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Estimation of the Particle Sizing Error Due to Particle Position in an Integrated PM2.5 Optical Particle Counter^{ †}

^{1}

^{2}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Lorentz-Mie Scattering Simulations

_{0}is the light intensity of the incident beam and 𝜎′𝑝 and 𝜎′𝑠 the differential scattering cross sections, defined as below:

_{p}and r

_{s}calculated using complex parameters S

_{1}and S

_{2}from Mie scattering theory [7]:

^{−1}] as:

_{Ω}in [W] as:

_{min}and d

_{max}, the minimum and maximum estimation of the particle diameter, corresponding to the sizing error for a certain particle size (Figure 2a).

## 4. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Optical particle sensor system with its components (modified from [4]), viewed from the top, (

**b**) and same sensor viewed from the side. In our example, we set the θ to 90° and α to 53° in both directions.

**Figure 2.**Theoretical response for the nominal and two negative and positive extremal positions for ±250 µm displacement in the direction of the (

**a**) axis of the laser source, (

**b**) axis of the air stream and (

**c**) optical axis of the detector. In (

**a**), the estimation procedure of the particle sizing error is shown. For the sake of this simulation, we set the λ = 650 nm, input intensity to I0 = 5 Kw/m

^{2}and the complex refractive index to m = 1.5 + i

_{0}.

**Figure 3.**(

**a**) Graph of sizing error with d

_{min}and d

_{max}diameter estimation for ±250 µm displacement in each of the axis. Here the 45° line indicates the ideal curve of zero sizing error. The gray area indicates the maximal error, obtained by the extremal error estimation of all three responses for each particle, here mostly dominated by the displacement in the detector axis. This way, we obtain a total particle diameter error for each particle, as indicated for 1.5µm particle. (

**b**) Graph of total particle diameter error as a function of particle size for different ranges of displacements ranging from ±50 µm to ±250 µm.

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**MDPI and ACS Style**

Pribošek, J.; Röhrer, G.
Estimation of the Particle Sizing Error Due to Particle Position in an Integrated PM2.5 Optical Particle Counter. *Proceedings* **2018**, *2*, 850.
https://doi.org/10.3390/proceedings2130850

**AMA Style**

Pribošek J, Röhrer G.
Estimation of the Particle Sizing Error Due to Particle Position in an Integrated PM2.5 Optical Particle Counter. *Proceedings*. 2018; 2(13):850.
https://doi.org/10.3390/proceedings2130850

**Chicago/Turabian Style**

Pribošek, Jaka, and Georg Röhrer.
2018. "Estimation of the Particle Sizing Error Due to Particle Position in an Integrated PM2.5 Optical Particle Counter" *Proceedings* 2, no. 13: 850.
https://doi.org/10.3390/proceedings2130850