System and method for sensing a paper roll ultrasonically

1. 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.

2. The method of claim 1 further comprising:

indicating, in response to the determining the amount of paper remaining on the paper roll, that the paper roll needs to be replaced.

3. The method of claim 1 wherein the ultrasonic signal has about a 100 nanosecond pulse width.

4. The method of claim 1 wherein the determining the amount of paper remaining on the paper roll comprises:

multiplying the speed of sound by an edge feature time.