Wavelength Measurements with a Concave Grating Spectrograph

Frank S. Tomkins; Mark Fred

doi:10.1364/AO.2.000715

Applied Optics
Vol. 2,
Issue 7,
pp. 715-725
(1963)
•https://doi.org/10.1364/AO.2.000715

Wavelength Measurements with a Concave Grating Spectrograph

Frank S. Tomkins and Mark Fred

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Frank S. Tomkins and Mark Fred, "Wavelength Measurements with a Concave Grating Spectrograph," Appl. Opt. 2, 715-725 (1963)

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Abstract

Certain disadvantages and limitations in conventional methods of measuring wavelengths from grating spectrograms are discussed, and some alternative procedures described. It is shown that by fitting thorium standards to the dispersion of the Argonne 9.15-m spectrograph, using a polynomial least-squares program with a digital computer, wavelengths accurate to 1 in 10⁸ can be obtained at a rate of 1000 per day.

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True λ^a	Measured λ	(T − M) in 10⁻⁴ Å	Intensity^b
3687.4560	0.4560	0	46,000
3709.2458	0.2456	2	57,300
3727.6187	0.6187	0	51,900
3734.8643	0.8631	12	473,000
3743.3614	0.3614	0	39,900
3749.4852	0.4843	9	326,000
3758.2326	0.2320	6	207,000
3763.7887	0.7885	2	115,000
3767.1912	0.1918	−6	71,600
3787.8800	0.8800	0	28,200
3795.0017	0.0025	−8	38,000
3798.5110	0.5115	−5	26,400
3799.5468	0.5473	−5	37,800

		Av ±44.2

Grating	Angle of incidence	Orientation	R (mm)	d (Å)	dsinα (Å)
	23°	A	9143.3	16666.89	6543.0
		B	9143.3	16666.89	6559.0
2
	53°	A	9143.3	16666.89	13312.0
		B	9143.3	16666.89	13328.0
	23°	A	9143.3	16666.46	6530.0
3
	53°	B	9143.3	16666.46	13340.0

True λ	p = 3			p = 4		p = 5			p = 6			Wt. av
True λ	λ		T − M^a	λ	T − M	λ		T − M	λ		T − M	T − M^b
3642.2487				Std	(0)	0.2480		7	0.2479		8	8(2)
3656.6936	0.6934		2	0.6938	−2	Std		(0)	0.6944		−8	−4(3)
3668.1396	0.1408		−12	0.1396	0				0.1402		−6	−6(2)
3669.9687	0.9694		−7						0.9687		0	− 1(2)
3682.4861	Std		(0)	0.4869	−8	0.4879		−18	Std		(0)	−15(2)
3692.5661	0.5671		−10	0.5670	−9	0.5664		−3				−7(4)
3700.9780	0.9787		−7	0.9792	−12	Std		(0)	0.9803		−23	−15(3)
3711.3037	0.3034		3	0.3040	−3	0.3031		6	0.3051		−14	−3(4)
3719.4345	0.4335		10	0.4332	13	0.4326		19	0.4351		−6	8(4)
3727.9022	0.9023		−1	Std	(0)	0.9027		−5	0.9023		−1	−2(3)
3742.9231	Std		(0)		12	0.9219
						0.9226		5	Std		(0)	8(2)
							0.5663	22		0.5665	20
3752.5685	0.5686		−1	0.5641	44							7(6)
							0.5693	−8		0.5711	−26
3762.9345	0.9324		21			0.9339		6	Std		(0)	12(2)
		0.3711	−8
3771.3703						Std		(0)	0.3730		−27
		0.3707	−4								4	−16(3)
3780.9663	0.9675		−12			0.9661		2	0.9659			0(3)
3785.5997	0.6013		−16	0.6001	−4	0.6014		−17	Std		(0)	−12(3)
3803.0750	Std		(0)	0.0747	3	0.0756		−6				−2(2)
3813.0674				Std	(0)	0.0691		−17	0.0666		8	−3(2)
3818.6855				0.6847	Std			(0)	Std		(0)	8(1)
											Av = ±7.2

True λ	p = 3		p = 4		p = 5			p = 6			Wt. av
True λ	λ	T − M^a	λ	T − M	λ		T − M	λ		T − M	T − M^b
3642.2487	0.2490	−3						0.2487		0	−3(1)
3656.6936	0.6925	11						0.6936		0	11(1)
3668.1396	0.1404	−s						0.1396		0	−8(1)
3669.9687	0.9689	−2						0.9687		0	−2(1)
3682.4861	0.4857	4	0.4862	−1	0.4862		−1	0.4861		0	0(3)
3692.5661	0.5667	−6	0.5657	4	0.5657		4	0.5659		2	2(4)
3700.9780	0.9783	−3	0.9783	−3	0.9783		−3	0.9786		−6	4(4)
3711.3037	0.3033	4	0.3042	−5	0.3041		−4	0.3030		7	1(4)
3719.4345	0.4333	12	0.4337	8	0.4337		8	0.4344		1	6(4)
3727.9022	0.9025	−3	0.9025	−3	0.9026		−4	0.9027		−5	−3(4)
3742.9231	0.9238	−7	0.9232	−1				0.9228		3	0(3)
						0.5685	0		0.5686	−1
3752.5685	0.5694	−9	0.5685	0							1(6)
						0.5686	−1		0.5685	0
3762.9345	0.9329	16			0.9340		5	0.9344		1	6(3)
3771.3703	0.3709	−6			0.3707		−4	0.3706		−3	−4(3)
3780.9663					0.9664		−1	0.9660		3	−1(2)
3785.5997					0.5996		1	0.5999		−2	−1(2)
3803.0750					0.0746		4	0.0750		0	0(2)
3813.0674					0.0680		−6				−6(1)
3818.6855					0.6852		3				3(1)
											Av = ±3.4

True λ	A all lines		B 1 eliminated		C 2 eliminated		D 3 eliminated
True λ	λ	T-M	λ	T-M	λ	T-M	λ	T-M
3642.2487	0.2490	−3	0.2491	−4	0.2490	−3	0.2487	0
3656.6936	0.6925	11	0.6924	12	0.6925	11	—	—
3668.1396	0.1404	−8	0.1403	−7	0.1404	−8	0.1399	−3
3669.9687	0.9689	−2	0.9689	−2	0.9689	−2	0.9685	2
3682.4861	0.4857	4	0.4857	4	0.4857	4	0.4855	6
3692.5661	0.5667	−6	0.5668	−7	0.5667	−6	0.5667	−6
3700.9780	0.9783	−3	0.9785	−5	0.9782	−2	0.9783	−3
3711.3037	0.3033	4	0.3034	3	0.3030	7	0.3032	5
3719.4345	0.4333	12	0.4334	11	—	—	—	—
3727.9022	0.9025	−3	0.9024	−2	0.9021	1	0.9022	0
3742.9231	0.9238	−7	0.9234	−3	0.9232	−1	0.9231	0
3752.5685	0.5694	−9	0.5688	−3	0.5688	−3	0.5686	−1
3762.9345	0.9329	16	—	—	—	—	—	—
3771.3703	0.3709	−6	0.3701	2	0.3702	1	0.3703	0
		Av ±6.7		Av ± 5.0		Av ±4.1		Av ± 2.4

σ_i	σ_j	Δσ	$\bar{Δ σ} - Δ σ$
27889.588 cm⁻¹	27064.171 cm⁻¹	825.417 cm⁻¹	0.016 cm⁻¹
24582.775	23757.351	825.424	0.009
26818.893	25993.462	825.431	0.002
25104.469	24279.037	825.432	0.001
27638.034	26812.601	825.433	0.000
25586.535	24761.097	825.438	−0.005
27078.811	26253.355	825.456	−0.023

		Av 825.433	±0.008

a_i	sin⁻¹x				sinx
a₀	1.570	796	321	8
a₁	−0.214	601	396	4	0.999	999	994	7
a₂	0.089	036	508	3
a₃	−0.050	648	632	2	−0.166	666	567	0
a₄	0.032	796	693	7
a₅	−0.021	224	217	6	0.008	333	025	2
a₆	0.011	631	517	6
a₇	−0.004	355	139	1	−0.000	198	074	1
a₈	0.000	781	921	9
a₉					0.000	002	601	9

True λ		With correction		Without correction
True λ	p	M	T − M	M	T − M
4178.0598	6	0.0603	−5	0.0605	−7
5017.2545	5	0.2536	9	0.2531	14
3592.7788	7	0.7794	−6	0.7797	−9
4193.0165	6	0.0160	5	0.0157	8
3598.1196	7	0.1200	−4	0.1203	−7
5049.7959	5	0.7951	8	0.7945	14
4214.8283	6	0.8283	0	0.8282	1
3615.1324	7	0.1328	−4	0.1331	−7
3622.7951	7	0.7950	1	0.7949	2
			Av ±4.7		Av ±7.7

True λ		With correction		Without correction
True λ	p	M	T − M	M	T − M
4178.0598	6	0.0603	−5	0.0605	−7
5017.2545	5	0.2536	9	0.2531	14
3592.7788	7	0.7794	−6	0.7797	−9
4193.0165	6	0.0160	5	0.0157	8
3598.1196	7	0.1200	−4	0.1203	−7
5049.7959	5	0.7951	8	0.7945	14
4214.8283	6	0.8283	0	0.8282	1
3615.1324	7	0.1328	−4	0.1331	−7
3622.7951	7	0.7950	1	0.7949	2
			Av ±4.7		Av ±7.7

Abstract

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Tables (8)

Equations (10)

Applied Optics