Structured Light 3D Scanning

Step 2 Theory: Three Phase Scanning

Imagine projecting a single gradient from white to black on a scene. The brightness of a given point then corresponds to the angle from the projector. But there are three problems here: this only yields 256 possible angles due to the bit depth of most cameras and projectors, the inherent color and reflectivity of the scene isn't accounted for, and the way light intensity drops off with distance isn't modeled.

If we project multiple gradients that are slightly offset from each other, we can overcome two of these problems. The light intensity drop off acts as a scaling factor on all light at a given point, the inherent color of a scene is an offset intensity. Sampling a point multiple times can help with the bit depth issue, but the better solution is to repeat the gradient as a triangle wave ("stripes"). This way adjacent lines don't have the same brightness.

With repeated gradients, we no longer have a unique angle identification for every line. To deal with this, we have to propagate the stripe number from one stripe to another. This is called phase unwrapping. There are a bunch of phase unwrapping algorithms, and they generally have a trade off between accuracy and speed. One of the simplest and fastest phase unwrapping algorithms uses a flood fill technique.

One remaining problem is that the pattern will blur as the scene moves away from the projector's focal plane. We can deal with this by using a sort of "pre-blurred" pattern: three cosine waves. This technique is called three phase scanning, and consist of the patterns: cos(θ - 2π/3), cos(θ), cos(θ + 2π/3).