# What causes 'quantum mottle'?

In medical imaging quantum mottle is described as the "random variation of photons incident on a radiation detector" (Huda,2010). But according to (Rangayyan,2004) is a distinct feature (specifically in PET images) from the random nature of gamma ray emissions. What other quantum effect causes these random variations of photons, i.e. what is the actual cause of quantum mottle?

The 'real' cause is that quantum mechanics is (either actually or unavoidably effectively) random.

When you can afford to get enough counts that isn't a big deal, you just take more data. But in a medial context you want to hold the dose down, so you make do with the bare minimum statistics that will do the trick. Which means that the counting noise will be distinguishable in the resulting image.

To expand a little, when you have a random process that presents events randomly in space or time, and you count the events in some window (spatial or temporal) you will get on average $\text{widow width} \times \text{rate}$ counts, but the number you get on any actual sample will vary a bit (because the process is random). If the density of events if modest, and you were to take many samples you would find the results conforming to a Poisson distribution. If the peak of the distribution represents $N$ counts the width of the peak will be about $\sqrt{N}$. That means the fractional width is $1/\sqrt{N}$ which is negligable for very large $N$ but significant for modest $N$. You need $N \approx 10\,000$ for the variation to run about 1% of the signal.

I'm not certain how much specific knowledge you have on the subject, so I'll try to be thorough without appearing to be condescending.

Radiography works in a similar manner to photography; chemical compounds embedded in film react when exposed to electromagnetic radiation. These reactions allow for chemical development to produce a " shadow image" which is visible to the human eye. Where photographs capture reflected light, radiographic film takes advantage of the properties of x-ray radiation.

This is important to note: x-ray emission does not produce perfectly uniform wavelengths of radiation. There is some variation to the wavelengths which are emitted (hence the aluminum filter), even though the kVp may be adjusted to change the energy (wavelength) of the x-rays, and the current may be adjusted to change the quantity of x-rays, these are not capable of limiting the production to a single, uniform wavelength.

Now, the effect of producing different wavelengths are twofold:

• The varying energies and wavelengths of these x-rays will cause them to pass through matter differently (why do aluminum filters block lower energy x-rays but not higher ones?)
• It takes energy to trigger the chemical reaction on the film; photons lose energy when passing through bone and other dense materials. The less energy they have when reaching the film, the less complete the reaction and thus the lighter the film appears. If you have some x-rays here and there with more initial energy, they will pass through with more ease and produce a darker image.

So, in conclusion, it is the variation in wavelengths of radiation produced which ultimately are responsible for "quantum mottle." The absolute best way to reduce quantum mottle would be to produce more uniform (narrow range of frequencies) x-rays. More practically, exposure could be increased to reduce the grainy appearance, although an increase in exposure with widely distributed frequencies of x-rays should be expected to dramatically reduce the contrast of your image.

It is worth noting that the smaller the ratio of the difference in wavelengths emitted to the difference in energy of photons striking the film, the more clear the image. If the difference in energy of photons making contact with the film is low (energy required to chemically alter the film), then fluctuations in wavelengths will have a more profound effect on the final image. Also, It should go without saying that once the compound undergoes what is essentially a photo-chemical reaction, the reaction can't simply be undone; If the maximum energy required for the reaction is applied, the compound at that location is permanently altered and subsequent photon impacts should have no effect on the image.

Simply put: an x-ray image is produced due to the difference in energy of photons after having passed through matter arrayed across a film. If the variance in energy of the photons before passing through the body were too great, then you would be hard pressed to ever get a clear image.

To simplify my original answer, "Quantum Mottle" is nothing more than an observed effect resulting from exposure to non-uniform distributions of non-uniform radiation. The greater the precision of x-ray producing sources (shorter range of wavelengths produced and more evenly emitted radiation), and/or decreased sensitivity of x-ray detecting equipment, the less prevalent the grainy appearance.

The techniques which are taught in order to produce "high-quality" images free from such phenomenon are more or less means of optimizing the use of imperfect devices.