Doppler-gated path tracer (DopplerGatedPathTracerInline)

This render pass renders the light whose Doppler frequency shift falls inside a gate, as measured by optical heterodyne detection (OHD) with a single-frequency laser. It relates to DopplerHistogramPathTracerInline as the time-gated path tracer relates to the transient histogram: one image for one gate instead of the whole spectrum. Every path is weighted by a gate kernel \(g\) at its Doppler shift

\[ \Delta f(\bar{\mathbf{x}}) = \frac{u(\bar{\mathbf{x}})}{\lambda}, \qquad I = \frac{1}{w} \int f(\bar{\mathbf{x}})\, g\!\left(\frac{\Delta f(\bar{\mathbf{x}}) - f_c}{w}\right) \mathrm{d}\bar{\mathbf{x}}, \]

with the path velocity \(u\) of the Doppler spectrum path tracer, the gate center \(f_c\) and the gate width \(w\) (MHz). Dividing by \(w\) gives radiance per MHz, the unit of the spectrum: a box gate one bin wide at the center of a bin gives that bin of the spectrum (the box is half-open, \([f_c - w/2, f_c + w/2)\), like the bins, so that a static path, at exactly 0 MHz, falls in one bin of both).

The scene does not move. Every object is given an instantaneous velocity (see Velocities), which only decides the shift of each path. A light connection outside the gate contributes nothing, so its visibility ray is skipped: narrow gates are cheaper than the full spectrum.

Parameters

Gate:

Parameter	Type	Description
frequencyCenter	float	Center \(f_c\) of a fixed gate, MHz. Sets frequencyMin = frequencyMax. Positive shifts come from paths that shorten, for example an object approaching a camera with the light next to it. (Default: 0)
frequencyGateWindow	float	Gate width \(w\), MHz. The output is divided by it. (Default: 1)
frequencyGateMode	string	Gate kernel, the same as the time-gated path tracer’s: box, tent, gaussian, exp (one-sided exponential), exp_two_side (two-sided exponential), epanechnikov, perlin, cos or all (no gating); see the kernels, with the shift in place of the path length. (Default: box)
shiftGate	boolean	Move the gate one step per frame from frequencyMin towards frequencyMax, then start again. (Default: false)
frequencyMin, frequencyMax	float	Range of gate centers scanned by shiftGate, MHz. (Default: 0, 0)
frequencyBin	integer	Number of gate positions in the scan. (Default: 512)

Doppler shift:

Parameter	Type	Description
wavelength	float	Laser wavelength \(\lambda\), nm. (Default: 1550)
velocities	dictionary	The motion of the scene objects; see Velocities. (Default: none)
sensorVelocity	float3	Velocity of the camera, m/s. (Default: [0, 0, 0])
lightVelocity	float3	Velocity of the light’s origin (the laser or point light), m/s. (Default: [0, 0, 0])

Sampling and output, as for the Doppler spectrum path tracer: samplesPerPixel (default 128), maxBounces (default 3), computeDirect (default false), useImportanceSampling, useAlphaTest, and useSingleChannel with singleChannel, which write the chosen channel to all three channels of the output.

Light

The light is set on the LaserLight pass, as for the time-gated path tracer. A lidar has its light next to the camera: isLightSourceLaser = false with laserCollocated = true puts a point light at the camera.

Inputs and outputs

Channel	Description
vbuffer (input)	Primary hits, from VBufferRT.
viewW (input, optional)	Primary ray directions, from VBufferRT.
color (output)	The Doppler-gated image of the frame, radiance per MHz, RGBA32Float. Average frames with AccumulatePass.

From Python: set_velocity(...), clear_velocities(), get_object_names(), which returns (instance, mesh name, material name, movable) for every object of the scene, and, for scans, increment_frequency_gate_frame() and set_frequency_gate_info(frequency_min, frequency_max, frequency_bin).

Example

The tall box of the Cornell box approaches at 20 m/s and the short box recedes; a Gaussian gate 2 MHz wide at +25.8 MHz (\(2v/\lambda\) at 1550 nm) keeps the light that the tall box reflected once:

testbed.load_scene("cornell-box/scene-v4-nolight.pbrt", falcor.SceneBuilderFlags.DontMergeMaterials)
graph = testbed.create_render_graph("DopplerGated")
graph.create_pass("VBuffer", "VBufferRT", {"samplePattern": "Center", "sampleCount": 1})
graph.create_pass("Light", "LaserLight", {"isLightSourceLaser": False, "laserCollocated": True})
graph.create_pass("Tracer", "DopplerGatedPathTracerInline", {
    "samplesPerPixel": 64, "maxBounces": 3, "computeDirect": True, "wavelength": 1550.0,
    "frequencyCenter": 25.8, "frequencyGateWindow": 2.0, "frequencyGateMode": "gaussian",
    "velocities": {"TallBox": {"linear": [0.0, 0.0, 20.0]}, "ShortBox": {"linear": [0.0, 0.0, -20.0]}},
})
graph.create_pass("Accumulate", "AccumulatePass", {})
graph.add_edge("VBuffer.vbuffer", "Tracer.vbuffer")
graph.add_edge("VBuffer.viewW", "Tracer.viewW")
graph.add_edge("Light", "Tracer")
graph.add_edge("Tracer.color", "Accumulate.input")
graph.mark_output("Accumulate.output")
testbed.render_graph = graph

The Doppler spectrum tutorial renders the same scene as a spectrum.