Abstract

An analysis of the various factors involved in several typical three-layered reflection-reducing coatings has been made from both an experimental and a theoretical standpoint. By taking into account the approximate dispersions of the materials, reasonable agreement between the experimental and calculated reflection curves has been obtained.

Interesting results were obtained on electron diffraction studies of the various coating materials. Thin films of titanium dioxide, the high index material used, were found to have crystalline patterns that varied with the coated material and that, in general, were not recognizable as titanium dioxide patterns. Thus it was considered impossible to assign any definite values to the refractive indices of such thin films without specifying the substrate.

© 1947 Optical Society of America

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References

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  1. U. S. Naval Technical Mission in Europe, of September1945.
  2. Swiss Patent223344 of January4, 1943, issued to Jena Glass Works, Schott and Genossen, Jena, Germany.
  3. H. A. Tanner and L. B. Lockhart, J. Opt. Soc. Am. 36, 701 (1946).
    [CrossRef]
  4. P. King and L. B. Lockhart, J. Opt. Soc. Am. 36, 513 (1946).
    [CrossRef]
  5. W. Geffcken, German Patent742,463 of January18, 1944.
  6. This was done by J. Karle and C. Glover of the Naval Research Laboratory; studies are being continued by them.

1946 (2)

Geffcken, W.

W. Geffcken, German Patent742,463 of January18, 1944.

Glover, C.

This was done by J. Karle and C. Glover of the Naval Research Laboratory; studies are being continued by them.

Karle, J.

This was done by J. Karle and C. Glover of the Naval Research Laboratory; studies are being continued by them.

King, P.

Lockhart, L. B.

Tanner, H. A.

J. Opt. Soc. Am. (2)

Other (4)

W. Geffcken, German Patent742,463 of January18, 1944.

This was done by J. Karle and C. Glover of the Naval Research Laboratory; studies are being continued by them.

U. S. Naval Technical Mission in Europe, of September1945.

Swiss Patent223344 of January4, 1943, issued to Jena Glass Works, Schott and Genossen, Jena, Germany.

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Figures (8)

F. 1
F. 1

Spectral reflections of coatings composed of three quarter-wave layers. Theoretical.

F. 2
F. 2

Spectral reflections of three-layered coatings composed of quarter-wave bottom layers of 1.80 index, half-wave middle layers of various indices, and quarter-wave top layers of 1.47 index on glass of 1.53 index. Theoretical.

F. 3
F. 3

Spectral reflections of coatings a quarter-wave and a half-wave-length in optical thickness. Experimental. Solid line—quarter-wave film of 2.09 index; broken line—two superimposed quarter-wave films of 2.09 index.

F. 4
F. 4

Dispersion curves of component parts of three-layered solution-type coatings.

F. 5
F. 5

Spectral reflections of coatings composed of three quarter-wave layers where n1 = 1.53, n2 = 1.80, n3 = 2.14, and n4 = 1.47. Experimental.

F. 6
F. 6

Spectral reflections of coatings composed of three quarter-wave layers where n1 = 1.53, n2 = 1.80, n3 = 2.14, and n4 = 1.47. Theoretical. Solid line—assuming no dispersion; broken line—assuming dispersion according to Fig. 4.

F. 7
F. 7

Spectral reflections of three-layered coatings composed of quarter-wave, half-wave, and quarter-wave superimposed films. Curve A—experimental; curve B—calculated curve assuming dispersion according to Fig. 4; curve C—calculated curve assuming no dispersion.

F. 8
F. 8

Comparison of spectral reflections of typical one-, two-, and three-layered coatings. Experimental. □ MgF2 on 1.517 index glass; ○ two-layered coating; Δ three-layered coating.

Tables (1)

Tables Icon

Table I Luminous reflection of various coatings toward I.C.I. illuminant C.

Equations (11)

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R = | ( X 1 ) / ( X + 1 ) | 2 ,
X = [ ( n 2 n 3 n 4 n 2 2 n 4 tan ω 2 tan ω 3 n 2 2 n 3 tan ω 2 tan ω 4 n 2 n 3 2 tan ω 3 tan ω 4 ) + i ( n 1 n 3 n 4 tan ω 2 + n 1 n 2 n 4 tan ω 3 + n 1 n 2 n 3 tan ω 4 n 1 n 3 2 tan ω 2 tan ω 3 tan ω 4 ) ] / [ ( n 1 n 2 n 3 n 4 n 1 n 3 2 n 4 tan ω 2 tan ω 3 n 1 n 3 n 4 2 tan ω 2 tan ω 4 n 1 n 2 n 4 2 tan ω 3 tan ω 4 ) + i ( n 2 2 n 3 n 4 tan ω 2 + n 2 n 3 2 n 4 tan ω 3 + n 2 n 3 n 4 2 tan ω 4 n 2 2 n 4 2 tan ω 2 tan ω 3 tan ω 4 ) ] ,
tan ω 2 = tan ω 3 = tan ω 4 = ,
X = n 1 n 3 2 / n 2 2 n 4 2
R = [ ( n 1 n 3 2 n 2 2 n 4 2 ) / ( n 1 n 3 2 + n 2 2 n 4 2 ) ] 2 .
n 3 = n 2 n 4 / n 1 1 2 .
X = n 2 2 / n 1 n 4 2
R = [ ( n 2 2 n 1 n 4 2 ) / ( n 2 2 + n 1 n 4 2 ) ] 2 .
n 2 2 = n 1 n 4 2 .
n f = [ n g ( 1 + R 1 2 ) / ( 1 R 1 2 ) ] 1 2 ,
n j = index of the film , n g = index of the glass , R = reflection .