Modulated light

Some imaging systems encode information in how their light varies. A continuous-wave time-of-flight (CW-ToF) camera modulates its light source in time and correlates the returning light with a reference signal, so the measurement depends on the phase of each path’s length. A structured light system projects a spatial pattern, so the measurement depends on the pattern value where each path is lit. Both measure a path integral weighted by a modulation term \(m\):

\[ I = \int f(\bar{\mathbf{x}})\, m(\bar{\mathbf{x}})\, \mathrm{d}\bar{\mathbf{x}}. \]

Measurement	Modulation \(m(\bar{\mathbf{x}})\)	Render pass
CW-ToF	a periodic waveform of the path length, \(w(\ell(\bar{\mathbf{x}}) / \lambda - \phi)\)	CWToFPathTracerInline
Structured light	the projector pattern at the path’s projector coordinates, \(P(\xi(\bar{\mathbf{x}}))\)	StructuredLightPathTracerInline

By default both passes use the zero-mean part of the modulation, in \([-1, 1]\) (the constant part is an ordinary image; unsignedModulation adds it back). With a high-frequency modulation, the indirect light, which reaches a pixel along many paths of different lengths or projector coordinates, largely cancels out. That is why these systems use high frequencies, but it also makes the indirect part hard to render: independent samples have random signs and cancel only slowly. Both passes therefore support antithetic sampling: every sampled path is paired with a geometrically close path whose modulation has the opposite sign, so the pair cancels the way the true signal does, and the two are combined with multiple importance sampling.

The tutorials render the indirect part only (computeDirect off), as a signed image shown with a diverging colormap (0 in white, positive in red, negative in blue), with antithetic sampling. Antithetic sampling for modulated light compares it with naive sampling at equal rendering time.

• Scene: the Cornell box without its area light, as in the ToF rendering tutorials. Download scene-v4-nolight.pbrt and save it as cornell-box/scene-v4-nolight.pbrt next to the scripts.

• Light: for CW-ToF, a point light at the camera, set on LaserLight; for structured light, a projector next to the camera, set on the render pass.

• Extra package: the scripts save the signed images with matplotlib (pip install matplotlib).

Tutorials

CW-ToF rendering (offline)

Render the indirect CW-ToF measurement with CWToFPathTracerInline and antithetic sampling.

CW-ToF rendering (offline)

Structured light rendering (offline)

Project fine sinusoidal stripes with StructuredLightPathTracerInline and antithetic sampling.

Structured light rendering (offline)

For more, see Antithetic sampling for modulated light (the modulation wavelength, the Newton-based shift, binary codes) and the applications (depth reconstruction, direct and global separation).