# Applications of Capacitive Imaging in Human Skin Texture and Hair Analysis
## 2 Materials and Methods
### Measurement Depth Simulation  
In capacitive measurements, the image resolution and sensitivity are important as well as the measurement depth. For in vivo skin measurements, the penetration depth of the electric field should not exceed the thickness of stratum corneum, which consists of dead and keratinized cells [1]. Otherwise, the pixel readouts will saturate because of the higher conductance in deeper skin layers. By contrast, in hair measurements the depth should be sufficient to reach the medulla to capture information from all layers in the hair shaft. In this work, the measurement depth is defined as the distance from the sensor surface for which the electric potential drops by 97%. To the best of our knowledge, this comes in agreement with experimental and theoretical results achieved by [PERSON] et al. [29], where the system capacity is used as a reference instead of the electric potential. Of course, in either approach, the system response changes with the hydration level of the sample, so the penetration depth of the electric field varies accordingly. In order to evaluate the performance of Epsilon E100, the penetration depth for different insulating materials is simulated using [PERSON]'s equations for both E100 and CM825 and the results are compared.  
A property of electromagnetics is that [PERSON]'s equations are linear. As a result, we can refer to an arbitrary distribution of charges by simple addition of the relevant contributions. In the case of interdigital sensors, such as Corneometer, for the charge distribution residing on a strip \((x_{1},x_{2})\), the electric potential at an arbitrary point \((x,y)\) is given by the expression in Equation (1). The simulation defined 6 driving and 5 sensing rectangular electrodes in the dimensions provided by CM825 literature. The electric potential was calculated for points on a line segment from the surface of the middle driving electrode to 60 \(\upmu\)m perpendicular displacement.  
\[\Phi(x,y)=\lambda k_{e}(\sinh^{-1}\frac{x_{2}-x}{|y|}-\sinh^{-1}\frac{x_{1}-x}{ |y|}) \tag{1}\]  
where:  
\(\Phi=\) the electric potential  
\(\lambda=\) the surface charge density and  
\(k_{e}=\) the dielectric of the insulating material under examination \((k_{e0})\)  
In the case of annular or disk sensors, such as Epsilon E100, Equation (2) calculates the electric potential in any given point perpendicular to the center of the electrode. For the purpose of this simulation, one driving electrode disk and one sensing electrode ring were used. The electric potential was measured from the center of the sensor surface to 60 \(\upmu\)m distance on a perpendicular line segment.  
\[\Phi(z)=\frac{\lambda}{2k_{e}}(\sqrt{R_{out}^{2}+z^{2}}-\sqrt{R_{in}^{2}+z^{2}}) \tag{2}\]  
where:  
\(R_{out}=\) the outer electrode radius  
\(R_{in}=\) the inner electrode radius  
\(z=\) the perpendicular point distance from the center of the sensor surface  
The hydration level of the samples is simulated by changing the dielectric permittivity parameter (\(k_{e}\)). The latter ranges from 1 to 80.1 in 20 \({}^{\circ}\)C, where higher value denotes more hydrated samples. For both instruments, the dielectric permittivity of the protective layers is assumed 3.9 and the simulation is repeated for samples with dielectric permittivity of 80, 7 and 3.9. The simulation results in Figure 3 show the Corneometer CM825 measurement depth ranges from 10 to 40 \(\upmu\)m, while for Epsilon E100 from 5 to 22 \(\upmu\)m. Assuming that stratum corneum thickness is between 10 \(\upmu\)m and 40 \(\upmu\)m, the results validate that both instruments are appropriate for human skin measurements with Corneometer with greater penetration depth. On hair measurements, assuming sample thickness 70-150 \(\upmu\)m, both instruments have insufficient penetration depth but still reach fraction of the cortex layer.