Improved phase-shifting method for automatic processing of moiré deflectograms

An improved moiré deflectometry phase-shifting technique is presented. A squared grating is used to multiplex the information of the deflections in two orthogonal directions in one image. This procedure avoids the need to rotate the gratings to obtain complete deflection information. However, the use of these gratings makes impossible the application of standard phase-shifting algorithms. Specifically, the problems associated with the nonsinusoidal profile of the moiré fringes and the low-modulation areas produced by the square gratings are solved. A modified moiré deflectometry phase-shifting method is designed to deal with these problems. In addition, a method to obtain the zero order of the prismatic effect is developed. The technique configures a complete and automatic method of mapping ray deflections. From them the refractive power maps can be derived. Experimental results obtained with a progressive-addition lens are shown.