Post-observation image restoration is necessary for reducing residual seeing effects after adaptive optics correction. Instrument design must take image restoration into account.
Figure 1. Conceptual design for the EST FBIs. (a) The simplest setup: one camera and a filter wheel with narrowband filters. (b) As (a) plus a beamsplitter and a synchronised, defocused camera for Phase Diversity. (c) The chosen setup, as (a) plus a Phase Diversity pair of cameras behind a wideband filter wheel. Graphics courtesy C. Quintero Noda.
The Earth's atmosphere is optically active, perturbing the image formed by a telescope. This effect, known as seeing, is the result of turbulence in the Earth's atmosphere, stirring air with varying temperature and therefore varying refractive index. This produces rapidly varying phase aberrations in the wavefronts entering the telescope, continually changing the image. These changes can be described as the convolution of the real image, the object, with varying point spread functions (PSFs).
EST will have Adaptive Optics (AO), which reduces the effects of seeing in real time. However, AO cannot remove these effects completely because there is necessarily a time lag between measurement and correction and they both have limited resolution.
We will reduce the effects of residual aberrations by using image restoration based on multiple short exposures. Short exposures, on the order of milliseconds, retain high resolution information, although scrambled. A long total integration time is needed to get a useful signal in many observing scenarios but in a long exposure different instances of the seeing are averaged, thus blurring the image and hiding the details. So the image restoration algorithm needs to combine multiple short exposures, but with the aberrations removed.
Untangling the object from the PSF in a single image is an ill-posed problem known as Blind Deconvolution. You need constraints to solve it. With varying aberrations and an object that evolves much slower, the problem becomes easier. Multi-Frame Blind Deconvolution (MFBD) uses a model-fitting approach to find the single object and the aberrations that fit multiple exposures. MFBD estimates the PSF in each exposure and uses this information to restore a sharper image.
The Fixed Band Imagers (FBI) of EST will collect data through narrowband (NB) filters, that can be changed with a filter wheel. How should they be designed so the data are good for MFBD? Figure 1 shows three alternative designs, with the first one as the simplest case. If you collect multiple exposures with a single camera behind a filter, you can do image restoration with MFBD. This brings out many of the small features in between the larger granules. The upper-right part of Figure 2 demonstrates the results with data from SST/CHROMIS. For comparison, the upper left part corresponds roughly to keeping the image steady while taking a long exposure. However, we then leave it to the atmosphere to provide the variations that we need to do it well.
Figure 2. Contrast and image quality comparison. Top left: shift-and-add by subfield. Top right: MFBD. Bottom: MFBD with PD. Based on 110 exposures in SST/CHROMIS Ca II continuum.
So if random variation in the aberrations helps with the restoration, can you introduce intentional, known variation, that is better? Yes, add one camera and put it slightly out of focus, as in Figure 1b, and you get Phase Diversity (PD). This can improve the MFDB algorithm's ability to identify and compensate for the aberrations considerably, as demonstrated in the bottom part of Figure 2. The trick here is that with synchronised cameras, you can collect pairs of images where the object is exactly the same and the wavefront phases differ in a specific way, corresponding to the amount of defocus. This constrains the problem and makes it easier for the algorithm to select the best of several solutions that fit the in-focus images almost equally well.
The chosen design, shown in Figure 1c, has three cameras. The PD camera pair is now behind a wideband (WB) filter, the light to which is split off before the NB filter. What do we gain by adding a third camera? As before, the cameras are synchronised so they all share the same aberrations and we assume the filter wavelengths are similar. This means we can find the aberrations in the WB, where there are plenty of photons, while the NB might be darker and noisier due to a narrower passband and perhaps being in an absorption line. We also do not waste precious NB photons in the out-of-focus image. We can use a variation of the MFBD algorithm where the WB and NB images can be processed together as a single data set: Multi-object MFBD (MOMFBD). We then solve for the aberrations of all exposures and two objects, one in the WB and one in the NB. Both the MFBD and MFBD+PD results in Figure 2 are actually processed as MOMFBD datasets as for the chosen FBI design.
Figure 3. Schematic representation of a MOMFBD dataset with PD. The WB images force MOMFBD to align the restored NB images.
MOMFBD allows for datasets where we switch NB filter while collecting the data. Then you get the kind of data set illustrated in Figure 3. Here we have to find the restored image of a single WB object and multiple NB objects. Because the fitted aberrations include image motions, which are then removed by the deconvolution, all the NB images come out aligned to the WB image—and therefore also to each other.
This is a useful property of the MOMFBD processing, as the NB images can look very different, e.g., in the core and in the wings of a spectral line, and therefore be difficult to align with other methods.
The continuum, on the other hand, is fairly similar in different parts of the spectrum. So even if the NB wavelengths are too far separated for processing as a joint MOMFBD dataset, the WB images are still useful for alignment. If the WB filter is also switched to nearby continuum wavelengths, the continuum images can be used post-restoration to find the misalignment and apply it to the restored NB images.
MOMFBD image restoration can be used for the Tunable Imaging Spectropolarimeter (TIS) instruments as well. The TIS design is not fixed yet, but from an image restoration point of view it can be very similar to the chosen FBI design. Just add an extra NB camera and a polarising beamsplitter for dual-beam polarimetry and replace the NB filter wheel with tunable Fabry-Pérot etalons and a polarisation modulator. With or without the PD WB camera, the image restoration problem becomes larger but is in essence the same as for the FBI instruments.