Modulation Frequency Selection and Efficient Look-up Table Inversion for Frequency Domain Diffuse Optical Spectroscopy

Significance: Frequency domain diffuse optical spectroscopy (FD-DOS) uses intensity modulated light to measure the absorption and reduced scattering coefficients of turbid media such as biological tissue. Some FD-DOS instruments utilize a single modulation frequency, whereas others use hundreds of frequencies. The effect of modulation frequency choice and measurement bandwidth on optical property (OP) extraction accuracy has not yet been fully characterized.

Aim: We aim to assess the effect of modulation frequency selection on OP extraction error and develop a high-speed look-up table (LUT) approach for OP estimation.

Approach: We first used noise-free simulations of light transport in homogeneous media to determine optimized iterative inversion model parameters and developed a new multi-frequency LUT method to increase the speed of inversion. We then used experimentally derived noise models for two FD-DOS instruments to generate realistic simulated data for a broad range of OPs and modulation frequencies to test OP extraction accuracy.

Results: We found that repeated measurements at a single low-frequency (110 MHz) yielded essentially identical OP errors as a broadband frequency sweep (35 evenly spaced frequencies between 50 and 253 MHz) for these noise models. The inclusion of modulation frequencies >300  MHz diminished overall performance for one of the instruments. Additionally, we developed a LUT inversion algorithm capable of increasing inversion speeds by up to 6  ×  , with 1000  inversions  /  s and ∼1  %   error when a single modulation frequency was used.

Conclusion: These results suggest that simpler single-frequency systems are likely sufficient for many applications and pave the way for a new generation of simpler digital FD-DOS systems capable of rapid, large-volume measurements with real-time feedback.