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. The same mathematics is also used in accelerator physics to track particles through the magnet installations of a particle accelerator, see electron optics.
This technique, as described below, is derived using the paraxial approximation, which requires that all ray directions (directions normal to the wavefronts) are at small angles θ relative to the optical axis of the system, such that the approximation remains valid. A small θ further implies that the transverse extent of the ray bundles (x and y) is small compared to the length of the optical system (thus "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 ray-tracing techniques.
The ray tracing technique is based on two reference planes, called the input and output planes, each perpendicular to the optical axis of the system. At any point along the optical train an optical axis is defined corresponding to a central ray; that central ray is propagated to define the optical axis further in the optical train which need not be in the same physical direction (such as when bent by a prism or mirror). The transverse directions x and y (below we only consider the x direction) are then defined to be orthogonal to the optical axes applying. A light ray enters a component crossing its input plane at a distance x1 from the optical axis, traveling in a direction that makes an angle θ1 with the optical axis.
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Geometrical optics, or ray optics, is a model of optics that describes light propagation in terms of rays. The ray in geometrical optics is an abstraction useful for approximating the paths along which light propagates under certain circumstances. The simplifying assumptions of geometrical optics include that light rays: propagate in straight-line paths as they travel in a homogeneous medium bend, and in particular circumstances may split in two, at the interface between two dissimilar media follow curved paths in a medium in which the refractive index changes may be absorbed or reflected.
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.
In physics, ray tracing is a method for calculating the path of waves or particles through a system with regions of varying propagation velocity, absorption characteristics, and reflecting surfaces. Under these circumstances, wavefronts may bend, change direction, or reflect off surfaces, complicating analysis. Ray tracing solves the problem by repeatedly advancing idealized narrow beams called rays through the medium by discrete amounts. Simple problems can be analyzed by propagating a few rays using simple mathematics.
Introduction to geometrical and wave optics for understanding the principles of optical microscopes, their advantages and limitations. Describing the basic microscopy components and the commonly used
Introduction to 0ptical imaging systems such as camera objectives and microscopes. Discussion of imaging formation. Principles of design of imaging optics with geometrical optics and analysis with ray
L'optique est un vieux domaine qui touche à beaucoup de sujets modernes, des techniques expérimentales aux applications courantes. Ce premier cours traite plusieurs aspects de base de l'optique: propa
Covers the 2x2 transfer matrix for optical systems and the characterization using height and angle parameters, along with lens systems and entrance pupils.
This thesis explores the application of recent advances in integrated photonics to the field of light detection and ranging (LiDAR).The progress in photonic integration allows for unprecedented levels of light manipulation on micrometer scales through the ...
The present work deals with monochromatic wavefront aberrations in optical systems without symmetries. The treatment begins with a class of systems characterized by misaligned spherical surfaces whose behavior is analyzed using the wavefront aberration exp ...
Analog computing has emerged as a promising candidate for real-time and parallel continuous data processing. This paper presents a reciprocal way for realizing asymmetric optical transfer functions (OTFs) in the reflection side of the on-axis processing ch ...