Abstract

A compact holographic projector system was built and tested. This projection system offers a practical approach for making a highly corrected mesh or grid pattern on curved surfaces. The pattern can range in size from multimicrometer to submicrometer dimensions and be recorded in either positive or negative photoresist. Standing-wave interference patterns in the form of a diverging close-packed lattice of either hexagonal or square rodlike intensity maxima extending outward from a point or a locus of points are produced by multiple-beam holography that involves the combination of a holographic diffraction grating and a hypercomatic focusing objective.

© 1999 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. U. Krackhardt, J. N. Mait, N. Streibl, “Upper bound on the diffraction efficiency of phase-only fanout elements,” Appl. Opt. 31, 27–37 (1992).
    [CrossRef] [PubMed]
  2. B. R. Brown, A. W. Lohmann, “Computer-generated binary holograms,” IBM J. Res. Dev. 13, 160–168 (1969).
    [CrossRef]
  3. W. J. Dallas, “Computer-generated holograms,” in The Computer in Optical Research and Applications, B. R. Frieden, ed. (Springer-Verlag, New York, 1980) pp. 291–363.
  4. S. M. Arnold, “Electron beam fabrication of computer-generated holograms,” Opt. Eng. 24, 803–807 (1985).
    [CrossRef]
  5. L. B. Lesem, P. M. Hirsch, J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
    [CrossRef]
  6. J. C. Patau, L. B. Lesem, P. M. Hirsch, J. A. Jordan, “Incoherent filtering using kinoforms,” IBM J. Res. Dev. 14, 485–491 (1970).
    [CrossRef]
  7. M. D. Levenson, N. S. Viswanathan, R. A. Simpson, “Improving resolution in photolithography with a phase-shifting mask,” IEEE Trans. Electron Devices ED-29, 1812–1846 (1982).
  8. Y. C. Pati, T. Kailath, “Phase-shifting masks for microlithography: automated design and mask requirements,” J. Opt. Soc. Am. A 11, 2438–2452 (1994).
    [CrossRef]
  9. K. Ronse, M. Op de Beeck, L. Van den hove, J. Engelen, “Fundamental principles of phase shifting masks by Fourier optics: theory and experimental verification,” J. Vac. Sci. Technol. B 12, 589–600 (1994).
    [CrossRef]
  10. R. L. Morrison, S. L. Walker, T. J. Cloonan, “Beam array generation and holographic interconnections in a free-space optical switching network,” Appl. Opt. 32, 2512–2518 (1993).
    [CrossRef] [PubMed]
  11. J. R. Leger, G. J. Swanson, W. B. Veldkamp, “Coherent laser addition using binary phase gratings,” Appl. Opt. 26, 4391–4399 (1987).
    [CrossRef] [PubMed]
  12. D. H. Raguin, “Subwavelength structured surfaces and their applications,” in Diffractive and Miniaturized Optics, Vol. CR49 of SPIE Critical Reviews (SPIE, Bellingham, Wash., 1993), pp. 234–261.
  13. P. Yeh, “A new optical model for wire grid polarizers,” Opt. Commun. 26, 289–292 (1978).
    [CrossRef]
  14. K. Shiraishi, T. Sato, S. Kawakami, “Experimental verification of a form-birefringent polarization splitter,” Appl. Phys. Lett. 58, 211–212 (1991).
    [CrossRef]
  15. L. H. Cescato, E. Gluch, N. Streibl, “Holographic quarter-wave plates,” Appl. Opt. 29, 3286–3290 (1991).
    [CrossRef]
  16. C. W. Haggans, L. Li, T. Fujita, R. K. Kostuk, “Lamellar gratings as polarization components for specularly reflected beams,” J. Mod. Opt. 40, 675–686 (1992).
    [CrossRef]
  17. E. N. Glytsis, T. K. Gaylord, “High-spatial-frequency binary and multilevel stairstep gratings: polarization-selective mirrors and broadband antireflection surfaces,” Appl. Opt. 31, 4459–4470 (1992).
    [CrossRef] [PubMed]
  18. H. Haidner, P. Kipfer, W. Stork, N. Streibl, “Zero-order gratings used as artificial distributed index medium,” Optik (Stuttgart) 89, 107–112 (1992).
  19. C. G. Bernhard, “Structural and functional adaptation in a visual system,” Endeavor 26, 79–84 (1967).
  20. J. J. Cowan, “The recording and large scale replication of crossed holographic grating arrays using multiple beam interferometry,” in Application, Theory, and Fabrication of Periodic Structures, Diffraction Gratings, and Moiré Phenomena II, J. M. Lerner, ed., Proc. SPIE503, 120–129 (1984).
    [CrossRef]
  21. J. J. Cowan, “The holographic honeycomb microlens,” in Applications of Holography, L. Huff, ed., Proc. SPIE523, 251–259 (1985).
    [CrossRef]
  22. J. J. Cowan, “Method and apparatus for exposing photosensitive material,” U.S. Patent4,496,216 (29January1985).
  23. Canon Kabushiki Kaisha, “Verfahren zur Herstellung eines Teil mit einer Anordnung von Mikrostrukturelementen auf demselben,” Ger. Offen.DE 2,952,607 (class G02B5/02) (publication date: 10July1980; application date: 28December1979; issue date: 14April1994). This patent is the oldest reference the author has found regarding the equiangular three-beam and equiangular four-beam interference patterns.
  24. T. Suzuki, K. Iizuka, K. Ohtaka, H. Mizutani, “Focusing plate,” U.S. patent4,421,398 (20December1983).
  25. W. T. Pawlewicz, P. M. Martin, R. W. Knoll, B. T. Smith, W. M. Myers, “Transparent conductive coatings for electro-optic windows,” (U.S. Army Missile Command, Redstone Arsenal, Ala., 1987).
  26. S. H. Zaidi, S. R. J. Brueck, F. M. Schellenberg, R. S. Mackay, K. Uekert, J. J. Persoff, “Interferometric lithography exposure tool for 180-nm structures,” in Emerging Lithographic Technologies, D. E. Seeger, ed., Proc. SPIE3048, 248–254 (1997).
    [CrossRef]
  27. X. Chen, S. H. Zaidi, S. R. J. Brueck, D. J. Devine, “Interferometric lithography of sub-micrometer sparse hole arrays for field-emission display applications,” J. Vac. Sci. Technol. B 14, 3339–3349 (1996).
    [CrossRef]
  28. M. M. Burns, J.-M. Fournier, J. A. Golovchenko, “Optical matter: crystallization and binding in intense optical fields,” Science 249, 749–754 (1990).
    [CrossRef] [PubMed]
  29. K. M. Baker, D. L. Shealy, W. Jiang, “Directional light filters: three-dimensional azo dye formed images within optical resins,” in Diffractive and Holographic Optics Technology II, I. Cindrich, S. H. Lee, eds., Proc. SPIE2404, 144–158 (1995).
    [CrossRef]
  30. K. M. Baker, “Directional light filter and holographic projector system for its production,” U.S. Patent5,642,209 (24June1997).
  31. C. H. Lin, Z. H. Zhu, Y. H. Lo, “New grating fabrication technology for optoelectronic devices: cascaded self-induced holography,” Appl. Phys. Lett. 67, 3072–3074 (1995).
    [CrossRef]
  32. C. H. Lin, Z. H. Zhu, Y. Qian, Y. H. Lo, “Cascade self-induced holography: a new grating fabrication technology for DFB/DBR lasers and WDM laser arrays,” IEEE J. Quantum Electron. 32, 1752–1759 (1996).
    [CrossRef]
  33. K. M. Baker, “Extreme depth-of-field optical lens and holographic projector system for its production,” U.S. patent5,822,091 (13October1998).
  34. W. Jiang, D. L. Shealy, J. C. Martin, “Design and testing of a refractive reshaping system,” in Current Developments in Optical Engineering III, R. E. Fischer, W. J. Smith, eds., Proc. SPIE2000, 64–75 (1993).
  35. W. Jiang, D. L. Shealy, K. M. Baker, “Optical design and testing of a holographic projection system,” in Diffractive and Holographic Optics Technology, I. Cindrich, S. H. Lee, eds., Proc. SPIE2152, 244–252 (1994).
    [CrossRef]
  36. W. Jiang, D. L. Shealy, K. M. Baker, “Physical optical analysis of the performance of a holographic projection system,” in Diffractive and Holographic Optics Technology II, I. Cindrich, S. H. Lee, eds., Proc. SPIE2404, 227–234 (1995).
    [CrossRef]
  37. Applied Physics Specialties, Ltd., 17 Prince Andrew Place, Dow Mills, Ontario M3C 2H2, Canada.
  38. R. Mathews, Optical Works, Inc., 26280 Olhava Road, NW, #A, Poulsbo, WA 98370–9435 (personal communication, 6November1997).
  39. R. P. Cargille Laboratories, Inc., 55 Commerce Road, Cedar Grove, NJ 07009–1289.
  40. E. H. Anderson, C. M. Horwitz, H. I. Smith, “Holographic lithography with thick photoresist,” Appl. Phys. Lett. 43, 874–875 (1983).
    [CrossRef]
  41. Processing instructions for the Shipley Microposit S1800 series photoresists are available from Shipley Company, 455 Forest Street, Marlboro, MA 01752.
  42. J. M. Kurmer, J. I. Halman, K. A. Ramsey, D. L. Jones, J. McManigal, “Polarization effects of resonant mesh structures fabricated on IR transmitting windows,” in Window and Dome Technologies and Materials II, P. Klocek, ed., Proc. SPIE1326, 165–175 (1990).
    [CrossRef]
  43. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998). See also the review and commentary of this paper by R. Sambles, “More than transparent,” Nature 391, 641–642 (1998).
  44. E. Betzig, J. K. Trautman, “Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit,” Science 257, 189–194 (1992).
    [CrossRef] [PubMed]

1998 (1)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998). See also the review and commentary of this paper by R. Sambles, “More than transparent,” Nature 391, 641–642 (1998).

1996 (2)

X. Chen, S. H. Zaidi, S. R. J. Brueck, D. J. Devine, “Interferometric lithography of sub-micrometer sparse hole arrays for field-emission display applications,” J. Vac. Sci. Technol. B 14, 3339–3349 (1996).
[CrossRef]

C. H. Lin, Z. H. Zhu, Y. Qian, Y. H. Lo, “Cascade self-induced holography: a new grating fabrication technology for DFB/DBR lasers and WDM laser arrays,” IEEE J. Quantum Electron. 32, 1752–1759 (1996).
[CrossRef]

1995 (1)

C. H. Lin, Z. H. Zhu, Y. H. Lo, “New grating fabrication technology for optoelectronic devices: cascaded self-induced holography,” Appl. Phys. Lett. 67, 3072–3074 (1995).
[CrossRef]

1994 (2)

Y. C. Pati, T. Kailath, “Phase-shifting masks for microlithography: automated design and mask requirements,” J. Opt. Soc. Am. A 11, 2438–2452 (1994).
[CrossRef]

K. Ronse, M. Op de Beeck, L. Van den hove, J. Engelen, “Fundamental principles of phase shifting masks by Fourier optics: theory and experimental verification,” J. Vac. Sci. Technol. B 12, 589–600 (1994).
[CrossRef]

1993 (1)

1992 (5)

U. Krackhardt, J. N. Mait, N. Streibl, “Upper bound on the diffraction efficiency of phase-only fanout elements,” Appl. Opt. 31, 27–37 (1992).
[CrossRef] [PubMed]

C. W. Haggans, L. Li, T. Fujita, R. K. Kostuk, “Lamellar gratings as polarization components for specularly reflected beams,” J. Mod. Opt. 40, 675–686 (1992).
[CrossRef]

E. N. Glytsis, T. K. Gaylord, “High-spatial-frequency binary and multilevel stairstep gratings: polarization-selective mirrors and broadband antireflection surfaces,” Appl. Opt. 31, 4459–4470 (1992).
[CrossRef] [PubMed]

H. Haidner, P. Kipfer, W. Stork, N. Streibl, “Zero-order gratings used as artificial distributed index medium,” Optik (Stuttgart) 89, 107–112 (1992).

E. Betzig, J. K. Trautman, “Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit,” Science 257, 189–194 (1992).
[CrossRef] [PubMed]

1991 (2)

K. Shiraishi, T. Sato, S. Kawakami, “Experimental verification of a form-birefringent polarization splitter,” Appl. Phys. Lett. 58, 211–212 (1991).
[CrossRef]

L. H. Cescato, E. Gluch, N. Streibl, “Holographic quarter-wave plates,” Appl. Opt. 29, 3286–3290 (1991).
[CrossRef]

1990 (1)

M. M. Burns, J.-M. Fournier, J. A. Golovchenko, “Optical matter: crystallization and binding in intense optical fields,” Science 249, 749–754 (1990).
[CrossRef] [PubMed]

1987 (1)

1985 (1)

S. M. Arnold, “Electron beam fabrication of computer-generated holograms,” Opt. Eng. 24, 803–807 (1985).
[CrossRef]

1983 (1)

E. H. Anderson, C. M. Horwitz, H. I. Smith, “Holographic lithography with thick photoresist,” Appl. Phys. Lett. 43, 874–875 (1983).
[CrossRef]

1982 (1)

M. D. Levenson, N. S. Viswanathan, R. A. Simpson, “Improving resolution in photolithography with a phase-shifting mask,” IEEE Trans. Electron Devices ED-29, 1812–1846 (1982).

1978 (1)

P. Yeh, “A new optical model for wire grid polarizers,” Opt. Commun. 26, 289–292 (1978).
[CrossRef]

1970 (1)

J. C. Patau, L. B. Lesem, P. M. Hirsch, J. A. Jordan, “Incoherent filtering using kinoforms,” IBM J. Res. Dev. 14, 485–491 (1970).
[CrossRef]

1969 (2)

L. B. Lesem, P. M. Hirsch, J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
[CrossRef]

B. R. Brown, A. W. Lohmann, “Computer-generated binary holograms,” IBM J. Res. Dev. 13, 160–168 (1969).
[CrossRef]

1967 (1)

C. G. Bernhard, “Structural and functional adaptation in a visual system,” Endeavor 26, 79–84 (1967).

Anderson, E. H.

E. H. Anderson, C. M. Horwitz, H. I. Smith, “Holographic lithography with thick photoresist,” Appl. Phys. Lett. 43, 874–875 (1983).
[CrossRef]

Arnold, S. M.

S. M. Arnold, “Electron beam fabrication of computer-generated holograms,” Opt. Eng. 24, 803–807 (1985).
[CrossRef]

Baker, K. M.

W. Jiang, D. L. Shealy, K. M. Baker, “Optical design and testing of a holographic projection system,” in Diffractive and Holographic Optics Technology, I. Cindrich, S. H. Lee, eds., Proc. SPIE2152, 244–252 (1994).
[CrossRef]

W. Jiang, D. L. Shealy, K. M. Baker, “Physical optical analysis of the performance of a holographic projection system,” in Diffractive and Holographic Optics Technology II, I. Cindrich, S. H. Lee, eds., Proc. SPIE2404, 227–234 (1995).
[CrossRef]

K. M. Baker, D. L. Shealy, W. Jiang, “Directional light filters: three-dimensional azo dye formed images within optical resins,” in Diffractive and Holographic Optics Technology II, I. Cindrich, S. H. Lee, eds., Proc. SPIE2404, 144–158 (1995).
[CrossRef]

K. M. Baker, “Directional light filter and holographic projector system for its production,” U.S. Patent5,642,209 (24June1997).

K. M. Baker, “Extreme depth-of-field optical lens and holographic projector system for its production,” U.S. patent5,822,091 (13October1998).

Bernhard, C. G.

C. G. Bernhard, “Structural and functional adaptation in a visual system,” Endeavor 26, 79–84 (1967).

Betzig, E.

E. Betzig, J. K. Trautman, “Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit,” Science 257, 189–194 (1992).
[CrossRef] [PubMed]

Brown, B. R.

B. R. Brown, A. W. Lohmann, “Computer-generated binary holograms,” IBM J. Res. Dev. 13, 160–168 (1969).
[CrossRef]

Brueck, S. R. J.

X. Chen, S. H. Zaidi, S. R. J. Brueck, D. J. Devine, “Interferometric lithography of sub-micrometer sparse hole arrays for field-emission display applications,” J. Vac. Sci. Technol. B 14, 3339–3349 (1996).
[CrossRef]

S. H. Zaidi, S. R. J. Brueck, F. M. Schellenberg, R. S. Mackay, K. Uekert, J. J. Persoff, “Interferometric lithography exposure tool for 180-nm structures,” in Emerging Lithographic Technologies, D. E. Seeger, ed., Proc. SPIE3048, 248–254 (1997).
[CrossRef]

Burns, M. M.

M. M. Burns, J.-M. Fournier, J. A. Golovchenko, “Optical matter: crystallization and binding in intense optical fields,” Science 249, 749–754 (1990).
[CrossRef] [PubMed]

Cescato, L. H.

Chen, X.

X. Chen, S. H. Zaidi, S. R. J. Brueck, D. J. Devine, “Interferometric lithography of sub-micrometer sparse hole arrays for field-emission display applications,” J. Vac. Sci. Technol. B 14, 3339–3349 (1996).
[CrossRef]

Cloonan, T. J.

Cowan, J. J.

J. J. Cowan, “The recording and large scale replication of crossed holographic grating arrays using multiple beam interferometry,” in Application, Theory, and Fabrication of Periodic Structures, Diffraction Gratings, and Moiré Phenomena II, J. M. Lerner, ed., Proc. SPIE503, 120–129 (1984).
[CrossRef]

J. J. Cowan, “The holographic honeycomb microlens,” in Applications of Holography, L. Huff, ed., Proc. SPIE523, 251–259 (1985).
[CrossRef]

J. J. Cowan, “Method and apparatus for exposing photosensitive material,” U.S. Patent4,496,216 (29January1985).

Dallas, W. J.

W. J. Dallas, “Computer-generated holograms,” in The Computer in Optical Research and Applications, B. R. Frieden, ed. (Springer-Verlag, New York, 1980) pp. 291–363.

Devine, D. J.

X. Chen, S. H. Zaidi, S. R. J. Brueck, D. J. Devine, “Interferometric lithography of sub-micrometer sparse hole arrays for field-emission display applications,” J. Vac. Sci. Technol. B 14, 3339–3349 (1996).
[CrossRef]

Ebbesen, T. W.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998). See also the review and commentary of this paper by R. Sambles, “More than transparent,” Nature 391, 641–642 (1998).

Engelen, J.

K. Ronse, M. Op de Beeck, L. Van den hove, J. Engelen, “Fundamental principles of phase shifting masks by Fourier optics: theory and experimental verification,” J. Vac. Sci. Technol. B 12, 589–600 (1994).
[CrossRef]

Fournier, J.-M.

M. M. Burns, J.-M. Fournier, J. A. Golovchenko, “Optical matter: crystallization and binding in intense optical fields,” Science 249, 749–754 (1990).
[CrossRef] [PubMed]

Fujita, T.

C. W. Haggans, L. Li, T. Fujita, R. K. Kostuk, “Lamellar gratings as polarization components for specularly reflected beams,” J. Mod. Opt. 40, 675–686 (1992).
[CrossRef]

Gaylord, T. K.

Ghaemi, H. F.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998). See also the review and commentary of this paper by R. Sambles, “More than transparent,” Nature 391, 641–642 (1998).

Gluch, E.

Glytsis, E. N.

Golovchenko, J. A.

M. M. Burns, J.-M. Fournier, J. A. Golovchenko, “Optical matter: crystallization and binding in intense optical fields,” Science 249, 749–754 (1990).
[CrossRef] [PubMed]

Haggans, C. W.

C. W. Haggans, L. Li, T. Fujita, R. K. Kostuk, “Lamellar gratings as polarization components for specularly reflected beams,” J. Mod. Opt. 40, 675–686 (1992).
[CrossRef]

Haidner, H.

H. Haidner, P. Kipfer, W. Stork, N. Streibl, “Zero-order gratings used as artificial distributed index medium,” Optik (Stuttgart) 89, 107–112 (1992).

Halman, J. I.

J. M. Kurmer, J. I. Halman, K. A. Ramsey, D. L. Jones, J. McManigal, “Polarization effects of resonant mesh structures fabricated on IR transmitting windows,” in Window and Dome Technologies and Materials II, P. Klocek, ed., Proc. SPIE1326, 165–175 (1990).
[CrossRef]

Hirsch, P. M.

J. C. Patau, L. B. Lesem, P. M. Hirsch, J. A. Jordan, “Incoherent filtering using kinoforms,” IBM J. Res. Dev. 14, 485–491 (1970).
[CrossRef]

L. B. Lesem, P. M. Hirsch, J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
[CrossRef]

Horwitz, C. M.

E. H. Anderson, C. M. Horwitz, H. I. Smith, “Holographic lithography with thick photoresist,” Appl. Phys. Lett. 43, 874–875 (1983).
[CrossRef]

Iizuka, K.

T. Suzuki, K. Iizuka, K. Ohtaka, H. Mizutani, “Focusing plate,” U.S. patent4,421,398 (20December1983).

Jiang, W.

W. Jiang, D. L. Shealy, K. M. Baker, “Physical optical analysis of the performance of a holographic projection system,” in Diffractive and Holographic Optics Technology II, I. Cindrich, S. H. Lee, eds., Proc. SPIE2404, 227–234 (1995).
[CrossRef]

K. M. Baker, D. L. Shealy, W. Jiang, “Directional light filters: three-dimensional azo dye formed images within optical resins,” in Diffractive and Holographic Optics Technology II, I. Cindrich, S. H. Lee, eds., Proc. SPIE2404, 144–158 (1995).
[CrossRef]

W. Jiang, D. L. Shealy, J. C. Martin, “Design and testing of a refractive reshaping system,” in Current Developments in Optical Engineering III, R. E. Fischer, W. J. Smith, eds., Proc. SPIE2000, 64–75 (1993).

W. Jiang, D. L. Shealy, K. M. Baker, “Optical design and testing of a holographic projection system,” in Diffractive and Holographic Optics Technology, I. Cindrich, S. H. Lee, eds., Proc. SPIE2152, 244–252 (1994).
[CrossRef]

Jones, D. L.

J. M. Kurmer, J. I. Halman, K. A. Ramsey, D. L. Jones, J. McManigal, “Polarization effects of resonant mesh structures fabricated on IR transmitting windows,” in Window and Dome Technologies and Materials II, P. Klocek, ed., Proc. SPIE1326, 165–175 (1990).
[CrossRef]

Jordan, J. A.

J. C. Patau, L. B. Lesem, P. M. Hirsch, J. A. Jordan, “Incoherent filtering using kinoforms,” IBM J. Res. Dev. 14, 485–491 (1970).
[CrossRef]

L. B. Lesem, P. M. Hirsch, J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
[CrossRef]

Kailath, T.

Kaisha, Canon Kabushiki

Canon Kabushiki Kaisha, “Verfahren zur Herstellung eines Teil mit einer Anordnung von Mikrostrukturelementen auf demselben,” Ger. Offen.DE 2,952,607 (class G02B5/02) (publication date: 10July1980; application date: 28December1979; issue date: 14April1994). This patent is the oldest reference the author has found regarding the equiangular three-beam and equiangular four-beam interference patterns.

Kawakami, S.

K. Shiraishi, T. Sato, S. Kawakami, “Experimental verification of a form-birefringent polarization splitter,” Appl. Phys. Lett. 58, 211–212 (1991).
[CrossRef]

Kipfer, P.

H. Haidner, P. Kipfer, W. Stork, N. Streibl, “Zero-order gratings used as artificial distributed index medium,” Optik (Stuttgart) 89, 107–112 (1992).

Knoll, R. W.

W. T. Pawlewicz, P. M. Martin, R. W. Knoll, B. T. Smith, W. M. Myers, “Transparent conductive coatings for electro-optic windows,” (U.S. Army Missile Command, Redstone Arsenal, Ala., 1987).

Kostuk, R. K.

C. W. Haggans, L. Li, T. Fujita, R. K. Kostuk, “Lamellar gratings as polarization components for specularly reflected beams,” J. Mod. Opt. 40, 675–686 (1992).
[CrossRef]

Krackhardt, U.

Kurmer, J. M.

J. M. Kurmer, J. I. Halman, K. A. Ramsey, D. L. Jones, J. McManigal, “Polarization effects of resonant mesh structures fabricated on IR transmitting windows,” in Window and Dome Technologies and Materials II, P. Klocek, ed., Proc. SPIE1326, 165–175 (1990).
[CrossRef]

Leger, J. R.

Lesem, L. B.

J. C. Patau, L. B. Lesem, P. M. Hirsch, J. A. Jordan, “Incoherent filtering using kinoforms,” IBM J. Res. Dev. 14, 485–491 (1970).
[CrossRef]

L. B. Lesem, P. M. Hirsch, J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
[CrossRef]

Levenson, M. D.

M. D. Levenson, N. S. Viswanathan, R. A. Simpson, “Improving resolution in photolithography with a phase-shifting mask,” IEEE Trans. Electron Devices ED-29, 1812–1846 (1982).

Lezec, H. J.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998). See also the review and commentary of this paper by R. Sambles, “More than transparent,” Nature 391, 641–642 (1998).

Li, L.

C. W. Haggans, L. Li, T. Fujita, R. K. Kostuk, “Lamellar gratings as polarization components for specularly reflected beams,” J. Mod. Opt. 40, 675–686 (1992).
[CrossRef]

Lin, C. H.

C. H. Lin, Z. H. Zhu, Y. Qian, Y. H. Lo, “Cascade self-induced holography: a new grating fabrication technology for DFB/DBR lasers and WDM laser arrays,” IEEE J. Quantum Electron. 32, 1752–1759 (1996).
[CrossRef]

C. H. Lin, Z. H. Zhu, Y. H. Lo, “New grating fabrication technology for optoelectronic devices: cascaded self-induced holography,” Appl. Phys. Lett. 67, 3072–3074 (1995).
[CrossRef]

Lo, Y. H.

C. H. Lin, Z. H. Zhu, Y. Qian, Y. H. Lo, “Cascade self-induced holography: a new grating fabrication technology for DFB/DBR lasers and WDM laser arrays,” IEEE J. Quantum Electron. 32, 1752–1759 (1996).
[CrossRef]

C. H. Lin, Z. H. Zhu, Y. H. Lo, “New grating fabrication technology for optoelectronic devices: cascaded self-induced holography,” Appl. Phys. Lett. 67, 3072–3074 (1995).
[CrossRef]

Lohmann, A. W.

B. R. Brown, A. W. Lohmann, “Computer-generated binary holograms,” IBM J. Res. Dev. 13, 160–168 (1969).
[CrossRef]

Mackay, R. S.

S. H. Zaidi, S. R. J. Brueck, F. M. Schellenberg, R. S. Mackay, K. Uekert, J. J. Persoff, “Interferometric lithography exposure tool for 180-nm structures,” in Emerging Lithographic Technologies, D. E. Seeger, ed., Proc. SPIE3048, 248–254 (1997).
[CrossRef]

Mait, J. N.

Martin, J. C.

W. Jiang, D. L. Shealy, J. C. Martin, “Design and testing of a refractive reshaping system,” in Current Developments in Optical Engineering III, R. E. Fischer, W. J. Smith, eds., Proc. SPIE2000, 64–75 (1993).

Martin, P. M.

W. T. Pawlewicz, P. M. Martin, R. W. Knoll, B. T. Smith, W. M. Myers, “Transparent conductive coatings for electro-optic windows,” (U.S. Army Missile Command, Redstone Arsenal, Ala., 1987).

Mathews, R.

R. Mathews, Optical Works, Inc., 26280 Olhava Road, NW, #A, Poulsbo, WA 98370–9435 (personal communication, 6November1997).

McManigal, J.

J. M. Kurmer, J. I. Halman, K. A. Ramsey, D. L. Jones, J. McManigal, “Polarization effects of resonant mesh structures fabricated on IR transmitting windows,” in Window and Dome Technologies and Materials II, P. Klocek, ed., Proc. SPIE1326, 165–175 (1990).
[CrossRef]

Mizutani, H.

T. Suzuki, K. Iizuka, K. Ohtaka, H. Mizutani, “Focusing plate,” U.S. patent4,421,398 (20December1983).

Morrison, R. L.

Myers, W. M.

W. T. Pawlewicz, P. M. Martin, R. W. Knoll, B. T. Smith, W. M. Myers, “Transparent conductive coatings for electro-optic windows,” (U.S. Army Missile Command, Redstone Arsenal, Ala., 1987).

Ohtaka, K.

T. Suzuki, K. Iizuka, K. Ohtaka, H. Mizutani, “Focusing plate,” U.S. patent4,421,398 (20December1983).

Op de Beeck, M.

K. Ronse, M. Op de Beeck, L. Van den hove, J. Engelen, “Fundamental principles of phase shifting masks by Fourier optics: theory and experimental verification,” J. Vac. Sci. Technol. B 12, 589–600 (1994).
[CrossRef]

Patau, J. C.

J. C. Patau, L. B. Lesem, P. M. Hirsch, J. A. Jordan, “Incoherent filtering using kinoforms,” IBM J. Res. Dev. 14, 485–491 (1970).
[CrossRef]

Pati, Y. C.

Pawlewicz, W. T.

W. T. Pawlewicz, P. M. Martin, R. W. Knoll, B. T. Smith, W. M. Myers, “Transparent conductive coatings for electro-optic windows,” (U.S. Army Missile Command, Redstone Arsenal, Ala., 1987).

Persoff, J. J.

S. H. Zaidi, S. R. J. Brueck, F. M. Schellenberg, R. S. Mackay, K. Uekert, J. J. Persoff, “Interferometric lithography exposure tool for 180-nm structures,” in Emerging Lithographic Technologies, D. E. Seeger, ed., Proc. SPIE3048, 248–254 (1997).
[CrossRef]

Qian, Y.

C. H. Lin, Z. H. Zhu, Y. Qian, Y. H. Lo, “Cascade self-induced holography: a new grating fabrication technology for DFB/DBR lasers and WDM laser arrays,” IEEE J. Quantum Electron. 32, 1752–1759 (1996).
[CrossRef]

Raguin, D. H.

D. H. Raguin, “Subwavelength structured surfaces and their applications,” in Diffractive and Miniaturized Optics, Vol. CR49 of SPIE Critical Reviews (SPIE, Bellingham, Wash., 1993), pp. 234–261.

Ramsey, K. A.

J. M. Kurmer, J. I. Halman, K. A. Ramsey, D. L. Jones, J. McManigal, “Polarization effects of resonant mesh structures fabricated on IR transmitting windows,” in Window and Dome Technologies and Materials II, P. Klocek, ed., Proc. SPIE1326, 165–175 (1990).
[CrossRef]

Ronse, K.

K. Ronse, M. Op de Beeck, L. Van den hove, J. Engelen, “Fundamental principles of phase shifting masks by Fourier optics: theory and experimental verification,” J. Vac. Sci. Technol. B 12, 589–600 (1994).
[CrossRef]

Sato, T.

K. Shiraishi, T. Sato, S. Kawakami, “Experimental verification of a form-birefringent polarization splitter,” Appl. Phys. Lett. 58, 211–212 (1991).
[CrossRef]

Schellenberg, F. M.

S. H. Zaidi, S. R. J. Brueck, F. M. Schellenberg, R. S. Mackay, K. Uekert, J. J. Persoff, “Interferometric lithography exposure tool for 180-nm structures,” in Emerging Lithographic Technologies, D. E. Seeger, ed., Proc. SPIE3048, 248–254 (1997).
[CrossRef]

Shealy, D. L.

W. Jiang, D. L. Shealy, K. M. Baker, “Physical optical analysis of the performance of a holographic projection system,” in Diffractive and Holographic Optics Technology II, I. Cindrich, S. H. Lee, eds., Proc. SPIE2404, 227–234 (1995).
[CrossRef]

W. Jiang, D. L. Shealy, K. M. Baker, “Optical design and testing of a holographic projection system,” in Diffractive and Holographic Optics Technology, I. Cindrich, S. H. Lee, eds., Proc. SPIE2152, 244–252 (1994).
[CrossRef]

W. Jiang, D. L. Shealy, J. C. Martin, “Design and testing of a refractive reshaping system,” in Current Developments in Optical Engineering III, R. E. Fischer, W. J. Smith, eds., Proc. SPIE2000, 64–75 (1993).

K. M. Baker, D. L. Shealy, W. Jiang, “Directional light filters: three-dimensional azo dye formed images within optical resins,” in Diffractive and Holographic Optics Technology II, I. Cindrich, S. H. Lee, eds., Proc. SPIE2404, 144–158 (1995).
[CrossRef]

Shiraishi, K.

K. Shiraishi, T. Sato, S. Kawakami, “Experimental verification of a form-birefringent polarization splitter,” Appl. Phys. Lett. 58, 211–212 (1991).
[CrossRef]

Simpson, R. A.

M. D. Levenson, N. S. Viswanathan, R. A. Simpson, “Improving resolution in photolithography with a phase-shifting mask,” IEEE Trans. Electron Devices ED-29, 1812–1846 (1982).

Smith, B. T.

W. T. Pawlewicz, P. M. Martin, R. W. Knoll, B. T. Smith, W. M. Myers, “Transparent conductive coatings for electro-optic windows,” (U.S. Army Missile Command, Redstone Arsenal, Ala., 1987).

Smith, H. I.

E. H. Anderson, C. M. Horwitz, H. I. Smith, “Holographic lithography with thick photoresist,” Appl. Phys. Lett. 43, 874–875 (1983).
[CrossRef]

Stork, W.

H. Haidner, P. Kipfer, W. Stork, N. Streibl, “Zero-order gratings used as artificial distributed index medium,” Optik (Stuttgart) 89, 107–112 (1992).

Streibl, N.

Suzuki, T.

T. Suzuki, K. Iizuka, K. Ohtaka, H. Mizutani, “Focusing plate,” U.S. patent4,421,398 (20December1983).

Swanson, G. J.

Thio, T.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998). See also the review and commentary of this paper by R. Sambles, “More than transparent,” Nature 391, 641–642 (1998).

Trautman, J. K.

E. Betzig, J. K. Trautman, “Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit,” Science 257, 189–194 (1992).
[CrossRef] [PubMed]

Uekert, K.

S. H. Zaidi, S. R. J. Brueck, F. M. Schellenberg, R. S. Mackay, K. Uekert, J. J. Persoff, “Interferometric lithography exposure tool for 180-nm structures,” in Emerging Lithographic Technologies, D. E. Seeger, ed., Proc. SPIE3048, 248–254 (1997).
[CrossRef]

Van den hove, L.

K. Ronse, M. Op de Beeck, L. Van den hove, J. Engelen, “Fundamental principles of phase shifting masks by Fourier optics: theory and experimental verification,” J. Vac. Sci. Technol. B 12, 589–600 (1994).
[CrossRef]

Veldkamp, W. B.

Viswanathan, N. S.

M. D. Levenson, N. S. Viswanathan, R. A. Simpson, “Improving resolution in photolithography with a phase-shifting mask,” IEEE Trans. Electron Devices ED-29, 1812–1846 (1982).

Walker, S. L.

Wolff, P. A.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998). See also the review and commentary of this paper by R. Sambles, “More than transparent,” Nature 391, 641–642 (1998).

Yeh, P.

P. Yeh, “A new optical model for wire grid polarizers,” Opt. Commun. 26, 289–292 (1978).
[CrossRef]

Zaidi, S. H.

X. Chen, S. H. Zaidi, S. R. J. Brueck, D. J. Devine, “Interferometric lithography of sub-micrometer sparse hole arrays for field-emission display applications,” J. Vac. Sci. Technol. B 14, 3339–3349 (1996).
[CrossRef]

S. H. Zaidi, S. R. J. Brueck, F. M. Schellenberg, R. S. Mackay, K. Uekert, J. J. Persoff, “Interferometric lithography exposure tool for 180-nm structures,” in Emerging Lithographic Technologies, D. E. Seeger, ed., Proc. SPIE3048, 248–254 (1997).
[CrossRef]

Zhu, Z. H.

C. H. Lin, Z. H. Zhu, Y. Qian, Y. H. Lo, “Cascade self-induced holography: a new grating fabrication technology for DFB/DBR lasers and WDM laser arrays,” IEEE J. Quantum Electron. 32, 1752–1759 (1996).
[CrossRef]

C. H. Lin, Z. H. Zhu, Y. H. Lo, “New grating fabrication technology for optoelectronic devices: cascaded self-induced holography,” Appl. Phys. Lett. 67, 3072–3074 (1995).
[CrossRef]

Appl. Opt. (5)

Appl. Phys. Lett. (3)

E. H. Anderson, C. M. Horwitz, H. I. Smith, “Holographic lithography with thick photoresist,” Appl. Phys. Lett. 43, 874–875 (1983).
[CrossRef]

K. Shiraishi, T. Sato, S. Kawakami, “Experimental verification of a form-birefringent polarization splitter,” Appl. Phys. Lett. 58, 211–212 (1991).
[CrossRef]

C. H. Lin, Z. H. Zhu, Y. H. Lo, “New grating fabrication technology for optoelectronic devices: cascaded self-induced holography,” Appl. Phys. Lett. 67, 3072–3074 (1995).
[CrossRef]

Endeavor (1)

C. G. Bernhard, “Structural and functional adaptation in a visual system,” Endeavor 26, 79–84 (1967).

IBM J. Res. Dev. (3)

B. R. Brown, A. W. Lohmann, “Computer-generated binary holograms,” IBM J. Res. Dev. 13, 160–168 (1969).
[CrossRef]

L. B. Lesem, P. M. Hirsch, J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150–155 (1969).
[CrossRef]

J. C. Patau, L. B. Lesem, P. M. Hirsch, J. A. Jordan, “Incoherent filtering using kinoforms,” IBM J. Res. Dev. 14, 485–491 (1970).
[CrossRef]

IEEE J. Quantum Electron. (1)

C. H. Lin, Z. H. Zhu, Y. Qian, Y. H. Lo, “Cascade self-induced holography: a new grating fabrication technology for DFB/DBR lasers and WDM laser arrays,” IEEE J. Quantum Electron. 32, 1752–1759 (1996).
[CrossRef]

IEEE Trans. Electron Devices (1)

M. D. Levenson, N. S. Viswanathan, R. A. Simpson, “Improving resolution in photolithography with a phase-shifting mask,” IEEE Trans. Electron Devices ED-29, 1812–1846 (1982).

J. Mod. Opt. (1)

C. W. Haggans, L. Li, T. Fujita, R. K. Kostuk, “Lamellar gratings as polarization components for specularly reflected beams,” J. Mod. Opt. 40, 675–686 (1992).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Vac. Sci. Technol. B (2)

K. Ronse, M. Op de Beeck, L. Van den hove, J. Engelen, “Fundamental principles of phase shifting masks by Fourier optics: theory and experimental verification,” J. Vac. Sci. Technol. B 12, 589–600 (1994).
[CrossRef]

X. Chen, S. H. Zaidi, S. R. J. Brueck, D. J. Devine, “Interferometric lithography of sub-micrometer sparse hole arrays for field-emission display applications,” J. Vac. Sci. Technol. B 14, 3339–3349 (1996).
[CrossRef]

Nature (1)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998). See also the review and commentary of this paper by R. Sambles, “More than transparent,” Nature 391, 641–642 (1998).

Opt. Commun. (1)

P. Yeh, “A new optical model for wire grid polarizers,” Opt. Commun. 26, 289–292 (1978).
[CrossRef]

Opt. Eng. (1)

S. M. Arnold, “Electron beam fabrication of computer-generated holograms,” Opt. Eng. 24, 803–807 (1985).
[CrossRef]

Optik (Stuttgart) (1)

H. Haidner, P. Kipfer, W. Stork, N. Streibl, “Zero-order gratings used as artificial distributed index medium,” Optik (Stuttgart) 89, 107–112 (1992).

Science (2)

E. Betzig, J. K. Trautman, “Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit,” Science 257, 189–194 (1992).
[CrossRef] [PubMed]

M. M. Burns, J.-M. Fournier, J. A. Golovchenko, “Optical matter: crystallization and binding in intense optical fields,” Science 249, 749–754 (1990).
[CrossRef] [PubMed]

Other (20)

K. M. Baker, D. L. Shealy, W. Jiang, “Directional light filters: three-dimensional azo dye formed images within optical resins,” in Diffractive and Holographic Optics Technology II, I. Cindrich, S. H. Lee, eds., Proc. SPIE2404, 144–158 (1995).
[CrossRef]

K. M. Baker, “Directional light filter and holographic projector system for its production,” U.S. Patent5,642,209 (24June1997).

K. M. Baker, “Extreme depth-of-field optical lens and holographic projector system for its production,” U.S. patent5,822,091 (13October1998).

W. Jiang, D. L. Shealy, J. C. Martin, “Design and testing of a refractive reshaping system,” in Current Developments in Optical Engineering III, R. E. Fischer, W. J. Smith, eds., Proc. SPIE2000, 64–75 (1993).

W. Jiang, D. L. Shealy, K. M. Baker, “Optical design and testing of a holographic projection system,” in Diffractive and Holographic Optics Technology, I. Cindrich, S. H. Lee, eds., Proc. SPIE2152, 244–252 (1994).
[CrossRef]

W. Jiang, D. L. Shealy, K. M. Baker, “Physical optical analysis of the performance of a holographic projection system,” in Diffractive and Holographic Optics Technology II, I. Cindrich, S. H. Lee, eds., Proc. SPIE2404, 227–234 (1995).
[CrossRef]

Applied Physics Specialties, Ltd., 17 Prince Andrew Place, Dow Mills, Ontario M3C 2H2, Canada.

R. Mathews, Optical Works, Inc., 26280 Olhava Road, NW, #A, Poulsbo, WA 98370–9435 (personal communication, 6November1997).

R. P. Cargille Laboratories, Inc., 55 Commerce Road, Cedar Grove, NJ 07009–1289.

W. J. Dallas, “Computer-generated holograms,” in The Computer in Optical Research and Applications, B. R. Frieden, ed. (Springer-Verlag, New York, 1980) pp. 291–363.

D. H. Raguin, “Subwavelength structured surfaces and their applications,” in Diffractive and Miniaturized Optics, Vol. CR49 of SPIE Critical Reviews (SPIE, Bellingham, Wash., 1993), pp. 234–261.

J. J. Cowan, “The recording and large scale replication of crossed holographic grating arrays using multiple beam interferometry,” in Application, Theory, and Fabrication of Periodic Structures, Diffraction Gratings, and Moiré Phenomena II, J. M. Lerner, ed., Proc. SPIE503, 120–129 (1984).
[CrossRef]

J. J. Cowan, “The holographic honeycomb microlens,” in Applications of Holography, L. Huff, ed., Proc. SPIE523, 251–259 (1985).
[CrossRef]

J. J. Cowan, “Method and apparatus for exposing photosensitive material,” U.S. Patent4,496,216 (29January1985).

Canon Kabushiki Kaisha, “Verfahren zur Herstellung eines Teil mit einer Anordnung von Mikrostrukturelementen auf demselben,” Ger. Offen.DE 2,952,607 (class G02B5/02) (publication date: 10July1980; application date: 28December1979; issue date: 14April1994). This patent is the oldest reference the author has found regarding the equiangular three-beam and equiangular four-beam interference patterns.

T. Suzuki, K. Iizuka, K. Ohtaka, H. Mizutani, “Focusing plate,” U.S. patent4,421,398 (20December1983).

W. T. Pawlewicz, P. M. Martin, R. W. Knoll, B. T. Smith, W. M. Myers, “Transparent conductive coatings for electro-optic windows,” (U.S. Army Missile Command, Redstone Arsenal, Ala., 1987).

S. H. Zaidi, S. R. J. Brueck, F. M. Schellenberg, R. S. Mackay, K. Uekert, J. J. Persoff, “Interferometric lithography exposure tool for 180-nm structures,” in Emerging Lithographic Technologies, D. E. Seeger, ed., Proc. SPIE3048, 248–254 (1997).
[CrossRef]

Processing instructions for the Shipley Microposit S1800 series photoresists are available from Shipley Company, 455 Forest Street, Marlboro, MA 01752.

J. M. Kurmer, J. I. Halman, K. A. Ramsey, D. L. Jones, J. McManigal, “Polarization effects of resonant mesh structures fabricated on IR transmitting windows,” in Window and Dome Technologies and Materials II, P. Klocek, ed., Proc. SPIE1326, 165–175 (1990).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (12)

Fig. 1
Fig. 1

Previously developed holographic projector system, shown end to end.

Fig. 2
Fig. 2

Tail-end section of the holographic projector system of Fig. 1. Only two off-axis beams are shown.

Fig. 3
Fig. 3

New holographic projector system, shown end to end.

Fig. 4
Fig. 4

Holographic diffraction gratings that (a) emit three equiangular spectral order beams and (b) emit four equiangular spectral order beams.

Fig. 5
Fig. 5

Hypercomatic objective with two beams at ±1°.

Fig. 6
Fig. 6

Caustic formed with (a) two beams at ±1°, (b) two beams at ±2°, (c) two beams at ±4°.

Fig. 7
Fig. 7

(a) Two-dimensional plot of the equiangular three-beam interference pattern. (b) Inverted isometric view of the equiangular three-beam interference pattern.

Fig. 8
Fig. 8

Geometric construction for the ellipse calculations.

Fig. 9
Fig. 9

(a) Two-dimensional plot of the equiangular four-beam interference pattern. (b) Inverted isometric view of the equiangular four-beams interference pattern.

Fig. 10
Fig. 10

Noninverted isometric view of the equiangular three-beam interference pattern.

Fig. 11
Fig. 11

SEM photomicrograph of the three-beam interference pattern recorded in positive photoresist.

Fig. 12
Fig. 12

Photomicrograph of an interferogram of the four-beam interference pattern recorded in dichromated gelatin.

Tables (2)

Tables Icon

Table 1 Lens Data for the Illuminator Section of the Holographic Projector System when Configured End to End and Scaled to 150 mm Outa

Tables Icon

Table 2 Lens Data for the Hypercomatic (Immersion) Objectivea

Equations (10)

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

d=mλsin θm,
θm=sin-1mλd,
Ψ=sin-1λ2D,
D=λ/2 sin Ψ,
rθ=cos2 θa2+sin2 θb2-11/2.
K=2rθ-90°s1,
Rθ=Kd1.
Rθ=2rθ-90°s1 d1.
Rθ=2d1s1cos2θ-90°a2+sin2θ-90°b2-11/2.
Rθ=d1b1cos2θ-90°a2+sin2θ-90°b21/2.

Metrics