Abstract

This paper presents a method for choosing a doublet design for the correction of longitudinal chromatic, spherical and coma aberrations. A secondary dispersion formula is utilized to sort out minimal longitudinal chromatic aberrations for the doublet. The program is developed with the Matlab software. An optimal doublet design to efficiently reduce both spherical aberration and coma will incorporate glass combination with a sufficiently large difference in the V-numbers and small powers. We succeed in obtaining an optimal doublet design with the proposed method.

©2009 Optical Society of America

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References

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  1. K. D. Sharma and S. V. Rama Gopal, “Design of achromatic doublets: evaluation of the double-graph technique,” Appl. Opt. 22, 497–500 (1983).
    [Crossref] [PubMed]
  2. S. Baberjee and L. Hazra, “Experiments with a genetic algorithm for structural design of cemented doublets with prespecified aberration targets,” Appl. Opt. 40, 6265–6273 (2001).
    [Crossref]
  3. P. N. Robb, “Selection of optical glasses. 1: Two materials,” Appl. Opt. 24, 1864–1877 (1985).
    [Crossref] [PubMed]
  4. C. L. Tien, W. S. Sun, C. C. Sun, and C. H. Lin, “Optimization design of the split doublet using the shape factors of the third-order aberrations for a thick lens,” J. Mod. Opt. 51, 31–47 (2004).
  5. R. E. Stephens, “Selection of glasses for three-color achromats,” J. Opt. Soc. Am. 49, 398–401 (1959).
    [Crossref]
  6. W. S. Sun and C. H. Chu, “The best doublet design,” 6th ODF’08, 10PS-018 (2008).
  7. SCHOTT, http://www.schott.com/optics_devices/english/download/.
  8. J. M. Geary, Introduction to Lens Design: with Practical ZEMAX (Willmann-Bell, 2002), Chap. 18.
  9. R. Kingslake, Lens Design Fundamentals (Academic Press, New York, 1978), Chap. 4.
  10. W. T. Welford, Aberrations of the Symmetrical Optical System (Academic Press, New York, 1974).
  11. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill), Chap. 4.

2004 (1)

C. L. Tien, W. S. Sun, C. C. Sun, and C. H. Lin, “Optimization design of the split doublet using the shape factors of the third-order aberrations for a thick lens,” J. Mod. Opt. 51, 31–47 (2004).

2001 (1)

1985 (1)

1983 (1)

1959 (1)

Baberjee, S.

Chu, C. H.

W. S. Sun and C. H. Chu, “The best doublet design,” 6th ODF’08, 10PS-018 (2008).

Geary, J. M.

J. M. Geary, Introduction to Lens Design: with Practical ZEMAX (Willmann-Bell, 2002), Chap. 18.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill), Chap. 4.

Hazra, L.

Kingslake, R.

R. Kingslake, Lens Design Fundamentals (Academic Press, New York, 1978), Chap. 4.

Lin, C. H.

C. L. Tien, W. S. Sun, C. C. Sun, and C. H. Lin, “Optimization design of the split doublet using the shape factors of the third-order aberrations for a thick lens,” J. Mod. Opt. 51, 31–47 (2004).

Rama Gopal, S. V.

Robb, P. N.

Sharma, K. D.

Stephens, R. E.

Sun, C. C.

C. L. Tien, W. S. Sun, C. C. Sun, and C. H. Lin, “Optimization design of the split doublet using the shape factors of the third-order aberrations for a thick lens,” J. Mod. Opt. 51, 31–47 (2004).

Sun, W. S.

C. L. Tien, W. S. Sun, C. C. Sun, and C. H. Lin, “Optimization design of the split doublet using the shape factors of the third-order aberrations for a thick lens,” J. Mod. Opt. 51, 31–47 (2004).

W. S. Sun and C. H. Chu, “The best doublet design,” 6th ODF’08, 10PS-018 (2008).

Tien, C. L.

C. L. Tien, W. S. Sun, C. C. Sun, and C. H. Lin, “Optimization design of the split doublet using the shape factors of the third-order aberrations for a thick lens,” J. Mod. Opt. 51, 31–47 (2004).

Welford, W. T.

W. T. Welford, Aberrations of the Symmetrical Optical System (Academic Press, New York, 1974).

Appl. Opt. (3)

J. Mod. Opt. (1)

C. L. Tien, W. S. Sun, C. C. Sun, and C. H. Lin, “Optimization design of the split doublet using the shape factors of the third-order aberrations for a thick lens,” J. Mod. Opt. 51, 31–47 (2004).

J. Opt. Soc. Am. (1)

Other (6)

W. S. Sun and C. H. Chu, “The best doublet design,” 6th ODF’08, 10PS-018 (2008).

SCHOTT, http://www.schott.com/optics_devices/english/download/.

J. M. Geary, Introduction to Lens Design: with Practical ZEMAX (Willmann-Bell, 2002), Chap. 18.

R. Kingslake, Lens Design Fundamentals (Academic Press, New York, 1978), Chap. 4.

W. T. Welford, Aberrations of the Symmetrical Optical System (Academic Press, New York, 1974).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill), Chap. 4.

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Figures (9)

Fig. 1.
Fig. 1. Human spectral response
Fig. 2.
Fig. 2. Partial dispersion vs. Abbe number
Fig. 3.
Fig. 3. Chromatic focal shift for the five glass combinations
Fig. 4.
Fig. 4. Flow chart for doublet design
Fig. 5.
Fig. 5. Plot of the V 555 and P 555,647
Fig. 6.
Fig. 6. Doublet design for K3 and F4
Fig. 7.
Fig. 7. Doublet design for LITHOTEC-CAF2, P-SK57
Fig. 8.
Fig. 8. Doublet design for LITHOTEC-CAF2, N-SF66
Fig. 9.
Fig. 9. Doublet design for N-PK51, N-LASF31A

Tables (12)

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Table 1. SCHOTT glass data

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Table 2. Data of the five glass combinations

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Table 3. Weighting factors for three different wavelengths

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Table 4. Comparison of the glass combinations

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Table 5. Doublet design for K3, F4

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Table 6. Ray fan area for doublet (K3, F4)

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Table 7. Doublet design for LITHOTEC-CAF2, P-SK57

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Table 8. Ray fan area for doublet (LITHOTEC-CAF2, P-SK57)

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Table 9. Doublet design for LITHOTEC-CAF2, N-SF66

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Table 10. Ray fan area for doublet (LITHOTEC-CAF2, N-SF66)

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Table 11. Lens Data for N-PK51, N-LASF31A

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Table 12. Ray fan area for doublet (N-PK51, N-LASF31A)

Equations (29)

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V 555 = n 555 1 n 460 n 647 .
K 555 = ( n 555 1 ) ( C 1 C 2 ) ,
δ = K 460 K 647 = K 555 V 555 .
P 555,647 = n 555 n 647 n 460 n 647 .
ε = K 555 K 647 = P 555,647 V 555 K 555 .
K 555 = ( K 555 ) 1 + ( K 555 ) 2 ,
δ = δ 1 + δ 2 = ( K 555 ) 1 ( V 555 ) 1 + ( K 555 ) 2 ( V 555 ) 2 ,
( K 555 ) 1 = ( V 555 ) 1 ( V 555 ) 1 ( V 555 ) 2 K 555 ,
( K 555 ) 2 = ( V 555 ) 2 ( V 555 ) 1 ( V 555 ) 2 K 555 .
ε = ε 1 + ε 2 ( P 555,647 ) 1 ( P 555,647 ) 2 ( V 555 ) 1 ( V 555 ) 2 K 555 ,
S I = 1 4 h 2 K [ ( hK n 555 n 555 1 ) 2 n 555 + 2 n 555 ( Λ + U ) 2 + 2 U ( Λ + U ) ] ,
S II = 1 2 h K 555 H [ U ( 2 n 555 + 1 n 555 ) + Λ ( n 555 + 1 n 555 ) ] .
S I = S I 1 + S I 2 ,
S II = S II 1 + S II 2 ,
U 1 = h ( K 555 ) 1 ,
U 2 = h [ ( K 555 ) 1 + K 555 ] .
Λ 1 = b ± b 2 4 ac 2 a ,
Λ 2 = d Λ 1 + e ,
a = h 2 4 [ ( n 1 + 2 n 1 ) ( K 555 ) 1 + ( n 2 + 2 n 2 ) d 2 ( K 555 ) 2 ]
b = h 2 4 [ 4 ( n 1 + 1 ) n 1 U 1 ( K 555 ) 1 + 2 ( n 2 + 2 ) n 2 de ( K 555 ) 2 + 4 ( n 2 + 1 ) n 2 d ( K 555 ) 2 U 2 ]
c = h 2 4 [ ( 3 n 1 + 2 ) n 1 U 1 2 ( K 555 ) 1 + ( K 555 ) 1 3 h 2 n 1 2 ( n 1 1 ) 2 + ( n 2 + 2 n 2 ) e 2 ( K 555 ) 2 U +
4 ( n 2 + 1 ) n 2 U 2 e ( K 555 ) 2 + ( 3 n 2 + 2 ) n 2 U 2 2 ( K 555 ) 2 + ( K 555 ) 2 3 h 2 n 2 2 ( n 2 1 ) 2 ] S I
d = ( K 555 ) 1 ( n 1 + 1 ) n 2 ( K 555 ) 2 ( n 2 + 1 ) n 1
e = S II 1 2 hH [ ( K 555 ) 1 U 1 ( 2 n 1 + 1 n 1 ) + ( K 555 ) 2 U 2 ( 2 n 2 + 1 n 2 ) ] 1 2 hH ( K 555 ) 2 ( n 2 + 1 n 2 )
h 1 K 555 = h 1 ( K 555 ) 1 + h 3 ( K 555 ) 2 ,
h 1 ( K 555 ) 1 = ( n 555 ) 1 1 ( h 1 C 1 h 2 C 2 ) = ( n 555 ) 1 1 ( α 1 α 2 ) ,
Λ 1 = h 1 C 1 + h 2 C 2 = α 1 + α 2 ,
h 3 ( K 555 ) 2 = ( n 555 ) 2 1 ( h 3 C 3 h 4 C 4 ) = ( n 555 ) 2 1 ( α 3 α 4 ) .
Λ 2 = h 3 C 3 + h 4 C 4 = α 3 + α 4 ,

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