17 – DIFFRACTION GRATINGS

Publisher Summary The chapter discusses diffraction gratings. This novel method of engine control and the development of high-fidelity replication processes made a variety of high-quality gratings commercially available in the 1950s. In these developments, every effort had been directed to rule perfectly equispaced parallel grooves. Holographic gratings of this kind are called “holographic gratings,” recorded with aspheric wavefronts to distinguish them from those recorded with spherical (or plane) wavefronts. The grooves of the holographic grating are neither straight nor spaced equally when projected onto the plane tangent to the grating surface at its vertex. In holographic grating, the aberrations and focal property of the grating can be adjusted to meet specific requirements by altering the fringe pattern for changing the curvature and spacing of the grooves. In contrast, a grating with equally spaced and straight grooves does not have such a property. Varied-line-spacing (VLS) ruled gratings can be tailored to meet specific requirements, and are used widely in various research fields. The geometric theory of the diffraction grating can be developed based on a single hypothesis, known as “Fermat's principle.” The third-order aberration theory of the grating can be developed by analytically following the exact ray-tracing formalism with the aid of power series expansions.