Monday, July 6, 2009

Spectral Plots and More MATLAB Functions

The plan for today (Thursday) was to learn more with MATLAB and to take some more scans at the FWHM of each x- and y- directions as well as the maximum. This is different from what we did earlier in the week, as I plan to take data at all five positions (max and FWHM for each) and take a series of shorter scans instead of one long scan. Then I can average the data for all of these scans, which should take better care of possible anomolies.

Unfortunately, I did not have time to take more data today. Instead I worked with MATLAB and importing data from the scans. To do this, I used specific functions that Guilhem wrote to handle such data. With said functions, it is possible to import and build the signal we initially took (temporal). Given a series of indexed data like what I mentioned above, this function will average those signals into one. The other important function was to take this temporal signal and create the spectrum.

I was able to make a few plots with this, one of which shows the spectra of each scan. This plot is shown below.

Notice that the red spectrum is that at the maximum position (0,0), and is greatest in amplitude, just as expected. We would expect the spectra colored in orange and green to be more symmetic, as they are on the positive and negative FWHM of the x-direction and so we would expect them to be very similar. Also, in this scan I took only one measurement in the y-direction. This is because the intensity plot showed the y-direction to be more symmetric than the x-direction (see plot from yesterday).

We can see from this plot that there are distinct frequencies at which there is no signal. This may be caused by absorption via water in the air. We might try to reduce this by putting the microscope in an air-tight container and filling it with nitrogen to remove the water.

From this point, I want to look at the relative ratio of signal at each point on the wafer. To do this, I need some sort of a reference spectrum to compare the other spectra to. The way to do this will be to use the (0,0) maximum point as the reference. I want to divide the spectra from each other position into this reference spectrum, and I should look at this in the next few days.

Also, I have added the compilation of the temporal scans, which is shown below. It is not very easy to see each pulse, but this plot is just to show the relative intensity of each position.

So I will hopefully be able to find the ratio of these two signals tomorrow and also take some more data which I can average out to attain more precise spectra.


  1. The data looks good for your first efforts at getting THz signals. Congrats.

    I have numerous suggestions, some that may come across better when we get to video chat.

    1) The dramatic fluctuations in your spectrum seem more likely to me to come from the FFT of the time-domain data rather than humidity in the air. Just how long is the THz beam path in the lab environment?

    2) You have several different types of reflections that appear in your large time-domain window - you may be able to sort these out by simple calculations of round-trip path times of the electromagnetic THz waves either within or between the different elements in your beam path. Possible sources of the reflections are:

    a) round trip time in the etalon formed by the faces of the Si (you would need to know Si index for microwave frequencies and Si thickness to compute a round-trip reflection time). These would only be present when the Si was in place.

    b) an electrical reflection within the emitter or receiver (most likely emitter). These are common for THz emitters, and they will be there no matter what other elements are in the THz beam path.

    c) reflections between elements (I believe you talked about F-P reflections when an aperture was used). The repeat times of these types of reflections is calculated the same as in a) above, but now the index is that of air, and the thickness is the distance between the 2 elements in question.

    I imagine you may be able to look at the THz beam path and find other places reflections could be present too. I would calculate possible reflection paths and compare with the periodic peaks in your time-domain data. Just knowing where these reflections come from is not by itself extremely useful, unless you can also eliminate the reflection sources. Some you can eliminate by changing the beam path, the materials used, etc. However, many times you are just stuck with the reflections and you have to work around them. This is partially addressed in 3).

  2. 3) The time-domain signal you are using is much longer than it has to be. Some of the dramatic changes in the spectrum are likely due to the fact that you include in your analysis all of those ringing reflections that continue out for many picoseconds. Once the initial bipolar-like pulse has passed through the system and been detected, you can throw out the stuff that arrives later. That cannot be done necessarily for spectroscopy applications, or for time-domain reflectometry, but that is not what you are doing here. One key to nice, smooth spectra is to have nice, well-behaved time-domain signals. That would mean having as flat of a trailing signal (i.e., the part after the main bipolar-like part of the THz pulse) as you have in the baseline before the pulse arrives. The trick is, when is the initial THz information done being transmitted through the system, and when do the reflections start (and, from a more advanced standpoint, can they be separated?). What we are doing when we "truncate" any THz signal before taking the FFT is applying an apodization function to the time-domain data. There are books written about this subject, so I can't do it justice here, but suffice to say that you'd like to find a place on the waveform, soon after the main bipolar-like pulse, that is back at the level of the baseline before the THz pulse arrived. The more gradually the THz signal is approaching this baseline level, the smoother the spectrum will be. (Another concept for some background reading - you will get a smoother, or at least more uniform spectrum if you "pad" the time-domain file, after the apodization function is applied, with a bunch of zeroes (i.e., the baseline amplitude level).

    If the truncation of the temporal data to the baseline level is abrupt, then you will be taking the FFT of essentially a step-like function, which yields the sinc-like ringing behavior that is very commonly observed in THz spectra.

    The best way to start will be to clean up your temporal waveforms. If that can't be done, for instance, by eliminating reflections, then it has to be done numerically. Your red curve above has a medium sized negative part, a large positive part, and then another smaller negative part. I would work to truncate the signal soon after the second negative part before the rest of the signal (i.e., before the reflections start).

    If there are drop-outs in the spectrum due to water, then you will still see them in the spectrum. However, I would work on eliminating those later only if it is really necessary to do so (not likely to be necessary, I would say).

    All of this clean-up work should also benefit the effort to take ratios of the spectra. I am not sure this will be possible without cleaner spectra.

  3. The length of the THz beam path between the two parabolic mirrors of the microscope is approximately 47 cm. The Si wafer is placed in about in the center of this path, and so the distance from the parabolic mirror from the transmitter to the Si is about 23 or 24 cm.

    In terms of the dramatic spectral fluctuations, it does make sense that these might be more due to the FFT than the H2O content of the air.

    For the Fabry-Perot effect, I think that the only place this may occur is within the Si wafer, as I explain in a later post. This explains why we get those secondary and tertiary pulses as shown in the time-domain traces, such as the one above. I do not think there are any other things which could result in a Fabry-Perot effect, as I have removed the aperture that was once used to limit the THz beam.

    I would like to calculate possible other reflection paths, as suggested above, though I need to look at where this may apply.

    There seems to be a variety of things which I can do to try and eliminate the reflections, and I shall try to do so. I think that possibly the easiest thing is going to be truncating the data (time-domain trace), as mentioned above. There is also the idea of replacing the environment with N2 gas, and this has actually been done to some extent by Antoine and I shall write about it shortly (July 17th or so).

    I hope to be able to clean up this data and from here be able to look at the ratios of the spectra a bit better.

  4. I also wanted to comment on what you said about padding for the spectrum. Guilhem explained this to me a bit and from what I understand, the MATLAB functions are written so as to add padding. If I am not mistaken, this is something that I am able to change the value of to increase the "smoothness" of the spectra.

  5. That is correct. If MATLAB is doing this reasonably, which is likely, then your greater concern is in the truncation of the THz data.