The Spherical Mirror Fabry-Perot Interferometer

Michael Hercher

doi:10.1364/AO.7.000951

Applied Optics
Vol. 7,
Issue 5,
pp. 951-966
(1968)
•https://doi.org/10.1364/AO.7.000951

The Spherical Mirror Fabry-Perot Interferometer

Michael Hercher

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Michael Hercher, "The Spherical Mirror Fabry-Perot Interferometer," Appl. Opt. 7, 951-966 (1968)

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Abstract

The theory, design, and use of the confocal spherical mirror Fabry-Perot interferometer (FPS) is described in detail. Topics covered include performance of an FPS for small departures from the confocal mirror separation, optimization of the (resolution) × (light gathering power) product, factors limiting realizable finesse, mode matching considerations, alignment procedures, and general design considerations. Two specific instruments are described. One is a versatile spectrum analyzer with piezoelectric scanning; the other is a highly stable etalon with fixed spacing. Examples of the performance of these instruments are given.

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Corrections

Michael Hercher, "Errata: The Spherical Mirror Fabry-Perot Interferometer," Appl. Opt. 7, 1336_1-1336 (1968)
https://opg.optica.org/ao/abstract.cfm?uri=ao-7-7-1336_1

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A	= area of FPS entrance aperture
c	= velocity of light
d	= FPP mirror separation
D	= aperture diameter (FPS or FPP)
F	= finesse = (πR/(1 − R²), (FPS)
L	= cavity loss per transit
M	= fringe pattern magnification factor
r	= FPS mirror radii and confocal separation
R	= mirror reflectivity
ℛ	= spectral resolving power
T	= mirror transmission
T₀	= FPS instrumental transmission
U	= étendue = ΩA
δ	= phase increment = 2πΔ/λ
Δ	= path difference
∊	= difference between FPS mirror separation and confocal spacing r.
λ	= wavelength
$\bar{ν}$	= optical frequency
Δν_m	= minimum resolvable frequency difference, or instrumental bandpass.
Δν_f	= free spectral range, c/4r(FPS)
ρ	= fringe radius
ρ_s	= radius of central spot = ${(λ r^{3} / F)}^{\frac{1}{4}}$
Ω	= solid angle subtended source by

Type	Region of high reflectivity	F	T₀	R
A	6200 Å to 7000 Å	225	0.45	0.993
B	4800 Å to 6900 Å	150	0.35	0.99
C	4900 Å to 6800 Å	180–200	0.02	0.992

A	= area of FPS entrance aperture
c	= velocity of light
d	= FPP mirror separation
D	= aperture diameter (FPS or FPP)
F	= finesse = (πR/(1 − R²), (FPS)
L	= cavity loss per transit
M	= fringe pattern magnification factor
r	= FPS mirror radii and confocal separation
R	= mirror reflectivity
ℛ	= spectral resolving power
T	= mirror transmission
T₀	= FPS instrumental transmission
U	= étendue = ΩA
δ	= phase increment = 2πΔ/λ
Δ	= path difference
∊	= difference between FPS mirror separation and confocal spacing r.
λ	= wavelength
$\bar{ν}$	= optical frequency
Δν_m	= minimum resolvable frequency difference, or instrumental bandpass.
Δν_f	= free spectral range, c/4r(FPS)
ρ	= fringe radius
ρ_s	= radius of central spot = ${(λ r^{3} / F)}^{\frac{1}{4}}$
Ω	= solid angle subtended source by

Type	Region of high reflectivity	F	T₀	R
A	6200 Å to 7000 Å	225	0.45	0.993
B	4800 Å to 6900 Å	150	0.35	0.99
C	4900 Å to 6800 Å	180–200	0.02	0.992

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