Klaus Donner

Wave-front reconstruction with a Shack–Hartmann sensor with an iterative spline fitting method

One limitation of the conventional Shack-Hartmann sensor is that the spots of each microlens have to remain in their respective subapertures. We present an algorithm that assigns the spots to their reference points unequivocally even if they are situated far outside their subaperture. For this assignment a spline function is extrapolated in successive steps of the iterative algorithm. The proposed method works in a single-shot technique and does not need any aid from mechanical devices. The reconstruction of a simulated steep aspherical wave front (approximately 100 lambda/mm slope) is described as well as experimental results of the measurement of a spherical wave front with a huge peak-to-valley value (approximately 400 lambda). The performance of the method is compared with the unwrapping method, which has been published before.

Telecentric line scanning system based on a ring surface mirror for inline processes

Abstract In many industrial applications, an inline measurement of a production process poses a difficult challenge for any optical system. Therefore, telecentric optical systems are being used to ensure an independence of the magnification of the object from the working distance. Usually, telecentric optical systems are impractical for inline applications with large objects due to the size of the telecentric optical system, which has to be larger than the object. Therefore, a new approach of telecentric line scanning systems was developed to gain access to this advantage.

Multisensorfusion bei der Verarbeitung mikrosystembasierter Signale

Multisensorfusion (oder kurz Sensorfusion) ist ein mehrschichtiger, vielgestaltiger Prozeß, der sich mit der automatischen Erfassung, der Assoziation, der Korrelation und der Kombination von Daten aus mehreren Quellen beschäftigt (nach einer Definition einer Arbeitsgruppe zur Sensorfusion des Verteidigungsministeriums der USA; siehe z.B. [1]). Neben Sensoren können auch andere Informationsquellen (z.B. Datenbanken oder Benutzereingaben) verwendet werden. Daher spricht man auch allgemeiner von Datenoder Informationsfusion.

Korovkin Closures In 0(X)

Publisher Summary This chapter discusses the korovkin closures in Ҟ 0 ( X ). The Korovkin closure Kor (ℋ) of a linear subspace ℋ in the space Ҟ 0 (X) of those continuous real-valued functions on a locally compact space X that vanish at infinity is characterized. The arbitrary locally compact space (always assumed to be Hausdorff) is denoted by X , the linear space of continuous real-valued functions on X vanishing at infinity are denoted by Ҟ 0 ( X ), and an arbitrary linear subspace of Ҟ 0 ( X ) is denoted by ℋ. ℋ-affine functions of order M and almost ℋ-bounded functions are described. The chapter also discusses M -contractive Korovkin Closures.

Integral representations by non-finite Radon measures and measures of finite variation

While Choquets representation theorems yield a natural and elegant approach to integral representations by probability measures, things become more complicated when unbounded Radon measures are involved. It is the aim of this note to remedy this disadvantage. Let X + {0} be a weakly complete cone in some locally convex Hausdorff space E. If H is a cap of X such that the cone generated by H is dense in X, then each point x E X is the resultant of a positive linear form on a suitable subspace ~ C ~(H\{0}) such that the continuous functions with compact support as well as the restrictions to H\{0} of continuous linear forms on E are contained in 6~. Moreover, each function f ~ 6 e is majorized and minorized by some continuous linear form on E. The convex members of ,5 e define an ordering <~ in the cone of all positive linear forms on 6 e similarly to the Choquet-Bishop-de Leeuw ordering. To each point x e X there exists a <~-maximal positive linear form # on 5 e with resultant x, and # is unique iff X is a lattice cone. Furthermore,/~ turns out to be a Radon measure whenever x is the supremum of an upward directed set in the cone generated by H. Thus, if H is an almost universal cap, each point x s X is representable by <~-maximal positive Radon measures. The <~-maximal measures are the complete analogues to the maximal probability measures in classical Choquet theory, and, in fact, generalize them. Applications to function algebras and integral representations of m-monotonic functions including the theorem of Bernstein and Widder for completely monotonic functions on open subcones of IR n demonstrate the efficiency of the general theory.