The smooth continuous wavefront deformation function (WDF) can be expanded into Zernike polynomials. The coefficients of polynomial expansion for Fizeau or Twyman-Green interferometry can be found with ease by applying the least-square approximation. In the Hartmann test, shearing interferometry methods, or the Ritchey-Common test, coefficients can be found by using the least-square approximation as well. In these cases, the measuring data is a result from applying a linear operator to the WDF (which is the differentiation operator in the Hartmann test). By applying this operator to Zernike polynomials, new polynomials can be found for the test data. The coefficients of test data expansion and WDF expansion are equal. As in lateral shearing interferometry, the data from several test pictures can be approximated in one step of the 'truss' approximation.© (1999) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.