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Vignetting


Excerpt from Field Guide to Geometrical Optics

While the stop alone defines the axial ray bundle, vignetting occurs when other apertures in the system, such as a lens clear aperture, block all or part of an off-axis ray bundle.

No vignetting occurs when all of the apertures pass the entire ray bundle from the object point. Each aperture radius a mustequal or exceed the maximum height of the ray bundle at the aperture.

Unvignetted

Unvignetted:


equation_1





The maximum FOV supported by the system occurs when an aperture completely blocks the ray bundle from the object point.

Fully vignetted:


equation_2fully_vignetted

The second vignetting condition ensures that the aperture passes the marginal ray and is not the system stop. By definition, vignetting cannot occur at the aperture stop or at a pupil.

A third vignetting condition is defined when an aperture passes about half of the ray bundle from an object point.

half_vignetted

Half vignetted:


equation_3



The vignetting conditions are used in two different manners:

  • For a given set of apertures, the FOV that the system will support with a prescribed amount of vignetting can be determined. A different chief ray defines each FOV.

  • For a given FOV and vignetting condition, the required aperture diameters can be determined.

A system with vignetting will have an image that has full irradiance or brightness out to a radius corresponding to the unvignetted FOV limit. The irradiance will then begin to fall off, going to about half at the half-vignetted FOV, and decreasing to zero at the fully vignetted FOV. This fully vignetted FOV is the absolute maximum possible. This discussion ignores the obliquity factors of radiative transfer, such as the cosine fourth law.

The diameter of the aperture stop is very important design parameter for an optical system as it controls five separate performance aspects of the system:
  • The system FOV determined by vignetting.
  • The radiometric or photometric speed of the system or its light collecting ability.
  • The depth of focus and depth of field of the system.
  • The amount of aberrations degrading image quality.
  • The diffraction-based performance of the system.
While some of these aspects are interrelated, they all derive from different physical phenomena.
Citation:

J. E. Greivenkamp, Field Guide to Geometrical Optics, SPIE Press, Bellingham, WA (2004).



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