On the single point resolution of on-axis digital holography

On-axis digital holography (DH) is becoming widely used for its time-resolved three-dimensional (3D) imaging capabilities. A 3D volume can be reconstructed from a single hologram. DH is applied as a metrological tool in experimental mechanics, biology, and fluid dynamics, and therefore the estimation and the improvement of the resolution are current challenges. However, the resolution depends on experimental parameters such as the recording distance, the sensor definition, the pixel size, and also on the location of the object in the field of view. This paper derives resolution bounds in DH by using estimation theory. The single point resolution expresses the standard deviations on the estimation of the spatial coordinates of a point source from its hologram. Cramér-Rao lower bounds give a lower limit for the resolution. The closed-form expressions of the Cramér-Rao lower bounds are obtained for a point source located on and out of the optical axis. The influences of the 3D location of the source, the numerical aperture, and the signal-to-noise ratio are studied.