SMS-based optimization strategy for ultra-compact SWIR telephoto lens design: erratum

We report and correct an error in [Opt. Express 20, 9726–9735 (2012)]. The author list has been modified. All other contents are unchanged.

Analytic design method for optimal imaging: coupling three ray sets using two free-form lens profiles

In this work, a new two-dimensional optics design method is proposed that enables the coupling of three ray sets with two lens surfaces. The method is especially important for optical systems designed for wide field of view and with clearly separated optical surfaces. Fermat’s principle is used to deduce a set of functional differential equations fully describing the entire optical system. The presented general analytic solution makes it possible to calculate the lens profiles. Ray tracing results for calculated 15th order Taylor polynomials describing the lens profiles demonstrate excellent imaging performance and the versatility of this new analytic design method.

Analytic free-form lens design in 3D: coupling three ray sets using two lens surfaces

The two-dimensional analytic optics design method presented in a previous paper [Opt. Express 20, 5576–5585 (2012)] is extended in this work to the three-dimensional case, enabling the coupling of three ray sets with two free-form lens surfaces. Fermat’s principle is used to deduce additional sets of functional differential equations which make it possible to calculate the lens surfaces. Ray tracing simulations demonstrate the excellent imaging performance of the resulting free-form lenses described by more than 100 coefficients.

Compact, high-efficiency sunlight harvesting

A new free-form optics design method could unleash the full potential of tracking integrated solar concentrators.

Obtaining contradiction measure on intuitionistic fuzzy sets from fuzzy connectives

In a previous paper, we proposed an axiomatic model for measuring self-contradiction in the framework of Atanassov fuzzy sets. This way, contradiction measures that are semicontinuous and completely semicontinuous, from both below and above, were defined. Although some examples were given, the problem of finding families of functions satisfying the different axioms remained open. The purpose of this paper is to construct some families of contradiction measures firstly using continuous t-norms and t-conorms, and secondly by means of strong negations. In both cases, we study the properties that they satisfy. These families are then classified according the different kinds of measures presented in the above paper.

Emissions and economic costs of cycling compact fluorescent lamps with integrated ballasts

This paper proposes a way to quantify the emissions of mercury (Hg) and CO2 associated with the manufacture and operation of compact fluorescent lamps with integrated ballasts (CFLis), as well as the economic cost of using them under different operating cycles. The main purpose of this paper is to find simple criteria for reducing the polluting emissions under consideration and the economic cost of CFLi to a minimum. A lifetime model is proposed that allows the emissions and costs to be described as a function of degradation from turning CFLi on and their continuous operation. An idealized model of a CFLi is defined that combines characteristics stated by different manufacturers. In addition, two CFLi models representing poor-quality products are analyzed. It was found that the emissions and costs per unit of time of operation of the CFLi depend linearly on the number of times per unit of time it is turned on and the time of continuous operation. The optimal conditions (lowest emissions and costs) depend on the place of manufacture, the place of operation and the quality of the components of the lamp/ballast. Finally, it was also found that for each lamp, there are intervals when it is turned off during which emissions of pollutants and costs are identical regardless of how often the lamp is turned on or the time it remains on. For CO2 emissions, the lamp must be off up to 5 minutes; for the cost, up to 7 minutes and for Hg emissions, up to 43 minutes. It is advisable not to turn on a CFLi sooner than 43 minutes from the last time it was turned off.

SMS-based optimization strategy for ultra-compact SWIR telephoto lens design

A new optical design strategy for rotational aspheres using very few parameters is presented. It consists of using the SMS method to design the aspheres embedded in a system with additional simpler surfaces (such as spheres, parabolas or other conics) and optimizing the free-parameters. Although the SMS surfaces are designed using only meridian rays, skew rays have proven to be well controlled within the optimization. In the end, the SMS surfaces are expanded using Forbes series and then a second optimization process is carried out with these SMS surfaces as a starting point. The method has been applied to a telephoto lens design in the SWIR band, achieving ultra-compact designs with an excellent performance.

Analytic free-form lens design for tracking integration in concentrating photovoltaics

In this work the concept of tracking integration in concentrating photovoltaics (CPV) is revisited and developed further. With respect to conventional CPV, tracking integration eliminates the clear separation between stationary units of optics and solar cells, and external solar trackers. This approach is capable of further increasing the concentration ratio and makes high concentrating photovoltaics (> 500x) available for single-axis tracker installations. The reduced external solar tracking effort enables possibly cheaper and more compact installations. Our proposed optical system uses two laterally moving plano-convex lenses to achieve high concentration over a wide angular range of ±24°. The lateral movement allows to combine both steering and concentration of the incident direct sun light. Given the specific symmetry conditions of the underlying optical design problem, rotational symmetric lenses are not ideal for this application. For this type of design problems, a new free-form optics design method presented in previous papers perfectly matches the symmetry. It is derived directly from Fermat's principle, leading to sets of functional differential equations allowing the successive calculation of the Taylor series coeficients of each implicit surface function up to very high orders. For optical systems designed for wide field of view and with clearly separated optical surfaces, this new analytic design method has potential application in both fields of nonimaging and imaging optics.

About t-norms on type-2 fuzzy sets.

Walker et al. defined two families of binary operations on M (set of functions of [0,1] in [0,1]), and they determined that, under certain conditions, those operations are t-norms (triangular norm) or t-conorms on L (all the normal and convex functions of M). We define binary operations on M, more general than those given by Walker et al., and we study many properties of these general operations that allow us to deduce new t-norms and t-conorms on both L, and M.

Geometric diagnostics of complex patterns: Spiral defect chaos

Motivated by the observation of spiral patterns in a wide range of physical, chemical, and biological systems, we present an automated approach that aims at characterizing quantitatively spiral-like elements in complex stripelike patterns. The approach provides the location of the spiral tip and the size of the spiral arms in terms of their arc length and their winding number. In addition, it yields the number of pattern components (Betti number of order 1), as well as their size and certain aspects of their shape. We apply the method to spiral defect chaos in thermally driven Rayleigh- Bénard convection and find that the arc length of spirals decreases monotonically with decreasing Prandtl number of the fluid and increasing heating. By contrast, the winding number of the spirals is nonmonotonic in the heating. The distribution function for the number of spirals is significantly narrower than a Poisson distribution. The distribution function for the winding number shows approximately an exponential decay. It depends only weakly on the heating, but strongly on the Prandtl number. Large spirals arise only for larger Prandtl numbers. In this regime the joint distribution for the spiral length and the winding number exhibits a three-peak structure, indicating the dominance of Archimedean spirals of opposite sign and relatively straight sections. For small Prandtl numbers the distribution function reveals a large number of small compact pattern components.

Reducing Cache Hierarchy Energy Consumption by Predicting Forwarding and Disabling Associative Sets

The first level data cache un modern processors has become a major consumer of energy due to its increasing size and high frequency access rate. In order to reduce this high energy con sumption, we propose in this paper a straightforward filtering technique based on a highly accurate forwarding predictor. Specifically, a simple structure predicts whether a load instruction will obtain its corresponding data via forwarding from the load-store structure -thus avoiding the data cache access - or if it will be provided by the data cache. This mechanism manages to reduce the data cache energy consumption by an average of 21.5% with a negligible performance penalty of less than 0.1%. Furthermore, in this paper we focus on the cache static energy consumption too by disabling a portin of sets of the L2 associative cache. Overall, when merging both proposals, the combined L1 and L2 total energy consumption is reduced by an average of 29.2% with a performance penalty of just 0.25%. Keywords: Energy consumption; filtering; forwarding predictor; cache hierarchy

Secure optical networks based on quantum key distribution and weakly trusted repeaters

Abstract—In this paper we explore how recent technologies can improve the security of optical networks. In particular, we study how to use quantum key distribution(QKD) in common optical network infrastructures and propose a method to overcome its distance limitations. QKD is the first technology offering information theoretic secretkey distribution that relies only on the fundamental principles of quantum physics. Point-to-point QKDdevices have reached a mature industrial state; however, these devices are severely limited in distance, since signals at the quantum level (e.g., single photons) are highly affected by the losses in the communication channel and intermediate devices. To overcome this limitation, intermediate nodes (i.e., repeaters) are used. Both quantum-regime and trusted, classical repeaters have been proposed in the QKD literature, but only the latter can be implemented in practice. As a novelty, we propose here a new QKD network model based on the use of not fully trusted intermediate nodes, referred to as weakly trusted repeaters. This approach forces the attacker to simultaneously break several paths to get access to the exchanged key, thus improving significantly the security of the network. We formalize the model using network codes and provide real scenarios that allow users to exchange secure keys over metropolitan optical networks using only passive components. Moreover, the theoretical framework allows one to extend these scenarios not only to accommodate more complex trust constraints, but also to consider robustness and resiliency constraints on the network.

Phase transitions in number theory: from the birthday problem to Sidon sets

In this work, we show how number theoretical problems can be fruitfully approached with the tools of statistical physics. We focus on g-Sidon sets, which describe sequences of integers whose pairwise sums are different, and propose a random decision problem which addresses the probability of a random set of k integers to be g-Sidon. First, we provide numerical evidence showing that there is a crossover between satisfiable and unsatisfiable phases which converts to an abrupt phase transition in a properly defined thermodynamic limit. Initially assuming independence, we then develop a mean-field theory for the g-Sidon decision problem. We further improve the mean-field theory, which is only qualitatively correct, by incorporating deviations from independence, yielding results in good quantitative agreement with the numerics for both finite systems and in the thermodynamic limit. Connections between the generalized birthday problem in probability theory, the number theory of Sidon sets and the properties of q-Potts models in condensed matter physics are briefly discussed

Planar point sets with large minimum convex decompositions

We show the existence of sets with n points (n ? 4) for which every convex decomposition contains more than (35/32)n?(3/2) polygons,which refutes the conjecture that for every set of n points there is a convex decomposition with at most n+C polygons. For sets having exactly three extreme pointswe show that more than n+sqr(2(n ? 3))?4 polygons may be necessary to form a convex decomposition.