Using the analogy of the Helmholtz equation with the Klein-Gordon equation and the Pauli-Villars approach to the Klein-Gordon equation a a formalism utilizing the powerful techniques of quantum mechanics has been developed for scalar optics including aberrations. This provides an alternative to the traditional square-root approach and gives rise to wavelength-dependent contributions modifying the aberration coefficients.
Dirac-like form of the Maxwell equations is well known in literature. Starting with the Dirac-like form of the Maxwell equations we build a formalism which provides a unified treatment of beam optics and polarization. The traditional results (including aberrations) of the scalar optics are modified by the wavelength-dependent contributions. Some of the well-known results in polarization studies are realized as the leading-order limit of a more general framework of our formalism.
The corrections to the traditional descriptions rigorously derived in the
above articles have a significant bearing on fiber optics.
An application for a patent shall be made in the near future!
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Quadricmeter is the instrument devised to identify (distinguish) and measure the various
parameters (axis, foci, latera recta, directrix, etc.,) completely characterizing the important
class of surfaces known as the quadratic surfaces. Quadratic surfaces (also known as quadrics)
include a wide range of commonly encountered surfaces including, cone, cylinder, ellipsoid,
elliptic cone, elliptic cylinder, elliptic hyperboloid, elliptic paraboloid, hyperbolic cylinder,
hyperbolic paraboloid, paraboloid, sphere, and spheroid. Quadricmeter is a generalized form of
the conventional spherometer and the lesser known cylindrometer (also known as the "Cylindro-Spherometer"
and "Sphero-Cylindrometer").
With a conventional spherometer it was possible only to measure the radii of spherical surfaces.
Cylindrometer can measure the radii of curvature of a cylindrical surface in addition to the spherical
surface. In both the spherometer and the cylindrometer one assumes the surface to be either spherical
or cylindrical respectively. In the case of the quadricmeter, there are no such assumptions.
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