## 2 Description of the Experiment
### Process to Extract Scalar Quantities  
A flow chart showing the process to extract the spray quantities is given in Figure 3. A general description of the process in steps is as follows:  
**Step 1** Conversion of SLIPI-LIF/Mie ratio to droplets mean diameters using PDA measurements  
The 2D matrix of SLIPI-LIF/Mie ratio is converted to two independent spray quantities, 2D maps of droplets SMD (D\({}_{32}\)) and droplets volume mean diameter (D\({}_{30}\)). This is performed according to the calibration between the SLIPI-LIF/Mie ratio and PDA measurements. At a given measurement  
Figure 2: Optical setup of the combined SLIPI laser-induced fluorescence/Mie scattering (SLIPI-LIF/Mie) ratio and SLIPI-scan method. The illumination section (in the green box) consists of a translation stage, spray nozzle, SLIPI illumination, and phase Doppler anemometry (PDA) probe volume. The optical signal detection section consists of a beam splitter, LIF and Mie optical filters, and two identical EM-CCD cameras. point, PDA records droplet size distribution, which can be used for the calculation of various mean diameters of droplets, for example, mean diameters D\({}_{32}\) and D\({}_{30}\) are deduced, here, according to the reference [27]. **Step 2** Conversion of SLIPI-LIF/Mie ratio matrix to \(\sigma_{\rm e}\) maps using PDA data and numerical calculations  
As mentioned above, the PDA measurements, performed at a point in the spray, provide the droplet size distribution. Here, the size distribution from PDA is used to calculate the corresponding averaged \(\sigma_{\rm e}\) (in mm\({}^{2}\)) according to [PERSON] theory [28]. A Mie calculator developed by the authors, here, based on the algorithm proposed by [PERSON] and [PERSON] in [29]. Consequently, each PDA measurement point of size distribution can be converted to averaged \(\sigma_{\rm e}\) of spray droplets. Therefore, now, the calibrated SLIPI-LIF/Mie ratio matrix (or droplets SMD) is converted to droplet extinction cross-section \(\sigma_{\rm e}\). **Step 3** Conversion of SLIPI-LIF/Mie ratio matrix to droplet volume  
As previously mentioned, the SLIPI-LIF/Mie ratio is converted to D\({}_{30}\) maps using the PDA calibration. Now, the matrix of the volume mean diameter is converted to droplet volume (V) using the formula of volume of a sphere [30]. **Step 4** Calculation of droplet local \(\mu_{\rm e}\) from SLIPI-scan  
The local \(\mu_{\rm e}\) of droplets in the spray is calculated using the transmitted light intensity which is recorded from the light fluorescing from a glass cuvette located on the other side of the spray. A light sheet scanning procedure starting from the outside of the spray toward its center is performed. The corrections of light extinction effects over the three-dimensional spray volume lead to the measurement of the local \(\mu_{\rm e}\) in mm\({}^{-1}\), a technique named SLIPI-scan [25; 26]. A detailed description of the SLIPI-scan is given in Section 4. **Step 5** Calculation of droplets N using \(\mu_{\rm e}\) and \(\sigma_{\rm e}\)  
To calculate droplets number density (N), two spray quantities, \(\mu_{\rm e}\) and \(\sigma_{\rm e}\), are required because calculating the ratio \(\mu_{\rm e}\)/\(\sigma_{\rm e}\), droplets N (#/mm\({}^{3}\)) can be deduced. The process to calculate \(\mu_{\rm e}\) is given in Step 4, while \(\sigma_{\rm e}\) calculation is discussed in Step 2. **Step 6** Calculation of droplets LVF  
Finally, to calculate the LVF of droplets, two quantities, droplets volume (V) and droplets N are required. The LVF is extracted from the pixel-wise multiplication between V and N. The process to deduce droplets V and N is given in Step 3 and Step 5, respectively. Therefore, using the simultaneously recorded SLIPI-LIF/Mie and SLIPI-scan data in the post-processing described in Figure 3, various scalar quantities of the spray can be calculated. Note that those calculations are made on each pixel of the spray images allowing 2D, as well as 3D mapping of the spray.