## Error analysis of the de-crosstalk algorithm for the multianode-PMT-based quadrant tracking sensor |

Optics Express, Vol. 20, Issue 28, pp. 29185-29195 (2012)

http://dx.doi.org/10.1364/OE.20.029185

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### Abstract

For the multianode-PMT-based quadrant tracking sensor, one of the tracking error sources is the crosstalk. The crosstalk can be reduced by de-crosstalk algorithm, so the tracking error of the de-crosstalk algorithm for the multianode-PMT-based quadrant tracking sensor are analyzed in theory and verified by experiments. Both the theoretical analysis and the experimental results showed that the spot displacement sensitivity could be improved by the de-crosstalk algorithm, but the spot centroid detecting error increased at the same time. So the de-crosstalk algorithm could not improve the tracking accuracy effectively.

© 2012 OSA

## 1. Introduction

2. G. A. Tyler and D. L. Fried, “Image-position error associated with a quadrant detector,” J. Opt. Soc. Am. **72**(6), 804–808 (1982). [CrossRef]

## 2. Principles of the quadrant tracking sensor

5. M. Toyoda, K. Araki, and Y. Suzuki, “Wave-front tilt sensor with two quadrant detectors and its application to a laser beam pointing system,” Appl. Opt. **41**(12), 2219–2223 (2002). [CrossRef] [PubMed]

6. M. Rome, H. G. Fleck, and D. C. Hines, “The quadrant multiplier phototube, a new star-tracker sensor,” Appl. Opt. **3**(6), 691–695 (1964). [CrossRef]

*i*quadrant of the quadrant detector.

^{th}*f*is the effective focal length of the tracking sensor.

## 3. Crosstalk of the multianode PMT

^{4}and 10

^{8}times, which can permit the PMT to achieve the single-photon detection sensitivity. As a feature of its spatial design, several PMTs can be integrated into one package which is called the multianode PMT. The output signals from different pins correspond to the spatial position of the photocathode, thus the 2 × 2 multianode PMT can be regarded as a quadrant detector.

*i*quadrant produces

^{th}*P*true photoelectron numbers, because of the crosstalk, the

_{i}*j*quadrant will produce

^{th}*P*pseudo photon counts. The crosstalk ratio between the

_{j}*i*and

^{th}*j*quadrants can be defined as

^{th}*k*, as shown in Fig. 3 .

_{s}*x*-direction and

*y*-direction are symmetrical, all the following discussion focuses on the

*x*-direction,

*y*-direction is similar.

## 4. The tracking error of the multianode-PMT-based quadrant tracking sensor

### 4.1 Spot displacement sensitivity

*x*as obtained by calculation from the true centroid position

_{c}*x*of the spot. It denotes the changing trend of the calculated spot centroid when the true spot centroid changes elsewhere within a slightly different locus (see Eq. (7)).

_{0}### 4.2 Spot centroid detecting error

8. X. Y. Ma, C. H. Rao, and H. Q. Zheng, “Error analysis of CCD-based point source centroid computation under the background light,” Opt. Express **17**(10), 8525–8541 (2009). [CrossRef] [PubMed]

*i*quadrant.

^{th}*i*and

^{th}*j*quadrants.

^{th}*i*quadrant is

^{th}*i*and

^{th}*j*quadrants is caused by crosstalk between them, so

^{th}### 4.3 Tracking error

## 5. Tracking error analysis of the de-crosstalk algorithm

*C*. Theoretically, the reconstructed photoelectron number vector

*R*which is the inverse matrix of crosstalk matrix

*C*by

### 5.1 Spot displacement sensitivity of the de-crosstalk algorithm

### 5.2 Centroid detecting error of the de-crosstalk algorithm

*i*quadrant after using the de-crosstalk algorithm.

^{th}*i*and

^{th}*j*quadrants.

^{th}### 5.3 Tracking error of the de-crosstalk algorithm

## 6. Experimental results

### 6.1 Measurement of crosstalk coefficient

### 6.2 The calculated value of spot centroid

*per*second (fps), thereby making the spot move on a locus bounded by a rectangular-based pyramid. The influence curves of crosstalk on spot centroid were then evaluated. The photoelectron number output by the quadrant detector with different spot locations is measured and processed with the de-crosstalk algorithm. Thus the curves indicating the calculated value of spot centroid and the true spot centroid were shown in Fig. 8 .

### 6.3 Tracking error

*C*). Acceptable correlation between experimental and theoretical values may also be noted.

## 7. Conclusion

## Acknowledgment

## References and links

1. | C. H. Rao, X. J. Zhang, W. H. Jiang, and G. M. Tang, “Performance comparison of photo counting quadrant tracking system and intensifier CCD tracking system,” Acta Opt. Sin. |

2. | G. A. Tyler and D. L. Fried, “Image-position error associated with a quadrant detector,” J. Opt. Soc. Am. |

3. | D. A. Golimowski, M. Clampin, S. T. Durrance, and R. H. Barkhouser, “High-resolution ground-based coronagraphy using image-motion compensation,” Appl. Opt. |

4. | Y. Hayano, H. Takami, W. Gaessler, N. Takato, M. Goto, Y. Kamata, Y. Minowa, N. Kobayshi, and M. Iye, “Upgrade plans for Subaru AO system,” Proc. SPIE |

5. | M. Toyoda, K. Araki, and Y. Suzuki, “Wave-front tilt sensor with two quadrant detectors and its application to a laser beam pointing system,” Appl. Opt. |

6. | M. Rome, H. G. Fleck, and D. C. Hines, “The quadrant multiplier phototube, a new star-tracker sensor,” Appl. Opt. |

7. | X. Y. Ma, J. Mu, and C. H. Rao, “Error analysis of four-quadrant-based tracking sensor when dead zone is inevitable,” Acta Phys. Sin. |

8. | X. Y. Ma, C. H. Rao, and H. Q. Zheng, “Error analysis of CCD-based point source centroid computation under the background light,” Opt. Express |

**OCIS Codes**

(010.1080) Atmospheric and oceanic optics : Active or adaptive optics

(040.5250) Detectors : Photomultipliers

(120.4820) Instrumentation, measurement, and metrology : Optical systems

(150.1135) Machine vision : Algorithms

**ToC Category:**

Instrumentation, Measurement, and Metrology

**History**

Original Manuscript: September 28, 2012

Revised Manuscript: November 29, 2012

Manuscript Accepted: November 30, 2012

Published: December 17, 2012

**Citation**

Xiaoyu Ma, Changhui Rao, Kai Wei, Youming Guo, and Xuejun Rao, "Error analysis of the de-crosstalk algorithm for the multianode-PMT-based quadrant tracking sensor," Opt. Express **20**, 29185-29195 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-28-29185

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### References

- C. H. Rao, X. J. Zhang, W. H. Jiang, and G. M. Tang, “Performance comparison of photo counting quadrant tracking system and intensifier CCD tracking system,” Acta Opt. Sin.22(1), 67–73 (2001).
- G. A. Tyler and D. L. Fried, “Image-position error associated with a quadrant detector,” J. Opt. Soc. Am.72(6), 804–808 (1982). [CrossRef]
- D. A. Golimowski, M. Clampin, S. T. Durrance, and R. H. Barkhouser, “High-resolution ground-based coronagraphy using image-motion compensation,” Appl. Opt.31(22), 4405–4416 (1992). [CrossRef] [PubMed]
- Y. Hayano, H. Takami, W. Gaessler, N. Takato, M. Goto, Y. Kamata, Y. Minowa, N. Kobayshi, and M. Iye, “Upgrade plans for Subaru AO system,” Proc. SPIE4839, 23–43 (2003).
- M. Toyoda, K. Araki, and Y. Suzuki, “Wave-front tilt sensor with two quadrant detectors and its application to a laser beam pointing system,” Appl. Opt.41(12), 2219–2223 (2002). [CrossRef] [PubMed]
- M. Rome, H. G. Fleck, and D. C. Hines, “The quadrant multiplier phototube, a new star-tracker sensor,” Appl. Opt.3(6), 691–695 (1964). [CrossRef]
- X. Y. Ma, J. Mu, and C. H. Rao, “Error analysis of four-quadrant-based tracking sensor when dead zone is inevitable,” Acta Phys. Sin.61(7), 072903 (2012).
- X. Y. Ma, C. H. Rao, and H. Q. Zheng, “Error analysis of CCD-based point source centroid computation under the background light,” Opt. Express17(10), 8525–8541 (2009). [CrossRef] [PubMed]

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