Abstract

This work deals with a method for primary optical design of superachromats, where chromatic aberration is corrected for several wavelengths. Equations for the calculation of optical power and curvature radii are described for aplanatic and nonaplanatic optical systems, which are composed of two or three thin lenses in contact. Results of the calculations are presented for chosen optical systems of superachromats with basic design parameters.

© 2013 Optical Society of America

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References

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  1. M. Herzberger, Modern Geometrical Optics (Interscience, 1958).
  2. H. Chretien, Calcul des Combinaisons Optiques (Masson, 1980).
  3. D. Argentieri, Ottica industriale (Hoepli, 1942).
  4. M. Born, E. Wolf, Principles of Optics (Oxford University, 1964).
  5. A. Mikš, Applied Optics (Czech Technical University, 2009).
  6. A. Mikš, J. Vondřich, “Method for design of superachromatic systems I,” Fine Mech. Opt. 10, 79–84 (1966).
  7. A. Mikš, J. Vondřich, “Auswahl der glaser fur ein verkittetes duplet,” Optik 28, 321–327 (1968/69).
  8. M. Herzberger, H. Jenkins, “Color correction in optical systems and types of glass,” J. Opt. Soc. Am. 39, 984–986 (1949).
    [CrossRef]
  9. M. Herzberger, “Colour correction in optical systems and a new dispersion formula,” Opt. Acta 6, 197–215 (1959).
    [CrossRef]
  10. M. Herzberger, N. R. McClure, “The design of superachromatic lenses,” Appl. Opt. 2, 553–560 (1963).
    [CrossRef]
  11. M. Herzberger, “Tables of superachromatic glasstriplets and their color correction,” Optik 35, 1–8 (1972).
  12. M. Herzberger, H. Pulvermacher, “Die farbfehlerkorrektion von multipletts,” Opt. Acta 17, 349–361 (1970).
    [CrossRef]
  13. R. E. Stephens, “Four-color achromats and superchromats,” J. Opt. Soc. Am. 50, 1016–1019 (1960).
    [CrossRef]
  14. N. v. d. W. Lessing, “Selection of optical glasses in superachromats,” Appl. Opt. 9, 1665–1668 (1970).
    [CrossRef]
  15. N. v. d. W. Lessing, “Further considerations on the section of optical glasses in superachromats,” Appl. Opt. 9, 2390–2391 (1970).
    [CrossRef]
  16. P. N. Robb, “Selection of optical glasses,” Proc. SPIE 554, 60–75 (1985).
    [CrossRef]
  17. J. L. Rayces, M. Rosete-Aguilar, “Selection of glasses for achromatic doublets with reduced secondary spectrum. I. Tolerance conditions for secondary spectrum, spherochromatism, and fifth-order spherical aberration,” Appl. Opt. 40, 5663–5676 (2001).
    [CrossRef]
  18. H. Pulvermacher, “Theorie der restspektrum von simpletts,” Optik 30, 297–313 (1969).
  19. B. F. Carneiro de Albuquerque, J. Sasian, F. L. de Sousa, A. S. Montes, “Method of glass selection for color correction in optical system design,” Opt. Express 20, 13592–13611 (2012).
    [CrossRef]
  20. T. N. Khatsevich, V. L. Parko, “Algorithm for calculating objective—achromats with separated components for telescopic and collimation systems,” J. Opt. Technol. 79, 395–398 (2012).
    [CrossRef]
  21. R. D. Sigler, “Glass selection for airspaced apochromats using the Buchdahl dispersion equation,” Appl. Opt. 25, 4311–4320 (1986).
    [CrossRef]
  22. R. I. Mercado, “Design of apochromats and superachromats,” Proc. SPIE 1, 270–296 (1992).
  23. H. H. Hopkins, V. V. Rao, “The systematic design of two component objectives,” Opt. Acta 17, 497–514 (1970).
    [CrossRef]
  24. M. I. Khan, “Cemented triplets: a method for rapid design,” Opt. Acta 31, 873–883 (1984).
    [CrossRef]
  25. C. H. Chen, S. G. Shiue, “Method of solving a triplet comprising a singlet and a cemented doublet with given primary aberrations,” J. Mod. Opt. 45, 2063–2084 (1998).
  26. A. Szulc, “Improved solution for the cemented doublet,” Appl. Opt. 35, 3548–3558 (1996).
    [CrossRef]
  27. M. H. Sussman, “Cemented aplanatic doublets,” J. Opt. Soc. Am. 52, 1185–1186 (1962).
    [CrossRef]
  28. S. Banerjee, L. Hazra, “Experiments with a genetic algorithm for structural design of cemented doublets with prespecified aberration targets,” Appl. Opt. 40, 6265–6273 (2001).
    [CrossRef]
  29. M. I. Khan, J. Macdonald, “Cemented doublets, a method for rapid design,” Opt. Acta 29, 807–822 (1982).
    [CrossRef]
  30. A. Mikš, J. Novák, “Design of a double-sided telecentric zoom lens,” Appl. Opt. 51, 5928–5935 (2012).
    [CrossRef]
  31. M. Berek, Grundlagen der Praktischen Optik (Walter de Gruyter, 1970).
  32. B. E. Hansen, “Econometrics,” Draft Textbook Website: http://www.ssc.wisc.edu/~bhansen/econometrics/ (2013). Chap. 7.

2012

2001

1998

C. H. Chen, S. G. Shiue, “Method of solving a triplet comprising a singlet and a cemented doublet with given primary aberrations,” J. Mod. Opt. 45, 2063–2084 (1998).

1996

1992

R. I. Mercado, “Design of apochromats and superachromats,” Proc. SPIE 1, 270–296 (1992).

1986

1985

P. N. Robb, “Selection of optical glasses,” Proc. SPIE 554, 60–75 (1985).
[CrossRef]

1984

M. I. Khan, “Cemented triplets: a method for rapid design,” Opt. Acta 31, 873–883 (1984).
[CrossRef]

1982

M. I. Khan, J. Macdonald, “Cemented doublets, a method for rapid design,” Opt. Acta 29, 807–822 (1982).
[CrossRef]

1972

M. Herzberger, “Tables of superachromatic glasstriplets and their color correction,” Optik 35, 1–8 (1972).

1970

M. Herzberger, H. Pulvermacher, “Die farbfehlerkorrektion von multipletts,” Opt. Acta 17, 349–361 (1970).
[CrossRef]

N. v. d. W. Lessing, “Selection of optical glasses in superachromats,” Appl. Opt. 9, 1665–1668 (1970).
[CrossRef]

N. v. d. W. Lessing, “Further considerations on the section of optical glasses in superachromats,” Appl. Opt. 9, 2390–2391 (1970).
[CrossRef]

H. H. Hopkins, V. V. Rao, “The systematic design of two component objectives,” Opt. Acta 17, 497–514 (1970).
[CrossRef]

1969

H. Pulvermacher, “Theorie der restspektrum von simpletts,” Optik 30, 297–313 (1969).

1968

A. Mikš, J. Vondřich, “Auswahl der glaser fur ein verkittetes duplet,” Optik 28, 321–327 (1968/69).

1966

A. Mikš, J. Vondřich, “Method for design of superachromatic systems I,” Fine Mech. Opt. 10, 79–84 (1966).

1963

1962

1960

1959

M. Herzberger, “Colour correction in optical systems and a new dispersion formula,” Opt. Acta 6, 197–215 (1959).
[CrossRef]

1949

Argentieri, D.

D. Argentieri, Ottica industriale (Hoepli, 1942).

Banerjee, S.

Berek, M.

M. Berek, Grundlagen der Praktischen Optik (Walter de Gruyter, 1970).

Born, M.

M. Born, E. Wolf, Principles of Optics (Oxford University, 1964).

Carneiro de Albuquerque, B. F.

Chen, C. H.

C. H. Chen, S. G. Shiue, “Method of solving a triplet comprising a singlet and a cemented doublet with given primary aberrations,” J. Mod. Opt. 45, 2063–2084 (1998).

Chretien, H.

H. Chretien, Calcul des Combinaisons Optiques (Masson, 1980).

de Sousa, F. L.

Hazra, L.

Herzberger, M.

M. Herzberger, “Tables of superachromatic glasstriplets and their color correction,” Optik 35, 1–8 (1972).

M. Herzberger, H. Pulvermacher, “Die farbfehlerkorrektion von multipletts,” Opt. Acta 17, 349–361 (1970).
[CrossRef]

M. Herzberger, N. R. McClure, “The design of superachromatic lenses,” Appl. Opt. 2, 553–560 (1963).
[CrossRef]

M. Herzberger, “Colour correction in optical systems and a new dispersion formula,” Opt. Acta 6, 197–215 (1959).
[CrossRef]

M. Herzberger, H. Jenkins, “Color correction in optical systems and types of glass,” J. Opt. Soc. Am. 39, 984–986 (1949).
[CrossRef]

M. Herzberger, Modern Geometrical Optics (Interscience, 1958).

Hopkins, H. H.

H. H. Hopkins, V. V. Rao, “The systematic design of two component objectives,” Opt. Acta 17, 497–514 (1970).
[CrossRef]

Jenkins, H.

Khan, M. I.

M. I. Khan, “Cemented triplets: a method for rapid design,” Opt. Acta 31, 873–883 (1984).
[CrossRef]

M. I. Khan, J. Macdonald, “Cemented doublets, a method for rapid design,” Opt. Acta 29, 807–822 (1982).
[CrossRef]

Khatsevich, T. N.

Lessing, N. v. d. W.

Macdonald, J.

M. I. Khan, J. Macdonald, “Cemented doublets, a method for rapid design,” Opt. Acta 29, 807–822 (1982).
[CrossRef]

McClure, N. R.

Mercado, R. I.

R. I. Mercado, “Design of apochromats and superachromats,” Proc. SPIE 1, 270–296 (1992).

Mikš, A.

A. Mikš, J. Novák, “Design of a double-sided telecentric zoom lens,” Appl. Opt. 51, 5928–5935 (2012).
[CrossRef]

A. Mikš, J. Vondřich, “Auswahl der glaser fur ein verkittetes duplet,” Optik 28, 321–327 (1968/69).

A. Mikš, J. Vondřich, “Method for design of superachromatic systems I,” Fine Mech. Opt. 10, 79–84 (1966).

A. Mikš, Applied Optics (Czech Technical University, 2009).

Montes, A. S.

Novák, J.

Parko, V. L.

Pulvermacher, H.

M. Herzberger, H. Pulvermacher, “Die farbfehlerkorrektion von multipletts,” Opt. Acta 17, 349–361 (1970).
[CrossRef]

H. Pulvermacher, “Theorie der restspektrum von simpletts,” Optik 30, 297–313 (1969).

Rao, V. V.

H. H. Hopkins, V. V. Rao, “The systematic design of two component objectives,” Opt. Acta 17, 497–514 (1970).
[CrossRef]

Rayces, J. L.

Robb, P. N.

P. N. Robb, “Selection of optical glasses,” Proc. SPIE 554, 60–75 (1985).
[CrossRef]

Rosete-Aguilar, M.

Sasian, J.

Shiue, S. G.

C. H. Chen, S. G. Shiue, “Method of solving a triplet comprising a singlet and a cemented doublet with given primary aberrations,” J. Mod. Opt. 45, 2063–2084 (1998).

Sigler, R. D.

Stephens, R. E.

Sussman, M. H.

Szulc, A.

Vondrich, J.

A. Mikš, J. Vondřich, “Auswahl der glaser fur ein verkittetes duplet,” Optik 28, 321–327 (1968/69).

A. Mikš, J. Vondřich, “Method for design of superachromatic systems I,” Fine Mech. Opt. 10, 79–84 (1966).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Oxford University, 1964).

Appl. Opt.

Fine Mech. Opt.

A. Mikš, J. Vondřich, “Method for design of superachromatic systems I,” Fine Mech. Opt. 10, 79–84 (1966).

J. Mod. Opt.

C. H. Chen, S. G. Shiue, “Method of solving a triplet comprising a singlet and a cemented doublet with given primary aberrations,” J. Mod. Opt. 45, 2063–2084 (1998).

J. Opt. Soc. Am.

J. Opt. Technol.

Opt. Acta

H. H. Hopkins, V. V. Rao, “The systematic design of two component objectives,” Opt. Acta 17, 497–514 (1970).
[CrossRef]

M. I. Khan, “Cemented triplets: a method for rapid design,” Opt. Acta 31, 873–883 (1984).
[CrossRef]

M. I. Khan, J. Macdonald, “Cemented doublets, a method for rapid design,” Opt. Acta 29, 807–822 (1982).
[CrossRef]

M. Herzberger, H. Pulvermacher, “Die farbfehlerkorrektion von multipletts,” Opt. Acta 17, 349–361 (1970).
[CrossRef]

M. Herzberger, “Colour correction in optical systems and a new dispersion formula,” Opt. Acta 6, 197–215 (1959).
[CrossRef]

Opt. Express

Optik

A. Mikš, J. Vondřich, “Auswahl der glaser fur ein verkittetes duplet,” Optik 28, 321–327 (1968/69).

M. Herzberger, “Tables of superachromatic glasstriplets and their color correction,” Optik 35, 1–8 (1972).

H. Pulvermacher, “Theorie der restspektrum von simpletts,” Optik 30, 297–313 (1969).

Proc. SPIE

P. N. Robb, “Selection of optical glasses,” Proc. SPIE 554, 60–75 (1985).
[CrossRef]

R. I. Mercado, “Design of apochromats and superachromats,” Proc. SPIE 1, 270–296 (1992).

Other

M. Berek, Grundlagen der Praktischen Optik (Walter de Gruyter, 1970).

B. E. Hansen, “Econometrics,” Draft Textbook Website: http://www.ssc.wisc.edu/~bhansen/econometrics/ (2013). Chap. 7.

M. Herzberger, Modern Geometrical Optics (Interscience, 1958).

H. Chretien, Calcul des Combinaisons Optiques (Masson, 1980).

D. Argentieri, Ottica industriale (Hoepli, 1942).

M. Born, E. Wolf, Principles of Optics (Oxford University, 1964).

A. Mikš, Applied Optics (Czech Technical University, 2009).

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Figures (1)

Fig. 1.
Fig. 1.

Aberration of objective lens ( f = 250 mm , F = 5 ).

Tables (11)

Tables Icon

Table 1a. Selected Optical Glass Types from Schott and Radii of Curvature of Doublets ( S I = S II = 0 , φ = 1 , First Solution)

Tables Icon

Table 1b. Selected Optical Glass Types from Schott and Radii of Curvature of Doublets ( S I = S II = 0 , φ = 1 , Second Solution)

Tables Icon

Table 2a. Selected Optical Glass Types from Schott and Radii of Curvature of Doublets with CaF 2 ( S I = S II = 0 , φ = 1 )

Tables Icon

Table 2b. Selected Optical Glass Types from Schott and Radii of Curvature of Doublets without Special Glass Types ( S I = S II = 0 , φ = 1 )

Tables Icon

Table 3a. Selected Optical Glass Types from Schott and Radii of Curvature of Triplets ( S I = S II = 0 , φ = 1 , First Solution)

Tables Icon

Table 3b. Selected Optical Glass Types from Schott and Radii of Curvature of Triplets ( S I = S II = 0 , φ = 1 , Second Solution)

Tables Icon

Table 4a. Selected Optical Glass Types from Schott and Radii of Curvature of Triplets ( r 3 = )

Tables Icon

Table 4b. Selected Optical Glass Types from Schott and Radii of Curvature of Triplets ( r 3 = ) with CaF 2

Tables Icon

Table 4c. Selected Optical Glass Types from Schott and Radii of Curvature of Triplets without Special Glass Types (First Solution)

Tables Icon

Table 4d. Selected Optical Glass Types from Schott and Radii of Curvature of Triplets without Special Glass Types (Second Solution)

Tables Icon

Table 5. Parameters of Objective Lens (Triplet)

Equations (33)

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φ = i = 1 N φ i = i = 1 N ( n i 1 ) ( 1 r i 1 r i ) = i = 1 N ( n i 1 ) K i ,
1 s 1 s = φ ,
δ s λ = m 2 δ s λ s 2 i = 1 N φ i ( λ 0 ) ν i , ν i = n i ( λ 0 ) 1 n i ( λ + d λ ) n i ( λ ) ,
ν ( λ d ) = ν d = n d 1 n F n C , P λ = n F n λ n F n C .
δ s λ = m 2 δ s λ s 2 i = 1 N φ i ν i P λ i = m 2 δ s λ f 2 ( 1 m ) 2 i = 1 N φ i ν i P λ i ,
i = 1 N φ i ν i P λ i = 0 .
Δ W λ = Δ s λ 8 F 2 < λ 4 ,
Δ s λ < 2 λ F 2 .
φ 1 + φ 2 = φ , i = 1 2 φ i ν i = 0 , i = 1 2 φ i ν i P d i = 0 ,
P d = n F n d n F n C .
φ 1 = ν 1 ν 1 ν 2 φ , φ 2 = φ φ 1 .
S I = i = 1 N a i ρ i 2 2 b i ρ i + c i , S II = i = 1 N e i ρ i b i .
a i = n i + 2 n i φ i , e i = n i + 1 n i φ i , ξ 1 = 1 / s + φ 1 / 2 , ξ i + 1 = ξ i + ( φ i + φ i + 1 ) / 2 , b i = φ i ξ i , c i = [ n i φ i 2 ( n i 1 ) ] 2 φ i , ρ i = 1 2 ( 1 r i + 1 r i ) ξ i ,
1 r i = ρ i + ξ i + φ i 2 ( n i 1 ) , 1 r i = ρ i + ξ i φ i 2 ( n i 1 ) ,
ρ 1 2 2 α ρ 1 + β = 0 , ρ 2 = b 1 + b 2 + S II e 1 ρ 1 e 2 ,
α = a 2 e 1 ( b 1 + b 2 + S II ) + e 2 ( b 1 e 2 b 2 e 1 ) a 1 e 2 2 + a 2 e 1 2 , β = a 2 ( b 1 + b 2 + S II ) 2 2 b 2 e 2 ( b 1 + b 2 + S II ) + e 2 2 ( c 1 + c 2 S I ) a 1 e 2 2 + a 2 e 1 2 ,
φ 1 + φ 2 + φ 3 = φ , i = 1 3 φ i ν i = 0 , i = 1 3 φ i ν i P d i = 0 , i = 1 3 φ i ν i P g i = 0 .
D = | 1 1 1 P d 1 P d 2 P d 3 P g 1 P g 2 P g 3 | = 0 ,
φ i = φ A i ν i k = 1 3 A k ν k , A 1 = P d 3 P d 2 , A 2 = P d 1 P d 3 , A 3 = P d 2 P d 1 .
B f = b ,
B = ( 1 1 1 P λ 1 1 / ν 1 P λ 1 2 / ν 2 P λ 1 3 / ν 3 P λ 2 1 / ν 1 P λ 2 2 / ν 2 P λ 2 3 / ν 3 P λ M 1 / ν 1 P λ M 2 / ν 2 P λ M 3 / ν 3 ) , f = ( φ 1 φ 2 φ 3 ) , b = ( φ 0 0 0 ) ,
f ¯ = X B T b ,
e ¯ = b B f ¯ .
B f = b , C f = φ ,
f ^ = f ¯ X C T ( C X C T ) 1 ( C f ¯ φ ) .
e ^ = b B f ^ .
k 2 ρ 3 2 + k 1 ρ 3 + k 0 = 0 , ρ 1 = d 2 d 3 ρ 3 , ρ 2 = ρ 1 p ,
d 0 = a 1 + a 2 , d 1 = b 1 + b 2 + a 2 p , d 2 = ( S II + b 1 + b 2 + b 3 + e 2 p ) / ( e 1 + e 2 ) , d 3 = e 3 / ( e 1 + e 2 ) , k 2 = a 3 + d 0 d 3 2 , k 1 = 2 d 1 d 3 2 b 3 2 d 0 d 2 d 3 , k 0 = c 1 + c 2 + c 3 + 2 b 2 p + a 2 p 2 + d 0 d 2 2 2 d 1 d 2 S I . p = n 1 φ 1 2 ( n 1 1 ) + n 2 φ 2 2 ( n 2 1 ) .
S I = ( a 3 ρ 3 2 2 b 3 ρ 3 + c 3 ) , S II = ( e 3 ρ 3 b 3 ) ,
ρ 3 = 0.5 φ 3 / ( n 3 1 ) ξ 3 ,
ρ 3 = 0.5 φ 3 / ( n 3 1 ) ξ 3 ,
ρ 3 = ξ 3 ,
ρ 3 = a 3 / b 3 .

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