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Abstract
Beam overlap accuracy in a wavelength beam combination system determines the beam quality and efficiency, so systematic monitoring of overlap accuracy is essential. In this work, a method of performing real-time synchronized monitoring and recording overlap accuracy for a combining beam spot is proposed. Firstly, theoretical calculations for monitoring different wavelength sub-beam positions and angular errors are established. Then, an optical design and grayscale centroid algorithm are developed to analyze and simulate the combination spots. A monitoring device was designed and constructed to meet the requirements of combining system applications, which achieved an accuracy of 8.86 µrad. Finally, the method successfully monitored the system spot fluctuation range within ±22 µrad. This study resolves the issue of distinguishing the different wavelength sub-beams and their response delays in traditional combining beams. It offers precise error data for real-time synchronized calibration of the overlap accuracy in laser beam combining technology.
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1. Introduction
In recent years, wavelength beam combining has evolved as a breakthrough method that enables the combination of multiple laser beams to increase the output power while maintaining beam quality [1–8]. It imposes less stringent requirements on various parameters, such as spectrum, polarization, frequency, and phase for each sub-beam. This approach is structurally stable, reliable, and is widely used in high-energy lasers, laser cladding, and material processing [9–15].
The beam quality and efficiency of wavelength beam combining strongly depend on the precision of the sub-beam overlap, which is mainly reflected by the angular deviations or position deviations of the sub-beams spots [16–20]. When the angular or positional errors are smaller, the precision of sub-beam overlap is enhanced, resulting thus in better performance of the combined laser beam. The angular deviation indicates the non-parallelism of the sub-beam axes, while the position deviation reflects the displacement of the sub-beam spot centers [17]. As the angular deviation is increased, the positional deviation is also increased with the distance of the laser propagation. However, in applications where the laser acts at relatively long distances, the angular deviation is the primary factor, and positional deviation has a minor influence [18,19,21]. To ensure or improve the precision of laser beam combination, it is thus necessary to design suitable monitoring methods or devices that can accurately monitor the angles or positions of the sub-beams within the combined beam and provide real-time data on the precision of the spot overlap.
Currently, some progress has been made in the literature on the development of monitoring methods or devices for the overlap precision (angular or positional) of laser combination beams. Particularly, Shi et al. [22] employed an indirect measurement method by switching the optical path mirror to redirect the He-Ne laser beam into the emission path. Thereby, angle monitoring and alignment of the high-energy laser system were accomplished. Zhou et al. [21] proposed a time-division monitoring method, where a small portion of each sub-laser beam was directed through a focusing lens into the quadrant detector, and a high-precision monitoring device with a 2’’ accuracy was achieved. Recently, Chen et al. [23] utilized an attenuated fraction of the combined laser, by rotating a target wheel, and different wavelength sub-beams were focused onto the position detector. The center positions of each sub-beam were calculated separately, achieving a position monitoring accuracy of 0.1 mm. Nonetheless, these monitoring methods or devices for the combination of laser beams can only monitor individual beams. When multiple overlapping beams enter simultaneously, the spots merge together, making it difficult to resolve the wavelength of each sub-beam and calculate each sun-beam angle or position values by using algorithms. Chen et al. and Zhou et al. added an electrically controlled switching shutter or a filter wheel, forcing the different wavelengths to sequentially enter the detector for identification. Nevertheless, this approach can compromise the accuracy of the monitoring process while increasing the complexities and instability of the system. Additionally, with this method, the position or angular errors of the sub-beams cannot be dynamically monitored in real-time synchronized. A time delay is also introduced and exhibits a slow response speed, which raises challenges for the subsequent dynamic monitoring algorithms. Consequently, it may not be suitable for monitoring high dynamic-response laser systems in real-time.
To solve the limitations of the above-mentioned monitoring methods, this work proposes a new approach for the real-time position or angular monitoring of multi-wavelength laser beam combining spots. The principle and calculation method of the new approach are described. The monitoring device was established and verified by carrying out the monitoring combining beam accuracy experiments, which proved the effectiveness and accuracy of the introduced method. Our analysis and experiment demonstrate that theoretical separation of the different wavelength sub-beams can be achieved, and the real-time synchronized angle or position values of each sub-beam can be obtained. Our work paves the way for improving the ability to monitor the overlap accuracy of combining beams and promoting the development of wavelength beam combinations.
2. Theoretical calculation
The underlying principle of monitoring the combining laser beam spot involves attenuating the combined beam and using a diffraction grating and a focusing optical system to separate and focus the sub-beams of the different wavelengths onto different positions on the image plane of a detector, the basic principle is illustrated in Fig. 1. In addition, by using the algorithm for determining the center position of the laser beam spot, the position information of the sub-beams can be accurately calculated. As a result, a precise determination of the angles or positional values of each sub-beam can be attained, and thus the coincidence accuracy of the combining beam can be determined. In theory, the different wavelengths of the sub-beams and the detector's image plane are sufficiently large. Hence, by designing and producing diffraction gratings, it is possible to achieve an unlimited number of sub-beams focused on the different positions of the detector, obtaining accurate angular or positional values for each sub-beam.
Fig. 1. The schematic diagram of the sub-beams of the combining beam focusing at different positions on the detector surface.
With a fixed incident angle for the combination beam, the grating exhibits different diffraction angles for different wavelengths. The diffraction angles for the various wavelengths can be calculated using the following grating Equation:
where d is the grating period, θmis the diffracting angle of each sub-beam after passing through the grating, θi is the angle at which the combining beam incident on the grating, k is the grating diffraction order, λ is the wavelength of the incident laser.After passing through the grating, the sub-beams of the different wavelengths converge at different positions on the detector surface, with the center of the detector surface serving as the reference point for symmetry. The angular deviation (Δθ) is the interpolated difference between θm and θ-mof any symmetric pair of sub-beams, as well as the focal length f of the optical system and the relationship between the positions of the different wavelength lasers on the detector surface, can be expressed using Eqs. (2) to (4), as follows:
where Δθ represents the angular separation between two adjacent beams at the focal plane, y represents the length of the phase plane, n denotes the number of the sub-beams for different wavelengths in the combining laser, f represents the focal length of the optical focusing system.Depending on the relationship between the camera precision and focal length, the minimum angular deviation for resolution can be calculated as shown in Eq. (5).
where δ is the camera precision, α represents the minimum required angle or position precision for the system.Based on the position or angular information on the detector surface, and using the laser spot center localization algorithm [24,25,26], it is possible to calculate the real-time center position within the corresponding region of the collected spots for the different wavelength sub-beams. Assuming the pixel size of each region image is a × b, where G(x,y) is the intensity of each pixel corresponds to a grayscale value, the calculation of the center position for each sub-beam spot can be derived by Eqs. (6) and (7).
According to the sub-beam spot centroid above-mentioned calculation method, the deviation between the theoretical position and the actual center position of the spot can be calculated as shown in Eqs. (8) and (9).
where xtheoryand ytheoryrepresent the theoretical center positions of the sub-beam spot in the x and y directions, respectively, xactual and yactualdenote the real-time acquired center positions of the sub-beam spot in the x and y directions, respectively, and Δx and Δy represent the positions’ deviation in the x and y directions, respectively.Based on the deviation of the sub-beam spot center on the detector, the angular deviation of each sub-beam can be calculated, as shown in Eqs. (10) and (11).
where δx and δy represent the actual angular deviation of each sub-beam in the x and y directions.From the above-mentioned method, the angles or position values of each sub-beam can be simultaneously monitored and calculated by selecting the corresponding detector. By using Eqs. (1) to (11), it is possible to accurately calculate the grating period (d), system focal length (f), accuracy of the monitoring device, as well as the angular deviation and positional deviation of each sub-beam. From a computational principle, it can be concluded that a longer focal length and a higher detector resolution result in higher monitoring accuracy. Therefore, based on the accuracy requirements of the different laser beam combining systems, suitable gratings and optical focusing systems can be designed, as well as appropriate detectors can be selected to meet the monitoring accuracy requirements. The monitoring method can be used for wider or other bandwidth combining beam accuracy monitoring. The practical application of this method is limited by primary factors that the manufacturing capability of gratings, wavelength response range and size of the phase plane of detectors (Please refer to Supplement 1).
3. Experimental design
To verify the feasibility and practicality of the proposed new method, a specific monitoring device was designed and constructed for the detection and measurement of the sub-beam spot combining accuracy in the existing 4-channel wavelength beam combining system. The specific experimental design and procedure are illustrated in Fig. 2.
3.1 Requirements for the monitoring device
For a long-distance application, systematic monitoring of the laser combining angle accuracy is sufficient to ensure the precision of beam overlap in the system. The wavelength combination system combines four sub-beams with wavelengths of 1060 nm, 1070 nm, 1080 nm, and 1090 nm to combine a single laser output. The specific technical parameters for monitoring the combined beam are presented in Table 1.
Table 1. Technical specifications of the monitoring device
3.2 Detector selection
Based on the theoretical calculations, the minimum resolution capability of the photodetector to some extent determines the performance of the system. A CMOS camera with a high cost-performance ratio, small size, and high frame rate was chosen as the photodetector to meet the demands of high-speed random jitter laser monitoring. The detector parameters are listed in Table 2.
Table 2. Parameters of the CMOS camera
According to Eqs. (1), (2), and (4), along with the system’s angle monitoring requirements, the focal length range can be calculated as follows:230 mm ≤ f ≤ 394.4034 mm.
3.3 Optical optimization design and theoretical calculations
Based on the above-mentioned calculated results, the Zemax optical design software was used to optimize the design of the monitoring optical system. More specifically, positive lenses, negative lenses, and suitable materials were adopted to eliminate chromatic aberration and prevent the reduction of the spot accuracy and size formed by the different wavelength sub-beams on the detector. The overall optical design is shown in Fig. 3, which consists of a transmission grating, optical focusing lens group, and detector phase. Its effective aperture was Φ30 mm, and the focal length was 390 mm. According to Eq. (5), the monitoring angular accuracy α=8.85 µrad was calculated, which was less than the required system combining beam accuracy of 15 µrad, meeting the monitoring requirements. A commercially available 300 lines/mm grating was adopted to validate the principles and methods, and hence the selection of an existing device.
According to the spot diagrams of the optical design results presented in Fig. 4, the Airy spot radius of the sub-beam laser with four different wavelengths can be obtained as 16.79 µm. The RMS radii of the four sub-beam design results are 6.094 µm, 1.146 µm, 1.172 µm, and 6.3 µm, all of which are significantly smaller than the Airy spot radius. This result demonstrates that the imaging quality of the sub-beam systems is excellent for the different wavelengths, and the chromatic aberration correction effect is also very good. According to the optical design results, the positions of each sub-beam on the detection phase plane and the relative positions between every two adjacent sub-beams can be also calculated, as shown in Fig. 5(a). The center in the corresponding region of each sub-beam spot can be calculated by using Eqs. (6) to (9), as displayed in Fig. 5(b).
Fig. 5. Based on the optical design theory, calculate the center positions of the spots in the corresponding region of each sub-beam. (a) Optical design results—positions of each sub-beam on the phase plane. (b) Calculation of the center position of the spots in the corresponding region of each sub-beam based on the grayscale centroid method.
3.4 Monitoring device
According to the above-mentioned design method, the design of the monitoring device was accomplished. Figure 6 depicts the actual monitoring device, which has dimensions of 210 mm✕86 mm✕85 mm. It features a compact size, stability, reliability, and easy integration. In the structural design, special treatments were applied to the interior of the barrel to eliminate stray light effects. Additionally, optimization design was performed on the overall structure to reduce the vibration effects. As these two aspects are not the focus of this work, they will not be analyzed in detail here.
Due to installation and adjustment errors, a certain deviation exists between the actual focal length and the theoretical focal length. Therefore, a collimator was used to measure the focal length of the monitoring device, which was 389.34 mm. Based on the measured focal length, the actual precision of the monitoring device was 8.86 µrad, meeting the requirements for system monitoring precision.
3.5 Application examples
An experiment on the overlap accuracy of combining spots was designed and accomplished, to detect the combining accuracy of the laser beam combining system using the designed monitoring device and algorithm, consisting of a laser beam combining system, high reflective mirror, attenuator and angle monitoring device, as shown in Fig. 7. Besides, the high reflection mirror has no exhibit thermal effects, it does not affect the shape of the beam spot and the accuracy of the monitoring device (Please refer to the Supplement 1). The design and selection of the reflectivity and transmittance of the optical components in the attenuation module are determined by the maximum energy that can be received by the detector of the monitoring device.
Figure 8 displays that the actual centroid positions of each sub-beam in their respective regions were calculated by utilizing the monitoring device to capture a single frame image. There is a certain error between the actual and theoretical collected spots, mainly due to the fact that circular spots transform into elliptical beams after passing through the grating, and the thermal effects cause deformation in the beams. However, the center position of the concentrated energy in the spot was not changed. By performing image threshold segmentation, binarization, and filtering, the central position within the corresponding region of each sub-beam spot was calculated. By calculating the difference between the actual spot position and the theoretical spot position from Fig. 5, the angular error can be calculated based on Eqs. (10) and (11).
Fig. 8. The captured single-frame images and the centroid positions of the spots (please refer to Supplement 1 for the original images taken with the monitoring device).
A total of 20 frames of spot images were captured over a duration of 0.5 s by employing the monitoring device (See Visualization 1 for the video captured in real time by the monitoring device). Each frame of the image undergoes the same processing, as shown in Fig. 8. By utilizing Eqs. (8) to (11), the curves depicting the changes in the centroid positions of the spot within the respective regions of each sub-beam, as well as the corresponding angle deviation changes, were calculated. These curves are illustrated in Figs. 9 to 12.
Fig. 9. Deviation of the 1060 nm sub-beam from the theoretical position and the corresponding angle error value in the x and y directions.
Fig. 10. Deviation of the 1070 nm sub-beam from the theoretical position and the corresponding angle error value in the x and y directions.
Fig. 11. Deviation of the 1080 nm sub-beam from theoretical position and the corresponding angle error value in the x and y directions.
Fig. 12. Deviation of the 1090 nm sub-beam from the theoretical position and the corresponding angle error value in the x and y directions.
The results corresponding to the left side of Figs. 9 to 12 indicate that the positions of the centroid of each sub-beam spot fluctuate within a range of ±22 px in the x direction, which corresponds to a fluctuation range of ±22 µrad in angle. The results corresponding to the right side of Figs. 9 to 12 indicate that the positions of the centroids of each sub-beam spot fluctuate within a range of ±22 px in the y direction, which corresponds to a fluctuation range of 22 µrad in angle. Based on the above-mentioned observations, it can be concluded that the co-alignment accuracy of the laser beam combining system fluctuates within a range of ±22 µrad in real-time, indicating poor beam pointing stability. To address this issue, it is recommended to incorporate real-time monitoring of dynamic angle errors and utilize fast steering mirrors to control the dynamic changes of the beam spots, ensuring thus beam pointing stability.
In addition, real-time monitoring of the combining beam spot and the monitoring device was further emphasized. Data acquisition was conducted separately using both the monitoring device and the CMOS camera for a duration of 10 seconds (Please refer to the Supplement 1, Visualization 1, and Visualization 2).
4. Conclusion
A laser combining spot overlap accuracy monitoring method was proposed in this work, which enabled real-time syn onized monitoring of the angles or positions of the different wavelength sub-beam spots or their relative positions. By elaborating on the theoretical calculations of the monitoring method and integrating research in optics, structure, and algorithms, a monitoring device suitable for high-energy laser spot overlap accuracy was designed. The actual accuracy of the monitoring device was better than 8.86 µrad, successfully detecting fluctuations in the overlap accuracy of the combining beam within ±22 µrad, thus verifying the reliability and practicality of the developed calculation method. The detailed conclusions included the following aspects:
1. Using the calculation method, it is possible to design a monitoring device with increased accuracy that meets the actual monitoring requirements. The device was characterized by its reliability, small size, and ease of integration.
2. Real-time synchronized calculation of the angle or position values was enabled to ensure high-precision monitoring. This method breaks through the limitations of traditional approaches in distinguishing post-combination sub-beam wavelengths and monitoring response delays.
3. Our work provides a high-precision error basis for real-time dynamic calibration of fast mirrors and offers a new method for the development of laser beam combining technology.
Funding
National Natural Science Foundation of China (62275196, 62061136008, 62192772, 62305251, 61925504, 61975153, 6201101335, 62020106009, 62192770, 61621001); Science and Technology Commission of Shanghai Municipality (17JC1400800, 20JC1414600, 21JC1406100); Major Projects of Special Development Funds in Zhangjiang National Independent Innovation Demonstration Zone, Shanghai ( ZJ2021-ZD-008);Shanghai Municipal Science and Technology Major Project (2021SHZDZX0100); Fundamental Research Funds for the Central Universities; National Key Research and Development Program of China (2022YFA1603403).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper arenot publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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