Bragg peak range uncertainties are a persistent constraint in proton therapy. Pulsed proton beams generate protoacoustic emissions proportional to absorbed proton energy, thereby encoding dosimetry information in a detectable acoustic wave. Here, we seek to derive and model 3D protoacoustic imaging with an ultrasound array and examine the frequency characteristics of protoacoustic emissions. A formalism is presented through which protoacoustic signals can be characterized considering transducer bandwidth as well as pulse duration of the incident beam. We have also collected an experimental proton beam intensity signal from a Mevion S250 clinical machine to analyze our formalism. We also show that proton-acoustic image reconstruction is possible even when the noise amplitude is larger than the signal amplitude on individual transducers. We find that a 4μ s Gaussian proton pulse can generate a signal in the range of MHz as long as the spatial heating function has sufficiently high temperature gradients
