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Lecture

Matrix Optics

In course

MICRO-561: Fundamentals of biomicroscopy

Introduction to the basic operational principles of the most commonly used optical microscopes such as widefield and fluorescence.
Introduction to essential microscopy components such as lenses, objectives, filters, cameras and light sources. ...

Description

This lecture covers the concepts of ray vectors and matrices in optical systems, focusing on the properties of paraxial optical systems under different conditions such as A=0, D=0, C=0, and B=0. It also explains how the matrix approach works and provides examples of conjugate matrices for thin lens imaging systems.

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Instructors (2)

Hatice Altug

2020-current Full Professor at the Institute of Bioengineering, EPFL, Switzerland2013-2020 Associate Professor (with tenure) at the Institute of Bioengineering, EPFL, Switzerland 2013 Associate Professor (with tenure) at Electrical and Computer Engineering Department of Boston University, USA 2007-2013 Assistant Professor (tenure-track) at Electrical and Computer Engineering Department of Boston University, USA 2007 Post-doctoral Fellow at Center for Engineering in Medicine of Harvard Medical School, USA 2000-2007 PhD. in Applied Physics at Stanford University, USA 1996-2000 B.S. in Physics at Bilkent University, Turkey

Arne Seitz

04/1996-06/2000 Scientific co-worker at Philipps-University of Marburg, Dep. of Physical Chemistry 07/2000-10/2002 Post Doc at Max-Planck Unit for Structural Molecular Biology in Hamburg 11/2002-11/2005 Post Doc at European Molecular Biolohy Laboratory (EMBL), Cell Biology and Cell Biophysics Programme 11/2005-03/2009 Staff Scientist at Advanced Light Microscopy Facility, EMBL 04/2009- Head of Bioimaging and Optics platforme (BIOP), Ecole Polytechnique Fédérale de Lausanne (EPFL)

Official source

Ontological neighbourhood

Mathematics

Algebra: Linear algebra

Related concepts (32)

Matrix (mathematics)

In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object. For example, is a matrix with two rows and three columns. This is often referred to as a "two by three matrix", a " matrix", or a matrix of dimension . Without further specifications, matrices represent linear maps, and allow explicit computations in linear algebra.

Ray transfer matrix analysis

Ray transfer matrix analysis (also known as ABCD matrix analysis) is a mathematical form for performing ray tracing calculations in sufficiently simple problems which can be solved considering only paraxial rays. Each optical element (surface, interface, mirror, or beam travel) is described by a 2×2 ray transfer matrix which operates on a vector describing an incoming light ray to calculate the outgoing ray. Multiplication of the successive matrices thus yields a concise ray transfer matrix describing the entire optical system.

Ray (optics)

In optics, a ray is an idealized geometrical model of light or other electromagnetic radiation, obtained by choosing a curve that is perpendicular to the wavefronts of the actual light, and that points in the direction of energy flow. Rays are used to model the propagation of light through an optical system, by dividing the real light field up into discrete rays that can be computationally propagated through the system by the techniques of ray tracing. This allows even very complex optical systems to be analyzed mathematically or simulated by computer.

Paraxial approximation

In geometric optics, the paraxial approximation is a small-angle 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 (θ) to the optical axis of the system, and lies close to the axis throughout the system. Generally, this allows three important approximations (for θ in radians) for calculation of the ray's path, namely: The paraxial approximation is used in Gaussian optics and first-order ray tracing.

Thin lens

In optics, a thin lens is a lens with a thickness (distance along the optical axis between the two surfaces of the lens) that is negligible compared to the radii of curvature of the lens surfaces. Lenses whose thickness is not negligible are sometimes called thick lenses. The thin lens approximation ignores optical effects due to the thickness of lenses and simplifies ray tracing calculations. It is often combined with the paraxial approximation in techniques such as ray transfer matrix analysis.

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