Physics 2000 Einstein's Legacy CAT Scans

Back Projection

I understand the idea behind all this, but it's hard enough to understand one x-ray, let alone imagining all of them at once. How am I supposed to make sense of all these x-rays?

Remember, the "C" in "CAT" stands for Computed, and computers do the hard work of interpreting the x-ray shadows from many angles. Although most CAT scanners today use highly complex programs to interpret the x-ray images, let's look at a simple method, called "Back Projection," that should at least give you an idea of how it works. Let's say we have two x-ray images of our slice:

Wait a second, what are those little pull-rings sticking out from our scans?

Those are like the pull-rings on a window shade. They will let us "stretch" out our scan. Use your mouse to click and drag the blue pull ring down.

What's the point of doing that?

Well, looking at our top scan, we can see that there is a lighter region somewhere in it, but we don't know whether the light region is high, low, or in the middle. In other words, we know where the light region is horizontallly but not vertically...

Oh! So by stretching it out we're kind of saying, "We don't know where the light spot is vertically, so for now give it all vertical values!"

Right. Now double click on the blue pull ring to rewind it and pull the red pull ring across.

OK, this does the same thing except in the other direction. Now we've taken the light spot whose location we know vertically and "smeared" it out across all horizontal positions.

Now let's leave the vertical scan in place, and pull the blue pull ring back down. This will average the two scans together.

Hey! You can see where the light areas cross and it gets even more light there. Does that mean there's a square hole in our slice right there?

What did we learn from the spotlights earlier?

Oh, of course, we would have to make more x-ray shadows to tell if it was a square or a circle.

Or even something else. The other thing that would happen by "adding" more shadows is that the medium light lines would eventually disappear.

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