Application Cases

Experiment Title: SPGD Beam Shaping Experimental System

Testing Purpose:The purpose of this experiment is to achieve laser beam focusing and shaping, thereby increasing the energy concentration of the focal spot. By utilizing the SPGD (Stochastic Parallel Gradient Descent) algorithm to control the deformable mirror, the experiment aims to correct wavefront aberrations introduced by factors such as poor beam quality of the laser itself and manufacturing and alignment errors of the optical system. This process optimizes the beam wavefront, improves the phase distribution of the laser, and obtains a beam that meets the requirements of practical applications.

Testing Equipment:High Voltage Amplifier, Laser, Attenuator, Beam Expander, Polarizing Beam Splitter, etc.

Experiment Process:

Figure 1: Schematic Diagram of the Laser Beam Shaping Experimental System

The principle of the SPGD beam shaping experimental system is shown in Figure 1, which mainly includes a laser, attenuator, beam expander, polarizing beam splitter, quarter-wave plate, MMDM (Multi-Actuator Deformable Mirror), imaging system, CCD camera, control computer, digital-to-analog converter, and high voltage amplifier. The attenuator serves a protective function, preventing the CCD from being damaged by the high energy of the collected spot. The beam expander is used to increase the spot size of the laser beam to match the aperture of the MMDM. The polarizing beam splitter and quarter-wave plate form an optical isolator, used in conjunction with the vertically reflected beam from the MMDM. The imaging system (i.e., lens) focuses the shaped beam. The control computer includes an image acquisition module and an SPGD program module.

Before the experiment, the experimental platform needs to be set up. First, adjust the laser beam to be horizontal. This is done by positioning the laser at a certain height and placing a pinhole near the emitted laser beam. Adjust the position and height of the pinhole so that the beam can just pass through it. Then, gradually move the pinhole away while observing the position changes of the spot, and adjust the tilt angle of the laser until the beam can always pass through the pinhole during the movement. Next, adjust the beam expander, polarizing beam splitter, MMDM, quarter-wave plate, imaging system, and CCD camera in sequence to ensure that all parts of the optical path are coaxial and that the beams reaching the MMDM and CCD are incident perpendicularly.

During the experiment, the laser beam first passes through the beam expander to match the aperture of the MMDM, then reaches the MMDM for wavefront phase modulation via the polarizing beam splitter and quarter-wave plate. After being vertically reflected, the beam is focused through the imaging system and reaches the CCD camera. The CCD captures the spot image and transmits it to the control computer to calculate the system's performance evaluation function. Based on this, the SPGD iterative formula is used to obtain the control signal for the MMDM in the next control loop. This signal is output in parallel by two 40-channel digital-to-analog converters, amplified by the high voltage amplifier, and then applied to the MMDM. Additionally, the CCD camera can display the collected laser spot in real-time on the computer, intuitively showing the changes in light intensity.

Experimental Results:

Figure 2: Curve of Performance Evaluation Function vs. Iteration Count

During the experiment, the threshold of the CCD image acquisition is set to approximately eliminate the influence of background noise, specifically set at a grayscale value of 5. The CCD camera has a resolution of 1024×1024 pixels, but a large area of the collected image is without a spot. Therefore, only a 200×200 pixel region near the spot is extracted during processing. For the selected performance evaluation functions, the convergence speed, convergence accuracy, and stability during the shaping process are comprehensively considered to select the parameter combination with the best shaping effect. Each group of experiments was performed with 1000 algorithm iterations, resulting in the curves of J1, J2, and J3 vs. iteration count as shown in Figure 2. It can be seen from the figure that there are differences in the convergence speed and stability of the three performance evaluation functions during the shaping process. J1 has an initial value of 47 and converges rapidly in the first 30 iterations but then experiences significant oscillations, resulting in poor stability, with the spot radius eventually stabilizing around 23. J2 has an initial value of 0.1277 and tends to converge after 260 iterations, with a relatively slow convergence speed and some jitter, converging to a value of 0.7339. J3 has an initial value of 0.2005, converges quickly in the first 140 iterations, and gradually stabilizes after 260 iterations with minimal jitter, converging to a value of 0.8640.

Figure 3: Laser Spot and Intensity Distribution Before and After Shaping

As shown in Figure 3, the initial spot before shaping and the spots after 1000 iterations of the algorithm under the three performance evaluation functions, along with their corresponding intensity distributions, are presented. It can be seen from the figure that when J1, J2, and J3 are used as performance evaluation functions, the MMDM has a significant correction effect on wavefront distortion, and the energy concentration of the focal spot is greatly improved, resulting in a noticeable improvement in beam quality. However, there are significant differences in the shaping results under different performance evaluation functions.

Based on the comparative analysis of the results, J1, as a performance evaluation function, has the advantage of fast convergence speed. However, due to its integer-only nature, it is prone to significant fluctuations and poor convergence stability. Additionally, the spot radius is not directly related to its intensity distribution. Given the limited shaping capability of the MMDM, the degree of spot reduction is limited, and the intensity changes during the optimization process are difficult to determine, affecting the shaping effect. J2, as a performance evaluation function, is directly related to the intensity distribution. However, the centroid position is independent of intensity, and weaker intensity parts can significantly affect the centroid position, thereby severely impacting the algorithm's optimization path and slowing down the convergence speed. J3, as a performance evaluation function, appropriately reflects the energy concentration of the focal spot, with faster convergence speed and better shaping effect and stability. Therefore, in the application of laser beam focusing and shaping based on the SPGD algorithm, J3 is the most suitable among the three performance indicators.

High Voltage Amplifier Recommendation: ATA-7050

Figure: Specifications of the ATA-7050 High Voltage Amplifier

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