Distortion

What is distortion?

Distortion is an aberration occurring because an image is more or less magnified as the object is moves further off axis. Magnification of the image is dependent on the off-axis image distance.

What causes distortion?

Different areas of the lens have different focal lengths and different magnifications. This causes the image as a whole to be misshaped, even though each individual point is still sharply focused.

What does distortion look like?

Smith, Modern Optical Engineering, 2nd ed., 1990.

figure 1. The original, undistorted, square image is distorted into a pincushion (b) or a barrel shape (c).

b

c

Positive distortion is also called pincushion distortion. With positive distortion, each image point is displaced radially outward from the center, with the most distant points moving the greatest amount because the magnification increases with axial distance (figure 1b).

Negative distortion is also called barrel distortion. With negative distortion, the magnification decreases with axial distance, causing each point on the image to move radially inward (figure 1c).

How is distortion prevented?

Unless the aperture is flush with the lens a stop in a system will always bring distortion.

figure 2. Barrel distortion - the original chief ray (green) is blocked by the stop, creating a new chief ray (red). This alteration of chief rays causes the image to shrink as it moves further off axis.

Hecht, Optics, 4th ed., 2002.

figure 3. Pincushion distortion – the original chief ray (green) is blocked by the stop, creating a new chief ray (red). The alteration of chief rays causes the image to increase in size as it moves further off axis.

Hecht, Optics, 4th ed., 2002.

A stop alters which ray is the chief ray in a system. This means that if a stop is in front of the lens, the path length along the chief ray is longer, creating a smaller magnification. If a stop is placed behind the lens, the path length along the chief ray is decreased, increasing the magnification.

Therefore, introducing a stop between two lenses can make the resulting distortion zero. The distortion is eliminated when the pincushion distortion from the first lens and stop exactly cancels the barrel distortion from the stop and second lens (figure 4).

Hecht, Optics, 4th ed., 2002.

figure 4. Placing a stop between two lenses can cause the resulting distortion to be zero.

Hecht, Eugene, Optics, 4th edition, San Francisco: Addison-Wesley, 2002.

Smith, Warren, Modern Optical Engineering, 2nd edition, New York: McGraw-Hill, Inc., 1990.