CT Beam Hardening Artifacts: Causes and Correction

Beam hardening is a spectral artifact: a CT x-ray beam contains many photon energies, and because the lower-energy photons are preferentially absorbed, the beam's mean energy rises as it crosses the patient, which the reconstruction misreads as a change in tissue attenuation. The visible consequences are cupping in uniform regions, dark bands between dense bones, and Hounsfield-unit values that drift with patient size — all of which degrade both image interpretation and any quantitative use of the CT number.¹²

Modern scanners suppress most beam hardening with beam filtration and a water-based software correction, but residual effects persist and can be amplified by bone, iodinated contrast, and metal. Understanding the physics is what lets a radiologist recognize a beam hardening artifact as an artifact rather than pathology, and lets a medical physicist verify that the correction is working during quality control.¹³

Introduction

Computed tomography reconstructs a map of linear attenuation coefficients from a large number of transmission measurements. The mathematics of filtered back-projection and iterative reconstruction assume that attenuation along each ray is a single, well-defined quantity. In reality, the x-ray beam is polychromatic — it spans photon energies from a few tens of keV up to the tube potential — and attenuation depends strongly on energy. This mismatch between the monochromatic assumption of the reconstruction and the polychromatic reality of the beam is the root of beam hardening.¹²

Beam hardening was recognized in the earliest days of clinical CT, and the first correction methods were published in the late 1970s.² It remains relevant today because CT is increasingly used quantitatively — for CT-to-electron-density conversion in radiation therapy, for tissue characterization, and for perfusion measurement — and because contrast agents, orthopedic hardware, and larger patients all stress the correction.³⁶

This guide explains what beam hardening is, how it manifests, the physics and mathematics behind it, the hardware and software corrections that address it, its clinical impact, practical steps to minimize it, the regulatory and quality-control context, and the questions clinical teams ask most often.

Topic Explanation

What is beam hardening?

Beam hardening is the progressive increase in the mean energy of a polychromatic x-ray beam as it passes through an attenuating medium. Because low-energy ("soft") photons are removed from the beam more efficiently than high-energy ("hard") photons, the surviving beam becomes, on average, more penetrating — "harder" — the farther it travels through tissue.¹

A few terms recur throughout this guide:

• Polychromatic (polyenergetic) beam — an x-ray beam containing a continuous spectrum of photon energies, as produced by a diagnostic x-ray tube.
• Effective (mean) energy — a single energy used to summarize a polychromatic beam's behavior. Beam hardening is, in effect, an increase in this effective energy with depth.
• Linear attenuation coefficient ($\mu$) — the probability per unit path length that a photon is removed from the beam. It decreases with increasing photon energy over the diagnostic range.
• Hounsfield unit (HU) — the CT number, a normalized expression of $\mu$ relative to water.
• Cupping — a beam hardening appearance in which the measured attenuation of a uniform object is lower at its center than at its edge.

Why a polychromatic beam creates an artifact

The attenuation of a monochromatic beam of intensity $I_0$ through a uniform object of thickness $x$ follows the Beer–Lambert law:

so the measured projection (the logarithm of transmission) is linear in path length:

This linearity is exactly what the reconstruction relies on. For a polychromatic beam, however, each energy $E$ has its own attenuation coefficient $\mu (E)$, and the transmitted intensity is an integral over the spectrum $S(E)$:

The measured projection is no longer linear in $x$. Because soft photons are stripped out first, $\mu$ effectively falls as the path lengthens, so the projection grows more slowly than $\mu x$ would predict. When the reconstruction treats this sub-linear projection as if it were linear, it assigns too little attenuation to the deepest parts of the object — the origin of cupping and of the dark bands that connect dense structures.¹²

How beam hardening shows up

Beam hardening produces three related effects:¹

1. Cupping. In a large, uniform region such as the water in a phantom or a patient's abdomen, the center reads lower in HU than the periphery because the central rays traverse the most tissue and harden the most.
2. Streaks and dark bands. Between two dense objects — classically the petrous bones of the skull base, but also metal implants or contrast-filled vessels — rays that pass through both are hardened the most, creating dark bands and streaks. In the head this is the familiar interpetrous or posterior-fossa artifact (sometimes called the Hounsfield bar).
3. CT number inaccuracy. Even away from obvious streaks, residual beam hardening shifts absolute CT numbers and makes them depend on object size and the surrounding anatomy, which undermines quantitative use.

Key Technical Principles

Quantifying the cupping error

The CT number is defined relative to water:

so water is 0 HU and air (with $\mu \approx 0$) is $-1000$ HU by construction. This relationship also lets us translate a fractional error in the apparent attenuation coefficient directly into an HU error. The classic analysis of beam hardening correction showed that systematic errors in the uncorrected attenuation coefficient of water are on the order of 5% and can be reduced to under 1% once a correction is applied.²

Consider the center of a uniform water phantom where beam hardening has depressed the apparent coefficient by 5%, so that the reconstruction recovers $\mu =0.95{\mu }_{\text{water}}$ instead of ${\mu }_{\text{water}}$. The resulting CT number is:

A 5% coefficient error therefore corresponds to a 50-HU depression at the center relative to the edge — a cupping magnitude that is unmistakable on a uniform phantom and large enough to mimic or mask real low-contrast findings in a patient. Applying a correction that brings the coefficient error under 1% shrinks the cupping to about 10 HU or less, which is why uncorrected head and body scans are essentially never used clinically.²

The effective-energy picture

A convenient way to summarize hardening is through the effective energy of the beam, which can be estimated from its half-value layer (HVL). As the beam penetrates, soft photons are removed, the HVL increases, and the effective energy rises. A diagnostic body CT beam at 120 kVp has an effective energy in roughly the 60–75 keV range at the patient surface, and this climbs with depth. Because $\mu$ for soft tissue and bone both fall with increasing energy — but at different rates, since bone retains a larger photoelectric component — the relative contrast between bone and soft tissue also changes with depth, compounding the artifact near bone.¹³

Hardware correction: filtration and the bowtie

The first line of defense is to harden the beam deliberately before it reaches the patient, so that the additional hardening within the patient is a smaller relative change:¹

• Flat added filtration (typically aluminum, sometimes with copper or other materials) removes the softest photons at the tube, raising the entrance effective energy.
• A shaped "bowtie" filter adds progressively more filtration toward the edge of the fan beam, where rays pass through less of the patient, equalizing the hardening across the field of view and reducing cupping. The bowtie is matched to the scan field of view, which is why selecting the correct field of view (head versus body) matters for artifact control as well as dose.

Pre-hardening cannot eliminate the effect, because the patient still adds path-dependent hardening, but it makes the residual smaller and more uniform so that the software correction has an easier job.

Software correction: water linearization

The dominant software correction restores the linearity the reconstruction expects. Because soft tissue is approximately water-equivalent, scanner manufacturers calibrate a water-linearization (monochromatic-equivalent) function that maps the measured polychromatic projection $p_{\text{meas}}$ to the projection a monochromatic beam would have produced, $p_{\text{mono}}$. In practice this is a polynomial fit, for example:

with coefficients determined from calibration scans of water phantoms of different diameters. This single-material correction removes nearly all cupping in soft-tissue-only anatomy and is applied automatically on every clinical scan.²⁵

Water linearization cannot fully correct hardening caused by bone, iodine, or metal, because those materials harden the beam differently than water does. Residual bone-induced streaks are addressed by higher-order and iterative corrections that estimate the bone contribution from a first reconstruction, then recompute and subtract its hardening effect — a segmentation-based approach that can be computationally intensive and depends on accurate segmentation.²⁶ More recent automatic and calibration-based methods reduce residual multi-material artifacts without requiring explicit knowledge of the x-ray spectrum.⁵⁶

Spectral approaches: dual-energy and photon-counting

Because beam hardening is fundamentally an energy-dependence problem, acquiring energy-resolved data attacks it at the source:

• Dual-energy CT acquires data at two tube potentials (or with a dual-layer or fast-kV-switching system) and reconstructs virtual monoenergetic images at a chosen keV. Because a monoenergetic image represents a single energy, it is intrinsically free of the polychromatic hardening effect, and higher-keV virtual monoenergetic images are routinely used to suppress beam hardening and metal-related streaks while trading off iodine contrast.³
• Photon-counting detector CT, an emerging technology, measures the energy of individual photons rather than integrating total signal. Energy-resolved data allow spectral reconstructions that can correct beam hardening and improve quantitative accuracy relative to conventional energy-integrating detectors.⁴

The table below summarizes how the main approaches relate to the appearances they address.

Clinical Impact

Beam hardening matters because it can both hide and mimic pathology, and because it corrupts quantitative CT numbers. In the posterior fossa, the interpetrous dark band can obscure the brainstem and simulate or conceal low-density lesions; recognizing it as a beam hardening artifact rather than infarct or hemorrhage is a routine but important interpretive skill.¹

Near orthopedic hardware, dental fillings, and contrast-filled structures, hardening contributes to the streaks that reduce diagnostic confidence in adjacent tissue — for example, around hip prostheses or in the maxillofacial region. Metal artifact reduction techniques and higher-keV virtual monoenergetic reconstructions are deployed specifically to recover this anatomy.³

Quantitative applications are the most sensitive. When the CT number is used as a physical measurement rather than a display value, residual beam hardening introduces bias. In radiation therapy planning, CT numbers are converted to electron density for dose calculation, and size- and position-dependent HU drift propagates into the plan. In cardiac CT perfusion, beam hardening from contrast in the ventricular cavities can create apparent myocardial perfusion deficits; dedicated automatic beam hardening correction algorithms have been developed and validated against spectral reference images precisely to keep these flow measurements accurate.⁶ Any program that reads CT numbers as data — not just pictures — needs to account for the residual artifact. Our discussion of CT number (HU) calibration and QC covers how these values are checked and maintained.

Practical Optimization Tips

Choose acquisition settings that minimize hardening

• Match the field of view and bowtie to the anatomy. Using a head field of view for head scans and a body field of view for body scans ensures the shaped filter is appropriate and keeps cupping controlled.
• Center the patient in the gantry. Off-center positioning places anatomy where the bowtie filtration no longer matches the path lengths, which can worsen cupping and CT number inaccuracy. Good centering helps both artifacts and dose, as discussed in our note on CT patient centering.
• Consider higher tube potential or added filtration for large patients or dense anatomy when it is dosimetrically appropriate, since a harder entrance beam reduces the relative hardening added by the patient.
• Use spectral or virtual monoenergetic reconstructions where available for anatomy dominated by bone, metal, or dense contrast.

Verify the correction during quality control

A beam hardening correction that drifts or is misconfigured shows up quickly in uniformity testing. During acceptance and annual physics evaluations, a medical physicist should:

• Scan a uniform water or water-equivalent phantom and measure CT number uniformity by comparing a central region of interest with peripheral regions. Residual cupping appears as a center-to-edge HU difference.
• Measure the CT number of water to confirm it sits near 0 HU without a systematic offset.
• Repeat across the clinically used field-of-view and reconstruction settings, because the correction is tied to the scan geometry.

These checks are standard components of the ACR CT accreditation phantom evaluation and of routine CT physics surveys. The ACR CT accreditation phantom specifies nominal CT numbers for water near 0 HU and for its other inserts, and evaluates uniformity by comparing peripheral regions of interest to the center.

Do not confuse beam hardening with other artifacts

Cupping and streaks also arise from scatter, photon starvation, and partial-volume effects. Distinguishing them matters because the corrections differ: photon starvation is a dose/noise problem addressed by technique and reconstruction, while beam hardening is a spectral problem addressed by filtration, linearization, and spectral imaging. Our broader guide to CT image artifacts, causes, and correction places beam hardening alongside the other major artifact classes.

Regulatory Considerations

CT scanners are regulated as radiation-producing machines, and beam hardening correction is part of the performance that acceptance testing and periodic physics surveys confirm. Unlike radioactive material, which falls under NRC or Agreement State materials licensing, CT equipment is regulated through a combination of federal equipment standards and state radiation-control programs.

• Federal equipment standard. CT equipment manufactured in the United States must meet the FDA performance standard at 21 CFR 1020.33, which governs CT system performance and dose information. Beam quality and filtration — the first line of beam hardening control — are part of system design and acceptance.
• Accreditation. The ACR CT Accreditation Program requires phantom-based image-quality testing, including CT number accuracy and uniformity measurements that are directly sensitive to residual beam hardening, together with an annual evaluation by a qualified medical physicist. The ACR–AAPM technical standard for CT physics performance monitoring and AAPM Report No. 233 describe the performance tests a physicist applies to modern CT systems.⁷
• State rules. X-ray-producing machines are regulated by state radiation-control programs. In Florida, diagnostic x-ray machines including CT are administered under Florida Administrative Code Chapter 64E-5, Part V; DRPS also serves Maryland, Virginia, Washington DC, California, Nevada, Pennsylvania, New York, New Jersey, and Delaware, where parallel state programs impose equipment-performance and physicist-survey expectations. Always confirm requirements with the authority having jurisdiction.

A physicist's acceptance test and annual survey document that the installed scanner's beam hardening correction is functioning — that water reads near 0 HU and uniformity is within tolerance — which is what ties the physics of this artifact to a facility's compliance obligations.

Frequently Asked Questions (FAQs)

What causes beam hardening in CT?

A CT beam is polychromatic — it contains a spectrum of photon energies. As the beam passes through tissue, lower-energy photons are absorbed more readily than higher-energy photons, so the mean energy of the surviving beam increases. Because the reconstruction assumes a single effective attenuation behavior, this energy shift is misinterpreted as a change in attenuation, producing artifacts.¹²

What does a beam hardening artifact look like?

The two classic appearances are cupping, where the center of a uniform object reads lower in Hounsfield units than its periphery, and dark bands or streaks between dense structures such as the petrous bones in the posterior fossa or between metal and bone. Beam hardening can also shift absolute CT numbers and make them depend on patient size.¹

How do CT scanners correct for beam hardening?

Scanners combine several strategies: a flat added filter and a shaped bowtie filter pre-harden the beam, and the reconstruction software applies a water-based linearization correction that converts the measured polychromatic projections to the values a monochromatic beam would have produced. Iterative and empirical bone-correction methods, dual-energy virtual monoenergetic images, and photon-counting detectors reduce residual artifacts further.²³⁴⁵

Does beam hardening affect CT number accuracy for quantitative work?

Yes. Residual beam hardening is one reason the CT number of a given tissue can shift by several Hounsfield units with changes in patient size, position, or the surrounding anatomy. This matters for any application that treats the CT number as a quantitative value, including CT-to-electron-density conversion for radiation therapy planning and tissue characterization.³⁶

Is beam hardening the same as photon starvation?

No. Beam hardening is a spectral effect caused by the energy dependence of attenuation. Photon starvation is a noise effect caused by too few photons reaching the detector through a highly attenuating path, which produces noisy streaks. Both can occur together — for example across the shoulders — but their causes and corrections differ.¹

Can a medical physicist detect beam hardening during routine QC?

Yes. Scanning a uniform water or water-equivalent phantom and measuring CT number uniformity — comparing center and peripheral regions of interest — reveals residual cupping, and measuring the CT number of water checks for a systematic offset. These are standard components of CT acceptance testing and annual physics surveys under accreditation and state programs.⁷

Key Takeaways

• Beam hardening arises because the CT beam is polychromatic and attenuation depends on energy; as soft photons are stripped out, the beam's mean energy rises with depth.¹²
• The artifact appears as cupping in uniform regions, dark bands and streaks between dense structures, and CT numbers that drift with patient size.¹
• A roughly 5% error in the apparent attenuation coefficient corresponds to about a 50-HU depression; corrections bring this under about 1% (near 10 HU or less).²
• Hardware filtration and the bowtie pre-harden the beam; water linearization restores projection linearity for soft tissue; iterative/empirical bone corrections, dual-energy virtual monoenergetic images, and photon-counting detectors address residual multi-material effects.²³⁴⁵⁶
• Quantitative CT — radiation therapy planning, perfusion, tissue characterization — is the most sensitive to residual beam hardening.³⁶
• Uniform-phantom CT number uniformity and water-value checks during acceptance and annual surveys confirm the correction is working.⁷

Conclusion

Beam hardening is one of the oldest recognized CT artifacts and remains one of the most consequential, because it sits at the intersection of image interpretation and quantitative accuracy. Its cause — the energy dependence of attenuation acting on a polychromatic beam — is simple to state but produces a family of appearances, from the posterior-fossa dark band to size-dependent HU drift. Modern scanners control it with a layered strategy of beam filtration, water linearization, higher-order and iterative corrections, and increasingly spectral acquisition. The role of the medical physicist is to verify, through uniform-phantom QC, that these corrections are doing their job, so that both radiologists and quantitative applications can trust the numbers the scanner reports.¹²³

How DRPS Can Help

Diagnostic Radiation Physics Services (DRPS) supports CT facilities across Florida, Maryland, Virginia, Washington DC, California, Nevada, Pennsylvania, New York, New Jersey, and Delaware with CT physics testing, ACR accreditation support, acceptance testing of new scanners, and annual physics surveys performed by board-certified medical physicists. Our evaluations include CT number accuracy and uniformity testing that directly verify beam hardening correction, along with protocol review to keep image quality and dose optimized. When a quantitative application — radiation therapy planning or perfusion — depends on CT numbers, we help facilities establish the measurements and documentation that keep those numbers defensible.

Related Resources

• CT image artifacts: causes and correction
• CT number (HU) calibration and QC
• Dual-energy CT spectral imaging
• Photon-counting CT physics and image quality
• ACR CT accreditation phantom QC
• CT physics testing services

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