Offsets are neccessary. The reason is the following.
The electophotons from the sky lands on a sensor, and are converted into an electrical current; thanks to one of Herr Einstein's Nobel winning paper for describing this "photoelectric effect." (Yep, no Einstein -- no camera sensor. :-)
This current is often converted into an electrical voltage, and then fed to an analog-to-digital converter (ADC) to be converted into numbers (ADU) . Or, directly sent to an ADC that measures currents (in which case, the Offset is a current and not a voltage).
Electrophotons (the "e-" parameters that you see in camera spec sheets) are discrete quanta. You can have one eletrophoton, two electro photons, etc, and never one and a half electro-photon, nor a negative amount of electrophotons. I.e., electrophotons are unipolar counts.
The ADC on the other hand is a bipolar device. It can measure positive or negative voltages (or currents). It also has noise sources, such as input noise and quantization noise.
So, before the currents from the sensor are sent to the ADC, a small offset voltage (or current) has to added to make sure that in spite of the noise in the ADC, the noise + sensor signal can never go negative. Having the sensor current bottoming out creates all sort of noise in the image that cannot be calibrated away.
For a deep (14 or 16 bit) sensor, you can add quite a bit of offset, and it will practically not change the dynamic range of the camera. So it is common practice to use a pretty large offset, so you don't have to change the offset when the camera ages, or the temperate changes, etc.
However, for a shallow (8 bit, or 256 levels) sensor, an offset that is too large can unneccessarily rob you of dynamic range. So, it behooves one to actually measure it -- typically, by making sure the histogram of the output ADU never touches zero ADU, or equivalently, the "Min ADU" number is above zero.
For a shallow sensor, you want to apply an offset that barely places the histogram above 0 ADU (sometimes a bit more so that the histogram stays above 0 with temperature changes, etc).
So, while you can just be conservative and choose a pretty large offset voltage for 14 or 16 bit cameras and never have to touch it ever, if you are interested in maximizing dynamic range with an 8 bit camera, you should be measuring your individual camera, and then set the proper offset. Unfortunately, this is not possible with the ASIAIR.
The next time you take an image, take a look at the histogram. You will find that the lowest histogram value (i.e., the "min ADU" value) never touches zero. If the "min ADU" starts to get too close to zero, you need to increase the Offset. Now you know why there is a "min ADU" display (I can't think of another good use for that number :-). Check the Min ADU number occasionally as the camera components age to make sure min ADU does not become zero.
You can also go change the camera gain (again, just not with ASIAIR) and watch the min ADU change, and the histogram shift.
Chen