Numerical comparison of LED directivity approximation functions for video displays

The approximation functions of the directivity of the light emitting diodes (LED) have been investigated. LEDs used in large scale LED video displays have been studied. LED directional properties among the other parameters define the video display image quality. The simplicity of an approximation function and ease of analytical handling have been targeted. These functions suppose to be used in display directivity engineering. Four candidate approximation functions were identified and their approximation performance analyzed. The evaluation is done on eight different type LEDs’ sample batches. These samples have been chosen to represent the variety of the main colors and the range of the most popular viewing angles used in large scale LED video displays design. The relative intensity approximation root mean square (RMS) error and approximation errors’ cross correlation have been used as performance estimation criteria. The radiometric intensity variation within a manufacturing lot was suggested as lower error bound. Approximation error variance was analyzed for various approximation ranges. Results of four candidate approximation functions’ performance on eight different type LEDs’ are presented.

Research highlights
► LEDs used in large scale LED video displays have smooth directivity function therefore simple approximation function is sufficient for LED directivity estimation.
► The simplicity of an approximation function and ease of analytical handling allow these to be used in large scale LED video display directivity engineering and analysis.
► Comparison of four simple functions’ approximation performance on eight different type LEDs’ sample batches is presented.
► The radiometric intensity variation within a manufacturing lot was suggested as lower error bound.
► Investigation indicates that simple, single term functions have 5–8% relative approximation error and are below double lower error bound in reduced angular range, corresponding to display half radiance angle.