3D Laser Triangulation Calibration

In many applications, 2D cameras are used to produce 3D imaging for general purpose inspections. There are many applications that benefit from 3D inspection, including reverse engineering, electronics, food and auto parts inspection, and recreational or sport simulation.

There are many ways to use 2D cameras for 3D inspection:

  • Laser triangulation using a 2D camera and a laser
  • Stereoscopy using two 2D cameras
  • Interferometer using a 2D camera and several optical devices
  • Scanners using a 2D camera
  • 3D dedicated software using a grey level image to obtain 3D measurements

In this article we will concentrate on one of the most commonly used techniques, laser triangulation.

Laser triangulation uses a laser line or laser pattern and a 2D camera mounted at an angle to produce a 3D vertical measurement obtained from a flat 2D image. How is this possible?

Below, the basic principle of optical triangulation is illustrated by a 2D image of a laser line being captured by a camera mounted at an angle. This technique gives a 3D representation of an object on a 2D image. The image below shows how the camera visualizes the laser line with its two dimensional perspective.

3D Triangulation

What is 3D calibration and how do we obtain real 3D measurements from a 2D image?

A good 3D calibration will not only produce accurate 3D measurements but also correct or compensate for optical problems like optical distortion, and camera rotation. A 3D calibration is in fact, simply mathematics applied to geometry.

The overall 3D system will usually be comprised of a standard 2D camera with dedicated 3D hardware to extract a laser line profile from the 2D image to produce what is called a 3D profile. The 3D profile is a collection of points representing vertical (height) depth positions.

The data streaming from the camera is raw un-calibrated height data.The data then has to be mathematically transformed into measurements such as inches or millimeters, to produce real 3D values (or height values).

The most common way of transforming raw data coming from a 2D camera is a calibration table or matrix. The matrix can be in the form of a Look up Table (LUT) or a mathematical formula. We have a choice depending on the level of precision we want.

To obtain real 3D measurements, the calibration matrix must be filled with numbers that will transform the raw profile points into real measurements. There are several ways to fill this calibration matrix. One approach would be to place a calibrated object in front of the camera, take some pictures and transform the raw data into real 3D measurements by applying the principle of mathematical translation.

For example, if the camera produces raw data from 0 to 2047 and a depth of field of 200 mm is desirable, then we simply multiply the raw data of the known distance (ie: 100 mm ) to obtain a calibrated value. Here is a basic math example:

The raw data obtained by the camera multiplied by the coefficient in table = 100 mm.

Let’s assume the raw data produced by the camera is 1017.  So the camera outputs raw data 1017 that is obtained from a known distance of 100 mm.

The table coefficient value would become 100mm/1017 = 0.098.

This is a simple way to explain the relationship between raw data coming out of the 2D camera and a real 3D measurement.

A matrix table will produce better results than a linear table, because it will take into account the lateral distortions and angles (camera rotation), optical distortions (lens issues), and geometrical mounting distortions (baseline etc) .

Why use 2D cameras for 3D inspection?

Using 2D cameras to produce a 3D vision system is desirable because of the many options 2D camera manufacturers have to offer. By combining additional 3D hardware with a 2D camera, real 3D vision systems are realized for lower cost and are easy to implement in any factory setting. While a specialized 3D camera design is possible, it’s also likely that such a camera might only be appropriate for its designed purpose and may also require specialized support. In deploying a standard 2D camera as the main component of the system, more options are available to the user in terms of resolution, speed, and cost.

Further, laser triangulation is easy to implement and low cost. Other techniques are more complicated and cost more. Of course, more sophisticated techniques may yield better results, but the difference may not be significant enough to justify the expense.

Raymond

About Raymond

Raymond is Product Manager for Teledyne DALSA’s Industrial Products Division. He holds a P.Eng. in Electronic Engineering and has more than 28 years experience in the design of imaging systems, including work in 2 and 3D cameras and laser triangulation. He has participated in many optical projects including a 5D camera (X,Y,Z space position, tilt and rotation).
In his spare time, Raymond enjoys designing, building and flying radio-controlled airplanes and helicopters. He enjoys watching NFL football and playing hockey.

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