Abstract

The accessibility of high-speed computing machinery makes practicable the use of a routine for the least-squares fitting of a three-term Sellmeier equation to a set of experimentally determined values of index of refraction. The constants of a two-term Sellmeier equation are evaluated by a method described previously [ O. N. Stavroudis and L. E. Sutton, J. Opt. Soc. Am. 51, 368 ( 1961)]. These are then used in a preliminary fitting of another term. The rough fit is then improved by an iterative process which includes an acceleration technique to speed convergence to the final result. In a typical example the average residual of index is only about 2 × 10−5 for 46 wavelengths from 0.2652μ to 10.346μ.

© 1961 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. W. Ditchburn, Light 1953, 456.
  2. O. N. Stavroudis and L. E. Sutton, J. Opt. Soc. Am. 51, 368 (1961).
    [CrossRef]
  3. M. B. Wilk, Ann. Math. Stat. 29, 618A (1958).

1961 (1)

1958 (1)

M. B. Wilk, Ann. Math. Stat. 29, 618A (1958).

Ditchburn, R. W.

R. W. Ditchburn, Light 1953, 456.

Stavroudis, O. N.

Sutton, L. E.

Wilk, M. B.

M. B. Wilk, Ann. Math. Stat. 29, 618A (1958).

Ann. Math. Stat. (1)

M. B. Wilk, Ann. Math. Stat. 29, 618A (1958).

J. Opt. Soc. Am. (1)

Light (1)

R. W. Ditchburn, Light 1953, 456.

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 (1)

Fig. 1
Fig. 1

Residuals (calculated minus measured refractive indexes). —Two-term equation. Three-term equation.

Tables (1)

Tables Icon

Table I Parameters of equations; fitted to 46 measurements.

Equations (24)

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

n 2 ( 1 K 2 ) = 1 + j A j λ 2 λ 2 λ j 2 + g j λ 2 / ( λ 2 λ j 2 ) ,
n 2 = 1 + j A j λ 2 / ( λ 2 λ j 2 ) .
n 2 1 = A 1 λ 2 λ 2 λ 1 2 + A 2 λ 2 λ 2 λ 2 2 ,
n 2 1 = B 1 λ 2 λ 2 l 1 2 + B 2 λ 2 λ 2 l 2 2 + B 3 λ 2 λ 2 l 3 2 ,
Case A ( l 1 and l 2 in the ultraviolet ) ( l 3 in the infrared ) Case B ( l 1 in the ultraviolet ) ( l 2 and l 3 in the infrared ) .
n 2 1 = ( 1 2 A 1 ) λ 2 λ 2 λ 1 2 + ( 1 2 A 1 ) λ 2 λ 2 λ 1 2 + A 2 λ 2 λ 2 λ 2 2 .
B 1 ( 0 ) = 1 2 A 1 B 2 ( 0 ) = 1 2 A 1 B 3 ( 0 ) = A 2 l 3 ( 0 ) 2 = λ 2 2 ,
N = n 2 1 = h [ λ 2 λ 2 l 1 ( 0 ) 2 + λ 2 λ 2 l 2 ( 0 ) 2 ] + T 2 ,
M = λ 2 λ 2 l 1 ( 0 ) 2 + λ 2 λ 2 l 2 ( 0 ) 2 ,
[ ( M 1 ) λ 2 ] S + [ M ] P = [ M 2 ] λ 4 ,
S = l 1 ( 0 ) 2 + l 2 ( 0 ) 2 P = l 1 ( 0 ) 2 · l 2 ( 0 ) 2 .
[ M 1 λ 2 ] S + [ M λ 4 ] P = [ M 2 ] .
n m ( n c 0 ) = i = 1 i = 6 ( n c p i ) 0 ( Δ p i ) ,
( p i ) 1 = ( p i ) + ( Δ p i ) ,
( p i ) 1 = ( p i ) + c · ( Δ p i ) ,
( p i ) mid = ( p i ) + α 2 ( Δ p i ) ,
x 1 = x 0 f ( x 0 ) / f ( x 0 ) ,
f ( x 0 ) = f ( x 0 ) ( Δ x 0 ) ,
x 1 = x 0 + ( Δ x 0 ) .
f ( x 1 ) f ( x 0 ) x 1 x 0 f ( x 0 + x 1 2 ) .
f ( x 0 ) = f [ ( x 0 + x 1 ) / 2 ] ( Δ x 0 ) ,
x 1 = x 0 + ( Δ x 0 ) ,
f ( P ± h ) = f ( P ) ± h f ( P ) + ( 1 / 2 ) h 2 f ( P ) ± ,
h = ( 1 / 2 ) ( x 1 x 0 ) .