## 1 Introduction  
Atomizing sprays are used for many industrial processes such as in internal combustion engines, crop treatment in agriculture, spray painting, production of powder in the food and pharmaceutical industry, etc. [1, 2]. Based on their applications, spray systems must have a given global structure, which is characterized by several parameters including, spray angle, penetration distance, droplets size distribution, droplets evaporation rate, droplets number density (N), and liquid volume fraction (LVF) [1, 3]. Spray quantities such as droplets SMD (Sauter mean diameter) give the information on the active surface area of the spray, while the LVF provides the spatial distribution of liquid in the spray. Therefore, measuring SMD, N, and LVF from a droplet cloud, is very important for the understanding of the fuel-air mixing process used in internal combustion engines [4]. Simultaneous measurement of these quantities could be very helpful for correlation studies in sprays. Owing to their non-intrusive nature, optical methods have been widely used for the measurement of spray quantities in a point-wise manner, as well as in three dimensions [5]. As a point-measurement optical method, phase Doppler anemometry (PDA) is one of the most reliable methods to extract droplets mean diameters, droplets sphericity, droplets number density, and droplet velocity in sprays [6]. However, in optically dense sprays, PDA measurements are restricted by effects from multiple light scattering and laser extinction [6]. Furthermore, point-wise approaches require large measurement times for fully mapping the spray. For two-dimensional (2D) mapping of a large cross-section of the spray, laser sheet imaging is commonly employed [5]. The method can easily be extended to three-dimensional (3D) imaging by means of \"slicing\" the spray in several 2D layers [7]. There are a variety of quantities that can be extracted using laser sheet imaging, for example, [PERSON] et al. [8] reported on the fuel concentration mapping of self-fluorescent diesel by exploiting its laser-induced fluorescence signal. The velocity vectors of droplets in a plane can be deduced using particle image velocimetry [9]. The fuel distributions in terms of liquid and vapor phases have been extracted by means of the exciplex-LIF (laser-induced fluorescence) [10]. The SMD of droplets in a plane of the spray has been reported using the ratio of laser-induced fluorescence (LIF) and Mie scattering (Mie) light intensity, known as LIF/Mie ratio or planar droplet sizing (PDS) method [11]. For the LVF mapping in sprays, [PERSON] and [PERSON] [12] used planar laser-induced fluorescence combined with particle and droplet image analysis. In this method, backlight illumination microscopic imaging-based calibration of LVF was implemented on macroscopic planar LIF and Mie images (recorded one after another; not simultaneously). However, in optically dense sprays, the planar imaging techniques are limited by effects from multiple light scattering and light extinction [13]. The extinction effects can be compensated for based on the exponential decay of transmitted light according to the Beer-Lambert's law [14]. Nevertheless, the light extinction is accurately deduced only under the single scattering regime (when a maximum of one interaction between photon and droplets is occurring in average; optical depth or OD \(\leq\) 1) and the suppression of the light intensity contribution from multiple scattering becomes very important in the intermediate and multiple scattering regimes (when the averaged number of interaction between photon and droplets is larger than one) [15; 16]. The suppression of multiple scattering intensity in planar imaging of sprays can be done using structured laser illumination planar imaging (SLIPI) [17; 18; 19].