Interpretation of the moiré method for obtaining contours of equal slope from an interferogram.

The moiré method has been extensively applied in many fields of optical measuring. For instance, if two identical copies of a two-beam interferogram are slightly displaced in any chosen direction and are superimposed, moiré fringes are produced. These fringes have been indicated graphically to be the contours of equal slope resolved in the direction of displacement by Duncan and Sabin in the special case when the angle θ of the interfering beams is zero. This paper describes the theoretical interpreta­ tion of the phenomena using spatial frequency analysis, not only when the angle θ = 0, but also in the general case when 0 ≠ 0. Experimental results showed that the contours of equal slope were obtained by the moiré method from the interferogram when the angle θ ≠ θ, as was expected. The orthogonal coordinate system is shown in Fig. 1. If g(x,y) represents the distortion of the wavefront along the z axis given by a phase object, the disturbance U (x,y) on the observing plane (z = 0) is given by