Geometric optics on phase space pdf

Pdf geometric optics in a phasespacebased level set. Geometrical optics uses the effective rule of thumb that light travels in straight lines in a homogeneous medium of uniform refractive index. Fermats principle and the geometric mechanics of ray optics. Tian, threedimensional 3d optical information processing, phd dissertation, mit 2006. Geometric optics on phase space kurt bernardo wolf. Wolf, discrete systems and signals on phase space, applied. Request pdf geometric optics in a phasespacebased level set and eulerian framework we introduce a level set approach for ray tracing and the construction of wavefronts in geometric optics. In flat optics, optical phase space is twodimensional and can be drawn. Propagation along a guide rotates phase space fractional fourier transformation paraxially.

Continuousvariable geometric phase and its manipulation. Geometric optics in a phasespace based level set and eulerian framework. Geometric phase microscopy for quantitative phase imaging. This treatise provides the mathematical background and also collects a host of useful methods of practical importance, particularly the fractional fourier transform. Publishers pdf, also known as version of record includes final page, issue and volume. Our approach automatically handles the multivalued solutions that appear and automatically resolves the wavefronts.

Phase space ray tracing for illumination optics technische. Geometric optics on phase space kurt bernardo wolf springer. Geometrical optical design in phase space dgao proceedings. Likewise the geometricoptical phase space is the 4d cartesian space of the ray. So far geometrical optics light propagation is described in terms of rays and their.

Geometric phase microscopy for quantitative phase imaging of isotropic, birefringent and space variant polarization samples skip to main content thank you for visiting. Phasespace optics is strongly connected with geometrical optics. Pdf on jan 1, 2004, kurt bernardo wolf and others published geometric optics on phase space find, read and cite all the research you need on researchgate. Show that when light reflects from two mirrors that meet each other at a right angle, the outgoing ray is parallel to. Geometrical optics please remember to photocopy 4 pages onto one sheet by going a3a4 and using back to back on the photocopier contents. The analogy of geometrical optics of light rays to hamiltonian mechanics of. The discrete quantization process is designed to preserve the geometry and dynamics of the geometric optical model determined by its two hamilton equations. We introduce a level set approach for ray tracing and the construction of wavefronts in geometric optics. Geometric optics on phase space develops both geometric optics and group theory from first principles in their hamiltonian formulation on phase space. We obtain the symplectic structure of the space of light rays in a medium. A formal solution can be obtained using raytracing techniques adapted from geometrical optics. Inflationary perturbation theory is geometrical optics in phase space. Pdf on jan 1, 2004, kurt bernardo wolf and others published geometric optics on phase space find, read and cite all the research you need on. Geometric optics in a phasespacebased level set and.

Geometric optics download ebook pdf, epub, tuebl, mobi. Wolf, geometrical optics on phase space, springer, chapters 1, 2 k. In describing the propagation of light as a wave we need to understand. This treatise provides the mathematical background and also collects a host of useful methods of practical importance, particularly the fractional fourier transform currently used for image processing. Free propagation deforms phase space spherical aberration. Geometric optics in a phasespacebased level set and eulerian framework. This is important in a wide variety of applications in wave propagation. Geometric phase, associated with holonomy transformation in quantum state space, is an important quantummechanical effect. In fact, optical systems geometric or wave have an even richer symmetry structure than mechanical ones.