Advanced Geometrical Optics

Dr. PD Lin is a distinguished Professor of Mechanical Engineering Department at National Cheng Kung University, Taiwan, where he has been since 1989. He earned his BS and MS from that university in 1979 and 1984, respectively. He received his Ph.D. in Mechanical Engineering from Northwestern University, USA, in 1989. He has served as an associate editor of Journal of the Chinese Society of Mechanical Engineers since 2000. He has published over 80 papers and supervised over 60 MS and 11 Ph.D. students. His research interests include geometrical optics and error analysis in multi-axis machines. In geometrical optics, he employs homogeneous coordinate notation to compute the first- and second-order derivative matrices of various optical quantities. It is one of the important mathematical tools for automatic optical design.

Mathematical Background.- Skew-Ray Tracing of Geometrical Optics.- Geometrical Optical Model.- Ray tracing Equations for Paraxial Optics.- Cardinal Points and Image Equations.- Ray Aberrations.- Jacobian Matrix of Ray Ri with Respect to Incoming ray Ri-1 and Boundary Variable Vector Xi.- Jacobian Matrix of Boundary Variable Vector Xi¬ with Respect to System Variable Vector Xsys.- Prism Analysis.- Prism Design Based on Image Orientation.- Determination of Prism Reflectors to produce required image orientation.- Optically Stable Systems.- Point Spread Function, Caustic Surfaces and Modulation Transfer Function.- Optical Path Length and Its Jacobian Matrix.- Wavefront Aberration and Wavefront Shape.- Hessian Matrix of Ray Ri with Respect to Incoming ray Ri-1 and Boundary Variable Vector Xi.- Hessian Matrix of Boundary Variable Vector Xi with Respect to System Variable Vector Xsys.- Hessian Matrix of Optical Path Length.