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Derive an equation which will give a minimum detectable fractional change in osteopototic bone, assuming,for simplicity a monenerget beam of incident photon.

User Leigha
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Step-by-step explanation:

To derive an equation for the minimum detectable fractional change in osteoporotic bone using a monochromatic beam of incident photons, we can consider the factors that affect the sensitivity of the measurement.

One important factor is the energy resolution of the detector, which determines the ability of the detector to distinguish between different energies of photons. The energy resolution can be represented by the parameter FWHM (full width at half maximum), which is the width of the energy peak at half of its maximum height. A higher FWHM corresponds to a lower energy resolution, which means that the detector is less sensitive to small changes in energy.

Another factor is the intensity of the incident photon beam, which determines the number of photons that are detected by the detector. A higher intensity corresponds to a higher number of photons and a higher signal-to-noise ratio, which makes it easier to detect small changes in the energy of the photons.

We can combine these factors into an equation that represents the minimum detectable fractional change in osteoporotic bone. Let ΔE be the minimum detectable change in energy of the photons, FWHM be the energy resolution of the detector, and I0 be the intensity of the incident photon beam. We can represent the minimum detectable fractional change in the osteoporotic bone as ΔE/E, where E is the average energy of the photons in the incident beam.

Using these variables, we can write the equation as:

ΔE/E = K * FWHM/I0

where K is a constant that depends on the specific properties of the detector and the measurement setup. This equation shows that the minimum detectable fractional change in osteoporotic bone

User Dennis Calla
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