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Each spectral order has different image geometry, and therefore different aberrations. Since the point spread function (PSF) differs between any two images, systematic errors are introduced when we use all three images together to invert for spectral line profiles. To combat this source of systematic error, we have developed a PSF equalization scheme.
Determination of the image PSFs is impractical for several reasons, including changes that may occur due to vibration during both launch and recovery operations. We have therefore developed a strategy using only the solar images obtained during flight to generate digital filters that modify each image so that they have the same effective PSF. Generation of the PSF equalization filters does not require that the PSFs themselves be known. Our approach begins with the assumption that there are only two things that cause the power spectra of our images to differ:
(1) aberrations; and
(2) the FOV average spectral line profile, which is known in principle from an abundance of historical data.
To validate our technique, we generate three synthetic images with three different PSFs. We compare PSF equalizations performed without knowledge of the PSF to corrections performed with that knowledge. Finally, we apply PSF equalization to solar images obtained in the 2006 MOSES flight and demonstrate the removal of artifacts.
Most of the solar emission within the instrument passband comes from a single bright emission line. The m = 0 image is simply an intensity as a function of position, integrated over the passband of the instrument. Dispersion in the images at m = ±1 leads to a field-dependent displacement that is proportional to Doppler shift. Our goal is to estimate the Doppler shift as a function of position for every exposure. However, the interpretation of the data is not straightforward. Imaging an extended object such as the Sun without an entrance slit results in the overlapping of spectral and spatial information in the two dispersed images.
We demonstrate the use of local correlation tracking as a means to quantify the differences between the m = 0 image and either one of the dispersed images. The result is a vector displacement field that may be interpreted as a measurement of the Doppler shift. Since two dispersed images are available, we can generate two independent Doppler maps from the same exposure. We compare these to produce an error estimate.
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