We require a means of determining the minimum achievable bunch length at the Linac Coherent Light Source (LCLS) at SLAC National Accelerator Laboratory. Current methods of measurement in the time domain do not have the resolution to measure ultra-short bunch lengths below 10 fs. An alternative method has been designed, using a single-shot near- to mid-infrared prism spectrometer for bunch length diagnosis in the frequency domain. This design requires the precision alignment of sensitive optical equipment and complete understanding of the spectrum reaching the spectrometers detector surface. This paper provides information on preliminary simulations designed to model beam behavior in the optical set-up and at the detector surface for comparison to measured values as an indication of the current achievable optical alignment and the study of optimal detector orientation. The results of these simulations indicate the necessity for a method of greater precision in optical alignment and further study of achievable spectrometer range. Show Partial Abstract