SUMMARYThere is a need for methods to display 3-dimensional data (volume data) obtained from such procedures as computer tomography (CT), magnetic resonance imaging (MRI), and 3-dimensional radar in a form that can easily be interpreted by humans. Methods that present such data via a 3-dimensional display are able to show the 3-dimensional image directly to humans and are well adapted to allow the recognition of 3-dimensional structure. In particular, 3-dimensional displays using holography are especially suited to assisting humans in interpreting 3-dimensional information. In this paper we propose a volume rendering computer-generated hologram (CGH) method that calculates a hologram directly from volume data using CGH technology without employing any intermediary images or photographic procedures. Since in this method the hologram is generated computationally, there is significant flexibility in how the 3-dimensional image can be displayed. As well as enabling images to be displayed with shading, a whole range of different 3-dimensional display techniques are possible; for example, at one extreme we can display only the surfaces in the volume data making the internal regions opaque, while by introducing transparency we can make the internal structures visible. We have confirmed the effectiveness of the proposed method by using it to create computergenerated holograms on the basis of 3-dimensional medical MRI data and conducting optical experiments.