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TODO: Biology deferred at the user's request: biological tracer behavior and clinical PET applications.

The generic physics of positron emission tomography uses electron-positron annihilation. A slowly moving electron-positron pair predominantly produces two nearly opposite photons with energy close to $m_e{c}^2=511\mathrm{keV}$ each. A ring of detectors records approximately simultaneous interactions; a coincidence identifies a coincidence line of response along which an annihilation could have occurred. Finite Positron travel before annihilation and nonzero pair momentum limit how directly this line identifies the original emission location.

Many such measurements constrain an emission distribution through a tomography model. Attenuation, scattered coincidences, unrelated random coincidences, finite detector resolution and dead time alter the observed counts and require calibration or modeling. With useful time-of-flight information, the arrival-time difference further localizes position along the line: a timing uncertainty $\delta t$ corresponds to a position scale $c\delta t/2$. The coincidence data therefore provide spatial constraints, rather than each event directly supplying a complete three-dimensional image point.

A CT number is a dimensionless relative attenuation measure, conventionally $H=1000({\mu }_{\mathrm{CT}}-{\mu }_{\mathrm{water},\mathrm{CT}})/{\mu }_{\mathrm{water},\mathrm{CT}}$. The X-ray spectrum used in computed tomography has an effective energy far below $511\mathrm{keV}$ and is polychromatic. Its photoelectric absorption contribution depends strongly on composition, whereas water and soft-tissue attenuation at the positron emission tomography energy is mainly Compton scattering. Thus a CT number is neither a $511\mathrm{keV}$ linear attenuation coefficient nor an energy-independent mass attenuation coefficient.

The usual conversion calibrates a piecewise linear or bilinear relation between CT numbers and $\mu (511\mathrm{keV})$. The air–water branch models predominantly density differences in lung and soft tissue; a separate water–bone branch accounts for the different energy dependence of mineralized tissue. The calibration depends on the computed tomography spectrum. After geometric registration, the resulting linear attenuation coefficient map is forward projected along each coincidence line of response to obtain $\exp (\int {\mu }_{511}ds)$. If a mass coefficient is stored, its conversion to a linear coefficient must also include mass density. Unusual high-atomic-number materials can violate the simple tissue calibration, so the conversion is a physical material model, not a universal arithmetic rescaling.^[ref][ref]

In the ideal unscattered coincidence model, let a positron annihilation occur at position $s$ on a coincidence line of response connecting detectors $A$ and $B$. Its two oppositely directed photons must both survive. Their independent attenuation factors multiply:The source position cancels because the complementary path integrals span the whole chord. In a uniform slab of chord length $L$, the same argument is $e^{-\mu s}{e}^{-\mu (L-s)}=e^{-\mu L}$. Therefore attenuation correction requires the full linear attenuation coefficient map along the chord, but not the depth of the particular annihilation along that chord. This argument addresses attenuation of true PET coincidences; scatter, random coincidences and detector efficiency need their own corrections.

A pair of nearly simultaneous detector events treated as a candidate two-photon positron annihilation. True unscattered pairs define a coincidence line of response. For attenuation along one such line, the complementary survival path integrals add to the full chord and are independent of the annihilation depth.