Dispersion-compensating diffraction grating

Claim 1

A dispersion-compensating transmission grating, formed as a relief pattern on the surface of a refractive optical element, that operated within an optical system to minimize chromatic dispersion, wherein the system comprises one or more optical surfaces (including the grating) that function conjunctively to channel a beam of polychromatic radiation comprising a distribution of wavelengths within a designated design spectrum, wherein the beam's phase in the portion of the beam preceding the grating may be represented by a function Φ, and its phase in the portion following the grating may be represented by a function Φ', wherein Φ and Φ' are functions of position and wavelength (the value of or Φ' at a general positional point P and wavelength being indicated as "Φ|P,λ" or "Φ|P,λ", respectively), the relation Φ|P,λ = 0 defines, for any particular wavelength x, a set of points P comprising a wavefront surface that precedes the first surface intercepted by the beam and is independent of wavelength (i.e., the incident beam at the system's first surface is spatially coherent), and in the system's intended mode of operation Φ' is intended to substantially match an ideal phase distribution Φ' ideal, wherein the relation Φ' ideal|P,λ = 0 defines, for any particular wavelength x, a set of points P comprising a wavefront surface that follows the last surface intercepted by the beam and is independent of wavelength (i.e., the exit beam at the system's last surface is intended to be substantially dispersionless), the grating substrate has a form specified by the condition that, for any two wavelengths λ 1 and X 2 in the design spectrum, the function is significantly less sensitive to position P over the substrate surface than it would be over an optimally-configured conventional refractive surface designed to replace the grating surface, whereby the function satisfies an approximate relation of the form where C is some function that depends only on wavelength, and hence the term (Φ - Φ ideal)|P,λ - C|λ is substantially independent of wavelength and can be represented substantially in terms of some function 0 that depends only on position P: the grating substrate is partitioned into a number of zones, each zone boundary being associated with a unique integer index m, wherein zone boundary m comprises the set of substrate points P for which the equation holds, whereby the grating generates a primary (1st or -1st) diffracted order whose phase function Φ' is implicitly defined at any wavelenqth and substrate point P by the equation from which it follows that Φ' and Φ' ideal are substantially identical over the substrate and throughout the primary diffracted order: and for each index m, zone boundary m is uniquely associated with a grating facet face designated as "face m". wherein each facet face extends over a substrate zone between two adjacent zone boundanes, with face m being bordered on one side by zone boundary m and on the other side by a short-profile facet sidewall joining face m to an adjacent facet face, and wherein the surface of face m between these borders comprises a set of points P defined by the relation where À s is a blaze wavelength (which may be a weakly-varying function of position P), whereby the grating region in the vicinity of a general substrate point P will exhibit high diffraction efficiency at wavelengths near λ B |P.