ASA or as we know it now, ISO, is a measure of the sensitivity of the sensors in digital cameras. Originally it was a measure of the sensitivity of analog film. The convention has been retained and today we speak of sensitivity of digital camera sensors in relation to the film of the analog era. This is largely due to the evolution of the digital camera from it’s film origins. This is rather important because digital cameras use the same pieces and arts as film cameras of old, that is lenses and fstops and shutter speeds. By using the conventional unit of sensitivity we are allowed to transfer our knowledge, and our equipment back and forth over the digital divide.
Sensors in digital cameras have some base or native exposure value equivalent, usually around ASA 100. By the use of amplifiers, the speed of the sensors can be raised to higher values, at the cost of some level of increased noise. These amplification values are chosen to result in the same standard increase in value as the old ASA ISO fstop sequence. There are two reasons to use amplifiers to raise sensitivity. One is to provide some range of adjustability in the same manner as changing film would have provided in the past. The second reason is that it possible to do this, and at very high relative ASA in todays modern cameras
The numbering system of ASA is not a linear progression, but rather a geometric sequence. Every doubling of the number is equal to a speed increase of one stop. Every doubling of the value is thus twice as sensitive as the previous value.
A different numbering system which is no longer in use was a linear progression with each value of 1 higher being 1/3 of a stop. See the notes diagram to see the scale.
Because of the doubling of numbers in the ASA ISO scale we now have cameras that have ridiculous ASA settings values like 102400 for example. This would have been 48 DIN so you can see it would have been a bit easier to see.
Increasing ASA from the base on digital cameras results in increased noise due to the amplification of the signal. The advice has always been to shoot at the very lowest ASA possible. Today most cameras have increasingly less noise at higher ASA than cameras of just a few years ago. This is due to the advances in the methods of building camera sensors. It is no longer required to shoot only at the very lowest ASA speeds.
This is a very good thing, because for example, going from ASA 100 to 800 can result in the EV change of going from f2.8 to f8. Likewise, the same EV increase will get you from 1/30th of a second to 1/250th. This can be the difference between getting a blurry shot, or a clear shot. And if you have a clean modern camera that will give reasonable performance at ASA 6400, then you can have both f8 and 1/250th.
Often a bit of noise will be a better image than a blurry one, or one with a larger than optimum circle of confusion due to inadequate depth of field. Noise in the final image is also dependant upon the magnification required to get to the final print size.
Just as in other camera controls and settings, on modern cameras, ASA needs to be thought of as a creative control. ASA is one of the three camera setting compromises, along with shutter speed and lens aperture. These oppose the other components of exposure which are Light level, composition, and desired effect. Additional factors also have to be considered and they are environmental. Strobes, Reflectors, Flash, time of day, choice of composition.
In addition to the controlled nature of the exposure triangle, it is also possible to use ASA as a creative tool, by using over and under exposure intentionally.
For example, it is possible to over expose 1 or 2 stops to lower a shutter speed or open a lens aperture for effect. As long as highlights are not blown out, light levels can usually be recovered in post process. It is also possible to underexpose by a stop or two, maybe even 3. This can be rocovered in post process using shadow recovery. This will allow you to increase shutter speed or gain some needed depth of field. Underexposure will also control highlights such as overly bright skies and water. It can be useful for shooting wildlife in dull sky. Underexposure is also useful for sunrise, sunset, and intentional silhouette.
Finally, noise is dependant on the sensor design of the camera and the software used to process the sensor data into an image file. Noise can be reduced in post process, either in camera, or in software, some of which is very effective.
Everything in photography is a compromise. You will have to make test shots to see what level of noise is acceptable, at what print size with what kind of subject. Once you have this down for a particular camera, you will be able to make sound judgements in the field.