Field flattener lens

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]

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.[2]

• Petzval field curvature
• Coma corrector