Much of the vibration of an SLR actually comes from the mirror, not the shutter. If the camera can raise the mirror in advance of making the exposure, this vibration can be eliminated.
Mirror vibration is rarely an issue in deep-sky work. It doesn't matter if the telescope shakes for a few milliseconds at the beginning of an exposure lasting several minutes; that's too small a fraction of the total time. On the other hand, in lunar and planetary work, my opinion is that DSLRs aren't very suitable even with mirror vibration eliminated because there's too much shutter vibration. That's one reason video imagers are better than DSLRs for lunar and planetary work.
1 The Nikon D80 takes only half as long for the second exposure as for the main one. It must scale the dark frame by a factor of 2 before subtracting it.
Nonetheless, it's good to have a way to control mirror vibration. There are two basic approaches, mirror prefire and mirror lock. To further confuse you, "mirror lock" sometimes denotes a way of locking up the mirror to clean the sensor, not to take a picture. And on Schmidt-Cassegrain telescopes, "mirror lock" means the ability to lock the telescope mirror in position so that it can't shift due to slack in the focusing mechanism. These are not what I'm talking about here.
Mirror prefire is how the Nikon D80 does it. Deep in the custom settings menu is an option called "Exposure Delay Mode." When enabled, this introduces a 400-millisecond delay between raising the mirror and opening the shutter. This delay can be slightly disconcerting if you forget to turn it off when doing daytime photography. For astronomy, though, it really makes a difference (Figure 3.5).
On the Canon XT (EOS 350D) and its successors, mirror lock is what you use. Turn it on, and you'll have to press the button on the cable release twice to take a picture. The first time, the mirror goes up; the second time, the shutter opens. In between, the camera is consuming battery power, so don't forget what you're doing and leave it that way.
There is no mirror lock (of this type, as distinct from sensor-cleaning mode) on the original Digital Rebel (300D), but some enterprising computer programmers have modified its firmware to add mirror lock. Information about the modification is available on www.camerahacker.com or by searching for Russian firmware hack. The modified firmware is installed the same way as a Canon firmware upgrade. I haven't tried it; it voids the Canon warranty.
The sure way to take a vibration-free lunar or planetary image is called the hat trick. Hold your hat (if you wear an old-fashioned fedora), or any dark object, in front of the telescope. Open the shutter, wait about a second for vibrations to die down, and move the hat aside. At the end of the exposure, put the hat back and then close the shutter. Instead of a hat, I usually use a piece of black cardboard. I find I can make exposures as short as 1/4 second by swinging the cardboard aside and back in place quickly.
Another way to eliminate vibration almost completely is to use afocal coupling (that is, aim the camera into the telescope's eyepiece) with the camera and telescope standing on separate tripods. This technique is as clumsy as it sounds, but it's how I got my best planetary images during the film era. Today, the best option is not to use a DSLR at all, but rather a webcam or a non-SLR digital camera with a nearly vibrationless leaf shutter.
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