Phase retrival

DPC

Developed in 1974

1. For each \((x, y)\) probe position, compute the weighted average position (center of mass) of the measured intensity. If no phase gradient is present, the average position should be zero.

2. The phase is proportional to the gradient, expressed as:

   \[\mathbf{R}_{\text{COM}}(\mathbf{r}) = C \nabla \phi(\mathbf{r})\]

   where \(\mathbf{R}_{\text{COM}}\) is the center of mass position, \(C\) is a proportionality constant, and \(\phi(\mathbf{r})\) is the phase at position \(\mathbf{r}\).

3. We now want intergrate the phase gradient to get the whole phase map of the x,y position.