Abstract

Fabrication of diffractive optics with binary masks requires multiple photolithographic processes to produce high-efficiency elements. Alignment or etching errors at any stage of fabrication decrease the efficiency of the element. We developed an easily accessible procedure that reduces fabrication complexity and costs by using a single gray-scale mask. The gray-scale patterns are generated by commercial slide imagers and are then photoreduced onto low-contrast film plates. Multiple-level or continuous relief structures (kinoforms) may be constructed by use of the photoreduced gray-scale patterns as lithographic masks. Diffractive-optic lenses and blazed gratings were fabricated in photoresist with this procedure. First-order diffraction efficiencies as high as 85% were measured for the blazed gratings. The advantages and the limitations of this technique are discussed.

© 1995 Optical Society of America

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References

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  1. PostScript is a trademark of Adobe Systems, Inc.
  2. D. O’Shea, J. Beletic, M. Poutous, “Binary-mask generation for diffractive optical elements using microcomputers,” Appl. Opt. 32, 2566–2572 (1993).
    [CrossRef]
  3. T. Suleski, D. O’Shea, Fidelity of PostScript-generated masks for diffractive optics fabrication,” Appl. Opt. 34, 627–635 (1995).
    [CrossRef] [PubMed]
  4. L. Domash, P. Levin, “Computer holographic elements using PostScript laser printers,” in Optical Computing, Vol. 9 of 1989 OSA Technical Digest Series(Optical Society of America, Washington, D.C., 1989), paper TUI32.
  5. C. Clark, Y. Demkov, “Making zone plates with a laser printer,” Am. J. Phys. 59, 158–162 (1991).
    [CrossRef]
  6. T. Yatagai, M. Geiser, R. Tian, H. Onda, “CAD system for CGH’s and laser beam lithography,” in Computer and Optically Generated Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 1555, 8–12 (1991).
  7. M. Geiser, “Software generates PostScript files of holograms,” Laser Focus World 269 (1990).M. Geiser, “Software generates PostScript files of holograms,” Laser Focus World 26, 51–54 (1990).
  8. Y. Carts, “Desktop manufacturing creates binary optics,” Laser Focus World 292, 123 (1993).
  9. J. Blatt, H. Ho, “Rapid fabrication of coarse transmission gratings and targets by microcomputer and laser printer,” Appl. Opt. 26, 2691 (1987).
    [CrossRef] [PubMed]
  10. G. J. Swanson, “Binary optics technology: the theory and design of multilevel diffractive optical elements,” MIT Lincoln Laboratory Rep. 854 (MIT, Cambridge, Mass., 1989).
  11. M. B. Stern, M. Holz, S. S. Medeiros, R. E. Knowlden, “Fabricating binary optics: process variables critical to optical efficiency,” J. Vac. Sci. Technol. B 9, 3117–3121 (1991).
    [CrossRef]
  12. H. Andersson, M. Ekberg, S. Hård, S. Jacobsson, M. Larson, T. Nilsson, “Single photomask, multilevel kinoforms in quartz and photoresist: manufacture and evaluation,” Appl. Opt. 28, 4259–4266 (1990).
    [CrossRef]
  13. D. O’Shea, W. Rockward, “Gray-scale masks for diffractive-optics fabrication. II. Spatially filtered halftone screens,” Appl. Opt. (this issue).
  14. M. T. Gale, M. Rossi, H. Schütz, P. Ehbets, H. P. Herzig, D. Prongué, “Continuous-relief diffractive optical elements for two-dimensional array generation,” Appl. Opt. 32, 2526–2533 (1993).
    [CrossRef] [PubMed]
  15. Rochester Photonics Corporation literature; Rochester, N.Y.
  16. Y. Opplinger, P. Sixt, J. M. Stauffer, J. M. Mayor, P. Regnault, G. Voirin, “One-step 3D shaping using a gray-tone mask for optical and microelectronic applications,” Microelectron. Eng. 23, 449–454 (1994).
    [CrossRef]
  17. A. G. Poleshchuk, “Fabrication of relief-phase structures with continuous and multilevel profiles for diffractive optics,” Opto-electron. Instrum. Data Process. 1, 67–79 (1992).
  18. G. Lemelin, R. A. Lessard, “New coding technique to obtain multilevel computer generated holograms in one step,” Opt. Eng. 32, 2227–2232 (1993).
    [CrossRef]
  19. V. E. Shrauger, L. L. Erwin, J. L. Ahn, C. Warde, “Computer-generated multiple phase level holograms using color printer techniques,” Appl. Opt. 33, 5318–5327 (1994).
    [CrossRef] [PubMed]
  20. mathematica is a trademark of Wolfram Research, Champaign, Ill.; freehand is a trademark of Macromedia, Inc., San Francisco, Calif.
  21. The Solitaire 8xp and Solitaire 16 are trademarks of Management Graphics, Minneaplis, Minn.
  22. Eastern Kodak Company, “Kodak technical Pan films,” Kodak Publ. P-255 (Eastman Kodak Company, Rochester, N.Y., 1987).
  23. imageanalyst is a trademark of Automatix, Inc., Billerica, Mass.
  24. Shipley Microposit S1400®Series Photoresist technical data sheet, Shipley, Newton, Mass.
  25. Figure 6 of Ref. 19.
  26. T. Suleski, “Diffraction efficiencies of imperfectly blazed phase gratings,” Appl. Opt. (to be published).
  27. Swanson’s result is presented in Ref. 10. Our notation differs from Swanson’s; his treatment of a perfect grating defines ηm = sin2[πT(β − m/T)]/[πT(β − m/T)]2, where β = [n(λ0) − 1]d/λ0T. Although the definition of the parameter α is not exactly the same, our notation is closer to that of Buralli et al. [D. Buralli, G. M. Morris, J. Rogers, “Optical performance of holographic kinoforms,” Appl. Opt. 38, 976–983 (1989)]. In their paper, α is defined as the fraction of a 2π phase delay that is introduced for illuminating wavelength λ incident upon a grating of depth d2π designed for wavelength λ0. Functionally, the two definitions are very similar, but the differences are mentioned for the sake of clarity.
  28. T. Fujita, H. Nishihara, J. Koyama, “Blazed gratings and Fresnel lenses fabricated by electron-beam lithography,” Opt. Lett. 7, 578–580 (1982).
    [CrossRef] [PubMed]
  29. Z. Yang, I. Menz, G. Dausmann, “Making blazed holograms with the new REFO-125 photoresist,” in Holographic Imaging and Materials, T. J. Jeong, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 2043, 14–17 (1993).

1995 (1)

1994 (2)

Y. Opplinger, P. Sixt, J. M. Stauffer, J. M. Mayor, P. Regnault, G. Voirin, “One-step 3D shaping using a gray-tone mask for optical and microelectronic applications,” Microelectron. Eng. 23, 449–454 (1994).
[CrossRef]

V. E. Shrauger, L. L. Erwin, J. L. Ahn, C. Warde, “Computer-generated multiple phase level holograms using color printer techniques,” Appl. Opt. 33, 5318–5327 (1994).
[CrossRef] [PubMed]

1993 (4)

1992 (1)

A. G. Poleshchuk, “Fabrication of relief-phase structures with continuous and multilevel profiles for diffractive optics,” Opto-electron. Instrum. Data Process. 1, 67–79 (1992).

1991 (2)

M. B. Stern, M. Holz, S. S. Medeiros, R. E. Knowlden, “Fabricating binary optics: process variables critical to optical efficiency,” J. Vac. Sci. Technol. B 9, 3117–3121 (1991).
[CrossRef]

C. Clark, Y. Demkov, “Making zone plates with a laser printer,” Am. J. Phys. 59, 158–162 (1991).
[CrossRef]

1990 (2)

M. Geiser, “Software generates PostScript files of holograms,” Laser Focus World 269 (1990).M. Geiser, “Software generates PostScript files of holograms,” Laser Focus World 26, 51–54 (1990).

H. Andersson, M. Ekberg, S. Hård, S. Jacobsson, M. Larson, T. Nilsson, “Single photomask, multilevel kinoforms in quartz and photoresist: manufacture and evaluation,” Appl. Opt. 28, 4259–4266 (1990).
[CrossRef]

1989 (1)

1987 (1)

1982 (1)

Ahn, J. L.

Andersson, H.

H. Andersson, M. Ekberg, S. Hård, S. Jacobsson, M. Larson, T. Nilsson, “Single photomask, multilevel kinoforms in quartz and photoresist: manufacture and evaluation,” Appl. Opt. 28, 4259–4266 (1990).
[CrossRef]

Beletic, J.

Blatt, J.

Buralli, D.

Carts, Y.

Y. Carts, “Desktop manufacturing creates binary optics,” Laser Focus World 292, 123 (1993).

Clark, C.

C. Clark, Y. Demkov, “Making zone plates with a laser printer,” Am. J. Phys. 59, 158–162 (1991).
[CrossRef]

Dausmann, G.

Z. Yang, I. Menz, G. Dausmann, “Making blazed holograms with the new REFO-125 photoresist,” in Holographic Imaging and Materials, T. J. Jeong, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 2043, 14–17 (1993).

Demkov, Y.

C. Clark, Y. Demkov, “Making zone plates with a laser printer,” Am. J. Phys. 59, 158–162 (1991).
[CrossRef]

Domash, L.

L. Domash, P. Levin, “Computer holographic elements using PostScript laser printers,” in Optical Computing, Vol. 9 of 1989 OSA Technical Digest Series(Optical Society of America, Washington, D.C., 1989), paper TUI32.

Ehbets, P.

Ekberg, M.

H. Andersson, M. Ekberg, S. Hård, S. Jacobsson, M. Larson, T. Nilsson, “Single photomask, multilevel kinoforms in quartz and photoresist: manufacture and evaluation,” Appl. Opt. 28, 4259–4266 (1990).
[CrossRef]

Erwin, L. L.

Fujita, T.

Gale, M. T.

Geiser, M.

M. Geiser, “Software generates PostScript files of holograms,” Laser Focus World 269 (1990).M. Geiser, “Software generates PostScript files of holograms,” Laser Focus World 26, 51–54 (1990).

T. Yatagai, M. Geiser, R. Tian, H. Onda, “CAD system for CGH’s and laser beam lithography,” in Computer and Optically Generated Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 1555, 8–12 (1991).

Hård, S.

H. Andersson, M. Ekberg, S. Hård, S. Jacobsson, M. Larson, T. Nilsson, “Single photomask, multilevel kinoforms in quartz and photoresist: manufacture and evaluation,” Appl. Opt. 28, 4259–4266 (1990).
[CrossRef]

Herzig, H. P.

Ho, H.

Holz, M.

M. B. Stern, M. Holz, S. S. Medeiros, R. E. Knowlden, “Fabricating binary optics: process variables critical to optical efficiency,” J. Vac. Sci. Technol. B 9, 3117–3121 (1991).
[CrossRef]

Jacobsson, S.

H. Andersson, M. Ekberg, S. Hård, S. Jacobsson, M. Larson, T. Nilsson, “Single photomask, multilevel kinoforms in quartz and photoresist: manufacture and evaluation,” Appl. Opt. 28, 4259–4266 (1990).
[CrossRef]

Knowlden, R. E.

M. B. Stern, M. Holz, S. S. Medeiros, R. E. Knowlden, “Fabricating binary optics: process variables critical to optical efficiency,” J. Vac. Sci. Technol. B 9, 3117–3121 (1991).
[CrossRef]

Koyama, J.

Larson, M.

H. Andersson, M. Ekberg, S. Hård, S. Jacobsson, M. Larson, T. Nilsson, “Single photomask, multilevel kinoforms in quartz and photoresist: manufacture and evaluation,” Appl. Opt. 28, 4259–4266 (1990).
[CrossRef]

Lemelin, G.

G. Lemelin, R. A. Lessard, “New coding technique to obtain multilevel computer generated holograms in one step,” Opt. Eng. 32, 2227–2232 (1993).
[CrossRef]

Lessard, R. A.

G. Lemelin, R. A. Lessard, “New coding technique to obtain multilevel computer generated holograms in one step,” Opt. Eng. 32, 2227–2232 (1993).
[CrossRef]

Levin, P.

L. Domash, P. Levin, “Computer holographic elements using PostScript laser printers,” in Optical Computing, Vol. 9 of 1989 OSA Technical Digest Series(Optical Society of America, Washington, D.C., 1989), paper TUI32.

Mayor, J. M.

Y. Opplinger, P. Sixt, J. M. Stauffer, J. M. Mayor, P. Regnault, G. Voirin, “One-step 3D shaping using a gray-tone mask for optical and microelectronic applications,” Microelectron. Eng. 23, 449–454 (1994).
[CrossRef]

Medeiros, S. S.

M. B. Stern, M. Holz, S. S. Medeiros, R. E. Knowlden, “Fabricating binary optics: process variables critical to optical efficiency,” J. Vac. Sci. Technol. B 9, 3117–3121 (1991).
[CrossRef]

Menz, I.

Z. Yang, I. Menz, G. Dausmann, “Making blazed holograms with the new REFO-125 photoresist,” in Holographic Imaging and Materials, T. J. Jeong, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 2043, 14–17 (1993).

Morris, G. M.

Nilsson, T.

H. Andersson, M. Ekberg, S. Hård, S. Jacobsson, M. Larson, T. Nilsson, “Single photomask, multilevel kinoforms in quartz and photoresist: manufacture and evaluation,” Appl. Opt. 28, 4259–4266 (1990).
[CrossRef]

Nishihara, H.

O’Shea, D.

Onda, H.

T. Yatagai, M. Geiser, R. Tian, H. Onda, “CAD system for CGH’s and laser beam lithography,” in Computer and Optically Generated Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 1555, 8–12 (1991).

Opplinger, Y.

Y. Opplinger, P. Sixt, J. M. Stauffer, J. M. Mayor, P. Regnault, G. Voirin, “One-step 3D shaping using a gray-tone mask for optical and microelectronic applications,” Microelectron. Eng. 23, 449–454 (1994).
[CrossRef]

Poleshchuk, A. G.

A. G. Poleshchuk, “Fabrication of relief-phase structures with continuous and multilevel profiles for diffractive optics,” Opto-electron. Instrum. Data Process. 1, 67–79 (1992).

Poutous, M.

Prongué, D.

Regnault, P.

Y. Opplinger, P. Sixt, J. M. Stauffer, J. M. Mayor, P. Regnault, G. Voirin, “One-step 3D shaping using a gray-tone mask for optical and microelectronic applications,” Microelectron. Eng. 23, 449–454 (1994).
[CrossRef]

Rockward, W.

D. O’Shea, W. Rockward, “Gray-scale masks for diffractive-optics fabrication. II. Spatially filtered halftone screens,” Appl. Opt. (this issue).

Rogers, J.

Rossi, M.

Schütz, H.

Shrauger, V. E.

Sixt, P.

Y. Opplinger, P. Sixt, J. M. Stauffer, J. M. Mayor, P. Regnault, G. Voirin, “One-step 3D shaping using a gray-tone mask for optical and microelectronic applications,” Microelectron. Eng. 23, 449–454 (1994).
[CrossRef]

Stauffer, J. M.

Y. Opplinger, P. Sixt, J. M. Stauffer, J. M. Mayor, P. Regnault, G. Voirin, “One-step 3D shaping using a gray-tone mask for optical and microelectronic applications,” Microelectron. Eng. 23, 449–454 (1994).
[CrossRef]

Stern, M. B.

M. B. Stern, M. Holz, S. S. Medeiros, R. E. Knowlden, “Fabricating binary optics: process variables critical to optical efficiency,” J. Vac. Sci. Technol. B 9, 3117–3121 (1991).
[CrossRef]

Suleski, T.

T. Suleski, D. O’Shea, Fidelity of PostScript-generated masks for diffractive optics fabrication,” Appl. Opt. 34, 627–635 (1995).
[CrossRef] [PubMed]

T. Suleski, “Diffraction efficiencies of imperfectly blazed phase gratings,” Appl. Opt. (to be published).

Swanson, G. J.

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

Tian, R.

T. Yatagai, M. Geiser, R. Tian, H. Onda, “CAD system for CGH’s and laser beam lithography,” in Computer and Optically Generated Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 1555, 8–12 (1991).

Voirin, G.

Y. Opplinger, P. Sixt, J. M. Stauffer, J. M. Mayor, P. Regnault, G. Voirin, “One-step 3D shaping using a gray-tone mask for optical and microelectronic applications,” Microelectron. Eng. 23, 449–454 (1994).
[CrossRef]

Warde, C.

Yang, Z.

Z. Yang, I. Menz, G. Dausmann, “Making blazed holograms with the new REFO-125 photoresist,” in Holographic Imaging and Materials, T. J. Jeong, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 2043, 14–17 (1993).

Yatagai, T.

T. Yatagai, M. Geiser, R. Tian, H. Onda, “CAD system for CGH’s and laser beam lithography,” in Computer and Optically Generated Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 1555, 8–12 (1991).

Am. J. Phys. (1)

C. Clark, Y. Demkov, “Making zone plates with a laser printer,” Am. J. Phys. 59, 158–162 (1991).
[CrossRef]

Appl. Opt. (8)

D. O’Shea, J. Beletic, M. Poutous, “Binary-mask generation for diffractive optical elements using microcomputers,” Appl. Opt. 32, 2566–2572 (1993).
[CrossRef]

T. Suleski, D. O’Shea, Fidelity of PostScript-generated masks for diffractive optics fabrication,” Appl. Opt. 34, 627–635 (1995).
[CrossRef] [PubMed]

J. Blatt, H. Ho, “Rapid fabrication of coarse transmission gratings and targets by microcomputer and laser printer,” Appl. Opt. 26, 2691 (1987).
[CrossRef] [PubMed]

H. Andersson, M. Ekberg, S. Hård, S. Jacobsson, M. Larson, T. Nilsson, “Single photomask, multilevel kinoforms in quartz and photoresist: manufacture and evaluation,” Appl. Opt. 28, 4259–4266 (1990).
[CrossRef]

D. O’Shea, W. Rockward, “Gray-scale masks for diffractive-optics fabrication. II. Spatially filtered halftone screens,” Appl. Opt. (this issue).

M. T. Gale, M. Rossi, H. Schütz, P. Ehbets, H. P. Herzig, D. Prongué, “Continuous-relief diffractive optical elements for two-dimensional array generation,” Appl. Opt. 32, 2526–2533 (1993).
[CrossRef] [PubMed]

V. E. Shrauger, L. L. Erwin, J. L. Ahn, C. Warde, “Computer-generated multiple phase level holograms using color printer techniques,” Appl. Opt. 33, 5318–5327 (1994).
[CrossRef] [PubMed]

Swanson’s result is presented in Ref. 10. Our notation differs from Swanson’s; his treatment of a perfect grating defines ηm = sin2[πT(β − m/T)]/[πT(β − m/T)]2, where β = [n(λ0) − 1]d/λ0T. Although the definition of the parameter α is not exactly the same, our notation is closer to that of Buralli et al. [D. Buralli, G. M. Morris, J. Rogers, “Optical performance of holographic kinoforms,” Appl. Opt. 38, 976–983 (1989)]. In their paper, α is defined as the fraction of a 2π phase delay that is introduced for illuminating wavelength λ incident upon a grating of depth d2π designed for wavelength λ0. Functionally, the two definitions are very similar, but the differences are mentioned for the sake of clarity.

J. Vac. Sci. Technol. B (1)

M. B. Stern, M. Holz, S. S. Medeiros, R. E. Knowlden, “Fabricating binary optics: process variables critical to optical efficiency,” J. Vac. Sci. Technol. B 9, 3117–3121 (1991).
[CrossRef]

Laser Focus World (2)

M. Geiser, “Software generates PostScript files of holograms,” Laser Focus World 269 (1990).M. Geiser, “Software generates PostScript files of holograms,” Laser Focus World 26, 51–54 (1990).

Y. Carts, “Desktop manufacturing creates binary optics,” Laser Focus World 292, 123 (1993).

Microelectron. Eng. (1)

Y. Opplinger, P. Sixt, J. M. Stauffer, J. M. Mayor, P. Regnault, G. Voirin, “One-step 3D shaping using a gray-tone mask for optical and microelectronic applications,” Microelectron. Eng. 23, 449–454 (1994).
[CrossRef]

Opt. Eng. (1)

G. Lemelin, R. A. Lessard, “New coding technique to obtain multilevel computer generated holograms in one step,” Opt. Eng. 32, 2227–2232 (1993).
[CrossRef]

Opt. Lett. (1)

Opto-electron. Instrum. Data Process. (1)

A. G. Poleshchuk, “Fabrication of relief-phase structures with continuous and multilevel profiles for diffractive optics,” Opto-electron. Instrum. Data Process. 1, 67–79 (1992).

Other (13)

PostScript is a trademark of Adobe Systems, Inc.

Rochester Photonics Corporation literature; Rochester, N.Y.

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

L. Domash, P. Levin, “Computer holographic elements using PostScript laser printers,” in Optical Computing, Vol. 9 of 1989 OSA Technical Digest Series(Optical Society of America, Washington, D.C., 1989), paper TUI32.

T. Yatagai, M. Geiser, R. Tian, H. Onda, “CAD system for CGH’s and laser beam lithography,” in Computer and Optically Generated Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 1555, 8–12 (1991).

Z. Yang, I. Menz, G. Dausmann, “Making blazed holograms with the new REFO-125 photoresist,” in Holographic Imaging and Materials, T. J. Jeong, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 2043, 14–17 (1993).

mathematica is a trademark of Wolfram Research, Champaign, Ill.; freehand is a trademark of Macromedia, Inc., San Francisco, Calif.

The Solitaire 8xp and Solitaire 16 are trademarks of Management Graphics, Minneaplis, Minn.

Eastern Kodak Company, “Kodak technical Pan films,” Kodak Publ. P-255 (Eastman Kodak Company, Rochester, N.Y., 1987).

imageanalyst is a trademark of Automatix, Inc., Billerica, Mass.

Shipley Microposit S1400®Series Photoresist technical data sheet, Shipley, Newton, Mass.

Figure 6 of Ref. 19.

T. Suleski, “Diffraction efficiencies of imperfectly blazed phase gratings,” Appl. Opt. (to be published).

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Figures (9)

Fig. 1
Fig. 1

Fabrication methods for efficient diffractive optics: (a) a two-step process that uses binary masks to create a four-level profile; (b) a single-step process that uses a variable-intensity exposure with a direct-write system; (c) a single-step process that uses a gray-scale mask.

Fig. 2
Fig. 2

Sample gray-scale patterns for diffractive-optics fabrication: (a) 8-level blazed grating and (b) 32-level kinoform lens.

Fig. 3
Fig. 3

Transmission linearity for gray-scale patterns on film and on photoreduced film plates. The gray percentage refers to the amount of gray in the original computer design. A gray value of 0 corresponds to opaque, and a value of 255 corresponds to transparent. Note that the reticle pattern is the photographic negative of the film pattern.

Fig. 4
Fig. 4

Transmission profiles of gray-scale masks for a range of grating periods. The patterns were measured from photoreduced patterns of 35-mm Kodak Technical Pan film slides. All the profiles were measured under the same lighting and magnification conditions.

Fig. 5
Fig. 5

Profiles of blazed-grating structures in photoresist: (a) 8-level 500-μm-period grating, (b) 16-level 127-μm-period grating, and (c) 8-level 32-μm-period grating.

Fig. 6
Fig. 6

(a) Profiles of a 32-level kinoform lens in photoresist. The central zone diameter is 337 μm. (b) Magnified image of a kinoform lens array. The horizontal and the vertical lines in the image are from the video caliper used to take the pictures and are not part of the lens array.

Fig. 7
Fig. 7

Intensity profile in the focal plane of a lens from the array shown in Fig. 6. The diffraction-limited spot diameter is 32.7 μm; diameters of 33–36 μm were measured. The diameter was measured between the nulls in the profile, not between the 1/e 2 intensity levels of the Gaussian beam.

Fig. 8
Fig. 8

An imperfectly blazed grating. Q = 1 for a perfectly blazed grating, and Q = 0.5 for a triangular grating.

Fig. 9
Fig. 9

Grating quality factors of gray-scale patterns. The quality factors were determined from photoreduced slides and transparencies for both Ektachrome and Pan film.

Tables (1)

Tables Icon

Table 1 Quality and Performance of Blazed Gratings Fabricated in Photoresist from a Single Gray-Scale Mask

Equations (3)

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

Q = 1 - x T ,
η m = Q 2 sin 2 [ π ( α - Q m ) ] [ π ( α - Q m ) ] 2 + ( 1 - Q ) 2 × sin 2 { π [ α + ( 1 - Q ) m ] } { π [ α + ( 1 - Q ) m ] } 2 + 2 Q ( 1 - Q ) × sin [ π ( α - Q m ) ] [ π ( α - Q m ) ] × sin { π [ α + ( 1 - Q ) m ] } { π [ α + ( 1 - Q ) m ] } × cos ( θ + m π ) ,
η m = sin 2 [ π ( α - m ) ] [ π ( α - m ) ] 2 .

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