Abstract: A beacon modulated by a pattern is authenticated by recording an array of light intensities for each point in a field of view; digitizing the array of light intensities; modifying a first array according to the digitized light-intensities and the modulation pattern; repeating these steps for additional frames at the current viewpoint; if the beacon is found then repeating these steps for additional frames; if the beacon is found and additional frames were processed then authenticating the beacon at the point in the current viewpoint corresponding to the value in the first array that exceeds a first threshold by the widest margin; if the beacon was not found, moving to a new point in the field of view and repeating the steps above; if the beacon is again not found, adjusting the modulation bit pattern x bits, and reprocessing the viewpoints in the field of view using the steps above.

Abstract: The present invention is a method of authenticating a beacon, such as used in optical and infrared signaling systems for communication or location determination, and aligning a beacon source and beacon sensor used for pointing or orientation-determining functions.

Abstract: A jump tip apparatus for pool cues having a ferrule end for releasable securement to the tip end of a pool cue in longitudinal alignment with the pool cue, and a resilient striking end in longitudinal alignement with the ferrule end. The resilient striking end having an annular ring on the striking end, with a concave depression extending within the annular ring. The striking end of the jump tip apparatus having a tapered angular profile extending exteriorily from the annular ring towards the ferrule end. The ferrule end of the jump tip apparatus may have external or internal threads sized to threadably engage existing threads on the tip end of the pool cue. Alternately, the ferrule end may be rigid or resilient, with an internal aperture sized to receive the tip end of the pool cue therein.