Optical distortion

**Figure 4.20:** Common optical distortions. (a) Original images. (b) Barrel distortion. (c) Pincushion distortion. For the upper row, the grid becomes nonlinearly distorted. For lower row illustrates how circular symmetry is nevertheless maintained.
$\begin{figure}\begin{center} \begin{tabular}{ccc} \psfig{file=figs/originalgrid.... ...,width=1.6truein} \\ (a) & (b) & (c) \\ \end{tabular}\end{center} \end{figure}$

**Figure 4.21:** An image with barrel distortion, taken by a fish-eyed lens. (Image by Wikipedia user Ilveon.)
$\begin{figure}\centerline{\psfig{file=figs/fisheye.ps,width=4.5truein}} % \end{figure}$

Even if the image itself projects onto the image plane it might be distorted at the periphery. Assuming that the lens is radially symmetric, the distortion can be described as a stretching or compression of the image that becomes increasingly severe away from the optical axis. Figure 4.20 shows how this effects the image for two opposite cases: barrel distortion and pincushion distortion. For lenses that have a wide field-of-view, the distortion is stronger, especially in the extreme case of a fish-eyed lens. Figure 4.21 shows an image that has strong barrel distortion. Correcting this distortion is crucial for current VR headsets that have a wide field-of-view; otherwise, the virtual world would appear to be warped.

Steven M LaValle 2020-11-11