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New gamma camera design

Dear Reader,

Having an academic interest in nuclear accident chemistry I search the literature every now and then for articles which mention “Fukushima”, I saw one which caught my interest it was about an idea which I think is truly interesting. It is about the age old problem of how do we see radiation.

Now two easy to imagine gamma camera’s exist, these are the pin hole type and the gamma camera with lots of holes, each hole has a well collimated detector at the bottom of it. These gamma cameras will require plenty of heavy lead shielding to operate and collect nice pictures. When the gamma energy is low (such as Am-241 or I-131) it will be possible to make these machines but when the gamma energy is much higher (Cs-137 or Co-60) it will be very hard to build these gadgets as the gamma rays need thick layers of lead to stop them.

Here is the most simple design the pin hole camera which uses a small hole to make the image appear.

Pin hole camera

Pin hole camera

The second design is the array of holes, this will work as long as the holes are much longer than their diameter. Also it will work better with low energy gamma emitters as they are easier to stop in the shielding. If the maker of the camera is clever there are some things that they can do to improve the image such as moving the camera around to reduce the effect of the grid of holes on the picture. In the following diagram it should be clear that while the red gamma ray can reach the thick black detector plate the blue and purple rays are blocked by the lead in the shielding / holes array.

Gamma camera design two

Gamma camera design two

The Compton effect camera works in a different and much smarter way, it uses something known as Compton scattering of gamma rays and two detector arrays. The idea is that when a gamma ray scatters off an electron it changes direction and at the same time loses some energy. At a bare minimum what is needed is an energy dispersive detector at the back of the camera and an ordinary detector at the front of the camera.

The geometry of the Compton camera

The geometry of the Compton camera

The classic formula for Compton scattering is

λ’ – λ = (h/mec).(1- cos θ)

We can rearrange and alter it a little to get

cos θ = 1 – [(c2 me)/E’] + [(c2 me)/E]

cos θ – 1 = [(c2 me)/E] – [(c2 me)/E’]

(cos θ – 1) / (c2 me) = 1/E – 1/E’

(c2 me) / (cos θ – 1) = E – E’

(c2 me/h) / (cos θ – 1) = v – v’

(cos θ – 1)(h / c2 me)  = (1/v) – (1/v’)

(cos θ – 1)(h / c me)  = (c/v) – (c/v’) = λ’ – λ

(cos θ – 1)  = (λ’ – λ)/(h / c me)

cos θ = 1 + (λ’ – λ)/(h / c me)

θ = cos-1 {1 + (λ’ – λ)/(h / c me)}

θ = cos-1 {1 + (λ’ – λ)/(h / c me)}

Now that algebra was fun, to digress the other day I speculated what would happen in a world where children were banned from doing maths and were forced to play video games and do facebook all day at school. I suspected that some children would rebel by forming illegal underground maths clubs where at clandestine meetings they would study geometry and calculus. Maybe they would pass around maths textbooks behind the bike shed or in the woods, some lads might hide a cache of maths books in their bed rooms out of reach and sight of their mothers. Just imagine the shock and horror of a woman when she discovers her 15 year old son is hanging around fully clothed with an immoral maths freak girl who is doing Laplace transformations, or maybe her son has fallen in with the bad of the bad Fourier transformers.

But back to the real world

If we assume that we have a monochromatic gamma source such as the 137mBa formed from 137Cs then we will have a original gamma energy (E) of 662 keV (1.0606 x 10-13 J), as we know the electron rest mass and the speed of light we can from the energy of the photon after scattering work out the angle it was scattered through.

If the Compton camera is used to image when the background is high or when the source emits photons with several different energies then the front detector also needs to be an energy dispersive detector. For example if we were to image a X-ray source or 192Ir source then we would need both detectors to be energy dispersive. We also have the advantage if both detectors are energy dispersive that we will also get a gamma spectrum from the object. This could be an advantage if two different sources are present in the field of view of the camera.

Here is a graph of the energy of the product photon as a function of the scattering angle.

Scattered photon energy as a function of scattering angle

Scattered photon energy as a function of scattering angle

For those of you who like log scales here is the graph with a log scale for the y axis

Graph of energy of scattered photon as a function of scattering angle for four different original gamma photons

Graph of energy of scattered photon as a function of scattering angle for four different original gamma photons

What happens in Compton scattering is that the photon scatters off an electron, the electron gains some of the energy of the photon. As the gamma photons have much more energy than the electrons it can be regarded as gamma photons bouncing off stationary electrons. As the electron takes some of the energy away from the photon the scattered photons have lower energies than the original photons.

What happens in the camera is that by measurement of the energies of the events in the two detectors the angle change of the photon in the first detector is measured. Then as we know the relative positions of the two events in the two detectors we know the angle of the scattered photon. This allows us to create a cone which will include the location of the original source. Here is a crude sketch I have made of the operation of the Compton camera.

The Compton camera is in operation

The Compton camera is in operation

What happens is that the camera will have a computer in it which trys to recreate the original image, it will for each photon event create a curved shape. By adding the data for different events it will be able to establish what the original image (where the gamma source was). This type of camera can be used for a range of tasks which include medical and industrial applications.

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One Response

  1. Reblogged this on Electronics Infoline.

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