Mikhail V. Konnik

Input scene restoration in pattern recognition correlator based on digital photo camera

Diffraction image correlator based on commercial digital SLR photo camera was reported earlier. The correlator was proposed for recognition of external scenes illuminated by quasimonochromatic spatially incoherent light. The correlator hardware consists of digital camera with plugged in optical correlation filter unit and control computer. The kinoform used as correlation filter is placed in a free space of the SLR camera body between the interchangeable camera lens and the swing mirror. On the other hand, this correlator can be considered as a hybrid optical-digital imaging system with wavefront coding. It allows not only to recognize objects in input scene but to restore, if needed, the whole image of input scene from correlation signals distribution registered by SLR camera sensor. Linear methods for image reconstruction in the correlator are discussed. The experimental setup of the correlator and experimental results on images recognition and input scenes restoration are presented.

On application of constrained receding horizon control in astronomical adaptive optics

Control system design for adaptive optics is becoming more complex and sophisticated with increasing demands on the compensation of atmospheric turbulence. Contemporary controllers used in adaptive optics systems are optimised in the sense of a cost function (linear quadratic regulators) or to a worst case scenario (robust H∞ controllers). Prediction, to some extent, can be incorporated into the controllers using the Kalman filter and a model of the atmospheric turbulence. Despite the growing number of publications on adaptive optics control systems, only the unconstrained case is usually considered. Accounting for the physical constraints of the adaptive optics system components, such as limited actuator stroke, still represents a problem. As a possible solution, one can consider constrained receding horizon control (RHC), also known as Model Predictive Control (MPC). The ability of RHC to handle constraints and make predictions of the future control signals makes it attractive for application in astronomical adaptive optics. The main potential difficulty with the application of RHC is its heavy computational load. This paper presents preliminary results on numerical simulations of an adaptive optics system controlled by constrained RHC. In particular, the case of output disturbance rejection is considered. The results of numerical simulations are provided. Finally, methods for improving the computational performance of constrained receding horizon controllers in adaptive optics are also discussed.

On numerical simulation of high-speed CCD/CMOS-based wavefront sensors in adaptive optics

Wavefront sensors, which use solid-state CCD or CMOS photosensors, are sources of errors in adaptive optic systems. Inaccuracy in the detection of wavefront distortions introduces considerable errors into wavefront reconstruction and leads to overall performance degradation of the adaptive optics system. The accuracy of wavefront sensors is significantly affected by photosensor noise. Thus, it is crucial to formulate high-level photosensor models that enable adaptive optic engineers to simulate realistic effects of noise from wavefront sensors. However, the complexity of solid-state photosensors and multiple noise sources makes it difficult to formulate an adequate model of the photosensor. Moreover, the characterisation of the simulated sensor and comparison with real hardware is often incomplete due to lack of comprehensive standards and guidelines. Owe to these difficulties, engineers work with oversimplified models of the wavefront sensors and consequently have imprecise numerical simulation results. The paper presents an approach for the modelling of noise sources for CCD and CMOS sensors that are used for wavefront sensing in adaptive optics. Both dark and light noise such as fixed pattern noise, photon shot noise, and read noises, as well as, charge-to-voltage noises are described. Procedures for characterisation of both light and dark noises of the simulated photosensors are provided. Numerical simulation results of a photosensor for a high-frame rate Shack-Hartmann wavefront sensor are presented.

Feasibility of constrained receding horizon control implementation in adaptive optics

Adaptive optics (AO) provide real-time compensation for atmospheric turbulence to improve the resolution of images acquired by ground-based optical telescopes. The actuators in deformable mirrors, which are used as correctors, are constrained by a maximal allowable movement. The control techniques used in current AO systems do not account for these constraints, leading to inferior performance and a risk of damage of the deformable mirrors surface. This paper presents a feasibility study for receding horizon control (RHC) with online constrained quadratic programming (QP). The results of numerical simulations provided in this paper are based on realistic models obtained from an optical test-bench. We compare QP algorithms that represent three main methods for convex optimization: 1) interior point; 2) active set (AS); and 3) gradient-based algorithms. It is shown that constrained RHC is computationally feasible for moderate-size AO systems using hot-started structure-exploiting AS QP solvers with bound constraints. An evaluation of performance indicates that RHC is advantageous in terms of atmospheric turbulence rejection in the case of active constraints.

Linear methods for input scenes restoration from signals of optical-digital pattern recognition correlator

Linear methods of restoration of input scenes images in optical-digital correlators are described. Relatively low signal to noise ratio of a cameras photo sensor and extensional PSFs size are special features of considered optical-digital correlator. RAW-files of real correlation signals obtained by digital photo sensor were used for input scenes images restoration. It is shown that modified evolution method, which employs regularization by Tikhonov, is better among linear deconvolution methods. As a regularization term, an inverse signal to noise ratio as a function of spatial frequencies was used. For additional improvement of restorations quality, noise analysis of boundary areas of the image to be reconstructed was performed. Experimental results on digital restoration of input scenes images are presented.

Waffle mode mitigation in adaptive optics systems: A constrained Receding Horizon Control approach

The wavefront sensors that are used in adaptive optics to sense the atmospheric turbulence have blind modes. One of those unseen modes, a waffle mode, occurs as a wavefront perturbation that produce a null or very small measurement on the wavefront sensor. In this paper we discuss a way of waffle mode mitigation by setting additional constraints in the Receding Horizon Control. The results on numerical simulations are presented. The increase in the computational load with the values of constraints is estimated. Output disturbance rejection performance for the constrained case is evaluated. Our numerical simulations suggest that the constrained receding horizon controller is feasible with present day computational capabilities for small and medium-sized adaptive optics systems.

Influence of photosensor noise on accuracy of cost-effective Shack-Hartmann wavefront sensors

A Shack-Hartmann (SH) wavefront sensor (WFS) is used in most modern adaptive optics systems where precision and robustness of centroiding are important issues. The accuracy of the SH WFS depends not only on lenslet quality but also on the measurement accuracy of centroids, especially in low-light conditions. In turn, accuracy depends on light and dark noises that are inevitably present in solid-state photosensors. Using a comprehensive mathematical model of the CMOS photosensor, the accuracy of the Shack-Hartmann wavefront sensor is assessed and analysed for each type of noise. In this paper, new results regarding the influence of different noise sources from a CMOS photosensor on centroiding in Shack-Hartmann wavefront sensors are presented. For the numerical simulations, a comprehensive mathematical model of photosensors noise was formulated. The influences of light and dark noises as well as pixelisation factor have been assessed. Analysis of the wavefront sensors accuracy is provided. Results should be of interest for further development of cost-effective wavefront sensors.

Hot-start efficiency of quadratic programming algorithms for fast model predictive control: A comparison via an adaptive optics case study

Model Predictive Control (MPC) with fast sampling rates can be extremely demanding in terms of the required computational time. However, the control problem in some cases does not change much from one sampling instance to the next, and therefore hot-start can be used to considerably accelerate the solution of an online optimisation problem. An adaptive optics system is used in this work as an example of such a control system to evaluate the benefits of hot-start for different families of optimisation algorithms. A comparison of the computational times and a discussion of hot-start efficiency for Interior Point, Active Set, Gradient-based and Augmented Lagrangian algorithms are provided in this contribution.

Preliminary evaluation and comparison of atmospheric turbulence rejection performance for infinite and receding horizon control in adaptive optics systems

Model-based optimal control such as Linear Quadratic Gaussian (LQG) control has been attracting considerable attention for adaptive optics systems. The ability of LQG to handle the complex dynamics of deformable mirrors and its relatively simple implementation makes LQG attractive for large adaptive optics systems. However, LQG has its own share of drawbacks, such as suboptimal handling of constraints on actuators movements and possible numerical problems in case of fast sampling rate discretization of the corresponding matrices. Unlike LQG, the Receding Horizon Control (RHC) technique provides control signals for a deformable mirror that are optimal within the prescribed constraints. This is achieved by reformulating the control problem as an online optimization problem that is solved at each sampling instance. In the unconstrained case, RHC produces the same control signals as LQG. However, when the control signals reach the constraints of actuator’s allowable movement in a deformable mirror, RHC finds the control signals that are optimal within those constraints, rather than just clipping the unconstrained optimum as commonly done in LQG control. The article discusses the consequences of high-gain LQG control operation in the case when the constraints on the actuator’s movement are reached. It is shown that clipping / saturating the control signals is not only suboptimal, but may be hazardous for the surface of a deformable mirror. The results of numerical simulations indicate that high-gain LQG control can lead to abrupt changes and spikes in the control signal when saturation occurs. The article further discusses a possible link between high-gain LQG and the waffle mode in the closed-loop operation of astronomical adaptive optics systems. Performance evaluation of Receding Horizon Control in terms of atmospheric disturbance rejection and a comparison with Linear Quadratic Gaussian control are performed. The results of the numerical simulations suggest that the disturbance rejection performance in the unconstrained case is the same for LQG and RHC, while RHC clearly outperforms the saturated LQG control in terms of atmospheric turbulence rejection. More importantly, RHC can be used in high-gain mode, unlike LQG, providing better atmospheric disturbance rejection in the constrained case.

Using wavefront coding technique as an optical encryption system: reliability analysis and vulnerabilities assessment

Wavefront coding paradigm can be used not only for compensation of aberrations and depth-of-field improvement but also for an optical encryption. An optical convolution of the image with the PSF occurs when a diffractive optical element (DOE) with a known point spread function (PSF) is placed in the optical path. In this case, an optically encoded image is registered instead of the true image. Decoding of the registered image can be performed using standard digital deconvolution methods. In such class of optical-digital systems, the PSF of the DOE is used as an encryption key. Therefore, a reliability and cryptographic resistance of such an encryption method depends on the size and complexity of the PSF used for optical encoding. This paper gives a preliminary analysis on reliability and possible vulnerabilities of such an encryption method. Experimental results on brute-force attack on the optically encrypted images are presented. Reliability estimation of optical coding based on wavefront coding paradigm is evaluated. An analysis of possible vulnerabilities is provided.