Three dimensional mapping of turbid media by hyper spectral imaging
Final Report Abstract
The research of this project was focused on the transformation of hyper spectral images into 3D images. Thereby, it was shown that depth information is present in hyper spectral images. Moreover, the depth information allow a quantification of the depth of inclusions. Under certain conditions an iso-point in the spectra similar to an isobestic point might be present. With a present inclusion, the depth of the inclusion does not influence the reflection spectra at the wavelength of the iso-point. The resulting reconstruction of the depth shows a linear regime close to the surface in which the reconstructed depth is proportional to the real depth. For deeper parts of the inclusion, the reconstructed depth drops exponentially with the real depth. Thus, the regimes are named the linear regime and exponential regime. Furthermore, the iso-point is not present for all parameters as the ink-concentration and, therefore, the absorption coefficient in the inclusions influences the fact if an iso-point is present. However, there is a large potential parameter space additional to the absorption coefficient in the inclusions which might influence the presence of an iso-point. As the amount of parameters is huge and the linear regime is close the surface, neither Monte-Carlo-simulations nor calculations by the diffusion approximation can be carried out. Hence, by theoretical calculations, verified by experiments, it can be shown that the total transmission (TT) and the collimated transmission (CT) are proportional to each other with the proportionality constant eµs . Hence, it is enough to simulate CT and derive the results for TT from it. By this, a wide simulation of parameters can be done very efficiently. This result has much further implication for many different fields of biophotonics as this two formerly independent variables are now clearly linked to each other. It might be used to measure the scattering coefficient with low influence of absorbers due to the fact that the absorbers influence CT and TT as well. As CT and TT are proportional, Lambert’s law can be used to describe for TT as well as CT. The simulation with Lambert’s law to evaluate the presence of an iso-point is done for a parameter space of seven potential important parameters under the conditions that a red absorber is used (stronger absorption in the blue range): the scattering coefficient in the substrate and the inclusion, the absorption coefficient in the red and blue range in the substrate and the inclusion and the amount of Fresnel reflection at the boundaries. The biggest influence is found for the scattering in the inclusion. In general, a high or very low scattering seems to beneficial. Moreover, the absorption coefficient in blue range should be high in the inclusion. This matches with the experimental results as higher ink concentrations were required for the presence of the iso-point. Despite the comparably wide range of studied parameters, the presence of the iso-points seems to be rather complex. Despite this complexity regarding the question if the iso-point is present, the reconstruction of the depth information is fairly easy and does not require large computing power like photo acoustic tomography or complicated interferometric set-ups like optical coherence tomography. By understanding the presence of an iso-point, standard hyper spectral images can be used to enable 3D-imaging. Therefore, more understanding of the iso-point is important. Especially, more detailed understanding under which conditions it occurs is essential as it is the key for a wide usage. Furthermore, a continuation of this research might provide a lot of insight into understanding of scattering, absorption and back reflection from a macroscopic point of view.
Publications
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"Direct reconstruction of qualitative depth information from turbid media by a single hyper spectral image", Proc. SPIE 10885, Optical Diagnostics and Sensing XIX, 2019
M. Hohmann, ..., M. Schmidt
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"Direct measurement of the scattering coefficient", Biomedical Optics Express, 2021, page 320-335
M. Hohmann, ..., M. Schmidt
