Closed-form expressions for digital-holographic detection in a laboratory setting

Digital-holographic detection provides a distinct way forward to combat the low signal-to-noise ratios (SNRs) associated with tactical applications. With that said, past efforts studied the major digital-holographic recording geometries used with tactical applications and derived closed-form expressions for their SNRs. They also used wave-optics simulations to validate the use of these closed-form expressions and found that for real-world scenarios, where we interfere a comparatively weak-signal beam with a strong-reference beam, the associated "weak-strong" expressions are accurate. For a laboratory setting, however, we often set the signal and reference beams to be nearly equal in power. As such, in this paper we derive closed-form expressions for this specific use case. We also use wave-optics simulations to explore the accuracy of these "equal-power" expressions. Overall, the results show that the equal-power expressions are accurate.