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This fraction is obviously the reason why ƒ/4 is a larger aperture than ƒ/8 — if you get a 1/4 (25%) of a cake, you’re getting more cake than if you’re getting 1/8 (12.5%) of a cake.

The star should focus down to nice point, with no asymmetric flaring. The overall sharpness of the star image will depend on the magnification and seeing conditions, but it should be symmetrical and perfectly round.

Collimation is critical to obtaining the best performance from your telescope. Aligning the optics of a Schmidt-Cassegrain telescope (SCT) is much easier than collimating a Newtonian telescope and can easily be learned by any user. However, there are some tricks to doing it right, and some things to avoid. If done right, collimation should only be necessary every few months. If you find it necessary to collimate your telescope every few weeks, the mirror is probably not being locked down properly after adjustment.

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Choose a fairly bright (1st magnitude) star for the test. It is important that the star be centered in the field of view when testing collimation. A star at the edge of the field may be distorted, especially at lower powers, and could make the telescope appear out of collimation when it is not.

Of course, the f-stop scale doesn’t operate exclusively with whole numbers; look at the second table to see what happens when I take a selection of fractions and plug them into the square root formula. Your camera will operate either with thirds- or halves of a stop, so when we look at different fractions of five (5-and-a half, 5-and-a-third and 5-and-two-thirds), we’ll get more f-stops you’ll probably recognise (f/6.7, f/6.3 and f/7.1, respectively).

It is very important to let the telescope thermally stabilize before collimation. A scope that is still cooling down to ambient temperature will produce a heat spike as warm air radiates off the optics. This can distort the star image and make the telescope appear out of collimation when it is not.

Before we dive into aperture-land, let’s take a look at shutter speeds. As I hinted at before, they are both pretty intuitive: A 2 second shutter speed means that the shutter is open twice as long as a 1 second shutter speed. The same goes for 1/100 and 1/200 — the former is half as fast as the latter.

In other words: if you shoot a photo at 1/100 second, f/4 and ISO 200, you would get exactly the same brightness in your photo if you halved the ISO and doubled the shutter speed (so 1/50 second and ISO 100) or the other way around (1/200 second shutter speed and ISO 400).

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It’s sort of important to know what ‘half the aperture’ is of any given aperture, because if you’re shooting in Manual mode (you’re not still shooting in automatic modes, are you?!), you can use something called ‘synonymous exposures’. That is; you can use two different sets of exposure settings, that let the same amount of light onto your light sensor.

You may have seen some lenses that have something like “18–35mm f/3.5–4.5” stamped on the side of them. That means that when the lens is zoomed out fully, you can shoot with a f/3.5 aperture. However, when you zoom in, you can only use f/4.5.

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Note: In our experience, the original screws on an SCT secondary mirror are much better to use for collimation purposes than the aftermarket thumbscrews that can be added. Thumbscrews cannot be turned as precisely, making accurate alignment difficult. Also, thumbscrews do not hold the mirror as tightly, increasing the need to collimate more often. Thumbscrews also tend to make people "collimation happy," tending to collimate a scope far more often than necessary. Under normal use, you should be able to go months without collimating a telescope.

Aperture is the one that always trips up my students, because it appears as if the F-stop scale doesn’t make any sense. For one thing, f/2.8 is a pretty weird number, but how can f/2.8 be a larger aperture opening than f/4?

Whether you tighten or loosen the screw you have found, depends on whether the image is inside or outside of focus. The usual method is to try tightening first and see if the star image improves. Also, note that turning a screw the correct direction will cause the entire star image to move toward the fat part of the donut (upper left in the diagram above). Begin by turning the screw about 1/8th of a turn.

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Defocus the star to produce a donut shape. The hole in the donut is the shadow of the secondary mirror. If the hole is offset from the center of the star, the collimation must be adjusted.

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A concave spherical mirror has a shape that is like the inside of a sphere or a bowl. It curves inward.

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The scale of F-stops is a geometric sequence of numbers: the sequence of the powers of the square root of 2. Which sounds pretty mystical, but have a look at the table that’s hovering to the right of this text; the actual square roots on the left-hand side of the table might look arcane, but you’ll no doubt recognise the aperture f-stops as ones that your camera comes up with when you’re taking photos.

After adjusting the screws, be sure to return the star to the center of the field of view by adjusting the position of the telescope. Once the adjustments have been completed, the screws should be snug and the image of the defocused star should appear perfectly concentric, as shown below.

ISO deals with light sensitivity; in the old days, we’d talk about film speeds of a certain ISO. These days, it refers to the sensitivity of your light sensor (or rather, a multiplication factor done by your camera’s processing chips). When you’re shooting at ISO 100, your camera will use the light capture data as-is. At ISO 200, it’ll take your light measurements and multiply them by 2 (because it used half the shutter speed in its exposure calculation). At ISO 400, it multiplies everything by 4 — and so on.

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This way of calculating apertures is the reason why you very rarely see f/3.0 or f/7.0, for example — although I have seen them on some cameras from time to time, bizarrely, especially camera phone cameras, who seem to relish throwing photographic convention to the wind.

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Collimating an SCT is simply a matter of adjusting the three screws on the secondary mirror. This changes the tilt of the mirror and aligns it with the (fixed) primary mirror. The tilt of the mirror is tested by viewing an out-of-focus star image through the telescope.

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Unlike collimating a Newtonian, there are no special tools required for an SCT. However, you will need to test the collimation on a star, so it must be clear and dark. Otherwise, all you will need is a screwdriver to adjust the screws on the secondary mirror.

If tightening one screw makes the collimation worse, return that screw to its starting position and try tightening the other two screws. The most important thing is that the screws end up snug in the end. Try not to loosen a screw without tightening the others to compensate. Leaving the screws loose can cause the collimation to be lost when moving the telescope.

You may have seen some very posh f/1.0 lenses (Canon’s version of the 50mm ƒ/1.0 costs around US$4,500, but you can pick up the ƒ/1.8 much cheaper; there are Nikon, Sony, Olympus, and Fujifilm equivalents, too), and if you’ve been around in the photography world for long enough, you may even have come across a couple of 50mm f/.95. If you’re immediately wondering how this is possible, simply go back to the math: The 50mm f/1.0 lens has a 50mm aperture opening. As such, the 50mm f/.95 isn’t a physics-defying freak of nature — it simply has an aperture opening that’s larger than its focal length; 52.6 mm, to be exact.

For the star test, use a relatively high power eyepiece. A 10 or 12mm is a good choice for most SCTs, providing a magnification of 200-300x.

The aperture opening is measured in f-stops, which are, in fact, a fraction. Specifically, an aperture opening is a fraction of the focal length of your lens. So, if you have a 100mm lens set to f/4, what you are really saying is that the aperture opening in the lens is 1/4th of 100mm. Let’s do the math: 1/4th of 100mm is 25mm — or about an inch.

Now the trick is figuring out which screw to turn. The low-tech trick is to reach up in front of the telescope and stick a finger in front of theaperture. You will see the shadow of your hand in the star image. Move your hand around until it reaches the narrowest (or widest) part of the donut. Take a look at the secondary mirror and see what screw your finger is nearest to (or opposite from). It doesn't matter whether you use the narrow or fat part of the donut, or whether your finger ends up next to a screw or across from one. The only difference will be whether you tighten or loosen the screw.

So why did they choose this scale? Well, F-stops increase and decrease go up and down (inverse-) geometrically in powers of the square root of two because when the aperture diameter increases by the square root of two, the size of the area of the aperture (in other words: the amount of light that hits the film/CCD) is doubled. The reason for choosing to use the ‘square root of two’ scale, then, is that it it keeps the intervals equivalent to the doubling and halving of exposures. Nifty, eh?

In a way, that makes sense, let’s do the math. At 18mm, f/3.5 is a 5.1mm opening. At 35mm, f/4.5 is a 7.7mm opening. Those are pretty similar; due to the way the lens is designed, it is able to have a bigger aperture opening when it is fully zoomed out; but because it has a longer focal length, the aperture is a smaller fraction of the lens length at full zoom than at full wide-angle.