| dc.description.abstract | Atmospheric turbulence limits the quality of imaging in ground-based astronomical telescopes (Hart; 2010). To obtain diffraction-limited imaging, there is a need for a technology that removes the effects of atmospheric distortions. Adaptive optics is such a technology (Hardy; 1998). The motivation for the thesis problem comes from the working principle and realization of a Shack Hartmann Wavefront Sensor (SHWS), which is widely used in astronomical adaptive optical imaging systems. SHWS is made up of an array of tiny lenses (microlenses) and an imaging detector placed at its focal plane (Shack and Platt; 1971). For plane incidence, the focal spots are equi-spaced and undistorted, but for the incidence of an aberrated wavefront, the spots are displaced from their ideal locations. It is possible to estimate the incident wavefront phase by detecting the magnitude and direction of the shift in the spots.
This kind of wavefront sensing involves two primary computational steps, namely, estimation of the local slopes of the wavefront using centroiding methods and wavefront estimation from the measured slope values using wavefront reconstruction methods. Centroiding contributes to most of the wavefront estimation error in the case of adaptive optical systems for astronomical telescopes. The accuracy of centroiding depends on many external and interdependent internal factors. Photon noise, the inherent natural variation of the incident photon flux, is unavoidable in any case. The readout noise limitation of the detector, its pixel size, and resolution are the instrumental constraints. Background and scintillation effects are additional noise concerns in a few cases. In contrast, the error due to wavefront phase measurement from the local slopes is dependent only on the algorithm used and the instrumental limitations. Also, there exist time lags which are comparable to optimum adaptive optics closed-loop bandwidth because of the time delay between the wavefront correcting instrument and the wavefront sensor. This servo-lag, which can be minimized via prediction algorithms, is essentially due to the finite exposure time and non-zero response times of the instruments in the feedback loop (McGuire et al.; 1999).
Astronomical targets under study are in general dim light sources and hence, a nearby bright star (called Natural Guide Star or NGS) is used as a reference to sense the variations due to atmospheric turbulence. It is not always possible to find an NGS near the object of interest for wavefront sensing, and in those situations, very low light level conditions might have to be dealt with. Hence, it is important to study the performance of centroiding algorithms at low light conditions. An artificial star (called Laser Guide Star), generated using high-power lasers, could be employed for wavefront sensing in such cases. LGS can be of two types—Rayleigh or sodium beacon. Rayleigh beacon is formed by the light scattered from molecules at lower altitudes (10–15 km). This low-altitude reference source would lead to cone effect and hence the problem of focal anisoplanatism arises. A high-power 589 nm laser can be used to excite the meteoric origin sodium atom layers in the mesosphere which are present at a mean altitude of 92 km and with a mean thickness of ~10 km. The limit on the power of LGS also limits the number of available photons for wavefront sensing. The number of available photons decides the centroiding accuracy and the minimum exposure time which in turn controls the adaptive optics servo bandwidth (Hardy; 1998).
The finite thickness of the sodium layer makes it difficult to generate an artificial source that is point-like. The situation becomes worse when dealing with large aperture telescopes (>10 m). The observed spots are elongated with the elongation length being a function of the distance of the spot from the laser launch point and the elongation axis in the direction of the line joining the subaperture center and the launch point. Another problem along with the elongation is the unstable nature of the vertical sodium density profile. Hence, an advanced image processing tool is necessary for accurate detection of the centroid position in the case of LGS-based Shack Hartmann sensor (Schreiber et al.; 2009).
Various centroiding algorithms that were suggested in the literature were implemented, like center of gravity (CoG), weighted center of gravity (WCoG), iteratively weighted center of gravity (IWCoG), intensity weighted centroiding (IWC), and matched filter (MFC). In view of the fact that WCoG gives large errors with large shift in the spots, it must be avoided and replaced by IWCoG method. It was observed that maintaining a small spot size in the case of IWCoG will help in keeping the centroiding error low. Better optimization of the number of iterations is necessary for the best utilization of time and efficiency. CoG method and IWC method perform better when compared to IWCoG in cases where Poisson noise is dominant.
At very low signal-to-noise ratio, most of the algorithms suggested above fail to maintain high wavefront sensing accuracy. Hence, a new algorithm based on image reconstruction of the SHWS spots using Zernike polynomials was suggested. The proposed method, called Thresholded Zernike Reconstructor (TZR) in conjunction with the WCoG algorithm, greatly improves the wavefront sensing accuracy at low signal-to-noise ratio (SNR). The TZR method involves three steps. Firstly, individual SHWS spots are reconstructed using low-order Zernike polynomials via the calculation of Zernike moments. The reconstructed spot images, free of high spatial frequency noise, are then thresholded to get rid of any unwanted image pixels and features. The resultant spot images are then used for centroiding; either CoG or WCoG can be used thereafter. The devised method was tested using Monte Carlo simulations for NGS and LGS cases.
For the NGS case, the TZR method can become a very effective tool for close to complete noise removal. This method is most applicable to cases where the signal-to-noise ratio is very small and the spatial extent of the noise is smaller compared to the signal. It is shown that the accuracy of centroiding improves nearly 20 times while using CoG algorithm in the presence of noise with SNR < 1. At high noise conditions, the thresholded Zernike reconstructed images can lead to multiple features. This is due to the fact that at high noise level conditions there can be large-scale features (scales comparable to the size of the spot) which might not be removed even after the denoising procedure. Implemented. To use this erroneous spot for accurate centroiding, we take advantage of the fact that the final spot formed at the focal plane of a lens must assume an Airy pattern, which can be approximated to a Gaussian-like structure. A Gaussian Pattern Matching algorithm, implemented in three steps—feature recognition, shape identification, and profile identification-is used for accurate spot detection.
In the case of LGS, the TZR method combined with WCoG performs better than any other algorithm for all SNRs. Although the elongation length has little effect on the centroiding algorithm, centroiding accuracy is best when the spots are oriented along the direction of the pixels. The TZR method was tested for different numbers of pixels per subaperture. Here, the choice of thresholding percentage is crucial.
Certain problems associated with the IWCoG method were identified. In the first place, it is an iterative process and hence there is a problem of error saturation. This problem is overcome by the new Iterative Addition of Random Numbers (IARN) method, wherein pseudo-random numbers are added iteratively to the ‘x’ and ‘y’ coordinates of the estimated centroid, forcing the iterations to non-convergence. This non-convergence of iterations makes it difficult to choose the iteration with minimum error. As a solution to this problem, we make the hypothesis that the iteration number with maximum correlation between the weighting function and the actual spot image function is the iteration with minimum error. This hypothesis was made after the observation of a strong negative correlation between the error propagation function and the correlation coefficient of the weighting function and the actual spot image function. This novel and hybrid method of centroiding, called the Improved IWCoG, is superior in comparison with other centroiding algorithms (other than TZR) at low SNR.
Narrow Field Infra-Red Adaptive Optics System (NFIRAOS) is a facility Multi-Conjugate Adaptive Optics (MCAO) system for the Thirty Meter Telescope (TMT) observatory. The vertical density profile of the sodium layer is not uniform, and the mean altitude and width of the sodium layer fluctuate in time (Davis et al.; 2006). Extremely Large Telescopes (ELTs) are highly sensitive to these continuous variations in the sodium layer profile. The design of NFIRAOS consists of a Moderate Order Radial (MOR) Truth Wavefront Sensor (TWFS, 12 × 12 Natural Guide Star (NGS)-based), which is intended to detect the bias in the LGS-based wavefront reconstruction that has occurred due to uncertainties and temporal variations in the sodium layer profile (Andersen et al.; 2008). The SHWS spots for the TWFS are seeing-limited since the WFS operates in the 0.6–0.8 micron spectral passband, and the LGS adaptive optics system only provides sufficient wavefront correction for reasonable Strehl ratios in the near-infrared. Also, each subaperture sees an effective telescope diameter less than 2 m, which by itself is much larger than the average Fried parameter of the TMT site (Mauna Kea), and hence the SH spots can be expected to be of various sizes and irregular shapes. Hence, it becomes important to know the impact of SH spot size variations on the TWFS wavefront reconstructions. A large part of the wavefront reconstruction error occurs from inaccurate centroiding of the SH spots, which in turn determines the local wavefront slopes.
Monte Carlo simulations run on all the centroiding algorithms for 10,000 sample spots, for each of the spot size cases (0.8 to 1.9 FWHM, in steps of 0.1) show that MFC, IWCoG, IARN, and IWC outperform CoG and WCoG in terms of the centroid estimation error (CEE). The absolute CEE in the case of MFC and IWCoG is nearly the same at signal levels better than 500 photons per subaperture per frame. Although MFC performs better than CoG, WCoG, and IWC, IWCoG and IARN perform better than MFC in the case of changing spot size. The degree of curvature in the plot of CEE against the spot size (FWHM) in the case of MFC method increases with reducing signal level, and the variation in the CEE seems to increase exponentially with reducing signal level in the case of MFC. The stability of the performance of IARN and IWCoG is nearly the same at different spot sizes. IARN, as expected, performs better than IWCoG in terms of the centroid estimation error due to the removal of the problems associated with IWCoG, including error saturation and non-uniform convergence of iterations.
Inconsistency in the wavefront reconstruction accuracy with an SHWS-based adaptive optics system depends on the time-varying centroiding error and a possible mismatch of the wavefront distortion points with the wavefront sensing locations. This instability severely limits the performance of an adaptive optics system while imaging variable sources requiring an exposure time much greater than the rate of fluctuations in the wavefront reconstruction accuracy. In my thesis, it is shown through numerical simulations that these fluctuations can be minimized and high wavefront reconstruction accuracy can be maintained consistently for a 1–2 m class telescope by using a dither-based SHWS, which is intelligent enough to move across the telescope aperture region of interest so as to significantly improve the consistency of the wavefront reconstruction. Also, further numerical analysis is performed to analyze the possibility of using such a sensor in the case of large telescopes. Our investigations suggest that for the case of very large telescopes, multiple dither sensors would do a better job than a simple single dither sensor.
Nullifying the servo bandwidth error improves the Strehl ratio by a substantial quantity in adaptive optics systems. An effective method based on data mining is presented for predicting atmospheric turbulence and reducing the servo bandwidth errors in real-time closed-loop correction systems. Here, the prediction parameters are the pixel values of the simulated phase screens. An attempt was made to predict Zernike moments corresponding to the incoming wavefronts using data mining. These methods were implemented on experimental and simulated data and shown that the errors induced by the servo lag delays can be greatly minimized. The simulation parameters—segment size and servo lag timescales—were optimized. Large segment size leads to poor prediction. This method of prediction was studied under different experimental parameters like segment size, decorrelation timescales of turbulence, and segmentation procedure. The prediction accuracy depends strongly on the atmospheric turbulence parameters, which fluctuate in time. Hence, there is a need to continuously monitor the atmospheric turbulence parameters for optimum performance. However, this requires highly sophisticated instruments and control. Here, we investigated this problem through numerical simulations by adaptively changing the prediction parameters using data stream mining of existing wavefront sensor data.
The use of Spatial Light Modulator (SLM) as a wavefront sensor and wavefront corrector has been demonstrated. Zernike aberrations were produced using the LC2002.Holoeye SLM. Wavefront correction was achieved by imposing phase corrections on the second SLM, Meadowlark Optics Hex127. Both the SLMs were characterized in terms of their nonlinearity and phase retardance for the best performance. Images were captured before and after the correction for comparison.
Under a thin lens and paraxial approximation, the phase transformation function of a lens was simulated on an SLM. The properties of an array of such lenses simulated on transmitting-type and reflecting-type SLMs were investigated. The effective refractive index of the LC-SLM material was measured to be ~2 for both the SLMs. The lens followed a Gaussian beam profile during its propagation. The centroid position of the spot had a standard deviation of 6 ?m under undisturbed conditions. It was observed that positioning of the detector exactly at the focal plane of the lens is not very critical in this case. This is because of a very long focal length and confocal parameter of the lenslets. The shift in the spots of the digital SHWS was linear with respect to the applied phase difference.
The frames captured with a compact, high-resolution, monochrome progressive scan CCD camera, of a continuous facesheet microelectromechanical systems (MEMS) deformable mirror (DM), include unwanted diffractive, background, and readout noises, which significantly reduce the quality of imaging in many applications. Processing these images before passing them on to meet later experimental objectives can improve performance greatly. A sequence of steps involving image intensity-weighted noise removal and other smoothing techniques were proposed to minimize the noise and improve the phase production and correction capabilities of the DM. | |
