We aim to realize non-invasive blood glucose measurements in daily life. The human body emits radiated light with an intensity that depends on the body temperature (approximately 300 K). Mid-infrared passive spectroscopic imaging obtains component information from this radiated light. Using radiated light measurements of the arm from a distance of 600 mm, we identified the specific emission spectral peaks, at wavelengths of 9.25 µm and 9.65 µm, derived from glucose components. In addition, we determined the correlation between the intensity of radiated light at the peak wavelength and blood glucose level. From these results, we previously reported the possibility of non-invasive blood glucose measurements from a distance using mid-infrared passive spectroscopic imaging. Therefore, we developed a passive one-shot Fourier spectrometer to apply this method to wearable devices. The apparatus was designed with a numerical aperture of 0.77 for passive spectroscopy of the living body. The field curvature due to the increased N.A. was mitigated by combining an imaging lens with a phase shifter. Additionally, the apparatus was configured with two lenses to enhance transmission. Owing to the small object lens (diameter of 6 mm) and short optical path (axis length of approximately 14 mm), the apparatus was mountable on wearable devices. Moreover, the apparatus was equipped with a multi-slit to prevent loss of interference sharpness. The multi-slit was designed with 5 lines comprising aperture patterns that enabled the detection of glucose. As a result, we succeeded in detecting spectral characteristics of polypropylene using a blackbody as background light source.