{"id":850,"date":"2006-11-27T11:42:45","date_gmt":"2006-11-27T11:42:45","guid":{"rendered":"http:\/\/scienceblogs.com\/principles\/2006\/11\/27\/the-making-of-a-graph\/"},"modified":"2006-11-27T11:42:45","modified_gmt":"2006-11-27T11:42:45","slug":"the-making-of-a-graph","status":"publish","type":"post","link":"http:\/\/chadorzel.com\/principles\/2006\/11\/27\/the-making-of-a-graph\/","title":{"rendered":"The Making of a Graph"},"content":{"rendered":"

One of my current thesis students has been plugging away for a while at the project described in the A Week in the Lab<\/a> series last year, and he’s recently been getting some pretty good data. I’ve spent a little time analyzing the preliminary results (to determine the best method for him to use on the rest of the data), and I thought I’d explain a little of the process here.<\/p>\n

Here’s the key graph from the first set of results:<\/p>\n

\"i-1dc687d10a023dd1ecebcc2ac90cf462-sm_pressure.JPG\"<\/p>\n

What we’re working with here is a system where we feed krypton gas into a vacuum system, and illuminate it with light from two sources: a really expensive ($7000) vacuum ultraviolet lamp at 123 nm, and infrared light from a diode laser at 819 nm. The combination of those two wavelengths should excite some of the krypton atoms into a “metastable state,” that is, a particular atomic energy level with an extremely long lifetime. To detect the metastable atoms, we shine in another laser at 811 nm, a wavelength that only atoms in the metastable state will absorb, and look for the fluorescence as the excited atoms re-emit 811 nm photons. The graph above shows the amount of fluorescence as a function of the pressure of the gas in the source region, which is the key measure of how well we’re doing: the pressure tells us how much gas we’re putting into the system, and the fluorescence tells us how many metastables we’ve made.<\/p>\n

Of course, getting to this graph takes a bit of effort…<\/p>\n

The raw data files we acquire look like this:<\/p>\n

<\/p>\n

\"i-b887d3ac321f4b7572db7dcf3deb2677-sm_raw.jpg\"<\/p>\n

What we see here is a plot of data saved from a fancy digital oscilloscope, showing the signal from a photo-multiplier tube (PMT) as a function of time. The PMT picks up light emanating from the region where we’re making the metastable atoms, and puts out a voltage proportional to the amount of light. The particular tube we’re using gives negative output voltages, so downward-going spikes are peaks in the intensity.<\/p>\n

We sweep the frequency of the 811 nm laser back and forth over a small range around the atomic resonance frequency, which accounts for the multiple peaks in the signal. We see four complete peaks, as the frequency increases, then decreases, then increases then decreases again. There are also two partial peaks at the edges, because the peak happens to be close to the turnaround point for the particular laser parameters used for this run.<\/p>\n

You can also see that the signal doesn’t go all the way to zero– the least negative value, corresponding to the smallest amount of light hitting the PMT, is about -280 in the screwy units that the digital scope uses for its saved files. This represents the background light level, due to light scattering off various surfaces in the system, and making its way into the system. The actual peaks are much smaller than the background for this data set– the peak height is something like 40 units, compared to a background of 280 units. To get at what we actually want to measure, we need to separate out the peaks from the background.<\/p>\n

We do this by fitting peaks to the data, as shown in this graph:<\/p>\n

\"i-1b19c9140f136f9002a38a8c5e9d50fc-sm_fit.jpg\"<\/p>\n

We read the raw data files into a data analysis program (SigmaPlot, for those who care), and chop each file into four pieces, each containing one complete peak. Then we use a built-in fit routine to determine a mathematical formula that describes the data (a Gaussian peak, because of the Central Limit Theorem). The points in this graph are a subset of the raw data shown above, and the solid line represents the best fit the computer could generate, which is pretty good in this case.<\/p>\n

From the fit, we extract four numbers: the height of the peak, the width of the peak, the center position of the peak, and the background level. We get four fits from each raw data file, and all of these numbers are potentially useful. To get the full range of data we’re after, we repeat this process for twenty-odd data files, and collect the results together to make the following graph:<\/p>\n

\"i-4520e1dde881ebed13dc0083bb698388-sm_time.jpg\"<\/p>\n

This shows the peak height (which is the best measure of the number of metastables created) as a function of the elapsed time since the start of the experiment. Each file yields four data points, and the scatter in those points gives you some idea of the quality of the data– there are four points at each time value, and they’re fairly close together except at the very end, when the signal gets small and the fit routine can’t generate sensible results any more (I did fits to more files than this, but left out the rest of the ones that were obviously garbage).<\/p>\n

Why does the signal vary in time? Well, the way the experiment works at the moment is that we open a valve to let gas into the system, which results in a very high initial pressure. As that gas gets pumped away, the pressure drops, and the signal changes depending on the pressure. The drop is very rapid early on, and slower at later times, and we record the pressure value for each data point at the file is saved. Replacing the time values with the pressure readings gets us back to the graph at the top of the post:<\/p>\n

\"i-1dc687d10a023dd1ecebcc2ac90cf462-sm_pressure.JPG\"<\/p>\n

This reverses the horizontal axis, so the group of points all the way out to the right is from three minutes in, and the lousy thirteen-minute data is all the way on the left. The early high-pressure points are stretched out a bit, and the later low-pressure ones are bunched together. There’s a clear peak at about 70 mT, which is a little higher than I’d like, but makes perfect sense, given what’s going on here.<\/p>\n

But I’ll save the explanation of what this graph means<\/strong> for another post…<\/p>\n","protected":false},"excerpt":{"rendered":"

One of my current thesis students has been plugging away for a while at the project described in the A Week in the Lab series last year, and he’s recently been getting some pretty good data. I’ve spent a little time analyzing the preliminary results (to determine the best method for him to use on… Continue reading The Making of a Graph<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"1","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[32],"tags":[],"class_list":["post-850","post","type-post","status-publish","format-standard","hentry","category-my_lab","entry"],"_links":{"self":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/posts\/850","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/comments?post=850"}],"version-history":[{"count":0,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/posts\/850\/revisions"}],"wp:attachment":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/media?parent=850"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/categories?post=850"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/tags?post=850"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}