Phase space ray tracing for illumination optics technische. In quantum optics, an optical phase space is a phase space in which all quantum states of an optical system are described. Applications of caustic methods to longitudinal phase. Fundamentals and applications details theoretical concepts of phase space as well as novel engineering applications in. For any such system, a plot of the quadratures against each other, possibly as functions of time, is called a phase diagram. When two or more waves reach a point in space simultaneously, the resultant displacement at that point at any instant of time is the algebraic sum of the displacements produced by the individual waves. Phase space optics firstorder optical system design and linear canonical transformations our main research line comprises the generation of laser beams either using holography or specific optical transformations as well as their optical characterization. Chebyshev interpolation of phase space mapping for efficient optical. The nonlinearity is typically observed only at very high light intensities values of atomic electric fields, typically 10 8 vm such as those provided by lasers. To prove this, phase space in geometrical optics is generally introduced, and some example systems are presented which allow us to relate phase space transformations to. The broader the signal, the easier it is to intercept. We show that nonlinear transformations of phase space, are key to understand freeform illumination designs and aberrations within freeform systems. Applications in computational imaging and optical image processing conference paper pdf available in proceedings of spie the international society for optical engineering.
Quantum optics in phase space provides a concise introduction to the rapidly moving field of quantum optics from the point of view of phase space. Lecture 2 the phase space of geometrical optics rays, 3d imaging, and computational photography markus testorf markus. There are, for example, sensors dependent on relative phase shift upon reflection from an interface. Optical phase space, wigner representation, and invariant. We introduce the statistical distribution in the phase space as density.
In general it would therefore be helpful for illumination designers, especially beginners, to have an engineering tool, which allows a fast, systematic and illustrative access to illumination design problems. The concept of phase space was developed in the late 19th century by ludwig boltzmann. Each point in the optical phase space corresponds to a unique state of an optical system. Dodin, wave kinetics of driftwave turbulence and zonal ows beyond the ray approximation, phys. Zhong and gross journal of the european optical societyrapid publications phase space of partially coherent light with discontinuous surfaces minyi zhong 0 herbert gross 0 0 friedrichschilleruniversity jena, institute of applied physics, jena 07743, germany we propagate partially coherent light through discontinuous surfaces and analyze the optical effects in phase space.
Fundamentals and applications details theoretical concepts of phase space as well as novel engineering applications in specific disciplines. Topologically enabled ultrahighq guided resonances robust to. In general, each microstate will be specified by one or more quantum numbers. Pdf lohmann favored the use of phase space representations for describing optical systems. If each point in the phase space is considered as a random quantity with a particular probability ascribed to every possible state i. Phase space optics offers an alternate understanding of freeform surfaces and their impact and potential. Phase space optics allows the simultaneous visualization of both space x and spatial frequency k information.
During the zf merging, most highkdriftons become runaways and dissipate. The reason is that optical phase measurement usually requires expensive interferometers. Also explore the seminar topics paper on free space optics with abstract or synopsis, documentation on advantages and disadvantages, base paper presentation slides for ieee final year electronics and telecommunication engineering or ece students for the year 2015 2016. In optics, a commonly cited example of caustics is an. However the latter expression, phase diagram, is more usually reserved in the physical sciences for a diagram showing the various regions of stability of the thermodynamic phases of a chemical system, which consists of pressure, temperature, and composition.
Quantum optics in phase space pdf quantum optics in phase space provides a concise introduction to the rapidly moving field of quantum optics from the point of view of phase. Applications of caustic methods to longitudinal phase space manipulation was discussed. Ru1nisometry, and constitute a family of solutions to the theory under consideration. But in a quantum sense, a vacuum is full of fluctuating. The true advantages of modeling dynamic systems in phasespace can be better appreciated when more complex systems are considered. Analogy between light optics and ionoptics is useful but limited. Phasespace representation of a nonhermitian system with. A theoretical framework 6 optical fibers book 3 of the radiation. In reality, the reconstructed phase space may be only a projection of a part of the original phase space due to the complexity of the underlying system s2 and the quality and quantity of the observational data sauer et al. Modern in style and didactically skillful, quantum optics in phase space prepares students for their own research by presenting detailed derivations, many illustrations and a large set of workable problems at the end of each chapter. Total internal reflection, though known by every student of optics, is remembered by 100% reflection at an interface when angle of. We can now introduce the leading element of this tutorial. If the quadratures are functions of time then the optical.
Phase space of partially coherent light with discontinuous. Optical heterodyne imaging and wigner phase space distributions. Pdf phasespace representations psrs of a signal contain the signals spatial and local frequency information, providing a powerful tool to. Nov 07, 20 phase space optics offers an alternate understanding of freeform surfaces and their impact and potential. Phasespace theory of the dimits shift and crossscale interactions in driftwave turbulence. The lf representation is defined in the geometrical optics realm, however it can be related to the phase space representation 38 used in wave optics 37, 39, 40. Phasespace optics and modern imaging systems lecture 5. Symmetric lattices because of periodic translational invariance, the crystal momentum is conserved and the eigenspectrum of a particle moving in the potential vrof equation 3 is most conveniently calculated in fourier space. Acknowledgments the authors would like to thank and acknowledge julian mckenzie for supplying the gun distribution. Integeral photography3d displaysplenoptic camera superresolution and compressive sensing the moire effect extended depth of field. Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Nonlinear optics nlo is the branch of optics that describes the behaviour of light in nonlinear media, that is, media in which the polarization density p responds nonlinearly to the electric field e of the light. Phase space optics, geometrical optics, ray tracing. One might preclude that for a continuous phase space, any finite volume would contain an infinite number of states.
The effective object phase space provides a way to avoid tracing rays that do not reach. Atomic, molecular and optical physics38s1s140 wannier state density distributions and tunnelling neighbourhoods p blair blakie and charles w clark2004. Phasespace measurement as the central task of signal recovery and imaging technology the phasespace toolbox applications. Because light is an electromagnetic wave, other forms of electromagnetic radiation such as xrays, microwaves, and radio waves. This authoritative guide includes full coverage of sampling, superresolution imaging, and the phase space interpretation of ultrafast optics.
We show that phase space methods can provide such a tool and moreover allow a consistent approach to radiometry. Publishers pdf, also known as version of record includes final page, issue. To do so, the method of phase space in optics is employed, which allows for a direct visualization of the radiance distribution, 14. Explore free space optics with free download of seminar report and ppt in pdf and doc format. Optical phase space, wigner representation, and invariant quality parameters. Quantum optics in phase space presents the subject of quantum optics as transparently as possible. A plot of position and momentum variables as a function of time is sometimes called a phase plot or a phase diagram. The state of a system of particles corresponds to a certain distribution of points in phase space.
Osa phase space transformations a different way to. Thomas department of physics, duke university, durham, north carolina 277080305 received may 6, 1996 we demonstrate that optical heterodyne imaging directly measures smoothed wigner phase space distributions. This authoritative guide includes full coverage of sampling, superresolution imaging, and the phasespace interpretation of ultrafast optics. Phasespace optics as a unification of optical modelling. An important phenomenon where optical phase manifests itself is total internal reflection. Berlin weinheim new york chichester brisbane singapore toronto. Schleich quantum optics in phase space wileyvch berlin. Symmetric lattices because of periodic translational invariance, the crystal momentum is conserved and the eigenspectrum of a particle moving in the potential vrof equation 3. Fso free space optics by, bhavik trivedi 29 october 20 1 2. On thermodynamics and phase space of near horizon extremal geometries by kamal hajian near horizon extremal geometries nheg, are geometries which may appear in the near horizon region of the extremal black holes. Diracpoint engineering and topological phase transitions in. Phasespace theory of the dimits shift and crossscale. The counting of the number of states available to a particle amounts to determining the available volume in phase space. Optical phase imaging using a synthetic aperture phase.
Iop quantum optics journals to merge stable droplets in the labyrinthine pattern d gomila, p colet, g oppo and m san miguel 2004journal of optics b. On thermodynamics and phase space of near horizon extremal. It implies the development of techniques and experimental setups in the field of phase. A comprehensive cross section of phasespace optics this definitive volume highlights an elegant, unified approach to optical rays, waves, and system design using cuttingedge phasespace techniques. Furthermore, the gaussian properties of these states may be preserved also during the dissipative evolution through noisy channels, both markovian and nonmarkovian. In dynamical system theory, a phase space is a space in which all possible states of a system are represented, with each possible state corresponding to one unique point in the phase space. The result is a remarkably concise yet comprehensive and accessible text and reference book an inspiring source of information. We demonstrate measurement of relative optical phase shift upon total internal reflection. Similarly to general relativity, where time and space are curved, transformation optics shows that. This technique can be used in a number of applications requiring parallel lightbeam encoding such as the generation of multiple beam optical traps. The programmable phase optics research is primarily engaged in applying the generalized phase contrast method, which facilitates lossless light transmission and direct conversion of input phase patterns to high contrast intensity distributions.
Previous experiments have focused mainly on coherent beams, which are fully described by a twodimensional complex field amplitude and phase. This, however, does not prevent us from using the reconstructed phase space. Historically, nonimaging optics that work as ideal concentrators have been discovered through such heuristic ideas as edge ray involutes, string method, simultaneous multiple surface, and tailored edge ray concentrator, without a. Dodin, on the structure of the drifton phase space and its relation to the rayleighkuo criterion of the zonalow stability, phys. Phase space optics might offer an alternative way to understand freeform optics and their impact within optical systems. One of the security risks of wireless transmissions is the interception of data. A comprehensive cross section of phase space optics this definitive volume highlights an elegant, unified approach to optical rays, waves, and system design using cuttingedge phase space techniques. It is often convenient in statistics to imagine a sixdimensional space. Phase contains valuable information such as refractive index variations or sample thickness that intensity alone cannot provide 1,2.
Modern in style and didactically skillful, quantum optics in phase space prepares students for their own research by presenting detailed derivations, many illustrations and a large set of workable. The main purpose of this tutorial is to introduce the reader to the phase space. Dec 02, 20 phase space optics might offer an alternative way to understand freeform optics and their impact within optical systems. Diracpoint engineering and topological phase transitions. A phase space model of fourier ptychographic microscopy. Free space optics seminar report, ppt, pdf for ece students.
The upper graph shows a shift in the horizontal betatron phase. Iop quantum optics journals to merge probing rydberg atoms through collisions with helium in the presence of static electric and magnetic fields s bivona et al2005 journal of physics b. Phase space methods have already prooven to be promising for improved raytracing of illumination systems 15. Nonimaging optics is the theory of thermodynamically efficient optics and as such, depends more on thermodynamics than on optics. Phase space optics firstorder optical system design and linear canonical transformations. Phase space in classical physics quantum mechanically, we can actually count the number of microstates consistent with a given macrostate, specified for example by the total energy. For mechanical systems, the phase space usually consists of all possible values of position and momentum variables. Applications of caustic methods to longitudinal phase space. Stochastic systems in merging phase space this page intentionally left blank. Phasespace measurement and coherence synthesis of optical. Charles acknowledges the support of the veski victoria fellowship. Optics usually describes the behaviour of visible, ultraviolet, and infrared light. Matical tools needed for phasespace description of a very common. A new computational imaging technique, termed fourier ptychographic microscopy fpm, uses a sequence of lowresolution.
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