Optimization of a triple etalon interferometer

Wilbert R. Skinner; Paul B. Hays; Vincent J. Abreu

doi:10.1364/AO.26.002817

Applied Optics
Vol. 26,
Issue 14,
pp. 2817-2827
(1987)
•https://doi.org/10.1364/AO.26.002817

Optimization of a triple etalon interferometer

Wilbert R. Skinner, Paul B. Hays, and Vincent J. Abreu

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Wilbert R. Skinner, Paul B. Hays, and Vincent J. Abreu, "Optimization of a triple etalon interferometer," Appl. Opt. 26, 2817-2827 (1987)

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Abstract

The High Resolution Doppler Imager (HRDI) is a triple etalon Fabry-Perot interferometer designed to measure Doppler shifts of rotational lines in the O₂ atmospheric system from the Upper Atmosphere Research Satellite. These shifts are used to determine wind vectors in the stratosphere and mesosphere. This paper presents the techniques used to determine the gap thicknesses and reflectivities of the three etalons of the HRDI instrument. The spacings are found to be 1.000, 0.186, and 0.025 cm. These spacings are independent of the reflectivity of the etalons. The reflectivities of the three etalons should be nearly equal to minimize the errors in the wind measurement caused by mistuning of the etalons. The choice of the reflectivity does not strongly influence the statistical error in the wind error when the values are less than ~0.90.

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wavelength (nm)	gap thicknesses (cm)

	n = 1	n = 2

630	0.884	1.769
690	0.968	1.937
765	1.074	2.147

		MRE		LRE		equal HRE spacing		equal resolution

Source	HRE	gap (cm)	$\frac{t (MRE)}{t (HRE)}$	gap (cm)	$\frac{t (LRE)}{t (HRE)}$	Signal light cm⁻¹	white light ratio	HRE thickness	white light ratio

Mack et al.9	0.3000	0.2790	0.9300	0. 1769	0.5897	13.1	0.320	0.620	0.222
McNutt13	1.000	–	0.8831	–	0.7244	12.9	0.390	0.605	0.161
Rees et al.23	1.000	0.182	0.182	0.0215	0.0215	21.2	0.150	1.00	0.150
Rees et al.23	1.000	0.182	0.182	0.0331	0.0331	21.2	0.107	1.00	0.107
Burnett and Burnett22	0.3438	0.3042	0.8848	0.0711	0.2068	14.6	0.271	0.700	0.193
this work	1.000	0.186	0.186	0.0250	0.0250	21.2	0.122	1.00	0.122

R(HRE)	R(MRE)	R(LRE)	optimum t(MRE)/t(HRE)	optimum t(LRE)/t(HRE)	white light

0.70	0.85	0.85	0.186	0.035	0.3731
0.75	0.85	0.85	0.186	0.035	0.3645
0.80	0.85	0.85	0.186	0.035	0.3558
0.83	0.85	0.85	0.186	0.035	0.3467
0.85	0.85	0.85	0.186	0.035	0.3471
0.83	0.85	0.90	0.186	0.034	0.1879
0.83	0.90	0.85	0.230	0.034	0.1931
0.90	0.85	0.85	0.186	0.035	0.3380
0.83	0.90	0.90	0.186	0.035	0.1068
0.90	0.90	0.90	0.186	0.035	0.0980

Reflectivity (HRE)	Reflectivity (MRE)	Reflectivity (LRE)	Loss (HRE)	Loss (MRE)	Loss (LRE)	$\frac{t (LRE)}{t (HRE)}$	$\frac{t (MRE)}{t (HRE)}$	total light (cm⁻¹)	signal light (cm⁻¹)	White light ratio W

0.83	0.85	0.85	0.00	0.00	0.00	0.035	0.186	0.0491	0.0365	0.35
0.83	0.85	0.85	0.01	0.00	0.00	0.035	0.186	0.0448	0.0325	0.37
0.83	0.85	0.85	0.00	0.01	0.00	0.035	0.186	0.0448	0.0333	0.35
0.83	0.85	0.85	0.00	0.00	0.01	0.035	0.186	0.0448	0.0333	0.35
0.83	0.85	0.85	0.01	0.01	0.01	0.035	0.186	0.0373	0.0277	0.35
0.83	0.85	0.85	0.02	0.02	0.02	0.035	0.186	0.0282	0.0209	0.34
0.90	0.90	0.90	0.00	0.00	0.00	0.035	0.186	0.0229	0.0209	0.10
0.90	0.90	0.90	0.02	0.02	0.02	0.035	0.186	0.0093	0.0086	0.09

			white light

Filter offset nm	$\begin{matrix} optimum \\ \frac{t (LRE)}{t (HRE)} \end{matrix}$	$\begin{matrix} optimum \\ \frac{t (MRE)}{t (HRE)} \end{matrix}$	optimum	$\begin{array}{l} \frac{t (LRE)}{t (HRE)} = 0.035 \\ \frac{t (MRE)}{t (HRE)} = 0.186 \end{array}$	$\begin{array}{l} \frac{t (LRE)}{t (HRE)} = 0.030 \\ \frac{t (MRE)}{t (HRE)} = 0.188 \end{array}$	$\begin{array}{l} \frac{t (LRE)}{t (HRE)} = 0.055 \\ \frac{t (MRE)}{t (HRE)} = 0.194 \end{array}$	$\begin{array}{l} \frac{t (LRE)}{t (HRE)} = 0.025 \\ \frac{t (MRE)}{t (HRE)} = 0.186 \end{array}$

0.0	0.035	0.186	0.347	0.347	0.363	0.513	0.417
0.1	0.030	0.188	0.398	0.661	0.398	0.479	0.427
0.2	0.055	0.194	0.417	0.741	0.776	0.417	0.457

Tangent height (km)	A band ^RQ15 position: 13156.2720 cm⁻¹ strength: 3.15 cm⁻¹/km-atm	B band P15 position: 14468.9840 cm⁻¹ strength: 0.676 cm⁻¹/km-atm	γ band P11 position: 15861.6700 cm⁻¹ strength: 0.0335 cm⁻¹/km-atm

7	–	0.43	0.62
15	–	0.57	0.71
25	–	0.73	0.71
35	–	0.76	0.68
45	0.75	0.79	0.64
55	0.75	–	–
65	0.76	–	–
75	0.80	–	–
85	0.76	–	–
95	0.76	–	–
105	0.74	–	–
115	0.72	–	–

		MRE		LRE		equal HRE spacing		equal resolutions

Source	HRE gap (cm)	gap (cm)	$\frac{t (MRE)}{t (HRE)}$	gap (cm)	$\frac{t (LRE)}{t (HRE)}$	Wind error for MRE displacment m/s/A	Wind error for LRE displacment m/s/A	HRE gap	Wind error for MRE displacment m/s/A	Wind error for LRE displacment m/s/A

Mack et al.9	0.3000	0.2790	0.9300	0.1769	0.5897	1.09	0.92	0.620	1.75	1.48
McNutt 13	1.000	–	0.8831	–	0.7244	1.15	1.06	0.605	1.90	1.77
Rees et al.23	1.000	0.182	0.182	0.0215	0.0215	0.55	0.0682	1.000	0.55	0.0682
Rees et al.23	1.000	0.182	0.182	0.0331	0.0331	0.55	0.150	1.000	0.55	0.150
Burnett and Burnett22	0.3438	0.3042	0.8848	0.0711	0.2068	1.55	0.421	0.700	2.21	0.601
this work	1.000	0.186	0.186	0.0250	0.0250	0.555	0.068	1.000	0.555	0.068

Etalon reflectivity				inferred wind error v/δt (m/s/A)

HRE	MRE	LRE	Defect finesse	MRE		LRE

				calculated from eqn. 24	simulation	calculated from eqn. 24	simulation

0.90	0.90	0.90	∞	0.644	0.555	0.0865	0.068
0.95	0.90	0.90	∞	0.153	0.164	0.0205	0.036
0.85	0.90	0.90	∞	1.534	1.345	0.206	0.214
0.80	0.90	0.90	∞	2.895	2.604	0.389	0.397
0.90	0.95	0.90	∞	2.711	1.873	0.0885	0.059
0.90	0.85	0.90	∞	0.270	0.244	0.0865	0.070
0.90	0.90	0.95	∞	0.644	0.550	0.365	0.253
0.90	0.90	0.85	∞	0.644	0.556	0.0363	0.029
0.90	0.90	0.90	25	0.644	0.601	0.0865	0.106

Parameter	Value

HRE gap	1.000 cm
MRE gap	0.186 cm
LRE gap	0.025 cm
HRE reflectivity	0.90
MRE reflectivity	0.90
LRE reflectivity	0.90

Abstract

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Equations (24)

Applied Optics