If we restrict the analysis to paraxial rays only, then. Comparison of matrix method and ray tracing in the study. A ray is defined by its height and its direction the angle it makes with the optical axis. Introduction to matrix methods in optics iopscience. Mar 31, 2016 matrix method for finding images from systems of thin lenses part 1. If you are interested in the mathematics of light, i cant think of a better reference. Clear, accessible guide requires little prior knowledge and considers just two topics. The text style is rather informal, and very clear, and many of the concepts and results presented are exposed in an intuitive way.
Introduction to matrix methods in optics anthony gerrard. Ebook introduction to matrix methods in optics as pdf. The wigner function is a central tool to explore the phase space of a system. Introduction this article is devoted to the study of complex optical systems in the framework of geometrical optics. Geometric optics of thick lenses and matrix methods mathematical. Although these methods have been somewhat neglected in the past, the authors point to the economy and elegance with which, for a linear system, a wealth of inputoutput relations can be expressed by a single matrix. 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.
Introduction to matrix methods in optics start download portable document format pdf and ebooks. Howell2 1the institute of optics, university of rochester, rochester, new york 14627, usa 2department of physics and astronomy, university of rochester, rochester, new york 14627, usa joseph. In paraxial optics, these surfaces are planes, normal to the optical axis. Within that approximation, it can be assumed that tan. We start with a notation for specifying optics systems. Carlson center for imaging science rochester institute of technology. This technique, as described below, is derived using the paraxial approximation, which requires that all. In the limit of paraxial optics, any optical system, from a simple lens to a combination of lenses, mirrors and ducts, can be described in terms of six special surfaces, called the cardinal surfaces of the system. Gaussian optics paraxial optics mainly we will discuss analysis based on paraxial optics simple ray tracing aperture and stop.
Thick lenses and the abcd formalism san jose state. The output is a ray matrix and some vectors related to the zaxis that make easier the visualization of the results. General transfermatrix method for optical multilayer systems with coherent, partially coherent, and incoherent interference, appl. To follow ray you have to have y ray height and u ray slope. Transfermatrix method optics linear canonical transformation. Ray transfer matrix analysis is a mathematical form for performing ray tracing calculations in. Ray tracing is the primary method used by optical engineers to determine optical system performance. Matrix optics is a technique for tracing paraxial rays.
Here the usual transfer matrix was modified to a generic form, with the ability to use the absolute squares of the fresnel coefficients, so as to include incoherent thick layers and partially coherent rough surface or interfaces reflection and transmission. Ray optics for imaging systems course notes for imgs321 11 december 20. In the paraxial approximation, r tan sin, so that snells law becomes. Buy introduction to matrix methods in optics dover books on physics. The use of vergence to describe the refraction at an interface can be used as a starting point for developing a matrix to perform the refraction. The basic ray matrix properties and paraxial focusing properties of a cascade system are entirely unchanged by small misalignments. Osa method of paraxial design of rifle scope with four. The ray optics is the branch of optics in which all the wave effects are neglected. After an introduction to matrix calculations, the first topic is paraxial optics, followed by optical resonators and laser beam propagation, polarization.
Moreover, the field of optics has been enormously enriched by contributions from other disciplines, such as microwave physics and electrical engineering, which employ matrix methods. If we restrict the analysis to paraxial rays only, then such process can be described in a matrix approach. Mathematical treatment of refraction for thick lenses shows the existence of principal planes in the paraxial. Since a decent imaging system where this is not the case for all rays must still focus the paraxial rays correctly, this matrix method will properly describe the positions of focal planes and magnifications, however aberrations still need to be evaluated using full raytracing techniques. The calculated parameters from proposed methods can be used in the aberration analysis and the optimization of the rifle scope parameters in optical design software. Paraxial optical ray and ray matrices ray propagation through cascaded elements rays in periodic focusing systems ray optics with misaligned. Matrix methods in paraxial optics refraction at a spherical interface. Despite much interest and progress in optical spatial cloaking. Here, the paraxial approximation means that the angle. The particular systems dealt with were all those definable within the framework of scalar paraxial optics, and our analysis based on the poincar6.
The asam offers a complete alternative to describe the paraxial optics of astigmatic optical systems. Geometrical optics ray optics describes light propagation in the form of geometric rays. System raytransfer matrix 405 i e i 406 chapter 18 matrix methods in paraxial optics 188 significance of system matrix elements we examine now the implications that follow when each of the matrix e ments in turn is zero. A paraxial raytrace is linear with respect to ray angles and heights since all paraxial angles u are defined to be the tangent of the actual angle u. Spatial and temporal pulse propagation for dispersive paraxial optical systems g.
Ray tracing is the act of manually tracing a ray of light through a system by calculating the angle of refractionreflection at each surface. Location of cardinal points from the abcd matrix for the. W e introduce the paraxial ray equation which is appropriate to systems with rotational. The matrix methods in paraxial optics for optical systems with many elements we use a systematic approach called matrix method. Lateral and angular magnifications in a pseudophakic model eye were analyzed using the matrix method of paraxial optics. Hence, a complete description of the paraxial optics of an eye should not only report the state of. Matrix method, cardinal elements, ray tracing, eye. Matrix method same as in optics applied to cavities, and gaussian beam propagations complex beam parameter q, and application to the calculation of the propagation of a gaussian beam resonators. Diffraction, point spread function, psf with aberrations, optical transfer function. The formalism for pulse propagation through dispersive paraxial optical systems. This method is extremely useful in systems with many surfaces, where gaussian and newtonian imaging.
Comparison of matrix method and ray tracing in the study of. Lucid discussions of paraxial imaging properties of a centered optical system, optical resonators and laser beam propagation, matrices in polarization optics and propagation of light through crystals, much more. The book then covers optical resonators for lasers with gaussian beams, followed by a chapter on polarization effects using the muller matrix approach. One of the remarkable properties of the matrix approach is that rays can be traced backward easily using. We follow two parameters for each ray as it progresses through the optical system.
According to the asam, an optical system is fully characterized by the back vertex vergence and the angular magnification matrix. I would like to recommend this book to everyone undergraduate, graduate, or beyond who needs an excellent, beautifully clear introduction to optics. Matrix method in paraxial optics in optics there are only two operation, translation and refraction reflection is not an operation. Script fundamentals of modern optics, fsu jena, prof. Optical elements sim classic mirrors lenses ray tracing diagram prisms filters science beamsplitters compressors guide 1 expanders detectors guide 2 delay lines 1. Describing a single thick lens in terms of its cardinal points. Ray transfer matrix analysis is a mathematical form for performing ray tracing calculations in sufficiently simple problems which can be solved considering only paraxial rays.
Bookmark file pdf introduction to optics by pedrotti solution 3rd. Pdf notes on matrix method of geometrical optics basic. In diopters want to know what happens to rays as they propagate in air and interact with lens and mirrors etc. Raytracing uses first term in paraxial approximation first order theory. Note that the approximations made are valid only for paraxial rays the vergence relationship for a surface is and the relevant paraxial approximations are. In this video i will explain how to convert the refracting equation on to a matrix format. Multiplication of the successive matrices thus yields a concise ray transfer matrix describing the entire optical system. Geometric optics of thick lenses and matrix methods. Chapter 18 matrix methods in paraxial optics erbion. Aug 30, 2017 regular class on matrix methods in paraxial optics by renowned vajpayee sir. It is important to notice that even if we choose to do paraxial optics for simplicity for a. An analysis and a description of methods for a paraxial design of rifle scopes with a fourelement imageerecting zoom system is performed.
Matrix method in paraxial optics regular class on matrix methods in paraxial optics by renowned vajpayee sir. It is described a method of the calculation of basic design parameters of the rifle scope with the fourelement imageerecting zoom system, where two inner elements are movable for ensuring zooming of the rifle scope. The ray definition i applied is commonly used in ophthalmic optics and physics, 46 whereas sheards can be found in technical optics. Matrix methods in paraxial optics 396 introduction this. Matrix methods in optics for more complicated systems use. Finally, two examples of what can be analyzed with the ray matrix are given, that consists of a few extra lines of code. Parametric resonance in periodic paraxial optical systems. The evolution of beam offset distance from the reference axis and. Very easy to understand and excellent introduction to optics. This text contains new results such as theorems on the design of variable optics, on integrating rods, on the optical layout of prism devices, etc. Standard frontilluminated sensors, for example, are more sensitive to green, red, and infrared wavelengths in the 500 to 800 nm range than they are to blue wavelengths 400 500 nm.
Paraxial optics is a method of determining the firstorder properties of an optical system that assumes all ray angles are small. Spatial and temporal pulse propagation for dispersive. Ray optics geometrical optics covered by lecture introduction to optical modeling the topic of ray optics geometrical optics is not covered in the course fundamentals of modern optics. Thick lenses 3 when the thickness of a lens is not negligible compared to the object and image distances we cannot make the approximations that led to the thin lens formula, and. Magnifications of single and dual element accommodative. The authors wish to encourage the adoption of simple matrix methods in the teaching of optics at the undergraduate and technical college level, and discuss tour main topics in this book. Geometrical optics is based on two laws of physics. It is important to notice that even if we choose to do paraxial optics for simplicity for a first. Matrix method for finding images from systems of thin lenses. It then applies matrix methods to paraxial rays through a cascade of lenses using the jones transfer matrix approach. Matrix methods in paraxial optics mit opencourseware. Ray optics for imaging systems course notes for imgs321 11 december 20 roger easton chester f. Introduction to matrix methods in optics dover books on. General transfermatrix method for optical multilayer systems with coherent, partially coherent, and incoherent interference.
The matrix method provides a means to study an optical system in the paraxial approximation. In geometric optics, the paraxial approximation is a smallangle approximation used in gaussian optics and ray tracing of light through an optical system such as a lens a paraxial ray is a ray which makes a small angle. Notes on matrix method of geometrical optics basic ideas of matrix methods in geometrical optics. Rectilinear propagation of light in homogeneous media 2. The analogy with paraxial optics is carried further by extending the matrix method to a complete hermitegaussian basis and thus to arbitrarily shaped and nonlinearly chirped pulses. Rays in the vicinity of the optical axis are used, and the surface sag is ignored or negligible. Th is is the cel ebrated helmhol tzlagrange formula of paraxial. Regular class on matrix methods in paraxial optics by renowned vajpayee sir.
The convenience of using matrix methods lies in the fact that the raytransfer matrix. The matrix methods in geometrical optics can be developed in. February 2001 optical system design 21 1 chapter 2. The interaction with the sensor requires the quantum model of discrete energy packets, so the number of packets is small if the hole diameter is small.