Context: The NIRSpec instrument for the James Webb Space Telescope (JWST) can be operated in multiobject (MOS), long-slit, and integral field (IFU) mode with spectral resolutions from 100 to 2700. Its MOS mode uses about a quarter of a million individually addressable minislits for object selection, covering a field of view of $sim$9 $mathrm{arcmin}^2$. Aims: The pipeline used to extract wavelength-calibrated spectra from NIRSpec detector images relies heavily on a model of NIRSpec optical geometry. We demonstrate how dedicated calibration data from a small subset of NIRSpec modes and apertures can be used to optimize this parametric model to the necessary levels of fidelity. Methods: Following an iterative procedure, the initial fiducial values of the model parameters are manually adjusted and then automatically optimized, so that the model predicted location of the images and spectral lines from the fixed slits, the IFU, and a small subset of the MOS apertures matches their measured location in the main optical planes of the instrument. Results: The NIRSpec parametric model is able to reproduce the spatial and spectral position of the input spectra with high fidelity. The intrinsic accuracy (1-sigma, RMS) of the model, as measured from the extracted calibration spectra, is better than 1/10 of a pixel along the spatial direction and better than 1/20 of a resolution element in the spectral direction for all of the grating-based spectral modes. This is fully consistent with the corresponding allocation in the spatial and spectral calibration budgets of NIRSpec.
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