I am adding some new entries to the AFM FAQ. Here they are below. To get the answer to your question, contact me with the contact page.

Sandhya asks:
Can you please tell me about feed back control. I found it difficult to understand Proportional control, gain and band
and integral gain. From your FAQ AFM, I understand that set point is force
applied on sample by tip.

A: This is a very common question when people start to use AFM. Most AFMs use a PI controller. This is a kind of simplified PID controller. To control the feedback circuits, you change the P and I values. P stands for proportional and I for Integral. However, commonly in the AFM software they are referred to simply as P and I. To understand what these really mean, look at PID controllers on wikipedia, or look at chapter 3. In some instruments, D (derivative) may also be available.
For both P and I values, increasing the value increases the amount of the input signal (form the photodetector) which is fed back into the output signal (the z piezo). SO, the higher the values, the faster the AFM will react to changes in topography in the sample. Thus, the higher you can have them, the better. The problem is that if they become TOO high, feedback oscillations will result (see figure 4.6 of my book, which shows the effect of having the PID values too high and too low). So, the trick is to set them as high as possible while avoiding oscillations in the image. Typically, I is increased first, followed by P.  As Sandhya suggests, the setpoint is related to how well the feedback behaves as well. In fact, PID values, setpoint scan size and scanning speed all affect the correct sample tracking by the AFM, and are interrelated with each other.

There is a more detailed explanation of this in Chapter 4 of my book.

Ruslan asked:
Actually, the thickness of individual graphene sheets equals to
monoatomic layer of graphite (0.34 nm). Should I use the calibration sample
for my thickness measurements? If yes, what kind calibration sample must I
use?

If the height measurement you get is important (it nearly always is!), then yes, you should calibrate. Since the calibration is scale-dependent, and you want to make a very specific measurement, the best thing is to calibrate with a height standard that has a step of height close to the value you are interested in. In your case, you ideally want a sub- nanometre step. A suitable sample would typically be other monoatomic steps. Look at Appendix A in my book for descriptions of appropriate samples. A more up to date list is also available here. Look also in appendix B for recalibration procedures. They might also be described in your instrument manual.

Anis asked:
Good evening. I am confused about what is the difference between free air amplitude
and setpoint? Both are vibrating amplitude of cantilever, right? If both are same what is the problem? Many thanks. Best regards.

The setpoint is effectively the amplitude the oscillation is *reduced to* by the interaction of the probe tip with the sample. If we take a simplistic view, the actual free air amplitude, and setpoint amplitude are not so important (in tapping mode), but the relationship between them is important, because it defines how "hard" the tip is hitting the sample. In some cases, the value can even be set as a percentage (e.g. 80% of free air amplitude). Lower than this would mean better tracking, but more risk of sample damage. Higher would be less likely to lead to damage, but may mean the probe tracking the sample less accurately.

On the other hand, changing the free oscillation amplitude can be done to avoid specific imaging problems, and it will be different in noncontact mode versus tapping mode. However, for most uses, users prefer a "standard" value, and rarely change the free oscillation amplitude.

Dear Mr. Peter,
 I am going to buy an AFM. Basically, how should I perform an acceptance test? Alternatively, when I do the acceptance test, what kind of the specifications do you think I should check? How to check? Thank you!

This depends somewhat on what the instrument is. FOr instance, you would want any "additional" features demonstrated, such as the sample movement motors, optical microscope, etc.
I think in general the engineers should install the instrument and demonstrate that it is scanning ok with some test sample. Often, a silicon test sample is included. This will help you to see that it at least is measuring images.

The factor that most people check is the z noise floor because:
A: It's very important for all applications and
B: It's relatively simple to check.

Typically the acceptable z noise floor will be specified in the description of the AFM. There may be values for piezo noise and sensor noise. I recommend you look at appendix B of my book. It has (I hope) easy to follow instructions on certification and calibration procedures for use on all AFMs. Section B5.4 has the procedure for z noise floor calibration.
Typically the manufacturer will specify an upper limit for this value, like" noise floor =<0.5 Angstrom". This way you can check the real minimum noise level you'll be able to get in your images. Other calibration routines are also in appendix B and feature things like lateral accuracy and linearity, xy and xyz coupling, z range etc.