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We perform revised spectral calibrations for the AKARI near-infrared grism toquantitatively correct for the effect of the wavelength-dependent refractiveindex. The near-infrared grism covering the wavelength range of 2.5--5.0 micronwith a spectral resolving power of 120 at 3.6 micron, is found to becontaminated by second-order light at wavelengths longer than 4.9 micron whichis especially serious for red objects. First, we present the wavelengthcalibration considering the refractive index of the grism as a function of thewavelength for the first time. We find that the previous solution is positivelyshifted by up to 0.01 micron compared with the revised wavelengths at 2.5--5.0micron. In addition, we demonstrate that second-order contamination occurs evenwith a perfect order-sorting filter owing to the wavelength dependence of therefractive index. Second, the spectral responses of the system from the first-and second-order light are simultaneously obtained from two types of standardobjects with different colors. The response from the second-order lightsuggests leakage of the order-sorting filter below 2.5 micron. The relationsbetween the output of the detector and the intensities of the first- andsecond-order light are formalized by a matrix equation that combines the twoorders. The removal of the contaminating second-order light can be achieved bysolving the matrix equation. The new calibration extends the available spectralcoverage of the grism mode from 4.9 micron up to 5.0 micron. The revision canbe used to study spectral features falling in these extended wavelengths, e.g.,the carbon monoxide fundamental ro-vibrational absorption within nearby activegalactic nuclei.

Revised Wavelength and Spectral Response Calibrations for AKARI Near-Infrared Grism Spectroscopy: Cryogenic Phase