1. Introduction

At present, hardware complexes based on the transmission of a laser beam through the Earth's atmosphere are being used more and more in the world [1]. Such complexes include: systems for recharging batteries of drones [2] and low-orbit satellites [3], for the destruction of space debris in low orbits [4], for the creation of crypto-protected communication channels [5], for free-space optical communication [6], etc. The laser beam used in such applications is affected by turbulent airflows as it passes through the atmosphere. In the turbulent flow, the local refractive index changes, which cause distortions of the wavefront of the laser beam. These distortions reduce the quality of the laser beam which leads to a decrease in the performance of the optical systems. Moreover, the decrease in productivity directly depends on the strength of the atmospheric turbulence, i.e. on the current state of the atmosphere.

To reduce the effect of turbulence it is proposed to use an adaptive optical system (AOS) to correct for the wavefront of the laser beam. To ensure quality correction the system must have appropriate bandwidth and spatial resolution.

As shown in [7], the spectrum of atmospheric oscillations rarely exceeds 150 Hz; therefore, the rate of discrete AOS should be at least 1000 - 1500 Hz (fps - frames per second) [8]. The system implemented on the conventional PC cannot provide stable operation at frequencies of 1 kHz and higher. One of the possible ways to solve this problem is to use the FPGA as the main control element of the entire closed loop adaptive optical system.

To compensate for the higher-order aberrations in the wavefront distorted by atmospheric turbulence, a stacked-actuator mirror with a sufficiently high spatial resolution need to be used. Moreover, the frequency of the first resonance of the stacked-actuator mirror is high enough (10 kHz and more), and thus allows it to be used in fast AOS.

2. Fast AOS implementation

There are several known FPGA-based adaptive optical system implementations (see for example [9,10]). In our experiments we used the modified traditional adaptive optical system [8]. The modification involves the use of the FPGA as a main AOS control element instead of a standard PC (Fig. 1).

 

Fig. 1. Test setup for FPGA-based adaptive optical system.

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A laser beam, the wavefront of which is distorted by the turbulence, hits the stacked-actuator deformable mirror and goes to a receiver. A part of the laser beam is reflected to the wavefront sensor (WFS – in our case Shack-Hartmann type) using a beam splitter (for the low-power beams) or a “blind” mirror (for the high-power beams). The radiation of a fiber-coupled diode laser with a wavelength of 650 nm was used in the experiments. Video information from the WFS enters the FPGA which processes this information and calculates the voltage vector. These voltages are applied to the mirror actuators to correct for wavefront distortions. The computer in this configuration sets the operation modes of the FPGA and monitors the correction process. In this setup, FPGA calculates the focal spots coordinates by the centroid method. To calculate the set of voltages, FPGA implements the phase conjugation algorithm, which is one of the fastest [11].

The main tasks to be solved by FPGA are (Fig. 2):

 

Fig. 2. FPGA functional structure.

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Compared to PC, FPGA allows faster calculations due to their implementation in hardware and through parallelization of computing processes. In addition, the FPGA has the low-level access to the WFS camera and mirror CU which allows to optimize the wavefront correction cycle. Usually in high-speed adaptive optical systems (1 kHz and faster) the frequency of the camera should be approximately twice the frequency of the AOS.

Our setup included a Shack-Hartmann sensor, the speed of which is determined by the camera. Here we used a fast camera JetCam-19 from Kaya Instruments [12], which at a resolution of 480 × 480 pixels provides a speed of 4000 frames per second. Image bytes are transferred to the frame grabber via 40 Gbps fiber interface. The spectral sensitivity range of this camera is from 350 nm to 1100 nm, which determines the operating wave range of the entire system.

Among several similar cameras, the JetCam-19 was preferred since it comes with a frame grabber containing an FPGA Arria V GZ. Thus, all the electrical circuits matching the camera and FPGA were already implemented. To create a closed-loop system it is necessary to reprogram the FPGA and provide additional I/O interfaces for communication with the mirror CU and PC. During the operation, the FPGA uses preloaded coordinates of the reference wavefront and the response function of the deformable mirror. UDP Interfaces for CU and PC were implemented through the corresponding SFP (small form-factor pluggable) expansion modules that were available on the frame grabber.

In addition to fast computational algorithms, the implementation of AOS based on FPGA allows optimization of the sequence of calculations. Unlike some other FPGA-based AOS implementations [10], in this setup, the FPGA performs all computational procedures simultaneously with the reception of image bytes from the WFS camera. FPGA allows to use the low-level connection to the WFS camera interface and makes it possible to work with individual image pixels right after their arrival to the frame-grabber, i.e. in the real-time. Receiving a part of the image containing the first row of the focal spots, it is possible to calculate their coordinates and, hence, fill the corresponding elements of the matrix designed to calculate the voltage array. Thus, immediately after receiving the entire image, the set of control voltages could be calculated. The total time of one cycle is about 0.65 ms, which corresponds to a frequency of 1500 Hz (fps) (Fig. 3). The exposure time in the experiments was short, 2 μs. With this parameter, the latency is approximately equal to the period of the system.

 

Fig. 3. Timing diagram of one cycle of FPGA-based closed system (not to scale).

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In our experiment, the stacked-actuator deformable mirror SADM-50-45 (produced by AKAoptics SAS) was used to correct for wavefront distortions. The diameter of this mirror was 50 mm, the number of actuators - 45. The photo and actuators configuration of the mirror is shown in Fig. 4. The maximal stroke of each actuator was +/- 3.5 µm [13].

 

Fig. 4. Stacked-actuator deformable mirror SADM-50-45.

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For independent verification of the correction quality, the setup (Fig. 1) contained a far-field intensity analyzer formed by a long-focus lens (f = 1 m) and a Gig-E camera DMK23GM021 [14] with a small pixel size (3.75 µm). The small pixel size was chosen for a more detailed examination of the intensity distribution focal spot, produced by the long-focus lens. For the laser beam diameter of 50 mm and wavelength 650 nm, the diffraction-limited focal spot size was expected to be 31.72 μm or 8.46 pixels.

There was no tilt correction provided in these experiments. It was assumed that there should be a separate system for the tip-tilt correction.

3. AOS testing

AOS testing was carried out on the setup presented in Fig. 1. A fan heater was used as a source of turbulence. The fan flow was directed perpendicular to the laser beam. In the experiments, the coordinates of the displacements of the WFS microlens array focal spots were recorded in the real-time. After that, the so-called ‘energy spectrum’ was calculated from the dynamics of one focal spot jitter. The spectral energy, in this case, is a frequency integral of the Fourier transform taken over the ensemble of coordinate shifts (Δx or Δy) of the focal spot in time. А sample of 10 seconds was used. From a statistical point of view, all focal spots at Shack-Hartmann wavefront sensor picture are approximately the same (excluding edges, where the effects of vignetting of the laser beam distort the spots dynamic behavior). This allows to use a single focal spot of the microlens array for the calculation of the energy spectrum. The amplitude of displacements of the focal spot directly depends on the intensity of turbulence (the higher the intensity of turbulence, the greater the amplitude of jitter of the focal point). Therefore, by analyzing the jitter of the spot, it is possible to conclude about the frequency spectrum of turbulent phase fluctuations.

The spectral energy of the focal spot jitter is shown in Fig. 5. The thick blue line corresponds to pure turbulence aberrations without any correction. From an examination of the figure it can be seen that the curve goes into saturation at the frequency of approximately 100 Hz. Because it is an integral of the input value (Fourier transform), we can say that frequencies above 100 Hz practically do not contribute to the composition of the turbulence. Processing the array of experimental values shows that about 99% of all turbulence energy is concentrated in the range up to 100 Hz.

 

Fig. 5. The spectral energy of Shack-Hartmann wavefront sensor focal spot jitter.

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After the start of the correction process we measured such an energy spectrum for different frequencies of AOS - from 10 fps to 1875 fps. Graphs in Fig. 5 presents the results of energy spectrum after introducing the correction process with various speed. This Figure shows that starting from the AOS speed of 300 fps we could efficiently compensate for wavefront distortions. It means that our AOS has some frequency reserve to correct for stronger turbulence.

Simultaneously with the measurements of the micro lens focal spot jitter, the intensity distribution in the far field of the laser beam was monitored. Figure 6 shows examples of images in the far field without wavefront correction (a) and when performing the wavefront correction (b).

 

Fig. 6. Far-field intensity distribution before (a) and after (b) correction.

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The part (a) of Fig. 6 shows several ‘frozen’ snapshots of intensity distribution in the far field without wavefront correction (Strehl < 0.1). Since the wavefront distortions change over time the shape of the far-field focal spot also varies. The intensity of the far-field focal spot without correction is lower, hence for clarity the images in Fig. 6 (a) are given at a larger camera exposure in contrast with corrected case (Fig. 6 (b)).

The focal spot shape after the wavefront correction is shown on the part (b) of this figure. The rightmost figure shows the same intensity distribution in the far zone on a larger scale. Experiments have shown that when correcting the wavefront of laser radiation with a sufficient frequency the focal spot practically stayed unchanged, was very stable. The focal spot size after correction was approximately 9 pixels which indicates that the AOS compensated the wavefront distortions almost to the diffraction limit (Strehl > 0.7).

4. Conclusion

The fast adaptive optical system was considered, which can correct for the wavefront of the laser radiation with a frequency of up to 1850 fps. Consideration of the Shack-Hartmann focal spot jitter energy spectrum graph allows to conclude that about 99% of all fluctuation energy lies within 100 Hz. It is shown that the use of wavefront correction improved the distribution of the laser beam intensity in the far-field rather close to diffraction limit. AOS operation at the frequencies below the turbulence spectrum upper frequency leads to a deterioration in the quality of the wavefront correction.