Accurate wavelength calibration in the near-infrared for multielement analysis without the need for reference spectra

George Asimellis; Aggelos Giannoudakos; Michael Kompitsas

doi:10.1364/AO.45.008855

Applied Optics
Vol. 45,
Issue 35,
pp. 8855-8862
(2006)
•https://doi.org/10.1364/AO.45.008855

Accurate wavelength calibration in the near-infrared for multielement analysis without the need for reference spectra

George Asimellis, Aggelos Giannoudakos, and Michael Kompitsas

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George Asimellis, Aggelos Giannoudakos, and Michael Kompitsas, "Accurate wavelength calibration in the near-infrared for multielement analysis without the need for reference spectra," Appl. Opt. 45, 8855-8862 (2006)

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Abstract

A new technique has been developed for an instant, precise, and accurate wavelength calibration over a wide pixel array for simultaneous, multielement spectral analysis based on an inverse numerical solution to the grating dispersion function. This technique is applicable to multielement analytical applications such as laser-induced breakdown spectroscopy (LIBS), particularly when using high-density gratings in the upper visible and in the near-infrared, where nonmetallic elements are detected. This application overcomes the need to use reference spectra for each window of observation and is tested on a commercially available LIBS instrument.

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Name	Symbol	Units	Typical Values
Grating groove frequency	G	lines∕mm	600–2400 mm⁻¹
Spectrometer focal length	F	mm	500–20 mm
Array pixel size	P	μm	26 μm
Spectrometer half-deviation angle	x		15.2°

Dispersion Linear Approximation Parameters
Grating: 2400 lines∕mm
Range (nm)	(1∕pixel)	(nm∕pixel)	(nm∕pixel)
Range (nm)	α	β	r = α × λ + β
200–250	−2.441 × 10⁻⁵	3.629 × 10⁻²	r = −2.441 × 10⁻⁵ λ + 3.629 × 10⁻²
300–350	−3.100 × 10⁻⁵	3.812 × 10⁻²	r = −3.100 × 10⁻⁵ λ + 3.812 × 10⁻²
400–450	−3.885 × 10⁻⁵	4.108 × 10⁻²	r = −3.885 × 10⁻⁵ λ + 4.108 × 10⁻²
500–550	−4.928 × 10⁻⁵	4.607 × 10⁻²	r = −4.928 × 10⁻⁵ λ + 4.607 × 10⁻²
600–650	−6.518 × 10⁻⁵	5.528 × 10⁻²	r = −6.518 × 10⁻⁵ λ + 5.528 × 10⁻²
700–750	−10.21 × 10⁻⁵	8.053 × 10⁻²	r = −1.021 × 10⁻⁴ λ + 8.053 × 10⁻²

Dispersion Linear Approximation Parameters
Grating: 2400 lines\mm
Range	(1\pixel)	(nm\pixel)	(nm\pixel)
(nm)	α	β	r = α × λ + β
200–250	−2.441 × 10⁻⁵	3.629 × 10⁻²	r = −2.441 × 10⁻⁵ λ + 3.629 × 10⁻²
300–350	−3.100 × 10⁻⁵	3.812 × 10⁻²	r = −3.100 × 10⁻⁵ λ + 3.812 × 10⁻²
400–450	−3.885 × 10⁻⁵	4.108 × 10⁻²	r = −3.885 × 10⁻⁵ λ + 4.108 × 10⁻²
500–550	−4.928 × 10⁻⁵	4.607 × 10⁻²	r = −4.928 × 10⁻⁵ λ + 4.607 × 10⁻²
600–650	−6.518 × 10⁻⁵	5.528 × 10⁻²	r = −6.518 × 10⁻⁵ λ + 5.528 × 10⁻²
700–750	−10.21 × 10⁻⁵	8.053 × 10⁻²	r = −1.021 × 10⁻⁴ λ + 8.053 × 10⁻²

Dispersion: Fourth-Order Approximation				Measured λ Discrepancy (Å)
λ (nm)	Regression	Exact	Difference (%)	Measured λ Discrepancy (Å)
327	0.027665	0.027987	−1.150	4.00
500	0.021516	0.021407	0.509	0.30
610	0.015138	0.015526	−2.500	4.80
670	0.011473	0.011384	−0.799	1.20

Dispersion: Sixth-Order Approximation				Measured λ Discrepancy (Å)
λ (nm)	Regression	Exact	Difference (%)	Measured λ Discrepancy (Å)
327	0.028119	0.027987	0.473	0.25
500	0.021464	0.021407	0.270	0.40
610	0.015516	0.015526	−0.067	1.40
670	0.011260	0.011384	−1.096	1.63

Experimental Results
λ (nm)	Regression	Exact	Difference (%)	Discrepancy (Å)	Computed	Difference (%)	Discrepancy (Å)
327	0.02799	0.02766	1.150	3.76	0.02806	0.259	0.45
500	0.02141	0.02152	0.509	2.54	0.02147	0.286	0.40
610	0.01553	0.01514	2.500	15.25	0.01550	0.153	1.30
670	0.01138	0.01137	0.099	0.63	0.01131	0.615	1.30
		Average	1.65	5.545 Å		0.328	0.862 Å
Calculated Differences
200	0.03140	0.03351	6.722	13.4	0.03118	0.691	1.38
250	0.03018	0.02964	1.784	4.45	0.03026	0.275	0.70
290	0.02909	0.02836	2.520	7.30	0.02925	0.568	1.65
400	0.02552	0.02599	1.815	7.28	0.02539	0.511	2.04
450	0.02358	0.02405	1.966	8.86	0.02351	0.310	1.39
480	0.02231	0.02258	1.234	5.90	0.02232	0.045	0.24
550	0.01895	0.01866	1.502	8.25	0.01905	0.541	2.97
		Average	2.15	7.93 Å		0.328	1.48 Å

Experimental Results
λ (nm)	Regression	Exact	Difference (%)	Discrepancy (Å)	Computed	Difference (%)	Discrepancy (Å)
327	0.02799	0.02766	1.150	3.76	0.02806	0.259	0.45
500	0.02141	0.02152	0.509	2.54	0.02147	0.286	0.40
610	0.01553	0.01514	2.500	15.25	0.01550	0.153	1.30
670	0.01138	0.01137	0.099	0.63	0.01131	0.615	1.30
		Average	1.65	5.545 Å		0.328	0.862 Å
Calculated Differences
200	0.03140	0.03351	6.722	13.4	0.03118	0.691	1.38
250	0.03018	0.02964	1.784	4.45	0.03026	0.275	0.70
290	0.02909	0.02836	2.520	7.30	0.02925	0.568	1.65
400	0.02552	0.02599	1.815	7.28	0.02539	0.511	2.04
450	0.02358	0.02405	1.966	8.86	0.02351	0.310	1.39
480	0.02231	0.02258	1.234	5.90	0.02232	0.045	0.24
550	0.01895	0.01866	1.502	8.25	0.01905	0.541	2.97
		Average	2.15	7.93 Å		0.328	1.48 Å

Abstract

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Figures (10)

Tables (6)

Equations (27)

Applied Optics