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Research on four-quadrant detector and its precise detection Dashe Li, Shue Liu International Journal of Digital Content Technology and its Applications. Volume 5, Number 4, April 2011

Research on Four-quadrant Detector and its Precise Detection

1, First Author

Dashe Li, 2Shue Liu Shandong Institute of Business and Technology,[email protected] *2,Corresponding Author Binzhou Medical University,[email protected]

doi:10.4156/jdcta.vol5. issue4.17

1

Abstract

Due to its high sensitivity and high response speed advantages, four-quadrant detector has been widely used in areas such as atmospheric laser communication. Based on the analysis of the detector operating principle, this article sets up the error signal processing model of the Gaussian spot and analyses the relationship between spots conditions of different radius and position offsets, achieving the result that as the light spot radius is getting smaller, the slope of the output voltage curve on both sides at the origin is getting greater, and vice versa, and that when the spot radius is greater than 0.5R, the voltage (current) output amplitude will decreases as the spot radius increases. This paper also concludes that the spots radius should be 0.5R~0.8R in optical design on the basis of effective measuring range concept.

Keywords: Gaussian Spot, Error Signal Processing Model, Effective Measuring Range 1. Introduction

Four-quadrant detector has the variety advantages such as high sensitivity and response speed, wide spectral range and dynamic scope, high position resolution and small size[1-2], and it can be used to detect the direction information of the objectives. So four-quadrant detector is widely applied in the areas of atmospheric laser communication, laser tracking and laser guidance. According to the formation principle of error signal in four-quadrant detector, this article establishes the error signal processing model of the Gaussian spot, analyses the imaging relationship between different spot radius conditions and proposes the effective measuring range concept.

2. Error signal model of the Gaussian spot

The four-quadrant detector is the combination of four identical detectors that are arranged as the four quadrants of the Cartesian coordinate system, separated by the cross-channel and integrated in a single chip, as show in Figure 1. Every quadrant has the same photoelectric characteristics.

r0

Figure 1.The schematic diagram of the four-quadrant detector

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Research on four-quadrant detector and its precise detection Dashe Li, Shue Liu International Journal of Digital Content Technology and its Applications. Volume 5, Number 4, April 2011

The photocurrent in each quadrant is proportional to the optical power. The generated current intensity is:

I q Re E

1

Where Re is the sensitivity of the four-quadrant detector (typically 0.1A / W order of magnitude). And E is the optical power in a specific quadrant, its mathematical express is:

E I ( x0 , y0 )dx0 dy0

Where

2

I is the distribution function of the photocurrent. If the beam is Gaussian beam, then

I ( x0 , y 0 ) I 0 1 2 r0 exp(r 2 / 2 2 )

3

Where I 0 is the light intensity in the beam center, constant. When the light spot is homogeneous,

r is the radial distance between the point

( x0, y 0 ) and the light spot center, and is the waist radius of the Gaussian spot, which is a

EA EB EC ED

0 0 0

r0 x

r0 2 ( x x0 ) 2 r0 2 ( x x0 ) 2

0

I 0 dy 0 dx0 I 0 dy 0 dx0

4

x r0 0 0 0

x r0 r0 2 ( x x0 ) r0 x 0

I 0 dy 0 dx0 2 I 0 dy 0 dx0

r0 2 ( x x0 ) 2

When the light spot meets Gaussian distribution,

EA EB EC ED

0 0

x r0 0

r0 x

r0 2 ( x x0 ) 2 r0 2 ( x x0 ) 2

0

I 0 exp{[( x x0 ) 2 ( y y 0 ) 2 ] / 2 2 }dy 0 dx 0 I 0 exp{[( x x 0 ) 2 ( y y 0 ) 2 ] / 2 2 }dy 0 dx0

5

0 0

x r 0 r0 2 ( x x0 ) r0 x 0

I 0 exp{[( x x 0 ) 2 ( y y 0 ) 2 ] / 2 2 }dy 0 dx0 2 I 0 exp{[( x x0 ) 2 ( y y 0 ) 2 ] / 2 2 }dy 0 dx0

0

r0 2 ( x x0 ) 2

According to the principle of photoelectric detector, the strength of the electric signal output from each quadrant (if the output is current signal, it can be converted into voltage signal) is consistent with the light power received by the photosensitive area in the certain quadrant. V x V y are the error signal extracted in the x-axis and y-axis respectively, V A V B VC V D

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Research on four-quadrant detector and its precise detection Dashe Li, Shue Liu International Journal of Digital Content Technology and its Applications. Volume 5, Number 4, April 2011

represent the output signal from the four quadrants respectively, and E A E B E C E D represent the light power incident to the respective quadrants. Normalize the energy of the output voltage on the horizontal and pitching directions, then:

Vx

(VA VD ) (VB VC ) ( E A E D ) ( EB EC ) VA VB VC VD E A EB EC ED (VA VB ) (VC VD ) ( E A EB ) ( EC E D ) VA VB VC VD E A E B EC ED

(6)

Vy

(7)

If it is the Gaussian beam, then

E A ED

r0 x

0

r0 2 ( x x0 ) 2

r0 2 ( x x0 ) 2

I 0 exp{[( x x0 ) 2 ( y y 0 ) 2 ] / 2 2 }dy 0 dx0

(8)

E B EC

0

x ro r0 2 ( x x0 ) 2

r0 x

r0 2 ( x x0 ) 2

I 0 exp{[( x x0 ) 2 ( y y 0 ) 2 ] / 2 2 }dy 0 dx0

(9)

E A E B EC E D

r 0 x r0 2 ( x x0 ) 2

r0 2 ( x x0 ) 2

I 0 exp{[( x x 0 ) 2 ( y y 0 ) 2 ] / 2 2 }dy 0 dx 0 (10)

E A EB

y r0

y r0 0

y r0 0

r0 2 ( y y0 ) 2

I 0 exp{[( x x 0 ) 2 ( y y 0 ) 2 ] / 2 2 }dy 0 dx0

(11)

EC E D

y r0

r0 2 ( y y 0 ) 2

I 0 exp{[( x x0 ) 2 ( y y 0 ) 2 ] / 2 2 }dy 0 dx 0 (12)

The equation (5-12) is the error signal processing model of the Gaussian spot. With the light spots located in x-axis, we can get different position offsets corresponding to the light spots in different radius[3].

Figure 2. The position offsets diagram with the light spots located in x-axis

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3. Research on the precise detection of the four-quadrant detector

The four-quadrant detector can be used to detect the light spot position, and the light spot size on the photosensitive area has a great impact on the number of resolvable points of the QD. The spatial resolution and the effective measuring range are significant indicators to measure the QD performance. With certain QD resolution, the more position points can be distinguished as the output voltage (current) amplitude is getting larger. So the optimal light spot should maximize the amplitude of the output voltage (current).The amplitude of the interference noise (Background light noise, dead zone noise) in the QD output would be smaller if the effective measuring range turns larger. So the radius of the incident light spots should satisfy: (1) as large amplitude of QD output voltage (current) as possible; (2) as wide QD effective measuring range as possible[4-5].

Figure 3. The relationship between detector position and light spot size The figure shown above is a light spot example of which the radius is 0.5R (R represents the radius value of QD) to illustrate the spot position in the detector. When the spot locates in the district I, completely outside the four-quadrant detector, no current (voltage) can be detected, so the position offset is 0; When the spot locates in the district II, only the second and the third quadrants are illuminated, so the position offset is negative; When the spot locates in district III, all the four quadrants are illuminated, so this district is in the effective detecting area; When the spot locates in the district IV, only the first and the second quadrants are illuminated, so the position offset is positive.

Figure 4. Relationship between light spots radius and position offset in Gaussian beam

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Figure 5.Relationship between light spots radius and position offset in homogeneous beam Figure 4 and Figure 5 illustrate the relationship between light spots radius and position offset in Gaussian beam and homogeneous beam, and the radius are 0.1R, 0.5R, 1R and 3R respectively. As shown above, as the spot radius is getting smaller, the slope of the output voltage curve on both sides at the origin is getting greater, and vice versa; when the spot radius is greater than 0.5R, the voltage (current) output amplitude will decreases as the spot radius increases. Assuming that the sensitivity Re remains stable, the number of resolved position points would become greater as the output amplitude gets larger. That is, once the spot radius is more than 0.5R, the larger the spot radius, the smaller the number of resolved points. When the spot radius is smaller than a certain value, the amplitude is 1 or -1, and become stable. That is, the number of the resolved position points would not change. Moreover, too small radius will make it difficult to receive the light spot. The effective measuring range means: (1) the whole light spot locates on the QD photosensitive area; (2) every quadrant in QD can receive light signal. If the condition (1) cannot be satisfied, it means that the light spot is partially or completely outside the detector. There will be loss of energy and the detector performance will also decline. If the condition (2) cannot be satisfied, at least one quadrant will receive no objective light signal and offer no useful information and the system is not fully utilized[4,6-8]. These two figures indicate that, for the Gaussian spot, the best radius value is a little less than 0.5R and that of the homogeneous spot is 0.5R. If the spot radius is greater than 0.5R, with a larger radius, the monotonically increasing interval and the effective detecting range would become larger, too.

4. Conclusion

The paper sets up the error signal processing model of the Gaussian spot and analyses the relationship between the radius and the position offset f the light spots based on the analysis of the operating principle of the four-quadrant detector, and concludes that the spots radius should be 0.5R~0.8R in optical design on the basis of effective measuring range concept.

5. Acknowledgment

This work is partially supported by National Natural Science Foundation (61070175),Shandong Province Natural Science Foundation(ZR2009GL011, 2009ZRB01737), Shandong Province University Science and Technology(J09LG22) of China. The authors also

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gratefully acknowledge the helpful comments and suggestions of the reviewers, which have improved the presentation.

6. References

[1] Piner R, Ruoff R, "Cross talk between friction and height signals in atomic microscopy", Review of Scientific Instruments, vol. 73, no. 9, pp. 3392-3394, 2002. [2] G. Kazovsky, "Theory of tracking accuracy of laser systems",Optical Engineering, vol. 22, no. 3, pp. 339-347, 1983. [3] Wen Tao, "Study on the key techniques of an Acquisition Tracking and Pointing system in wireless Laser Communication", National UniversityofDefense Technolog,China,2006.

[4] D.S Xu, "Optimal design for signal light spot of detecting systems with quadrant detectors",Journal of Hunan

Institute of Science and Technology (Natural Sciences),vol. 20,no.1,50-55,2007. [5] Zhang zhifeng,Yu tao,Su zhan,Kuang cuifang, "The research of four-quadrant detector and the size of the spot", Photon Technology, Vol. 9, No. 3, pp. 128 ~130, 2005 [6] Yen-Lin Chen, Chuan-Yen Chiang, Wen-Yew Liang,Cheng-Hung Chuang, "Embedded Vision-based Nighttime Driver Assistance System", JCIT: Journal of Convergence Information Technology, Vol. 6, No. 2, pp. 283 ~ 292, 2011 [7] Do-Yoon Ha, Chang-Yong Lee, Hyun-Cheol Jeong, ,Bong-Nam Noh, "Design and Implementation of SIPaware DDoS Attack Detection System", AISS : Advances in Information Sciences and Service Sciences, Vol. 2, No. 4, pp. 25 ~ 32, 2010 [8] Jin-Wook Lee, Jae-Soo Cho, "Effective lane detection and tracking method using statistical modeling of color and lane edge-orientation", AISS : Advances in Information Sciences and Service Sciences, Vol. 2, No. 3, pp. 40 ~ 47, 2010

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