CT Scanner: Sinograms and Slice Rebuilding

The Rotating Gantry and X-ray Attenuation

Inside a CT scanner, an X-ray tube and an arc of detectors sit bolted to opposite sides of a heavy ring called the gantry, and that entire ring spins around the patient several times per second. As the beam fans out through a thin cross-section of the body, different tissues absorb different fractions of it: dense bone blocks most of the X-rays, soft tissue lets more through, and air-filled lungs barely attenuate the beam at all. The detector array on the far side simply measures how much intensity survived the trip along each ray path. That single measurement, repeated for every ray in the fan and at every rotation angle, is the only raw data a CT scanner ever collects — no photograph of the inside is ever taken directly.

Building the Sinogram, One Angle at a Time

At each gantry angle, the detector array records a full 1D profile: the total attenuation along every parallel ray crossing the slice at that orientation, essentially a shadow of the cross-section from one viewing direction. Stack these profiles as rows in an image, with ray position along one axis and rotation angle along the other, and you get a sinogram — named because a single dense point in the body traces out a sine-wave curve across the image as the angle sweeps through 180 or 360 degrees. A full scan produces hundreds of these angular projections, and the sinogram itself looks nothing like the anatomy; it is a compressed, angle-encoded record that must be mathematically unscrambled before any organ becomes recognizable.

Filtered Back-Projection: From Shadows to Slice

Reconstruction works by reversing the acquisition: take each 1D projection and smear it back across a 2D grid along the same direction it was measured from, a process called back-projection. Doing this naively for every angle and summing the results does recover a blurry version of the original density map, since real structures reinforce each other across many angles while noise mostly cancels out — but the raw sum comes out overly blurred, dominated by a 1/r halo around every dense feature. Filtered back-projection fixes this by first passing each projection through a high-pass filter (mathematically, multiplying its frequency spectrum by a ramp) before smearing it back, which sharpens edges and cancels the blur so the final summed image converges on a faithful cross-section.

Why It Matters: Resolution, Dose, and 3D Anatomy

Every design choice in CT trades against the others: more projection angles and a finer detector pitch sharpen resolution but require more X-ray dose to the patient, so scanners constantly balance image quality against radiation safety, especially in pediatric and repeat imaging. Injected iodine or barium contrast agents boost attenuation differences between tissues that would otherwise look nearly identical, making blood vessels, tumors, and the gut wall stand out. Because a scanner reconstructs one thin slice at a time, moving the patient table through the gantry produces a whole stack of slices that software can restack into a full 3D volume, letting radiologists scroll through the body or render bones and organs from any angle.

Frequently asked questions

Why is the raw sinogram not already a usable image?

The sinogram plots ray-sum attenuation values against ray position and rotation angle, not against physical x-y location in the body, so a single point in the sinogram does not correspond to a single point in the patient. Each pixel of the actual anatomy contributes to many different points across the sinogram, spread out along a sine-shaped curve, and conversely each sinogram value blends contributions from many anatomical points along one ray. Only after reconstruction algorithms like filtered back-projection redistribute and combine all those overlapping ray sums correctly does a spatially meaningful image of organs and tissue emerge. Looked at directly, a sinogram just resembles a grid of wavy grey stripes with no obvious anatomical meaning.

Why does plain back-projection produce a blurry image, and how does filtering fix it?

Simple back-projection smears every 1D projection across the reconstruction grid along its acquisition angle and adds all the smears together. Real dense features do build up correctly because contributions from every angle overlap at the true location, but the smearing also leaves star-shaped streaks and a 1/r intensity falloff radiating outward, since a point source back-projects to a line at every angle, not just at its own location. Filtering counteracts this mathematically: convolving each projection with a ramp-shaped high-pass filter before back-projecting cancels that predictable blur in the frequency domain, so summing the filtered projections converges on a sharp, accurate density map instead of a smeared approximation.

How does a CT scan differ from a plain X-ray photograph?

A plain X-ray photograph collects just one 2D projection through the entire body thickness, so overlapping structures like ribs, lungs, and soft tissue all superimpose onto the same flat image with no depth information. A CT scan instead collects hundreds of thin 1D projections around a single cross-sectional slice from every angle, then reconstructs that slice as a true 2D density map showing exactly where each tissue sits, free of overlap. Repeating this slice by slice down the body and stacking the results yields a full 3D dataset, which is why CT can distinguish a small tumor sitting behind bone or overlapping organs that a plain X-ray would completely hide.

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