The Source to Image Distance (SID) is an important parameter in x-ray imaging as the x-ray beam is divergent (i.e. spreading out as it leaves the focal spot). The beam divergence leads to the inverse square law in x-ray imaging. The formula for the inverse square law in x-ray imaging is: mAs_new = mAs * (SID_new/SID)^2.
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X-rays in medical imaging are generated within an X-ray tube at the focal spot, which is where the electrons are incident onto the anode. The x-rays are generated within the anode material and come back out of the anode and travel towards the patient. Each x-ray travels in a straight line and the x-rays collectively form a cone shape where the x-rays are spreading out as they leave the anode.
This spreading out of the x-rays as they leave the anode is referred to as a divergent beam since the individual x-rays are spreading out as they travel further from the x-ray anode. If the x-rays all traveled in straight parallel lines the distance of the image receptor from the x-ray source would not impact the intensity of the x-ray beam that is incident on the image receptor.
Since the beam is spreading out the number of x-rays passing through a given area is reduced when it is further from the x-ray source. For instance if you have a kiosk ball you can see that towards the center of the kiosk ball there are lots of outshoots in a given area and they decrease as you move further away.
In this figure we show that as you move further away from the x-ray source within the cone that the x-rays fluency, or the number of x-rays passing through a given area is reducing as 1/R^2 where R is the distance from the x-ray source to the image receptor. This is why this effect is termed the inverse square law and is also written as 1/(SID)^2.
We have a second figure of the same scenario from another angle where we have drawn a few sample x-rays. In reality there are typically at least tens of thousands of x-rays in the beam but we have drawn nine x-rays here as a representative sample.
The intensity of x-rays at distance R is define as I. Then at a distance 2R from the x-ray source the intensity with be I/4, and at a distance of 3R from the x-ray source the intensity of x-rays with be I/9. Thus, you can appreciate that the inverse square law can actually have a significant effect on the intensity of x-rays incident on the image receptor.
Often in Radiography there is a desire to maintain the same exposure on the image receptor. Therefore if we start with a given Source to Image Distance (SID) and given exposure parameters mAs , and then we need to move the image receptor to a new location SID_new we need to compensate by changing the exposure parameters to mAs_new.
The beam intensity at the image receptor is directly proportional to the exposure parameters mAs. Therefore if we specify that the intensity at the image plane should not be changed we get the equation:
mAs * (1/SID)^2 = mAs_new * (1/SID_new)^2
If we solve this for the ratio of the mAs change we get:
mAs_new/mAs=(SID_new/SID)^2.
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