Image Spherizing-Based Three-Dimensional Displacement Measurement Technique for Microscope with Single Camera

Abstract

The detection of three-dimensional displacement, caused by micro-nano scale deformation, is of great significance for the industrial production of glass or quartz optical fiber products. Considering the detection cost and practicability, an image spherizing-based three-dimensional displacement measurement method for a monocular microscopic imaging system (a microscope with a normal industrial camera) is proposed. Differential theory tells us that an arbitrary large-scale deformation can be approximatively considered as the sum of slope-shaped deformations. In this paper, an ordinary slope model is presented by the idea of image spherizing and differential theory, which reveals the mathematical relation between in-plane displacement and out-of-plane displacement in the deformed images captured by an optical microscope. After obtaining the in-plane displacement field, the out-of-plane displacement field can be extracted from the in-plane displacement field by the ordinary slope model, which indicates that the out-of-plane displacement information carried by the in-plane displacement is fully utilized. Simulation and application experiments are performed to demonstrate the effectiveness and all the absolute errors of the measurement by optical microscope with a magnification of 50× are less than 0.2 μm. Unlike conventional methods, the new method does not need a phase unwrapping process during detection and has many attractive characteristics such as low-cost, simple arrangements and good applicability. Because the measurement precision of this technique can meet the detection requirement, it has been applied to the industrial detection of glass or quartz optical fiber products.