**6. Method and electronic device to locate signal energy centre**

The principal focus of this chapter is a method to find the energy centre of the signal gener‐ ated by optical scanners and to reduce errors in position measurements. The method is based on the assumption that the signal generated by optical scanners for position measure‐ ment is a Gaussian-like shape signal, and this signal is processed by means of an electronic circuit.

#### **6.1. Electronic method operating theory**

A signal V(t) is obtained from the optical scanning aperture, as shown in Figure 22.

**Figure 22.** a) Chanel 1 Original signal from apertureb) Original signal representation.

The signal V(t) is amplified through an operational amplifier until saturation to obtain a square signal, this signal can be expressed as:

$$V\_s(t) = V\_s \max \tag{20}$$

which is a constant for a≤t ≤bas shown in Figure 23.

The signal Vs (t) is integrated with respect to dt in order to get the ramp Vr(t) as shown be‐ low in Figure 24.

$$\mathcal{V}\_r(t) = \mathcal{V}\_s(t)dt \tag{21}$$

**Figure 25.** Electronic control circuit representation.

**6.2. Electronic control circuit method experimentation**

triangle signal and an Airy function, as illustrated in figure 26.

handled in Matlab [8].

gle signal d)Airy function signal.

the energetic centre, as shown in figure 27.

The advantage of this method is that the mathematical processing is performed by using electronic components in real time to get the data vector of the saturated signal which can be

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413

The first stage of the experimentation started with regular signals simulated by a function generator, the signals utilized were: a rectified sin signal, a rectified square signal, rectified

**Figure 26.** Regular signals simulated by a function generator: a)Rectified Sin signal. b) Square ignal. c) Rectified trian‐

The second stage consisted of processing each signal by means of the electronic circuit to get

then energetic signal centre is located in Vrmax/2= Vsmax /2 as shown in Figure 24.

**Figure 24.** a)Channel 1 original signal from aperture, Channel 2 ramp signal. b) Channel 1 ramp signal, Channel 2 Pulse indicating the energetic signal centre overlapped on ramp signal c) Energetic signal centre search process repre‐ sentation.

All this process is carried out by a circuit similar to the one shown in figure 25.

**Figure 25.** Electronic control circuit representation.

which is a constant for a≤t ≤bas shown in Figure 23.

412 Optoelectronics - Advanced Materials and Devices

low in Figure 24.

sentation.

**Figure 23.** a) Channel 1 Original Signal from aperture. Channel 2 Square Signal. b) Square signal representation.

then energetic signal centre is located in Vrmax/2= Vsmax /2 as shown in Figure 24.

The signal Vs (t) is integrated with respect to dt in order to get the ramp Vr(t) as shown be‐

**Figure 24.** a)Channel 1 original signal from aperture, Channel 2 ramp signal. b) Channel 1 ramp signal, Channel 2 Pulse indicating the energetic signal centre overlapped on ramp signal c) Energetic signal centre search process repre‐

All this process is carried out by a circuit similar to the one shown in figure 25.

*V <sup>r</sup>*(*t*) =*∫Vs*(*t*)*dt* (21)

The advantage of this method is that the mathematical processing is performed by using electronic components in real time to get the data vector of the saturated signal which can be handled in Matlab [8].

#### **6.2. Electronic control circuit method experimentation**

The first stage of the experimentation started with regular signals simulated by a function generator, the signals utilized were: a rectified sin signal, a rectified square signal, rectified triangle signal and an Airy function, as illustrated in figure 26.

**Figure 26.** Regular signals simulated by a function generator: a)Rectified Sin signal. b) Square ignal. c) Rectified trian‐ gle signal d)Airy function signal.

The second stage consisted of processing each signal by means of the electronic circuit to get the energetic centre, as shown in figure 27.

**7. Conclusion**

**Author details**

**References**

A pertinent method to detect the energetic centre of signal generated by optical scanning with a rotating mirror and a simple photodiode was presented. The results of a series of ex‐ periments and simulations were used to analyse the performance of the method and the cir‐ cuit considering regular signals. Consequently, further work is required to reduce problems encountered in processing real signals. Besides, The method can also be used to detect geo‐ metrical centre of the light distribution on CCD and PSD, future experiments with this kind of sensors should be considered. The results suggest that the circuit proposed can support different patterns of light distributions. To conclude, it is strongly recommended that this

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circuit and the photodiode be manufactured in the same integrated circuit.

Engineering Institute of Autonomous University of Baja California (UABC), Mexico

[1] Rivas, L., Moisés, Sergiyenko., Oleg, Tyrsa., Vera, Hernández., & Wilmar, . Optoelec‐ tronic method for structural health monitoring. International Journal of Structural

[2] Flores, F., Wendy, Rivas. L., Moisés, Sergiyenko., Oleg, Y., Rivera, C., & Javier, . Comparison of Signal Peak Detection Algorithms in the Search of the Signal Energy Center for measuring with optical scanning. In: Falcon S. Bertha, Trejo O. René, Gó‐ mez E. Raúl: IEEE ROC&C2011:XXII autumn international conference on communi‐ cations, computer, electronics, automation, robotics and industrial

[3] Rodríguez Q. Julio C., Sergiyenko Oleg, Tyrsa Vera,. Básaca P Luis C., Rivas L. Moi‐ sés, Hernández B. Daniel, 3D Body& Medical Scanners`Technologies: Methodology and Spatial Discriminations, in: Srgiyenko Oleg (ed.) Optoelectronic Devices and

[4] Kennedy, William. P. The Basics of triangulation sensors, Cyber Optics Corp. http:// archives.sensorsmag.com/articles/0598/tri0598/main.shtml,accessed June 18 (2012).

[5] Vahelal, Ahmedabad. Seminar report 3 of Cryptography: Sensors on 3D Digitization,

exposition:ROC&C2011, 27 Nov-1 Dec. (2011). Acapulco Gro., México.

Hasmukh Goswami College of Engineering, Gujarat, India:. (2010).

Moisés Rivas, Wendy Flores, Javier Rivera, Oleg Sergiyenko, Daniel Hernández-Balbuena and Alejandro Sánchez-Bueno

Health Monitoring (2010). , 9(1), 105-120.

Proprieties. In-Tech: 2011.p307-322.

**Figure 27.** Detailed example. a)Channel 1: original signal from function generator; Channel 2: square signal obtained from saturation. b) Channel 1: saturated signal Channel 2: ramp signal obtained from integration. c) Channel1: origi‐ nal signal from generator; Channel 2: impulse signal overlapped on original signal from generator to indicate the en‐ ergetic signal centre.

The circuit was tested with different signals obtaining satisfactory results. In figure 28, the results are illustrated with a triangle signal and an airy function signal.

**Figure 28.** Impulse signal indicating the energetic signal centre overlapped on: a) triangle signal. b)Airy function signal.

Finally, to characterize and increase the accuracy and resolution of signal measurements four methods were selected and compared to obtain the most applicable settingsin order to find the energetic centre of the signal. The given results are shown in [2].
