Field flattener lenses counteract the Petzval field curvature of an optical system, mitigating 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.
Due to refraction, the focal point of the beam is shifted by
It can be shown, then, that the radius of curvature for the lens that would flatten out the field is given by In the 21st century, the New Horizons spacecraft, which was an 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.