Influence of Uncertainties in Optode Positions on Self-Calibrating or Dual-Slope Diffuse Optical Measurements

Self-calibrating and dual-slope measurements have been used in the field of diffuse optics for robust assessment of absolute values or temporal changes in the optical properties of highly scattering media and biological tissue. These measurements employ optical probes with a minimum of two source positions and a minimum of two detector positions. This work focuses on a quantitative analysis of the impact of errors in these source and detector positions on the assessment of optical properties. We considered linear, trapezoidal, and rectangular optode arrangements and theoretical computations based on diffusion theory for semi-infinite homogeneous media. We found that uncertainties in optodes' positions may have a greater impact on measurements of absolute scattering versus absorption coefficients. For example, a 4.1% and 19% average error in absolute absorption and scattering, respectively, can be expected by displacing every optode in a linear arrangement by 1 mm in any direction. The impact of optode position errors is typically smaller for measurements of absorption changes. In each geometrical arrangement (linear, trapezoid, rectangular), we identify the direction of the position uncertainty for each optode that has minimal impact on the optical measurements. These results can guide the optimal design of optical probes for self-calibrating and dual-slope measurements.