Curved diffractive optical elements: Design and applications

This chapter reviews the research on diffractive optical elements that are fabricated on curved surfaces. For the design of such elements, the substrate shape as well as the grating function may be used as free parameters, leading to a more flexible design than is possible for flat diffractive optical elements. It is shown that when a diffractive optical element (DOE) is fabricated on a curved substrate, the shape of the substrate can provide additional degrees of freedom in the design. The chapter reviews the properties of spherical/cylindrical curved diffractive optical elements (CDOEs) and their applications for aberration-free imaging and Fourier transformation. Aplanatic spherical/cylindrical CDOEs satisfying the sine condition are also capable of concentrating quasi-monochromatic diffuse light onto a flat target at the theoretical limit imposed by brightness conservation. The application of CDOEs for optical transformations is discussed and the principle with optical systems capable of coordinate transformation is illustrated in the chapter.