Elongation and foreshortening

Elongation and foreshortening are the two halves of one vertical angulation error. An elongated radiograph shows teeth longer than they are; a foreshortened one shows them shorter. Neither is a uniform magnification, so neither can be scaled back out afterwards — which makes them a reading problem, not only a technique one.

Synonyms: elongated image; foreshortened image; vertical angulation error; image distortion; lengthened teeth on radiograph

What are elongation and foreshortening?

They are the same mistake, made in opposite directions.

Vertical angulation is the up-or-down tilt of the beam relative to the tooth and the receptor. When the beam is aimed along the object instead of perpendicular to the line bisecting the tooth–receptor angle, the projected image lengthens. When the beam is left perpendicular to the receptor while the tooth is tilted away from it, the projected image shortens. Aiming perpendicular to that bisecting line — Cieszynski's rule of isometry, and the basis of the bisecting angle technique — greatly reduces the distortion without eliminating it.¹

This is a radiographic artifact of geometry rather than of the receptor or the processing. Nothing has gone wrong with the image. The projection is simply reporting a length the tooth does not have.

Name the relationship early, because it is the one that makes both errors legible. This is the vertical twin of overlapped contacts. Overlap is what horizontal angulation error does to a radiograph; elongation and foreshortening are what vertical angulation error does. The two axes are independent, and a radiograph can carry both at once.²

What they look like, and how you tell them apart

Elongation runs the teeth long. Foreshortening runs them short. That much is the easy half, and it is where most descriptions of this artifact stop.

The hard half is that you cannot reliably tell, from the image alone, that distortion is what you are looking at. Measuring radiopaque gauges fixed to a dry skull on cephalometric films, one study found the projected length could be longer than, shorter than, or the same as the true length, and that which of those had happened "cannot be predicted, corrected, or compensated for from the images alone". Across that setup the projective transformation ranged from 7.32% elongation to 69.63% foreshortening.³

The size of the error tracks the geometry rather than the anatomy. Exposing dry human mandible sections 95 times at angulations from 0° to 40°, length errors were significantly correlated with the tooth's inclination relative to the receptor (p < 0.0001).⁴ So a small deviation gives you a small lie and a large one gives you a large lie, and neither announces itself.

One cue does sit inside the image, for posterior teeth. The beam's angular deviation can be estimated from a cusp height score — the ratio of lingual cusp height to buccal cusp height, multiplied by 100.⁵

What they're confused with

Why it happens

The beam went where the bisector was not.

In a phantom study — a forearm rather than a tooth, but the same projection geometry — a control bone measuring 21.4 cm elongated past the 43 cm edge of the detector when the central ray was aimed along the object, and foreshortened to 13.5 cm when the tube was left straight while the object stayed tilted. Applying the bisecting angle brought it to 24.1 cm: much reduced, not eliminated.¹ A laboratory study of mandibular teeth taken with the bisecting technique found the same directionality directly, with the vertical angle shifted off the correct angle producing foreshortening one way and elongation the other.⁸

Some of it is anatomy rather than operator error. Across 294 plaster models of the upper jaw, the unavoidable angle between a rigid receptor and the tooth's long axis averaged 36.7° for central incisors (range 19–56°) and 42.5° for first molars (range 26–56°).⁷ The periapical radiograph you are looking at may be the best geometry that mouth allows.

Technique choice moves the odds. A systematic review of 26 studies published between 1976 and 2021 found most advocated the paralleling technique for general, endodontic and implant indications, with the bisecting angle technique advocated for patients with a low palatal vault.⁹

What it means clinically

The cost is measurement. Everything on a distorted radiograph that depends on a distance is affected, and the two distances that matter most are bone level and root length.

Bone level. How much angulation it takes is genuinely contested. In five human mandibles imaged as bitewings at −10°, 0° and +10°, the apparent alveolar crest level differed by between 1.84 mm and 3.70 mm at individual sites, with over- and underestimation both occurring.¹⁰ In human skulls, deviation of up to 20° from a 90° baseline changed crest level little in the premolar and incisor regions, with the molars the sensitive site — the same work recommends the bitewing for longitudinal crest-height measurement in the molar region.⁵ The two studies used different tooth regions and expressed crest level differently, which is most of why the numbers diverge. What they agree on is that the inaccuracy scales with how far the beam sits from perpendicular.

That carries into patients. Across 50 periodontally diseased teeth in 50 patients, measured against an intrasurgical gold standard, image filters had a significant influence on the reproducibility of the cementoenamel junction-to-defect measurement in correlation with the vertical angulation difference between images (p = 0.001), and the radiographic measurements tended to overestimate bone loss.²

Root length. In the upper-jaw models above, the resulting foreshortening ranged from 5.4% to 44.1%, an underestimation of true tooth length of up to 44% — and that error cannot be removed by correcting for magnification afterwards.⁷

The practical shape of the risk: distortion moves the apparent crest level and the apparent root length in either direction, and a reader who takes either number at face value is reading the geometry, not the patient.

How to be sure

The question is not whether the radiograph is distorted. It is whether it still answers the question you took it for.

UK guidance rates an image diagnostically acceptable when there are "no errors or minimal errors in either patient preparation, exposure, positioning, image (receptor) processing or image reconstruction and of sufficient image quality to answer the clinical question", and not acceptable when the errors "render the image diagnostically unacceptable". The targets are not less than 95% acceptable for digital images and not less than 90% for film.¹¹

That criterion is the one to read carefully. The standard is the clinical question, not the geometry. A foreshortened radiograph may still settle whether a restoration has an overhang. The same radiograph cannot settle a working length or a crest height, and asking it to is where the harm happens.

When length is the question, the literature offers three things:

• For longitudinal studies of bone height, one study of intraoral radiographs of human skulls recommends measuring the crest-to-CEJ distance on bitewings, particularly in the molar region.⁵
• On posterior teeth, the same study used a cusp height score — lingual cusp height to buccal cusp height, multiplied by 100 — to estimate the beam's angular deviation.⁵
• Reproduce the geometry between visits. In 50 patients, the vertical angulation difference between images was part of what degraded the reproducibility of a crest-level measurement.²

Common errors

Treating a long root as a finding. It is the most expensive mistake on this page, because the image gives you nothing to contradict it.

Assuming digital fixed it. It helped. Comparing 107 film sets with 122 photostimulable phosphor sets exposed on phantoms in preclinical exams, PSP showed significantly less foreshortening, elongation and bending — but significantly more placement and overlapping errors.¹² The vertical error got rarer; it did not go away.

Assuming your set is clean. In an audit of 506 digital periapical radiographs taken by students at one undergraduate clinic and graded against Health Protection Agency standards, 231 (45.7%) were Grade 1, 190 (37.6%) Grade 2, and 85 (16.7%) Grade 3 — diagnostically unacceptable and requiring a repeat.¹³ Those are student operators at a single institution, not general practice, and the grades cover all technique errors together — the audit reports no separate rate for foreshortening or elongation.

Confusing it with a cone cut. A cone cut removes part of the image. Vertical distortion keeps all of it and changes its length.