Orthonormal derivative polynomial bases for GRIN manufacturability

Orthogonal basis sets have many benefits in the world of optimization problems in lens design. GRIN material manufacturability, while improving with emerging technologies such as 3D printed glasses and plastics, are still limited in their overall change in index from center to edge and more rapid changes in the index on a smaller scale. By utilizing the properties of orthogonal polynomials in the derivatives of non-rotationally symmetric polynomial sets for GRIN materials in a manner similar to Forbes Polynomials for aspheres, the designer is at once able to achieve smoother optimization and an increased intuition of manufacturability. This new QGRN polynomial set has this benefit of the slope of the gradient is the RSS of the coefficients of each polynomial, giving greater intuition into manufacturability for the designer while also retaining similar features related to aberrations in freeform design.