Properties of All-Dielectric Interference Filters. II. Filters in Parallel Beams of Light Incident Obliquely and in Convergent Beams

P. H. Lissberger; W. L. Wilcock

doi:10.1364/JOSA.49.000126

Journal of the Optical Society of America
Vol. 49,
Issue 2,
pp. 126-130
(1959)
•https://doi.org/10.1364/JOSA.49.000126

Properties of All-Dielectric Interference Filters. II. Filters in Parallel Beams of Light Incident Obliquely and in Convergent Beams

P. H. Lissberger and W. L. Wilcock

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P. H. Lissberger and W. L. Wilcock, "Properties of All-Dielectric Interference Filters. II. Filters in Parallel Beams of Light Incident Obliquely and in Convergent Beams," J. Opt. Soc. Am. 49, 126-130 (1959)

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Abstract

The basic formulas derived in Part I are used to determine the wavelength of the transmission band when all-dielectric interference filters are used in parallel beams incident obliquely. Experimental results agree well with the theoretical predictions provided that the dispersion of the layers is taken into account.

The transmission characteristics of filters in convergent beams are evaluated on the basis of the expressions for oblique incidence.

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Corrections

P. H. Lissberger and W. L. Wilcock, "Errata," J. Opt. Soc. Am. 49, 1228_1-1228 (1959)
https://opg.optica.org/josa/abstract.cfm?uri=josa-49-12-1228_1

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Equations (51)

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	ZnS spacer (even k)			Cryolite spacer (odd k)
n	k=4	k=6	k=∞	k=5	k=7	k=∞
1	0.311	0.316	0.317	0.421	0.421	0.420
2	0.270	0.274	0.276	0.463	0.462	0.461
3	0.249	0.253	0.254	0.485	0.484	0.483
4	0.236	0.239	0.241	0.499	0.498	0.497
5	0.227	0.230	0.231	0.508	0.507	0.507
10	0.206	0.208	0.209	0.530	0.529	0.529
∞	0.181	0.181	0.181	0.557	0.557	0.557

	Experimental			Theoretical
n	λ₀	$\frac{P}{1 - Q}$	Obs (rms) error	P	−Q	$\frac{P}{1 - Q}$
	(A)		±
1	4542	0.268	0.004	0.306	0.137	0.269
2	4523	0.246	0.004	0.263	0.160	0.227
2	4507	0.240	0.003	0.263	0.160	0.227
3	4497	0.199	0.002	0.241	0.173	0.205
3	4493	0.196	0.002	0.241	0.173	0.205
5	4506	0.181	0.002	0.217	0.185	0.183
3	6558	0.249	0.004	0.259	0.074	0.241

λ₀(A)	μ_z	$- \frac{\partial μ_{z}}{\partial λ} (A^{- 1})$
4500	2.44	11.8×10⁻⁵
5000	2.39	6.87×10⁻⁵
6560	2.32	3.28×10⁻⁵

α	F number	$\frac{T_{max}}{τ_{max}}$	$\frac{T λ_{0}, α}{τ_{max}}$	−(δλ)_α	(Δλ)_α
		%	%	A	A
0.05	10.0	100	100	1	50
0.10	5.0	100	98	3	50
0.15	3.3	98	92	7	52
0.20	2.5	93	79	12	56
0.25	2.0	86	65	19	63

	ZnS spacer (even k)			Cryolite spacer (odd k)
n	k=4	k=6	k=∞	k=5	k=7	k=∞
1	0.311	0.316	0.317	0.421	0.421	0.420
2	0.270	0.274	0.276	0.463	0.462	0.461
3	0.249	0.253	0.254	0.485	0.484	0.483
4	0.236	0.239	0.241	0.499	0.498	0.497
5	0.227	0.230	0.231	0.508	0.507	0.507
10	0.206	0.208	0.209	0.530	0.529	0.529
∞	0.181	0.181	0.181	0.557	0.557	0.557

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Tables (4)

Equations (51)

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