Abstract

This paper defines and discusses a glass dispersion formula that is adaptive. The formula exhibits superior convergence with a minimum number of coefficients. Using this formula we rationalize the correction of chromatic aberration per spectrum order. We compare the formula with the Sellmeier and Buchdahl formulas for glasses in the Schott catalogue. The six coefficient adaptive formula is found to be the most accurate with an average maximum index of refraction error of 2.91 × 10−6 within the visible band.

© 2014 Optical Society of America

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References

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  1. L. E. Sutton, O. N. Stavroudis, “Fitting refractive index data by least squares,” J. Opt. Soc. Am. 51(8), 901–905 (1961).
    [CrossRef]
  2. P. J. Reardon, R. A. Chipman, “Buchdahl’s glass dispersion coefficients calculated from Schott equation constants,” Appl. Opt. 28(16), 3520–3523 (1989).
    [CrossRef] [PubMed]
  3. G. W. Forbes, “Chromatic coordinates in aberration theory,” J. Opt. Soc. Am. A 1(4), 344–349 (1984).
    [CrossRef]
  4. R. A. Chipman, P. J. Reardon, “Buchdahl’s glass dispersion coefficients calculated in the near infrared,” Appl. Opt. 28(4), 694–698 (1989).
    [CrossRef] [PubMed]
  5. Y. Pi, P. J. Reardon, D. B. Pollock, “Applying the Buchdahl dispersion model to infrared hybrid refractive-diffractive achromats,” Proc. SPIE 6206, 62062O (2006).
    [CrossRef]
  6. P. N. Robb, R. I. Mercado, “Calculation of refractive indices using Buchdahl’s chromatic coordinate,” Appl. Opt. 22(8), 1198–1215 (1983).
    [CrossRef] [PubMed]
  7. K. S. R. Krishna, A. Sharma, “Evaluation of optical glass composition by optimization methods,” Appl. Opt. 34(25), 5628–5634 (1995).
    [CrossRef] [PubMed]
  8. M. Bolser, “Mercado/Robb/Buchdahl coefficients - an update of 243 common glasses,” Proc. SPIE 4832, 525–533 (2002).
    [CrossRef]
  9. Schott glass catalogue (2011), http://www.us.schott.com .
  10. J. Sasian, Introduction to Aberrations in Optical Imaging Systems (Cambridge University, 2013), Chap. 6.

2006

Y. Pi, P. J. Reardon, D. B. Pollock, “Applying the Buchdahl dispersion model to infrared hybrid refractive-diffractive achromats,” Proc. SPIE 6206, 62062O (2006).
[CrossRef]

2002

M. Bolser, “Mercado/Robb/Buchdahl coefficients - an update of 243 common glasses,” Proc. SPIE 4832, 525–533 (2002).
[CrossRef]

1995

1989

1984

1983

1961

Bolser, M.

M. Bolser, “Mercado/Robb/Buchdahl coefficients - an update of 243 common glasses,” Proc. SPIE 4832, 525–533 (2002).
[CrossRef]

Chipman, R. A.

Forbes, G. W.

Krishna, K. S. R.

Mercado, R. I.

Pi, Y.

Y. Pi, P. J. Reardon, D. B. Pollock, “Applying the Buchdahl dispersion model to infrared hybrid refractive-diffractive achromats,” Proc. SPIE 6206, 62062O (2006).
[CrossRef]

Pollock, D. B.

Y. Pi, P. J. Reardon, D. B. Pollock, “Applying the Buchdahl dispersion model to infrared hybrid refractive-diffractive achromats,” Proc. SPIE 6206, 62062O (2006).
[CrossRef]

Reardon, P. J.

Robb, P. N.

Sharma, A.

Stavroudis, O. N.

Sutton, L. E.

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Figures (4)

Fig. 1
Fig. 1

Index variation for N-BK7 glass: (a) total variation, (b) linear variation, (c) quadratic variation, (d) cubic variation, (e) quartic variation, and (f) quintic variation.

Fig. 2
Fig. 2

Fitting error graphical analyses.

Fig. 3
Fig. 3

Index fitting errors of the adaptive formula for N-BK7 as fitted to the six-coefficient Sellmeier formula: (a) six-coefficient adaptive formula, (b) four-coefficient adaptive formula.

Fig. 4
Fig. 4

Cancelation of primary and secondary spectrum in a doublet by using N-FK51A and N-PSK3 glasses: (a) linear term, (b) quadratic term, (c) residual cubic term.

Tables (3)

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Table 1 Fitting Errors for Different Dispersion Formulas (Units: × 10−6)

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Table 2 Index Fitting Comparison (Errors are in units of 10−6)

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Table 3 Coefficients of the Adaptive Dispersion Formula

Equations (9)

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n 2 ( λ )=1+ B 1 λ 2 λ 2 C 1 + B 2 λ 2 λ 2 C 2 ++ B i λ 2 λ 2 C i ,
n( ω )= n 0 + ν 1 ω 1 + ν 2 ω 2 ++ ν j ω j ,
ω= λ- λ 0 1+α(λ- λ 0 ) ,
n= n 0 + a 1 ( λ- λ 0 ) 1 + a 2 ( λ- λ 0 ) 2 ++ a p ( λ- λ 0 ) p ,
Δλ= λ λ 0 Λ ,
n= n 0 + A 1 (Δλ)+ A 2 (Δλ) 2 ++ A q (Δλ) q + A q+1 (Δλ) q+1 1+K(Δλ) ,
λ W 020 = i=1 N [ y i 2 2 ( c 1i - c 2i )( n i -n 0i ) ] = i=1 N [ S i ( A 1i ( Δλ )+ A 2i ( Δλ ) 2 ++ A qi ( Δλ ) q + A q+1,i ( Δλ ) q+1 1+ K i ( Δλ ) ) ] ,
S= y 2 2 ( c 1 c 2 )
0= i=1 N S i A 1i = i=1 N S i A 2i = i=1 N S i A 3i .

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