0 ) = − ∫ μ ( x , y ) d l = − ∫ − ∞ ∞ μ ( l ( t ) ) | l ˙ ( t ) | d t p_=\ln(i/i_)=-\int \mu (x,y)\,dl=-_^\mu (l(t))\,|(t)|dt\end (2) here, the direction from the light source toward the screen is defined as the t direction and that perpendicular to the t direction and parallel with the screen is defined as the s direction. (both the ( t , s ) and ( x , y ) coordinate systems are chosen such that they are reflections of each other without mirror-reflective transformation.) by using a parallel beam irradiation optical system, one can experimentally obtain the series of fluoroscopic images (these are one-dimensional images p θ ( s ) (s)} of a specific cross section of a scanned object) for each angle θ between the object and the transmitted light beam. in fig.3, the ( x , y ) plane rotates counter clockwise. around the point of origin in the plane in such a way “to keep mutual positional relationship between the light source (2) and screen (7) passing through the trajectory (5).” rotation angle of this case is same as above-mentioned θ. the beam having an angle θ is the collection of lines l θ , s ( t ) _(t)} , represented by equation (3) below. l θ , s ( t ) = t [ − sin ⁡ θ cos ⁡ θ ] + [ s cos ⁡ θ s sin ⁡ θ ] _(t)=t-\sin \theta \\\cos \theta \\\end+s\cos \theta \\s\sin \theta \\\end (3) the function p θ ( s ) (s)} is defined by equation (4). that p θ ( s ) (s)} is equal to the line integral of μ(x,y) along l [ θ , s ] ( t ) _(t)} of (eq. 3) as the same manner of (eq.2). this means that, p ( s , θ ) of following (eq. 5) is a resultant of radon transformation of μ(x,y). p θ ( s ) = − ∫ − ∞ ∞ μ ( s cos ⁡ θ − t sin ⁡ θ , s sin ⁡ θ + t cos ⁡ θ ) d t (s)=-_^\mu (s\cos \theta -t\sin \theta ,s\sin \theta +t\cos \theta )\,dt} (4) one can define following function of two variables (5). in this article, p ( s , θ ) is the collection of fluoroscopic images. p ( s , θ ) = p θ ( s ) (s)} (5) (2)μ(x, y) is restored by performing inverse radon transform to measurement results “what we want to know (μ(x,y))” can be reconstructed from “what we measured ( p(s,θ))” by using inverse radon transformation . in the above-mentioned descriptions, “what we measured” is p(s,θ) . on the other hand, “what we want to know ” is μ(x,y). so, the next will be "how to reconstruct μ(x,y) from p(s,θ)". spiral ct spiral computed tomographymeshd036542 spiral computed tomography, or helical computed tomography, is a computed tomography (ct) technology in which the source and detector travel along a helical path relative to the object. typical implementations involve moving the patient couch through the bore of the scanner whilst the gantry rotates. spiral ct can achieve improved image resolution for a given radiation dose, compared to individual slice acquisition. most modern hospitals currently use spiral ct scanners. willi kalender is credited with invention of the technique, and uses the term spiral ct. kalender argues that the terms spiral and helical are synonymous and equally acceptable. there are a class of image artifacts specific to helical acquisition. single-slice and multi-slice spiral ct since its invention by kalender in the 1980s, helical scan ct machines have steadily increased the number of rows of detectors (slices) they deploy. the prototype 16 multi-slice scanner was introduced in 2001 and in 2004, 64 multislice scanners are on the market. these can produce an image in less than a second and thus can obtain images of the heart and its blood vessels (coronary vessels) as if frozen in time. in order to illuminate multiple rows of detector elements in a multi-slice scanner, the x-ray source must emit a beam which is divergent along the axial direction (i.e. a cone beam instead of a fan beam). pitch the field of view (fov) multiplied by scan range creates a volume of voxels (abdominal ct pictured). a helical ct beam trajectory is characterized by its pitch, which is equal to the table feed distance along the scan range over one gantry rotation divided by the section collimation. when pitch is greater than 1, the radiation dose for a given axial field of view (fov) is decreased compared to conventional ct. at high pitches there is, however, a trade-off in terms of noise and longitudinal resolution. helical (or spiral) cone beam computed tomography further information: cone beam computed tomography in cone-beam computed tomography (commonly abbreviated cbct), the x-ray beam is conical. helical (or spiral) cone beam computed tomography is a type of three-dimensional computed tomography (ct) in which the source (usually of x-rays) describes a helical trajectory relative to the object while a two-dimensional array of detectors measures the transmitted radiation on part of a cone of rays emanating from the source. in practical helical cone beam x-ray ct machines, the source and array of detectors are mounted on a rotating gantry while the patient is moved axially at a uniform rate. earlier x-ray ct scanners imaged one slice at a time by rotating source and one-dimensional array of detectors while the patient remained static. the helical scan method reduces the x-ray dose to the patient required for a given resolution while scanning more quickly. this is, however, at the cost of greater mathematical complexity in the reconstruction of the image from the measurements. history further information: history of computed tomography the earliest sensors were scintillation detectors, with photomultiplier tubes excited by (typically) cesium iodide crystals. cesium iodide was replaced during the 1980s by ion chambers containing high-pressure xenon gas. these systems were in turn replaced by scintillation systems based on photodiodes instead of photomultipliers and modern scintillation materials (for example rare-earth garnet or rare-earth oxide ceramics) with more desirable characteristics. initial machines would rotate the x-ray source and detectors around a stationary object. following a complete rotation, the object would be moved along its axis, and the next rotation started. newer machines permitted continuous rotation with the object to be imaged slowly and smoothly slid through the x-ray ring. these are called helical or spiral ct machines. a subsequent development of helical ct was multi-slice (or multi-detector) ct; instead of a single row of detectors, multiple rows of detectors are used effectively capturing multiple cross-sections simultaneously.