Optical Range Sensors

Optical range sensing devices have been used in a variety of opto-mechatronic products and processes including automatic 35-mm cameras, vehicle guidance systems, visual servoing, online product inspection, precision measurement, and machine condition monitoring. Most range measurement devices consist of a small light source and a position-sensitive detector (PSD) such as a one-dimensional photodiode array or two-dimensional CCD matrix (see Figure 2.14). The light-emitting diode and collimating lens transmit a pulse in the form of a narrow light beam that strikes the surface of the object and is reflected back through a focusing lens to the PSD array.

The PSD array is a silicon device that generates current values proportional to the distance, x, of the incident light spot from the array center. The photoelectric current produced at each terminal, i1 and i2, is a function of the resistance between the electrode and the point of incidence. If i is the total current produced by the detected light, and i1 is the current at one output electrode, then the current produced at each terminal will be a function of the corresponding distance between the point of incidence light and electrode. Thus, the current at each terminal can be computed with respect to distances [Shetty and FIGURE 2.13 An illustration of a fiber optic load sensor based on the principle of microbending.

Light intensity at detector

Deformer separation 0 Infinity

Photodetector Optical fiber

Light source

Light coupled out of fiber Displacement

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Kolk, 1997] using,

(2.2) where X is the distance between terminals i1 and i2. Because the ratio of the resulting current values at the two terminals is

(2.3) the distance x can be determined using

(2.4) Finally, the range distance R1 from the object surface to the activated element in the PSD can be calculated using simple trigonometric principles as

(2.5) where f is the focal length of the lens, and D is the fixed baseline distance between the optical axis of the light projector and the center of the PDS array.

2.4.1.3.1 Measuring Material Thickness

To further illustrate the concept of triangulation, consider the problem of measuring the thickness of a material sheet. The light source projects a beam onto the planar material surface and the reflected spot of light is detected by the PSD array. Because the photodetector is positioned at a fixed distance from the base or table surface, R2, the thickness of the material, dth, can be determined using:

(2.6)

FIGURE 2.14 The triangulation principle applied to the position-sensitive detector (PSD).

i i X x

X i ix

1= ( − ) 2= X

,

Q I I

X

= ¹ = x −

2

1

x X

=Q +1

R f D

x f D X Q

1= = ( +1)

d_th=R2− =R1 R2−D tanφ

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Opto-Mechatronic Products and Processes: Design Considerations 2-15

where f is the focal length of the lens, and D is the fixed distance between the optical axis of the light source and center of the PSD array.

2.4.1.3.2 Three-Dimensional Range Sensing

The digitization of three-dimensional objects can be achieved by moving a projected light spot over the entire surface and then performing a range calculation at each point in the scanned area. Many com-mercially available three-dimensional digitizers utilize a rotating mirror to traverse the beam from right to left and top to bottom over the scanned region. The projected beam and reflected light spot at any instant in time creates a triangle that can be used to calculate the range R. The distance of the brightest image point, x, from the center of the sensor array can be determined as described above. Figure 2.15 is a simple range sensing system that utilizes a moving laser spot projector and a one-dimensional PSD.

Because the focal length of the lens, f, and the baseline distance between the projector and optic axis of the PSD are fixed, it is possible to calculate R for different φ as the beam traverses the object surface. The angle α can be calculated as

α= tan⁻¹ (2.7)

Depending on whether the detect point is to the right (+) or the left (−) of the center of the PSD array, x can be positive or negative.

The angle the light projector makes, φ, is known, and from the above information it is possible to calculate the range value, R, using the law of sines [Shetty and Kolk, 1997]:

(2.8)

(2.9)

FIGURE 2.15 Range sensing using a moving laser spot projector.

Light source

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Thus, the range or distance of a surface point with respect to the optic axis of the lens is given by two parameters (α, dob), where dob is

(2.10) The basic principle of triangulation can be extended to light-stripe or projected-pattern range sensing.

In general, a structured light pattern is projected onto an object, and a charge-coupled device (CCD) camera captures a two-dimensional image of the deformed pattern formed on the object surface (see Figure 2.16). The two-dimensional pixel coordinates of the captured light pattern in the image plane are used to determine the three-dimensional (x, y, z) object coordinates in the world space. When only a single light line is projected, it generates a plane of light through space that forms a profile on the object surface. Because the profile lies in the plane of the projected light, the measured object points are planar and correspond directly to the two-dimensional image coordinates. The three-dimensional reconstruc-tion of object points is therefore simplified and can be performed after the relareconstruc-tionship between image-plane and object-image-plane coordinates is determined through range-sensor calibration methods [Knopf and Kofman, 1998]. The complete surface geometry of the object surface is achieved by translating the light plane perpendicularly to new known positions along one of the world coordinates and performing the measurement and reconstruction using the same image-plane to object-plane relationship.

Calibration is essential for this range-sensing method to work. It is often carried out using the known optical and geometric parameters of the laser-camera system, or by extracting the parameters by sampling object and image points. However, these calibration methods rely on valid models of the system geometry and optics, which must account for alignment of system components and lens distortion. Alternatively, methods to map image-plane coordinates to object-plane coordinates without the use of sensor optical and geometric models have been proposed [Knopf and Kofman, 1998]. One limitation of the light stripe or projected pattern approach is the poor depth resolution for surfaces parallel to the light plane. This limitation can be overcome by scanning the image in two directions, one perpendicular to the other. The benefit of light-striping methods is that they are relatively simple and fast compared to light-spot scanning.

Furthermore, the light stripe can assist the process of image segmentation.