Locus of Focus

To analyze the sequence of 2D-projections, the so-called slices, we use digital image processing. As an approximation we assume that the surface derived from a single hologram has no undercuts. Therefore there can be no two surface points with the same $(x,y)$-coordinate and the surface can be represented by a relief map. As already mentioned, each captured slice contains the specific focused information representing the object shape contour and a defocused background. The task is thus to distinguish between focused and defocused image regions: To evaluate the sharpness of an image in an conventional imaging system, several algorithms have been proposed in the field of image processing. We found that the best measure for image sharpness is the statistical variance $V_{(x,y)}$ of the light intensity on pixel adjacent to $(x,y)$. For each lateral coordinate $(x,y)$, the sharpness measure $V_{(x,y)}(z)$ is a positive, real number. The axial coordinate $z_{(x,y)}$ is assigned by choosing $z_{(x,y)}$ to satisfy $V_{(x,y)}(z_{(x,y)}) \geq V_{(x,y)}(z)\quad \forall \quad z$. Thus each holographic real image gives a relief map of the object surface.