In this article, Part 1, we have synthetically resonance scattered and Thomson scattered a measured solar chromospheric $\mathrm{Ly}\alpha $ spectral radiance (CLSR) spectrum off the neutral hydrogen [ $N_{1}$ ] atoms in ground state and free electrons [ $N_{\mathrm{e}}$ ], respectively, contained in a 3D coronal model of the 14 July 2000 (“Bastille Day”) Coronal Mass Ejection (CME). From these two scatters, we have computed maps of the associated resonance scattered spectral radiance (RSSR) spectrum and the Thomson scattered spectral radiance (TSSR) spectrum in ultraviolet (UV) from 121.3 to 121.8 nm with a wavelength resolution of 0.1 nm, which encompasses the $\mathrm{Ly}\alpha $ center line at 121.57 nm. We then integrated the maps over the above wavelength range and have created two 2D resonance scattered radiance (RSR) and Thomson scattered radiance (TSR) maps. As expected, the TSSR spectrum is $\approx 1000$ times dimmer than the RSSR spectrum, which we can deem for it to contribute towards noise in the center of the RSSR spectrum. In a follow up article, Part 2, we intend to do the following with these maps. First, we will use the computed RSSR spectra along each line of sight (LOS) to derive the proton temperature [ $T_{\mathrm{p}}$ ] and speed [ $V_{\mathrm{p}}$ ] using the Doppler Dimming technique (DDT). Second, we will compare these derived proton parameters along each LOS with the actual values contained within the Bastille Day CME model at the plane of the sky and compute the differences. If we find they are different we will then determine where along the LOS they closely match and their distances from the plane of the sky. Finally, we will quantify an estimate of the systematic error from using DDT to measure the proton parameters at the plane of the sky, which is different from the statistical error margins reported in the literature from real RSSR experiments conducted from space-based instruments.
