Analysis and correction of distortions in a spatial heterodyne spectrometer system

Jilin Liu; Daikang Wei; Oliver Wroblowski; Qiuyu Chen; Klaus Mantel; Friedhelm Olschewski; Martin Kaufmann; Martin Riese

doi:10.1364/AO.58.002190

Applied Optics
Vol. 58,
Issue 9,
pp. 2190-2197
(2019)
•https://doi.org/10.1364/AO.58.002190

Analysis and correction of distortions in a spatial heterodyne spectrometer system

Jilin Liu, Daikang Wei, Oliver Wroblowski, Qiuyu Chen, Klaus Mantel, Friedhelm Olschewski, Martin Kaufmann, and Martin Riese

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Jilin Liu, Daikang Wei, Oliver Wroblowski, Qiuyu Chen, Klaus Mantel, Friedhelm Olschewski, Martin Kaufmann, and Martin Riese, "Analysis and correction of distortions in a spatial heterodyne spectrometer system," Appl. Opt. 58, 2190-2197 (2019)

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Abstract

In this paper a method for correcting the radial distortion of interferograms generated by a spatial heterodyne spectrometer system is presented. Instead of utilizing calibration patterns, the distortion model parameters are estimated based on the distorted fringe features generated by projecting the straight interference stripes onto the detector. Comparisons between polynomial models and division models indicate that division models can deliver competitive performance on the reconstructed image with fewer parameters. Simulated interferograms based on ray-tracing are used to demonstrate the correction of errors in the spatial, phase, and spectral domain caused by optical distortion.

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Component	Item	Value
Filter	Wavelength range	761.9–765.3 nm
Fore optics	Field of view	$\pm 0.65 °$
Fore optics	Aperture diameter	66 mm
SHS	Littrow wavelength	761.8 nm
	Littrow angle	27.2°
	Grating groove density	$1200 lines {mm}^{- 1}$
Detector optics & detector	Numerical aperture (obj. space)	0.12
	Magnification factor	0.55
	Focal length	28 mm
	Utilized detector pixel number	$800 \times 800 pixels$
	Detector pixel size	$5.04 \times 5.04 {μm}^{2}$

Model	Expression	Mean Residual [pixels]	Max Residual [pixels]	Estimated Parameters
Polynomial	$1 + k_{1} r^{2}$	0.535	1.878	$k_{1} = 2.57 \times 10^{- 7}$
	$1 + k_{1} r + k_{2} r^{2}$	0.506	1.404	$k_{1} = - 1.12 \times 10^{- 5}$ , $k_{2} = 2.82 \times 10^{- 7}$
	$1 + k_{1} r^{2} + k_{2} r^{4}$	0.505	1.319	$k_{1} = 2.37 \times 10^{- 7}$ , $k_{2} = 1.19 \times 10^{- 13}$
Division	$1 / (1 + k_{1} r^{2})$	0.512	1.336	$k_{1} = - 2.46 \times 10^{- 7}$
	$1 / (1 + k_{1} r + k_{2} r^{2})$	0.506	1.324	$k_{1} = 4.43 \times 10^{- 6}$ , $k_{2} = - 2.58 \times 10^{- 7}$
	$(1 + k_{1} r) / (1 + k_{2} r + k_{3} r^{2})$	0.505	1.318	$k_{1} = - 2.73 \times 10^{- 4}$ , $k_{2} = - 2.77 \times 10^{- 4}$ , $k_{3} = - 2.07 \times 10^{- 7}$

Component	Item	Value
Filter	Wavelength range	761.9–765.3 nm
Fore optics	Field of view	$\pm 0.65 °$
Fore optics	Aperture diameter	66 mm
SHS	Littrow wavelength	761.8 nm
	Littrow angle	27.2°
	Grating groove density	$1200 lines {mm}^{- 1}$
Detector optics & detector	Numerical aperture (obj. space)	0.12
	Magnification factor	0.55
	Focal length	28 mm
	Utilized detector pixel number	$800 \times 800 pixels$
	Detector pixel size	$5.04 \times 5.04 {μm}^{2}$

Model	Expression	Mean Residual [pixels]	Max Residual [pixels]	Estimated Parameters
Polynomial	$1 + k_{1} r^{2}$	0.535	1.878	$k_{1} = 2.57 \times 10^{- 7}$
	$1 + k_{1} r + k_{2} r^{2}$	0.506	1.404	$k_{1} = - 1.12 \times 10^{- 5}$ , $k_{2} = 2.82 \times 10^{- 7}$
	$1 + k_{1} r^{2} + k_{2} r^{4}$	0.505	1.319	$k_{1} = 2.37 \times 10^{- 7}$ , $k_{2} = 1.19 \times 10^{- 13}$
Division	$1 / (1 + k_{1} r^{2})$	0.512	1.336	$k_{1} = - 2.46 \times 10^{- 7}$
	$1 / (1 + k_{1} r + k_{2} r^{2})$	0.506	1.324	$k_{1} = 4.43 \times 10^{- 6}$ , $k_{2} = - 2.58 \times 10^{- 7}$
	$(1 + k_{1} r) / (1 + k_{2} r + k_{3} r^{2})$	0.505	1.318	$k_{1} = - 2.73 \times 10^{- 4}$ , $k_{2} = - 2.77 \times 10^{- 4}$ , $k_{3} = - 2.07 \times 10^{- 7}$

Abstract

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Tables (2)

Equations (4)

Applied Optics