Abstract: Most modern computing tasks are constrained to having digital electronic input and output data. Due to these constraints imposed by the user, any analog computing accelerator must perform an analog-to-digital conversion on its input data and a subsequent digital-to-analog conversion on its output data. This places performance limits on analog computing accelerator hardware. To avoid this the analog hardware must replace the full functionality of traditional digital electronic computer hardware. This is not currently possible for optical computing accelerators due to limitations in gain, input-output isolation, and information storage in current optical hardware. We conducted a case study on an analog optical Fourier transform and convolution accelerator, using 27 empirically-measured benchmarks, we estimate that an ideal optical accelerator that accelerates Fourier transforms and convolutions can produce an average speedup of $9.4 \times$, and a median speedup of $1.9 \times$ for the set of benchmarks. The maximum speedups achieved were $45.3 \times$ for a pure Fourier transform and $159.4 \times$ for a pure convolution. An optical Fourier transform and convolution accelerator only produces significant speedup for applications consisting exclusively of Fourier transforms and convolutions.