2.1.

Imaging Scheme Modified for Laser Detectors

The typical imaging system used in machine-vision-based applications cannot be directly applied to laser detectors; this is because in the detector comparison process, the laser beam is supposed to be incident on the detector at a 90 deg orientation, which would be in conflict with the position of the camera. Imaging lasers from off-center positions is also negated, because for detectors with deep input ports, the active area may be partly blocked, resulting in locating failure, as shown in Fig. 1(a).

Fig. 1

Imaging system for detector positioning: (a) imaging the incident laser from an off-center position, (b) modified imaging scheme using a lens with a large aperture to ensure a complete FOV, and (c) view blocked by the laser via hole of diameter 15 mm.

For these reasons, a modified imaging scheme was designed for specific application to laser power measurement, and its diagram is shown in Fig. 1(b). The imaging structure contains a reflector placed at 45 deg along the main optical axis, with a 45 deg oblique via a hole at its center. On the one hand, the reflector allows the laser beam to pass through and be vertically incident on the detector’s active area. On the other hand, it allows imaging along the detector’s axis to avoid center separation. Given that the via hole on the reflector blocks a part of the image beam, to maintain the complete field of view (FOV), we use lenses with large effective apertures. While the effective aperture angles of the lenses are larger than the solid angles of the blocked area, most of the image beam would still converge on the CMOS chip of the camera. The FOV that is partly shadowed by the small effective aperture angle is shown in Fig. 1(c) as a contrast. This imaging scheme provides a noninvasive method suitable for most laser detector comparison applications. Additional setups to reduce measurement errors, such as power stabilization and beam shaping, can also be easily coordinated with this imaging scheme. The detailed experimental setup is described in Sec. 3.

2.2.

Algorithms for Shape Detection

Before performing shape detection, the images are preprocessed. The images are first binarized, and connected component labeling is then applied to find the contiguous regions.²¹ In a binary image, a four-connected region composed of a center pixel $(x_i,y_i)$ and its adjacent pixels can be determined as follows:

Commonly, the geometric center of a detector is selected to coincide with that of the laser beam. The center of a laser beam is easy to locate because its brightness is several orders of magnitude higher than that of the background. The center of the laser point is calculated using the centroid of the target area, with the pixels weighted by their gray values. In the case of the laser power detectors, considering that most input ports are either rectangular or round, shape detection methods are used to distinguish the target area. These methods are introduced in Secs. 2.2.1 and 2.2.2.

2.2.2.

Shape Detection for Round Detector

For round detectors, the circle Hough transform (CHT) method is applied.²¹ The CHT allows finding circles in a target area and works well for defective circles or even arcs. Consider a target circle $i$, which is approximately the ideal boundary of a round detector. The points $(x_i,y_i)$ on circle $i$, circle center $(a_i,b_i)$, and diameter $r$ are all bounded to the equation of the circle. If we project the circle equation from the original $xy$ coordinate system into three-dimensional (3D) space whose coordinate axes are represented by $(a,b,r)$, then the circle equation becomes

Eq. (4)

$$f_i(a,b,r)={(a-x_i)}^2+{(b-x_i)}^2-r^2=0(a>0,b>0,r>0).$$

In the $(a,b,r)$ coordinate system, Eq. (4) represents a conical surface with its vertex at $(x_i,y_i,0)$, as shown in Fig. 2. It is clear that for any point $(x,y)$ in the original two-dimensional (2D) space, there will be a corresponding conical surface in the 3D coordinate system. However, with respect to the points on circle $i$, the corresponding conical surfaces all intersect at a single point $(a_i,b_i,r_i)$ in the 3D coordinate system. Given this feature, a circle can be found if an accumulator is established in the $(a,b,r)$ space. For every point $(x,y)$ on the target circle, the weights of the points on the corresponding conical surface are added to the accumulator. After traversing all the pixels in the 2D image, the corresponding point $(a_i,b_i,r_i)$ in the 3D space with the maximum weight represents the target circle. Here, $(a_i,b_i)$ is the center of the circle, and $r_i$ is its radius. Thus, the center of the circular detector as well as its boundary can be obtained.

Fig. 2

Schematic of the CHT. Points $(x_{\mathrm{i}1},y_{\mathrm{i}1})$ and $(x_{\mathrm{i}2},y_{\mathrm{i}2})$ on the target circle are the vertices of two cones, and all of the conical surfaces related to the circle intersect at the point $(a_i,b_i,r_i)$.

3.1.

Experimental Setup for Implementing the Proposed Approach

The experimental apparatus used in this work has all the modified vision components integrated into the detector calibration device, as shown in Fig. 3. The vision part mainly consists of the prime lens (50-mm focal length, F1.4 maximum aperture, HC5005A, Chiopt Optotech), the CMOS (1”, $2048\times 2048\text{pixels}$, Flir Systems) and the ring illuminator. The laser beam on the main optical path passes through a Glan–Taylor prism and a power stabilizer to achieve a power stability of $<0.1\%$. The attenuator and aperture along the main optical path are used to adjust the power level and geometric form of the laser beam. Then, the fixed-diameter power-stabilized laser beam passes through via hole of the reflector, then the ring illuminator, thereafter being incident on the detector for value scale transfer. It is worthy to note that to minimize the blocking angle of the via-hole, the ideal position of via hole should be set overlapping with the imaging aperture diaphragm, such that the prime lens needs to be placed as near as the reflector. The transfer detectors, which commonly include reference detectors and under-test detectors, are mounted on a 2D motion-controlled translation stage. Once the detectors are imaged, programed algorithms are used to locate the center of the detectors and the laser point, then send the coordinates to the 2D translation stage, ensure that the detector centers accurately coincide with the laser points, so as to complete automatic positioning of the detectors during the scale transfer process. The procedures can be processed for more than one round to further reduce the misalignment introduced by imaging distortion.

Fig. 3

Experimental setup for comparison of detectors using the imaging system.

3.2.

Resolution Test of the Modified Imaging System

Imaging resolution is one of the key parameters of any vision system and directly limits the precision of the detector position. Based on the object–image relationship, the complete object field is a $75\times 75{\mathrm{mm}}^2$ square area that is composed of $2048\times 2048\text{pixels}$. Therefore, each pixel corresponds to an area of $\sim 37\times 37{\mu \mathrm{m}}^2$ in the object field. Considering the extra aberrations from the lens, imperfect reflector, and via-hole blocking, the effective spatial resolution may be lower.

To determine the upper limit of the imaging resolution of our apparatus, we placed an optical resolution test board at the reference detector surface and used a complete reflector (without via holes) for imaging. The test board was illuminated by a homogeneous backlight, and the lens was focused on the front surface of the board. A complete image of the board is shown in Fig. 4(a). The region labeled “20” is magnified and presented in Fig. 4(c), in which 20 black stripes can be clearly distinguished per 2 mm, while the stripes labeled “40” are blurry, as shown in Fig. 4(b). These image results indicate an effective resolution of $\le 100\mu \mathrm{m}$, which is in accordance with the speculation of the object–image relationship.

Fig. 4

Resolution test results of the imaging scheme: (a) original image of the test board with $75\times 75{\mathrm{mm}}^2$ FOV; (b) stripes spaced at 20 lines/mm; and (c) stripes spaced at $10\text{lines}/\mathrm{mm}$.

3.3.

Effect of Via-Hole Blocking

Although the imaging scheme proposed here guarantees a complete FOV, via hole that allows lasers through still blocks a part of the image beam. A via hole of larger diameter renders the system suitable for more laser applications but will also reduce image quality. To quantitatively determine the effect of the via hole on image quality, we processed reflectors with via holes of diameters 0, 3, 7, 12, and 15 mm; then, we installed and tested the contrast ratios of the stripes labeled as “20.” In the experiment, the contrast ratio $C$ is calculated as follows:

Fig. 5

Influence of via-hole blocking on image quality: (a)–(e) stripes labeled as “20” under via-hole blocking for 0-, 3-, 7-, 12-, and 15-mm diameters, respectively; (f) grayscale values of the stripes, where the five curves with different colors represent the amplitudes along the transverse lines marked in (a)–(e); (g) relationship between image contrast and via-hole diameter.

4.1.

Positioning Repeatability for Rectangular Detector

To maintain generality, we selected a commonly used commercial detector in optical labs as the experimental sample. The device has a square window for laser power detection. By adjusting the lens focal length and illumination, the original image of the detector was clearly captured with sharp and clean edges, as shown in Fig. 6(a). Then, the image is preprocessed on programming software (algorithms introduced in Sec. 2.2 are programmed and executed on Matlab). By setting the appropriate thresholds for the grayscale values and pixel amounts for the connected region, the target connected region that represents the active area of the detector is obtained, as labeled in blue in Fig. 6(b). Then, we applied the minimum bounding rectangle described in Sec. 2.2.1 and acquire its center, and these results are shown in Fig. 6(c). The images in Fig. 6 are $2048\times 2048\text{pixel}$ arrays. The red asterisk in Fig. 6(c) represents the center of the blue square, and its coordinates are (1024.3, 993.3); the point (0, 0) represents the top left corner of the square and (2048, 2048) represents the bottom right corner of the square.

Fig. 6

Location of rectangular detector: (a) original image of the detector; (b) three major connected region, the blue one stands for the active area of the detector; (c) minimum bounding rectangle and the center of the target rectangle, the center is marked by the red asterisk.

To examine the reliability of this positioning process, we tested and analyzed the positioning repeatability of the system. Although the edges of the square are represented by integer coordinates, the center, which is calculated using the edge points can be fractional and surpass the pixel resolution limit. In fact, we can set the datatype of the coordinates as double-precision variables in the calculation program, which would allow 16 significant digits for the results. However, this does not represent real precision. The valid precision is a composite result of image resolution, algorithm, control accuracies of the translation stages, real-time changes in the dynamic image, noisy point, and other interference.

In our experiment, the translation stages have a controlling precision of $5\mu \mathrm{m}$, which sets the upper limit of the positioning precision. The repeatability tests were performed as follows. The spacing of each step was set to $100\mu \mathrm{m}$. Each time the detector is shifted, we perform the imaging and recognition processes and record the center coordinates. The procedure was repeated 28 times in total. The acquired coordinates along the matching direction are plotted against the stepped distance, as shown in Fig. 7.

Fig. 7

Positioning repeatability of rectangular detector. The blue dots represent the coordinates of the recognized centers, and the red dots represent their deviations from the ideal displacement.

The $x$ axis represents the stage movement, the 28 steps corresponds to a detector displacement of 2.8 mm. The $y$ axis represents the detector movement scaled by pixels. From the graph, we can see that the coordinates of the recognized center (denoted as blue dots) increase monotonously and smoothly with stage movement. To evaluate the positioning repeatability quantitatively, we subtracted the coordinates using their ideal references (obtained by the least-squares fitting method, shown in Fig. 7 as the black line); these results are denoted as red dots. The maximum deviation is thus within 0.7 pixels, corresponding to a distance of $26\mu \mathrm{m}$ in the image space. The standard deviation is estimated using the range method as follows:

4.2.

Positioning Repeatability for Round Detector

For most laser power detectors, the input ports are either rectangular or round. To inspect the practicality of the proposed method, experiments were also performed for a round detector using the algorithm described in Sec. 2.2.2, and the coordinates of the center points were successfully acquired. The original image, its four major connected regions, and recognized center are displayed in Figs. 8(a), 8(b), and 8(c), respectively. In Fig. 8(c), the red asterisk represents the center of the inner circle of the yellow region, and its coordinates are (1069.4, 1058.3), while (0, 0) and (2048, 2048) represent the top-left and bottom-right boundary points of this area.

Fig. 8

Location of round detector: (a) original image of the detector; (b) four major connected regions, the inner boundary of the yellow region is the input port of the detector; (c) recognized circle and the circle center, the red asterisk represents the center of the recognized circle.

We verified the positioning repeatability of our apparatus for round detectors as well. With spacing steps of $100\mu \mathrm{m}$, a displacement distance of 1.5 mm was traversed along the motor stage, and the centering program was executed for 16 times. The positioning results of the round detector are shown in Fig. 9.

Fig. 9

Positioning repeatability of the round detector. The blue dots represent the coordinates of the recognized centers, and the red dots represent their deviations from the ideal displacement.

The detector displacement shows a stable and uniform increment along the motor axis, similar to the positioning results of the rectangular detector. Specifically, in the 1.5-mm displacement range, the maximum deviation is within 1.2 pixels, corresponding to a distance of $46\mu \mathrm{m}$ in the image space. With a range coefficient of ${\mathrm{C}}_{16}\approx 3.5$, the standard deviation was estimated to be $13\mu \mathrm{m}$. These repeatability results prove that the proposed positioning system is compatible with different detector shapes, and the positioning reliability is of the order of $10\mu \mathrm{m}$.

4.3.

Comparison with Conventional Methods and Discussion

In this section, we analyze the amount of additional error from positioning precision. For the axisymmetric probability of uniformity, the experiments focus on a single axis of the detectors. Power-stabilized beams with a diameter of 1 mm and wavelengths of 532 and 980 nm were applied to the detectors. Both detectors were moved horizontally for 4 mm with $100\text{-}\mu \mathrm{m}$ steps. Owing to detector nonuniformities, the response currents generated by the photodiode detector were not constant in the active area. These currents are recorded at every step, normalized, and then plotted against the detector displacement, as shown in Fig. 10.

Fig. 10

Detector uniformity and relative errors of power measurements: (a) response uniformity of the round Si detector; (b) response uniformity of the rectangular Ge detector.

In the 4-mm range, the response current of the Si detector monotonously decreased by 0.8% (peak-to-peak), and for the Ge detector, this relative deviation was a maximum of 1.6% (peak-to-peak). The uniformities of both detectors are among the average levels for conventional commercial photodiodes. The red areas in Figs. 10(a) and 10(b) show the repeatability ranges of the positioning operations along the $x$ axis. In Sec. 1, we described the typical alignment limitations for arbitrary laser detectors,⁴ which are 1 mm with the help of a ruler and 0.2 to 0.5 mm with the help of a crosshair or fiber coupler adaptor. To further testify the alignment precision by human vision, alignment experiments were conducted in our laboratory with five technicians. The maximum difference based on their observations is 1 mm at 409 nm and 0.8 mm at 635 nm in the vertical direction, which is generally consistent with the data from NIST and common experience. Within the $\pm 0.5\text{-}\mathrm{mm}$ visual-alignment range, the light-blue areas represent the corresponding maximum measured deviations, which are 0.19% and 1.2% for the Si and Ge detectors, respectively. For the $\pm 100\mu \mathrm{m}$ aperture-alignment range, the corresponding errors were 0.06% and 0.3%, respectively. With respect to the machine-vision system, with positioning precisions of $\pm 13$ and $\pm 7\mu \mathrm{m}$, the corresponding measured errors further decreased to 0.01% and 0.03%, respectively.

For typical calibration of the aforementioned detectors, the uncertainty component of detector alignment ($u_{DA}$) is combined with the standard uncertainty of the calibrated response ($u_{CR}$) and other uncertainty components ($u_O$):