Conventional optical imaging systems suffer from the presence of many imperfections, such as spherical aberrations, astigmatism, or coma. If the imaging system is corrected for spherical aberrations and fulfills the Abbe sine condition, perfect imaging is guaranteed between two parallel planes but only in a small neighborhood of the optical axis. It is therefore worth asking for optical systems that would allow for perfect imaging between arbitrary smooth surfaces without restrictions in shape or extension. In this Letter, we describe the application of transformation optics to design refractive index distributions that allow perfect, aberration-free imaging for various imaging configurations in Rn. A special case is the imaging between two extended parallel lines in R2, which leads to the well-known hyperbolic secant index distribution that is used for the fabrication of gradient index lenses.
© 2011 Optical Society of America
Original Manuscript: September 27, 2010
Revised Manuscript: December 7, 2010
Manuscript Accepted: December 10, 2010
Published: January 11, 2011
Klaus Mantel, Dustin Bachstein, and Ulf Peschel, "Perfect imaging of hypersurfaces via transformation optics," Opt. Lett. 36, 199-201 (2011)