Computation of the Optical Point Spread Function of a Ball Lens

• Main Authors: Chun-Yu Lien, 連峻宇
• Other Authors: Hung-Wen Chang
• Format: Others
• Language: zh-TW
• Published: 2012
• Online Access: http://ndltd.ncl.edu.tw/handle/70597694527432796887

碩士 === 國立中山大學 === 光電工程學系研究所 === 101 === In this thesis, we analyze the simplest optical imaging system: a ball lens. The traditional method of using a geometric optics analysis on an optical system only gives the roughest qualitative solution due to the lack of consideration of wave properties. Therefore, for accurate quantitative results, we need to analyze said system with a complete wave theory approach. The reason that we chose a ball lens as the focus of this research is due to its spherical symmetry properties which allows us to rigorously investigate it with different analytic methods. We will apply geometric optics, Fourier optics, scalar wave optics, and electromagnetic optics methods to compute the point spread functions (PSF) of a ball lens under the assumption that the point source is isotropic. We will follow up by predicting the spot sizes that correspond to each mean. First, with geometric optics (GO), we apply the analytic ray tracing method to correlate the origins of light rays passing through the ball lens to their respective positions on the receptive end. We can then evaluate the energy distribution function by gathering the density of rays on image plane. Second, in the theory of Fourier optics (FO), to obtain the analytic formula of the point spread function, the integral kernel can be approximated as the Fresnel integral kernel by means of paraxial approximation. Compared to GO, the results from FO are superior due to the inclusion of wave characteristics. Furthermore, we consider scalar wave optics by directly solving the inhomogeneous Helmholtz equation which the scalar light field should satisfy. However, the light field is not assigned to an exact physical meaning in the theory of scalar wave optics, so we reasonably require boundary conditions where the light field function and its first derivative are continuous everywhere on the surface of ball lens. Finally, in the theory of electromagnetic optics (EMO), we consider the polarization of the point source, and the two kinds of Hertz vectors and , both of which satisfy inhomogeneous Helmholtz equation, and are derived from Maxwell’s equations in spherical structures. In contrast with the scalar wave optics, the two Hertz vectors are defined concretely thus allowing us to assign exact boundary conditions on the interface. Then the fields corresponding to and are averaged as the final point spread function.