A method and apparatus for constructing a 3-dimensional image of the internal organs invisible by the conventional method is provided. The apparatus comprises: generating means for generating a monochromatic and parallel X-ray beam from an X-ray beam; a reflection-type angle analyzer for reflecting the monochromatic and parallel X-ray beam at reflecting points on both slopes of a reflection curve of the reflection-type analyzer, angle information being extracted to a maximum extent at the reflecting points, the monochromatic and parallel X-ray beam including an X-ray beam which passed through the object when the object is positioned on a rotatable goniometer in the monochromatic and parallel X-ray beam and an X-ray beam from the generating means when the object is not positioned in the monochromatic and parallel X-ray beam; an imaging device for generating a refraction angle data by receiving the monochromic and parallel X-ray beam reflected on the reflection-type angle analyzer to detect the intensity thereof, and output a refraction angle data; andan arithmetic device for constructing the 3-dimensional image by carrying out au arithmetical operation for the refraction angle data from the imaging device.