Wavelength optimization of spectral near-infrared optical tomography using available laser diodes

As optimized wavelengths are used, a nearinfrared (NIR) tomographic imaging system using multiwavelengths in continuous wave has the potential to provide accurate information of chromophores. In this paper, we discuss wavelength optimization with commercial laser diodes. Through theoretical analysis, we use the residual norm (R) and the condition number (κ) representing the uniqueness of this matrix problem (Eq. (6)) and the smooth singular-value distribution of each chromophore, respectively. The optimum wavelengths take place as large R and small κ. We found 37 wavelengths in total from the 633nm-980nm range available in the market to discover optimum wavelength sets for a broad range of chromophore combinations. From a complete set of 37 wavelengths, there exist 7770 (C³⁷ ₃), 66045 (C³⁷ ₄), and 435897 (C³⁷ ₅) combinations of three, four, and five wavelength sets, respectively, for accurately estimating chromophores (HbO₂ and HbR) plus the scattering prefactor A. With the numerical calculation, top 10 wavelength sets were selected based on high R and low k. Furthermore, it is found that 650, 730, 905, 705, and 690 nm are optimal with a same part for three, four, and five wavelength sets, respectively.