Phase-Shift vs. Line-Shift: Two ways to do Deflectometry

Phase-Shifting Deflectometry (PMD) has proven to be a powerful and versatile measurement principle, facilitating a wide variety of industrial applications. The key idea is to determine the optical effect of a specular surface by measuring how the chief rays of a known imaging system are deflected by the object under test. On last year’s DGaO conference, we presented a new deflectometric technique called "Line-Shift-Deflectometry", replacing the classical phase evaluation by a proper localization of the intensity peak of a moving slit mask. Whereas for PMD the potentials and limitations have been extensively studied in the past (cumulated in an uncertainty relation linking the product of lateral and angular resolution to the signal-to-noise ratio of the system), it has been far from obvious whether these considerations also hold for the line-shifting case. In this contribution we present a generalized theoretical background for deflectometric techniques, revealing how the uncertainty relation has to be modified for different cases. A comparison is given to the Shack-Hartmann case, which can be viewed as just another special implementation of a deflectometric sensor.