Telephoto Lenses
This is a continuation from the previous tutorial - Petzval lenses.
A telephoto lens provides an effective focal length \(efl\) that is longer than its overall length \(s_{ol}\) as measured from the front of the lens to the image plane. The telephoto ratio is defined as \(s_{ol}/efl\), thus a lens with a ratio less than one is a telephoto lens.
The basic concept of a telephoto lens is illustrated by the dialyte lens configuration in which a negative lens is inserted between the objective lens and the image plane. This concept goes back to Kepler, but Peter Barlow developed the idea in the early 1800s by including a negative achromat in telescopes to increase their magnification.
Barlow type lenses are widely used today. As the telephoto ratio is made smaller, the design of the lens becomes more difficult, primarily due to the Petzval sum increasing.
When most telephoto lenses are used to view objects that are relatively close, the image quality degrades rapidly due to the typical unsymmetrical lens configuration. Some modern telephoto lenses include one or more elements that move as the lens is focused for the purpose of aberration correction.
Inverted or Reverse Telephoto Lenses
A reverse telephoto lens has a telephoto ratio greater than unity and exhibits a shorter focal length than its overall length, a larger \(bfl\) than is provided by normal lenses of the same \(efl\), lenses with generally large apertures and wide fields of view, and lens elements of physically larger size that allow easier manufacture and handling.
The basic configuration has a large negative lens located in front of a positive objective lens. Since the negative lens makes the object appear closer to the objective lens, the resultant image moves beyond the focal point, thereby making the \(bfl\) greater than the \(efl\).
An extreme form of the reverse telephoto lens is the fish-eye or sky lens. Such lenses have a total field of view of 180° or more. The image formed by these lenses has very large barrel distortion.
Recalling that the image height for a distortionless lens on a flat image surface is \(f\tan\theta\), the reverse telephoto lens has mapping relationships such as \(f\theta\) and \(f\sin\theta\).
When the barrel distortion is given by \(f\sin\theta\), the illumination across the image will be constant if such effects as vignetting and stop distortion are absent.
Barrel distortion has the effect of compressing the outer portions of the image towards the central portion, thereby increasing the flux density appropriately.
After World War II, the Russian designer M. M. Roosinov patented a double-ended reverse-telephoto lens that was nearly symmetrical with large negative lenses surrounding a pair of positive lenses with a central stop. Although the back focal length is quite short, it provides relatively large aperture with a wide field of view and essentially no distortion. Lenses of this type have found significant use in aerial photography and photogrammetry.
The next tutorial introduces origins of chromatic dispersion.