Three-dimensional displacement measurement of image point by point-diffraction interferometry

This paper presents a method for measuring the three-dimensional (3-D) displacement of an image point based on point-diffraction interferometry. An object Point-light-source (PLS) interferes with a fixed PLS and its interferograms are captured by an exit pupil. When the image point of the object PLS is slightly shifted to a new position, the wavefront of the image PLS changes. And its interferograms also change. Processing these figures (captured before and after the movement), the wavefront difference of the image PLS can be obtained and it contains the information of three-dimensional (3-D) displacement of the image PLS. However, the information of its three-dimensional (3-D) displacement cannot be calculated until the distance between the image PLS and the exit pupil is calibrated. Therefore, we use a plane-parallel-plate with a known refractive index and thickness to determine this distance, which is based on the Snell's law for small angle of incidence. Thus, since the distance between the exit pupil and the image PLS is a known quantity, the 3-D displacement of the image PLS can be simultaneously calculated through two interference measurements. Preliminary experimental results indicate that its relative error is below 0.3%. With the ability to accurately locate an image point (whatever it is real or virtual), a fiber point-light-source can act as the reticle by itself in optical measurement.