The 3-D family has 347 ops, but where the point clouds that feed them come from was not written anywhere. This document is not a description of ops — it is teaching material on the origin of the values passed to lidar_projection / range_image / structured_light / plane_sweep_stereo / two_view / depth_denoise / tsdf_fusion, and on how real devices fail. It sits in the same position as optics/guides/mv_*.md on the 2-D side (sensors, cameras, frame grabbers, cables, standards); this is the 3-D counterpart.
The first thing to look at in selection is not the absolute accuracy but how the accuracy scales with distance. Get this wrong and you pick the model whose catalogue numbers look good, and miss on site.
| Principle | Representative | Distance dependence of ranging error | Design values that matter |
| --- | --- | --- | --- |
| Passive stereo | Ordinary stereo cameras | σ_Z ∝ Z² | Baseline B, focal length f, sub-pixel precision of disparity |
| Active stereo | RealSense D4xx | Same as above (it only adds texture by projection) | In addition to the above, the reach of the projector |
| Structured light (phase shift / Gray code) | Zivid, Photoneo | Same as above, but B can be made large, so the coefficient is small | Period, gradation and exposure of the projected pattern |
| Laser triangulation (line profiler) | Keyence LJ-X | Same as above. Cuts the measuring range to a few mm to deliver µm | Reference distance, receiving angle, X pitch |
| Direct ToF (dToF) | Ouster, Livox | Almost independent of distance (set by time resolution) | Pulse width, time resolution, amount of returned light |
| (Indirect ToF / iToF) | Some ToF cameras | Set by phase resolution. Has wrap-around | Modulation frequency (= unambiguous range) |
Z = B·f / d B = baseline [mm], f = focal length [px], d = disparity [px] δZ = Z² / (B·f) · δd
It worsens with the square of distance. That is why passive / active stereo cannot be used at long range, and the reason structured light can deliver µm-class results is that it makes B·f large and fixes Z small.
*Reading a catalogue % figure as disparity error*: the D455 has a 95 mm baseline, 1280×720 and HFOV 87°, so f ≈ (1280/2)/tan(43.5°) ≈ 674 px (a rough estimate — strictly, use the HFOV of the left imager. The published "depth FOV" is narrower by the invalid band, so this f comes out somewhat small). The nominal "under 2% at 4 m" corresponds to
δd = δZ·B·f / Z² = 80 × 95 × 674 / 4000² ≈ 0.32 px
In other words, this number is a claim that "sub-pixel matching is working at 1/3 pixel", and it does not hold as is on surfaces without texture. When you see a % figure, do this conversion.
σ_Z = c·σ_t / 2 c = speed of light, σ_t = time resolution
Distance does not enter — this is why LiDAR can hold cm even at 100 m. However, the returned light falls off as 1/Z², so at long range it is not the accuracy but the detection probability that drops. This is why catalogues write ranges with reflectance attached, such as "170 m @ 80% reflectivity" and "90 m @ 10% reflectivity". A maximum range that does not state reflectance cannot be used for comparison.
No guessed values are included. Everything below is from manufacturers' published specifications (sources at the end).
| Item | Value |
| --- | --- |
| Method | Stereo (with IR projector) |
| Baseline | 95 mm (D435 series 50 mm, D415 55 mm, D405 18 mm) |
| Depth FOV (16:9) | H 87° / V 58° / D 95° |
| Depth output | Up to 1280×720, up to 90 fps |
| Recommended range | 0.6 – 6 m |
| Min-Z (1280×720) | 520 mm (350 at 848×480, 180 at 424×240) |
The key point is that Min-Z changes with resolution. Lowering the resolution lets you get closer — because the upper limit of disparity is set by the pixel count; "too close to measure" can sometimes be avoided by lowering the resolution.
Invalid depth band (a structural dropout for which Intel publishes a formula):
invalid band width [px] = B·f / Z
For the D455 at Z = 1 m, 95 × 674 / 1000 ≈ 64 px at the left edge is always invalid. It is a region not seen by the right imager, so in principle it cannot be filled. If you make synthetic depth images, always include this band (without it, the learning side ends up with a model that trusts the image edge).
| Item | Value |
| --- | --- |
| Imaging | 2448×2048 (5.0 MPx), native 3D colour |
| Focus distance | 1300 mm / working range 800 – 2700 mm / optimal 1000 – 1600 mm |
| Field of view | 790 × 650 mm @ 1300 mm |
| Point precision 1σ | 210 µm @ focus distance |
| Local planarity precision 1σ | 300 µm |
| Global planarity trueness error | < 0.24 mm |
| Dimension trueness error | < 0.35 % (focus distance, room temperature) / < 0.60 % (optimal range, full temperature range) |
| Acquisition time | 50 ms – 1500 ms (including processing) |
| Light source | Projector 360 lm (1×) to 900 lm (2.5×), IEC 62471-5 RG2 |
Listing precision and trueness separately is this manufacturer's virtue, and that is what to read for. A point precision of 210 µm is "how little it scatters over consecutive captures"; a dimension trueness of 0.35 % is "how far off it is when measuring a calibrated length". For measurement applications, the latter is what matters. A catalogue that lists only the former is showing only the numbers that improve by averaging. Furthermore, it is stated explicitly that trueness degrades from 0.35 % → 0.60 % with temperature — in equipment that warms up inside a cabinet, using the room-temperature spec as is will not match.
| Item | Value |
| --- | --- |
| Reference distance | 64 mm |
| Z measuring range | ±7.3 mm (F.S. 14.6 mm) |
| X measuring range | 15 mm (near side) / 16 mm (reference distance) |
| Light source | 405 nm visible, Class 2M |
| Profile data interval (X pitch) | 5 µm |
| Z repeatability | 0.4 µm |
| X repeatability | 0.5 µm |
| Points per 1 profile | 3200 points |
The essence is that it cuts the measuring range to ±7.3 mm to deliver µm. The triangulation δZ ∝ Z² does not change, so there is no other way than narrowing the range. And what is listed here is repeatability, not linearity — reading it as "it can measure to 0.4 µm" is wrong. If you claim absolute dimensions, linearity and calibration are needed separately.
| Item | Value |
| --- | --- |
| Wavelength / class | 865 nm / Class 1 (IEC 60825-1:2014) |
| Range | 170 m @ 80% Lambertian / 90 m @ 10% Lambertian (1024@10 Hz, detection probability > 90%, 100 klx sunlight) |
| Minimum range | 0.0 m (default 0.5 m, 0.3 m selectable) |
| Vertical FOV | 42.4° ±1.0° (+21.2° to −21.2°) |
| Resolution | Vertical 32 / 64 / 128 ch, horizontal 512 / 1024 / 2048, rotation 10 / 20 Hz |
| Range accuracy | ±2.5 cm (Lambertian) / ±5 cm (retroreflector) |
| Range precision 1σ | ±0.5 cm (minimum) to ±3 cm (maximum) |
| Range resolution | 0.1 cm |
| Point rate | Up to 5,242,880 points/s (128 ch) |
| Beam | Exit diameter 9.5 mm, divergence 0.18° (FWHM) |
| Data per 1 point | Range, signal intensity, reflectivity, near-infrared, channel, azimuth, timestamp |
| False positive rate | 1/10,000 |
What matters is that accuracy is worse on retroreflective targets (±5 cm). It is counter-intuitive, but the returned light is so strong that the received waveform saturates and the rise time shifts (range walk). Synthetic data that uses reflective tape or signs as references will not match reality unless this error is included.
Also, the beam angles are not evenly spaced (the sensor's specification returns beam angles as intrinsics). Building a range image on the assumption that channel numbers are evenly spaced elevation angles distorts it systematically.
| Item | Value |
| --- | --- |
| Wavelength | 905 nm |
| Range | 70 m @ 80% reflectivity / 40 m @ 10% reflectivity (ambient 25 °C) |
| Minimum range | 0.1 m |
| FOV | Horizontal 360° / vertical −7° to +52° |
| Point rate | 200,000 points/s (first return) |
| Range precision 1σ | ≤ 2 cm @ 10 m, ≤ 3 cm @ 0.2 m |
| Angular precision 1σ | < 0.15° |
| Built-in IMU | ICM40609 |
Because the scan is non-repetitive, looking at only 1 frame shows it full of holes, and it becomes denser the more you accumulate. Algorithms that assume "1 scan gives a complete point cloud" break down here. That the vertical FOV is asymmetric up/down (−7° to +52°) also matters in practice — it cannot see directly below.
Putting uniform Gaussian noise on depth is the most common lie in this field. The way real devices fail is determined by each principle, and each has its own shape.
| Principle | Failure modes that appear |
| --- | --- |
| Passive stereo | Holes on textureless surfaces / disparity jumps on repetitive patterns (mismatches become smooth errors, so they are hard to notice) / dropouts on only one side at occlusion boundaries |
| Active stereo | In addition to the above, degrades to passive at long range beyond the projector's reach / the pattern is drowned out in sunlight (performance drops suddenly outdoors) |
| Structured light | Jumps on specular surfaces (no return) / interreflection in concave regions breaks the phase and makes the surface bulge / on transparent or translucent material, subsurface scattering shifts it deeper |
| dToF | Inside corners rounded by multipath / flying pixels at edges (2 distances mix in 1 pixel, giving an intermediate value) / range walk on retroreflectors / false points from rain, fog and dust |
| iToF | Multipath is even stronger / phase wrap-around turns far objects into near ones (when beyond the unambiguous range set by the modulation frequency) |
| Laser triangulation | 2 kinds of occlusion (shadow on the projector side, shadow on the receiver side) / no return from specular surfaces / coordinates get dragged at step edges |
Common to all: reflectance and intensity channels depend on distance and incidence angle (1/Z², cos θ). Using raw intensity as a feature as is leads to learning that depends on distance. Normalise it, or give the distance explicitly.
1. Is depth "z along the optical axis" or "slant range"? Range images (from LiDAR) are slant range; depth cameras usually give optical-axis z. Mix them up and they agree at the centre and drift systematically only at the edges of the field of view, so a test that looks only at the centre will pass. fullseye adopts optical-axis z in optscene_depth (the machine-vision convention).
2. Depth scale. RealSense defaults to 1 unit = 1 mm, but this changes with model and settings. When you receive a depth image as uint16, always carry the scale along with it.
3. LiDAR rings / channels are not evenly spaced. As in §2.4.
4. Origin of the point cloud. A camera's origin is not the front glass (RealSense: centre of the left imager;
Ouster: the reference plane of the housing). This becomes a systematic offset of a few mm to a dozen or more mm.
5. Time. On a moving platform, things move during the scan even within 1 frame (LiDAR skew). For a sensor that attaches a timestamp to each point, the point cloud is meant to be corrected using it.
It is decided in the order application → distance → required accuracy → principle. In reverse order (starting from the model) you miss.
| Application | Distance | Required accuracy | Principle |
| --- | --- | --- | --- |
| Inline shape and step inspection | Tens of mm | µm | Laser triangulation (line profiler) |
| Bin picking, assembly | 0.5 – 2 m | 0.1 – 0.5 mm | Structured light |
| Rough perception of people and fixtures | 0.5 – 6 m | cm | Active stereo |
| Localisation and obstacles for mobile robots | 0.5 – 100 m | cm | LiDAR |
| Outdoor wide area, terrain | 10 m and up | cm | LiDAR / photogrammetry |
The core of the decision can be said in 1 line — if you need µm, cut the measuring range (triangulation); if you need distance, use a method whose accuracy does not depend on distance (ToF). You cannot have both.
| Value passed | Origin | Ops used |
| --- | --- | --- |
| Vertical FOV, channel count, angular resolution | §2.4 / §2.5 | lidar_projection family (3 op), range_image family (4 op) |
| Baseline, focal length, Min-Z, invalid band | §2.1 | two_view family (5 op), plane_sweep_stereo (2 op) |
| Pattern period, number of phase steps | §2.2 | structured_light family (7 op) |
| Point precision 1σ, planarity | §2.2 | surface_fit / registration_metrics / metrics |
| Flying pixels, edge dropouts | §3 | depth_denoise family (3 op) |
| Point spacing (voxels coarser than this) | Spatial resolution in §2.2 | tsdf_fusion (3 op), occupancy (4 op) |
| Distance and angle dependence of reflectance | End of §3 | photometric family (4 op) |
• There is no op for a sensor error model. The 2-D side has optscene, which assembles lens, lighting and sensor and produces defect images with ground truth. Of the 3-D counterparts — putting Z²-dependent noise on depth / creating an invalid depth band / growing flying pixels / rounding inside corners by multipath — not even 1 exists. If synthetic 3-D data is used for learning, this is what is needed first.
• There is no entry point for handling non-uniform beam angles (lidar_projection assumes even spacing).
• There is no vocabulary for timestamped point clouds (skew correction).
• There is no means of reproducing iToF phase wrap-around.
This is what to open first on site. A symptom can always be explained by tracing it back to the principle.
| Symptom | Suspect first | How to check |
| --- | --- | --- |
| Accuracy is poor only at long range | Triangulation used at long range (σ_Z ∝ Z²) | Change the distance, measure σ, and see whether it follows Z². If it does, it is the limit of the method and post-processing will not fix it |
| A plane warps / dimensions do not match | A trueness-side problem — calibration, temperature | Shoot a calibrated flat plate at several positions in the field of view and look at the plane-fit residuals. Compare before and after warm-up (10 min) |
| Holes appear on only one side of the image | Stereo invalid depth band | Calculate whether the width matches B·f/Z px. If it does, it is a dropout by principle and cannot be filled |
| Only black parts or shiny parts drop out | Returned light (reflectance for ToF, specular reflection for structured light) | Re-shoot with a white matte dummy of the same shape. If that fixes it, it is due to the material |
| Rounded inside corners / points at intermediate distance on edges | ToF multipath and flying pixels | Extract only the points near the edge and look at the distance histogram. Points sit in the valley between the two peaks |
| Only the position of reflective tape is off | Range walk (receiver saturation) | Lower the exposure or intensity and re-measure. If the offset decreases, it is due to saturation |
| The point cloud is dragged diagonally | Movement during the scan (skew) / per-point timestamps not used | Re-shoot while stationary. If that fixes it, motion compensation is needed |
| Horizontal stripes appear when made into a range image | Assumed channel = evenly spaced elevation | Query the sensor's beam angles (intrinsics) and re-project |
| Agrees at the centre but drifts only at the edges of the field | Mixing up optical-axis z and slant range | At edge points, look at the ratio of z to ‖p‖. If it is a factor of cos θ, they were mixed up |
| 1 frame is full of holes | A non-repetitive-scanning LiDAR used with a single frame | Accumulate several frames and see whether the density rises |
• Livox Mid-360 Specs — <https://www.livoxtech.com/mid-360/specs>
• Ouster OS1 Rev7 Datasheet (FW 3.1.x) — <https://data.ouster.io/downloads/datasheets/datasheet-rev7-v3p1-os1.pdf>
• Zivid 2+ M130 Technical Specification (1.5 – 7/25) — <https://www.zivid.com/hubfs/User%20guides%20and%20datasheets/Zivid%202+%20M130%20Datasheet.pdf>
• Intel RealSense D400 Series Datasheet, Doc. 337029-017 (Oct 2025) — <https://realsenseai.com/wp-content/uploads/2025/09/Intel-RealSense-D400-Series-Datasheet-October-2025.pdf>
• Keyence LJ-X8000 series — LJ-X8060 — <https://www.keyence.com/products/measure/laser-2d/lj-x8000/models/lj-x8060/>