Blind Deconvolution Page

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Tau CMa

The binary star Tau Canis Majoris (=HR 2782) was observed with the ADONIS system at the 3.6m on La Silla in February 1996. Observations were made in the J, H, & K-bands. These were taken in "speckle" mode, i.e. 200 observations of 50ms each. Figure 1 shows the best and worst frames for each waveband.

Figure 1: Left-to-right: K, H & J-bands. Top: Best Images. Bottom: Worst Images. Note: Logarithmic colour table.

Figure 2 shows the corresponding long-exposure image, i.e. no residual tilt correction, the centroid image, i.e. centroid corrected, and the peak-tracked or shift-and-add images for all 200 frames. The peak-tracked image can be considered to be an average compensated images with the effect of residual tracking errors removed. The Strehl ratios are shown for the different post-processing techniques.

Figure 2: Left-to-right: Long exposure, Centroid and Peak-tracked images for (top-to-bottom) J, H & K-bands.

The blind deconvolution algorithm was applied to 16 frames each of the J, H & K-band data. In all three cases it took approximately 10000 iterations to converge which is rather slow. The convergence of the K data is illustrated in the figures 3 & 4 for the object and PSF's.

Figure 3: Convergence of the target object for the first 16 frames of the K-band data for (from left-to-right and top-to-bottom) 0, 20, 40, 80, 1000, and 13675 iterations.

The initial object estimate was the peak-tracked image shown in figure 2. Note the initial rapid convergence removing the extended low-frequency structure of the image bur the much slower convergence which removes the "limpy" Airy disk. Note that these reconstructions have been filtered back with a gaussian beam smaller than that of the diffraction-limit of FWHM=0.83".

Figure 4: Convergence of the 16 PSF's for the K-band data for (top-to-bottom) measurements, 0, 20, 40, 80, 1000, and 13675 iterations.

The initial PSF's were gaussians which rapidly converge to the measured beam size although there is still a residual companion. Note that the bandpass limit is in effect. However, it takes longer for the residual Airy ring structure to be reconstructed. Note the similarity of the final reconstructed PSF's to the original measurements.

The final reconstructed objects for all three wavebands are shown in figures 5-7. These have been reconstructed with Gaussians of FWHM equivalent to that of the theoretical diffraction-limits for the three wavebands. These reconstructions were obtained by averaging the results from the first and second sixteen frames.

Figure 5: Reconstructed image of the target object at K.

Figure 6: Reconstructed image of the target object at H.

Figure 7: Reconstructed image of the target object at J.

The K-band data shows a small residual systematic at the 1% level, the H-band data is very clean and the J-band data which had poorer compensation and therefore had a stronger uncompensated halo, has residuals at the 0.5% level. These results demonstrate the ability of a blind deconvolution algorithm to restore the target object in the absence of a unresolved reference object. These reconstructions are clean down to approximately the 1.5% level, i.e. a magnitude difference of 4.6.

An ESO report has been prepared describing the above in more detail. It is available here in compressed postcript format.

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T Tauri

T Tauri was observed in the K-band with the ADONIS system at the ESO 3.6m in October 1996 during a technical run. The electron-bombarded CCD (EBCCD) was used as the wavefront sensor and for this run we simulated the performance of the EBCCD on a star of magnitude 12 - 13. Note that T Tau has a magnitude of 9. The PSF calibrator used was SAO076597. Four sets of 75 frames each of T Tau and one set of 30 frames of the PSF calibrator were obtained. The SAA images of each are shown in figure 1.

Figure 1: SAA images for T Tau and the PSF calibrator. The binary nature of T Tau is clearly visible.

The results of applyind the blind deconvolution algorithm to each of the four data sub-sets using the twenty highest Strehl ratio frames in each sub-set, is shown in figure 2.

Figure 2: Application of Blind Deconvolution to the four data sub-sets of T Tau.

An ESO report has been prepared comparing different deconvolution techniques applied to these T Tau data. It is available here in compressed postcript format.

Blind Deconvolution Applied to Wavefront Sensing derived PSF

Jean-Pierre Veran from Meudon Observatory kindly supplied some binary star adaptive optics data. This data compreised a set of six compensated images and an estimated PSF obtained from statistical analysis of the closed-loop wavefront sensor data.

Single Frame Analysis

The top row of figure 1 shows the average of the 6 compensated data frames and the corresponding PSF estimate. These were used as the initial estimates for the application of the blind deconvolution code. The bottom row shows the coreesponding object and PSF estimates after blind deconvolution. Note that the object has been filtered with a gaussian PSF of FWHM = 1 pixel.

Figure 1: Application of blind deconvolution to an average compensated image of a binary star using the wavefront-sensor derived PSF as the initial PSF estimate.

Six Frame Analysis

Figure two shows the result of applying blind deconvolution to all six compensated images simultaneously. The top row shows these images and the bottom row shows the reconstructed object estimate, filtered by a gaussian of FWHM = 1 pixel, and the six corresponding PSF's.

Figure 2: Application of blind deconvolution to the six individual compensated binary star images. The top row shows the raw data frames and the bottom, the reconstructed object and PSF's.

Comparison of Results

Figure 3 compares the reconstructed object obtained with the single frame data (left) to that obtained with the multiple frames (n=6) (center) and the result from a fixed PSF sigle frame reduction. Figure 4 shows a logarithmic contour plot of the same figure which permits a more direct comparison. These contours are at 1, 1.6, 2.5, 4, 6.3, 10, 16, 25, 40, & 63% of the peak intensity. Note that the differences in the BD results only occur at the lowest contour levels, i.e. at less than 2% corresponding to a dynamic range of approximately 4.2 magnitudes.

Figure 3: Comparison of the filtered reconstructed object estimates for blind deconvolution with a single frame (left), and six frames (center) from figures 1 compared with the single frame fixed PSF recontruction (right).

Figure 4: Comparison of the filtered reconstructed object estimates for blind deconvolution with a single frame (left), and six frames (center) from figures 1 compared with the single frame fixed PSF recontruction (right). Logaritmic contours.

The fixed PSF reduction clearly illustrates the difference between the measured and estimated PSF. Both sources appear to have a companion immediately to the right. There is also substantial noise in the reconstruction when compared to the blind deconvolution results.

The consistency in these results can be seen from the preliminary astrometry and photometry of the two stars. These are:

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Last modified: January 6, 1997