Field flattener lens

Field flattener lens is a type of lens used in modern binocular designs and in astronomic telescopes to improve edge sharpness. Field flattener lenses counteract the Petzval field curvature of an optical system, mitigating the field-angle dependence of the focal length of a system.

Details
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 $$\delta_{x}$$ dependent on the thickness of the glass. Thus we have a thickness as a function of focal shift:
 * $$t(\delta_{x})=\left(\frac{n}{n-1}\right)\delta_{x}$$.

$$\delta_{x}(y)$$ is given by the radius of curvature of the Petzval surface, $$R_{p}$$. It can be shown, then, that the radius of curvature for the lens that would flatten out the field is given by
 * $$R_{f}=\left(\frac{n-1}{n}\right)R_{p}.$$

Examples of use
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. LORRI was a reflecting telescope but incorporated a field-flattening lens, with three elements.