Abstract: A method for specifying desired quantities of the energy flux of the combined waves of acoustic radiation pressure to apply producing a mid-air haptic pushing force, which has the effect of simultaneously reducing the harmonic distortion present is described. Further, a method for communicating only the summaries of acoustic field contributions at the required locations in the form of summed portions of the relatively small matrix whose row and column count depend only on the control point count is described. Further, phased arrays of ultrasonic speakers can produce a relatively large amount of acoustic energy which is usually directed in a specific direction or focused to a particular point depending on the application of the array. Further, to allow the system to be driven more strongly than usual, the complex-valued linear system that governs the drive signal to each control point is solved twice.

Abstract: Reducing the maximum output of transducers near boundaries is described. In further refinements, the distribution of the transducer's maximum amplitude is determined by analyzing the Fourier dual of band-limited functions. This enables the Gibbs phenomena, or side lobes, to be effectively mitigated. Further, apodization is used to adjust transducer amplitudes, which in the context of emitting phased arrays, yields output with specific side lobe structure. A modification to the general principles of the method of apodization that are capable of working around transducer limitation will be described. Further, a shared horn structure modifies the distribution of acoustic power over emission angle from a group of transducers.

Abstract: A method for specifying desired quantities of the energy flux of the combined waves of acoustic radiation pressure to apply producing a mid-air haptic pushing force, which has the effect of simultaneously reducing the harmonic distortion present is described. Further, a method for communicating only the summaries of acoustic field contributions at the required locations in the form of summed portions of the relatively small matrix whose row and column count depend only on the control point count is described. Further, phased arrays of ultrasonic speakers can produce a relatively large amount of acoustic energy which is usually directed in a specific direction or focused to a particular point depending on the application of the array. Further, to allow the system to be driven more strongly than usual, the complex-valued linear system that governs the drive signal to each control point is solved twice.

Abstract: A method for specifying desired quantities of the energy flux of the combined waves of acoustic radiation pressure to apply producing a mid-air haptic pushing force, which has the effect of simultaneously reducing the harmonic distortion present is described. Further, a method for communicating only the summaries of acoustic field contributions at the required locations in the form of summed portions of the relatively small matrix whose row and column count depend only on the control point count is described. Further, phased arrays of ultrasonic speakers can produce a relatively large amount of acoustic energy which is usually directed in a specific direction or focused to a particular point depending on the application of the array. Further, to allow the system to be driven more strongly than usual, the complex-valued linear system that governs the drive signal to each control point is solved twice.