I've got a fun problem and would be curious to get feedback on how some of you would go about solving this.
Imagine I have a probe and am scanning the surface of some material. This material surface is described by a perfect cosine signal. If my probe is perfectly normal to the surface, my probe will output a "1 to 1" match of the surface signal (excluding some DC offset).
However, if my probe is not perfectly normal to the surface, the collected signal would appear to be a skewed sinusoid. I've put together a simple diagram of set up.
Currently, my method for determining the probe angle would be to determine the frequency content of the signal. In the case of the probe being perfectly normal to the surface, I would expect that frequency domain would show a single impulse corresponding to the surface frequency.
In the case of the angled probe, I would expect to a find a range of frequencies. Obviously the peak would still correspond to the dominant spatial frequency, however, there would now be a certain bandwidth associated the frequency domain. This bandwidth is associated with the fact that the collect signal is a skew sinusoid.
My question would then be, how would I correlate signal bandwidth to probe angle?It would be nice to get an analytical solution to signal bandwidth and probe angle.
Furthermore, if anyone else could see a way of determining probe angle that isn't frequency domain related, I would be interested in hearing it.
Edit: As I think about this problem more, I'm becoming less confident in whether or not probe angle would create a skewed sinusoid. Assuming the angle doesn't exceed the max slope found in the signal, I'm starting to think the resulting signal would simply be a phased offset sinusoid...