John Macdonald

The Calculation of the Optical Transfer Function

In previous OTF computer programs, various geometrical optical aspects of image formation appear often to have been ignored. The neglect of factors associated with anamorphotic imagery, pupil aberrations and vignetting, and a shift of focal plane can lead to considerable errors in the computed values of the transfer function, particularly for high-aperture or wide-angle systems. In addition, the numerical integration processes employed have not always been entirely satisfactory in terms of efficiency, generality, and convenience.

Optical design and multiobjective optimization of miniature zoom optics with liquid lens element

We propose an optical design for miniature 2.5x zoom fold optics with liquid elements. First, we reduce the volumetric size of the system. Second, this newly developed design significantly reduces the number of moving groups for this 2.5x miniature zoom optics (with only two moving groups compared with the four or five groups of the traditional zoom lens system), thanks to the assistance of liquid lens elements in particular. With regard to the extended optimization of this zoom optics, relative illuminance (RI) and the modulation transfer function (MTF) are considered because the more rays passing through the edge of the image, the lower will be the MTF, at high spatial frequencies in particular. Extended optimization employs the integration of the Taguchi method and the robust multiple criterion optimization (RMCO) approach. In this approach, a Pareto optimal robust design solution is set with the aid of a certain design of the experimental set, which uses analysis of variance results to quantify the relative dominance and significance of the design factors. It is concluded that the Taguchi method and RMCO approach is successful in optimizing the RI and MTF values of the fold 2.5x zoom lens system and yields better and more balanced performance, which is very difficult for the traditional least damping square method to achieve.

Eliminating chromatic aberration in Gauss-type lens design using a novel genetic algorithm

Two different types of Gauss lens design, which effectively eliminate primary chromatic aberration, are presented using an efficient genetic algorithm (GA). The current GA has to deal with too many targets in optical global optimization so that the performance is not much improved. Generally speaking, achromatic aberrations have a great relationship with variable glass sets for all elements. For optics whose design is roughly convergent, glass sets for optics will play a significant role in axial and lateral color aberration. Therefore better results might be derived from the optimal process of eliminating achromatic aberration, which could be carried out by finding feasible glass sets in advance. As an alternative, we propose a new optimization process by using a GA and involving theories of geometrical optics in order to select the best optical glass combination. Two Gauss-type lens designs are employed in this research. First, a telephoto lens design is sensitive to axial aberration because of its long focal length, and second, a wide-angle Gauss design is complicated by lateral color aberration at the extreme corners because Gauss design is well known not to deal well with wide-angle problems. Without numbers of higher chief rays passing the element, it is difficult to correct lateral color aberration altogether for the Gauss design. The results and conclusions show that the attempts to eliminate primary chromatic aberrations were successful.

Optimizing chromatic aberration calibration using a novel genetic algorithm

Advances in digitalized image optics has increased the importance of chromatic aberration. The axial and lateral chromatic aberrations of an optical lens depends on the choice of optical glass. Based on statistics from glass companies worldwide, more than 300 optical glasses have been developed for commercial purposes. However, the complexity of optical systems makes it extremely difficult to obtain the right solution to eliminate small chromatic aberration. Even the damped least-squares technique, which is a ray-tracing-based method, is limited owing to its inability to identify an enhanced optical system configuration. Alternatively, this study instead attempts to eliminate even negligible axial and lateral colour aberration by using algorithms involving the theories of geometric optics in triplet lens, binary and real encoding, multiple dynamic crossover and random gene mutation techniques.

Optical design and extended multi-objective optimization of miniature L-type optics

In ordinary optical design and optimization, it is difficult to strike a balance between relative illuminance (RI) and the modulation transfer function (MTF); this is even more difficult for special fold optical zoom lenses. We propose a thinning L-type zoom lens design that exploits the reflecting and refracting surfaces that constitute a prismatic lens. However, in L-type designs, the lens RI is comparatively low compared with that in its coaxial counterparts. Attempts to improve the RI also cause MTF degradation. We propose a combination of the Taguchi method and principal component analysis to improve both the RI and MTF in L-type zoom systems. We analysed an orthogonal array L9 using the Taguchi method. The resulting experimental values of the orthogonal array L9 were used as inputs for principal component analysis to obtain the total point value. The total point value was then analysed by variance, revealing that the two most significant factors were (1) the semi-aperture of the front element and (2) the surface 7 to image length. Our proposed method increased the MTF and RI by 0.16% and 0.44%, respectively, in system wide-angle ends.

Measurement of the MTF and MRTD for focal plane arrays

The use of focal plane arrays (FPAs) in infrared imaging systems is becoming increasingly important. There are problems, however, in measuring their modulation transfer function (MTF) and their minimum resolvable temperature difference (MRTD) since these performance measures vary with the exposition of the image on the FPA. This limitation has been overcome through the introduction of a discrete MTF for these imaging systems using discrete Fourier transform techniques. This discrete MTF is a unique function of spatial frequency and has been measured using a microscanned discrete line spread function. It has also formed the basis of an objective MRTD, the results of which have been compared with subjective measurements.

On the Design of Fabry-Perot Reflectors for the Vacuum Ultraviolet

A method of comparing the theoretical optical performance of metal films and absorbing multilayer stacks is given. It is shown analytically how the thickness of a nonabsorbing spacer layer between two absorbing stacks may be chosen to maximize either the reflectance or reflectance + transmittance of the complete system. Some numerical examples are given.

Optimization of a lens design using a neural network

The graded-response Hopfield neural network model has been used to solve the traveling salesman optimization problem. However, the mapping of an optical design optimization problem onto a neural net is more difficult. This paper describes how it can be done for the case of minimizing the chromatic aberration in a complicated twenty-element zoom-lens system by the selection of glass types. The problem is combinatorial in nature. It is suited to neural networks, and its solution is non-trivial by other means. Thus the use of neural networks to solve optical optimization problems is demonstrated.

Optimization of optics with micro diffractive optical element via a hybrid Taguchi genetic algorithm

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 lenss chromatic aberration could be significantly reduced, compared to results from the traditional least damping square (LDS) method.

Distance-learning postgraduate education in optics and optical design

Although optics is a common area of activity among professional physicists and engineers, the subject itself is typically not a significant component of Bachelor degrees in physics or engineering. Consequently, large numbers of scientists and engineers find themselves working in the field of optics without formal education in the subject. Although such education would often prove valuable to them, it is not conveniently available via conventional full-time courses. Another group of persons includes those who are not working in an optics-related field, but would like to be, and yet cannot contemplate the cost and dislocation associated with a conventional full-time Masters course. For both these groups, a flexible Masters course in optics by distance-learning could be appropriate. It is for these reasons that interest has arisen recently in such forms of optics education. This paper describes a flexible distance-learning model for postgraduate education in optics that has been implemented at the University of Reading, England, where there has been a full-time optics Masters course in Applied and Modern Optics for almost 40 years. The model is modular and credit-based, and includes various levels of qualification from CPD to Masters. A distance-learning module on optical design is discussed as an example, and it is hoped to make this module freely available on-line via the internet to delegates at this conference for them to explore in their own time. The importance of choosing optical-design case studies appropriate to this learning style is discussed. The problem of lab work within a distance-learning optics course is described, and current and possible future solutions are discussed.