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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 Optical Society of America
1. Introduction
There are many optical sensors that are currently available [1]. Among them, CCD camera is widely used in many applications due to the distinct advantages afforded by its sensitivity, dynamic range, and linearity [2].
Occasionally, more than two CCDs are necessary for certain applications [3–6] in order to obtain more information about a sample target. For these applications, the alignment between the CCDs is an important issue, as the accuracy of the results depends on it. However, there have been no clear alignment procedures thus far. Usually, the CCDs are aligned via user experience. Hence, this paper proposes an alignment procedure that can guide the alignment of CCDs simply and quantitatively. For this procedure, we employ the matched filter algorithm which is widely used in pattern recognition fields [7].
2. Principle of matched filter algorithm
Figure 1 shows the principle of matched filter algorithm. When a plane wave passes through the input mask, the input signal a(x, y) is generated at the front focal plane of the lens L1. By L1, a(x, y) is transformed to A(fx, fy) 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*(fx, fy) 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*(fx, fy) represents the complex conjugate of A(fx, fy).
Fig. 1 (a) Matched filter algorithm based on the 4-f optical system (f: focal length of lenses L1 and L2, (b) Simplified description of the matched filter algorithm represented by the Fourier Transform (FT).
However, if the input signal that enters into the matched filter system is different from a(x,y) which is used for designing the matched filter A*(fx, fy), the filter A*(fx, fy) cannot generate a plane wave. This results in causing some noises over the output plane as illustrated in Fig. 2(b) .
Fig. 2 Power distribution in the output plane: (a) when the input is exactly a(x, y) and (b) when the input is deviated from the signal a(x, y).
3. Experiment setup
A similar concept to the matched filter algorithm can be applied to the experiment setup, as shown in Fig. 3 . The experiment setup consists of an object, a beam splitter, and two CCDs. The two CCDs see mirror images of each other because of the beam splitter. Let the intensity acquired from CCD1 be a1 and let the mirror intensity of CCD2 be a2. Then, we make A1*(fx, fy) as the matched filter which is the complex conjugate of the Fourier transform of a1.
If the two CCDs are aligned exactly at the same position from the object, a1 and a2 will be the same. And also, A2(fx, fy) which can be obtained through the Fourier transform at the filter plane becomes the same as A1(fx, fy). Therefore, we can expect a focus at the output plane when a2 enters the matched filter algorithm, as shown in Fig. 1(b). a2 is the input at this time, and the filter is A1*(fx, fy). 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 .
Fig. 4 Six geometric variables which needed to be aligned in the proposed matched filter based scheme.
If the two CCDs are not aligned perfectly, a1 and a2 will have different intensity distributions. In this case, since the input a2 becomes different from A1(fx, fy) 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.
Figure 3 shows the experiment setup conducted with a USAF resolution target (38-257, Edmund) as an object. The object intensities acquired at the CCDs are shown in Figs. 5(a) and 5(b). As mentioned above, Fig. 5(b) shows the mirror image of Fig. 5(a). As you can see, CCD2 has some alignment errors relative to CCD1. We defined nine regions to show alignment errors more efficiently as shown in Figs. 5(c) and 5(d). The intensity of each region in CCD1 can be thought as a1, which is used for making a filter A1*(fx, fy). The intensity of each region in CCD2 can also be thought of as a2. Then, a matched filter algorithm was applied in each corresponding region. Here, a2 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.
Fig. 5 Input images captured in the two CCDs: (a) Object intensity at CCD1. (b) Object intensity at CCD2. (c) Object intensity at CCD1 with nine regions. (d) Object intensity at CCD2 with nine regions.
4. Results
Figure 6 shows experimental results for the three cases. Figure 6(a) depicts the ideally aligned case. In this case, only the intensity of CCD1 was used. Let the intensity be a1(x, y). A filter A1*(fx, fy) was made from it. And, we let a1(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.
Fig. 6 Experimental results of the matched filtering procedures: (a) Ideally aligned, (b) Not aligned, and (c) Practically aligned.
It is worth to note that each alignment variable has a distinct effect on the output plane distribution: 1) If the alignment errors in x or y direction exist, the peaks move laterally with keeping the same level of the noise. This is a consequence of the space invariance of the matched filter. 2) If the alignment errors in z direction exist, all the peaks tend to reduce and the noise increases. 3) If roll error exists, the surrounding eight regions are greatly affected, compared to the center region. 4) If pitch or yaw error exists, the regions far from the rotation axis are greatly affected compared to the near regions.
By using these properties, the alignment could be accomplished gradually and efficiently until the maximum peak and minimum noise values are obtained in all nine regions. Consequently, we could eliminate most alignment errors, as shown in Fig. 6(c).
To quantify the noise, the Root Mean Square (RMS) value was calculated. The peak and RMS values are summarized in Table 1 , according to the three cases mentioned above.
Table 1. Peak and RMS values of the experimental results described in Fig. 6.
5. Discussion
We found that the location and separation of the nine regions are more important than the size of each region on the performance of the matched filter algorithm. This may be well explained by Fig. 7 . In Fig. 7(a), the nine regions are concentrated toward the center. On the other hand, Fig. 7(b) is a case that those regions are spread out. As shown in Fig. 7(c) and (d), as we choose the nine regions the farer from the central area, the sensitivity of the matched filter algorithm will be increased. Therefore, it is recommended to have the nine regions spread out.
The pixel size of the CCD is also more critical than the fill factor of the CCD on the performance of the matched filter algorithm. As the size of the CCD pixel becomes smaller, the spatial resolution of intensity at CCD will be increased. Therefore, the sensitivity of the matched filter algorithm will get higher. Because the matched filter algorithm uses variations of intensity according to the six alignment variables, the use of either a broad band source or a laser source makes no difference. We believe that the proposed alignment procedure can also be applied for the alignment of more than two CCDs. Assume that there are N CCDs. And, let the each intensity be a1, a2, …, aN. Then, we make a filter A1*(fx, fy) from the CCD image a1. By using a2, a3, …, aN, as the inputs to the matched filter algorithm one by one, all of the CCDs can be aligned each other.
The proposed alignment procedure can also be applied to complementary metal-oxide-semiconductor (CMOS) cameras as well. We just used CCDs as a representative of solid state camera.
6. Conclusions
In conclusion, this study proposes a simple and quantitative alignment procedure between CCD cameras. By applying this procedure, we could eliminate alignment errors which can be made during the alignment between two CCDs. We believe that the proposed alignment scheme can be widely used in various applications that need accurate multiple CCD alignment.
Acknowledgements
This research was supported by the Center for Nanoscale Mechatronics & Manufacturing, one of the 21st Century Frontier Research Programs, which is supported by the Ministry of Education, Science and Technology, Korea with grant (04-K14-01-013-00).
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