Fig. 2.

(a) Simulated workflow of multifrequency synthesis and extraction (MSE) algorithm on a turbid sample containing a circular absorbing lesion. First, a square wave ($\text{duty cycle}=50\%$) and a DC (planar) image are acquired. Here, the low-pass filtering properties of the sample damp the higher-ordered harmonics of the square wave, such that only the fundamental frequency component is preserved. These images are applied to a two-dimensional Hilbert transform method, from which the phase angle map of the square wave pattern is derived. Using the known Fourier series representation of a square wave [Eq. (3)], the frequency coefficient matrix ($C_k$) is generated. Finally, $C_k$ is inverted and multiplied by the raw data vector ($\mathbf{I}$). (b) Extracted spatial frequency intensities from simulation shown in (a), including (1) DC and (2) fundamental frequencies. (3) Cross-section of extracted reflectance comparing MSE to conventional, three-phase SFDI.