Fringe visibility for pulsed digital holography with large optical path differences

In interferometry and holography systems, the optical path difference (OPD) between the beams must be kept smaller than the source coherence length to obtain stable interference fringes. When the OPD is larger than the coherence length, the fringe phase drifts on time scales comparable to the source coherence time. This reduces fringe visibility and causes fringes to wash out completely for observation times longer than the coherence time. High fringe visibility measurements, however, can be obtained with pulsed sources (or very short detector integration times), if the pulse duration is shorter than the source coherence time, thereby limiting the amount of fringe phase drift over the pulse duration. We analyze cases where optical pulses are carved from a continuous-wave laser source. We derive an expression for the squared magnitude of the fringe visibility for pulsed interference measurements and demonstrate that high visibility fringes can be obtained even when the OPD is much longer than the source coherence length. As a rule of thumb, the source coherence time should be at least 10 times greater than the pulse duration to obtain expected fringe visibilities greater than 95% when the source laser has a Lorentzian line shape. This result is important to the design of digital holography systems for long-range remote sensing applications, where it is difficult to implement a dynamic optical delay line for path length matching with non-cooperative objects.