We explore modifications of the classical Hartmann wavefront
sensing technique that can be used to improve its accuracy, dynamic
range, and spatial resolution. We describe a differential sensor with variable
sensitivity. We review the use of various possible Hartmann masks
and discuss their interferometric properties. We propose the use of Fourier
analysis and show its relationship to moire methods. We finally envisage
the possibility of mapping both the slope and the total curvature (Laplacian)
of the wavefront with the same setup.