# How do I measure the temperature of a tiny water droplet?

How do I accurately (+/- 0.1 degrees Celsius or better) measure the temperature of a small (5 to 50 microliter) water droplet without noticeably affecting its temperature?

The mass of a thermistor or thermocouple could exceed that of the droplet I'm measuring, and putting it in contact with the droplet would reduce the droplet's temperature and mess up my reading (and experiment).

If it helps, the droplet is sitting on three thin metallic-film electrodes on a translucent plastic substrate.

I thought about IR, the beam width on the IR thermometers I have is pretty wide so I couldn't target a small droplet.

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IR thermometer+magnifying glass? – Ron Maimon Sep 14 '12 at 3:23
also probably the accuracy of your infrared thermometerwill be +/- 2C – anna v Sep 14 '12 at 4:12
Try experimenting with an infrared camera iecinfrared.com/IEC-infrared-FAQs.html#Q8 which seem to have accuracies of fractions of C – anna v Sep 14 '12 at 4:16
@user2018790: newport.com/Infrared-Lenses/381068/1033/info.aspx – Ron Maimon Apr 12 '13 at 21:56

The original question was how to measure temperature in a small liquid samplewith some degree of precision. I then asked in responce whether it would suffice to measure a temperature change, as opposed to an absolute temperature. interest in this led me to write up the following. I've included a few papers, but there is a huge literature; If you need more citations, just ask.

Imagine an object which is "somewhat isolated." By this I mean that energy in the form of mechanical or EM waves which enters the body, will experience some trapping, leading to a delay as the wave bounces around. The attenuation of the body can't be too large or the wave will disappear before it has bounced around enough to sample the properties.

We can illuminate or insonify the body with an impulse or a CW excitation. For the former we record the impulse response for a "long" time. I.e., until the response has decayed to the background noise level. For a CW excitation we sweep over the same range of signals present in the (band-limited) impulse response.

For an impulsive source the pulse bounces around inside the sample. Since we are assuming relatively low attenuation, the pulse bounces around many time and we record the complete time-history of the sample response on the surface (see below). The late-time part of the recorded signal is called the coda. Now suppose we record a baseline signal (before) and then another after we have made some perturbation such as change the temperature. The early part of the impulse response will be relatively insensitive to these changes since the wave has not had time to bounce around. But the late time signal will have sampled the perturbation many times. If we use this late time signal (before and after the perturbation) to make inferences about the small changes we are doing "coda wave interferometry" http://mesoscopic.mines.edu/acoustics-old/preprints/science_cwi.pdf (Science, 2002).

Now consider using a band-limited CW sweep instead of an impulse. The response of the system will be a spectrum. The before/after comparison will give us a shift in the eigenfrequencies and their line-widths. Provided the width of the resonance is smaller than the perturbation in the system we are trying to resolve, then we can uses this technique (essentially cavity perburbation) to resolve the physical parameter that gives rise to the perturbation. In this tutorial http://acoustics.mines.edu/preprints/time_frequency.pdf (Am. J. Phys, 2005) we give a number of examples from the lab, including one in which small temperature perturbations are resolved both with coda wave interferometry and spectral perturbation. Here are more experimental examples: http://acoustics.mines.edu/preprints/Gret_JGR_06.pdf (J. Geophysical Res.)

Finally, I should say something about how we inject the signal and measure it. In my lab we use both laser ultrasound (pulsed IR lasers are the source of mechanical vibrations and a laser interferometer measures the mechanical response). But we also now use sub-THz swept CW electromagnetic sources and heterodyne receivers. However, many ultrasound labs use non-contacting ultrasound transducers (capacitive or magneto-restrictive, etc). But that is a huge field in itself and my terse explanation reflects the equipment I have in my lab.

So, in summary, when you measure an impulse response always make sure you keep recording until the signal is lost in the background noise; you'll be amazed at how much information is just above the noise level. And although the invertibility of the Fourier Transform has convinced many people the impulse response and swept CW measurement are the same, you are to consider the following fact: No matter how many repeated impulse responses you record, you cannot overcome the finite signal length imposed by the attenuation in the sample. The resolution in Fourier domain is limited by 1/Tmax. Whereas with a CW excitation, you can pump energy into the system "forever".

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This has the potential to be useful. Would you care to edit your answer to include the techniques? – Steven T. Snyder Aug 13 '13 at 20:59
I do delta-t measurements with laser ultrasound but could use one of various types on non-contacting ultrasound transducers. The idea is to measure a long impulse response, or a chunk of the normal mode spectrum. The coda of the time domain signal will be sensitive small changes in the sample. Similarly, the eigenfrequencies will be more or less equally sensitive. If we assume that the only change to the sample is caused by T change, then you can relate delta-T to delta-frequency. "A tutorial on interferometry and spectroscopy: resolving small changes." Am. J of Phys. 2005. Email? – user27777 Aug 13 '13 at 22:48
thanks for the info! I think you should add that to your answer (instead of a comment) and provide a link to the paper if possible. It could be helpful to others as well. – Steven T. Snyder Aug 14 '13 at 16:59
OK, Series8217, done. Hope you like it. – user27777 Aug 14 '13 at 19:43
Awesome answer. Thanks!! This technique goes beyond our current equipment capabilities, but I shared your papers with my colleagues and we are looking further into it. – Steven T. Snyder Aug 14 '13 at 22:16