Shape reconstruction from gradient data.

We present a generalized method for reconstructing the shape of an object from measured gradient data. A certain class of optical sensors does not measure the shape of an object but rather its local slope. These sensors display several advantages, including high information efficiency, sensitivity, and robustness. For many applications, however, it is necessary to acquire the shape, which must be calculated from the slopes by numerical integration. Existing integration techniques show drawbacks that render them unusable in many cases. Our method is based on an approximation employing radial basis functions. It can be applied to irregularly sampled, noisy, and incomplete data, and it reconstructs surfaces both locally and globally with high accuracy.

Microdeflectometry--a novel tool to acquire three-dimensional microtopography with nanometer height resolution.

We introduce "microdeflectometry," a novel technique for measuring the microtopography of specular surfaces. The primary data are the local slope of the surface under test. Measuring the slope instead of the height implies high information efficiency and extreme sensitivity to local shape irregularities. The lateral resolution can be better than 1 microm, whereas the resulting height resolution is in the range of 1nm. Microdeflectometry can be supplemented by methods to expand the depth of field, with the potential to provide quantitative 3D imaging with scanning-electron-microscope-like features.