Optimization of a field-widened Michelson interferometer

William A. Gault; Sean F. Johnston; David J. W. Kendall

doi:10.1364/AO.24.001604

Optimization of a field-widened Michelson interferometer

William A. Gault, Sean F. Johnston, and David J. W. Kendall

Applied Optics
Vol. 24,
Issue 11,
pp. 1604-1608
(1985)
•https://doi.org/10.1364/AO.24.001604

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William A. Gault, Sean F. Johnston, and David J. W. Kendall, "Optimization of a field-widened Michelson interferometer," Appl. Opt. 24, 1604-1608 (1985)

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History
- Original Manuscript: September 27, 1984
- Published: June 1, 1985

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Abstract

This paper considers the optical design of a wide-angle fixed-path Michelson interferometer consisting of two arm glasses and an air gap. It is shown that this configuration can be optimized to give (a) extra large fringes (over 50° in diameter) over a range of wavelength, (b) a path difference nearly independent of wavelength, or (c) a path difference specified differently at two different wavelengths for observing a pair of doublets. Specific examples refer to the airglow wavelengths of 557.7, 630.0, 732.0 nm and others, and to a path difference of 4.5 cm. The properties of different glass combinations are discussed.

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Glass	n	$\frac{d n}{d λ} \times 10^{5} ({nm}^{- 1})$	$\frac{d n}{d λ} \cdot \frac{n^{2}}{n^{2} - 1} \times 10^{5} ({nm}^{- 1})$
FK5	1.486094	−3.0012	−3.691
BK7	1.515186	−3.4629	−4.049
K10	1.499607	−3.7681	−4.525
KF9	1.521409	−4.2683	−4.939
LLF1	1.545798	−4.9748	−5.534
LF5	1.580165	−5.5039	−5.810
F4	1.613340	−6.8711	−6.916
TiF2	1.530301	−4.7938	−5.467
BaK4	1.566824	−4.2802	−4.609
SK4	1.610645	−4.4314	−4.477
PSK3	1.550580	−3.7340	−4.123
BaLF4	1.577440	−4.5340	−4.805
SSK2	1.619993	−4.9140	−4.901
BaF8	1.621146	−5.5063	−5.483
SF5	1.668692	−8.4410	−7.893
SF4	1.749990	−10.9471	−9.289
SF57	1.839958	−14.0352	−10.83
BaSF10	1.646947	−6.7905	−6.531
BaSF51	1.720052	−7.7729	−6.826
LaK8	1.710372	−5.6222	−4.994
LaF21	1.784848	−6.9191	−5.650
LaF22	1.777719	−8.6052	−7.081
LaSF5	1.876499	−8.8943	−6.620

Glasses^b	t_1,2,3 (cm)	λ (nm)	Δ₀ (cm)	θ_max (deg)	$\frac{\partial^{2} Δ}{d λ \partial T} ({cm nm}^{- 1} K^{- 1})$	$\frac{\partial Δ}{\partial T} ({cm K}^{- 1})$
FK5/SF57	5.1918	557.7	4.5985	2.7	(No data)
	4.9920	630.0	4.5000	17.8
	0.7805	732.0	4.4142	3.3
FK5/SF4	7.1554	557.7	4.5963	2.6	1.3 × 10⁻⁷	1.2 × 10⁻⁴
	6.8462	630.0	4.5000	17.4
	0.9027	732.0	4.4156	3.2
FK5/LaF22	6.4200	557.7	4.5600	3.5	7.0 × 10⁻⁸	2.9 × 10⁻⁵
	6.1477	630.0	4.5000	17.5
	0.8619	732.0	4.4463	4.3
FK5/LaSF5	4.6547	557.7	4.5459	4.5	−1.8 × 10⁻⁸	2.3 × 10⁻⁵
	4.4918	630.0	4.5000	18.0
	0.7385	732.0	4.4580	5.5
K10/LaF21	6.4854	557.7	4.5329	6.2	1.5 × 10⁻⁹	1.0 × 10⁻⁵
	6.2478	630.0	4.5000	17.6
	0.8243	732.0	4.4693	7.5
F4/LaSF5	6.4186	557.7	4.5221	10.6	−6.0 × 10⁻⁸	−1.6 × 10⁻⁵
	6.4208	630.0	4.5000	18.5
	0.5568	732.0	4.4781	24.5

Glasses	t_1,2,3 (cm)	λ (nm)	θ_max (deg)	$\frac{\partial^{2} Δ}{d λ \partial T} ({cm nm}^{- 1} K^{- 1})$	$\frac{\partial Δ}{\partial T} ({cm K}^{- 1})$
LF5/SF57	5.1263	530.0	4.0	(No data)
	2.0103	630.0	5.8
	2.1516	730.0	7.2
SK4/SF5	5.2527	530.0	5.6	3.9 × 10⁻⁹	2.3 × 10⁻⁵
	2.7575	630.0	6.1
	1.6087	730.0	6.7
LaK8/SF4	2.2204	530.0	6.1	−2.0 × 10⁻⁸	1.6 × 10⁻⁵
	4.3234	630.0	6.3
	−1.2589^b	730.0	7.0

Glasses	t_1,2,3 (cm)	λ (nm)	Δ₀ (cm)	θ_max (deg)
SK4/SF57	9.2595	650.0	4.4871	6.7
	5.3467	697.8	4.5120	5.9
	2.8390	714.9	4.5193	5.6
		732.0	4.5260	5.4
		780.0	4.5416	5.1
LaK8/SF57	6.0999	650.0	4.4867	7.9
	9.0077	697.8	4.5120	6.4
	−1.9461	714.9	4.5194	6.1
		732.0	4.5260	5.7
		780.0	4.5414	5.2
SK4/SF57	9.3656	550.0	4.4000	3.9
	5.4254	641.0	4.4807	5.4
	2.8655	732.0	4.5260	4.3
LaK8/SF57	6.0592	550.0	4.4000	3.3
	8.9649	641.0	4.4815	6.9
	−1.9475	732.0	4.5260	4.2
SK4/SF57	8.0092	550.0	4.8000	2.0
	7.9074	641.0	4.6284	13.9
	0.6731	732.0	4.5260	3.0
LaK8/SF57	8.4494	550.0	4.8000	2.0
	7.6666	641.0	4.6278	8.3
	0.1119	732.0	4.5260	3.0

Glass	n	$\frac{d n}{d λ} \times 10^{5} ({nm}^{- 1})$	$\frac{d n}{d λ} \cdot \frac{n^{2}}{n^{2} - 1} \times 10^{5} ({nm}^{- 1})$
FK5	1.486094	−3.0012	−3.691
BK7	1.515186	−3.4629	−4.049
K10	1.499607	−3.7681	−4.525
KF9	1.521409	−4.2683	−4.939
LLF1	1.545798	−4.9748	−5.534
LF5	1.580165	−5.5039	−5.810
F4	1.613340	−6.8711	−6.916
TiF2	1.530301	−4.7938	−5.467
BaK4	1.566824	−4.2802	−4.609
SK4	1.610645	−4.4314	−4.477
PSK3	1.550580	−3.7340	−4.123
BaLF4	1.577440	−4.5340	−4.805
SSK2	1.619993	−4.9140	−4.901
BaF8	1.621146	−5.5063	−5.483
SF5	1.668692	−8.4410	−7.893
SF4	1.749990	−10.9471	−9.289
SF57	1.839958	−14.0352	−10.83
BaSF10	1.646947	−6.7905	−6.531
BaSF51	1.720052	−7.7729	−6.826
LaK8	1.710372	−5.6222	−4.994
LaF21	1.784848	−6.9191	−5.650
LaF22	1.777719	−8.6052	−7.081
LaSF5	1.876499	−8.8943	−6.620

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Tables (4)

Equations (27)

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