Abstract: Techniques and systems for decoding optical codes using symbol-based algorithms are described. In one example, a method includes acquiring a signal representative of light reflected from an optical code comprising one or more symbols of a finite set of symbols and applying a decoding model to the signal. The decoding model may relate measured signals to the finite set of symbols, such that each of the symbols of the finite set of symbols are associated with a respective encoded character of a finite set of encoded characters. The method may also include determining, by a processor, a sequence of one or more of the encoded characters based on the application of the decoding model to the signal. In this manner, the optical code may be decoded by directly fitting an acquired signal from the optical code to possible symbols within the optical code and the associated encoded characters.

Abstract: Multifocal optical device designs receive input parameters to specify a desired power distribution function, a power deviation weight function, and an astigmatism weight function over the design field. A fourth-order partial differential variational equation is linearized by defining the optical surface in terms of perturbations from a base surface such as a sphere or a toric. The solution may be expressed as piecewise quadratic splines superposed over a triangulation of the field. Evaluation of the surface may use a set of tensor-product splines. An astigmatic base surface permits both multiple magnifying powers and a prescribed astigmatism correction in a single optical surface.

Abstract: Multifocal optical device designs receive input parameters to specify a desired power distribution function, a power deviation weight function, and an astigmatism weight function over the design field. A fourth-order partial differential variational equation is linearized by defining the optical surface in terms of perturbations from a base surface such as a sphere or a toric. The solution may be expressed as piecewise quadratic splines superposed over a triangulation of the field. Evaluation of the surface may use a set of tensor-product splines. An astigmatic base surface permits both multiple magnifying powers and a prescribed astigmatism correction in a single optical surface.

Abstract: Multifocal optical device designs receive input parameters to specify a desired power distribution function, a power deviation weight function, and an astigmatism weight function over the design field. A fourth-order partial differential variational equation is linearized by defining the optical surface in terms of perturbations from a base surface such as a sphere or a toric. The solution may be expressed as piecewise quadratic splines superposed over a triangulation of the field. Evaluation of the surface may use a set of tensor-product splines. An astigmatic base surface permits both multiple magnifying powers and a prescribed astigmatism correction in a single optical surface.