Abstract

For many applications the high reflectance of conventional multilayer interference filters is undesirable. It is possible to design and construct interference filters in which the transmittance and reflectance are independently controlled and in which the reflectance is very low. However, to do this it is necessary to employ absorbing coating materials and, as a result, a reduction in the peak transmittance must be accepted. We describe three different methods for the design of such coatings. Examples are given of a number of bandpass filters, neutral density filters, cutoff filters, and of an x¯λ tristimulus filter, all having a low reflectance. This reflectance is frequently 15 to 50 times lower than that of conventional filters.

© 1995 Optical Society of America

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References

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  1. J. A. Dobrowolski, “Coatings and filters,” in Handbook of Optics, W. G. Driscoll, W. Vaughan, eds. (McGraw-Hill, New York, 1978), pp. 8.1–8.124.
  2. J. A. Dobrowolski, G. E. Marsh, D. G. Charbonneau, J. Eng, P. D. Josephy, “Colored filter glasses: an intercomparison of glasses made by different manufacturers,” Appl. Opt. 16, 1491–1512 (1977).
    [Crossref] [PubMed]
  3. J. A. Dobrowolski, B. T. Sullivan, R. C. Bajcar, “Optical interference, contrast-enhanced electroluminescent device,” Appl. Opt. 31, 5988–5996 (1992).
    [Crossref] [PubMed]
  4. J. A. Dobrowolski, D. Lowe, “Optical thin film synthesis program based on the use of Fourier transforms,” Appl. Opt. 17, 3039–3050 (1978).
    [Crossref] [PubMed]
  5. B. T. Sullivan, J. A. Dobrowolski, “Deposition error compensation for optical multilayer coatings. II. Experimental results—sputtering system,” Appl. Opt. 32, 2351–2360 (1993).
    [Crossref] [PubMed]
  6. P. G. Kard, “Theory of multilayer asymmetric reflectors,” Opt. Spektrosk. 10, 384–389 (1961).
  7. P. Kard, “On the theory of asymmetric mirrors,” Eesti NSV Tead. Akad. Toim. Fuus.-Mat. 12, 359–368 (1963).
  8. P. Baumeister, R. Gelber, “Generalized equation for the absorptance of a multilayer stack,” J. Opt. Soc. Am. 58, 736 (1968), abstract FF12.
  9. N. D. Goldina, “Design of asymmetric mirrors with thin absorbing film,” Opt. Spectrosc. (USSR) 47, 776–779 (1979).
  10. N. V. Grishina, “Synthesis of wideband metal-dielectric coatings,” Opt. Spectrosc. (USSR) 72, 562–565 (1992).
  11. B. T. Sullivan, K. L. Byrt, “Metal/dielectric transmission interference filters with low reflectance. 2. Experimental results,” Appl. Opt. 34, 5684–5694 (1995).
    [Crossref] [PubMed]
  12. J. A. Dobrowolski, “Optical properties of films and coatings,” in Handbook of Optics, M. Bass, ed. (McGraw-Hill, New York, 1995), pp. 42.1–42-130.
  13. J. H. Apfel, R. M. Gelber, “Multilayer filter with metal dielectric period,” U.S. patent3,649,359 (14March1972).
  14. J. H. Apfel, R. M. Gelber, “Filter with neutral transmitting multilayer coating having asymmetric reflectance,” U.S. patent3,679,291 (25July1972).
  15. R. J. Fay, J. R. Cicotta, “Neutral density filter element with reduced surface reflection,” U.S. patent3,781,089 (25December1973).
  16. K. Yamamoto, T. Koike, “Light absorptive film provided with a reflection preventive means,” U.S. patent4,381,883 (3May1983).
  17. D. H. Cushing, “Neutral density filters for the ultraviolet that obey Beer’s law,” in Ultraviolet Technology III, R. E. Huffman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1158, 189–193 (1989).
  18. D. H. Cushing, “Broad band nonreflective neutral density filter,” U.S. patent4,960,310 (2October1990).
  19. A. Bittar, “Design of ultraviolet neutral density filters using metal-insulator inhomogeneous layers,” Appl. Opt. 31, 6122–6126 (1992).
    [Crossref] [PubMed]
  20. J. Rancourt, “Anti-halo coatings for CRT faceplates,” Soc. for Inf. Disp. Dig.22–23 (1983).
  21. J. D. Rancourt, “Anti-halo coatings for cathode ray tube faceplates,” Proc. of the Soc. for Inf. Disp. 25, 43–47 (1984).
  22. J. R. Jacobsson, “Protective device for protection against radiation during welding,” U.S. patent4,169,655 (2October1979).
  23. W. H. Southwell, “Coating design using very thin high- and low-index layers,” Appl. Opt. 24, 457–460 (1985).
    [Crossref] [PubMed]
  24. J. A. Dobrowolski, “Comparison of the Fourier transform and flip–flop thin-film synthesis methods,” Appl. Opt. 25, 1966–1972 (1986).
    [Crossref] [PubMed]
  25. J. A. Dobrowolski, R. A. Kemp, “Flip-flop thin-film design program with enhanced capabilities,” Appl. Opt. 31, 3807–3812 (1992).
    [Crossref] [PubMed]
  26. H. Dupoisot, J. Morizet, P. Lostis, “Pièges à lumière interfèrentiels à larges bandes azimuthale et spectrale,” Appl. Opt. 13, 1605–1609 (1974).
    [Crossref] [PubMed]
  27. H. Pohlack, “Über die reflexionsvermindernde Wirkung dünner Metallschichten auf Glas,” in Jenaer Jahrbuch 1956, P. Görlich, ed. (Fischer, Jena, Germany, 1956), pp. 87–93.
  28. L. F. J. Drummeter, G. Hass, “Solar absorptance and thermal emittance of evaporated coatings,” in Physics of Thin Films, G. Hass, R. E. Thun, eds. (Academic, New York, 1964), pp. 305–361.
  29. J. A. Dobrowolski, E. H. Hara, B. T. Sullivan, A. J. Waldorf, “High performance optical wavelength multiplexer–demultiplexer,” Appl. Opt. 31, 3800–3806 (1992).
    [Crossref] [PubMed]
  30. J. A. Dobrowolski, R. A. Kemp, “Refinement of optical multilayer systems with different optimization procedures,” Appl. Opt. 29, 2876–2893 (1990).
    [Crossref] [PubMed]
  31. H. A. Macleod, Thin-Film Optical Filters, 2nd ed. (McGraw-Hill, New York, 1986).
    [Crossref]
  32. E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, Orlando, Fla., 1985), pp. 313–323, 350–356, 749–764.
  33. J. A. Dobrowolski, R. Kemp, B. T. Sullivan, “Black bandpass interference filters,” in Annual Meeting Technical Digest, Vol. 16 of OSA 1993 Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 115.
  34. L. Li, J. A. Dobrowolski, B. T. Sullivan, “Low reflection optical coatings with arbitrary transmission shapes,” in Annual Meeting Technical Digest, Vol. 16 of OSA 1993 Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 114.
  35. B. T. Sullivan, J. A. Dobrowolski, “Deposition of metal/dielectric multilayers,” in Optical Interference Coatings, F. Abeles, A. Duparre, G. Emiliani, J.-P. Gailliard, K. H. Guenther, R. P. Netterfield, E. P. Pelletier, H. Rudigier, A. Macleod, C. Boccara, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2253, 1213–1217 (1994).

1995 (1)

1993 (1)

1992 (5)

1990 (1)

1986 (1)

1985 (1)

1984 (1)

J. D. Rancourt, “Anti-halo coatings for cathode ray tube faceplates,” Proc. of the Soc. for Inf. Disp. 25, 43–47 (1984).

1983 (1)

J. Rancourt, “Anti-halo coatings for CRT faceplates,” Soc. for Inf. Disp. Dig.22–23 (1983).

1979 (1)

N. D. Goldina, “Design of asymmetric mirrors with thin absorbing film,” Opt. Spectrosc. (USSR) 47, 776–779 (1979).

1978 (1)

1977 (1)

1974 (1)

1968 (1)

P. Baumeister, R. Gelber, “Generalized equation for the absorptance of a multilayer stack,” J. Opt. Soc. Am. 58, 736 (1968), abstract FF12.

1963 (1)

P. Kard, “On the theory of asymmetric mirrors,” Eesti NSV Tead. Akad. Toim. Fuus.-Mat. 12, 359–368 (1963).

1961 (1)

P. G. Kard, “Theory of multilayer asymmetric reflectors,” Opt. Spektrosk. 10, 384–389 (1961).

Apfel, J. H.

J. H. Apfel, R. M. Gelber, “Multilayer filter with metal dielectric period,” U.S. patent3,649,359 (14March1972).

J. H. Apfel, R. M. Gelber, “Filter with neutral transmitting multilayer coating having asymmetric reflectance,” U.S. patent3,679,291 (25July1972).

Bajcar, R. C.

Baumeister, P.

P. Baumeister, R. Gelber, “Generalized equation for the absorptance of a multilayer stack,” J. Opt. Soc. Am. 58, 736 (1968), abstract FF12.

Bittar, A.

Byrt, K. L.

Charbonneau, D. G.

Cicotta, J. R.

R. J. Fay, J. R. Cicotta, “Neutral density filter element with reduced surface reflection,” U.S. patent3,781,089 (25December1973).

Cushing, D. H.

D. H. Cushing, “Neutral density filters for the ultraviolet that obey Beer’s law,” in Ultraviolet Technology III, R. E. Huffman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1158, 189–193 (1989).

D. H. Cushing, “Broad band nonreflective neutral density filter,” U.S. patent4,960,310 (2October1990).

Dobrowolski, J. A.

B. T. Sullivan, J. A. Dobrowolski, “Deposition error compensation for optical multilayer coatings. II. Experimental results—sputtering system,” Appl. Opt. 32, 2351–2360 (1993).
[Crossref] [PubMed]

J. A. Dobrowolski, E. H. Hara, B. T. Sullivan, A. J. Waldorf, “High performance optical wavelength multiplexer–demultiplexer,” Appl. Opt. 31, 3800–3806 (1992).
[Crossref] [PubMed]

J. A. Dobrowolski, R. A. Kemp, “Flip-flop thin-film design program with enhanced capabilities,” Appl. Opt. 31, 3807–3812 (1992).
[Crossref] [PubMed]

J. A. Dobrowolski, B. T. Sullivan, R. C. Bajcar, “Optical interference, contrast-enhanced electroluminescent device,” Appl. Opt. 31, 5988–5996 (1992).
[Crossref] [PubMed]

J. A. Dobrowolski, R. A. Kemp, “Refinement of optical multilayer systems with different optimization procedures,” Appl. Opt. 29, 2876–2893 (1990).
[Crossref] [PubMed]

J. A. Dobrowolski, “Comparison of the Fourier transform and flip–flop thin-film synthesis methods,” Appl. Opt. 25, 1966–1972 (1986).
[Crossref] [PubMed]

J. A. Dobrowolski, D. Lowe, “Optical thin film synthesis program based on the use of Fourier transforms,” Appl. Opt. 17, 3039–3050 (1978).
[Crossref] [PubMed]

J. A. Dobrowolski, G. E. Marsh, D. G. Charbonneau, J. Eng, P. D. Josephy, “Colored filter glasses: an intercomparison of glasses made by different manufacturers,” Appl. Opt. 16, 1491–1512 (1977).
[Crossref] [PubMed]

J. A. Dobrowolski, R. Kemp, B. T. Sullivan, “Black bandpass interference filters,” in Annual Meeting Technical Digest, Vol. 16 of OSA 1993 Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 115.

L. Li, J. A. Dobrowolski, B. T. Sullivan, “Low reflection optical coatings with arbitrary transmission shapes,” in Annual Meeting Technical Digest, Vol. 16 of OSA 1993 Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 114.

B. T. Sullivan, J. A. Dobrowolski, “Deposition of metal/dielectric multilayers,” in Optical Interference Coatings, F. Abeles, A. Duparre, G. Emiliani, J.-P. Gailliard, K. H. Guenther, R. P. Netterfield, E. P. Pelletier, H. Rudigier, A. Macleod, C. Boccara, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2253, 1213–1217 (1994).

J. A. Dobrowolski, “Coatings and filters,” in Handbook of Optics, W. G. Driscoll, W. Vaughan, eds. (McGraw-Hill, New York, 1978), pp. 8.1–8.124.

J. A. Dobrowolski, “Optical properties of films and coatings,” in Handbook of Optics, M. Bass, ed. (McGraw-Hill, New York, 1995), pp. 42.1–42-130.

Drummeter, L. F. J.

L. F. J. Drummeter, G. Hass, “Solar absorptance and thermal emittance of evaporated coatings,” in Physics of Thin Films, G. Hass, R. E. Thun, eds. (Academic, New York, 1964), pp. 305–361.

Dupoisot, H.

Eng, J.

Fay, R. J.

R. J. Fay, J. R. Cicotta, “Neutral density filter element with reduced surface reflection,” U.S. patent3,781,089 (25December1973).

Gelber, R.

P. Baumeister, R. Gelber, “Generalized equation for the absorptance of a multilayer stack,” J. Opt. Soc. Am. 58, 736 (1968), abstract FF12.

Gelber, R. M.

J. H. Apfel, R. M. Gelber, “Filter with neutral transmitting multilayer coating having asymmetric reflectance,” U.S. patent3,679,291 (25July1972).

J. H. Apfel, R. M. Gelber, “Multilayer filter with metal dielectric period,” U.S. patent3,649,359 (14March1972).

Goldina, N. D.

N. D. Goldina, “Design of asymmetric mirrors with thin absorbing film,” Opt. Spectrosc. (USSR) 47, 776–779 (1979).

Grishina, N. V.

N. V. Grishina, “Synthesis of wideband metal-dielectric coatings,” Opt. Spectrosc. (USSR) 72, 562–565 (1992).

Hara, E. H.

Hass, G.

L. F. J. Drummeter, G. Hass, “Solar absorptance and thermal emittance of evaporated coatings,” in Physics of Thin Films, G. Hass, R. E. Thun, eds. (Academic, New York, 1964), pp. 305–361.

Jacobsson, J. R.

J. R. Jacobsson, “Protective device for protection against radiation during welding,” U.S. patent4,169,655 (2October1979).

Josephy, P. D.

Kard, P.

P. Kard, “On the theory of asymmetric mirrors,” Eesti NSV Tead. Akad. Toim. Fuus.-Mat. 12, 359–368 (1963).

Kard, P. G.

P. G. Kard, “Theory of multilayer asymmetric reflectors,” Opt. Spektrosk. 10, 384–389 (1961).

Kemp, R.

J. A. Dobrowolski, R. Kemp, B. T. Sullivan, “Black bandpass interference filters,” in Annual Meeting Technical Digest, Vol. 16 of OSA 1993 Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 115.

Kemp, R. A.

Koike, T.

K. Yamamoto, T. Koike, “Light absorptive film provided with a reflection preventive means,” U.S. patent4,381,883 (3May1983).

Li, L.

L. Li, J. A. Dobrowolski, B. T. Sullivan, “Low reflection optical coatings with arbitrary transmission shapes,” in Annual Meeting Technical Digest, Vol. 16 of OSA 1993 Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 114.

Lostis, P.

Lowe, D.

Macleod, H. A.

H. A. Macleod, Thin-Film Optical Filters, 2nd ed. (McGraw-Hill, New York, 1986).
[Crossref]

Marsh, G. E.

Morizet, J.

Pohlack, H.

H. Pohlack, “Über die reflexionsvermindernde Wirkung dünner Metallschichten auf Glas,” in Jenaer Jahrbuch 1956, P. Görlich, ed. (Fischer, Jena, Germany, 1956), pp. 87–93.

Rancourt, J.

J. Rancourt, “Anti-halo coatings for CRT faceplates,” Soc. for Inf. Disp. Dig.22–23 (1983).

Rancourt, J. D.

J. D. Rancourt, “Anti-halo coatings for cathode ray tube faceplates,” Proc. of the Soc. for Inf. Disp. 25, 43–47 (1984).

Southwell, W. H.

Sullivan, B. T.

B. T. Sullivan, K. L. Byrt, “Metal/dielectric transmission interference filters with low reflectance. 2. Experimental results,” Appl. Opt. 34, 5684–5694 (1995).
[Crossref] [PubMed]

B. T. Sullivan, J. A. Dobrowolski, “Deposition error compensation for optical multilayer coatings. II. Experimental results—sputtering system,” Appl. Opt. 32, 2351–2360 (1993).
[Crossref] [PubMed]

J. A. Dobrowolski, B. T. Sullivan, R. C. Bajcar, “Optical interference, contrast-enhanced electroluminescent device,” Appl. Opt. 31, 5988–5996 (1992).
[Crossref] [PubMed]

J. A. Dobrowolski, E. H. Hara, B. T. Sullivan, A. J. Waldorf, “High performance optical wavelength multiplexer–demultiplexer,” Appl. Opt. 31, 3800–3806 (1992).
[Crossref] [PubMed]

J. A. Dobrowolski, R. Kemp, B. T. Sullivan, “Black bandpass interference filters,” in Annual Meeting Technical Digest, Vol. 16 of OSA 1993 Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 115.

L. Li, J. A. Dobrowolski, B. T. Sullivan, “Low reflection optical coatings with arbitrary transmission shapes,” in Annual Meeting Technical Digest, Vol. 16 of OSA 1993 Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 114.

B. T. Sullivan, J. A. Dobrowolski, “Deposition of metal/dielectric multilayers,” in Optical Interference Coatings, F. Abeles, A. Duparre, G. Emiliani, J.-P. Gailliard, K. H. Guenther, R. P. Netterfield, E. P. Pelletier, H. Rudigier, A. Macleod, C. Boccara, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2253, 1213–1217 (1994).

Waldorf, A. J.

Yamamoto, K.

K. Yamamoto, T. Koike, “Light absorptive film provided with a reflection preventive means,” U.S. patent4,381,883 (3May1983).

Appl. Opt. (12)

J. A. Dobrowolski, G. E. Marsh, D. G. Charbonneau, J. Eng, P. D. Josephy, “Colored filter glasses: an intercomparison of glasses made by different manufacturers,” Appl. Opt. 16, 1491–1512 (1977).
[Crossref] [PubMed]

J. A. Dobrowolski, B. T. Sullivan, R. C. Bajcar, “Optical interference, contrast-enhanced electroluminescent device,” Appl. Opt. 31, 5988–5996 (1992).
[Crossref] [PubMed]

J. A. Dobrowolski, D. Lowe, “Optical thin film synthesis program based on the use of Fourier transforms,” Appl. Opt. 17, 3039–3050 (1978).
[Crossref] [PubMed]

B. T. Sullivan, J. A. Dobrowolski, “Deposition error compensation for optical multilayer coatings. II. Experimental results—sputtering system,” Appl. Opt. 32, 2351–2360 (1993).
[Crossref] [PubMed]

B. T. Sullivan, K. L. Byrt, “Metal/dielectric transmission interference filters with low reflectance. 2. Experimental results,” Appl. Opt. 34, 5684–5694 (1995).
[Crossref] [PubMed]

A. Bittar, “Design of ultraviolet neutral density filters using metal-insulator inhomogeneous layers,” Appl. Opt. 31, 6122–6126 (1992).
[Crossref] [PubMed]

W. H. Southwell, “Coating design using very thin high- and low-index layers,” Appl. Opt. 24, 457–460 (1985).
[Crossref] [PubMed]

J. A. Dobrowolski, “Comparison of the Fourier transform and flip–flop thin-film synthesis methods,” Appl. Opt. 25, 1966–1972 (1986).
[Crossref] [PubMed]

J. A. Dobrowolski, R. A. Kemp, “Flip-flop thin-film design program with enhanced capabilities,” Appl. Opt. 31, 3807–3812 (1992).
[Crossref] [PubMed]

H. Dupoisot, J. Morizet, P. Lostis, “Pièges à lumière interfèrentiels à larges bandes azimuthale et spectrale,” Appl. Opt. 13, 1605–1609 (1974).
[Crossref] [PubMed]

J. A. Dobrowolski, E. H. Hara, B. T. Sullivan, A. J. Waldorf, “High performance optical wavelength multiplexer–demultiplexer,” Appl. Opt. 31, 3800–3806 (1992).
[Crossref] [PubMed]

J. A. Dobrowolski, R. A. Kemp, “Refinement of optical multilayer systems with different optimization procedures,” Appl. Opt. 29, 2876–2893 (1990).
[Crossref] [PubMed]

Eesti NSV Tead. Akad. Toim. Fuus.-Mat. (1)

P. Kard, “On the theory of asymmetric mirrors,” Eesti NSV Tead. Akad. Toim. Fuus.-Mat. 12, 359–368 (1963).

J. Opt. Soc. Am. (1)

P. Baumeister, R. Gelber, “Generalized equation for the absorptance of a multilayer stack,” J. Opt. Soc. Am. 58, 736 (1968), abstract FF12.

Opt. Spectrosc. (USSR) (2)

N. D. Goldina, “Design of asymmetric mirrors with thin absorbing film,” Opt. Spectrosc. (USSR) 47, 776–779 (1979).

N. V. Grishina, “Synthesis of wideband metal-dielectric coatings,” Opt. Spectrosc. (USSR) 72, 562–565 (1992).

Opt. Spektrosk. (1)

P. G. Kard, “Theory of multilayer asymmetric reflectors,” Opt. Spektrosk. 10, 384–389 (1961).

Proc. of the Soc. for Inf. Disp. (1)

J. D. Rancourt, “Anti-halo coatings for cathode ray tube faceplates,” Proc. of the Soc. for Inf. Disp. 25, 43–47 (1984).

Soc. for Inf. Disp. Dig. (1)

J. Rancourt, “Anti-halo coatings for CRT faceplates,” Soc. for Inf. Disp. Dig.22–23 (1983).

Other (16)

J. R. Jacobsson, “Protective device for protection against radiation during welding,” U.S. patent4,169,655 (2October1979).

H. Pohlack, “Über die reflexionsvermindernde Wirkung dünner Metallschichten auf Glas,” in Jenaer Jahrbuch 1956, P. Görlich, ed. (Fischer, Jena, Germany, 1956), pp. 87–93.

L. F. J. Drummeter, G. Hass, “Solar absorptance and thermal emittance of evaporated coatings,” in Physics of Thin Films, G. Hass, R. E. Thun, eds. (Academic, New York, 1964), pp. 305–361.

H. A. Macleod, Thin-Film Optical Filters, 2nd ed. (McGraw-Hill, New York, 1986).
[Crossref]

E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, Orlando, Fla., 1985), pp. 313–323, 350–356, 749–764.

J. A. Dobrowolski, R. Kemp, B. T. Sullivan, “Black bandpass interference filters,” in Annual Meeting Technical Digest, Vol. 16 of OSA 1993 Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 115.

L. Li, J. A. Dobrowolski, B. T. Sullivan, “Low reflection optical coatings with arbitrary transmission shapes,” in Annual Meeting Technical Digest, Vol. 16 of OSA 1993 Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 114.

B. T. Sullivan, J. A. Dobrowolski, “Deposition of metal/dielectric multilayers,” in Optical Interference Coatings, F. Abeles, A. Duparre, G. Emiliani, J.-P. Gailliard, K. H. Guenther, R. P. Netterfield, E. P. Pelletier, H. Rudigier, A. Macleod, C. Boccara, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2253, 1213–1217 (1994).

J. A. Dobrowolski, “Coatings and filters,” in Handbook of Optics, W. G. Driscoll, W. Vaughan, eds. (McGraw-Hill, New York, 1978), pp. 8.1–8.124.

J. A. Dobrowolski, “Optical properties of films and coatings,” in Handbook of Optics, M. Bass, ed. (McGraw-Hill, New York, 1995), pp. 42.1–42-130.

J. H. Apfel, R. M. Gelber, “Multilayer filter with metal dielectric period,” U.S. patent3,649,359 (14March1972).

J. H. Apfel, R. M. Gelber, “Filter with neutral transmitting multilayer coating having asymmetric reflectance,” U.S. patent3,679,291 (25July1972).

R. J. Fay, J. R. Cicotta, “Neutral density filter element with reduced surface reflection,” U.S. patent3,781,089 (25December1973).

K. Yamamoto, T. Koike, “Light absorptive film provided with a reflection preventive means,” U.S. patent4,381,883 (3May1983).

D. H. Cushing, “Neutral density filters for the ultraviolet that obey Beer’s law,” in Ultraviolet Technology III, R. E. Huffman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1158, 189–193 (1989).

D. H. Cushing, “Broad band nonreflective neutral density filter,” U.S. patent4,960,310 (2October1990).

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Figures (11)

Fig. 1
Fig. 1

Measured spectral performance of A, a metallic neutral density filter with reduced spectral reflectance (from Apfel and Gelber14); B, a narrow-band transmission filter with reduced spectral reflectance for use in welding glasses (from Jacobsson22).

Fig. 2
Fig. 2

Calculated spectral performance, A, and refractive-index profile, B, of a bandpass filter with reduced reflectance obtained by the modified flip–flop method.

Fig. 3
Fig. 3

Schematic diagram of a reflectance-reducing coating.

Fig. 4
Fig. 4

Diagram representing the various steps in the admittance approach to the design of coatings with reduced reflectance. Also shown are the intermediate results for the design of a cutoff filter.

Fig. 5
Fig. 5

Calculated spectral performance and refractive-index profiles of metal/dielectric bandpass filters with one (A–C) and two (D and E) cavities: A, D, conventional filters; B, E, and C, filters with reflectance reduced for light incident onto the filter in one and both directions, respectively.

Fig. 6
Fig. 6

Calculated spectral performances of induced transmission filters with one (A and B) and two (C and D) metal layers: A, C, conventional designs; B, D, filters with reduced reflectance.

Fig. 7
Fig. 7

Calculated spectral performances of all-dielectric bandpass filters with one (A and B) and two (C and D) metal layers: A, C, conventional designs; B, D, filters with reduced reflectance. LR, luminous reflectance.

Fig. 8
Fig. 8

Variation with angle of incidence of the transmittance for light of wavelength λ = 0.5495 μm and of the luminous reflectance (LR) of the filter of Fig. 7D.

Fig. 9
Fig. 9

Calculated spectral performance of neutral density filters with low reflectance: A, B, a series of neutral density filters with transmittances ranging from 0.75 to 0.0001; C, variation of performance with angle of incidence of a neutral density filter with a nominal transmittance of 0.001; D, T, R, and R′ of a neutral density filter consisting of identical coatings on both sides of the substrate.

Fig. 10
Fig. 10

Calculated spectral performance of short-wavelength (A and B) and long-wavelength (C and D) cutoff filters: A, C, conventional designs; B, D, filters with reduced reflectance.

Fig. 11
Fig. 11

Calculated spectral performance of x ¯ λ tristimulus filters: A, conventional design; B, filter with a reduced reflectance.

Tables (1)

Tables Icon

Table 1 Construction Parameters of the Low-Reflectance Neutral Density Filters of Fig. 9

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