Paraxial approximation: Difference between revisions

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In [[geometric optics]], the '''paraxial approximation''' is an [[approximation]] used in [[Ray tracing (physics)|ray tracing]] of light through an optical system (such as a [[lens (optics)|lens]]).<ref name=Greivenkamp>{{cite book | first=John E. | last=Greivenkamp | year=2004 | title=Field Guide to Geometrical Optics | publisher=SPIE | others=SPIE Field Guides vol. '''FG01''' | id=ISBN 0-8194-5294-7 |pages=pp. 19–20 }}</ref>

{{Unreferenced|date=April 2008}}

In [[geometric optics]], the '''paraxial approximation''' is an [[approximation]] used in [[Ray tracing (physics)|ray tracing]] of light through an optical system (such as a [[lens (optics)|lens]]).

A '''paraxial ray''' is a [[Ray (optics)|ray]] which makes a small angle (''θ'') to the [[optical axis]] of the system, and lies close to the axis throughout the system.<ref name=Greivenkamp/> Generally, this allows three important approximations (for ''θ'' in [[radian]]s) for calculation of the ray's path:<ref name=Greivenkamp/>

:<math> \sin(\theta) \approx \theta </math>

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:<math> \cos(\theta) \approx 1 </math>

The paraxial approximation is used in ''first-order'' raytracing and [[Gaussian optics]].<ref name=Greivenkamp/> [[Ray transfer matrix analysis]] is one method that uses the approximation.

In some cases, the second-order approximation is also called "paraxial". The approximations above for sine and tangent are already accurate to second order in ''θ'', but the approximation for cosine needs to be expanded by including the next term in the [[Taylor series]] expansion. The third approximation then becomes

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For larger angles it is often necessary to distinguish between [[meridional ray]]s, which lie in a plane containing the [[optical axis]], and [[sagittal ray]]s, which do not.

==References==

{{reflist}}

== External links ==