You Can Make Them Brighter

by Rick Scott

A few months ago I wrote an article titled "You Can’t Make Them Brighter". So why am I now writing that you can make them brighter. The point of this article is about point objects like stars. Because stars are so far away, even the largest of them are effectively points, that is they subtend virtually zero degrees of arc, at least for amateur equipment. Some observatories with large telescopes and special auxiliary equipment have been able to measure the angular size of some of the close large stars, but that doesn’t count for us.

So if stars are just points of light, then no matter how much magnification you push your scope to, the result would still be a point if it wasn’t for physics and something called diffraction. In the very early telescope days, before diffraction was understood or even known about, the opticians thought that the image of a focused star ought to have infinite brightness because the light captured by the aperture was all going to be contained in an infinitely small point. No matter how hard they tried to make better optics, the size of the focused star didn’t get any smaller for a telescope of a given f-ratio. Eventually the scientists of the time figured out what diffraction is and how it applied to the telescope problem.

In a most general sense, light can be thought of as rays travelling in straight lines. That works for figuring out shadows and the general direction the light is travelling, but for focused images or light passing through small holes or thin slits, diffraction has to be considered. Diffraction causes light to bend when it passes an edge. In the case of our telescopes that edge is whatever defines the aperture or entrance pupil. For the common Newtonian scope, the aperture is defined by the size of the primary mirror unless the diagonal mirror is undersized. For scopes that use corrector lenses like Schmidt Cassegrain’s, Maksutovs’s or my Lurie-Houghton, or the main lens in refracting telescopes, the opening of the lens cell sets the aperture.

The image of a focused star is actually a small disk called the Airy disk, named after the 19^th century scientist Sir George Airy. The Airy disk is surrounded by a series of rings, with the first being the brightest and the others falling off in brightness. Usually, only the first ring is easily seen, but good seeing conditions is necessary and only with stars that are not so bright that they dazzle the eye. In a perfect telescope, 83.9% of the light energy is contained in the Airy disk, 7.1% in the first diffraction ring, and 2.8% in the second ring. The diameter of the Airy disk only depends on the f-ratio of the telescope, being smaller for lower f-ratios (faster). The Airy disk of an f/5 scope is half the size of the disk of an f/10 scope, this should give you a hint about the title of this article. For a given aperture, a smaller Airy disk means that the light is focused to a smaller disk and is therefore brighter. The area of a circle is proportional to the square of its diameter, so a circle of half the size has one fourth the area. If a given amount of light is concentrated into a disk with one fourth of the area, it will appear four times brighter. Remember that this only works for point objects like stars in a scope that is diffraction limited or nearly so.

Since all the light of a star is focused into the Airy disk and rings for any magnification, it’s possible to increase the magnification to see dimmer stars. Referring to my earlier article, the sky itself is a diffuse object so higher magnifications will make the sky background darker, but not the stars. Using this to our advantage, higher magnifications can be used to see more stars in galactic and globular clusters.

Here’s an example using two of my telescopes. My Celestron 8 inch scope has an f-ratio of f/10 and a central obstruction of 2.75 inches. My 9.8 inch Lurie-Houghton (LH) has an f-ratio of f/4.5 and a central obstruction of 3.1 inches. In terms of aperture area, the Celestron has 44.33 square inches and the LH has 67.88 square inches, so the LH collects 1.53 times more light or 0.46 magnitudes brighter. That doesn’t take into account the difference in f-ratios hence the size difference of the Airy disks. The area of the Airy disk in the LH is the square of 4.6 divided by 10 smaller than the disk in the Celestron, so the star image appears brighter by the square of 10 divided by 4.6 which is 4.73 or another 1.68 magnitudes for a total of 2.15 magnitudes! Now that makes for a very visible difference and I can certainly see the difference between the two scopes. Since I built the LH, clusters never looked so good and it became very apparent when I looked through the Celestron after using the LH for a year. I guess I’m now spoiled by having a fast f-ratio telescope.

I hope that between this article and the last you can see why fast scopes are desirable for observing stars and why large apertures are desirable for dim diffuse objects. Combining these two traits is a great combination for deep sky observing, but high quality, large aperture, fast optics are very difficult to make. When you get a good one, the viewing is very enjoyable indeed!