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.
Numerical simulators for adaptive optics systems have become an essential tool for the research and development
of the future advanced astronomical instruments. However, growing software code of the numerical simulator
makes it difficult to continue to support the code itself. The problem of adequate documentation of the astronomical
software for adaptive optics simulators may complicate the development since the documentation must
contain up-to-date schemes and mathematical descriptions implemented in the software code. Although most
modern programming environments like MATLAB or Octave have in-built documentation abilities, they are
often insufficient for the description of a typical adaptive optics simulator code.
This paper describes a general cross-platform framework for the documentation of scientific software using open-source
tools such as LATEX, mercurial, Doxygen, and Perl. Using the Perl script that translates M-files MATLAB
comments into C-like, one can use Doxygen to generate and update the documentation for the scientific source
code. The documentation generated by this framework contains the current code description with mathematical
formulas, images, and bibliographical references.
A detailed description of the framework components is presented as well as the guidelines for the framework
deployment. Examples of the code documentation for the scripts and functions of a MATLAB-based adaptive
optics simulator are provided.
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.
The wavefront coding is a widely used in the optical systems to compensate aberrations and increase the depth
of field. This paper presents experimental results on application of the wavefront coding paradigm for data
encryption. We use a synthesised diffractive optical element (DOE) to deliberately introduce a phase distortion
during the images registration process to encode the acquired image. In this case, an optical convolution of
the input image with the point spread function (PSF) of the DOE is registered. The encryption is performed
optically, and is therefore is fast and secure. Since the introduced distortion is the same across the image, the
decryption is performed digitally using deconvolution methods. However, due to noise and finite accuracy of a
photosensor, the reconstructed image is degraded but still readable.
The experimental results, which are presented in this paper, indicate that the proposed hybrid optical-digital
system can be implemented as a portable device using inexpensive off-the-shelf components. We present the
results of optical encryption and digital restoration with quantitative estimations of the images quality. Details
of hardware optical implementation of the hybrid optical-digital encryption system are discussed.
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.
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 photosensor's noise was formulated. The influences of light and dark noises as well as
pixelisation factor have been assessed. Analysis of the wavefront sensor's accuracy is provided. Results should
be of interest for further development of cost-effective wavefront sensors.
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.
Linear methods of restoration of input scene's images in optical-digital correlators are described. Relatively low
signal to noise ratio of a camera's photo sensor and extensional PSF's size are special features of considered
optical-digital correlator. RAW-files of real correlation signals obtained by digital photo sensor were used for
input scene's 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 restoration's quality, noise
analysis of boundary areas of the image to be reconstructed was performed. Experimental results on digital
restoration of input scene's images are presented.
The registration of correlation signals with high dynamic range leads to increase of recognition's accuracy and
robustness. Digital photo sensors with common Bayer colour filter array can be used for this purpose. In case
of quasimonochromatic illumination used in optical-digital correlator, it is possible to register correlation signals
with high dynamic range. For signal's registration it can be used not only colour channel, which corresponded
to the wavelength of illumination, but other colour channels too.
In this work the application of the spatially varying pixels exposures technique for obtaining linear high
dynamic range images of correlation signals from digital photo sensors with Bayer mosaic is presented. Bayer
colour filters array is considered as an array of attenuating filters in a quasimonochromatic light. Images are
reconstructed using information from all colour channels and correction coeficients that obtained at the preliminary
calibration step. The registered image of the correlation signal is mapped to the linear high dynamic
range image using a simple and eficient algorithm. Calibration procedure for correction coeficients obtaining is
described. Quantitative estimation of optical-digital correlator's accuracy is provided. Experimental results on
obtaining images of correlation signals with linear high dynamic range are presented.
In optical-digital correlators for pattern recognition, linear registration of correlation signals is significant for
both of recognition reliability and possible input image restoration. This usually achieves with scientific graduated
technical cameras, but most of commercial digital cameras now have an option of RAW data output.
With appropriate software and parameters of processing, it is possible to get linearized image data from photo
camera's RAW file. Application of such photo cameras makes optical-digital systems cheaper, more flexible and
brings along their wider propagation.
For linear registration of correlation signals, open-source Dave Coffins's RAW converter DCRAW was used in
this work. Data from photo camera were linearized by DCRAW converter in "totally RAW documental mode"
with 16-bit output.
Experimental results of comparison between linearized and non-linearized correlation signals and digitally restored
input scene images are presented. It is shown, that applied linearization allows to increase linear dynamic
range for used Canon EOS 400D camera more that 3 times.
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.
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