A sampling-based framework for finding the optimal representation of a finite energy optical field using a finite number of bits is presented. For a given bit budget, we determine the optimum number and spacing of the samples in order to represent the field with as low error as possible. We present the associated performance bounds as trade-off curves between the error and the cost budget. In contrast to common practice, which often treats sampling and quantization separately, we explicitly focus on the interplay between limited spatial resolution and limited amplitude accuracy, such as whether it is better to take more samples with lower amplitude accuracy or fewer samples with higher accuracy. We illustrate that in certain cases sampling at rates different from the Nyquist rate is more efficient.