New technique to estimate non-absorbing temporal point spread function for diffuse optical tomography using backscattered light Takeshi Namita, Masafumi Otani, Yuji Kato and Koichi Shimizu Graduate School of Information Science and Technology, Hokkaido University, N14, W9, Kita-ku, Sapporo, 060-0814, JAPAN tnamita@bme.ist.hokudai.ac.jp Abstract: To reconstruct cross-sectional absorption distribution of diffuse medium, a new technique to estimate non-absorbing temporal point spread function in time-resolved measurement was developed. The feasibility and effectiveness were verified in Monte Carlo simulation. 1. Introduction CT imaging with backscattered light from a diffuse medium has practical advantage over the conventional diffuse optical tomography for whole cross-section. We can obtain the CT image only to certain depth, but it is applicable to the body part through which enough light cannot penetrate. We have developed a technique to reconstruct the cross- sectional image of diffuse medium using time-resolved measurement of backscattered light [1]. In this technique, we need the temporal path-length distribution (TPD, temporal change of propagation path-length of received photons which have passed the specific layer of the diffuse medium) of each layer and the temporal point spread function (TPSF) for a non-absorbing case N(t). TPD and N(t) depend on only scattering property of the object. The accuracy of the reconstruction of absorption distribution is dependent on the appropriateness of N(t). So far N(t) has been obtained in a computer simulation or the measurement with a non-absorbing model phantom. To obtain a true N(t) of the target object, we developed a new technique to calculate N(t) from the measured wave shapes of backscattered light. This paper presents the theoretical principle of the proposed technique and the results of a feasibility test in Monte Carlo simulation. 2. Reconstruction of cross-sectional  a distribution The TPSF R(t) of the object with unknown absorption distribution can be written as , (1) where M,  ai and L i (t), respectively, represent the number of layers, the absorption coefficient of the ith layer, and the TPD of the ith layer. Absorption coefficients of each layer can be obtained by solving the following simultaneous equations [1]:             . , , 2 , 1 , , , , ln ln 0 1 0 1 1 0 1 M j i dt t L t L t N t L t L dt t L t R t N dt t L t R t N j i ij i i M i Mi ai M M i i ai                                                     We must assume many thin layers to apply this technique to a scattering object with unknown structure or complicated structure, such as an animal body. However, the error in the inversion process increases rapidly as either the imaginary layers increase or their thicknesses decrease. We devised a technique to assume only two thick layers and to repeat the inversion with variable thickness to overcome this problem [1]. In this technique, we combine the M-layers into two layers, and estimate the two absorption coefficients. This process is repeated M-1 times with different grouping of adjacent layers. In addition, more photon propagates in shallower layers than in deeper layers. Thus, the absorption coefficient of a deeper layer is obtained using that of the shallower layer estimated in the previous sequence. With these two ideas, we can expect more accurate estimation for the absorption distribution than the common techniques which solve the inverse problem at once. The concrete processes of this technique are as follows. We consider the layers above the k-th layer as an upper layer, and the layers below the k+1-th layer as a deeper layer. The attenuation of TPSF is expressed in the following equation,               M i i ai t N t L t N t R 1 exp  (2) ACOFT Presentation ● IQEC/CLEO Pacific Rim 2011 ● 28 August - 1 September 2011 ● Sydney, Australia 978-0-9775657-7-1  2011 AOS 701