This paper proposes a stereoscopic model for DFD display that explains the continuous depth modulation and protruding
depth perception. The model is composed of four steps: preparation of DFD images, geometrical calculation of viewed
images, human visual function for detecting intensity changes, and stereoscopic depth perception. In this paper, two
types of displayed images for DFD display are prepared: the former pairs are for conventional DFD, where a fused image
is located between the layered images; the latter pairs are for protruding DFD, where a fused image is located closer than
the foreground image or further than the background image. Viewed images at both eye positions are simulated
geometrically in computer vision optics model. In order to detect intensity changes, we have utilized Laplacian operation
on a Gaussian blurred image. Stereoscopic depths are calculated by matching the zero crossing position on the Laplacian
operated images. It is revealed that our stereoscopic model explains both conventional and protruding DFDs.
We can successfully solve the problem in DFD display that the maximum depth difference of front and rear planes is limited because depth fusing from front and rear images to one 3-D image becomes impossible. The range of continuously perceived depth was estimated as depth difference of front and rear planes increases. When the distance was large enough, perceived depth was near front plane at 0~40 % of rear luminance and near rear plane at 60~100 % of rear luminance. This maximum depth range can be successfully enlarged by spatial-frequency modulation of front and rear images. The change of perceived depth dependence was evaluated when high frequency component of front and rear images is cut off using Fourier Transformation at the distance between front and rear plane of 5 and 10 cm (4.9 and 9.4 minute of arc). When high frequency component does not cut off enough at the distance of 5 cm, perceived depth was separated to near front plane and near rear plane. However, when the images are blurred enough by cutting high frequency component, the perceived depth has a linear dependency on luminance ratio. When the images are not blurred at the distance of 10 cm, perceived depth is separated to near front plane at 0~30% of rear luminance, near rear plane at 80~100 % and near midpoint at 40~70 %. However, when the images are blurred enough, perceived depth successfully has a linear dependency on luminance ratio.