Paraxial approximation

The paraxial optics, also Gaussian optics or optics of the first order, is a simplification of geometrical optics, where only light rays are considered, which make small angles with the optical axis and have small distances from it.

Through the border crossing with infinitely small center distances and angles are linear formulas for calculation of the system by the light beams and the resulting pictures. Paraxial rays do not cause aberrations except chromatic aberration. When using monochromatic light (ie light of only one wavelength ) is ruled out also this error.

Then: paraxial rays emanating from the same object point are in the image space ( after passing through the system ) either parallel or all intersect in the same image point. Levels are mapped to planes and lines on a line, even if they are not perpendicular to the optical axis ( Scheimpflug rule).

The paraxial optics can be described in three ways and use:

  • The axial distances of the beams and their angle to the axis as infinitesimal quantities are considered ( smaller than any positive real number, but greater than zero). Then the results are accurate.
  • It is calculated with finite but small distances and angles. Then the results can be seen as an approximation.
  • It is expected that arbitrarily large values ​​, but must correct before, so that the results are approximately the aberrations of the system using the geometrical optics. So you studied an optical system under the assumption that it possessed no aberrations.

The paraxial optics in the latter approach is referred to as Gaussian optics ( after Carl Friedrich Gauss, not to be confused with the concept of the Gaussian beam, and wave-optical phenomena taken into account). In this way, the force in the paraxial optics linear equations - primarily the imaging equation - also to the numerous optical use devices with normally large diameter apply.

For the important parameters that determine the imaging performance of an optical system are the paraxial optics definitions before, including:

  • Focal length
  • Focus
  • Positions of the principal planes
  • Object and image distance
  • Entrance and exit pupil
  • Image scale.
  • Paraxial optics
Optical aberration Cardinal point (optics)#Principal planes and points Entrance pupil
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