## 2 Experimental and Theoretical Tools
### Diagnostic Techniques
#### 2.3.3 Diffused Back Illumination (DBI) Extinction Imaging  
Diffused back-illumination (DBI) is a technique based on measuring the amount of light attenuated by liquid droplets or by soot particles within the flame, which is related to the liquid and soot concentration, respectively. A red LED (\(\lambda\) = 660 nm) was used in these experiments as the light source to create short flashes synchronized with the camera frames. An engineered diffuser (EDC-20 by RPC Photonics, Henrietta, NY, USA) was placed in front of the LED to create a diffused Lambertian intensity profile [30]. On the collection side, the transmitted light from the LED and the flame radiation went through a beam splitter with a 50% reflection rate. Then, half of the light was collected by the Photron SA-X2 camera. The exposure time was 1 \(\upmu\)s and the resolution was 896x384 with a magnification of 6.85 pixel/mm. The sampling frequency was 25 kfps. The images taken were analyzed considering that the total light registered by the camera has two contributions: the transmitted LED light intensity and the flame radiation. Due to the use of a bandpass filter centered at 660 nm (FWHM = 10 nm), the crosstalk of flame radiation into the DBI signal is minimized. However, the flashing frequency of the LED was set as quarter of the camera frame rate to capture a LED image between every three consecutive dark images. This configuration was used to deal with the non-ideal CMOS sensor behavior, that occurs when the camera is exposed to a sudden change in light intensity between two consecutive frames [18]. The flame luminosity from dark image before the LED image (third dark image) was quantified and used to isolate the transmitted LED light from the total registered radiation. Then, the light attenuation can be related with the optical properties of the soot cloud by means of Lambert-Beer's law, as described in Equation (1):  
\[\frac{I_{on}-I_{off}}{I_{o}}=e^{-KL} \tag{1}\]  
where \(I_{on}\) is the light intensity recorded by the camera when the LED is on, i.e., the sum of the transmitted LED intensity and the flame luminosity. \(I_{off}\) is the intensity of the flame acquired when the LED is off. \(I_{O}\) is the LED light intensity obtained from images recorded before the start of injection (SOI). K is the soot dimensional extinction coefficient and L is the light beam path length through the soot cloud. Thus, the product KL represents the integral value of the soot extinction coefficient along the light path, which is related with the soot concentration [24]. Besides determining soot production through the KL factor, DBI is also suggested as an experimental standard to measure the liquid length (LL) of fuels by ECN [20]. The method uses the extinction produced by the spray droplets to provide a quantitative parameter related to the liquid volume fraction along the path of the light. ECN recommends also taking care with vapor phase beam steering from temperature gradients, which could disturb the measurement. In the current work, the liquid length has been determined only at 800 K and 900 K. It was observed that at higher temperature the measurement is not reliable because the flame lift-off zone is close to the liquid jet zone and more intense beam steering exists there. The image processing method to get KL was based on creating a mask from the dark image \(I_{off}\) with the aim of collecting the information only corresponding to flame radiation. Based upon this mask, attenuation (\(I_{on}-I_{Off}\)) is calculated, from which Equation (1) is applied. Figure 2 shows a KL profile along the spray axis at a time instant where the flame is well developed (3500 \(\upmu\)s), within the quasi- steady period chosen in this study (between 3000 \(\upmu\)s and 4000 \(\upmu\)s). The confidence interval at 95% (red shadow) for the measurement of the ensemble averaged KL value and the standard deviation (blue shadow) have been represented. The operating condition shown is the nominal case and the fuel chosen is the diesel.