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Accuracy and resolution in Laser-Triangulation technology

Resolution vs Accuracy

It is quite common in laser triangulation to mix the words accuracy and resolution, however, they can be totally different values.

Before comparing the two concepts, we should add a definition of the two words:

Accuracy is the proximity of measurement results to the true value. Not to confuse with precision, the repeatability, or reproducibility of the measurement.

resolution is a measurement of the smallest detail that can be distinguished.

Resolution

In 2D machine vision usually the resolution corresponds to 1 pixel. If the projection of one object to the image plane is smaller than a pixel, camera can not see, so, it is under the camera resolution.

In laser triangulation it is important to distinguish between the different resolutions (one on each coordinate, X, Y, and, Z). These three resolutions are the motion resolution, the resolution along the laser line, and the depth resolution.

The resolution on the motion direction, X resolution (or Y depending on the convention) is the metric distance between consecutive profiles. Usually, it is function of the spacing between camera pictures (encoder signal or frames per second) and the thickness of the line (laser or LED).

The resolution along the laser line, Y resolution (or X depending on the convention) is the ration between the length of the laser line observed in the camera (in pixels) and the corresponding length in millimeters. Due to the perspective distortion, the Y resolution is not constant, and it is higher when the object is closer to the camera.

The depth resolution, Z resolution, is the minimum depth detected by the camera. As in case of Y resolution, the depth resolution depends on the distance between the object and the camera. In this case, it is also depends on the angle camera-laser. With a higher angle, the same depth variation (in metric units) is observed in the camera as with a higher variation (in pixel units). In addition, most part of the laser line detector algorithms determine the position of the laser stripe in subpixel accuracy, increasing the resolution of the detection. However, despite that the PeakFinder can have a resolution of 1/64 of pixel, this is only related to the number of bits (typically 6) to represent the subpixel data.

Considering these numbers, one could wrongly assume that if the 640 rows of the camera image corresponds to 41mm (in depth variation), we have a resolution close to 1micron

resol = mm / (pixel * subpixelfactor) = 41/(640*64) = 0.001mm

However, it cannot be said that we have a resolution of 1 micron if, for example, the minimal thickness of the laser line is dozens of microns, in the focused area. In addition, the noise introduced by the laser speckle may also be quite important, specially in case of high magnification and long wavelength. So, we can not talk about resolution without analysing the level of noise on the acquisition.

In short, it is not easy to distinguish the real resolution and the noise variation along the laser line.

In 2D Machine vision it is quite common that when people needs more accuracy, they look closer to the object (or use a lens with higher focal length) to increase the resolution. Due to the different types of noise, in 3D laser triangulation this is not always true. In some cases, more resolution only means more noise.

Accuracy

In case of laser triangulation, as the accuracy is the discrepancy of the measurement and the real data, we can only talk about accuracy when the system is calibrated, so, is is possible to get metric 3D coordinates.

In laser triangulation there are several error sources affecting the final accuracy. As example, curvature of the laser line, innaccuracies in the movement, vibrations, innaccuracies on the calibration pattern (source of reference metric measures), etc. Due to these error sources, typically the accuracy is worse than the resolution. For example, in case of discrepancy between the calibration pattern measures and the measures supplied to the calibration algorithm, this discrepancy will affect the the measures of all the following reconstructed points.

Typical error sources to consider in laser triangulation applications

There are several error sources to consider on laser triangulation: