Abstract

In this paper we have completed an error analysis of the Buchdahl glass model for 813 glasses available from five manufacturers. A quadratic model has a standard deviation of 0.00002 and a maximum absolute error of 0.0001 in the visible spectral region. A cubic model has a standard deviation of 0.00005 and a maximum absolute error of 0.00026 over the full spectral region from 0.365 to 1.014 μm. A table giving the Buchdahl fitting coefficients for all the glasses, as well as the standard deviation and maximum error for each glass, is included for the quadratic model. The results indicate that the Buchdahl model is ideally suited for theoretical studies of refracting optical systems.

© 1983 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966), pp. 147 and 148.
  2. H. A. Buchdahl, Optical Aberration Coefficients (Dover, New York, 1968).
  3. P. J. Sands, J. Opt. Soc. Am. 61, 777 (1971).
    [CrossRef] [PubMed]
  4. R. E. Stephens, J. Opt. Soc. Am. 56, 213 (1966).
    [CrossRef]
  5. Schott Optical Glass, Inc., Optical Glass Catalogue (Duryea, Pa., 1980).
  6. Ohara Optical Glass Manufacturing Co., Ltd., Optical Glass Catalogue (Sagamihara, Japan, 1980).
  7. Hoya Corp., Optical Glass Catalogue (Tokyo, Japan, 1980).
  8. Corning-France, Optical Glass Catalogue (Avon, France, 1980).
  9. Chance Pilkington, Ltd., Optical Glass Catalogue (St. Asaph, Clwyd, U.K., 1980).
  10. Ref. 6, p. 2.
  11. Ref. 2, pp. 151 and 152.

1971 (1)

1966 (1)

Buchdahl, H. A.

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

Sands, P. J.

Smith, W. J.

W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966), pp. 147 and 148.

Stephens, R. E.

J. Opt. Soc. Am. (2)

Other (9)

Schott Optical Glass, Inc., Optical Glass Catalogue (Duryea, Pa., 1980).

Ohara Optical Glass Manufacturing Co., Ltd., Optical Glass Catalogue (Sagamihara, Japan, 1980).

Hoya Corp., Optical Glass Catalogue (Tokyo, Japan, 1980).

Corning-France, Optical Glass Catalogue (Avon, France, 1980).

Chance Pilkington, Ltd., Optical Glass Catalogue (St. Asaph, Clwyd, U.K., 1980).

Ref. 6, p. 2.

Ref. 2, pp. 151 and 152.

W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966), pp. 147 and 148.

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

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 (8)

Fig. 1
Fig. 1

Number of decimal places vs polynomial order for the visible and extended spectral regions. The number of decimal places is based on the maximum error for all glasses, not the standard deviation.

Fig. 2
Fig. 2

Perspective plots of the glass population density as a function of wavelength and refractive-index error for the quadratic model in the visible. The logarithm of the glass population is used in Fig. 2(b) so that the few glasses which contribute to the maximum error may be seen.

Fig. 3
Fig. 3

Error envelope as a function of wavelength for the quadratic model. Note that the error is zero at the base wavelength.

Fig. 4
Fig. 4

Statistical analysis of the index error function. Absolute refractive-index error is plotted vs wavelength for the indicated number of glasses for the quadratic model.

Fig. 5
Fig. 5

Perspective plots of the glass population density as a function of wavelength and refractive-index error for the cubic model over the extended spectral region. The logarithm of the glass population is used in Fig. 5(b) so that the few glasses which contribute to the maximum error may be seen.

Fig. 6
Fig. 6

Error envelope as a function of wavelength for the cubic model. Note that the error is zero at the base wavelength.

Fig. 7
Fig. 7

Statistical analysis of the index error function. Absolute refractive-index error is plotted vs wavelength for the indicated number of glasses for the cubic model.

Fig. 8
Fig. 8

Plots of ν1 vs ν2 for the quadratic model. To improve the resolution of the data, seven glasses having coordinates below the lower right corner were not included. These glasses are Schott SF57, SF58, and SF59; Ohara SFS01, SF03, and SFS1; and Hoya FD59.

Tables (5)

Tables Icon

Table I Base Wavelength and Least-Squares Weights for the Visible Spectral Region

Tables Icon

Table II Base Wavelength and Least-Squares Weights for the Extended Spectral Region

Tables Icon

Table III Glass Error Data, Quadratic Model

Tables Icon

Table IV Glass Error Data, Cubic Model

Tables Icon

Table V Buchdahl Fitting Coefficients, Quadratic Model, Visible Spectral Region

Equations (9)

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

N = a 0 + a 1 X + a 2 X 2 + + a k X k ,
N = N 0 + ν 1 ω + ν 2 ω 2 + ν 3 ω 3 + + ν k ω k .
n 2 1 n 2 + 2 = e 2 3 π m i j F i j ν i j 2 ν 2 ,
n 2 = A 0 + A 1 λ 2 + A 2 λ 2 + A 3 λ 4 + A 4 λ 6 + A 5 λ 8 .
Δ N = a 0 ( Δ λ ) + a 1 ( Δ λ ) 2 + a 2 ( Δ λ ) 3 + .
N ( λ ) = N 1 + c λ λ 1 ,
Δ N = α 2 c Δ λ 1 + α Δ λ .
ω = λ λ 0 1 + 2.5 ( λ λ 0 ) ,
N = N 0 + ν 1 + ν 2 ω 2 + ν 3 ω 3 + .

Metrics