Abstract

Methods are described for measuring accurately the half-widths of frustrated total reflection filters (see reference 1) of very narrow pass bands, and for detecting extremely small non-uniformities in the spacer layers of these filters. The latter method, permitting observation and measurement of thin film non-uniformities appreciably less than one unit cell provides a very sensitive means of studying thin film structures and the mechanism of formation.

© 1949 Optical Society of America

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References

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  1. P. Leurgans and A. F. Turner, “Frustrated total reflection interference filters,” J. Opt. Soc. Am. 37, 983A (1947).
  2. Harry D. Polster, J. Opt. Soc. Am. 39, 1038 (1949).
    [Crossref]

1949 (1)

1947 (1)

P. Leurgans and A. F. Turner, “Frustrated total reflection interference filters,” J. Opt. Soc. Am. 37, 983A (1947).

Leurgans, P.

P. Leurgans and A. F. Turner, “Frustrated total reflection interference filters,” J. Opt. Soc. Am. 37, 983A (1947).

Polster, Harry D.

Turner, A. F.

P. Leurgans and A. F. Turner, “Frustrated total reflection interference filters,” J. Opt. Soc. Am. 37, 983A (1947).

J. Opt. Soc. Am. (2)

P. Leurgans and A. F. Turner, “Frustrated total reflection interference filters,” J. Opt. Soc. Am. 37, 983A (1947).

Harry D. Polster, J. Opt. Soc. Am. 39, 1038 (1949).
[Crossref]

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Figures (3)

F. 1
F. 1

Maxwellian field photograph of the transmission of collimated, monochromatic radiation through an FTR filter. Angle of incidence changed ten minutes between exposures, corresponding to a thickness change of approximately 5A.

F. 2
F. 2

Contour line for rapid evaporation of spacer layer (100A/sec.).

F. 3
F. 3

Contour line for slow evaporation of spacer layer (10A/sec).

Equations (23)

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δ 0 + Δ = N π , N = 0 , 1 , 2 , ,
d δ 0 + d Δ = 0 .
tan ( Δ / 2 ) = t 1 ,
t 1 = μ 1 cos θ 1 i μ 0 cos θ 0 ,
t 1 = μ 0 cos θ 1 i μ 1 cos θ 0 ;
μ 2 sin θ 2 = μ 1 sin θ 1 = μ 0 sin θ 0 ,
cos θ 1 = i ( sin 2 θ 1 1 ) 1 2 .
tan Δ = csch β ,
β = log t 1 = ± log ( μ 1 / μ 0 ) + log ( cos θ 1 / i cos θ 0 ) .
d δ 0 δ 0 = ( 1 μ 0 d μ 0 d λ 1 λ ) d λ + d ( d 0 ) d 0 tan θ 0 d θ 0 ,
d Δ = sech β d β = sech β ( ± d log ( μ 1 / μ 0 ) d λ d λ tan θ 1 d θ 1 + tan θ 0 d θ 0 ) .
cot θ r d θ r = d log ( μ 2 / μ r ) d λ d λ + cot θ 2 d θ 2 , r = 0 , 1 tan 2 θ 1 = sin 2 θ 1 / ( sin 2 θ 1 1 ) .
( A 1 μ 0 d μ 0 d λ B 1 μ 1 d μ 1 d λ C 1 μ 2 d μ 2 d λ 1 λ ) d λ C cot θ 2 d θ 2 + d ( d 0 ) / d 0 = 0 ,
A = ( 1 ± ( sech β ) / δ 0 ) + ( 1 + ( sech β ) / δ 0 ) tan 2 θ 0 , B = tan 2 θ 1 ( sech β ) / δ 0 ± ( sech β ) / δ 0 , C = ( 1 + ( sech β ) / δ 0 ) tan 2 θ 0 tan 2 θ 1 ( sech β ) / δ 0 .
( d λ / d θ 2 ) d 0 , ( d d 0 / d θ 2 ) λ , or ( d d 0 / d λ ) θ 2 .
d ( d 0 ) d θ a = d ( d 0 ) d θ 2 d θ 2 d θ a ,
d λ d θ a = d λ d θ 2 d θ 2 d θ a .
d ( d 0 ) d θ a = [ d ( d 0 ) ] / [ d θ 2 ] ( d λ ) / ( d θ 2 ) d λ d θ a = d ( d 0 ) d λ d λ d θ a .
d ( d 0 ) d λ = d 0 λ [ 1 ( A μ 0 d μ 0 d λ B μ 1 d μ 1 d λ C μ 2 d μ 2 d λ ) λ ] .
( A μ 0 d μ 0 d λ B μ 1 d μ 1 d λ C μ 2 d μ 2 d λ ) λ = . 26 at 6500 A .
d ( d 0 ) d θ a = d 0 λ d λ d θ a
d ( d 0 ) = d 0 λ ( d λ d θ a ) d θ a = 2270 × 1 × 10 6563 = 3.46 A ,
d ( d 0 ) = 1.26 × 3.46 = 4.35 A .