## Obstacle detection and spectral discrimination using multi-wavelength motionless wide angle laser scanning

Optics Express, Vol. 16, Issue 8, pp. 5822-5831 (2008)

http://dx.doi.org/10.1364/OE.16.005822

Acrobat PDF (354 KB)

### Abstract

Static laser scanning over a wide angle is demonstrated by ranging to 20 laser beams generated by a novel cylindrical quasi-cavity waveguide, using laser triangulation. Baseline distances and outgoing angles unique to each laser beam are calculated by modelling the triangulation arrangement using a system of linear equations and plotting principal rays. The quasi-cavity waveguide, imaging lens and focal plane are also plotted. The system is calibrated by finding optimal values for uncertain instrumental parameters using constrained non-linear optimization. Distances calculated over 5m indoors result in accuracies above 93%. Discrete laser spectroscopy using 640nm and 785nm laser diodes is also demonstrated. Both injected laser beams follow the same optical path through the quasi-cavity waveguide, enabling spectral measurements to be made from the same point on an object for both wavelengths. The reflected red and infrared laser light is digitally recorded by a CCD imager and differences in reflected intensity enable discrimination between various natural objects. This provides more complete information about the perturbing object, including its 3D coordinates as well as limited identification of its surface material.

© 2008 Optical Society of America

## 1. Introduction

## 2. Methodology

### 2.1 Ray modelling of the novel triangulation system

*f*is positioned in line with the

*Z*-axis and has the

*X*-axis running through its lens centre. To the left of the lens, at a baseline distance

*β*, a laser source launches a light beam at a variable angle

*w*, as shown in Fig. 1.

*x*-axis, together with

*β*,

*w*and

*f*determine the

*X*and

*Z*coordinates of the illuminated target point

*P*. The distance

*Z*, from the projected laser spot to the lens center is calculated by [5

5. M. Hartrumpf and R. Munser, “Optical three-dimensional
measurements by radially symmetric structured light
projection,” Appl. Opt. **36**, 13 (1997). [CrossRef]

*β*and

*w*values in relation to the rotated lens line,

*L*. Note that Fig. 2 is to scale and represents the actual experimental setup.

*α*, it was found that relying on the law of reflection and Snell’s law produced theoretically correct values but did not predict the real angles. This could be attributed to several factors, namely, a non-homogeneous cavity substrate, an imperfect cylindrical shape or non-uniform dielectric thin film coatings. To derive accurate

_{n}*a*values, the laser incident angle and cavity index defined in the model were altered so the exit beam position, shown in Fig. 2, coincided with the real point of exit at the end of the cavity, within 1mm accuracy. For any outgoing ray, the predicted coordinates of beam intersection with the outer cavity surface,

_{n}*C*(

*x*,

*z*) were recorded. The coordinates

*S*(

*x*,

*z*) of the corresponding laser spot on the laboratory wall were recorded manually by hand. In this case, the angle of a ray with respect to the

*X*-axis is given by:

*L*is:

_{m}*β*is calculated as:

*P*,

_{m}*L*and

_{m}*P*,

_{b}*L*are the slope and y-intercept of a projected ray and the lens line, respectively.

_{b}### 2.2 Multi-wavelength object discrimination method

*R*(

*λ*

_{n}), where

*λ*is the wavelength of the emitted laser beam. This is achieved by applying three-parameter, non-normalized Gaussian curve fitting to the one-dimensional intensity profile of the laser spot image. The intensity profile is defined by a row of pixels crossing the middle of the laser spot, along the

_{n}*x*-axis. The Gaussian function of the fitted curve is defined as:

*a*,

*b*and

*σ*are the maximum value, maximum position and standard deviation, respectively. After fitting this Gaussian curve,

*R*(

*λ*

_{n})=

*a*and is expressed in digital numbers on a scale according to the image sensor’s bit depth.

*S*, between any two (

*j*,

*k*) of the multiple wavelengths used. This approach has already been successfully validated for short range vegetation discrimination [6

6. K. Sahba, S. Askraba, and K. E. Alameh, “Non-contact laser spectroscopy for
plant discrimination in terrestrial crop
spraying,” Opt. Express **14**, 25 (2006). [CrossRef]

*S*, is defined as:

*NDI*) is also used. It is defined as:

*NDI*and

*S*values are expressed in arbitrary units (a.u).

*NDI*is especially useful when objects of interest absorb solar radiation around

*λ*, but reflect and transmit solar radiation in the spectral region around

_{j}*λ*[7

_{k}7. B. R. Myneni, F. G. Hall, J. P. Sellers, and A. L. Marshak, “The interpretation of spectral
vegetation indexes,” IEEE Trans. Geosci.
Remote Sens. **33**, 2 (1995). [CrossRef]

## 3. Experimental setup

### 3.1 Experimental set up for triangulation using the quasi-cavity

*µ*m. A C-mount TV lens of focal length

*f*=12.5mm, collects the reflected laser light. The lens iris was adjusted appropriately to avoid saturation of the imaged spot. Images from the camera are digitized in 12-bit form using a Spiricon Plug and Play PCI frame grabber.

*B*=0.3m. The arrangement is shown in Fig. 3.

*L*, was set at 46° and 69° for images 1(a) and 1(b) respectively, with respect to the

_{θ}*X*-axis.

*L*, was set at 64.5°. The image is shown in Fig. 4(b).

_{θ}*x*is the pixel position of the observed peak sensor reading with an intensity of

*f*(

*x*). The real peak position is at pixel

*x*+

*δ*. Since the accuracy of

*δ*depends on the imaged laser spots falling within the camera’s depth-of-field (DOF), it was ensured that the laser spots were in focus, by appropriately adjusting the focal length and iris of the camera.

*Z*is the actual range and

_{i}*Ẑ*is the calculated range for the

_{i}*i*laser spot. For the second set of ranges in Image 2,

^{th}*i*=12, since only spots 12 to 20 were imaged. The two most significant uncertainties in the experimental setup were:

- Imager pixel size. Although already manufacturer-specified, the pixel pitch was not precisely known, thus producing error in calculating the captured ray’s physical position on the image sensor. Hence, a pixel scaling factor,
*η*, was used in modelling the pixel size. *L*is not totally accurate since the camera’s rotating stage was fastened onto the sliding rail using a single bolt, hence making it subject to rotational movement due to slight knocks or vibrations._{θ}

*B*, running directly through the lens centre could also have existed. Note that if the camera was displaced vertically, the lens would not be in the same plane as

*B*, leading to inaccuracy in range measurements.

### 3.2 Experimental set up for multi-wavelength object discrimination

*S*and

*NDI*values for every object as explained in Section 2.2.

## 4. Experimental results and discussion

### 4.1 Laser triangulation results

*L*angle and the mean forward range,

_{θ}*Z*, to every spot obtained as shown in Fig. 6. The first set of estimated range measurements, for spots 1 to 20 projected on the laboratory walls, is shown in Fig. 6(a). The second set, from spots 12 to 20, is shown in Fig. 6(b).

*β*and

*w*using linear algebra as described in previously. The minimum ranging accuracies achieved were 93.63% and 98.81% for spot 1 of measurement set 1 and spot 12 of measurement set 2, respectively. Standard deviation of the mean

*Z*for every laser spot range measurement remained below 7.68cm and 0.525cm for measurement sets 1 and 2 respectively, demonstrating system stability in terms of repeatability.

### 4.2 Object discrimination results

*S*and

*NDI*values, the sample objects can be clearly discriminated into 3 groups. The bark, wood, brick and soil samples display slope and

*NDI*values of less than zero. The black polyester and aluminum values were also negative but there was a significant difference between the slope and

*NDI*values. The Spathiphyllum and Anthurium green plant slope and

*NDI*values are between 0.4 and 0.8, respectively, this clearly distinguishing them from the other samples objects. The slope and

*NDI*values are shown in Fig. 7. Standard deviation of both the mean slope and

*NDI*values for every sample object remained under 0.17 a.u.

*NDI*values can be used to for more accurate discrimination between larger varieties of objects.

## 4. Conclusion

*NDI*values for each object, limited object discrimination has also been demonstrated. The laser beam combination module architecture can easily be expanded by adding more wavelengths, thus improving the discrimination accuracy.

## References and links

1. | K. Sahba, K. E. Alameh, C. L. Smith, and A. Paap, “Cylindrical quasi-cavity waveguide
for static wide angle pattern projection,”
Opt. Express |

2. | L. F. Marshall, |

3. | A. B. Colquhoun, D. W. Cowan, and J. Shepherd, “Trade-offs in rotary mirror scanner
design,” Proc. SPIE |

4. | H. Horikawa, M. Miura, and T. Uchida, “Relationship between jitter and
deformation of mirrors,” Proc. SPIE |

5. | M. Hartrumpf and R. Munser, “Optical three-dimensional
measurements by radially symmetric structured light
projection,” Appl. Opt. |

6. | K. Sahba, S. Askraba, and K. E. Alameh, “Non-contact laser spectroscopy for
plant discrimination in terrestrial crop
spraying,” Opt. Express |

7. | B. R. Myneni, F. G. Hall, J. P. Sellers, and A. L. Marshak, “The interpretation of spectral
vegetation indexes,” IEEE Trans. Geosci.
Remote Sens. |

8. | R. B. Fisher and D. K. Naidu, “A Comparison of Algorithms for
Subpixel Peak Detection,” Sanz, ed., in |

**OCIS Codes**

(080.1510) Geometric optics : Propagation methods

(120.0280) Instrumentation, measurement, and metrology : Remote sensing and sensors

(280.3420) Remote sensing and sensors : Laser sensors

(300.6360) Spectroscopy : Spectroscopy, laser

(150.3045) Machine vision : Industrial optical metrology

**ToC Category:**

Remote Sensing and Sensors

**History**

Original Manuscript: March 7, 2008

Revised Manuscript: April 6, 2008

Manuscript Accepted: April 6, 2008

Published: April 10, 2008

**Citation**

Kaveh Sahba, Kamal E. Alameh, and Clifton L. Smith, "Obstacle detection and spectral discrimination using multi-wavelength motionless wide angle laser scanning," Opt. Express **16**, 5822-5831 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-8-5822

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### References

- K. Sahba, K. E. Alameh, C. L. Smith, and A. Paap, "Cylindrical quasi-cavity waveguide for static wide angle pattern projection," Opt. Express 15, 6 (2007). [CrossRef]
- L. F. Marshall, Handbook of Optical and Laser Scanning (Marcel Dekker Inc., 2004), Chap. 4. [CrossRef]
- A. B. Colquhoun, D. W. Cowan, and J. Shepherd, "Trade-offs in rotary mirror scanner design," Proc. SPIE 1454, 12-19 (1991).
- H. Horikawa, M. Miura, and T. Uchida, "Relationship between jitter and deformation of mirrors," Proc. SPIE 1454, 20-32 (1991).
- M. Hartrumpf and R. Munser, "Optical three-dimensional measurements by radially symmetric structured light projection," Appl. Opt. 36, 13 (1997), http://www.opticsinfobase.org/abstract.cfm?URI=ao-36-13-2923. [CrossRef]
- K. Sahba, S. Askraba, and K. E. Alameh., "Non-contact laser spectroscopy for plant discrimination in terrestrial crop spraying," Opt. Express 14, 25 (2006). [CrossRef]
- B. R. Myneni, F. G. Hall, J. P. Sellers, and A. L. Marshak, "The interpretation of spectral vegetation indexes," IEEE Trans. Geosci. Remote Sens. 33, 2 (1995). [CrossRef]
- R. B. Fisher and D. K. Naidu, "A Comparison of Algorithms for Subpixel Peak Detection," Sanz, ed., in Advances in Image Processing, Multimedia and Machine Vision (Springer-Verlag, 1996).

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