Interpolation algorithm for recovering the missing phase values in 3D measurement

In the three-dimensional (3D) phase measurement, some marks are usually adhered to the object in order to make the 3D registration process faster and easier. As covered with marks, local phase data are missing and have to be interpolated later. Considering the phase distribution nearby the marks, a gradient estimate (GE) interpolation algorithm is provided here. This algorithm recovers one pixel's missing phase value with the average of the estimated values which is calculated by gradients in eight directions nearby. Since this algorithm is a local processing, the missing phase values should be interpolated from the edge of the marks to the center. In the computer simulation and the practical experiment, compared with the same-size neighborhood mean (NM) algorithm and the Gerchberg–Saxton (GS) algorithm, this new algorithm achieves very good fit results with the least time. So it can be used as a practical tool for automatic missing phase interpolation.