Skip to main content
\(\require{cancel}\)
Physics LibreTexts

4.6: Distortion

  • Page ID
    7092
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)

    Let us suppose that, by dint of great labour and overcoming many obstacles, we have finally designed a lens system that is free from chromatic aberration, spherical aberration, astigmatism, coma and curvature of field, or at least have minimized these aberrations or have come to a tolerable compromise for a particular purpose, can we at last relax? Unfortunately, no, we cannot. The magnification of an image is image distance divided by object distance, and image distance is different off-axis than on-axis, so the image magnification varies with distance from the axis. This means that the image of an object like this:

    OBJECT.png

    may look like this:

    OBJECT PINCUSHION DISTORTION.png

    or like this:

    OBJECT BARREL DISTORTION.png

    If the distortion is quite small, it may not be noticed in ordinary pictorial photography, but if one is using a photograph for precise positional measurements (for example, in astrometry) it is necessary to correct for the distortion. Often barrel distortion is introduced into a lens system if a stop is placed in front of a lens, while pincushion distortion results if a stop is placed behind a lens. The drawing below, in which I have exaggerated the situation by drawing a very small stop, may explain the reason why. I have placed the object at twice the focal distance from the lens, so that, on axis, the image and object distances are equal, and the magnification is unity. A symmetric air-spaced doublet with a stop half way between the two components minimises distortion.

    FIGURE IV.16 .png


    4.6: Distortion is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Jeremy Tatum via source content that was edited to conform to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.

    • Was this article helpful?