Results and Discussions A simulation is used to validate the performance of the project-constraint decoupling method for the aberration correction, coupling error elimination, stability, and computation complexity. It can compensate the aberration better than the traditional method to decoupling method for the wave front sensor-free system (Fig. 2). Additionally, it can effectively eliminate the decoupling error between the Woofer and the Tweeter (Fig. 3), as the aberration is broken down into low order Zernike modes and high order modes before being corrected by the Woofer and Tweeter. During the decoupling operation, it is more stable than the conventional approach, and the advancements have improved its performance in the control process. Finally, the decoupling method suggests in the research has a lower computational complexity than the conventional method (Fig. 4). An experimental system was built to evaluate the effectiveness of the method. The experiment demonstrates that the decoupling algorithm can effectively compensate for phase distortions (Fig. 6 and Fig. 7) and significantly suppress the coupling error between the dual deformable mirrors and decompose the aberration accurately (Fig. 8).

Dual deformable mirrors are often used to create wave front-sensor-free adaptive optics systems that can be used to correct aberrations with broad strokes and high spatial frequencies. The Woofer, which has big amplitude and is used to correct low order aberrations, and the Tweeter, which has a high spatial resolution and is used to correct high order aberrations, are two examples of dual deformable mirrors. However, without the decoupling process, it is difficult to avoid the coupling error, which would cause the deformable mirrors to generate an opposite surface shape and waste the ability of aberration correction in the dual deformable mirror adaptive optics system. To solve this problem and make the Woofer and Tweeter could work efficiently together; a decoupling method must be developed. Even the decoupling algorithms are the subject of considerable study, most of them focus on dual deformable mirror adaptive optics systems with wave front sensors. These techniques frequently employ the data from the wave front sensor to aid in decoupling. A few decoupling methods are used for the wave front sensor-free adaptive optics system, and their performances are usually not satisfactory for the engineering project. To improve the performance in the aberration correction, coupling error reduction, stability, and computation complexity for the wave front sensor-free adaptive optics system, a new decoupling technique must be developed. This might lead to further applications for the adaptive optics technology in things like large-scale telescopes, vision equipment, and laser beam cleanup.

To make the dual deformable mirrors in the system work together to correct the aberration, a straightforward but effective decoupling method based on the mode project-constraint is proposed. The Woofer is controlled by a low order Zernike mode coefficient to avoid correcting the high order modes, and the Tweeter is constrained by the project-constraint method to eliminate the low order modes in its corrections. Obtaining the related matrix of the mode coefficients to the Woofer control signal is essential to the decoupling control process. It can be obtained through the Woofer’s influence functions and the low order Zernike modes which will be corrected by the Woofer. The project-constraint, which requires the following processes, can also limit the use of low order modes in the Tweeter. To start, a relationship matrix between the Zernike mode coefficients and the Tweeter’s control signals needs to be produced. Then, the component of the signals in the Tweeter-induced coupling error can be solved by the relation matrix. Finally, by subtracting the component-induced coupling error from the initial Tweeter control signals, the signals free of coupling error can be obtained. These techniques result in the realization of the Woofer and Tweeter’s decoupling.

In this paper, a simple and effective method was proposed based on project-constraint to restrict the coupling error and eliminate the aberration in a wave front sensor less adaptive optics system with a dual deformable mirror. This method can outperform the conventional method in terms of aberration correction, coupling error elimination, stability, and processing complexity. It can be used to make the Woofer and Tweeter cooperate efficiently to correct the aberration by Zernike mode decomposition. Then the low order Zernike modes of the aberration can be compensated by the Woofer, and the other Zernike modes of the aberration can be corrected by the Tweeter.