Abstract

A new method of selecting glass combinations for the correction of paraxial chromatic aberration in optical systems has been developed. This new method corrects axial color for at least three wavelengths using two different types of glass, and certain combinations may be found which are corrected at four and five wavelengths. The Abbe number and relative partial dispersions are not utilized in this new approach; instead the Buchdahl chromatic coordinate is used in characterizing the dispersion of the glasses. While the method is of general validity, in this first paper the number of different materials is restricted to two. Thick air-spaced doublets and Mangin mirror designs are presented as examples which demonstrate color correction at three, four, and five wavelengths and which are corrected for spherical aberration and spherochromatism as well. Tables are included listing glass combinations that have favorable power distributions and color correction at three, four, and five wavelengths.

© 1985 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. N. v. d. W. Lessing, “Selection of Optical Glasses in Apochromats,” J. Opt. Soc. Am. 47, 955 (1957).
    [CrossRef]
  2. N. v. d. W. Lessing, “Further Considerations on the Selection of Optical Glasses in Apochromats,” J. Opt. Soc. Am. 48, 269 (1958).
    [CrossRef]
  3. N. v. d. W. Lessing, “Selection of Optical Glasses in Superachromats,” Appl. Opt. 9, 1655 (1970).
  4. R. E. Stephens, “Selection of Glasses for Three-Color Achromats,” J. Opt. Soc. Am. 49, 398 (1959).
    [CrossRef]
  5. R. E. Stephens, “Four-Color Achromats and Superachromats,” J. Opt. Soc. Am. 50, 1016 (1960).
    [CrossRef]
  6. M. Herzberger, “Color Correction in Optical Systems and a New Dispersion Formula,” Opt. Acta 6, 197 (1959).
    [CrossRef]
  7. M. Herzberg, N. R. McClure, “The Design of Superachromatic Lenses,” Appl. Opt. 2, 553 (1963).
    [CrossRef]
  8. M. Herzberger, H. Pulvermacher, “Die Farbfehlerkorrektion von Multipletts,” Optica Acta 17, 349 (1970).
    [CrossRef]
  9. Herzberger, “Tables of Superachromatic Glasstriples and their Color Correction,” Optik 35, 1 (1972).
  10. H. Drucks, “Bemekung zur Theorie der Suprachromaten,” Optik, 23, 523 (1966).
  11. H. Schultz, “Zum Problem der Superachromate,” Optik 25, 203 (1967).
  12. H. Schulz, “Superchromate,” Optik 25, 208 (1967).
  13. H. Pulvermacher, “Theorie der Restspektren von Simpletts,” Optik 30, 297 (1969).
  14. H. Pulvermacher, “New Proofs for the Fundamental Rules for the Correction of Chromatic Aberrations,” Optik 30, 395 (1970).
  15. B. L. Nefedov, “The Design of Apochromats Made from Two and Three Different Glasses,” Sov. J. Opt. Technol. 40, 46 (1973).
  16. A. B. Agurok, “Some Superchromatization Problems,” Sov. J. Opt. Technol. 44, 114 (1977).
  17. M. G. Shpyakin, “Design of Four-Color Thin Apochromats,” Sov. J. Opt. Technol. 45, 81 (1978).
  18. M. G. Shpyakin, “Calculation of the Components of Apochromats Made from Four Types of Glass for a Broad Spectral Region,” Sov. J. Opt. Technol. 45, 219 (1978).
  19. G. A. Mozharov, “Graphical Analysis Method of Choosing the Glasses for the Design of a Four-Lens Three-Color Apochromat,” Sov. J. Opt. Technol. 44, 146 (1977).
  20. G. A. Mozharov, “Two-Component, Four-Color Apochromats,” Sov. J. Opt. Technol. 47, 398 (1980).
  21. R. I. Mercado, P. N. Robb, “Design of Thick Doublets Corrected at Four and Five Wavelengths,” J. Opt. Soc. Am. 71, 1639 (1981).
  22. P. N. Robb, R. I. Mercado, “Glass Selection for Hyperachromatic Triplets,” J. Opt. Soc. Am. 73, 1882 (1983).
  23. P. J. Sands, “Inhomogeneous Lenses, Chromatic Aberrations,” J. Opt. Soc. Am. 61, 777 (1971).
    [CrossRef] [PubMed]
  24. G. W. Forbes, “Chromatic Coordinates in Aberration Theory,” J. Opt. Soc. Am. A 1, 344 (1984).
    [CrossRef]
  25. H. A. Buchdahl, Optical Aberration Coefficients (Dover, New York, 1968).
  26. P. N. Robb, R. I. Mercado, “Calculation of Refractive Indices Using Buchdahl's Chromatic Coordinate,” Appl. Opt. 22, 1198 (1983).
    [CrossRef] [PubMed]
  27. R. I. Mercado, P. N. Robb, “Color-Corrected Optical Systems,” U.S. Patent Application (1982).

1984 (1)

1983 (2)

P. N. Robb, R. I. Mercado, “Calculation of Refractive Indices Using Buchdahl's Chromatic Coordinate,” Appl. Opt. 22, 1198 (1983).
[CrossRef] [PubMed]

P. N. Robb, R. I. Mercado, “Glass Selection for Hyperachromatic Triplets,” J. Opt. Soc. Am. 73, 1882 (1983).

1981 (1)

R. I. Mercado, P. N. Robb, “Design of Thick Doublets Corrected at Four and Five Wavelengths,” J. Opt. Soc. Am. 71, 1639 (1981).

1980 (1)

G. A. Mozharov, “Two-Component, Four-Color Apochromats,” Sov. J. Opt. Technol. 47, 398 (1980).

1978 (2)

M. G. Shpyakin, “Design of Four-Color Thin Apochromats,” Sov. J. Opt. Technol. 45, 81 (1978).

M. G. Shpyakin, “Calculation of the Components of Apochromats Made from Four Types of Glass for a Broad Spectral Region,” Sov. J. Opt. Technol. 45, 219 (1978).

1977 (2)

G. A. Mozharov, “Graphical Analysis Method of Choosing the Glasses for the Design of a Four-Lens Three-Color Apochromat,” Sov. J. Opt. Technol. 44, 146 (1977).

A. B. Agurok, “Some Superchromatization Problems,” Sov. J. Opt. Technol. 44, 114 (1977).

1973 (1)

B. L. Nefedov, “The Design of Apochromats Made from Two and Three Different Glasses,” Sov. J. Opt. Technol. 40, 46 (1973).

1972 (1)

Herzberger, “Tables of Superachromatic Glasstriples and their Color Correction,” Optik 35, 1 (1972).

1971 (1)

1970 (3)

H. Pulvermacher, “New Proofs for the Fundamental Rules for the Correction of Chromatic Aberrations,” Optik 30, 395 (1970).

N. v. d. W. Lessing, “Selection of Optical Glasses in Superachromats,” Appl. Opt. 9, 1655 (1970).

M. Herzberger, H. Pulvermacher, “Die Farbfehlerkorrektion von Multipletts,” Optica Acta 17, 349 (1970).
[CrossRef]

1969 (1)

H. Pulvermacher, “Theorie der Restspektren von Simpletts,” Optik 30, 297 (1969).

1967 (2)

H. Schultz, “Zum Problem der Superachromate,” Optik 25, 203 (1967).

H. Schulz, “Superchromate,” Optik 25, 208 (1967).

1966 (1)

H. Drucks, “Bemekung zur Theorie der Suprachromaten,” Optik, 23, 523 (1966).

1963 (1)

1960 (1)

1959 (2)

M. Herzberger, “Color Correction in Optical Systems and a New Dispersion Formula,” Opt. Acta 6, 197 (1959).
[CrossRef]

R. E. Stephens, “Selection of Glasses for Three-Color Achromats,” J. Opt. Soc. Am. 49, 398 (1959).
[CrossRef]

1958 (1)

1957 (1)

Agurok, A. B.

A. B. Agurok, “Some Superchromatization Problems,” Sov. J. Opt. Technol. 44, 114 (1977).

Buchdahl, H. A.

H. A. Buchdahl, Optical Aberration Coefficients (Dover, New York, 1968).

Drucks, H.

H. Drucks, “Bemekung zur Theorie der Suprachromaten,” Optik, 23, 523 (1966).

Forbes, G. W.

Herzberg, M.

Herzberger,

Herzberger, “Tables of Superachromatic Glasstriples and their Color Correction,” Optik 35, 1 (1972).

Herzberger, M.

M. Herzberger, H. Pulvermacher, “Die Farbfehlerkorrektion von Multipletts,” Optica Acta 17, 349 (1970).
[CrossRef]

M. Herzberger, “Color Correction in Optical Systems and a New Dispersion Formula,” Opt. Acta 6, 197 (1959).
[CrossRef]

Lessing, N. v. d. W.

McClure, N. R.

Mercado, R. I.

P. N. Robb, R. I. Mercado, “Calculation of Refractive Indices Using Buchdahl's Chromatic Coordinate,” Appl. Opt. 22, 1198 (1983).
[CrossRef] [PubMed]

P. N. Robb, R. I. Mercado, “Glass Selection for Hyperachromatic Triplets,” J. Opt. Soc. Am. 73, 1882 (1983).

R. I. Mercado, P. N. Robb, “Design of Thick Doublets Corrected at Four and Five Wavelengths,” J. Opt. Soc. Am. 71, 1639 (1981).

R. I. Mercado, P. N. Robb, “Color-Corrected Optical Systems,” U.S. Patent Application (1982).

Mozharov, G. A.

G. A. Mozharov, “Two-Component, Four-Color Apochromats,” Sov. J. Opt. Technol. 47, 398 (1980).

G. A. Mozharov, “Graphical Analysis Method of Choosing the Glasses for the Design of a Four-Lens Three-Color Apochromat,” Sov. J. Opt. Technol. 44, 146 (1977).

Nefedov, B. L.

B. L. Nefedov, “The Design of Apochromats Made from Two and Three Different Glasses,” Sov. J. Opt. Technol. 40, 46 (1973).

Pulvermacher, H.

H. Pulvermacher, “New Proofs for the Fundamental Rules for the Correction of Chromatic Aberrations,” Optik 30, 395 (1970).

M. Herzberger, H. Pulvermacher, “Die Farbfehlerkorrektion von Multipletts,” Optica Acta 17, 349 (1970).
[CrossRef]

H. Pulvermacher, “Theorie der Restspektren von Simpletts,” Optik 30, 297 (1969).

Robb, P. N.

P. N. Robb, R. I. Mercado, “Glass Selection for Hyperachromatic Triplets,” J. Opt. Soc. Am. 73, 1882 (1983).

P. N. Robb, R. I. Mercado, “Calculation of Refractive Indices Using Buchdahl's Chromatic Coordinate,” Appl. Opt. 22, 1198 (1983).
[CrossRef] [PubMed]

R. I. Mercado, P. N. Robb, “Design of Thick Doublets Corrected at Four and Five Wavelengths,” J. Opt. Soc. Am. 71, 1639 (1981).

R. I. Mercado, P. N. Robb, “Color-Corrected Optical Systems,” U.S. Patent Application (1982).

Sands, P. J.

Schultz, H.

H. Schultz, “Zum Problem der Superachromate,” Optik 25, 203 (1967).

Schulz, H.

H. Schulz, “Superchromate,” Optik 25, 208 (1967).

Shpyakin, M. G.

M. G. Shpyakin, “Design of Four-Color Thin Apochromats,” Sov. J. Opt. Technol. 45, 81 (1978).

M. G. Shpyakin, “Calculation of the Components of Apochromats Made from Four Types of Glass for a Broad Spectral Region,” Sov. J. Opt. Technol. 45, 219 (1978).

Stephens, R. E.

Appl. Opt. (3)

J. Opt. Soc. Am. (7)

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

Opt. Acta (1)

M. Herzberger, “Color Correction in Optical Systems and a New Dispersion Formula,” Opt. Acta 6, 197 (1959).
[CrossRef]

Optica Acta (1)

M. Herzberger, H. Pulvermacher, “Die Farbfehlerkorrektion von Multipletts,” Optica Acta 17, 349 (1970).
[CrossRef]

Optik (6)

Herzberger, “Tables of Superachromatic Glasstriples and their Color Correction,” Optik 35, 1 (1972).

H. Drucks, “Bemekung zur Theorie der Suprachromaten,” Optik, 23, 523 (1966).

H. Schultz, “Zum Problem der Superachromate,” Optik 25, 203 (1967).

H. Schulz, “Superchromate,” Optik 25, 208 (1967).

H. Pulvermacher, “Theorie der Restspektren von Simpletts,” Optik 30, 297 (1969).

H. Pulvermacher, “New Proofs for the Fundamental Rules for the Correction of Chromatic Aberrations,” Optik 30, 395 (1970).

Sov. J. Opt. Technol. (6)

B. L. Nefedov, “The Design of Apochromats Made from Two and Three Different Glasses,” Sov. J. Opt. Technol. 40, 46 (1973).

A. B. Agurok, “Some Superchromatization Problems,” Sov. J. Opt. Technol. 44, 114 (1977).

M. G. Shpyakin, “Design of Four-Color Thin Apochromats,” Sov. J. Opt. Technol. 45, 81 (1978).

M. G. Shpyakin, “Calculation of the Components of Apochromats Made from Four Types of Glass for a Broad Spectral Region,” Sov. J. Opt. Technol. 45, 219 (1978).

G. A. Mozharov, “Graphical Analysis Method of Choosing the Glasses for the Design of a Four-Lens Three-Color Apochromat,” Sov. J. Opt. Technol. 44, 146 (1977).

G. A. Mozharov, “Two-Component, Four-Color Apochromats,” Sov. J. Opt. Technol. 47, 398 (1980).

Other (2)

H. A. Buchdahl, Optical Aberration Coefficients (Dover, New York, 1968).

R. I. Mercado, P. N. Robb, “Color-Corrected Optical Systems,” U.S. Patent Application (1982).

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 (10)

Fig. 1
Fig. 1

N-Color doublet: (N − 1)th degree glass dispersion model.

Fig. 2
Fig. 2

Examples of N-color doublets: (N − 1)th degree glass dispersion model.

Fig. 3
Fig. 3

Plot of η1 vs η2 for five glass catalogs.

Fig. 4
Fig. 4

Plot of the upper left region of the five catalogs showing the nine key glasses.

Fig. 5
Fig. 5

Paraxial ray height and rms spot radius vs wavelength for two achromats.

Fig. 6
Fig. 6

Paraxial ray height and rms spot radius vs wavelength for two airspaced doublets, three focal crossings.

Fig. 7
Fig. 7

Paraxial ray height and rms spot radius vs wavelength for two airspaced doublets, four focal crossings.

Fig. 8
Fig. 8

Paraxial ray height and rms spot radius vs wavelength for two airspaced doublets, five focal crossings.

Fig. 9
Fig. 9

Paraxial ray height and rms spot radius vs wavelength for two airspaced Mangin mirrors, three and four focal crossings.

Fig. 10
Fig. 10

Change in deviation angle vs wavelength for a two-element prism.

Tables (2)

Tables Icon

Table I Glass Combinations Corrected at Three Wavelengths

Tables Icon

Table II Glass Combinations Corrected at Four and Five Wavelengths

Equations (36)

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

N 2 = A 0 + A 1 λ 2 + A 2 λ 2 + A 3 λ 4 + A 4 λ 6 + A 5 λ 8 .
ω ( λ ) = λ λ 0 1 + 5 / 2 ( λ λ 0 ) ,
N ( ω ) = N 0 + ν 1 ω + ν 2 ω 2 + ν 3 ω 3 + + ν n ω n .
D ( λ ) = δ N ( λ ) N 0 1 ,
δ N ( λ ) = i = 1 ν i ω i .
D ( λ ) = i = 1 n η i ω i ( λ ) ,
D ( λ 1 , λ 2 ) = i = 1 n η i [ ω i ( λ 1 ) ω i ( λ 2 ) ] .
ϕ = ( C 1 C 2 ) ( N 1 ) = K ( N 1 ) .
ϕ ( λ ) = K ( N 0 1 + ν 1 ω + ν 2 ω 2 + ν 3 ω 3 + ) ,
ϕ ( λ ) = ϕ ( λ 0 ) + K ( ν 1 ω + ν 2 ω 2 + ν 3 ω 3 + ) ,
ϕ ( λ ) = ϕ ( λ 0 ) ( 1 + η 1 ω + η 2 ω 2 + η 3 ω 3 + ) ,
ϕ ( λ ) = ϕ ( λ 0 ) [ 1 + D ( λ ) ] .
ϕ j ( λ i ) = ϕ j [ 1 + D j ( λ i ) ] .
ϕ ( λ 1 ) ϕ ( λ 2 ) = 0 .
ϕ 1 [ 1 + D 1 ( λ 1 ) ] + ϕ 2 [ 1 + D 2 ( λ 1 ) ] ϕ 1 [ 1 + D 1 ( λ 2 ) ] ϕ 2 [ 1 + D 2 ( λ 2 ) ] = 0 .
D ( λ ) = η 1 ω ( λ ) .
ϕ 1 = η 12 / ( η 12 η 11 ) , ϕ 2 = η 11 / ( η 12 η 11 ) ,
ϕ ( λ 1 ) ϕ ( λ 2 ) = 0 , ϕ ( λ 2 ) ϕ ( λ 3 ) = 0 .
ϕ 1 [ 1 + D 1 ( λ 1 ) ] + ϕ 2 [ 1 + D 2 ( λ 1 ) ] ϕ 1 [ 1 + D 1 ( λ 2 ) ] ϕ 2 [ 1 + D 2 ( λ 2 ) ] = 0 , ϕ 1 [ 1 + D 1 ( λ 2 ) ] + ϕ 2 [ 1 + D 2 ( λ 2 ) ] ϕ 1 [ 1 + D 1 ( λ 3 ) ] ϕ 2 [ 1 + D 2 ( λ 3 ) ] = 0 .
ϕ 1 D 1 ( λ 1 , λ 2 ) + ϕ 2 D 2 ( λ 1 , λ 2 ) = 0 , ϕ 1 D 1 ( λ 2 , λ 3 ) + ϕ 2 D 2 ( λ 2 , λ 3 ) = 0 .
D ( λ ) = η 1 ω + η 2 ω 2 .
Ω ¯ η ¯ Φ ¯ = 0 ¯ ,
Ω ¯ = [ ( ω 1 ω 2 ) ( ω 1 2 ω 2 2 ) ( ω 2 ω 3 ) ( ω 2 2 ω 3 2 ) ] , η ¯ = [ η 11 η 12 η 21 η 22 ] , Φ ¯ = [ ϕ 1 ϕ 2 ] , 0 ¯ = [ 0 0 ] .
| η ¯ | = | η 11 η 12 η 21 η 22 | = 0 .
η 11 η 21 = η 12 η 22 .
ϕ 1 = η 12 / ( η 12 η 11 ) , ϕ 2 = η 11 / ( η 12 η 11 ) .
ϕ ( λ 1 ) ϕ ( λ 2 ) = 0 , ϕ ( λ 2 ) ϕ ( λ 3 ) = 0 , ϕ ( λ 3 ) ϕ ( λ 4 ) = 0 .
ϕ 1 D 1 ( λ 1 , λ 2 ) + ϕ 2 D 2 ( λ 1 , λ 2 ) = 0 , ϕ 1 D 1 ( λ 2 , λ 3 ) + ϕ 2 D 2 ( λ 2 , λ 3 ) = 0 , ϕ 1 D 1 ( λ 3 , λ 4 ) + ϕ 2 D 2 ( λ 3 , λ 4 ) = 0 .
D ( λ ) = η 1 ω + η 2 ω 2 + η 3 ω 3 .
η 11 η 21 = η 12 η 22 , η 11 η 31 = η 12 η 32 , η 21 η 31 = η 22 η 32 .
ϕ 1 + ϕ 2 = 1 ,
D ¯ ϕ ¯ = 0 ¯ ,
ϕ ¯ = [ ϕ 1 ϕ 2 ] ,
D ¯ = [ D 1 ( λ 1 , λ 2 ) D 2 ( λ 1 , λ 2 ) D 1 ( λ 2 , λ 3 ) D 2 ( λ 2 , λ 3 ) D 1 ( λ j 1 , λ j ) D 2 ( λ j 1 , λ j ) ] ,
D 1 ( λ 1 , λ 2 ) D 2 ( λ 1 , λ 2 ) = D 1 ( λ 2 , λ 3 ) D 2 ( λ 2 , λ 3 ) = D 1 ( λ j 1 , λ j ) D 2 ( λ j 1 , λ j ) .
G ¯ 1 = α G ¯ 2 ,

Metrics