## 1 Introduction
The virtue of the SLIPI method is that it utilizes the intensity modulation (usually a sinusoidal) on the laser sheet as a \"fingerprint\" to distinguish between the singly and multiply scattered photons reaching the detector after droplet/photon interaction in sprays [17]. Considering that a sinusoidal pattern is superimposed upon the light sheet, consequently, after the droplet/photon interaction, the resulting image intensity \(I(x,y)\) of the probed spray is described as:  
\[I(x,y)\ =\ \ I_{C}(x,y)+I_{S}(x,y)\cdot\sin(2\pi xv+\phi) \tag{1}\]  
where \(v\) represents the spatial frequency of the modulation and \(\phi\) is the spatial phase, \(I_{C}(x,y)\) is the non-modulated intensity component and \(I_{S}(x,y)\) is the modulated intensity component. Here, \(I_{C}(x,y)\) is equivalent to the intensity recorded with a conventional homogeneous light sheet, while \(I_{S}(x,y)\) is the amplitude of the spatial modulation corresponding to the desired SLIPI signal. The \(I_{C}(x,y)\) consists of both multiply and singly scattered intensities, while \(I_{S}(x,y)\) represents the intensity mostly from singly scattered photons. Therefore, if there was no modulation superimposed on the laser sheet, then, all the intensity components in Equation (1) would be defined only by \(I_{C}(x,y)\) and it is not possible to differentiate between singly and multiply photons. To extract \(I_{S}(x,y)\) a triplet of modulated sub-images \(I_{0}\), \(I_{120}\) and \(I_{240}\) are recorded, having a spatial phase \(\phi\) of \(0^{\circ}\), \(120^{\circ}\), and \(240^{\circ}\), respectively. The change of \(\phi\) is achieved by shifting the \"line pattern\" one-third of the spatial period between each recording. Using these sub-images, a SLIPI image is constructed from the root-mean-square of the differences between sub-image pairs, described mathematically as:  
\[I_{S}\ =\ \frac{\sqrt{2}}{3}\cdot\left[\left(I_{0}-I_{120}\right)^{2}+\left(I _{0}-I_{240}\right)^{2}+\left(I_{120}-I_{240}\right)^{2}\right]^{\frac{1}{2}} \tag{2}\]Note that an image equivalent to a homogeneous illumination can be reconstructed by averaging the three modulated images and is usually termed as \"conventional\" image. Numerical Monte Carlo simulations have been used in the past in [19], to quantify the suppression of the intensity contribution from multiple light scattering intensity when applying Equation (2). Figure 1 summarizes the results of the study presented by the authors in [19] where it can be observed that the SLIPI image (Figure 1d) reconstructed from Equation (2) shows a similar light intensity distribution as the one corresponding to single scattering detection (Figure 1c). Here, the simulation is performed via a validated Monte Carlo code in association with a ray-tracing approach, to simulate the propagation of the incident laser radiation in the spray, the collection of the light by the camera lens, and the image formation on a matrix simulating the camera sensor. The light transmission is set to 5% near the nozzle tip and 27% in the dilute region, with a droplet size distribution ranging from 8 to 68 \(\upmu\)m. From these numerical calculations, it is observed that the resultant SLIPI signal tends to be closer to the pure single scattering signal when reducing the spatial period of the incident modulated light, as shown in Figure 1e. However, the remaining differences between SLIPI and only single scattering detection are mostly due to the highly forward scattering lobe of the scattering phase function. Nevertheless, it is observed that the technique is capable of suppressing 90% of the unwanted light intensity which is detected in the \"conventional\" planar imaging detection scheme. Similar Monte Carlo simulation studies of the SLIPI process can be found in [20] but in the case of homogeneous spray medium. The combination of SLIPI with LIF/Mie ratio was reported in 2014 for the 2D mapping of droplets absolute SMD in a steady hollow-cone water spray [21].