Talbot interferometer for radial and lateral derivatives

The theory and experimental evidence of a shearing interferometer based on the Talbot effect are presented. Multiple-shearing interferences are obtained that can be reduced to triple-shearing or doubleshearing interferences by the addition of simple spatial filtering. When the shear is less than the width of the details in the object, these interferences become either the second or first derivative of the object under test, respectively. Either lateral or constant radial shear can be introduced by choosing Ronchi rulings or circular gratings. Thus both lateral and radial derivatives are easily obtained. If white light is used as a source, color fringes of high contrast are observed.