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

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  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

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

1985

1983

1959

Baberjee, S.

Hazra, L.

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).

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).

Appl. Opt.

J. Mod. Opt.

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.

Other

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.

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 (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)

Tables Icon

Table 1. SCHOTT glass data

Tables Icon

Table 2. Data of the five glass combinations

Tables Icon

Table 3. Weighting factors for three different wavelengths

Tables Icon

Table 4. Comparison of the glass combinations

Tables Icon

Table 5. Doublet design for K3, F4

Tables Icon

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

Tables Icon

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

Tables Icon

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

Tables Icon

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

Tables Icon

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

Tables Icon

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

Tables Icon

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

Equations (29)

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

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 ,

Metrics