A special structure is present in the lens design landscape that makes it different from a general global optimization problem: many local minimums are closely related to minimums of simpler problems and can therefore be found by decomposing the search for them in simple steps. We show here that in the design landscape of a wide-angle pinhole lens and in closely related optimization landscapes, all good local minimums found by other methods can be obtained easily with a succession of one-dimensional searches starting from simpler systems. By replacing high-dimensional searches with a succession of one-dimensional searches, the design efficiency can be increased significantly. By combining this method with conventional design methods, the wide-angle pinhole lens can be designed starting from a single lens.

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The present research is part of an effort to develop tools that make the lens design process more systematic. In typical optical design tasks, the presence of many local minima in the optical merit function landscape makes design non-trivial. With the method of Saddle Point Construction (SPC) which was developed recently ([F. Bociort and M. van Turnhout, Opt. Engineering 48, 063001 (2009)]) new local minima are obtained efficiently from known ones by adding and removing lenses in a systematic way. To illustrate how SPC and special properties of the lens design landscape can be used, we will present the step-by-step design of a wide-angle pinhole lens and the automatic design of a 9-lens system which, after further development with traditional techniques, is capable of good performance. We also give an example that shows how to visualize the saddle point that can be constructed at any surface of any design of an imaging system that is a local minimum.

Throughout their long history, the towns of Lod and Ramle have been severely affected by strong earthquakes. The last destructive earthquake occurred on July 11, 1927 and caused the destruction of large parts of these cities, reaching a seismic intensity of VIII-IX on the MSK scale. Such a high intensity from a relatively distant earthquake (about 70 km) of magnitude 6.2 is likely to be the result of local site effects of the sedimentary layers that may have significantly enhanced earthquake ground motions.This study is focused on estimating the seismic hazard to Lod and Ramle by implementing a three-step process: (1) detailed mapping of the characteristics of the H/V spectral ratios from ambient noise, (2) incorporating geological information and well data to construct subsurface models for different sites within the investigated area and (3) estimating the seismic hazard in terms of uniform hazard site-specific accelerations.The horizontal-to-vertical spectral ratios of ambient noise were used to approximate the fundamental resonance frequencies of the subsurface and their associated amplitudes. About 360 sites in Lod and Ramle were instrumented for varying periods. The soil sites exhibits H/V peak amplitudes ranging from 4 to 6 in the frequency range 0.5-2.5 Hz. These data were used to constrain 1-D subsurface models that were developed using geological data and borehole information. H/V spectral ratio observations were checked against theoretical subsurface transfer functions at locations where borehole information is available farther constraint the range of possible V s velocities of the different layers and thus, by means of trial an error it was possible to conclude a systematic spatial distribution of the V s velocity and thickness in the substrata that are also consistent with the spatial distribution of the fundamental resonance frequencies of the soft sediments obtained by means of the H/V spectral ratios, and other geological and geophysical information available at different locations in the study area.The evaluated subsurface models are introduced using the SEEH procedure of Shapira and van Eck [(1993) Natural Hazards 8, 201-205] to assess Uniform Hazard Site-Specific Acceleration Spectra for different zones within the towns of Lod and Ramle. These evaluations are very important for realistic assessment of the vulnerabilities of all types of existing and newly designed structures and for urban and land use planning. 356Y. ZASLAVSKY ET AL.