## 1 Introduction  
The restricted emissions regulations imposed and special issues related with CO\({}_{2}\) reduction are some of the challenges that the automotive industry has faced in the last few decades [1; 2; 3]. As a result, car manufacturers have focused their research into new combustion concepts such as low temperature combustion (LTC) [4] and partially premixed combustion (PPC) [5]. Consequently, a good understanding of the combustion process is extremely important for the optimization of different engine systems and a better comprehension of the phenomena. In this context, optical engines are a very important tool to visualize and obtain information about the combustion process that is not available in metal engines [6; 7]. During the last few years, it has become one of the most important and common experimental undertakings to study and develop new combustion strategies and injection systems [8]. This kind of test bench permits the use of a wide variety of techniques that can be either thermodynamically based (in-cylinder pressure measurements) and/or non-intrusive optical ones such as PIV [9], Mie scattering, natural emission of the flame [10], etc. Basically, an optical engine is a metal engine rebuilt with optical access either in the side of the chamber, through the cylinder liner, or from below through the piston, or both. Furthermore, it is necessary to have a piston extension for access from below (Bowditch design) [11]. In this way, to obtain optical access, some modifications are required in the standard engine, which can affect the thermodynamic evolution inside the cylinder. The thermodynamic evolution is the link between optical and metal engines, thus it has great importance to relate physical and chemical phenomena observed via optical techniques to the real behavior inside metal engines. Thermodynamic analysis can be performed either by in-cylinder pressure measurements through rate of heat release (RoHR) calculations or predictive models that provide an estimation of the pressure and temperature evolution inside the chamber for each operating condition [11; 12]. This kind of analysis is directly affected by some uncertainties such as the effective compression ratio, heat transfer coefficient, top dead center (TDC) position, etc. Thus, it is necessary to minimize errors, and for this purpose, different methodologies have been carried out to more accurately estimate these parameters [13; 14]. However, when dealing with optical engines, it is more difficult to estimate these uncertainties due mainly to differences in heat transfer and mechanical deformations. Differences in heat transfer are basically caused by the optical access and this is related to the lower heat conductivity of quartz in comparison with aluminum and steel. Mechanical deformations occur in several parts of the engine but they are mainly related to the elongated piston caused by the high values of in-cylinder pressure, thermal expansion, and to a lesser extent, the acceleration due to piston movement. Cylinder volume is affected directly by mechanical deformations due to different forces (inertial, thermal, and pressure) that actuate expanding or compressing different engine parts while it is running. Pressure forces act to compress the moving parts and they are higher near the TDC. Inertial forces act to expand the moving engine parts near the TDC and compresses them near the BDC. Considering that cylinder volume is critical to the RoHR calculation, quantifying the deformation is extremely important to obtain the correct instantaneous volume. Furthermore, mechanical deformation impairs the compression ratio. Some authors have already developed simple models of mechanical deformation to include in the thermodynamic analysis [15; 16]. [PERSON] et al. [17] obtained the deformation in a piston of an optical engine measuring the variation of piston position with a high speed camera.