## 1 Introduction
### Algorithms for Optical Particle Sensors
#### 1.2.3 Algorithms Offered by Plantower  
The Plantower manual v2.5 for the PMS 1003 sensor describes two algorithms for determining PM\({}_{1}\), PM\({}_{2.5}\), and PM\({}_{10}\). One algorithm is labeled as \"CF = 1, standard particle\", the other as \"under atmospheric environment\". The Plantower manual v2.3 for the PMS 5003 sensor has the same labels for the two algorithms, but there is an added note for the CF1 algorithm: \"CF = 1 should be used in the factory environment.\"  
Some have interpreted these cryptic descriptions as indicating that the CF = 1 algorithm should be used indoors and the \"under atmospheric environment\" algorithm should be used for outdoor measurements. However, Plantower presented no data to support their characterization of the two algorithms. It is easy to determine the relation of the two algorithms. A 10-day run of data in a Santa Rosa home from 24 April 2019 to 3 May 2019 using a PurpleAir PA-II monitor gave these results for the relationship (Figure 2). It should be immediately evident that one of  
Figure 1: Contribution of each bin to total PM\({}_{2.5}\) during one year of monitoring indoor air PM\({}_{2.5}\) in a home. Bin midpoints are the geometrical mean of the bin boundaries. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Bin (\(\mu\)m)**} & **Mass per Particle** & **\# Particles (Ni)** & **Mass per Bin** & **Fraction of** \\  & **(\(\mu\)g/m\({}^{3}\)/100)** & **per Deciliter** & **(\(\mu\)g/m\({}^{3}\))** & **PM2.5** \\ \hline
0.3–0.5 & 0.000304183 & 445 & 0.135 & 0.146 \\ \hline
0.5–1 & 0.001851201 & 147 & 0.272 & 0.294 \\ \hline
1–2.5 & 0.020697059 & 25 & 0.518 & 0.560 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Contribution of each bin to PM\({}_{2.5}\) over 1 year monitoring indoor particles. these two algorithms can have no physical reality; the relationship is simply a mathematical model. The two algorithms give identical results for all particle concentrations below about 28 \(\upmu\)g/m\({}^{3}\); a linear relation above that concentration, in which the CF_ATM/CF_1 ratio increases by about 0.01 unit for the next 50 steps of 1 \(\upmu\)g/m\({}^{3}\) for the CF_1 algorithm; and then, beginning at about 78 \(\upmu\)g/m\({}^{3}\), it curs over to become ultimately fixed at a constant ratio on the order of 1.5. No possible actual physical process could behave in this way. This observation by itself does not allow the problematic algorithm to be identified. However, based on correlations with measurements by other methods, the physically unrealizable algorithm is CF_ATM, which should, therefore, not be used (See Supplementary Materials Section S1.2 and Figures S1-S4). It is uncertain why this algorithm was developed, but the fact that the CF_1 algorithm is found by almost all investigators to overpredict PM mass may have caused the Plantower engineers to search for a new algorithm that would give better estimates. In fact, the CF_ATM algorithm does give lower estimates that may be closer to the truth, but for wrong reasons. Unfortunately, the PurpleAir corporation has chosen to adopt the CF_ATM algorithm for their outdoor map because it would partially correct the overestimate of the CF_1 algorithm. While this is true, at least for the small number of outdoor concentrations >28 \(\upmu\)g/m\({}^{3}\), it means that a meaningless algorithm is being used widely by >25,000 consumers with no indication of its lack of scientific basis. Several studies have concluded that the CF_1 algorithm should be used in place of the CF_ATM algorithm [9; 18]. Figure 2: Relationship of the CF_1 algorithm to the “atmospheric environment” (CF_ATM) algorithm. Danger of \"Proprietary\" Algorithms  
Plantower presents no information regarding the composition, density, or index of refraction of the test aerosol used to calibrate its sensors. In fact, it does not even mention whether a test aerosol was used, or whether its instruments are calibrated.