Free-Form Surface Reconstruction Method from Second-Derivative Data

Abstract

We present an algorithm for surface reconstruction from the second-derivative data for free-form aspherics, which uses a subaperture scanning system that measures the local surface profile and determines the three second-derivative values at those local sampling points across the free-form surface. The three second-derivative data were integrated to get a map of x-and y-slopes, which went through a second Southwell integration step to reconstruct the surface profile. A synthetic free-form surface 200 mm in diameter was simulated. The simulation results show that the reconstruction error is 19 nm RMS residual difference. Finally, the sensitivity to noise is diagnosed for second-derivative Gaussian random noise with a signal to noise ratio (SNR) of 16, the simulation results proving that the suggested method is robust to noise.

Design Method for a Total Internal Reflection LED Lens with Double Freeform Surfaces for Narrow and Uniform Illumination

“…In this method, first the location of a ray of light emitted from the LED to impinge on a target plane is determined, depending on an illumination model selected to form a desired illuminance distribution on the target plane. Then the surface slope of a corresponding incident point on the freeform surface is determined so that the ray incident upon the surface will pass through a designated point on the target plane [8][9][10][11]. Though the freeform surface is easily determined, as long as the related simultaneous differential equations can be derived completely, the luminous ISSN: 1226-4776(Print) / ISSN: 2093-6885(Online) DOI: http://dx.doi.org/10.3807/JOSK.2016.…”

“…The LED lens can be designed using a differential equation method [8][9][10][11], a parameter optimization method [12][13][14][15], or a simultaneous multiple surface (SMS) method [16][17][18], and it often includes one or more freeform surfaces, for the sake of low price and high efficiency. The differential equation method is an LED lens design method in which differential equations relating to the propagation of rays through an LED lens are solved assuming that one surface of the lens is already known; then the other surface is freeform.…”