What is a phase map and how is it used in structured light 3D scanners?

[ahkcasfm]

What is a "phase map"?

I am doing some reading on Structured Light 3D Scanners using digital fringe projection, where a projector shines light (e.g. sinusoidal patterns) onto an object, a camera takes some pictures, and some software uses them to extract a 3D model of the object.

The papers I have been reading talk about acquiring a "phase map" of the surface and comparing it to a "reference phase map". None of them seem to actually define what this means, and searching on Google seems to just give links to papers.

Here is an example: http://www.cadanda.com/V2No6_04.pdf (ctrl-F "phase map" will give plenty of results)

Can anyone explain in relatively simple terms? I have quite a good understanding of time/frequency domain, Fourier Transforms, etc. but have never heard this term before.

 

[HallsofIvy]

A "phase map" for a differential equation is a graph consisting of short line segments showing, at each point (x,y), the slope of the function y= f(x), satisfying the differential equation and passing through the given point. Actual solutions to the differential equation will be tangent to those line segments so the phase map can show properties of solutions even if you cannot solve the equations.

 

[ahkcasfm]

Hmmm ... so in the context of measuring surface shape, would the phase map be a table of values (one for each pixel) giving the slope of the depth function (z = f(x,y))? Or perhaps the slope in a particular direction (probably the x direction)?

Thanks