Phase errors on interferograms: influence on the determination of positions, intensities, and widths of lines in the infrared

Victor Dana; Jean-Yves Mandin; Abdelhamid Hamdouni

doi:10.1364/AO.31.001937

Applied Optics
Vol. 31,
Issue 12,
pp. 1937-1941
(1992)
•https://doi.org/10.1364/AO.31.001937

Phase errors on interferograms: influence on the determination of positions, intensities, and widths of lines in the infrared

Victor Dana, Jean-Yves Mandin, and Abdelhamid Hamdouni

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Victor Dana, Jean-Yves Mandin, and Abdelhamid Hamdouni, "Phase errors on interferograms: influence on the determination of positions, intensities, and widths of lines in the infrared," Appl. Opt. 31, 1937-1941 (1992)

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Abstract

The effect of a phase error on line parameter measurements by using Fourier-transform spectra is studied, showing that, to obtain accurate results without modifying the interferogram, it is necessary to adjust a computed spectrum to an experimental spectrum in which the phase error is taken into account.

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σ₀ (cm⁻¹)					2000												10000
γ_d (10⁻³ cm⁻¹)					3.0												14.5
Δ_max = (cm)	200				100				50				200				100				50
FWHM (10⁻³ cm⁻¹)	2.5				5.0				10.0				2.5				5.0				10.0
Fitted spectral range	0.1				0.2				0.4				0.1				0.2				0.4
γ₁ (10⁻³ cm⁻¹)	1	5	10	20	1	5	10	20	1	5	10	20	1	5	10	20	1	5	10	20	1	5	10	20
y	0.3	1.4	2.9	5.7	0.3	1.4	2.9	5.7	0.3	1.4	2.9	5.7	0.1	0.3	0.6	1.2	0.1	0.3	0.6	1.2	0.1	0.3	0.6	1.2
Intensity (10⁻³ cm⁻²)	7	15	20	40	7	15	25	50	10	15	25	40	20	30	40	60	20	30	40	50	25	30	40	60
Average depth (in %)	56	55	45	46	55	54	51	54	52	51	51	45	45	51	53	53	46	51	53	47	53	51	52	53

σ₀	2000 cm⁻¹				10 000 cm⁻¹
φ	0.02	0.04	0.08	0.16	0.02	0.04	0.08	0.16
Δ_max	200				200
γ₁	1				1
2γ	7.7	7.7	7.8	8.0	33.5	33.6	33.6	33.6
Δσ_d	57	116	234	465	244	488	982	1963
Δσ_f	75	151	301	603	261	522	1042	2080
γ₁	5				5
2γ	15.3	15.3	15.3	15.5	39.7	39.7	39.7	39.7
Δσ_d	99	200	399	799	270	544	1101	2194
Δσ_f	138	276	552	1105	281	562	1123	2242
γ₁	10				10
2γ	25.1	25.2	25.2	25.3	47.7	47.8	47.6	47.5
Δσ_d	155	308	614	1223	300	602	1217	2423
Δσ_f	200	400	799	1598	299	597	1194	2384
γ₁	20				20
2γ	48.0	48.0	48.4	47.9	65.5	65.7	65.7	65.5
Δσ_d	260	523	1055	2103	344	686	1387	2762
Δσ_f	279	557	1113	2223	324	643	1285	2566
σ₀	2000 cm⁻¹				10 000 cm⁻¹
φ	0.02	0.04	0.08	0.16	0.02	0.04	0.08	0.16
Δ_max	100				100
γ₁	1				1
2γ	8.6	8.6	8.7	8.8	33.5	33.6	33.7	34.2
Δσ_d	69	138	262	507	254	502	984	1988
Δσ_f	78	156	313	626	298	597	1193	2386
γ₁	5				5
2γ	15.1	15.1	15.2	15.4	39.7	39.7	39.7	39.7
Δσ_d	101	202	401	802	288	575	1148	2283
Δσ_f	147	293	587	1176	346	692	1384	2769
γ₁	10				10
2γ	25.2	25.2	25.5	25.7	47.7	47.7	47.7	47.8
Δσ_d	159	318	642	1286	327	659	1318	2641
Δσ_f	239	478	956	1912	400	800	1600	3198
γ₁	20				20
2γ	49.7	49.7	49.8	50.0	64.1	64.1	64.3	64.4
Δσ_d	300	600	1195	2375	414	826	1646	3285
Δσ_f	397	795	1588	3173	480	959	1918	3832
σ₀	2000 cm⁻¹				10 000⁻¹
φ	0.02	0.04	0.08	0.16	0.02	0.04	0.08	0.16
Δ_max	50				50
γ₁	1				1
2γ	13.7	13.5	13.6	14.1	34.3	34.4	34.6	35.0
Δσ_d	98	194	393	857	262	522	1015	2058
Δσ_f	113	226	451	902	315	631	1261	2522
γ₁	5				5
2γ	17.7	17.8	17.8	18.0	39.4	39.5	39.7	40.0
Δσ_d	139	274	521	1016	282	566	1142	2285
Δσ_f	161	323	646	1290	367	734	1469	2937
γ₁	10				10
2γ	25.8	25.8	26.0	26.3	47.0	47.1	47.3	47.8
Δσ_d	178	347	684	1361	333	668	1329	2655
Δσ_f	254	507	1014	2030	440	880	1761	3522
γ₁	20				20
2γ	46.0	46.5	46.8	47.4	65.7	65.8	65.8	66.0
Δσ_d	287	575	1141	2307	429	866	1730	3467
Δσ_f	443	886	1771	3550	588	1175	2351	4698

σ₀ (cm⁻¹)					2000												10000
γ_d (10⁻³ cm⁻¹)					3.0												14.5
Δ_max = (cm)	200				100				50				200				100				50
FWHM (10⁻³ cm⁻¹)	2.5				5.0				10.0				2.5				5.0				10.0
Fitted spectral range	0.1				0.2				0.4				0.1				0.2				0.4
γ₁ (10⁻³ cm⁻¹)	1	5	10	20	1	5	10	20	1	5	10	20	1	5	10	20	1	5	10	20	1	5	10	20
y	0.3	1.4	2.9	5.7	0.3	1.4	2.9	5.7	0.3	1.4	2.9	5.7	0.1	0.3	0.6	1.2	0.1	0.3	0.6	1.2	0.1	0.3	0.6	1.2
Intensity (10⁻³ cm⁻²)	7	15	20	40	7	15	25	50	10	15	25	40	20	30	40	60	20	30	40	50	25	30	40	60
Average depth (in %)	56	55	45	46	55	54	51	54	52	51	51	45	45	51	53	53	46	51	53	47	53	51	52	53

σ₀	2000 cm⁻¹				10 000 cm⁻¹
φ	0.02	0.04	0.08	0.16	0.02	0.04	0.08	0.16
Δ_max	200				200
γ₁	1				1
2γ	7.7	7.7	7.8	8.0	33.5	33.6	33.6	33.6
Δσ_d	57	116	234	465	244	488	982	1963
Δσ_f	75	151	301	603	261	522	1042	2080
γ₁	5				5
2γ	15.3	15.3	15.3	15.5	39.7	39.7	39.7	39.7
Δσ_d	99	200	399	799	270	544	1101	2194
Δσ_f	138	276	552	1105	281	562	1123	2242
γ₁	10				10
2γ	25.1	25.2	25.2	25.3	47.7	47.8	47.6	47.5
Δσ_d	155	308	614	1223	300	602	1217	2423
Δσ_f	200	400	799	1598	299	597	1194	2384
γ₁	20				20
2γ	48.0	48.0	48.4	47.9	65.5	65.7	65.7	65.5
Δσ_d	260	523	1055	2103	344	686	1387	2762
Δσ_f	279	557	1113	2223	324	643	1285	2566
σ₀	2000 cm⁻¹				10 000 cm⁻¹
φ	0.02	0.04	0.08	0.16	0.02	0.04	0.08	0.16
Δ_max	100				100
γ₁	1				1
2γ	8.6	8.6	8.7	8.8	33.5	33.6	33.7	34.2
Δσ_d	69	138	262	507	254	502	984	1988
Δσ_f	78	156	313	626	298	597	1193	2386
γ₁	5				5
2γ	15.1	15.1	15.2	15.4	39.7	39.7	39.7	39.7
Δσ_d	101	202	401	802	288	575	1148	2283
Δσ_f	147	293	587	1176	346	692	1384	2769
γ₁	10				10
2γ	25.2	25.2	25.5	25.7	47.7	47.7	47.7	47.8
Δσ_d	159	318	642	1286	327	659	1318	2641
Δσ_f	239	478	956	1912	400	800	1600	3198
γ₁	20				20
2γ	49.7	49.7	49.8	50.0	64.1	64.1	64.3	64.4
Δσ_d	300	600	1195	2375	414	826	1646	3285
Δσ_f	397	795	1588	3173	480	959	1918	3832
σ₀	2000 cm⁻¹				10 000⁻¹
φ	0.02	0.04	0.08	0.16	0.02	0.04	0.08	0.16
Δ_max	50				50
γ₁	1				1
2γ	13.7	13.5	13.6	14.1	34.3	34.4	34.6	35.0
Δσ_d	98	194	393	857	262	522	1015	2058
Δσ_f	113	226	451	902	315	631	1261	2522
γ₁	5				5
2γ	17.7	17.8	17.8	18.0	39.4	39.5	39.7	40.0
Δσ_d	139	274	521	1016	282	566	1142	2285
Δσ_f	161	323	646	1290	367	734	1469	2937
γ₁	10				10
2γ	25.8	25.8	26.0	26.3	47.0	47.1	47.3	47.8
Δσ_d	178	347	684	1361	333	668	1329	2655
Δσ_f	254	507	1014	2030	440	880	1761	3522
γ₁	20				20
2γ	46.0	46.5	46.8	47.4	65.7	65.8	65.8	66.0
Δσ_d	287	575	1141	2307	429	866	1730	3467
Δσ_f	443	886	1771	3550	588	1175	2351	4698

Abstract

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Figures (3)

Tables (2)

Equations (7)

Applied Optics