On the single point resolution of on-axis digital holography

Corinne Fournier (1) , Loïc Denis (2) , Thierry Fournel (1)

1 LHC - Laboratoire Hubert Curien
2 CRAL - Centre de Recherche Astrophysique de Lyon

On-axis Digital Holography is becoming widely used for its time-resolved 3D imaging capabilities. A 3D volume can be reconstructed from a single hologram. Digital Holography (DH) is applied as a metrological tool in experimental mechanics, biology, 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. Cramer-Rao lower bounds give a lower limit for resolution. The closed-form expressions of the Cramer-Rao lower bounds are obtained for a point-source located on and out of the optical axis. The influence of the 3D location of the source, the numerical aperture and the signal-to-noise ratio are studied.

Mots clés: digital holography; Image processing; three-dimensional reconstruction; Inverse problems; estimation theory; Cramer Rao Lower Bound

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement des images [eess.IV]; Traitement du signal et de l'image [eess.SP]

Corinne Fournier, Loïc Denis, Thierry Fournel. On the single point resolution of on-axis digital holography. Journal of the Optical Society of America. A Optics, Image Science, and Vision, 2010, 27 (8), pp.1856-1862. ⟨10.1364/JOSAA.27.001856⟩. ⟨hal-00464787⟩