Patent ID: 7464594

Claim:
A method of sensing paper on a paper roll, the method comprising: transmitting an ultrasonic signal into the paper roll; detecting an ultrasonic return echo transmit signal from the paper roll, the ultrasonic return echo transmit signal resulting from the ultrasonic signal interacting with the paper roll; and determining an amount of paper remaining on the paper roll in response to the ultrasonic return echo transmit signal, wherein a length of paper remaining on the paper roll is determined in accordance with the expression: L =( D o 2− D i 2 )π/4 T : where L is the length of paper remaining on the paper roll, D o is an outer diameter of the paper roll, D i is an inner diameter of the paper roll, wherein the inner diameter of the paper roll is equivalent to an outside diameter of a carrier on which the paper roil is disposed, and T is a thickness of one layer of the paper on the paper roll.