Incremental Measurement of the Numerical Aperture of Gradient Index Lenses Based on Image Recognition

Aiming at the precise measurement of numerical aperture which is a key optical parameter of gradient index (GRIN) lens. An incremental measurement method based on image recognition is proposed. Based on the definition of numerical aperture of GRIN lens by geometrical optics, the sinusoidal value of the maximum receiving angle is measured by imaging method. Incremental measurement means the GRIN lens images the light-emitting mesh twice, and calculates the sinusoidal value of the maximum receiving angle with the object heights of two images and the relative displacement. Two object heights are obtained by computer image recognition algorithm. According to the characteristics of mesh and the edge of field of view on the image, the complete object height in the longitudinal truncation is extracted which includes the central object height and the edge object height. The central height is determined by all the fringes on the truncation line, and the edge height that equals to the distance between the edge of field of view and the outermost fringe is determined by the extrapolation algorithm. The error analysis of the measurement system is carried out by establishing the error model, and the main source of the system error is determined. The experiment proves the stability of the sub-measurement method meets the practical needs. The measurement of the numerical aperture of a GRIN lens, which combines image recognition with incremental measurement, can reduce the measurement error caused by absolute measurement and discrimination of our eye, and it is simple, fast and accurate.