Abstract

The thermal properties of lenses play an important role in the performance of optical systems. We discuss the effects of uniform temperature changes and thermal gradients on diffractive lens performance. Comparisons are made between the thermal sensitivity of refractive and diffractive lenses. Useful design equations are presented that describe focal length, phase coefficients, and diffraction efficiency as functions of temperature. We present important thermal data for a number of lens materials. The optothermal expansion coefficient is used to design athermalized lenses that combine refractive and diffractive surfaces.

© 1993 Optical Society of America

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References

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  1. P. Morkry, “Unique applications of computer-generated diffractive optical elements,” in Holographic Optics: Optically and Computer Generated, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1052, 163–170 (1989).
  2. A. McKay, J. White, “Effects of simulated space environments on dichromated gelatin holograms,” in Optomechanical Design of Laser Trnsmitters and Receivers, B. D. Seery, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1044, 269–275 (1989).
  3. M. Tanigami, S. Ogata, S. Aoyama, T. Yamashita, K. Imanaka, “Low-wavefront aberration and high temperature stability molded micro Fresno lens,” IEEE Photon. Technol. Lett. 1, 384–385 (1989).
    [CrossRef]
  4. J. Jahns, Y. H. Lee, C. A. Burns, J. Jewell, “Optical interconnects using top-surface-emitting microlasers and planar optics,” Appl. Opt. 31, 592–597 (1992).
    [CrossRef] [PubMed]
  5. C. Londono, W. T. Plummer, P. P. Clark, “Athermalization with diffractive optics,” in Diffractive Optics: Design, Fabrication, and Applications, Vol. 9 of 1992 Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 7.
  6. G. P. Behrmann, J. P. Bowen, “Thermal effects in diffractive lenses,” in Diffractive Optics: Design, Fabrication, and Applications, Vol. 9 of 1992 Technical Digest Series (Optical Society of America, Washington, D. C., 1992), pp. 8–10.
  7. T. H. Jamieson, “Thermal effects in optical systems,” Opt. Eng. 20, 156–160 (1981).
  8. D. S. Grey, “Athermalization of optical systems,” J. Opt. Soc. Am. 38, 542–546 (1948).
    [CrossRef] [PubMed]
  9. M. Roberts, “Athermalization of infrared optics: a review,” in Recent Trends in Optical Systems Design and Computer Lens Design Workshop II, R. E. Fischer, R. C. Juergens, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1049, 72–81 (1989).
  10. Jamieson’s entries for acrylic and polycarbonate appear to be in error.
  11. G. J. Swanson, “Binary optics technology: the theory and design of multi-level diffractive optical elements,” Tech. Rep. 854 (MIT Lincoln Laboratory, Cambridge, Mass., 1989).
  12. S. M. Arnold, “How to test an asphere with a computer generated hologram,” in Holographic Optics: Optically and Computer Generated, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1052, 191–195 (1989).
  13. M. Muranaka, M. Takagi, T. Maruyama, “Precision molding of aspherical plastic lens for camcorder and projection TV,” in Replication and Molding of Optical Components, M. J. Riedl, ed., Proc. Soc. Photo-Opt. Instrum. Eng.896, 123–131 (1988).
  14. P. P. Clark, C. Londono, “Production of kinoforms by single point diamond machining,” Opt. News 15(12), 39–40 (1989).
    [CrossRef]
  15. T. Stone, N. George, “Hybrid diffractive-refractive lenses and achromats,” Appl. Opt. 27, 2960–2971 (1988).
    [CrossRef] [PubMed]
  16. A. E. Ennos, “Stresses developed in optical film coatings,” Appl. Opt. 5, 51–61 (1966).
    [CrossRef] [PubMed]
  17. W. E. Asher, “Epoxy replication: advantages and limitations,” in Replication and Molding of Optical Components, M. J. Riedl, ed., Proc. Soc. Photo-Opt. Instrum. Eng.896, 2–11 (1988).

1992

1989

P. P. Clark, C. Londono, “Production of kinoforms by single point diamond machining,” Opt. News 15(12), 39–40 (1989).
[CrossRef]

M. Tanigami, S. Ogata, S. Aoyama, T. Yamashita, K. Imanaka, “Low-wavefront aberration and high temperature stability molded micro Fresno lens,” IEEE Photon. Technol. Lett. 1, 384–385 (1989).
[CrossRef]

1988

1981

T. H. Jamieson, “Thermal effects in optical systems,” Opt. Eng. 20, 156–160 (1981).

1966

1948

Aoyama, S.

M. Tanigami, S. Ogata, S. Aoyama, T. Yamashita, K. Imanaka, “Low-wavefront aberration and high temperature stability molded micro Fresno lens,” IEEE Photon. Technol. Lett. 1, 384–385 (1989).
[CrossRef]

Arnold, S. M.

S. M. Arnold, “How to test an asphere with a computer generated hologram,” in Holographic Optics: Optically and Computer Generated, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1052, 191–195 (1989).

Asher, W. E.

W. E. Asher, “Epoxy replication: advantages and limitations,” in Replication and Molding of Optical Components, M. J. Riedl, ed., Proc. Soc. Photo-Opt. Instrum. Eng.896, 2–11 (1988).

Behrmann, G. P.

G. P. Behrmann, J. P. Bowen, “Thermal effects in diffractive lenses,” in Diffractive Optics: Design, Fabrication, and Applications, Vol. 9 of 1992 Technical Digest Series (Optical Society of America, Washington, D. C., 1992), pp. 8–10.

Bowen, J. P.

G. P. Behrmann, J. P. Bowen, “Thermal effects in diffractive lenses,” in Diffractive Optics: Design, Fabrication, and Applications, Vol. 9 of 1992 Technical Digest Series (Optical Society of America, Washington, D. C., 1992), pp. 8–10.

Burns, C. A.

Clark, P. P.

P. P. Clark, C. Londono, “Production of kinoforms by single point diamond machining,” Opt. News 15(12), 39–40 (1989).
[CrossRef]

C. Londono, W. T. Plummer, P. P. Clark, “Athermalization with diffractive optics,” in Diffractive Optics: Design, Fabrication, and Applications, Vol. 9 of 1992 Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 7.

Ennos, A. E.

George, N.

Grey, D. S.

Imanaka, K.

M. Tanigami, S. Ogata, S. Aoyama, T. Yamashita, K. Imanaka, “Low-wavefront aberration and high temperature stability molded micro Fresno lens,” IEEE Photon. Technol. Lett. 1, 384–385 (1989).
[CrossRef]

Jahns, J.

Jamieson, T. H.

T. H. Jamieson, “Thermal effects in optical systems,” Opt. Eng. 20, 156–160 (1981).

Jewell, J.

Lee, Y. H.

Londono, C.

P. P. Clark, C. Londono, “Production of kinoforms by single point diamond machining,” Opt. News 15(12), 39–40 (1989).
[CrossRef]

C. Londono, W. T. Plummer, P. P. Clark, “Athermalization with diffractive optics,” in Diffractive Optics: Design, Fabrication, and Applications, Vol. 9 of 1992 Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 7.

Maruyama, T.

M. Muranaka, M. Takagi, T. Maruyama, “Precision molding of aspherical plastic lens for camcorder and projection TV,” in Replication and Molding of Optical Components, M. J. Riedl, ed., Proc. Soc. Photo-Opt. Instrum. Eng.896, 123–131 (1988).

McKay, A.

A. McKay, J. White, “Effects of simulated space environments on dichromated gelatin holograms,” in Optomechanical Design of Laser Trnsmitters and Receivers, B. D. Seery, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1044, 269–275 (1989).

Morkry, P.

P. Morkry, “Unique applications of computer-generated diffractive optical elements,” in Holographic Optics: Optically and Computer Generated, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1052, 163–170 (1989).

Muranaka, M.

M. Muranaka, M. Takagi, T. Maruyama, “Precision molding of aspherical plastic lens for camcorder and projection TV,” in Replication and Molding of Optical Components, M. J. Riedl, ed., Proc. Soc. Photo-Opt. Instrum. Eng.896, 123–131 (1988).

Ogata, S.

M. Tanigami, S. Ogata, S. Aoyama, T. Yamashita, K. Imanaka, “Low-wavefront aberration and high temperature stability molded micro Fresno lens,” IEEE Photon. Technol. Lett. 1, 384–385 (1989).
[CrossRef]

Plummer, W. T.

C. Londono, W. T. Plummer, P. P. Clark, “Athermalization with diffractive optics,” in Diffractive Optics: Design, Fabrication, and Applications, Vol. 9 of 1992 Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 7.

Roberts, M.

M. Roberts, “Athermalization of infrared optics: a review,” in Recent Trends in Optical Systems Design and Computer Lens Design Workshop II, R. E. Fischer, R. C. Juergens, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1049, 72–81 (1989).

Stone, T.

Swanson, G. J.

G. J. Swanson, “Binary optics technology: the theory and design of multi-level diffractive optical elements,” Tech. Rep. 854 (MIT Lincoln Laboratory, Cambridge, Mass., 1989).

Takagi, M.

M. Muranaka, M. Takagi, T. Maruyama, “Precision molding of aspherical plastic lens for camcorder and projection TV,” in Replication and Molding of Optical Components, M. J. Riedl, ed., Proc. Soc. Photo-Opt. Instrum. Eng.896, 123–131 (1988).

Tanigami, M.

M. Tanigami, S. Ogata, S. Aoyama, T. Yamashita, K. Imanaka, “Low-wavefront aberration and high temperature stability molded micro Fresno lens,” IEEE Photon. Technol. Lett. 1, 384–385 (1989).
[CrossRef]

White, J.

A. McKay, J. White, “Effects of simulated space environments on dichromated gelatin holograms,” in Optomechanical Design of Laser Trnsmitters and Receivers, B. D. Seery, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1044, 269–275 (1989).

Yamashita, T.

M. Tanigami, S. Ogata, S. Aoyama, T. Yamashita, K. Imanaka, “Low-wavefront aberration and high temperature stability molded micro Fresno lens,” IEEE Photon. Technol. Lett. 1, 384–385 (1989).
[CrossRef]

Appl. Opt.

IEEE Photon. Technol. Lett.

M. Tanigami, S. Ogata, S. Aoyama, T. Yamashita, K. Imanaka, “Low-wavefront aberration and high temperature stability molded micro Fresno lens,” IEEE Photon. Technol. Lett. 1, 384–385 (1989).
[CrossRef]

J. Opt. Soc. Am.

Opt. Eng.

T. H. Jamieson, “Thermal effects in optical systems,” Opt. Eng. 20, 156–160 (1981).

Opt. News

P. P. Clark, C. Londono, “Production of kinoforms by single point diamond machining,” Opt. News 15(12), 39–40 (1989).
[CrossRef]

Other

W. E. Asher, “Epoxy replication: advantages and limitations,” in Replication and Molding of Optical Components, M. J. Riedl, ed., Proc. Soc. Photo-Opt. Instrum. Eng.896, 2–11 (1988).

M. Roberts, “Athermalization of infrared optics: a review,” in Recent Trends in Optical Systems Design and Computer Lens Design Workshop II, R. E. Fischer, R. C. Juergens, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1049, 72–81 (1989).

Jamieson’s entries for acrylic and polycarbonate appear to be in error.

G. J. Swanson, “Binary optics technology: the theory and design of multi-level diffractive optical elements,” Tech. Rep. 854 (MIT Lincoln Laboratory, Cambridge, Mass., 1989).

S. M. Arnold, “How to test an asphere with a computer generated hologram,” in Holographic Optics: Optically and Computer Generated, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1052, 191–195 (1989).

M. Muranaka, M. Takagi, T. Maruyama, “Precision molding of aspherical plastic lens for camcorder and projection TV,” in Replication and Molding of Optical Components, M. J. Riedl, ed., Proc. Soc. Photo-Opt. Instrum. Eng.896, 123–131 (1988).

C. Londono, W. T. Plummer, P. P. Clark, “Athermalization with diffractive optics,” in Diffractive Optics: Design, Fabrication, and Applications, Vol. 9 of 1992 Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 7.

G. P. Behrmann, J. P. Bowen, “Thermal effects in diffractive lenses,” in Diffractive Optics: Design, Fabrication, and Applications, Vol. 9 of 1992 Technical Digest Series (Optical Society of America, Washington, D. C., 1992), pp. 8–10.

P. Morkry, “Unique applications of computer-generated diffractive optical elements,” in Holographic Optics: Optically and Computer Generated, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1052, 163–170 (1989).

A. McKay, J. White, “Effects of simulated space environments on dichromated gelatin holograms,” in Optomechanical Design of Laser Trnsmitters and Receivers, B. D. Seery, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1044, 269–275 (1989).

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Figures (6)

Fig. 1
Fig. 1

Simple optical system.

Fig. 2
Fig. 2

Surface-relief diffractive lens: h, blaze height; f, focal length; λ0,a design wavelength.

Fig. 3
Fig. 3

Radial temperature gradient, where TEDGE = T0 + ΔT.

Fig. 4
Fig. 4

Transverse-ray aberrations for an acrylic singlet with a focal length of 100 mm and an aluminum mount: (a) 20 °C, (b) 40 °C; ∊y transverse ray error; ρy, pupil coordinate.

Fig. 5
Fig. 5

Transverse-ray aberrations for an acrylic refractive–diffractive hybrid element with a focal length of 100 mm and an aluminum mount: (a) 20 °C, (b) 40 °C; ∊y, transverse ray error; ρy, pupil coordinate.

Fig. 6
Fig. 6

Acrylic hybrids with focal lengths of 100 mm: (a) athermalized hybrid (f1 = −173.9 mm, f2 = 63.5 mm), (b) achromatized hybrid (f1 = 106.6 mm, f2 = 1607.3 mm).

Tables (2)

Tables Icon

Table 1 Refractive and Diffractive Optothermal Expansion Coefficients (xf,r and xf,d) with the Properties Used in Their Calculationa

Tables Icon

Table 2 Focal Lengths for Each Surface of a Thermally Corrected Refractive–Diffractive Acrylic Hybrid with a Focal Length of 100 mm

Equations (26)

Equations on this page are rendered with MathJax. Learn more.

x f , r = 1 f d f d T = α g 1 n n 0 ( d n d T n d n 0 d T ) ,
Δ f = f x f , r Δ T .
r m 2 = f 2 ( f + m λ 0 n 0 ) 2 ,
f = n 0 r m 2 2 m λ 0 , m = 1 , 2 , 3 , .
r m ( T ) = r m ( 1 + α g Δ T ) .
n 0 ( T ) = n 0 + d n 0 d T Δ T .
f ( T ) = f [ 1 + 2 α g Δ T + α g 2 ( Δ T ) 2 + 1 n 0 d n 0 d T Δ T + 2 1 n 0 d n 0 d T α g ( Δ T ) 2 + 1 n 0 d n 0 d T α g 2 ( Δ T ) 3 ] .
x f , d = 2 α g + 1 n 0 d n 0 d T .
Δ f = f ( 2 α g + 1 n 0 d n 0 d T ) Δ T .
ϕ ( r ) = 2 π λ 0 [ s 1 r 2 + s 2 r 4 + s 3 r 6 + ] ,
r ( T ) = r ( 1 + α g Δ T ) ,
d s 1 d T = 2 α g s 1 , d s 2 d T = 4 α g s 2 , d s 3 d T = 6 α g s 3 , .
r m = r m + Δ r m = r m [ 1 + α g Δ T 2 ( r m r max ) ] .
r = r [ 1 + α g Δ T 2 ( r r max ) ] .
ϕ ( r ) = 2 π λ 0 [ s 1 ( r 2 + α g Δ T r 3 ) + s 2 ( r 4 + 4 α g Δ T r 5 ) ] .
h = λ 0 n n 0 ,
η 1 = [ sin ( π∊ ) π∊ ] 2 .
h d = λ 0 [ n + ( d n / d T ) Δ T ] [ n 0 + ( d n 0 / d T ) Δ T ] .
h a = h ( 1 + α g Δ T ) .
δ = h a h d .
= | δ | / h d .
ϕ = 1 / f .
1 / f = 1 / f 1 + 1 / f 2 ,
x f , net = ( f / f 1 ) x f 1 + ( f / f 2 ) x f 2 .
f 2 / f 1 = V 1 / V 2
x f , net = V 1 x f 1 V 2 x f 2 ( V 1 V 2 ) .

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