is an axial coordinate, said steps satisfying the relationship;

117. A stepped diffractive surface having an optical axis and a clear aperture, said surface comprising, within said clear aperture, N concentric planar steps orthogonal to the optical axis which define a non-planar, aspheric base curve defined by the equation φ

(R,z)=0, where R is a radial coordinate and z is an axial coordinate, said steps satisfying the relationship;

118. A method for reducing at least one aberration of an optical system which has an optical axis and comprises:

(i) a stepped diffractive surface (SDS) which has a clear aperture and within said clear aperture comprises N concentric planar steps orthogonal to the system'"'"'s optical axis which define a non-planar base curve, said steps satisfying the relationship;

119. A method for reducing at least one aberration of an optical system which has an optical axis and comprises at least one optical element, said method comprising:

(a) incorporating an additional optical element in the system which comprises a stepped diffractive surface (SDS) which has a clear aperture and within said clear aperture comprises N concentric planar steps orthogonal to the system'"'"'s optical axis which define a non-planar base curve, said steps satisfying the relationship;