Efficient Solar Scene Wavefront Estimation with Reduced Systematic and RMS Errors: Summary


Paper:	Efficient Solar Scene Wavefront Estimation with Reduced Systematic and RMS Errors: Summary
Volume:	504, Coimbra Solar Physics Meeting: Ground-based Solar Observations in the Space Instrumentation Era
Page:	113
Authors:	Anugu, N.; Garcia, P.
Abstract:	Wave front sensing for solar telescopes is commonly implemented with the Shack-Hartmann sensors. Correlation algorithms are usually used to estimate the extended scene Shack-Hartmann sub-aperture image shifts or slopes. The image shift is computed by correlating a reference sub-aperture image with the target distorted sub-aperture image. The pixel position where the maximum correlation is located gives the image shift in integer pixel coordinates. Sub-pixel precision image shifts are computed by applying a peak-finding algorithm to the correlation peak Poyneer (2003); Löfdahl (2010). However, the peak-finding algorithm results are usually biased towards the integer pixels, these errors are called as systematic bias errors Sjödahl (1994). These errors are caused due to the low pixel sampling of the images. The amplitude of these errors depends on the type of correlation algorithm and the type of peak-finding algorithm being used. To study the systematic errors in detail, solar sub-aperture synthetic images are constructed by using a Swedish Solar Telescope solar granulation image¹. The performance of cross-correlation algorithm in combination with different peak-finding algorithms is investigated. The studied peak-finding algorithms are: parabola Poyneer (2003); quadratic polynomial Löfdahl (2010); threshold center of gravity Bailey (2003); Gaussian Nobach & Honkanen (2005) and Pyramid Bailey (2003). The systematic error study reveals that that the pyramid fit is the most robust to pixel locking effects. The RMS error analysis study reveals that the threshold centre of gravity behaves better in low SNR, although the systematic errors in the measurement are large. It is found that no algorithm is best for both the systematic and the RMS error reduction. To overcome the above problem, a new solution is proposed. In this solution, the image sampling is increased prior to the actual correlation matching. The method is realized in two steps to improve its computational efficiency. In the first step, the cross-correlation is implemented at the original image spatial resolution grid (1 pixel). In the second step, the cross-correlation is performed using a sub-pixel level grid by limiting the field of search to 4 × 4 pixels centered at the first step delivered initial position. The generation of these sub-pixel grid based region of interest images is achieved with the bi-cubic interpolation. The correlation matching with sub-pixel grid technique was previously reported in electronic speckle photography Sjö'dahl (1994). This technique is applied here for the solar wavefront sensing. A large dynamic range and a better accuracy in the measurements are achieved with the combination of the original pixel grid based correlation matching in a large field of view and a sub-pixel interpolated image grid based correlation matching within a small field of view. The results revealed that the proposed method outperforms all the different peak-finding algorithms studied in the first approach. It reduces both the systematic error and the RMS error by a factor of 5 (i.e., 75% systematic error reduction), when 5 times improved image sampling was used. This measurement is achieved at the expense of twice the computational cost. With the 5 times improved image sampling, the wave front accuracy is increased by a factor of 5. The proposed solution is strongly recommended for wave front sensing in the solar telescopes, particularly, for measuring large dynamic image shifts involved open loop adaptive optics. Also, by choosing an appropriate increment of image sampling in trade-off between the computational speed limitation and the aimed sub-pixel image shift accuracy, it can be employed in closed loop adaptive optics. The study is extended to three other class of sub-aperture images (a point source; a laser guide star; a Galactic Center extended scene). The results are planned to submit for the Optical Express journal.