Deriving the basic cell-reciprocal integrating nephelometer equation and its use for calibration purposes: a comprehensive approach

Abstract

The problem defined in the title has partially been addressed by various studies, in a complicated manner, without providing sufficient details or in ways that are to some extent confusing. For these reasons the basic equation governing the operation of the cell-reciprocal integrating nephelometer (CRIN) has been deduced by a comprehensible and didactic approach in this work. A comparison of this equation with the respective one for the cell-direct integrating nephelometer (CDIN) has been undertaken. An introductory review analysis of the equation and its first and second corrections, due to the so-called truncation error and light extinction error, respectively, has been performed. An indication of how they can, in theory, be minimized is given. The essential CRIN-calibration procedure has been described with special emphasis on the convenient use of a monodisperse, non-absorbing and spherical aerosol as a calibration substance instead of using toxic and environmentally damaging gases. However, in this respect, some comments on fundamental technical problems and possible errors arising in generating, sampling and operating an aerosol of this kind for calibration purposes have been added. For the various aspects analysed in this work it is shown that the CRIN-calibration procedure is a very difficult task to accomplish, especially when an aerosol is used.

Detailed characterization of the CAPS single-scattering albedo monitor (CAPS PMssa) as a field-deployable instrument for measuring aerosol light absorption with the extinction-minus-scattering method

“…(4) are detailed in Appendix A. These equations have been given in several previous publications (Anderson et al, 1996;Heintzenberg and Charlson, 1996;Moosmüller and Arnott, 2003;Müller et al, 2011b;Peñaloza, 1999). The novel aspect of our formulation is that we explicitly define a function representing the efficiency with which an integrating nephelometer is able to collect scattered light, η(θ, λ), which is a simple function varying between 0 and 1.…”

“…(A1) for calculating aerosol scattering coefficients b sca (λ). Following on from earlier integrating nephelometry studies (Anderson et al, 1996;Heintzenberg and Charlson, 1996;Moosmüller and Arnott, 2003;Müller et al, 2011b;Peñaloza, 1999), we express this equation as a function of the scattering function of the particle population S p (θ, λ), the light collection efficiency of the integrating sphere η(θ, λ), and the angular sensitivity function Z(θ ) of the combined optical system:…”

Detailed characterization of the CAPS single scattering albedo monitor (CAPS PMssa) as a field-deployable instrument for measuring aerosol light absorption with the extinction-minus-scattering method

“…(A1) for calculating aerosol scattering coefficients bsca(λ). Following on from earlier integrating nephelometry studies (Anderson et al, 1996;1085 Heintzenberg andCharlson, 1996;Moosmüller and Arnott, 2003;Müller et al, 2011b;Peñaloza M, 1999), we express this equation as a function of the scattering function of the particle population Sp(θ, λ), the light collection efficiency of the integrating sphere η(θ, λ), and the angular sensitivity function Z(θ) of the combined optical system: , , .…”

“…(4) are detailed in Appendix A1. These equations have been given in several previous publications (Anderson et al, 1996;Heintzenberg and Charlson, 1996;Moosmüller and 335 Arnott, 2003;Müller et al, 2011b;Peñaloza M, 1999). The novel aspect of our formulation is that we explicitly define a function representing the efficiency with which an integrating nephelometer is able to collect scattered light, η(θ, λ), which is a simple function varying between 0 and 1.…”