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  "body": "\n## Description\n\nLet $f$ be a function on $\\R^2$ with [[Radon transform|VJNZJ352PC]] $R f$.\nParametrize directions by an angle, $\\theta(\\varphi) = (\\cos\\varphi, \\sin\\varphi)$.\nThe *sinogram* of $f$ is the function $(\\varphi, s) \\mapsto R f(\\theta(\\varphi), s)$ on $[0, \\pi) \\times \\R$.\nIt is drawn as an image with the angle $\\varphi$ on one axis and the offset $s$ on the other.\nThe range $[0, \\pi)$ suffices, because $R f(-\\theta, -s) = R f(\\theta, s)$.\n\nCheck of the name: let $f$ be concentrated near a single point $p = (\\abs{p}\\cos\\alpha, \\abs{p}\\sin\\alpha)$, a narrow bump of total mass $1$.\nA line $x \\cdot \\theta(\\varphi) = s$ meets the bump only when $s$ is close to $p \\cdot \\theta(\\varphi) = \\abs{p} \\cos(\\varphi - \\alpha)$.\nSo the sinogram is concentrated near the curve $s = \\abs{p} \\cos(\\varphi - \\alpha)$, a sinusoid in $\\varphi$.\n\nSecond check: take the indicator of a disk of radius $a$ centered at $0$.\nIts sinogram is $2\\sqrt{a^2 - s^2}$ for $\\abs{s} \\le a$ and $0$ otherwise, independent of $\\varphi$: a band of constant profile.\n\n## Explanations\n\n### L1 human\n\nA CT scanner measures, for each angle of the X-ray source, a profile of absorption values along the detector.\nStacking these profiles row by row, one row per angle, gives an image called the sinogram.\nEach small dense spot in the body traces a sine wave across this image, because its shadow moves back and forth on the detector as the source turns.\nA whole body gives a superposition of many such sine waves, and reconstruction means turning the sinogram back into the picture of the body.\n",
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