Multi-wavelength spatial frequency domain diffuse optical tomography using single-pixel imaging based on lock-in photon counting

We present a spatial frequency domain (SFD) diffuse optical tomography for simultaneous acquisition of multi-wavelength tomographic images of turbid media. We propose a highly sensitive single-pixel SFD imaging system for simultaneously collecting multi-wavelength spatially modulated reflectance images, instead of using the expensive electron-multiplying charge-coupled device camera that requires switching between the multi-wavelength collections. The single-pixel SFD imaging system using three low-power light sources (455, 532 and 660 nm) that were intensity-modulated by square waves with three different frequencies for frequency encoding, and all the light sources were focused onto one digital micromirror device (DMD) for generating wide-field sinusoidal illumination patterns. Reflected light from the surface of the turbid media was modulated by the other DMD with many sampling patterns before being spatially integrated. Spatially integrated light signals were frequency decoded with a novel highly sensitive lock-in photon counting detection, then multi-wavelength spatially modulated reflectance images were recovered with the single-pixel imaging (SPI) method. We incorporated the two-dimensional discrete cosine transform (DCT) into the SPI method to reduce the number of sampling patterns, and, thereby, the proposed DCT-SPI scheme achieved a fast acquisition of SFD reflectance images that is desired for a dynamic SFD imaging application. Direct current (DC) and alternating current (AC) amplitudes at all the locations on the media surface were extracted from the recovered images. Multi-wavelength tomographic images were reconstructed with an inversion algorithm based on the first-order Rytov approximation of the diffusion equation, using both the extracted DC and AC amplitudes. We performed experiments using a series of tissue simulating phantoms to verify the performances of the proposed approach and compared the experimental results with those using a conventional camera-based SFD imaging system. The results demonstrate that our DCT-SPI based SFD-DOT approach is well suited for simultaneous reconstruction of multi-wavelength tomographic images to pave the way for many SFD imaging applications.