PET Depth of Interaction and Parallax Error

Depth of interaction (DOI) and parallax error are the reason a PET scanner's spatial resolution is sharpest at the center of the field of view and blurs toward the edge. When a detector cannot tell how deep inside a crystal a 511 keV photon interacted, obliquely incident photons are assigned to the wrong line of response, and the radial blur grows with distance from the scanner axis. DOI-encoding detectors measure that depth and restore uniform resolution. ^{1, 2, 3}

Introduction

Positron emission tomography reconstructs images from pairs of 511 keV annihilation photons detected in coincidence. Each coincidence defines a line of response (LOR) joining the two detector elements that fired, and the reconstruction assumes the annihilation occurred somewhere along that line. The accuracy of that assumption is limited by several physical effects, and one of the most geometry-dependent is the depth of interaction within the scintillator. ¹

A 511 keV photon does not stop at the front face of a crystal. It penetrates a few millimeters, on average, before undergoing a photoelectric or Compton interaction. If the detector records only which crystal fired, not how deep the interaction occurred, it effectively collapses the interaction to a fixed depth. For photons that arrive nearly perpendicular to the detector face, that simplification costs little. For photons that cross the crystal at an angle, it produces a systematic positioning error called parallax error, and the error increases toward the periphery of the field of view (FOV). ^{2, 3}

This matters more today than it did a decade ago. Small-bore preclinical, organ-dedicated, and long-axial-FOV total-body scanners all push geometry in directions that amplify parallax, so DOI capability has moved from a research curiosity to a mainstream design consideration. ^{4, 5} This guide explains the underlying physics, how the resolution loss is quantified, how DOI-encoding detectors work, and what the effect means for quantitative imaging. DRPS supports PET and PET/CT programs through PET/CT and nuclear medicine physics services across Florida, Maryland, Virginia, Washington DC, California, Nevada, Pennsylvania, New York, New Jersey, and Delaware.

Topic Explanation

What "depth of interaction" actually means

In a conventional block or array detector, scintillation crystals are arranged in a ring facing the center of the scanner. When a photon is absorbed, the detector decodes the signal to identify the crystal of interaction in the transverse (and axial) direction, giving a two-dimensional location on the detector face. The third coordinate, the radial depth at which the photon interacted inside the crystal, is usually discarded. ⁴

The depth coordinate is not fixed because photon absorption is a probabilistic, exponential process. The probability that a photon has not yet interacted after traveling a distance $x$ into the crystal follows

P (x) = e^{- μx}

where $μ$ is the linear attenuation coefficient of the scintillator at 511 keV. The mean depth of interaction is therefore the attenuation length, $\overset{ˉ}{d} = 1/ μ$ . For a dense, high- $Z$ scintillator such as LSO or LYSO, the attenuation length at 511 keV is on the order of 12 mm, which is why detector crystals are typically 15–20 mm long to stop most photons. ^{1, 4} The consequence is that the true interaction point is spread across more than a centimeter of crystal depth, and ignoring that spread is what produces parallax error.

What "parallax error" means

Parallax error is the displacement between the true LOR and the LOR the scanner assigns, caused by the unknown depth of interaction combined with an oblique angle of incidence. Consider a photon that enters a crystal at angle $φ$ measured from the crystal's long axis. If it interacts at depth $d$ , the lateral (radial) displacement of that interaction from the crystal's front face is

x_{radial} = d tan φ

Because $d$ is not measured, the scanner assigns a fixed depth, and the positioning error scales with both the depth uncertainty and $tan φ$ . At the center of the FOV, photons arrive almost perpendicular to the ring ( $φ \approx 0$ ), so $tan φ \approx 0$ and the error nearly vanishes. At a large radial offset, $φ$ can approach 45° or more, and the same depth spread now projects into a radial blur of many millimeters. ^{2, 3}

The hallmark of parallax error is therefore non-stationary, non-isotropic resolution: resolution stays good tangentially and near the axis but degrades in the radial direction as the source moves off-center. ²

Key Technical Principles

The budget of resolution-limiting effects

Spatial resolution in PET is a sum, in quadrature, of several independent contributions. Moses's analysis of the fundamental limits identifies the dominant terms as the detector element size, positron range, photon acollinearity, decoding/readout error, and crystal penetration — the last of which is the DOI/parallax term. ¹

Two of these set a geometry-dependent floor:

Acollinearity. The two annihilation photons are not emitted exactly 180° apart; the angular distribution has a full width at half maximum (FWHM) of about 0.5°. This smears the LOR by an amount that grows with ring diameter $D$ :

Δ_{acol} \approx 0.0022 D

For an 80 cm bore ( $D = 800$ mm), $Δ_{acol} \approx 0.0022 \times 800 \approx 1.8$ mm. ¹

Crystal penetration / DOI (parallax). As above, this term is near zero on-axis and grows radially. Using $x_{radial} = d tan φ$ with an LSO attenuation length near 12 mm, a photon crossing at $φ = 45°$ can be mispositioned by roughly $12 \times tan (45°) = 12$ mm before any depth correction. ^{1, 2}

The practical point is that parallax is not a fixed penalty you can subtract once; it is a position-dependent blur that interacts with ring diameter, crystal length, and scintillator density.

How much resolution is actually lost off-center

Monte Carlo and simulation studies put concrete numbers on the effect.

A classic quantitative model by Sánchez-Crespo and Larsson analyzed BGO and other scintillators and reported, for a BGO camera with a 412 mm radius in 2D mode, that the radial resolution loss attributable to DOI grew from about 1.3 mm at the center to about 6.7 mm at 20 cm from the center. When non-collinearity was included, the corresponding figures were about 3.0 mm at the center and 7.3 mm at 20 cm. Their conclusion was blunt: without a DOI technique, it is difficult to improve PET resolution simply by shrinking the ring or extending the axial length. ²

For modern lutetium-based detectors, Schmall and colleagues simulated 4 × 4 × 20 mm LSO crystals and found the transverse resolution (averaging radial and tangential directions) degraded from 4.9 mm at the center to 7.7 mm at a 23 cm radial offset — a parallax-driven loss of nearly 3 mm. The same study showed that long-axial-FOV geometry introduces axial parallax as well: opening the axial acceptance angle to ±67° (a 2 m total-body scanner) degraded axial resolution from 4.8 mm to 5.7 mm at the center, and a two-layer DOI detector recovered part of that, improving axial resolution back to about 5.0 mm. ³

The table below summarizes where parallax error comes from and how it behaves.

Effect	Physical cause	Where it is worst	Depends on	Fixed by DOI?
Radial (transverse) parallax	Oblique incidence + unknown depth in small-ring / off-center geometry	Edge of transverse FOV	Ring diameter, crystal length, scintillator $μ$	Yes — directly
Axial parallax	Large axial acceptance angle in long-AFOV scanners	Ends of axial FOV, oblique planes	Axial FOV length, acceptance angle	Yes — directly
Acollinearity	~0.5° angular spread of annihilation photons	Larger for bigger bore	Ring diameter $D$	No (geometry only)
Positron range	Positron travels before annihilating	Isotope-dependent (worse for high-energy emitters)	Radionuclide	No
Crystal element size	Finite detector pixel pitch	Uniform across FOV	Crystal pitch	No

Geometry trade-offs without DOI

Parallax error forces an uncomfortable design compromise in scanners that lack depth encoding: ^{2, 3, 4}

Smaller ring diameter raises sensitivity and reduces acollinearity blur, but increases oblique incidence and therefore parallax.
Longer crystals stop more photons (higher sensitivity) but give the depth coordinate more room to vary, worsening parallax.
Longer axial FOV dramatically increases sensitivity — total-body designs predict sensitivity gains on the order of 10–40× for whole-body scans compared with a conventional 20 cm axial-FOV system — but the large axial acceptance angles create axial parallax. ⁵

DOI capability relaxes all three trade-offs at once, which is why it is central to small-bore, organ-dedicated, and total-body PET design. ^{4, 5}

Clinical Impact

Quantification, not just sharpness

Parallax blur does more than soften edges. Because PET is a quantitative modality, position-dependent resolution degrades the recovery coefficient for small lesions near the periphery, biasing standardized uptake value (SUV) measurements low where resolution is worst. Non-uniform resolution across the FOV means the same lesion can measure differently depending on where the patient is positioned, which undermines the consistency that quantitative reads and harmonization programs depend on. ³ For related background on how small-structure quantification is affected by resolution, see the partial volume effect in PET and PET detector scintillators and SiPMs.

Small-bore and organ-dedicated systems

Dedicated brain, breast, and preclinical PET systems place the object very close to the detector ring to maximize sensitivity and resolution. That geometry maximizes oblique incidence, so without DOI the resolution gain from a small ring is partly given back as radial parallax at the edges of the organ being imaged. This is precisely the setting where DOI-encoding detectors have shown the largest benefit, enabling sub-millimeter-class resolution with long crystals that would otherwise be unusable. ^{4, 6}

Long-axial-FOV and total-body PET

Total-body scanners such as the 2 m uExplorer and the 70 cm PennPET Explorer accept coincidences across very large axial angles. The sensitivity payoff is enormous, but the oblique axial LORs introduce axial parallax that two-layer or continuous DOI detectors are designed to contain. ^{3, 5} As clinical adoption of long-AFOV systems grows, understanding how a given scanner handles axial parallax becomes part of evaluating its real-world resolution uniformity.

Practical Optimization Tips

DOI-encoding detector designs

Several detector architectures measure or estimate depth. Each trades cost, complexity, and performance differently. ^{4, 6, 7, 8, 9, 10}

DOI approach	How depth is encoded	Reported DOI resolution (FWHM)	Notes
Dual-ended readout	Photosensors on both crystal ends; depth from signal ratio	~2.5 mm (45° tilted SiPM design)	Accurate but needs photosensors at both ends ⁷
Multi-layer / phoswich	Stacked crystal layers identified by decay time or light pattern	Layer-resolved; ~1.45 mm crystals in a 4-layer design	Discrete depth bins; proven in PET/MRI inserts ⁸
Engineered light sharing (e.g., prismatoid light guide)	Single-ended readout with deterministic inter-crystal light sharing	~2.5 mm (Prism-PET, 4-to-1)	Mimics dual-ended behavior with half the sensors; smaller rings possible ⁶
Cross-strip / highly multiplexed	Perpendicular photosensor strips on crystal faces	~2.9 mm	Fewer readout channels; MR-compatible designs ⁹
Statistical / machine-learning estimation	Model- or network-based depth estimate from light distribution	~3.0 mm (neural-network method)	Improves uniformity; can reduce calibration burden ¹⁰

The common thread is that adding depth information narrows the radial blur and makes resolution more uniform across the FOV, often while also improving timing resolution, because DOI lets the system correct depth-dependent time-walk. ^{6, 7}

What a physicist should check

Review the vendor's NEMA report, not just the on-axis number. A single "4 mm resolution" figure usually refers to a 1 cm radial offset. Ask for radial, tangential, and axial FWHM at 10 cm and 20 cm to see how much the scanner degrades off-center. ¹²
Know whether the system has DOI capability and, if so, how many depth bins or what continuous depth resolution it provides. This predicts how flat the radial resolution curve will be.
Use point-spread-function (resolution-recovery) reconstruction appropriately. Modeling crystal penetration in reconstruction partially compensates for parallax, but it cannot recreate depth information the detector never measured — validate quantitative accuracy at the periphery rather than assuming uniformity. ³
Standardize patient positioning so that clinically important anatomy is kept nearer the axis when practical, and so that serial scans place lesions in comparable radial positions for consistent SUV.
Confirm acceptance and periodic QC follow NEMA NU 2 methodology so resolution-versus-position is documented at commissioning and tracked over time. ¹²

For broader context on scanner characterization and the tests that reveal these effects, see PET/CT NEMA NU 2 performance testing and PET point spread function and resolution recovery.

Regulatory Considerations

Performance characterization of PET systems, including spatial resolution as a function of radial position, is governed by the NEMA NU 2 standard. NEMA NU 2-2024, Performance Measurements of Positron Emission Tomographs, is the current edition and defines standardized methods for spatial resolution, sensitivity, scatter fraction, count-rate performance, time-of-flight resolution, and image quality. Spatial resolution is measured with point sources at specified radial offsets (near the center and at 10 cm and 20 cm), which is exactly the measurement that exposes parallax-driven radial degradation. ¹²

NEMA testing is not itself a regulatory license requirement for routine clinical use, but it is the common language for comparing scanners, for acceptance testing, and for documenting that a system performs within specification. A qualified medical physicist typically verifies NEMA-style performance at acceptance and tracks key metrics through the facility's ongoing quality control program. Accreditation bodies expect documented acceptance testing and routine QC, and the physicist's survey is the natural venue to confirm that resolution uniformity, SUV calibration, and reconstruction settings are commissioned and behaving as expected.

Facilities evaluating or commissioning a new PET/CT, PET/MR, or total-body system should fold resolution-versus-position and quantitative accuracy at the periphery into their acceptance criteria, and should align the review with medical physicist consulting and accreditation support.

Frequently Asked Questions (FAQs)

What is depth of interaction (DOI) in PET?

Depth of interaction is the radial depth within a scintillation crystal at which an annihilation photon actually deposits its energy. Because 511 keV photons penetrate several millimeters into the crystal before interacting, the true interaction point is distributed along the crystal length. When a detector cannot measure that depth, it assumes the interaction occurred at a fixed location, which introduces positioning uncertainty.

What is parallax error in PET imaging?

Parallax error is the mispositioning of a line of response that occurs when photons enter a crystal obliquely and the depth of interaction is unknown. The assigned line of response is displaced from the true one, blurring spatial resolution. The effect is small near the center of the field of view and grows larger toward the edge, where incidence angles are steepest.

Why does PET resolution get worse away from the center of the scanner?

Near the center, photons strike the detector ring close to perpendicular, so the unknown depth of interaction causes little lateral error. At radial offsets, photons cross crystals at oblique angles, so the same depth uncertainty projects into a large radial positioning error. Without DOI measurement, radial resolution can degrade substantially from the center to the periphery.

How do DOI-encoding detectors fix parallax error?

DOI-encoding detectors measure or estimate the interaction depth so the reconstruction can place the line of response more accurately. Common approaches include dual-ended readout, multi-layer (phoswich) crystals, engineered light sharing such as prismatoid light guides, and monolithic crystals with statistical positioning. Adding depth information narrows the radial blur and makes resolution more uniform across the field of view.

Does parallax error matter more in small-bore or long-axial-FOV scanners?

It matters in both. Small-ring preclinical and organ-dedicated systems place the object close to the detectors, creating steep transverse incidence angles. Long-axial-field-of-view and total-body scanners accept photons at large axial angles, which introduces axial parallax. Both geometries benefit from depth-of-interaction capability to preserve resolution uniformity.

How is spatial resolution at different radial positions measured?

The NEMA NU 2 standard specifies measuring spatial resolution with point sources at defined radial offsets, typically at 1 cm and at 10 cm and 20 cm from the center of the transverse field of view. Reporting radial, tangential, and axial full width at half maximum at these positions documents how much resolution degrades off-center, which is the signature of parallax error.

Can image reconstruction correct for parallax error without a DOI detector?

Reconstruction can partly mitigate it. Modeling the detector response, including crystal penetration, within a resolution-recovery or point-spread-function reconstruction reduces radial blurring. However, software modeling cannot fully recover information that the detector never measured, so hardware DOI capability remains the most direct way to achieve uniform resolution.

Key Takeaways

Parallax error comes from unmeasured depth of interaction. A 511 keV photon interacts somewhere along a 15–20 mm crystal; if the depth is unknown, obliquely incident photons are assigned to the wrong line of response. ^{1, 4}
The blur is radial and position-dependent. It is near zero on-axis and grows with $tan φ$ toward the edge of the field of view. Reported radial losses run from roughly 1 mm at center to several millimeters at 20 cm offset. ^{2, 3}
Both small rings and long axial FOVs make it worse. Small-bore systems create steep transverse angles; long-AFOV and total-body systems create axial parallax. ^{3, 5}
It is a quantitative problem. Non-uniform resolution biases recovery coefficients and SUV for peripheral lesions, not just image sharpness. ³
DOI-encoding detectors are the direct fix. Dual-ended readout, phoswich layers, engineered light sharing, and statistical estimation all add depth information and flatten the radial resolution curve, often improving timing too. ^{6, 7, 8, 9, 10}
Characterize resolution versus position. Use NEMA NU 2-2024 methodology at acceptance and QC to document off-center resolution rather than relying on a single on-axis number. ¹²

Conclusion

Depth of interaction and parallax error explain one of the most important and most misunderstood facts about PET: a scanner's resolution is not a single number. It is a function of where in the field of view the signal originates. The physics is straightforward — unmeasured interaction depth, projected through oblique incidence, produces a radial blur that grows toward the periphery — but the consequences reach all the way into quantitative accuracy and lesion detectability.

As PET pushes toward smaller organ-dedicated rings and longer total-body geometries, the pressure to measure depth of interaction only increases. DOI-encoding detectors, and reconstruction that models crystal penetration, are the tools that keep resolution uniform across the whole field of view. For facilities selecting, commissioning, or troubleshooting a PET system, the practical takeaway is to look past the headline resolution figure and ask how the scanner behaves off-center.

How DRPS Can Help

Diagnostic Radiation Physics Services helps nuclear medicine and PET/CT programs translate detector physics into practical acceptance testing, QC, and quantitative-imaging decisions. That includes PET/CT and nuclear medicine physics support, NEMA-style performance verification, SUV and quantitative calibration reviews, reconstruction and protocol consultation, and accreditation support aligned with manufacturer specifications and current standards.

DRPS supports facilities across our service locations, including Florida, Maryland, Virginia, Washington DC, California, Nevada, New York, Pennsylvania, New Jersey, and Delaware.

Understanding how a scanner handles depth of interaction is part of knowing what its images can and cannot quantify — especially at the edge of the field of view.

Related Resources

References

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