Subpixel analysis of the signal from the CMOS matrix sensor

practice in case of in-line sensors (Logvinov, 1992); however, those sensors have restricted sensitivity because of signal noise, which is proportional to the size of the light sensitive area of photodiode. This size is relatively high compared with the particle size. In this chapter a sensor based on the CMOS matrix is proposed, in order to achieve higher sensitivity and accuracy. The sensitivity of the CMOS sensor can be estimated based on the equation (3.16) obtained for the response of a single pixel, illuminated by LED, for the case where the particle size is smaller than pixel size.

Figure 3.8 Schematic showing a matrix sensor consisting of one pixel width line with a particle moving above and past it.

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Particle floats above the surface of the matrix sensor as it is shown in Figure. 3.8.

For the purposes of estimation it can be supposed, that the matrix surface is illuminated uniformly and the projection of the particle onto the sensor is of equal size and shape to the particle. The shape of the particle (Figure 3.8) can be described using the R( ) function, and its area is _Sp. The symbol v stands for the velocity of the particle. The numbers from 1 to 6 denote the position of the particle above the pixels of the matrix during the exposure time _texp. The count starts with number

‘1’. Each pixel has a size of p and the total number of pixels is N_p. Each pixel can be represented as a very small photodiode connected to a capacitor during the exposure time (Stempkovsky, Shilin, 2003).

Therefore, this capacitor is charging by photocurrent i ( t ) during _p exposure time and the capacitor accumulated the charge q after _p exposure time is elapsed:

0

 ^exp



t

p p

q ( t ) i ( t )dt, (3.9)

Figure 3.9 Photocurrent of the central pixel as it is shown in Figure 3.8

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The dependence between photocurrent and time for the central pixel in Figure 3.8 is shown in Figure 3.9. Therefore, the charge accumulated by the central pixel can be determined as follows:

particle and covered by it respectively.

The relation between I₀ and I_p can be estimated using the area of the Therefore, using (3.12) the (3.11) can be rewritten as follows:

0 0 The I₀ can be obtained using (3.9) as there was no particle under such pixel:

0 0 0

0

^texp



q I dt I t , (3.14) Eventually, the level of the charge that is proportional to the particle is in the difference  q q₀q_p, therefore, (3.13) can be rewritten:

  0

 ^d _exp q q S

p v t , (3.15)

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Figure 3.10 The 6 um pixel charge (measured in electrons), that was covered by particle with velocity 1 m/s depending on the exposure time.

The blue line (square data point) stands for a particle size of 5 microns and red one (diamond data point) for a particle size of 2 microns.

As follows from (3.15), it is necessary for the charge of q₀to reach as near to saturation as possible, in order to get a stronger signal from the particle. There are two approaches to achieve a state near saturation:

either to increase the brightness of the LED, or to increase the exposure time. Figure 3.10 reflects the relationship between the value of the signal

q and the exposure time for the case in which the saturation of q₀ is reached by increased LED brightness. It should be mentioned that where saturation of q₀ is obtainable, a short exposure time is preferable as the signal level is not distributed between several pixels.

Signal to noise ratio can be estimated using following relation:

0

exp d n

S q S

N q pvt , (3.16)

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where q_n stands for noise (in electrons) of pixel.

The maximum sensitivity would be for the particle size equal to the pixel size, the minimum size of particle track is also one pixel size. Therefore, the maximum signal to noise ratio can be estimated as follows:

 0 This is true for the particle and the pixel sizes are both of 6 micron. In case of the lower size of the particle, the level of signal is lower as well.

In case of the signal to noise ratio equals to the level of 3, the minimum particle size to be identified is the following:

0

Therefore, the potential sensitivity of the MT9V032C12STM image sensor is 0.6 microns.

Nevertheless, typical CMOS matrix image sensors, for example, such as MT9V032, offer only the minimum 50 microseconds exposure time.

This means that the signal obtained will represent a particle track rather than an instantaneous image of the particle. In case of a particle velocity of 1 m/s, which is similar to the real conditions, this track would consist of at least 6 pixels. This factor decreases the potential sensitivity of the matrix sensor. There are two possible approaches to resolve this problem. One approach would be to use pulsed light from the LED. The alternative is to record and analyse the accumulated charge from several adjacent pixels.

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Let q_n stands for the average noise (in electrons) of several adjacent pixels within the particle track. If it can be assumed that the noise associated with each pixel is independent, then:

2 2 2

1 2 ... ( 1)

     

n n n n Np

q q q q , (3.19)

where q_n1, q_n2,..., q_{n Np( 1)} denote the noise in each pixel within the track between pixel 1 and pixel N_p₁.

Figure 3.11 shows the calculated signal to noise ratio, for the case of a 2 microns particle, with and without consideration of electron accumulation.

Figure 3.11 Signal to noise ratio for pixels (with the size of 6 microns), that was covered by 2 micron particle with velocity 1 m/s depending on the exposure time. The blue line (square data point) stands for accumulated signal and red one (diamond data point) for the case without accumulation.

Ultimately, it can be noted, that the achievable signal to noise ratio is approximately 3, for in-line sensors based on a single photodiode and for

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particle sizes of 5 microns. Using a matrix sensor, even without any optics, it is possible to reach a signal to noise ratio of 10, even for smaller 2 microns particles. Therefore, CMOS matrix sensors can be recommended as a means for obtaining significant improvement in the sensitivity and accuracy of in-line sensors.

3.3 Diffraction effects and numerical simulations using