[wikipedia]
A Computed Tomography (CT) machine acquires xray images from different angles around the head-to-toe axis of the patient.
The machine provides a stack of 2D axial xray "slices" of the patient, giving a 3D view of the internals.
Pre-operative applications are in diagnosis, modelling, and planning.
Intraoperative CT (iCT) can be used for tool guidance (e.g. brachytherapy and biopsy), but out-of-plane tool tracking is difficult as only a slice of the tool appears.
Some facts:
The CT is an xray machine that spins around the patient.
Below, T is the xray tube, X are the xrays, D is the detector, and R is the direction of rotation.
[radiopaedia.org]
CT machines have gone through several generations of development:
[radiologykey.com]
The raw output for one CT slice is a 2D "sinogram", g(θ,ρ):
Angles range in only [0,180] degrees because the rays at angles θ and θ+180 have almost the same attenuation. (Why not the same?)
The value in the sinogram at (θ,ρ) is the total xray attenuation along the corresponding ray, or
∫μ(t)dt ,
where the integral is taken betweeen the xray source and detector.
Recall the Beer-Lambert law:
Iout=Iine−∫μ(t)dt
Then the total xray attenuation stored in the sinogram is
∫μ(t)dt=lnIin−lnIout
Iin is the known energy of the emitted xray.
Iout is the detected energy at the detector element.
Question: What does the sinogram of an isolated fiducial look like?