Akira Yabe papers on optical design

Abstract: Mid-spatial-frequency (MSF) surface errors are left after processing aspheres or freeforms by small bits. MSF errors have sometimes significant effects on the image quality of optical systems. The efforts on the analysis and tolerancing of the MSF errors have been paid. This paper focuses on the desensitization to the MSF errors. The design target for the desensitization to the MSF errors is defined. The possibility of the desensitization is shown for optical systems in which freeforms are used with spheres.

Abstract: In my career as a lens designer, IODC lens design problems have been offering very important occasions. I would like to explain how I tackled the problems.

Abstract: In this report a novel optical system for very thin zoom lenses is shown. The key point of this system is the use of the intermediate image. The system consists of 3 lens groups with the positive optical power. The possibility of the zooming and focusing types is investigated, as well as the possibility of the power distribution of 3 lens groups. Finally the procedure to realize such an unprecedented optical system is shown.

Abstract: Axially asymmetric optical systems treated in this paper contain both of freeform surfaces and spheres. In those systems, freeform surfaces need to be allocated at the most effective position. The problem can be elegantly solved with the method of traveling freeform sufaces. The purpose of this paper is to show that the sensitivity control can be included in this design process.

Abstract: The purpose of the tolerancing is the higher yield and the lower cost. This optimization problem seems complicated, if the tolerance parameters are considered to be independent variables. But this optimization problem becomes very simple, if the approximated variances and averages of performance criteria are considered to be independent variables. The procedure will be explained through a practical tolerance problem.

Abstract: The tolerances are given to keep the performance criteria within the acceptable values in the manufactured lenses. If the tolerances and the performance criteria are given, the yield of the manufacturing can be estimated with the Monte Carlo simulation. The tolerance determines the manufacturing cost. The manufacturing cost should be as low as possible. The cost-based tolerancing is to determine the tolerances accounting for the manufacturing cost. This optimization problem looks complicated and time-consuming when the yield is viewed as a function of the tolerances. The author found the problem is dramatically simplified if the variances or averages of the critical performance criteria are used as the independent variables of the optimization. The optimal tolerance set can be found with a few trials of the Monte Carlo simulation.

Abstract: To represent the freeform surface shape, the axially asymmetric quadric and a new set of the orthogonal polynomials are introduced. In this representation, the surface tilt, the paraxial properties, and the higher order surface shape are clearly separated. With this representation, the optimization process can be simple and efficient.

Abstract: In this paper, a rapid optimization method of cost-based tolerancing is proposed. An example shows that only a few cases of the Monte Carlo simulation are necessary to find the best balance of the yield and the tolerance cost for the practical tolerancing problem.

Abstract: The subject of this paper is a construction method of axially asymmetric lenses, which consist of freeform surfaces and spherical surfaces. To minimize the fabrication cost, the total number of freeform surfaces should be as few as possible. Freeform surfaces should be used at the most efficient position. The question arises, how the optimal position of the freeform surfaces can be found. One way to find the optimal position of freeform surfaces is to include the surface numbers of freeform surfaces in the independent variables of the optimization. The surface number is the integer. If the surface number is extended to the real number, in other words, if the optical system with the real-number surface numbers is consistently defined, the real-number surface numbers can be treated as ordinary independent variables of the optimization.

Abstract: A method to find the optimal position of tilt surfaces to construct the axially asymmetric lens systems is proposed. The tilt surface number is extended to the real number and included in the independent variables of the optimization.

Abstract: In this paper the sensitivity control to manufacturing errors is treated from 3 aspects. A wavefront-based sensitivity function is proposed, the effect of which is verified with the MTF-based Monte Carlo simulation. Then the direct optimization of the MTF-based Monte Carlo simulation result is proposed. Finally the effect of the sensitivity control function to get the better lens types is shown.

Abstract: The author proposes a way to extend the aspheric surface number to a continuous variable. It is reported that the optimal aspheric surface numbers are achieved through the global optimization for practical lens design problems.

Abstract: The surface irregularity of the aspherics frequently causes troubles. So it is necessary to design the aspherics insensitive to the manufacturing errors. In this paper a universal method to design the insensitive aspherics is proposed.

Abstract: When we design lenses, we always wonder if any better design exists than the current design. If the current design could be proved to be the global minimum under given conditions, we could be fully confident on our design.

In this paper I would show an example of such a proof. The design example is the "reversible lens" [1985 International Lens Design Conference lens design problem]. This problem requests the aberration control at the lateral magnifications -1/2 and -2 simultaneously. From the nature of light, the perfect imaging at the 2 magnifications can not be realized.

Some researchers have been interested enough in the problem to predict the performance limit quantitatively, and to find the real design that attain this performance limit.

In 1992 Forbes and Jones applied a global optimization to this problem and showed some solutions with different element numbers, and in 1995 Forbes and Wallace predicted a performance limit by the method of the optimization of the Eikonal function. However this predicted limit was much better than the performance of the then-found solutions.

In this paper I investigated the prediction of Forbes and Wallace and modified their prediction. I also designed a real lens that reaches the predicted performance limit.

Abstract: Optical systems frequently use aspheric surfaces to improve performance. Typically the designer uses a combination of experience and trail and error to decide which surfaces to make aspheric, then the shape of the aspheric surface is optimized as part of the optical system.

In this paper, a method of optimally choosing which surfaces are to be made aspheric is developed. This is implemented by allowing the surface number of the asphere to become a variable in the optimization. Imaginary surfaces are used as an intermediary to make the problem continuous for the optimization. The method of implementation and design examples are given.

Abstract: I present a fast MTF optimization method. In this MTF optimization the aberration merit function is optimized.

The basic concept of this MTF optimization is to connect the improvement of the aberration merit function to the improvement of the MTF merit function. The target values and weights of aberration target functions are automatically adjusted in order that the improvement of the aberration merit function is also linked to the improvement of the MTF merit function.

Through examples it is shown that the MTF optimization used with the global optimization is effective to find good solutions as to the MTF merit function.

Abstract: Global optimization with escape function was applied to a zoom lens with aspherical surfaces. Good solutions of various types were found within a short time.