  Proton computed tomography (CT) is similar to x-ray CT but relies on protons
rather than photons to form an image. In its most common operation mode, the
measured quantity is the amount of energy that a proton has lost while
traversing the imaged object from which a relative stopping power map can be
obtained via tomographic reconstruction. To this end, a calorimeter which
measures the energy deposited by protons downstream of the scanned object has
been studied or implemented as energy detector in several proton CT prototypes.
An alternative method is to measure the proton's residual velocity and thus its
kinetic energy via the time of flight (TOF) between at least two sensor planes.
In this work, we study the precision, i.e. image noise, which can be expected
from TOF proton CT systems. We rely on physics models on the one hand and
statistical models of the relevant uncertainties on the other to derive closed
form expressions for the noise in projection images. The TOF measurement error
scales with the distance between the TOF sensor planes and is reported as
velocity error in ps/m. We use variance reconstruction to obtain noise maps of
a water cylinder phantom given the scanner characteristics and additionally
reconstruct noise maps for a calorimeter-based proton CT system as reference.
We find that TOF proton CT with 30 ps/m velocity error reaches similar image
noise as a calorimeter-based proton CT system with 1% energy error (1 sigma
error). A TOF proton CT system with a 50 ps/m velocity error produces slightly
less noise than a 2% calorimeter system. Noise in a reconstructed TOF proton CT
image is spatially inhomogeneous with a marked increase towards the object
periphery. This systematic study of image noise in TOF proton CT can serve as a
guide for future developments of this alternative solution for estimating the
residual energy of protons after the scanned object.
