This paper proposes a new method for optimization optics with a diffractive optical element (DOE) via a Hybrid
Taguchi Genetic Algorithm. A Diffractive Optical Element, based the theory of wave phase difference, takes advantage
of the negative Abbe number which might significantly eliminate the axial chromatic aberrations of optics. Following
the advanced technology applied to the micro lens and etching process, precisely-made micro DOEs can now be
manufactured in large numbers. However, traditional least damping square has its limitations for the optimization of
axial and chromatic aberrations with DOE. In this research, we adopted the genetic algorithm (GA) and incorporated the
steady Taguchi method into GA. Combining the two methods produced a new hybrid Taguchi-genetic algorithm
(HTGA). Suitable glass combinations and DOE positions were selected to minimize both axial and lateral chromatic
aberration in the optical system. This new method carries out the task of eliminating both axial and lateral chromatic
aberration, unlike DOE optimization by LDS, which works for axial aberration only and with less efficiency. Experiments show that the surface position of the DOE could be determined first; in addition, regardless of whether chromatic aberration was axial or longitudinal, issues concerning the optical lens's chromatic aberration could be significantly reduced, compared to results from the traditional least damping square (LDS) method.
Chromatic Aberration plays a part in modern optical systems, especially in digitalized and smart optical systems.
Much effort has been devoted to eliminating specific chromatic aberration in order to match the demand for advanced
digitalized optical products. Basically, the elimination of axial chromatic and lateral color aberration of an optical lens
and system depends on the selection of optical glass. According to reports from glass companies all over the world, the
number of various newly developed optical glasses in the market exceeds three hundred. However, due to the complexity
of a practical optical system, optical designers have so far had difficulty in finding the right solution to eliminate small
axial and lateral chromatic aberration except by the Damped Least Squares (DLS) method, which is limited in so far as
the DLS method has not yet managed to find a better optical system configuration.
In the present research, genetic algorithms are used to replace traditional DLS so as to eliminate axial and lateral
chromatic, by combining the theories of geometric optics in Tessar type lenses and a technique involving Binary/Real
Encoding, Multiple Dynamic Crossover and Random Gene Mutation to find a much better configuration for optical glasses. By implementing the algorithms outlined in this paper, satisfactory results can be achieved in eliminating axial and lateral color aberration.
In this study, an optimization problem on the robot arm machining is formulated and solved by using genetic algorithms
(GAs). The proposed approach adopts direct kinematics model and utilizes GA's global search ability to find the
optimum solution. The direct kinematics equations of the robot arm are formulated and can be used to compute the end-effector
coordinates. Based on these, the objective of optimum machining along a set of points can be evolutionarily
evaluated with the distance between machining points and end-effector positions. Besides, a 3D CAD application,
CATIA, is used to build up the 3D models of the robot arm, work-pieces and their components. A simulated experiment
in CATIA is used to verify the computation results first and a practical control on the robot arm through the RS232 port
is also performed. From the results, this approach is proved to be robust and can be suitable for most machining needs
when robot arms are adopted as the machining tools.
Advances in digital image optics have increased the significance of lateral color aberration because it is easily seen in the projected area. The choice of optical glass plays a role in the elimination of lateral color aberration. Current optical software still has difficulty in finding the optimal combination of optical glasses for twelve or more elements in a projection lens, the choice being among at least 300 optical glasses that have been developed. Even the modern damped least squares, a ray-tracing-based method, is limited, owing to its inability to identify an enhanced optical system configuration. As an alternative, this research proposes a new optimization process by using algorithms involving the theory of geometric optics in a projector lens, real encoding, multiple dynamic crossover, and random gene mutation techniques. Results and conclusions show that attempts to achieve negligible axial and lateral color aberration are successful.
In this paper, we propose a method, which uses Coloured Petri Net (CPN) and genetic algorithm (GA) to obtain an optimal deadlock-free schedule and to solve re-entrant problem for the flexible process of the cluster tool. The process of the cluster tool for producing a wafer usually can be classified into three types: 1) sequential process, 2) parallel process, and 3) sequential parallel process. But these processes are not economical enough to produce a variety of wafers in small volume. Therefore, this paper will propose the flexible process where the operations of fabricating wafers are randomly arranged to achieve the best utilization of the cluster tool. However, the flexible process may have deadlock and re-entrant problems which can be detected by CPN. On the other hand, GAs have been applied to find the optimal schedule for many types of manufacturing processes. Therefore, we successfully integrate CPN and GAs to obtain an optimal schedule with the deadlock and re-entrant problems for the flexible process of the cluster tool.
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