This paper uses wave-optics simulations to explore the validity of signal-to-noise models for digital-holographic detection. In practice, digital-holographic detection provides access to an estimate of the complex-optical field which is of utility to long-range imaging applications. The analysis starts with an overview of the various recording geometries used within the open literature (i.e., the on-axis phase shifting recording geometry, the off-axis pupil plane recording geometry, and the off-axis image plane recording geometry). It then provides an overview of the closed-form expressions for the signal-to-noise ratios used for the various recording geometries of interest. This overview contains an explanation of the assumptions used within to write the closed-form expressions in terms of the mean number of photoelectrons associated with both the signal and reference beams. Next, the analysis formulates an illustrative example with weak, moderately deep, and deep turbulence conditions. This illustrative example provides the grounds in which to rewrite the closed-form expressions in terms of the illuminator power. It also enables a validation study using wave-optics simulations. The results show that the signal-to-noise models are, in general, accurate with respect to the percentage error associated with a performance metric referred to as the field-estimated Strehl ratio.