## 1 Introduction  
### Low-Cost Optical Sensors  
In recent years, there has been an explosion of interest in low-cost particle monitors. The fundamental question is accuracy. Accuracy can be determined under field conditions by comparison to nearby regulatory monitors employing the gravimetric-based Federal Reference Methods (FRM), which require collection of particles over 24 h followed by weighing filters under strict regulation of temperature and humidity. Since typically only one day out of every three can be monitored in this way, monitors were developed to estimate continuous variation of PM mass. The best of these monitors have passed stringent tests to determine their agreement with the FRM monitors. These monitors are called Federal Equivalence Monitors (FEM) and are in use at several hundred regulatory monitor sites in the United States. The accuracy of low-cost monitors can therefore be determined by comparing to either FRM or FEM monitors at regulatory sites. (For further information on the development of health standards such as PM\({}_{2.5}\) and PM\({}_{10}\), and the development of optical monitors, see Sections S1.0 and S1.1 of Supplementary Materials).  
Accuracy can also be determined by laboratory or chamber investigations. In this approach, several monitors (usually in triplicate) to be tested are placed side by side with one or more reference monitors in a chamber with controlled temperature and humidity. A particle source (often organic PSL spheres, inorganic sodium chloride, or Arizona road dust) is activated and either maintained at a steady concentration or allowed to rise to a peak and then decay so that a wide variety of concentrations can be created.  
A major source of both field and laboratory investigations of low-cost monitors is the program known as AQ-SPEC, operated by the South Coast Air Quality Management District (SCAQMD) in California. (This management district includes about 17 million people, 44% of the California population.) Monitors must pass a field test before being administered a chamber test. In the field, sensors are tested alongside one or more of South Coast AQMD's existing air monitoring stations using traditional federal reference/equivalent method instruments over a 30- to 60-day period to gauge overall performance. Sensors demonstrating acceptable performance in the field are then brought to the AQ-SPEC laboratory for more detailed testing in an environmental chamber under controlled conditions alongside traditional federal reference/equivalent method and/or best available technology instruments [1].  
About 100 field evaluation reports and 49 laboratory evaluation reports are presently available [2].  
Both field and laboratory investigations of low-cost monitors have been carried out by multiple investigators [3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25]. Many of these involve Plantower sensors.  
This paper focuses on Plantower sensors. This focus is supported by the fact that 14 of 47 manufacturers of low-cost particle monitors tested in the AQ-SPEC program use Plantower sensors (Table 1). In addition, the largest national network of low-cost monitors (PurpleAir with perhaps 25,000 monitors) uses Plantower sensors exclusively.