Complete description of effects on reconstruction of dynamic objects from time-averaged digital holography to high-speed digital holography

Abstract

Time-averaged holography (TAH) is a specialized technique for studying objects subjected to sinusoidal vibration, characterized by presenting a Bessel J0 envelope in the object’s reconstruction, a condition that occurs when the vibration period is much shorter than the hologram exposure time. In this work, we present an analytical expression that describes the reconstruction effects when both the exposure time and the period can take arbitrary values, allowing the application of the TAH technique for exposure times as fractions of the period. We observe that the presented function contains higher-order Bessel functions. Additionally, we found that the envelope not only depends on the relationship between the exposure time and the vibration period but is also directly related to the vibration amplitude. The expression we introduce applies to conditions where exposure times are very short, possible with pulsed lasers, called high-speed holography (HSH), where the object reconstructs as if it were static. This mathematical expression serves as a bridge that continuously connects the techniques of HSH and TAH, enabling a smooth transition between both techniques.