We perform revised spectral calibrations for the AKARI near-infrared grism to quantitatively correct for the effect of the wavelength-dependent refractive index. The near-infrared grism covering the wavelength range of 2.5--5.0 micron with a spectral resolving power of 120 at 3.6 micron, is found to be contaminated by second-order light at wavelengths longer than 4.9 micron which is especially serious for red objects. First, we present the wavelength calibration considering the refractive index of the grism as a function of the wavelength for the first time. We find that the previous solution is positively shifted by up to 0.01 micron compared with the revised wavelengths at 2.5--5.0 micron. In addition, we demonstrate that second-order contamination occurs even with a perfect order-sorting filter owing to the wavelength dependence of the refractive index. Second, the spectral responses of the system from the first- and second-order light are simultaneously obtained from two types of standard objects with different colors. The response from the second-order light suggests leakage of the order-sorting filter below 2.5 micron. The relations between the output of the detector and the intensities of the first- and second-order light are formalized by a matrix equation that combines the two orders. The removal of the contaminating second-order light can be achieved by solving the matrix equation. The new calibration extends the available spectral coverage of the grism mode from 4.9 micron up to 5.0 micron. The revision can be used to study spectral features falling in these extended wavelengths, e.g., the carbon monoxide fundamental ro-vibrational absorption within nearby active galactic nuclei.
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