The Effect of Bandwidth upon CRTs

More than you ever wanted to know

The question of bandwidth and CRTs is a perennial one. This topic has been covered before, but I thought it deserved a more permanent review.

First let's look at the source material. Let's use the letter 'A' as an example. We'll zoom in VERY close so you can see SUB PIXEL what is going on. Here's what the ideal 'A' would look like:

What's fed to the CRT control grid is a signal which tells it how hard to turn on the beam for during it's scan. Let's represent that by a series of lines in an image we'll call 'A':

You have to remember that when the CRT scans the screen, it's not like an LCD panel or a plasma display. It's actually sweeping a dot across the screen. To see what effect that has, we can perform a 'convolution' between the shape of the CRT spot and this scanning pattern. (With apologies to mathematicians everywhere since there is no convolution symbol, I'll use © for convolution.) You might think that a perfect spot with infinite bandwidth would produce a perfectly pixelated image, but this isn't so. Because the dot has a physical size, the image is "smeared out" a bit.

If the final image is named 'f' and a perfect pixel is called 'p', then

f=p©a

and it looks like this:

Remember, that's with infinite bandwidth and a perfectly square CRT spot!

In real life, the spot produced isn't perfect. It looks more like this, which we'll call 'c':

It turns out that having an imperfect spot doesn't really make that much difference. This is because the smearing averages out over space, and you can't tell the crt spot wasn't perfect. Even if you had infinite bandwidth, the result

f=c©a

would look like this:

So, now, let's assume we have imperfect bandwidth. That causes the signal being delivered to the CRT control grid to get smeared out a bit itself. We'll call our low-bandwidth version of the letter 'LBA'. Here's what LBA looks like before it hits the big screen:

But before you ever see LBA, it has to undergo the CRT scanning process and be convolved against a real-world CRT spot. So, as before,

f=c©LBA

and here's what THAT looks like:

So you wanted to know the difference the extra bandwidth makes? Here it is, side by side, showing you at the sub-pixel level, what 'real difference' a little bandwidth makes. Don't forget we're comparing infinite bandwidth to about 1x bandwidth! The difference between 1x bandwidth and 3x bandwidth will be even less than this! Here they are:

The easiest place to see the difference is right under the cap of the A where there's a place that has a black area one pixel wide. Note that in the low bandwidth version, the black dot is close to disappearing! Also note that the left leg of the "A" is getting "thinner", almost to the point of being invisible. Even in the infinite-bandwidth version, the black dot isn't as sharp as you'd expect it to be. This is why details will get a little lost with not enough bandwidth, and why crt images are so "smooth."

As you can see, it's not THAT big a difference though. Don't forget, there's still haloing and brain-function to consider, and most films don't contain images where such dramatic changes happen over just one pixel. so what you really see will be even less different than above. But now you know what effect bandwidth really has, and can make good choices about how to spend your $$$. You're really not giving up that much by having a 1x bandwidth, especially if you don't have an LC projector.

-- TWikiGuest - 05 Feb 2007