

Optical Diffuser:
A diffuser is an optical element that scatters light and
is widely used to soften or shape light in illumination and
display applications. Most commercially available diffusers
are implemented as a refractive element with a random surface
profile.






The basic idea of DFDiff:
When a diffuser is placed between a camera and an object, the
captured image will appear blurred, where the amount of
blurring is proportional to the objectdiffuser distance.
From the amount that an object is diffused, we can infer its
depth. The image formation model with a diffuser placed
between the camera and the scene is carefully studied in this
project.






A pinhole camera with a diffuser:
For a pinhole camera, we prove that the pinholediffuser distance U, the objectdiffuser distance Z, and the diffuser size on the diffuser AB follow a diffusion law, which has a similar form as the Gaussian lens law. In particular, for a given image magnification (U+Z)/V, the blur size on the sensor r is proportional to the objectdiffuser distance Z. It should also be noted that tilting the diffuser by a small angle will not change the blur size r, as long as the projection center C is not changed.






A lens camera with a diffuser:
For a lens camera, the blur in the image is caused by a combination of lens defocus and diffusion due to the diffuser. It is proved that the overall blur kernel is the convolution of the defocus kernel and the diffusion kernel.






The equivalence between DFDiff and DFD:
Diffusion due to a diffuser is shown to be equivalent to lens defocus. The diameter of the virtual aperture A'B' is proportional to the diffusion angle and the diffuserlens distance. This equivalence implies that most depth from defocus (DFD) algorithms can also be used for depth from diffusion (DFDiff).






Depth sensitivity:
DFDiff is able to achieve a high precision depth estimation without a large lens. For a given image magnification, the depth sensitivity of DFD is proportional to aperture size and inversely proportional to the objectcamera distance. Meanwhile, the depth sensitivity of DFDiff is proportional to the diffusion angle and is independent of the object distance. Note that large angle diffusers are much cheaper to manufacture than large aperture lenses.






On lens aberrations:
Lens aberrations cause the shape of the defocus point spread function
(PSF) to vary with field position. This effect is strong,
particularly in the case of inexpensive lenses, and degrades
the precision of depth estimation. In contrast, we show that diffusion PSFs are more invariant to field position. Even a lowend consumer camera can be used for high precision depth estimation, when coupled with an appropriate diffuser.






Experimental results  Playing Cards:
DFDiff results for five playing cards, each of which was only 0.29mm thick. A Canon EOS 20D camera and a 20 degree Gaussian diffuser were used.






Experimental results  A small sculpture:
DFDiff results for a thin sculpture. A Canon G5 camera and a five degree Gaussian diffuser were used.






Experimental results  Egyptian relief on a vase:
DFDiff results for a thin Egyptian relief on a vase. A Canon EOS 20D camera and five degree Gassian diffuser were used.






Experimental results  A large sculpture on a curved surface:
DFDiff results for a large 650mm x 450mm sculpture on a curved surface. A Canon EOS 20D camera with a 50mm lens was placed 2000mm from the object. Ten diffused images were captured by swiping diffuser over the surface.



