Stable multipass Fabry-Perot interferometer: design and analysis

Chandrasekhar Roychoudhuri; Michael Hercher

doi:10.1364/AO.16.002514

Applied Optics
Vol. 16,
Issue 9,
pp. 2514-2520
(1977)
•https://doi.org/10.1364/AO.16.002514

Stable multipass Fabry-Perot interferometer: design and analysis

Chandrasekhar Roychoudhuri and Michael Hercher

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Chandrasekhar Roychoudhuri and Michael Hercher, "Stable multipass Fabry-Perot interferometer: design and analysis," Appl. Opt. 16, 2514-2520 (1977)

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Abstract

A multipass plane parallel Fabry-Perot interferometer (FPP-M) can give extremely high contrast (in excess of 10⁶) over a wide range of finesse values without reducing the transmission significantly. Curves and tables are provided along with a brief outline of Chabbal’s analysis for the residual defects of the Fabry-Perot mirrors to aid a quick assessment of the optimum parameters for a desired spectrometric work. The exploitation of the advantages of an FPP-M depends upon the maintenance of its stability. So, we have constructed a passive interferometer of low thermal expansion material, Cer-Vit, along with nonkinematic design and thermally compensated mirror mounts to achieve long term stability without the use of a servo control device.

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(a) N_r/N_d = 1.0; N/N_d = 0.71; τ_d = 0.79

Parameters	Symbols	One-pass	Two-pass	Three-pass	Five-pass
λ/100 plate	N_n	35.35	54.92	69.33	91.67
N_d = 50	τ_aⁿτ_dⁿ	0.739	0.546	0.404	0.220
N_r = 50	C_n	5.075 × 10²	2.576 × 10⁵	1.307 × 10⁸	3.366 × 10¹³
R = 0.939
τ_a = 0.936
λ/200 plate	N_n	70.7	109.85	138.67	183.35
N_d = 100	τ_aⁿτ_dⁿ	0.693	0.480	0.333	0.16
N_r = 100	C_n	2.03 × 10³	4.11 × 10⁶	8.33 × 10⁹	3.42 × 10¹⁶
R = 0.969
τ_a = 0.877
λ/400 plate	N_n	141.4	219.71	277.36	366.69
N_d = 200	τ_aⁿτ_dⁿ	0.593	0.352	0.209	0.073
N_r = 200	C_n	8.10 × 10³	6.57 × 10⁷	5.32 × 10¹¹	3.49 × 10¹⁹
R = 0.985
τ_a = 0.751

(b) N_r/N_d = 0.3; N/N_d = 0.29; T_d = 0.79

Parameters	Symbols	One-pass	Two-pass	Three-pass	Five-pass
λ/100 plate	N_n	14.35	22.3	28.15	37.24
N_d = 50	τ_aⁿτ_dⁿ	0.95	0.902	0.857	0.772
N_r = 15	C_n	8.34 × 10	7.04 × 10³	5.90 × 10⁵	4.15 × 10⁹
R = 0.81
τ_a = 0.979
λ/200 plate	N_n	28.7	44.59	56.3	74.43
N_d = 100	τ_aⁿτ_dⁿ	0.927	0.860	0.797	0.685
N_r = 30	C_n	3.35 × 10²	1.12 × 10⁵	3.75 × 10⁷	4.21 × 10¹²
R = 0.91
τ_a = 0.956
λ/400 plate	N_n	57.4	89.19	112.59	148.86
N_d = 200	τ_aⁿτ_dⁿ	0.895	0.802	0.718	0.575
N_r = 60	C_n	1.34 × 10³	1.78 × 10⁶	2.38 × 10⁹	4.25 × 10¹⁵
R = 0.949
τ_a = 0.923

(a) N_r/N_d = 1.0; N/N_d = 0.65; T_d = 0.71

Parameters	Symbols	One-pass	Two-pass	Three pass	Five pass
λ/100 plate	N_n	13.89	21.59	27.25	36.03
N_d = 21.23	τ_aⁿτ_dⁿ	0.689	0.475	0.328	0.156
N_r = 21.23	C_n	7.92 × 10	6.28 × 10³	4.97 × 10⁵	3.12 × 10⁹
R = 0.863
τ_a = 0.971
λ/200 plate	N_n	27.79	43.18	54.50	72.06
N_d = 42.55	τ_aⁿτ_dⁿ	0.671	0.450	0.302	0.136
N_r = 42.55	C_n	3.14 × 10²	9.86 × 10⁴	3.09 × 10⁷	3.05 × 10¹²
R = 0.929
τ_a = 0.945
λ/400 plate	N_n	55.57	86.35	109.01	144.12
N_d = 85.11	τ_aⁿτ_dⁿ	0.634	0.402	0.255	0.102
N_r = 85.11	C_n	1.25 × 10³	1.57 × 10⁶	1.97 × 10⁹	3.09 × 10¹⁵
R = 0.964
τ_a = 0.893

(b) N_r/N_d = 0.3; N/N_d = 0.28; T_d = 0.94

Parameters	Symbols	One-pass	Two-pass	Three-pass	Five-pass
λ/100 plate	N_n	5.85	9.09	11.48	15.17
N_d = 21.28	τ_aⁿτ_dⁿ	0.930	0.865	0.805	0.697
N_r = 6.39	C_n	1.36 × 10	1.86 × 10²	2.53 × 10³	4.69 × 10⁵
R = 0.614
τ_a = 0.99
λ/200 plate	N_n	11.70	18.18	22.95	30.35
N_d = 42.55	τ_aⁿτ_dⁿ	0.923	0.852	0.786	0.669
N_r = 12.77	C_n	5.65 × 10	3.19 × 10³	1.80 × 10⁵	5.76 × 10⁸
R = 0.782
τ_a = 0.982
λ/400 plate	N_n	23.40	36.37	45.91	60.69
N_d = 85.11	τ_aⁿτ_dⁿ	0.908	0.824	0.748	0.617
N_r = 25.53	C_n	2.23 × 10²	4.97 × 10⁴	1.11 × 10⁷	5.51 × 10¹¹
R = 0.884
τ_a = 0.966

(a) N_r/N_d = 1.0; N/N_d = 0.71; τ_d = 0.79

Parameters	Symbols	One-pass	Two-pass	Three-pass	Five-pass
λ/100 plate	N_n	35.35	54.92	69.33	91.67
N_d = 50	τ_aⁿτ_dⁿ	0.739	0.546	0.404	0.220
N_r = 50	C_n	5.075 × 10²	2.576 × 10⁵	1.307 × 10⁸	3.366 × 10¹³
R = 0.939
τ_a = 0.936
λ/200 plate	N_n	70.7	109.85	138.67	183.35
N_d = 100	τ_aⁿτ_dⁿ	0.693	0.480	0.333	0.16
N_r = 100	C_n	2.03 × 10³	4.11 × 10⁶	8.33 × 10⁹	3.42 × 10¹⁶
R = 0.969
τ_a = 0.877
λ/400 plate	N_n	141.4	219.71	277.36	366.69
N_d = 200	τ_aⁿτ_dⁿ	0.593	0.352	0.209	0.073
N_r = 200	C_n	8.10 × 10³	6.57 × 10⁷	5.32 × 10¹¹	3.49 × 10¹⁹
R = 0.985
τ_a = 0.751

Abstract

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Figures (9)

Tables (2)

Equations (15)

Applied Optics