Optical monitoring of nonquarterwave multilayer filters

B. Vidal; A. Fornier; E. Pelletier

doi:10.1364/AO.17.001038

Applied Optics
Vol. 17,
Issue 7,
pp. 1038-1047
(1978)
•https://doi.org/10.1364/AO.17.001038

Optical monitoring of nonquarterwave multilayer filters

B. Vidal, A. Fornier, and E. Pelletier

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B. Vidal, A. Fornier, and E. Pelletier, "Optical monitoring of nonquarterwave multilayer filters," Appl. Opt. 17, 1038-1047 (1978)

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Abstract

Many spectral filtering problems require the use of assemblies of layers having thicknesses which bear no obvious relationship to each other. Successful production of these multilayers requires films with thicknesses approximating theoretical values. We show that the optical methods currently used in the production of film assemblies of quarterwave layer thicknesses, which are based on the use of just one single wavelength, are poorly adapted to monitoring the deposition of nonintegral thickness multilayers. In contrast we show that with an optical control system utilizing a broad spectral bandwidth, thickness errors can be reduced. Transmittance measurements with the precision necessary to achieve this improved thickness control are attainable with existing instrumentation. This result is established by a computer simulation of the construction of a specific multilayer and remains valid for other nonquarterwave multilayer filters.

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Layer number	1	2	3	4	5	6	7
Control wavelength (nm)	497.3	449.2	456.0	431.2	742.9	427.2	427.8
Maximum or minimum	max	mm	max	mm	nun	max	mm
T initial	0.960	0.884	0.889	0.826	0.643	0.772	0.939
Intermediate extremum of T	0.659	0.982	0.744	0.960	none	none	none
T final	0.957	0.867	0.891	0.820	0.219	0.935	0.323

Simulation n⁰	1	2	3	4	5	6	7	8	9
${\bar{T}}_{s}$	0.274	0.389	0.413	0.427	0.340	0.341	0.568	0.352	0.345
$\bar{Δ T_{s}}$	0.072	0.107	0.074	0.065	0.086	0.104	0.163	0.098	0.043
\|ΔT_s\|_m	0.210	0.210	0.466	0.393	0.198	0.245	0.342	0.223	0.157

Simulation n⁰	1	2	3	4	5	6	7	8	9
${\bar{T}}_{s}$	0.281	0.368	0.382	0.404	0.334	0.334	0.494	0.346	0.324
$\bar{Δ T_{s}}$	0.068	0.068	0.094	0.058	0.090	0.075	0.149	0.083	0.043
\|ΔT_s\|_m	0.191	0.448	0.191	0.382	0.211	0.185	0.268	0.207	0.125

Simulation n⁰	1	2	3	4	5	6	7	8	9
${\bar{T}}_{s}$	0.298	0.371	0.352	0.375	0.330	0.331	0.420	0.339	0.318
$\bar{Δ T_{s}}$	0.059	0.066	0.056	0.050	0.063	0.071	0.086	0.067	0.047
\|ΔT_s\|_m	0.156	0.154	0.367	0.286	0.154	0.165	0.178	0.171	0.110

Simulation n⁰	1	2	3	4	5	6	7	8	9
${\bar{T}}_{s}$	0.353	0.402	0.420	0.410	0.340	0.375	0.450	0.352	0.337
$\bar{Δ T_{s}}$	0.049	0.090	0.076	0.069	0.059	0.054	0.105	0.059	0.047
\|ΔT_s\|_m	0.358	0.258	0.453	0.398	0.223	0.415	0.339	0.331	0.182

Layer i δT_i	1	2	3	4	5	6	7
0.015	1.5	4.7	1.5	6.5	1.0	4.0	1.5
0.010	1.0	3.2	1.0	4.5	0.5	3.0	1.0
0.005	0.5	1.5	0.5	2.5	0.2	1.5	0.5

Simulation n⁰	1	2	3	4	5	6	7	8	9
${\bar{T}}_{s}$	0.356	0.339	0.335	0.345	0.362	0.344	0.354	0.349	0.337
$\overset{̅}{Δ T}$	0.061	0.052	0.046	0.052	0.049	0.047	0.046	0.047	0.050
\|ΔT\|_m	0.190	0.116	0.141	0.165	0.129	0.108	0.118	0.100	0.118

Simulation n⁰	1	2	3	4	5	6	7	8	9
${\bar{T}}_{s}$	0.356	0.343	0.337	0.343	0.355	0.355	0.343	0.346	0.340
$\bar{Δ T}$	0.056	0.051	0.045	0.049	0.046	0.047	0.045	0.047	0.048
\|ΔT\|_m	0.168	0.108	0.107	0.121	0.116	0.119	0.108	0.095	0.108

Abstract

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Equations (19)

Applied Optics