We have previously developed a global optimization method using an escape function that finds multiple local solutions in the multidimensional parameter space of a lens. We have applied this method to various actual design problems and have been able to understand some topological features of the merit function in its parameter space. These experiences have led us to develop an improved global optimization method that takes into account the robustness of the lens with respect to manufacturing and assembly errors. The method uses a technique that we call "θ-segmentation" to perform the escape function search in a smaller parameter space. After reaching an acceptable solution with the escape function, it often seems impossible to reduce the sensitivity in tolerance without degrading the image quality already acquired. Generally speaking, performance and robustness are in a trade-off relation, i.e. reduced sensitivity can be obtained only by increasing the merit function of the system. However, in reality, it is often possible to reduce sensitivity without substantial increase of the merit function. Furthermore, in many cases, it is possible to reduce the merit function and the sensitivity simultaneously by using our new method.
Immediately following an optimization sequence, many designers typically implement sensitivity analysis prior to more intensive tolerance analysis and system error budgeting. This paper proposes a method of automating optical design optimization into a two stage process which incorporates design sensitivity into the optimization process. The first stage consists of the standard optimization approach where the error function is a user defined combination of system performance as well as optical and physical parameter constraints. The second stage amends the error function to include the minimization of incident ray angles on each optical surface as part of the error function. The amendment to the error function in the second stage targets the root mean square of incident angles of sample rays. These rays may typically consist of the marginal ray to the image center, as well as the upper and lower rim rays to the image corner. A priority is placed on reducing large angles as the result of a least squares method. This paper will address the detailed implementation of the proposed approach inside of the optical design program. Practical examples will be presented where the proposed optimization has reduced the system sensitivity to manufacturing errors without substantially effecting image quality. The results of incorporating the amended error function into an automated global optimization approach will be described.
The Global Explorer (GE) algorithm proposed by Isshiki is implemented in the GOLD program developed by Beijing Institute of Technology. Global optimization with GE consists of many local optimization runs with or without the escape function using the damped-least-squares method. In order to improve the efficiency of the local optimization, two search schemes are incorporated into the program. The first one searches for the best damping factor which effectively determines the optimum direction of the solution vector in the multi-dimensional variable space, and the second search is conducted along that direction to find the optimum length of the solution vector. Experiments are also made to determine the optimum default values for the parameters of the escape function.
Real-time displacement and vibration measurements are presented, Which are based on a spatial phase-shifting with a tilt holographic interferogram. Three intensity data sampled at every one-third of the fringe spacing of the tilt fringes are used to calculate the phase and the modulation term of the fringe which are functions of a displacement and a vibration amplitude, respectively. Three-dimensional look-up tables perform the calculations in a TV repetition rate to give a phase distribution and a new fringe profile which contours the vibration amplitude. Experimental results are given in two cases of a displacement measurement for a cantilever-like object and a vibration measurement at resonant frequencies of a flat speaker.
Two real-time phase mapping methods for finge patterns are presented, which are based on a spatial phase-shifting with three fringe patterns, and on a spatial synchronous detection for a tilted fringe pattern. A digital TV-image processor is implemented which bases on the two fringe processing techniques. Applications of the present methods to surface shape measurements using a polarization interferometer and a fringe projection technique, and to a surface deformation measurement using a holographic interferometer are described. Worst phase errors are analyzed theoretically which are caused by an additive intensity noise of input fringe signals and a multiplicative intensity noise due to misalignments of a measuring system. A phase error due to a digitization of calculations is also evaluated numerically.