In daily-life environment, the quantitative measurement of biological substances, such as the blood glucose level in the human skin, is strongly required to realize the non-invasive healthcare apparatus. Fourier-spectroscopic-tomography of the little-finger-size with high time-resolution and with the strong robustness for mechanical vibrations is proposed. The proposed method is a kind of near-common-path interferometer with spatial phase-shift method. We install the transmission-type relative-inclined phase-shifter on the optical Fourier transform plane of the infinity corrected optical system. The phase shifter is constructed with the cuboid and wedge prisms to give the relative phase-shift spatially between each half-flux of the objective beams. The interferograms from each single-bright-point on an objective surface in a line are formed as fringe patterns on 2-dimensional imaging array devices. And because the proposed method is based on the imaging optics, only emitted rays from a focal plane can contribute forming of interferograms. Thus, the measurement plane can be limited onto the focal plane only. From the spectroscopic tomography, only at a localized vessel area in human skins, we can get the pinpointed near-infrared spectroscopic data. And we can expect the improvement of the determination precision, because a Fourier spectroscopic-character is acquired from multiple intensity data in accordance with amount of phase-shift. From the statistical point of view, the gradation of detector is improved with the square root of sample number, based on t-distribution. We constructed the statistical model to assure the determination accuracy, and demonstrated the feasibility of the glucose sensor using liquid cells.