# Robust Full-Screen Wavelength Calibration Algorithm
###### Abstract  
In spectrometer measurement, it is very important to accurately calibrate the wavelength of all target characteristic spectra. Although wavelength calibration methods have long been investigated, no techniques have been designed for the scanning, double-layer, secondary diffraction, linear-array CCD spectrometer, to the best of our knowledge. Based on the grating diffraction equation and experimental results, a mathematical model of wavelength calibration was established for the scanning, double-layer, secondary diffraction, linear-array CCD spectrometer. In this study, a robust, full-screen, wavelength calibration algorithm is proposed, based on the related working principle and the requirements of both accuracy and robustness. The detailed steps are as follows. First, we established a wavelength calibration model at central pixels, following the grating diffraction equation. Then, according to the relationship between the difference in pixels and the feedback values of the grating ruler, a model was established to show the association between these factors. Finally, we combined the two models and built a full-screen wavelength calibration model. We theoretically and experimentally demonstrate that the proposed calibration algorithm is an excellent calibration tool, which can conveniently and accurately calibrate the wavelengths of central and non-central pixels at the same time. scanning; double-layer; secondary diffraction; linear-array CCD spectrometer; full-screen; wavelength calibration; Levenberg-Marquardt algorithm; Huber regression +
Footnote †: journal: Medical Imaging and Imaging  
1
Footnote 1: email: _Applied Sciences_  
Footnote †: journal: Medical Imaging and Imaging  
of central pixels, which can ensure accuracy near the fitting points, but there may be a large gap in the accuracy of the other points [4]. [PERSON] et al. [5] proposed a simple, laser, wavelength calibration technique based on the second harmonic signals to improve the performance of a quartz-enhanced photoacoustic spectroscopy (QEPAS) gas-sensing system. [PERSON] et al. [6] employed the peak method and gravity method to calibrate the wavelength of the prism-grating imaging spectrometer. This work shows that the difference between the two calibration results is within 0.3 nm. The gravity method was found to be insensitive to spot energy mutations, and can effectively improve the efficiency and accuracy of wavelength calibration. Moreover, some researchers also proposed wavelength calibration algorithms for laser spectral measurements based on cubic spline interpolation and the kernel regression method [7]. Research on robust calibration has also attracted much attention. [PERSON] and [PERSON] [8] proposed a method to calibrate wavelength offset using multiple regression equations, which can make the calibration robust. [PERSON] et al. [9] used robust wavelength selection to make the calibration robust to more general forms of between-instrument variation. At present, wavelength calibration methods are mainly used for the following two kinds of spectrometer. 1. At present, calibration methods are mostly used for spectrometers with a fixed grating. This type of spectrometer is commonly characterized by the small line-pairs grating and linear-array CCD. Spectrometers with this structure tend to have a lower wavelength calibration accuracy and a lower spectral resolution. 2. For the grating rotational spectrometer, a single-element detector and large line-pairs grating are usually used. However, there is no suitable wavelength calibration method for spectrometers using linear-array CCD and rotational grating with large line pairs. To solve the problems with the existing technology, a wavelength calibration method for the scanning, double-layer, secondary-diffraction, linear-array CCD spectrometer is proposed in this study. In this study, we propose a novel wavelength calibration method for this type of spectrometer. The main contributions of our work are summarized as follows. 1.