7.2 Long exposure

Besides aiding in understanding and optimizing the AO performance estimates of the AO PSF can be used to post-facto deconvolve long exposure images. The advantage of applying post-facto deconvolution techniques was clearly demonstrated by Marino and Rimmele (2010). Accurate photometry, for example, requires that the PSF is well known. Measurements of physical parameters often are performed by computing difference images. A dopplergram that measures flows on the solar surface is essentially computed by subtracting the images taken in the red and blue wing of a spectral line. If the red and blue wing images are recorded sequentially the impact of varying seeing conditions and the resulting variations in AO Strehl on the quantitative velocity measurements can be so severe that the scientific interpretation becomes impossible. Most notably, wing images with significantly different Strehl produce dopplergrams that display residual intensity signal. This is referred to as intensity-velocity cross talk that in severe cases can render the velocity measurement completely useless. The same issue exists when polarimetric measurements are performed. PSF estimation and subsequent deconvolution of line wing images can restore the relevant information to a large extent and, thus, lead to useful scientific results.
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Figure 31: Long exposure narrow-band images taken in the red wing of the spectral line Fe i 5576 Å. The image on the top right was recorded with a Fried parameter r0 = 16.5 cm and a Strehl of S = 0.88. The image on the top left has a significantly lower Strehl of S = 0.46 and was recorded with r0 = 5.4 cm. The high spatial frequency information is still present in the poor seeing image on the left but the contrast is reduced significantly. The corresponding deconvolved images are displayed at the bottom. Post processing these long exposure images can restore the contrast, i.e., the amplitudes.
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Figure 32: Radial PSDs of long exposure narrow-band images shown in Figure 31View Image.

Figure 31View Image shows a sample pair of long exposure images, which compare images before and after deconvolution. The top row shows the AO corrected red wing images captured within a few seconds of each other but during vastly different seeing conditions. The image on the right was recorded with a Fried parameter r0 = 16.5 cm and a Strehl of S = 0.88. The image on the left has a significantly lower Strehl of S = 0.46 and was recorded at r0 = 5.4 cm. The high spatial frequency information is still present in the poor seeing image on the left but the contrast is reduced significantly and the image appears “soft”. The corresponding deconvolved images are displayed at the bottom row of Figure 31View Image. The deconvolution process clearly enhances the contrast of the poor seeing image close to the level of the restored high Strehl image. The power spectra of these images are shown in Figure 32View Image. The restored PSDs closely match each other throughout the frequency range.

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Figure 33: Doppler maps obtained from long exposure filtergrams shown in Figure 31View Image. Top: unprocessed. Bottom: dopplergram from deconvolved filtergrams.

The top row of Figure 33View Image displays the velocity maps obtained from the two sets of unprocessed blue and red wing pairs, the first (left) captured during different seeing conditions and the second (right) set during very good seeing conditions. The bottom row of the figure displays the velocity maps obtained from the deconvolved wing images. The dopplergram produced from raw filtergrams exhibits severe intensity-velocity crosstalk. In particular, velocities measured in the sunspot umbra display the resulting artifacts and spurious velocities. Deconvolution of the wing images significantly reduces intensity-velocity crosstalk.

Rimmele and Marino (2006) give an example of science results achieved by deploying PSF estimation and post-facto deconvolution. In general, quantitative analysis of AO data can be significantly improved by applying post-facto deconvolution techniques even in the case of long exposures. At present, solar astronomers are very familiar with and heavily apply post-facto reconstruction to short exposure images and do so with much success.


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