Paraxial optics

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The paraxial optics , also Gaussian optics or optics of first order , is a simplification of geometrical optics can be considered in which only light beams with the optical axis of small angular form and small distances from it have (so-called. Paraxial rays).

The limit transition to infinitely small center distances and angles results in linear formulas for calculating the light rays passing through the system and the images . Apart from chromatic aberration, paraxial rays do not cause any aberrations ; when using monochromatic light (ie light with only one wavelength ), this error is also ruled out.

Then the following applies: rays emanating from the same object point are either parallel in the image space (after passing through the system) or all intersect in the same image point; Planes are mapped to planes and straight lines to straight lines, even if they are not perpendicular to the optical axis ( Scheimpflug's rule ).

Paraxial optics can be described and used in three ways:

  • One regards the center distances of the rays and their angles to the axis as infinitesimal quantities “smaller than any positive real number , but greater than zero”. Then the results apply exactly.
  • One calculates with finite but small distances and angles. Then the results can be seen as an approximation .
  • You can calculate with arbitrarily large values, but the imaging errors of the system must be corrected beforehand using geometric optics so that the results are approximately valid. So one examines an optical system under the assumption that it has no aberrations. The paraxial optics in the last-mentioned perspective are called Gaussian optics (after Carl Friedrich Gauß ; not to be confused with the concept of the Gaussian beam , which also takes wave-optical phenomena into account). In this way, the linear equations applicable in paraxial optics - predominantly the imaging equation - can  also be applied to the numerous optical appliances with a generally large diameter.

For the important parameters that determine the imaging behavior of an optical system, there are definitions in paraxial optics, including: