SO and LNO Channel Instrument Forward Model
The SO and LNO channels both operate with an echelle diffraction grating, which diffracts different wavelengths of incoming radiation in different directions, to be imaged on the detector.The grating operates at high incidence angles, and therefore in high diffraction orders, which means that wavelengths of all the measurable orders are diffracted within the same range of angles, through collecting optics towards the detector. This means that spectra from around 100 diffraction orders can be recorded, allowing the SO and LNO channels to observe across a huge possible wavelength range - and by isolating the wavelengths of a single diffraction order, a small spectral range can be measured at very high spectral resolution.
Acousto-Optic Tunable Filter
To select the desired spectral range, an additional filter is used which lets pass the wavelengths within that diffraction order, blocking out wavelengths from the other orders: in NOMAD's SO and LNO channels this is an Acousto-Optic Tunable Filter (AOTF). The AOTF is a birefringent crystal whose optical properties depends on a radio frequency signal applied to the crystal: by driving it at specific frequencies, the AOTF's bandpass can be centred on any desired diffraction order almost instantaneously.In an ideal world, the order-sorting filter would have a bandpass exactly equal to the spectral range of the diffraction order being measured, blocking all radiation from outside the desired diffraction order; however in reality this is not possible, and so the shape of the AOTF transmittance must be taken into account when analysing SO and LNO spectra. In particular, the filter transmittance has a sinc-squared shape, with wings that allow some radiation from outside the selected diffraction order to pass through to the detector.
Crucially, the means that raw spectrum recorded by the detector is a sum of the radiation (from Mars or the Sun) not only of the desired diffraction order, but also a number of adjacent orders also, multiplied by the transmittance of the AOTF at each wavelength and the throughput of the instrument.
The SO AOTF and diffraction grating efficiencies, centred on order 134, are shown below:
As can be seen, the AOTF frequency is chosen so that the bandpass is centred on diffraction order 134, and so the majority of the contribution to the recorded spectrum comes from these wavelengths, but due to the wings of the AOTF there is also a non-negligible contribution from radiation of wavelengths in nearby diffraction orders.
Instrument Spectral Response Function
The Instrument Spectral Response Function (ISRF, also called the ILS, or Instrument Line Shape) determines the range of wavelengths that can hit each pixel on the detector. The shape of the response is typically a Gaussian, such as in the LNO channel, or can be a combination of two or more different shapes. The SO channel ISRF is modelled as two Gaussians, where one is smaller and shifts relative to the main Gaussian between pixel 0 on the left of the detector and pixel 319 on the right-hand side. Therefore on the right of the detector, the ISRF is wider and therefore the effective spectral resolution is slightly lower than on the left.Considering just the central diffraction order, 134, the ISRFs for all 320 pixels are shown below - note that the x-axis can be zoomed in to see the difference in shape between left and right:
Calculating the total pixel contribution
The radiation that reaches each pixel on the SO or LNO detector can be calculated by taking into account the transmittance of the AOTF, diffraction efficiency, and pixel spectral response for all diffraction orders.An example for pixel 100 is given below:
The total signal on this pixel is therefore the input radiation convolved with the pixel ISRF, multiplied by the diffraction grating efficiency and the AOTF transmittance, summed for each diffraction order. As can be seen, the diffraction grating efficiency shape is very similar between nearby diffraction orders, and so the relative contribution of each order is determined primarily by the AOTF transmittance. In the example above for pixel 100, the AOTF transmittances are ~6% in order 132, ~11% in order 133, ~84% in order 134 (the desired wavelength range), ~8% in order 135 and ~4% in order 136; therefore ~75% of the measured spectrum comes from the main diffraction order, ~17% comes from the two adjacent orders, and ~8% from the two orders beyond that. The relative contribution drops off for orders further from the centre of the AOTF; therefore the number of orders that need to be considered can be limited to those around the desired diffraction order.
Forward Model Example
The forward model starts with a high-resolution gas transmittance spectrum. Order 134 contains water absorption lines, and so a spectrum is taken from HITRAN covering the 5 diffraction orders 132 to 136 for an example of Martian conditions at 30km altitude, assuming at path length of 100km:By convolving the high-resolution water transmittance spectrum by each pixel ISRF, multiplying by the AOTF transmittance and diffraction order efficiency, and then summing the result for each pixel gives the simulated spectrum that NOMAD-SO would observe:
Calculating Instrument Parameters
More information about the SO channel AOTF shape and peak wavenumber, diffraction grating efficiency width and peak wavenumber, and ISRF shape and wavenumber of each pixel can be found in the Appendix of Villanueva et al. (2022) https://doi.org/10.1029/2022GL098161. For python users, the NASA Goddard Planetary Spectrum Generator github repository contains code to calculate the various parameters: https://github.com/nasapsg/ExoMars. Note that the parameters are order- and instrument temperature-dependent; the instrument temperature can be found in all NOMAD data products.For LNO, the calibration is described in Liuzzi et al. 2019 https://doi.org/10.1016/j.icarus.2018.09.021 and the latest instrument parameters can be found in the Supporting Information of Hendrick et al. 2026 https://doi.org/10.1029/2025JE009592 (a direct link can be found here). LNO nadir spectra are converted to reflectance factor, to remove the shape of the solar spectrum. More information can be found in Thomas et al. 2022 https://doi.org/10.1016/j.pss.2021.105410.
UVIS Channel Instrument Forward Model
The UVIS channel is also a grating spectrometer, but operating in diffraction orders +1 and +2, with a second-order filter to block unwanted second-order wavelengths above 325 nm.The UVIS forward model is much simpler, as it does not use an AOTF, and so only the pixel ISRFs need to be considered, with data provided directly in transmittance (for solar occultation) or radiance (for nadir and limb observations). Below are figures showing the full-width-half maximum (FWHM) of each pixel in both occultation and nadir/limb modes. Note that spectral binning is regularly applied to UVIS spectra, hence there are multiple curves. A binning of 0 denotes unbinned, 1 denotes that adjacent pixels binned (half-resolution), 3 for quarter-resolution and 7 for eighth-resolution:
The tabulated values can be found here: UVIS approximate spectral resolution.
More information on the calibration of the UVIS chanel can be found in Willame et al. 2022 https://doi.org/10.1016/j.pss.2022.105504.
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