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Rochester, NY, United States

Forbes G.W.,QED Technologies Inc.
Optics Express | Year: 2010

Whether in design or the various stages of fabrication and testing,an effective representation of an asphere's shape is critical. Some algorithms are given for implementing tailored polynomials that are ideally suited to these needs. With minimal coding, these results allow a recently introduced orthogonal polynomial basis to be employed to arbitrary orders. Interestingly, these robust and efficient methods are enabled by the introduction of an auxiliary polynomial basis. © 2010 Optical Society of America. Source


Forbes G.W.,QED Technologies Inc.
Optics Express | Year: 2010

Mathematical methods that are poorly known in the field of optics are adapted and shown to have striking significance. Orthogonal polynomials are common tools in physics and optics, but problems are encountered when they are used to higher orders. Applications to arbitrarily high orders are shown to be enabled by remarkably simple and robust algorithms that are derived from well known recurrence relations. Such methods are demonstrated for a couple of familiar optical applications where, just as in other areas, there is a clear trend to higher orders. © 2010 Optical Society of America. Source


Forbes G.W.,QED Technologies Inc.
Optics Express | Year: 2011

Some simple measures of the difficulty of a variety of steps in asphere fabrication are defined by reference to fundamental geometric considerations. It is shown that effective approximations can then be exploited when an asphere's shape is characterized by using a particular orthogonal basis. The efficiency of the results allows them to be used not only as quick manufacturability estimates at the production end, but more importantly as part of an efficient design process that can boost the resulting optical systems' cost-effectiveness. © 2011 Optical Society of America. Source


Forbes G.W.,QED Technologies Inc.
Optics Express | Year: 2013

Orthogonality is exploited for fitting analytically-specified freeform shapes in terms of orthogonal polynomials. The end result is expressed in terms of FFTs coupled to a simple explicit form of Gaussian quadrature. Its efficiency opens the possibilities for proceeding to arbitrary numbers of polynomial terms. This is shown to create promising options for quantifying and filtering the mid-spatial frequency structure within circular domains from measurements of as-built parts. © 2013 Optical Society of America. Source


Forbes G.W.,QED Technologies Inc.
Optics Express | Year: 2012

A recently introduced method for characterizing the shape of rotationally symmetric aspheres is generalized here for application to a wide class of freeform optics. New sets of orthogonal polynomials are introduced along with robust and efficient algorithms for computing the surface shape as well as its derivatives of any order. By construction, the associated characterization offers a rough interpretation of shape at a glance and it facilitates a range of estimates of manufacturability. © 2012 Optical Society of America. Source

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