What is paraxial: Definition and 2 Discussions

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 that 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:




sin
⁡
θ
≈
θ
,

tan
⁡
θ
≈
θ


and


cos
⁡
θ
≈
1.


{\displaystyle \sin \theta \approx \theta ,\quad \tan \theta \approx \theta \quad {\text{and}}\quad \cos \theta \approx 1.}


The paraxial approximation is used in Gaussian optics and first-order ray tracing. 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 do not change for the "second-order" paraxial approximation (the second term in their Taylor series expansion is zero), while for cosine the second order approximation is




cos
⁡
θ
≈
1
−



θ

2


2



.


{\displaystyle \cos \theta \approx 1-{\theta ^{2} \over 2}\ .}


The second-order approximation is accurate within 0.5% for angles under about 10°, but its inaccuracy grows significantly for larger angles.
For larger angles it is often necessary to distinguish between meridional rays, which lie in a plane containing the optical axis, and sagittal rays, which do not.

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