Decoding the Plantower CF1 algorithm

Some manufacturers of particle sensors do not reveal details of how they translate their instrument response into particle mass (e.g., PM2.5). They may, for example, not reveal the calibration particle mixture, or what assumptions they made as to particle shape , density etc. This is contrary to the idea that information should be free. So I wondered if I could guess what they did. I think I guessed correctly. The details are in the link, which should get the full article for the next 50 days before it goes behind a paywall.


Thanks for coming out of retirement! Would it be allowed to attach a PDF of your article to this thread — in case somebody stumbles upon this after 50 days? Failing that, how might someone obtain a (free) copy of your article once it “disappears” behind the paywall?

If the input to the algorithm (software) is the raw data from the device (hardware), how much is divulged by the manufacturer about the tolerances of the device itself? In general, I suppose the software can only be as good as the hardware?

Good questions. After 50 days, in theory, no one can obtain a (free) copy of the article as printed in the journal However, one can get a copy of the article as prepared by the author prior to the journal setting it up in print. Researchgate was created to deal with this problem, and soon I will load my final (Word) manuscript there. Or I could send it as an attachment to PurpleAir. I guess I will do that.

Very astute point about the fact that the software is only as good as the hardware. In fact, no one feels comfortable about the number of particles in the various size categories. When I compared the numbers in the two smallest size categories (0.3-0.5 um and 0.5-1 um) to a research-grade instrument with 16 size categories (the TSI Model 3330), the Plantower sensor was underpredicting by a factor of 10 or 5. This is not necessarily fatal, since if it has really great precision (which I believe it does), and most devices are nearly identical (which I think they are), then a single correction factor may get us back to agreement with the gravimetric (Federal Reference Monitor) system used in the EPA network.

However, some studies find that its response is greatly limited in all size categories greater than the smallest one. One study claims that it has no way to estimate particle numbers in different size categories. Several studies say that it is sensitive to particles even smaller than 0.3 um. Nonetheless, somehow it is found to agree pretty well with the FRM results. My last paper compared about 300 PurpleAir monitors to about 100 nearby (100 m) EPA FEM/FRM sites over a 5-year period and using the pm2.5 alt algorithm, with the most recent calibration factor of 3.4, the PurpleAir PM2.5 mean estimates matched within 2% of the FEM/FRM sites.

Does this high precision mean it’s underpredicting
by a consistent factor — i.e., underpredicting, but underpredicting predictably? What’s going on under the hood if this is the case?

I must say this is fascinating to try to understand, even if I am failing miserably! If, for example, we are “binning” particles in various size categories, then surely the discrete distribution of these categories has a great degree of variation among samples? If we assume that a particular sample is a “cocktail” of various pollutants with differing size distributions, and in different quantities, one would think this would be the case? Or is agreement between the cheap and expensive instrumentation being achieved because often the distribution of particle sizes in the soup is convergent?

Sorry for all the questions. Just trying to get a view of the big picture. Certainly I need to spend more time reading to better appreciate the subject material. Appreciate your work and reply!


Lots of good questions. Lance addressed some of the issues but here is some more detail.

The TSI 3330 uses PSL spheres which are perfectly round for calibration. The instrument assumes a refractive index that is correct for PSL spheres. If the atmospheric particles have a different refractive index they might be detected more, or less efficiency. So the counts could be high or low and this is unpredictable. The average refractive index of atmospheric particles is similar to the refractive index of PSL spheres so this may not be a big issue.

The PSL spheres are spherical but atmospheric particles are rarely spherical. This is important because the laser may be reflecting off the flat side or the edge (or anything in-between) and it will look bigger or smaller than it is. Plus the mass is calculated assuming a spherical particle. It is also possible that the particle will be put in the wrong size bin. The hope is that this averages out over time.