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