## A simple and quantitative alignment procedure between solid state cameras

Optics Express, Vol. 17, Issue 26, pp. 23947-23952 (2009)

http://dx.doi.org/10.1364/OE.17.023947

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### Abstract

There are many applications that use multiple charge-coupled device (CCD) cameras. Accordingly it is important to ensure alignment between the CCDs. However, a simple and quantitative alignment procedure has not been introduced thus far. For this reason, this paper proposes an alignment procedure that uses a matched filter algorithm. By using the proposed procedure, the six alignment errors which are x, y, z, roll, pitch, and yaw between the two CCDs can be eliminated. Moreover, the procedure can be applied to the alignment of more than two CCDs. It is believed that the proposed alignment procedure is helpful for precise experiments in many applications that use multiple CCDs.

© 2009 OSA

## 1. Introduction

3. M. Akiba, K. P. Chan, and N. Tanno, “Full-field optical coherence tomography by two-dimensional heterodyne detection with a pair of CCD cameras,” Opt. Lett. **28**(10), 816–818 (2003). [CrossRef] [PubMed]

6. J.-W. You, D. Kim, S. Y. Ryu, and S. Kim, “Simultaneous measurement method of total and self-interference for the volumetric thickness-profilometer,” Opt. Express **17**(3), 1352–1360 (2009). [CrossRef] [PubMed]

## 2. Principle of matched filter algorithm

_{x}, f

_{y}) at the back focal plane of L1, which is the Fourier transform of a(x, y). If we put a filter which can be defined as A*(f

_{x}, f

_{y}) into the filter position, then a plane wave will be produced and it will be focused at the output plane by the lens L2 as depicted in Fig. 1(a). Here, A*(f

_{x}, f

_{y}) represents the complex conjugate of A(f

_{x}, f

_{y}).

_{x}, f

_{y}), the filter A*(f

_{x}, f

_{y}) cannot generate a plane wave. This results in causing some noises over the output plane as illustrated in Fig. 2(b) .

## 3. Experiment setup

_{1}and let the mirror intensity of CCD2 be a

_{2}. Then, we make A

_{1}*(f

_{x}, f

_{y}) as the matched filter which is the complex conjugate of the Fourier transform of a

_{1}.

_{1}and a

_{2}will be the same. And also, A

_{2}(f

_{x}, f

_{y}) which can be obtained through the Fourier transform at the filter plane becomes the same as A

_{1}(f

_{x}, f

_{y}). Therefore, we can expect a focus at the output plane when a

_{2}enters the matched filter algorithm, as shown in Fig. 1(b). a

_{2}is the input at this time, and the filter is A

_{1}*(f

_{x}, f

_{y}). Notice that the position of the CCD1 is fixed as a reference in the beginning stage of the alignment procedure. The CCD2 is aligned so that it can be positioned at the same distance and pose. Here, the same alignment means that the two CCDs have the same values of x, y, z, roll, pitch, and yaw for the object. The six variables are defined in Fig. 4 .

_{1}and a

_{2}will have different intensity distributions. In this case, since the input a

_{2}becomes different from A

_{1}(f

_{x}, f

_{y}) at the filter plane, some power losses which induce background noises incur at the output plane as shown in Fig. 2(b). By investigating the level of focus at the output plane, we can estimate the level of alignment between the two CCDs.

_{1}, which is used for making a filter A

_{1}*(f

_{x}, f

_{y}). The intensity of each region in CCD2 can also be thought of as a

_{2}. Then, a matched filter algorithm was applied in each corresponding region. Here, a

_{2}is the input again. In our experiment, each region was 30X30 pixels. The entire CCD area was 752X570 pixels with the pixel size of 11.6X11.2µm.

## 4. Results

_{1}(x, y). A filter A

_{1}*(f

_{x}, f

_{y}) was made from it. And, we let a

_{1}(x, y) enter the matched filter algorithm as an input. As an auto-correlation result, there are nine sharp peaks and no noise at all as shown in Fig. 6(a). Figure 6(b) illustrates a cross-correlation result when the two CCDs were just roughly aligned initially without any accurate alignment method. As can be expected, there are many noises at the output plane. Finally, for the accurate alignment between the two CCDs, six alignment variables are adjusted until we get the maximum peak and minimum noise values for the nine regions. However, as shown in Fig. 6(c), it is not possible to eliminate all of the noise because of the intrinsic differences between CCDs; i.e. sensitivity, linearity and so on. We also do not know the absolute error values that CCD2 has relative to CCD1. The maximum peak and minimum noise values in nine regions have been found by using the six-axis stage (K6X, Thorlabs), which has 250µm/rev in x and y, and 5mrad/rev in pitch and yaw.

## 5. Discussion

_{1}, a

_{2}, …, a

_{N}. Then, we make a filter A

_{1}*(f

_{x}, f

_{y}) from the CCD image a

_{1}. By using a

_{2}, a

_{3}, …, a

_{N}, as the inputs to the matched filter algorithm one by one, all of the CCDs can be aligned each other.

## 6. Conclusions

## Acknowledgements

## References and links

1. | G. C. Righini, A. Tajani, and A. Cutolo, |

2. | G. C. Holst, and T. S. Lomheim, “CMOS/CCD sensors and camera systems,” (SPIE-International Society for Optical Engine, 2007). |

3. | M. Akiba, K. P. Chan, and N. Tanno, “Full-field optical coherence tomography by two-dimensional heterodyne detection with a pair of CCD cameras,” Opt. Lett. |

4. | D. Kim, and B. J. Baek, “On-Axis Single Shot Digital Holography Using Polarization Based Two Sensing Channels,” in |

5. | W. Ko, Y. Kwak, and S. Kim, “Measurement of Optical Coefficients of Tissue-like Solutions using a Combination Method of Infinite and Semi-infinite Geometries with Continuous Near Infrared Light,” Jpn. J. Appl. Phys. |

6. | J.-W. You, D. Kim, S. Y. Ryu, and S. Kim, “Simultaneous measurement method of total and self-interference for the volumetric thickness-profilometer,” Opt. Express |

7. | J. W. Goodman, |

**OCIS Codes**

(070.5010) Fourier optics and signal processing : Pattern recognition

(100.3008) Image processing : Image recognition, algorithms and filters

**ToC Category:**

Imaging Systems

**History**

Original Manuscript: July 31, 2009

Revised Manuscript: October 26, 2009

Manuscript Accepted: November 14, 2009

Published: December 16, 2009

**Citation**

Hyungchul Lee, Daesuk Kim, and Soohyun Kim, "A simple and quantitative alignment procedure between solid state cameras," Opt. Express **17**, 23947-23952 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-26-23947

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### References

- G. C. Righini, A. Tajani, and A. Cutolo, An introduction to optoelectronic sensors, (World Scientific Publishing Company, 2009).
- G. C. Holst, and T. S. Lomheim, “CMOS/CCD sensors and camera systems,” (SPIE-International Society for Optical Engine, 2007).
- M. Akiba, K. P. Chan, and N. Tanno, “Full-field optical coherence tomography by two-dimensional heterodyne detection with a pair of CCD cameras,” Opt. Lett. 28(10), 816–818 (2003). [CrossRef] [PubMed]
- D. Kim, and B. J. Baek, “On-Axis Single Shot Digital Holography Using Polarization Based Two Sensing Channels,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2008), paper DTuC1.
- W. Ko, Y. Kwak, and S. Kim, “Measurement of Optical Coefficients of Tissue-like Solutions using a Combination Method of Infinite and Semi-infinite Geometries with Continuous Near Infrared Light,” Jpn. J. Appl. Phys. 45(No. 9A), 7158–7162 (2006). [CrossRef]
- J.-W. You, D. Kim, S. Y. Ryu, and S. Kim, “Simultaneous measurement method of total and self-interference for the volumetric thickness-profilometer,” Opt. Express 17(3), 1352–1360 (2009). [CrossRef] [PubMed]
- J. W. Goodman, Introduction to Fourier Optics, (Roberts & Company, 2004).

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