Raymarching vsraytracing

Vom 9.-13. Mai 2005 fand der Workshop "Biotopverbund und Kohärenz nach Artikel 10 der Fauna-Flora-Habitat-Richtlinie" auf der Insel Vilm statt. Wesentlicher Anlass für die Tagung war, zum einen die aus fachlicher Sicht erforderliche Umsetzung von Art. 10 FFH-Richtlinie in der EU zu konkretisieren und zu unterstützen, und zum anderen einen Beitrag zur Klärung der besonderen Situation in Deutschland im Hinblick auf die Zusammenhänge und gegenseitige Ergänzung von länderübergreifendem Biotopverbund und der Umsetzung von Art. 10 FFH-Richtlinie zu leisten.

In unserer zunehmend stärker fragmentierten und überformten Kulturlandschaft ist die Berücksichtigung der funktionalen und räumlichen Kohärenz von Schutzgebietssystemen von großer Bedeutung für einen erfolgreichen Naturschutz. Zudem können viele Arten und Lebensraumtypen nicht isoliert in Schutzgebieten erhalten werden, da sie auf bestimmte Wechselbeziehungen mit ihrer Umwelt angewiesen sind. Dies macht den Aufbau eines funktionalen Biotopverbundes erforderlich. Entsprechend haben die ökologische Kohärenz und Aspekte des Biotopverbunds Berücksichtigung in Richtlinien der EU (FFH-Richtlinie, Vogelschutzrichtlinie), internationalen Konventionen und Abkommen (z. B. Konvention zum Erhalt der biologischen Vielfalt) sowie politischen Willenserklärungen (z. B. Erklärung des EU-Ministerrats den Rückgang der Biodiversität bis 2010 zu stoppen) gefunden. In der FFH-Richtlinie wird den Mitgliedstaaten in Art. 3 und 10 die Förderung von "verbindenden Landschaftselementen" nahe gelegt, die z. B. die Wanderung und Ausbreitung von Arten und den genetischen Austausch dauerhaft ermöglichen und somit die ökologische Kohärenz des Schutzgebietsnetzes Natura 2000 verbessern. Dabei handelt es sich z. B. um Trittsteine, lineare Strukturen wie Flussauen oder Hecken.

Wave optics

When a ray hits an interface between two different transparent media, a portion is reflected, and another portion is transmitted; for the latter one, which is refracted, the propagation direction is generally modified according to the Snellius law of refraction. Figure 2 shows an example case for a ball lens, where only the refracted rays (which are usually stronger) have been drawn.

An dem Workshop nahmen fast 40 Teilnehmer teil: von der EU-Kommission (DG Umwelt), der Expertengruppe für die Entwicklung des PEEN des Europarats, Teilnehmern aus 11 Mitgliedstaaten der EU, über unabhängige Experten und NGO-Vertreter bis hin zu Kollegen aus den deutschen Bundesländern.

In many situations, one can use simplified equations which describe the approximate propagation of rays which stay close to the optical axis in terms of lateral offset and direction. Any terms of second or higher order are ignored; for example, one may consider the deflection of a ray at a curved lens surface as occurring in the plane touching the surface, ignoring a longitudinal position error of second order in the lateral offset.

optics期刊

The main limitation of geometrical optics is that it ignores the wave properties of light, as described in wave optics. In particular, that means that the phenomena of diffraction, interference and polarization are not taken into account. This is not a substantial problem in many practical cases, where such effects may be negligible or can be taken into account separately. For example, one can study the optical aberrations of an imaging system with geometrical optics, being aware that even for perfect compensation of aberrations one will not obtain perfectly sharp images due to the diffraction limit. Anyway, aberrations often remain a more severe limitation than diffraction, which can thus often be safely ignored.

Optics simulation online

Ray tracing can be used for many purposes, for example for studying the detailed properties of imaging systems including their optical aberrations and effects of misalignment and imperfections from optical fabrication, or for the design of illumination systems.

The propagation of light rays, as shown in the figures above, is calculated based on purely geometrical considerations. The used technique is called ray tracing and is usually applied with specialized optics software. The calculations can be geometrically exact, i.e., valid even for large incidence angles. Curved surface may have any geometrical shapes. Depending on the initial direction of a light ray, it may or may not hit a certain optical component.

Ignoring diffraction becomes a serious problem when treating the propagation of light under conditions where it experiences tight confinement. For example, light propagation in single-mode fibers can not be realistically described at all with geometrical optics. One may still define the numerical aperture of a fiber, for example, based on geometrical optics, but such a quantity then has only a limited meaning for the actual propagation of light in the fiber. Even for multimode fibers with many modes, geometrical optics is only of quite limited utility. It can be completely misleading, for example, concerning optical phase delays of fiber modes [1].

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One may not only need to know the paths of multiple rays, but also derive various results from them. For example, ray tracing software may locate focal planes, calculate image magnification or estimates resulting optical intensities and colors.

Modified laws can be applied in the case of diffraction gratings, where additional diffracted rays emerge at different angles.

Cosmicray

Vorträge fanden statt zu den Themen "Kohärenz von Schutzgebietsnetzen", "Kohärenz von Natura 2000 in Abhängigkeit von der Gebietsmeldung" sowie "Räumliche und funktionale Aspekte der Kohärenz".

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On the surface of a flat mirror, a light ray is assumed to be reflected such that the output angle equals the input angle (both measured against the normal direction). For a curved mirror, one does that calculation based on a tangential flat plane. Figure 1 shows an example with reflection on a curved mirror.

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Optical simulation

Figure 4 shows how the beam radius, calculated with wave optics, evolves. Here, one can see that the beam radius in the focal point has a finite value related to diffraction.

Many useful relations can be derived based on such paraxial optics, which would otherwise be far more complicated or not analytically solvable at all.

Ein weiterer wissenschaftlicher Austausch ist erforderlich - auch im Lichte globaler Klimaveränderungen - und eine Sammlung von Methoden und praktischen Umsetzungsbeispielen wird auch von dem Habitatausschuss der EU-Kommission bzw. der Direktorenkonferenz für Naturschutz der EU-Mitgliedstaaten als wichtige künftige Aufgabe gesehen.

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History of optics

In optically inhomogeneous media, light beams may propagate along curves instead of straight lines. In geometrical optics, one may correspondingly assume curved ray paths. An example is shown in Figure 3, showing the focusing of light in a gradient-index lens. The rays get deflected in the lens and may exactly meet in a focal point if the lens is optimized.

Rays may be split up into multiple rays, e.g. due to partial reflection and transmission that interfaces, or due to multiple diffraction orders at gratings. In the context of diffuse optical scattering, one may employ stochastic methods for representing the scattered light with some limited number of rays. For multiple diffuse reflections, this may of course result in a very large number of rays to be treated.

Chiefray

Similarly, light propagation in multilayer coatings cannot be realistically analyzed with ray optics because interference effects are essential.

In Deutschland bestehen mit dem § 20 Abs. 1 BNatSchG, der die Länder zur Einrichtung eines länderübergreifenden Biotopverbunds auf mindestens 10% der Landesfläche verpflichtet, und dem § 21 Abs. 6 BNatSchG zum Erhalt bzw. der Förderung von zur Vernetzung von Biotopen erforderlichen linearen oder punktförmigen Elementen bereits weiterreichende rechtliche Grundlagen, die auch für die Umsetzung der Forderungen aus Art. 3 und 10 der FFH-Richtlinie relevant sind.

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Art. 10 der FFH-Richtlinie bezieht sich auf die Förderung "verbindender Landschaftselemente", die keine Verpflichtung enthält neue Schutzgebiete auszuweisen, sondern eine ergänzende Regelung darstellt, die für jede Art und jeden Lebensraumtyp in unterschiedlicher Weise zum Tragen kommen kann.

To some extent, the deficits of geometrical optics can be amended by adding additional properties to rays. For example, one may attribute some optical power to each ray in a ray tracing simulation, taking into account power losses by absorption, incomplete reflection, etc. Similarly, one may add polarization properties and optical phases, for example for calculations on an interferometer setup. A simpler example is the calculation of different ray paths for different polarization directions, for example when analyzing a polarizing prism.

Geometrical optics is a widely used concept in optics, where the propagation of light is described with geometric light rays. An equivalent term is ray optics.

Attempts for physical interpretations of light rays can be successful only to a quite limited extent. For example, rays were interpreted as the paths of some rapidly moving light particles, but this picture is not consistent with various observations. There are some similarities between geometrical light rays and real light beams, in particular with laser beams; for example, a laser beam can at least be relatively narrow and propagate along a straight line in a homogeneous medium. However, real light beams always have a finite transverse extension and exhibit the phenomenon of diffraction. Therefore, geometrical rays are only a rather abstract representation of actual light rays. Their behavior can be derived from wave optics in the limiting case of vanishing optical wavelength.

Im Anschluss an die Vorträge wurden in Gruppen konkrete Fragen zur Kohärenz bearbeitet und weitere Handlungsvorschläge aufgezeigt. Aus den Ergebnissen wurde zum Abschluss des Workshops Schlussfolgerungen im Sinne einer Empfehlung erarbeitet. Der Originaltext der Schlussempfehlung ist in Ssymank et al. 2006 in der Zeitschrift Naturschutz und Landschaftsplanung veröffentlicht.