# Field flattener lens

Field flattener lens is a type of lens used in modern binocular designs (e.g. Canon 10 x 42 L IS WP, 18 x 50 IS All Weather and Swarovski EL 8.5 x 42, EL 10 x 42) and in astronomic telescopes.

Field flattener lenses in binoculars improve edge sharpness and lower the distortion.

Field flattener lenses counteract the Petzval field curvature of an optical system. In other words, the function of a field flattener lens is to counter the field-angle dependence of the focal length of a system.

The object in designing a field flattening lens is to create a lens that shifts the focal points of the Petzval surface to lie in the same plane. Consider inserting a pane of glass in a focusing beam. Due to refraction, the focal point of the beam is shifted by ${\displaystyle \delta _{x}}$ dependent on the thickness of the glass. Thus we have a thickness as a function of focal shift:

${\displaystyle t(\delta _{x})=\left({\frac {n}{n-1}}\right)\delta _{x}}$.

${\displaystyle \delta _{x}(y)}$ is given by the radius of curvature of the Petzval surface, ${\displaystyle R_{p}}$. It can be shown, then, that the radius of curvature for the lens that would flatten out the field is given by

${\displaystyle R_{f}=\left({\frac {n-1}{n}}\right)R_{p}.}$ [1]

## Examples of use

In the 21st century, the New Horizons spacecraft, which was unmanned space probe sent past Pluto and the Kuiper belt, had a telescope instrument called the Long Range Reconnaissance Imager.[2]LORRI was a reflecting telescope but incorporated a field-flattening lens, with three elements.[3]

## References

1. ^ Geary, Joseph (2002). Introduction to Lens Design with Practical ZEMAX Examples. Willmann-Bell. ISBN 0943396751.
2. ^ [1]
3. ^ [2]
Petzval field curvature

Not to be confused with flat-field correction, which refers to brightness uniformity.

Petzval field curvature, named for Joseph Petzval, describes the optical aberration in which a flat object normal to the optical axis (or a non-flat object past the hyperfocal distance) cannot be brought properly into focus on a flat image plane.

This page is based on a Wikipedia article written by authors (here).
Text is available under the CC BY-SA 3.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.