Method for displaying three-dimensional images using composite driving waveforms

Claim 1

A method for displaying a three-dimensional image in a system including a flexible membrane mirror, a cathode ray tube (CRT) screen, and a loudspeaker for driving the mirror and thereby moving an apparent image plane toward and away from a viewer, comprising the steps of: (a) driving the mirror with a composite waveform h(t) having the following characteristics: ______________________________________ h(t) = A · t for t = 0 to t* h(t) = B · sin(w.sub.B · t) + X for t = t* to (T/2 - t*) h(t) = (A · T/2) - (A · t) for t = (T/2 - t*) to (T/2 + t*) h(t) = B · sin(w.sub.B · t) - X for t = (T/2 + t*) to (T - t*) h(t) = (A · t) - (A · T) for t = (T - t*) to T ______________________________________ wherein "h(t)" is a displacement "h" of the mirror as a function of time, "A" is a slope, having a value greater than zero, of a triangle portion of the waveform h(t), "t" is time, "B" is an amplitude, having an absolute value greater than zero, of a sinusoidal portion of the waveform h(t), "t*" is the time when the triangle portion and sinusoidal portion of the waveform h(t) have equal values and equal slopes, "w B " is a frequency, having a value which is an odd harmonic of a fundamental frequency, of the sinusoidal portion of the waveform h(t), "X" is an offset of the sinusoidal portion of the waveform h(t), and "T" is a fundamental period of the waveform h(t); and (b) displaying a sequence of two-dimensional images synchronized to the displacement of the mirror so that a viewer perceives a three-dimensional image.

Claim 2

A method for displaying a three-dimensional image in a system including a flexible membrane mirror, a cathode ray tube (CRT) screen, and a loudspeaker for driving the mirror and thereby moving an apparent image plane toward and away from a viewer, comprising the steps of: (a) driving the mirror with a composite waveform h(t) having the following characteristics: ______________________________________ h(t) = A · t for t = 0 to t* h(t) = B · sin(w.sub.B · t) + X for t = t* to (T/2 - t*) h(t) = (A · T/2) - (A · t) for t = (T/2 - t*) to (T/2 + t*) h(t) = B · sin(w.sub.B · t) - X for t = (T/2 + t*) to (T - t*) h(t) = (A · t) - (A · T) for t = (T - t*) to T ______________________________________ wherein "h(t)" is a displacement "h" of the mirror as a function of time, "A" is a slope, having a value greater than zero, of a triangle portion of the waveform h(t), "t" is time, "B" is an amplitude, having an absolute value greater than zero, of a sinusoidal portion of the waveform h(t), "t*" is the time when the triangle portion and sinusoidal portion of the waveform h(t) have equal values and equal slopes, "w B " is a frequency, having a value which is an odd harmonic of a fundamental frequency, of the sinusoidal portion of the waveform h(t), "X" is an offset of the sinusoidal portion of the waveform h(t), and "T" is a fundamental period of the waveform h(t); and (b) displaying a sequence of two-dimensional images synchronized to the displacement of the mirror so that a viewer perceives a three-dimensional image.

Claim 3

A method for displaying a three-dimensional image in a system including a flexible membrane mirror, a cathode ray tube (CRT) screen, and a loudspeaker for driving the mirror and thereby moving an apparent image plane toward and away from a viewer, comprising the steps of: (a) driving the mirror with a hybrid waveform h'(t) having the following characteristics: h'(t)=(D.sup.2 /16)[(1/s)-(1/(s+i'(t)))] wherein "h'(t)" is a displacement "h'" of the mirror as a function of time, "D" is a diameter of the mirror, "s" is a distance between the mirror and the CRT screen, and "i'(t)" is a function of time having the following values: ______________________________________ i'(t) = A · t for t = 0 to t* i'(t) = B · sin(w.sub.B · t) + X for t = t* to (T/2 - t*) i'(t) = (A · T/2) - (A · t) for t = (T/2 - t*) to (T/2 + t*) i'(t) = B · sin(w.sub.B · t) - X for t = (T/2 + t*) to (T - t*) i'(t) = (A · t) - (A · T) for t = (T - t*) to T ______________________________________ wherein "A" is a slope, having a value greater than zero, of a triangle portion of the waveform h'(t), "t" is time, "B" is an amplitude, having an absolute value greater than zero, of a sinusoidal portion of the waveform h'(t), "t*" is the time when the triangle portion and sinusoidal portion of the waveform h(t) have equal values and equal slopes, "w B " is a frequency, having a value which is an odd harmonic of a fundamental frequency, of the sinusoidal portion of the waveform h'(t), "X" is an offset of the sinusoidal portion of the waveform h'(t), and "T" is a fundamental period of the waveform h'(t); and (b) displaying a sequence of two-dimensional images synchronized to the displacement of the mirror so that a viewer perceives a three-dimensional image.

Claim 4

A method for displaying a three-dimensional image in a system including a flexible membrane mirror, a cathode ray tube (CRT) screen, and a loudspeaker for driving the mirror and thereby moving an apparent image plane toward and away from a viewer, comprising the steps of: (a) driving the mirror with a hybrid waveform h'(t) having the following characteristics: h'(t)=(D.sup.2 /16)[(1/s)-(1/(s+i'(t)))] wherein "h'(t)" is a displacement "h'" of the mirror as a function of time, "D" is a diameter of the mirror, "s" is a distance between the mirror and the CRT screen, and "i'(t)" is a function of time having the following values: ______________________________________ i'(t) = A · t for t = 0 to t* i'(t) = B · sin(w.sub.B · t) + X for t = t* to (T/2 - t*) i'(t) = (A · T/2) - (A · t) for t = (T/2 - t*) to (T/2 + t*) i'(t) = B · sin(w.sub.B · t) - X for t = (T/2 + t*) to (T - t*) i'(t) = (A · t) - (A · T) for t = (T - t*) to T ______________________________________ wherein "A" is a slope, having a value greater than zero, of a triangle portion of the waveform h'(t), "t" is time, "B" is an amplitude, having an absolute value greater than zero, of a sinusoidal portion of the waveform h'(t), "t*" is the time when the triangle portion and sinusoidal portion of the waveform h(t) have equal values and equal slopes, "w B " is a frequency, having a value which is an odd harmonic of a fundamental frequency, of the sinusoidal portion of the waveform h'(t), "X" is an offset of the sinusoidal portion of the waveform h'(t), and "T" is a fundamental period of the waveform h'(t); and (b) displaying a sequence of two-dimensional images synchronized to the displacement of the mirror so that a viewer perceives a three-dimensional image.