Abstract

The senior author’s interpolation formula for computing the dispersion of glass has been appropriately modified and applied to infrared materials. Indices of refraction for 14 optical materials that are suitable for practical refracting systems have been fitted by the modified formula and have been tabulated at increments of 0.5 μ for the useful transmittance range of each material. The method of applying the dispersion formula is discussed and is illustrated by the design of two three-element superachromats corrected for the region of 2.0–5.0 μ.

© 1962 Optical Society of America

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References

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  1. M. Herzberger, Optica Acta 6, 197 (1959).
    [Crossref]
  2. E. D. McAlister, J. J. Villa, and C. D. Salzberg, J. Opt. Soc. Am. 46, 485 (1956).
    [Crossref]
  3. W. S. Rodney, I. H. Malitson, and T. A. King, J. Opt. Soc. Am. 48, 633 (1958).
    [Crossref]
  4. S. S. Ballard, K. A. McCarthy, and W. L. Wolfe, , Willow Run Laboratories, University of Michigan, Ann Arbor, Michigan.

1959 (1)

M. Herzberger, Optica Acta 6, 197 (1959).
[Crossref]

1958 (1)

1956 (1)

Ballard, S. S.

S. S. Ballard, K. A. McCarthy, and W. L. Wolfe, , Willow Run Laboratories, University of Michigan, Ann Arbor, Michigan.

Herzberger, M.

M. Herzberger, Optica Acta 6, 197 (1959).
[Crossref]

King, T. A.

Malitson, I. H.

McAlister, E. D.

McCarthy, K. A.

S. S. Ballard, K. A. McCarthy, and W. L. Wolfe, , Willow Run Laboratories, University of Michigan, Ann Arbor, Michigan.

Rodney, W. S.

Salzberg, C. D.

Villa, J. J.

Wolfe, W. L.

S. S. Ballard, K. A. McCarthy, and W. L. Wolfe, , Willow Run Laboratories, University of Michigan, Ann Arbor, Michigan.

J. Opt. Soc. Am. (2)

Optica Acta (1)

M. Herzberger, Optica Acta 6, 197 (1959).
[Crossref]

Other (1)

S. S. Ballard, K. A. McCarthy, and W. L. Wolfe, , Willow Run Laboratories, University of Michigan, Ann Arbor, Michigan.

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Figures (7)

Fig. 1
Fig. 1

Refractive index as a function of the squares of the wavelength (in microns) of the 14 materials listed in Table I.

Fig. 2
Fig. 2

Plot of n−1 vs nn4.0 for the 14 materials.

Fig. 3
Fig. 3

Plot of P1.5 vs ν for the 14 materials.

Fig. 4
Fig. 4

Plot of P5.0 vs ν for the 14 materials.

Fig. 5
Fig. 5

Plot of P1.5 vs P5.0 for the 14 materials. Any three materials whose partials lie on a straight line have data which will satisfy Eqs. (9) and permit design of a superachromat. Line A and encircled points represent lens A of Figs. 6 and 7; line B and dashed points represent lens B.

Fig. 6
Fig. 6

Chromatic correction of two thin triplets of focal length 100 made of materials selected according to Eqs. (9). A, silicon (11), Irtran-2 (13), and calcium fluoride (9). B, germanium (14), Irtran-2 (13), and barium fluoride (10).

Fig. 7
Fig. 7

Superachromatic cemented triplets made of the materials of Fig. 6. The radii of the lens elements in order are: A: +100.00, +70.91, −208.51, and +231.42 mm; B: +100.00, +91.16, −218.21, and +100.97 mm. Each element is 0.50 mm thick. The aberrations plotted are in order: marginal spherical aberration, marginal isoplanatism, longitudinal and lateral chromatism as a function of wavelength.

Tables (8)

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Table I List of materials. Except where noted, the index data were obtained at Eastman Kodak Company by using the method described in reference 2.

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Table II Constants to be used with the interpolation formula, Eq. (1).

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Table III Differences in the fourth decimal place between the measured indices for silicon and the values computed from the dispersion formula n = 3.41696 + 0.138497 L + 0.013924 L 2 - 0.0000209 λ 2 + 0.000000148 λ 4 .

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Table IV Differences in the fourth decimal place between the measured indices n0 for arsenic trisulfide and the values computed from the following dispersion formulas: n 1 = 2.41326 + 0.055720 L + 0.006177 L 2 - 0.0003044 λ 2 - 0.000000232 λ 4 , n 2 = 2.41089 + 0.065938 L - 0.004735 L 2 - 0.0002216 λ 2 - 0.000001176 λ 4 , n 3 = 2.38344 + 1.322826 L - 20.281247 L 2 + 0.000005 λ 2 - 0.00000135 λ 4 .

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Table V Physical constants and index of refraction computed from interpolation formula, Eq. (1).

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Table VI Universal coefficients. Matrix of aik in Eq. (3) for the five wavelengths λ=1.5, 2.5, 3.5, 4.0, and 5.0 μ.

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Table VII Universal functions ai(λ) calculated for eight wavelengths (λ) from 1.5 μ to 5.0 μ, at intervals of 0.5 μ.

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Table VIII Computational data for the 14 materials studied.

Equations (16)

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n = A + B L + C L 2 + D λ 2 + E λ 4 ,
L = 1 / ( λ 2 - 0.028 ) .
a i ( λ ) = a i 1 + a i 2 L + a i 3 L 2 + a i 4 λ 2 + a i 5 λ 4 ,
( 1 L 1 L 1 2 λ 1 2 λ 1 4 1 L 2 L 2 2 λ 2 2 λ 2 4 1 L 3 L 3 2 λ 3 2 λ 3 4 1 L 4 L 4 2 λ 4 2 λ 4 4 1 L 5 L 5 2 λ 5 2 λ 5 4 ) - 1 = ( a 11 a 12 a 13 a 14 a 15 a 21 a 22 a 23 a 24 a 25 a 31 a 32 a 33 a 34 a 35 a 41 a 42 a 43 a 44 a 45 a 51 a 52 a 53 a 54 a 55 ) .
n ( λ ) = a 1 ( λ ) n 1 + a 2 ( λ ) n 2 + a 3 ( λ ) n 3 + a 4 ( λ ) n 4 + a 5 ( λ ) n 5 .
λ 1 = 1.5 μ ,             λ 2 = 2.5 μ ,             λ 3 = 3.5 μ , λ 4 = 4.0 μ ,             λ 5 = 5.0 μ .
n ( 2.0 ) = 0.11699 × 1.8347 + 2.03478 × 1.8220 - 3.27487 × 1.8063 + 2.43788 × 1.7964 - 0.31478 × 1.7714 = 1.8284 ,
P λ = ( n - n λ ) / ( n - n 4.0 ) = ν / ν λ .
Φ = ϕ = ( n - 1 ) ( ρ - ρ ) ,
Φ - Φ λ = ( ϕ - ϕ λ ) = [ ( n - n λ ) ( ρ - ρ ) ] = ( ϕ / ν λ ) = ( ϕ / ν ) P λ ,
Φ - Φ 4.0 = ϕ I / ν I + ϕ I I / ν I I = 0 ,
ϕ I + ϕ I I = Φ , ϕ I = Φ ν I / ( ν I - ν I I ) ,             ϕ I I = Φ ν I I / ( ν I I - ν I ) .
ϕ I / ν I + ϕ I I / ν I I = 0 ( ϕ I / ν I ) P λ , I + ( ϕ I I / ν I I ) P λ , I I = 0 ,
( ϕ / ν ) I + ( ϕ / ν ) I I + ( ϕ / ν ) I I I = 0 , ( ϕ / ν ) I P 1.5 , I + ( ϕ / ν ) I I P 1.5 , I I + ( ϕ / ν ) I I I P 1.5 , I I I = 0 , ( ϕ / ν ) I P 5.0 , I + ( ϕ / ν ) I I P 5.0 , I I + ( ϕ / ν ) I I I P 5.0 , I I I = 0.
n = 3.41696 + 0.138497 L + 0.013924 L 2 - 0.0000209 λ 2 + 0.000000148 λ 4 .
n 1 = 2.41326 + 0.055720 L + 0.006177 L 2 - 0.0003044 λ 2 - 0.000000232 λ 4 , n 2 = 2.41089 + 0.065938 L - 0.004735 L 2 - 0.0002216 λ 2 - 0.000001176 λ 4 , n 3 = 2.38344 + 1.322826 L - 20.281247 L 2 + 0.000005 λ 2 - 0.00000135 λ 4 .