Bright and Dark

 

Now let's look at objects, both bright and faint. Let's put little lines across them that sample and print out the pixel values, and see what they look like.

Here's one from the brightest star in the image: its profile in a graph, along with an actual slice of the image along the area that was sampled. And I have scaled up the tiny image slice to correspond pixel-for-pixel with what you see in the graph.

 

 What's interesting about this profile is that it does not rise to a point, but instead is mesa-shaped. That flat area at the top is probably what we should consider to be the 'real' object, while the rapidly falling off light of the steeply sloping sides is side-glow.

But don't imagine that the flat area -- 5 pixels across -- is the actual image of the star, though! We are nowhere near that kind of resolving power. A single one of telescope T11's pixels is 0.81 arc-seconds across. Even if we were looking at the very closest star -- 4 light-years away -- just one of T11's pixels would cover a distance of 22 million miles at that range. That is a span 26 times bigger than our own sun. So the 5-pixel flat area of this light profile covers a space 130 times wider than the Sun, even at the range of the closest star in the sky. Which is not what we are looking at.

So what we are seeing here is a tiny intense point of light, far away in space, spreading out as it passes through the Earth's atmosphere and moving around randomly because of motions of the air during what was a 10-minute exposure.

Still, the fact that some of that profile is so nice and flat rather than looking like a normal curve suggests that there are two different processes involved in illuminating the central 5 pixels and the 5 or 6 on either side of it. If I had to pick a specific boundary for this object in my image, I would pick that flat area from 325 to 330 on this image's X-axis.

Is that what all bright objects look like? Let's do another one. Here is a sample line across the bright star near the center of this image.

Yes, it looks similar. In fact, at 4 pixels diameter it's almost the same size. Just a little smaller, probably because this object is a little dimmer. It fills the central pixels to 47,000 gray values or so, while the first one filled them to 55,000. The central flat area is 4 pixels across here rather than 5, and the sides -- where light falls off to one-tenth of the central illumination in the space of 3 pixels, are also a little smaller. The brighter object takes 4 pixels on both sides to fall off the one-tenth of the center.

SO! We have a way to determine the edge of bright objects. If you look at these two curves, the point where the sloping wall meets the top of the mesa is a place where the slope of that line changes very quickly. That would be easy to find programatically. 

Now how about doing the same sample-line trick to a couple of extremely faint objects? 

The brightest pixels in this sample line are almost 200 times fainter than in the brightest star, but we can still discern something like the same mesa pattern. Except that this 'mesa' has a flat top only 2 pixels across, and it slopes down on either side less symetrically -- taking only a single pixel on the left side to reach the background, and several pixels on the right.

Can we find an object this faint, when its height above background is only a couple times higher than the average background fluctuations?

The second bright star is close enough to this faint star in the image that we can see both in a single view. Take a look:

The faint star isn't much, but I bet you can see it with no problem -- and with little doubt that it is not just a random background fluctuation.

Why is that?

I think I know -- but another faint object will illustrate the idea better. Let's look at a galaxy!

 

 

That is what you call a galaxy far, far away. (And long ago!) It's very faint, but you can clearly see it, right? Looking at the profile we see that, again, the height of the galaxy brightness profile is no better than double the average brightness fluctuations of the dark background.

If you were to try doing a normal grayscale threshold automatically, I think you would have a very hard time separating this kind of object from the background. But I think, with the help of a little bit of statistics, it might become a lot easier. 

But that ... is Another Story.