Method of Auto-Revising the Conversion Coefficients of Four-Quadrant Photodetector

Xiaojun Tang, Junhua Liu, Liping Dang, Jian Chen

School of Electrical Engineering, Xi’an Jiaotong University, Xi’an 710049, China)

Abstract: The balance among photovoltaic conversion coefficients of four channels of four-quadrant photodetector is the premise of subsequent correct signal analysis of four-quadrant photodetector when used in practice. In this paper, the relation between compound outputs of four-quadrant photodetector and the photovoltaic conversion coefficients of four channels are discussed by analyzing the light-path of four-quadrant photodetector. And the equations about the relation and the way to solve the equations set are also given. Then auto-revising balance of photovoltaic conversion coefficients of four channels are achieved by multiplying/dividing every photovoltaic conversion coefficient by an appropriate coefficient. From the waveforms of compound outputs of detector after auto-revising has been done, one finds that these waveforms have all the characters that the waveforms must have when photovoltaic conversion coefficients of four channels are equal to each other. So this method of auto-revising photovoltaic conversion coefficients of four channels is effective. It is obvious that high detect precision can be achieved with auto-revising balance because random errors carried manually can be eliminated.

Key-words: Four-quadrant photodetector; Photovoltaic conversion coefficient; Channel balance; Auto-revising; Signal analysis

1 Introduction

Photodetector, as a kind of detector for light signals, has been wide used in many fields, such as vibration monitoring [1], detection of biological warfare agents [2], and even detection of buried land mines [3]. With the development of manufacturing engineering, the ability of monitoring and control to manufacturing condition [4], the level of testing for characteristics of performance with a condition parameter [5,6], and so on, have been further improved. On the basis of the testing of performance characteristic of photodetector, the optional compounding formula of photochromics and the optional structure of photodetector can been achieved. The precise monitoring and control of manufacturing condition make the manufacturing of photodetecor with optional structure and that of photochromics with compounding formula turn true. And then advancing performances, such as suppressing noise [7], of detector are achieved, a great variety of new photodetectors are also developed. However, although the advanced monitoring and control technique can improve the performance of detector to a certain degree in certain aspects, in some times, digital signal analysis and numerical compensation maybe more convenient, efficient and economical. On one hand, either optimizing the structure of detector or optimizing the compounding formula of photochromics is always in certain constraint of manufacturing condition. On the other hand, it is expensive to improve the performance of detector by advancing the manufacturing engineering. Due to above reasons, in practice, numerical method is always used at first if it is possible to improve the performance of detector using digital analysis. For example, K.Wada presented a method based on numerical fittings for the spectral profile distortion for pulse due to the gain saturation [8]; N.Imam performed the global optimization of quantum-well infrared photodetector performance parameters using numerical method [9]. With the emergence of novel detector and the development of digital signal analysis technique, numerical method will be used more widely in many fields.

Four-quadrant photodetector, as one kind of a great variety of photodetector, has been also used in many fields such as measurement of light signals, photoelectric direction, photoelectric level, photoelectric tracking, photoelectric control and guide, and so on [10]. The photosurface of four-quadrant photodetector, shown in Fig.1, is divided into four parts. And there is an output channel corresponding to every part. The measurand is calculated by analyzing the difference among the outputs of four channels of four-quadrant photodetector. So the balance among the photovoltaic conversion coefficients of four parts of photosurface of four-quadrant photodetector is the premise of performing precise measurement. One must revise the photovoltaic conversion coefficients of all channels to make them be as same as possible before perform detecting using four-quadrant photodetector. In this paper, the absurdity of conventional method for revising the photovoltaic conversion coefficients of four channels to balance is pointed out at first. And then a new method is presented. For the new method, the relation expressions between the four outputs of detector and photovoltaic conversion coefficients are shown, and then the expressions for calculating the photovoltaic conversion coefficients are given by solving equation set. In the end of this paper, a practical application example is given. The practical application results indicate that the waveforms of compound outputs of photodetector have the characteristics of a four-quadrant photodetector with balance photovoltaic conversion coefficients. Thus, it is easy to revise the photovoltaic conversion coefficients of four channels to balance well by the new method.

2 Method for revising the Photovoltaic conversion coefficients to balance

2.1 Conventional method

The photosurface of detector is shown in Fig.1. It is divided into four parts equably, denoted with I, II, III and IV. There is an adjustable resistance called attenuation resistance linking a part to an output terminal, which forms an output channel of photodetector. Denote the photovoltaic conversion coefficient of every parts of photosurface with ρI, ρII, ρIII and ρIV, respectively. And denote the outputs of four parts of photosurface with uI, uII, uIII and uIV. It is obvious that the output of every channel of four-quadrant photodetector equals to each other if the whole photosurface is placed in parallel light with even illuminance and the photovoltaic conversion coefficient of every quadrant of the photosurface equals to each other. This theory is just used in conventional method to adjust the photovoltaic conversion coefficient to balance.

The structure for coefficient adjusting used in conventional method is shown in Fig.2. Parallel light passes through ground glass and changes as scattered light. The scattered light passed through convex lens and reaches photosurface of photodetector. In this case, the illuminance is looked even and the photosurface is considered be whole placed in light with even illuminance. Then, adjust the attenuation resistances, which is equivalent to adjust the photovoltaic conversion coefficients of four-quadrant of photosurface for the outputs of photodetector, up until the output of every channel equals to each other. Up to this point, the process of adjusting attenuation resistances, called coefficients adjusting, end.

However, the illuminance of light reach photosurface is Guassian, in fact, but not even [10], and we can’t determine that the disproportion among the outputs of photodetector is due to the disproportion of photovoltaic conversion coefficients or that the incidence light isn’t normal to the photosurface. Added to this, the photovoltaic conversion coefficient of a pels is not same to each other and the beam spot is generally in the center part, which is marked with a circle in Fig.4, of photosurface when photedetector is used in practice. So the coefficient adjusting result maybe error.

2.2 New method for balancing the conversion coefficients

Here, the sketch map of device we use to adjust the photovoltaic conversion coefficient of photodetector is shown in Fig.3. Laser from dot laser source passes the convex lens called condensing lens and becomes parallel light. Parallel light reflected by reflector converges on the photosurface of photodetector and forms a beam spot after have passed the convex lens of photodetector. Reflector swings left and right and the incidence light of photodetector is deflected back and forward, which make the beam spot moves back and forward. If the track of beam spot is as that shown in Fig.4 (a), we call it as 0˚ assembly. If the detector is assembled on the testing platform after having been revolved for 90˚ relative to last time assembling, and the track beam spot of is as that shown in Fig.4 (b), we call it as 90˚ assembly. The distance between photosurface and focal plane of is so much shorter than the focus photodetector that a little deflection angle of deflector will make the beam spot move from the left side to the right side of axis x. Thus, the photometric brightness can be considered as constant. Then, return the beam spot along light path to convex lens of photodetector, and there is an area in the convex lens corresponding to that of beam spot in every quadrant. Denote the area of the area, which correspond to the beam spot in quadrant I in photosurface, in convex lens with SI, that corresponding to quadrant II with SII, quadrant III with SIII, and quadrant IV with SIV, the area of whole convex lens with S, and there are:

uI =pI SI (1)

uII =pII SII (2)

uIII =pIII SIII (3)

uIV =pIV SIV (4)

where pj =ρjσ (j=I,II,III,IV) is called converted photovoltaic conversion coefficient of quadrant j of photosurface, ρj denotes the true photovoltaic conversion coefficient of quadrant j of photosurface, σ denotes the photometric brightness of incidence light. Set

ux=(uI+ uIV)- (uII+ uIII) (5)

and uy=(uI+ uII)- (uIII+ uIV) (6)

The waveforms of ux, uy, ux`and uy` are shown in Fig.5. While the maximum (minimum) of ux is obtained, beam spot locates whole in left (right) side of axis y, that is to say that locates whole in quadrant II and quadrant III (quadrant I and quadrant IV). If the photovoltaic conversion coefficients of four-quadrant are identic, the absolute value of the minimum of ux should equal to the maximum of ux according to (1)-(6). But it is obvious that the waveforms of ux shown in Fig.5 show that it’s maximum is not equal to the absolute value of the minimum of it, and does the waveform of ux`. This means that the photovoltaic conversion coefficients of four quadrants are not equal to each other. In fact, in case of 0˚ assembly, while beam spot locates whole in quadrant I and quadrant IV, there exist

pI SI + pIV SIV =Q1 (7)

pI SI - pIV SIV =R1 (8)

SI + SIV =S (9)

where Q1 and R1 denote the value of ux and uy, respectively, while beam spot locates whole in quadrant I and quadrant IV.

In the same way, while beam spot locates whole in quadrant II and quadrant III, there exist

pII SII + pIII SIII =Q2 (10)

pII SII - pIII SIII =R2 (11)

SII +SIII =S (12)

where Q2 and R2 are the value of ux and uy, respectively, while beam spot locates whole in quadrant II and quadrant III.

Corresponding to 0˚ assembly, in case of 90˚ assembly, there exist following equations analogous to (7)-(12).

pISI`+ pIISII`=Q1` (13)

pISI`- pIISII`=R1` (14)

SI`+ SII`=S (15)

pIII SIII`+ pIVSIV`=Q2` (16)

pIII SIII`- pIVSIV`=R2` (17)

SIII`+ SIV`=S (18)

where SI`, SII`, SIII`, SIV`, denote the area of the area, which correspond to the beam spot in 1th, 2th, 3th 4th quadrant in photosurface, respectively, in convex lens, in case of 90˚ assembly. Q2` and R2` denote the corresponding value of ux and uy, respectively.

In (7)-(18), Q1, Q2, R1, R2, Q1`, Q2`, R1` and R2` can be calculated according to the measurement signals ux and uy, S is known for a given photodetector, and p1~p4, S1~S4, S1`~S4`, are unknown. Obviously, There are 12 unknown quantities, and 12 independent equations, and then all the unknown quantities can be calculated by solving the equation set. But in practice, what we care for are p1~p4, and S1~S4, S1`~S4` are need not to be calculated.

Together (7) with (8), there are:

(19)

(20)

Together (10) with (11), there exist

(21)

(22)

Together (13) with (14), there exist

(23)

(24)

and together (15) with (16), there are

(25)

(26)

By solving simultaneous equations set (19)-(26), (15) and (18), p1~p4 are obtained as:

(29)

(30)

(31)

(32)

In (29)-(32), A, B, C, D, A`, B`, C` and D` are known due to Q1, Q2, R1, R2, Q1`, Q2`, R1` and R2` are known. So p1~p4 have been calculated. Then, every output si (i=I, II, III, IV) of four channels of four-quadrant photodetector divided by it’s corresponding photovoltaic conversion coefficient pi (i=I, II, III, IV) is the normalization output si` (i=I, II, III, IV) of every channel. In other words, the outputs after photovoltaic conversion coefficient have been adjusted are obtained. And more exact analysis result can be obtained with the normalization outputs in sequent signal analysis when four quadrants photodetector is used in practice.

3 Practical application

In this section, filtering for the output of every channel has been done at first because there are strong noises in the outputs, and then the photovoltaic conversion coefficients of four-quadrant photodetector are adjusted by the method discussed in section 2.

3.1 signal filtering

From Fig.5, one finds that there exists strong noise in every channel output of photodetector. And if we want to adjust the photovoltaic conversion coefficient using above method, signal filtering must be done at first. For digital signal filtering, presently, there are two popular methods, one is the classical time-frequency analysis method which take sine signal as the fundamental wave, another is wavelet analysis. Wavelet analysis is a flexible method for signal filtering and has been used wide due to it’s fundamental wave can be selected according to practice. Now, there are a great variety of functions for signal filtering in application software such as LabWindows/CVI [12], MATLAB [13], and so on. Then it is very convenient to perform signal filtering with these functions. Here, we use function WDEN in MATLAB and select Mexican Hat wavelet to perform signal filtering to the output of every channel of photodetetor, i.e, uI, uII, uIII and uIV, due to the flatness of Mexican Hat wavelet and that of the anticipant output of every channel of photodetetor. The waveforms of ux and uy after signal filtering having been done are shown in Fig.6. Comparing Fig.6 to Fig.5, it is easy to find that the noise of ux and uy shown in Fig.6 has been reduced greatly.

What to account is that author finds that there is less difference between the signals uI, uII, uIII and uIV filtered with wavelet and that by classical time-frequency analysis method.