For anyone new to fourier methods, this remarkable book will illuminate the subject like no other currently available. Hadamard transforms intends to bring together different topics concerning current developments in hadamard matrices, transforms, and their applications. In the module to follow, you will learn about the otherphysical wave optics. Transformation electromagnetics and optics dohoon kwon department of electrical and computer engineering, university of massachusetts amherst, amherst, ma 01003, usa email. Transformation optics and metamaterials ping sheng. Blt in optics and its computer realization let us consider an elementary optical system with a single. Departures of the exit pupil wavefront from a spherical wave are called aberrations.
If we restrict the analysis to paraxial rays only, then. Optics physical optics wave optics quantum optics geometrical optics. Simplified timelens based system configuration for. Transformation optics applies metamaterials to produce spatial variations, derived from. Fermats principle and the geometric mechanics of ray optics. 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. Optics notes topics in these notes are wave properties polarization focal lengths geometrical optics i. The following lecture notes for phys 221, optics and thermal physics, are the sole property of the author, prof. In geometric optics, the following statements are true for real and virtual images. The power of the lens is the inverse of focal length. In this module, you will learn about one of the two main divisions of basic opticsgeometrical ray optics. Includes chapters on fourier transforms, image formation, optical coherence, diffraction, interference, holography, interferometry, analog optical computing, synthetic aperture imaging, and others. Programmable twodimensional optical fractional fourier processor.
Fast algorithm for bilinear transforms in optics a. Anharmonic waves the spectrum of a light wave fourier transform of an exponential the dirac delta function the fourier transform of ej t, cos t exp fftjtdt 1 exp 2 f tf j td. This paper gives a brief survey of the design of masks for. Fermats principle and the geometric mechanics of ray. The fourier transform is just a different way of representing a signal in the frequency domain rather than in the time domain. Sloane, martin harwit, and minghing tai this paper analyzes the systematic errors in hadamard transform optical instruments caused by moving masks, incorrect mask alignment, faulty mask fabrication, missing data, diffraction, etc. This approach can be used to engineer various optical illusion effects, such as the invisibility cloak.
A secret scene or image is first embedded into a host image to perform optical image watermarking by use of joint fresnel transform correlator architecture. An optimized nonimaging optics example the flux at the surface of the sun, 6. Optical conformal mapping and dielectric invisibility devices. We use a chromaticity curve to calculate the color change. Compressive optical image watermarking using joint fresnel transform correlator architecture. The fourier transform of et contains the same information as the original function et. Recall the point spread function is a scaled fourier transform of the pupil. Geometric optics post university of california, berkeley. Masks for hadamard transform optics, and weighing designs. Nonlinear optical security system based on a joint. Nonimaging optics is the theory of thermodynamically efficient optics and as such, depends more on thermodynamics than on optics. February 2, 2008 an invisibility device should guide light around an object as if nothing were there. The block letter f is the sample and has an intensity transmittance of 12% at 780ev all five reference holes penetrate the entire structure with a mean diameter of 1406nm w. Beam transformers can be based on refractive 16, re.
In section 2 we show some of the effects of diffraction on light transmitted through different slits and in section 3 we consider the fundamental limitations on resolution due to diffraction. Light is a form of energy which produces the sensation of sight in us. Light rays tend to bend at the interface of two different medium where the refractive index changes. In this paper, using a novel transformation, we propose the design procedure of a horn antenna having low backlobe and sidelobe levels in its eplane. A light source emits light uniformly in all directions of the three. The light ray in geometrical optics is an instrument which is used to approximate models of how the light will propagate.
Fermats principle and the geometric mechanics of ray optics summer school lectures, fields institute, toronto, july 2012 darryl d holm imperial college london d. Fourier series and optical transform techniques in contemporary optics. An anticloak 14 was designed to partially defeat the purpose of. Optics notes massachusetts institute of technology. Masks for hadamard transform optics, and weighing designs article pdf available in applied optics 151. In optics the definite integral is integral of the time required for the transit of the light ray from starting to finishing proper value of x that minimizes the optical path length and keeps it stationary at the vicinity. Nonlinear optical security system based on a joint transform correlator in the fresnel domain juan m. Conformal transformation optics a particular variant of this feature can be used to design devices with novel functionalities from inhomogeneous, isotropic dielectric media. Archimedes and other ancient greek thinkers made original contributions but we mention here heron of alexandria c. The fast algorithm for calculating the bilinear transform in the optical system is proposed. Diffraction, fourier optics, optical information processing, fractional fourier transforms. You can understand the operation of these instruments without knowing anything about newtons laws, kinetic and potential energy, electric or magnetic fields, or the particle and wave nature of matter. Fth mask fourier transform holography mask focused ion beam milling was used to pattern the au structure. The multidisciplinary perspectives for inquiry and designing of materials develop understanding of their behaviors, properties, and potential.
Nasa goddard photo and video, via flickr learning objectives 25. The following lecture notes for phys 221, optics and. Transformation optics and the geometry of light ulf leonhardt1 and thomas g. Optics describe the light propagation in terms of the light ray. Transformation optics and the geometry of light arxiv. Nonlinear optical security system based on a joint transform. Wave optics propagation, interference and diffraction of waves axel kuhn, oxford 2016 paul ewarts lecture notes and problem sets. Assumes that light is a stream of particles called photon. But the spectrum contains less information, because we take the. Osa masks for hadamard transform optics, and weighing. Download fulltext pdf edgeray principle of nonimaging optics article pdf available in journal of the optical society of america a 1110. Hadamard transform imager and imaging spectrometer. Pedrotti cord waco, texas optics is the cornerstone of photonics systems and applications.
When an object is dropped in still water, the circular wave fronts that are produced move out from the contact point over the two. This algorithm is based on the coherentmode representation of the crossspectral density function of the illumination. Compressive optical image watermarking using joint fresnel. Pdf masks for hadamard transform optics, and weighing. If you capture sunlight in a mirror or lens you can feel the heat where the sunlight is reflectedrefracted as a real image but you cannot feel the heat where the sunlight is. Hadamard transform optics focuses on hadamard transform optics and hadamard encoded optical instruments. Masks for hadamard transform optics, and weighing designs osa. If you capture sunlight in a mirror or lens you can feel the heat where the sunlight is reflectedrefracted as a real image. We propose and analyze a novel ultrafast optical pulse filtering design based on the abovesimplified configuration for transformlimited rtft. The techniques developed to date are described, and a unified mathematical treatment that should facilitate comparisons between different classes of instruments is presented. The htfli uses a fourier transform phasemodulation fluorometer ftpmf for fluorescencelifetime measurements, where the modulation frequency of the excitation light is swept linearly in frequency from zero to a specific maximum during a fixed duration. Approaches the topic of physical optics with examples drawn from the physical processes described. Fermats principle leads to principle of reversibility. Optics 2 the subject of geometrical optics is the study of the behavior of light when the phenomena can be explained by ray tracing, where shadows are sharp and.
In principle, ray tracing can help us to analyze image formation in any given optical system as the rays refract or reflect at all interfaces in the optical train. Lecture notes optics pdf 57p this note covers the following topics. We discuss a hadamard transform based fluorescencelifetimeimaging htfli technique for fluorescencelifetimeimaging microscopy flim. This is because we observe the processes emission, reflection, scattering at a distance 10cms with bare eyes that are much longer than the wavelength of light 107.
A digital micromirror device projector is used to project a color map consisting of a series of differentfrequency colormarked fringe patterns onto the target object. A light ray from a source goes in a straight line through the air, but when it encounters a lens, prism, or mirror it bends or changes direction. Periodic nonlinear fourier transform for fiberoptic. Each chapter begins with the basics of the theory, progresses to more advanced topics, and then discusses cuttingedge implementation techniques. Longitudal waves are those in which the displacement of the mediumor eld is in the direction of the wave. In this proposed filtering configuration, the time lens process is implemented using a phase electrooptic modulator driven by a rf tone. Transformation optics is the foundation for exploring a diverse set of theoretical, numerical, and experimental developments, involving the perspectives of the physics and engineering communities.
Wave properties in general there are two types of waves. The lens formula for focal length is written in terms of image distance and object distance. Then, the watermarked image is compressed to much smaller signal data using singlepixel compressive holographic imaging in optical domain. Atlas of optical transforms 1975 edition open library. Interference as a first example of interference, consider the situation shown in figure 22.
It is used extensively for measuring the spectrum of light in the infrared, a technique known as fouriertransform infrared spectroscopy ftir. Using transformation optics shaghayegh shahcheraghi and alireza yahaghi abstracttransformation optics is a convenient way to control the pattern of electromagnetic. Philbin2 1school of physics and astronomy, university of st andrews, north haugh, st andrews ky16 9ss, uk 2max planck research group optics, information and photonics, gun therscharowsky str. Kutay, the fractional fourier transform with applications in optics and. The fourier transform in optics what is the fourier transform. Fourier series and optical transform techniques in. Based on rectilinear propagation of light valid only if. Periodic nonlinear fourier transform for fiberoptic communications, part ii.
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