Astra Image is a commercial software program that provides for sharpening via wavelets and deconvolution. It does not do stacking.

Wavelets sharpens details in an image based on their scale or size. Deconvolution uses special mathematical algorithms that restore sharpness in an image caused by seeing and optical aberrations in a telescope.

Astro Image also performs some basic image manipulations such as brightness, contrast and color adjustments.

Astra Image is available in a professional version, a Photoshop plug-in, and a lighter Essential Tools SI version (which was used here).

Astra Image Basic Interface

Convolution, Point Spread Functions and Deconvolution

Stars are so far away that they are really point sources. When a point source passes through the atmosphere it is blurred. When the starlight enters the aperture of a telescope, it is diffracted. Aberrations in the optical system can add more blurring.

Diffraction and blurring by the atmosphere spread out the light of a star so it is no longer a point. It becomes an extended disk. The amount of blurring is described as the point spread function (PSF). The image at the focal plane can be thought of as the original image convolved, or mixed, together with the point spread function.

If we know what the point spread function is, we can attempt to deconvolve the point spread function from the blurred image and restore the original image. If we don't know exactly what it is, we can guess at it and use trial and error.

Because diffraction is part of the quantum nature of light, it can't be deconvolved. The effects of seeing and optical aberrations however, which blur stars and images, can be improved by deconvolution. The most famous example is the use of Lucy-Richardson deconvolution to improve the original Hubble Space Telescope images that were blurred by the spherical aberration of the telescope.

Astra Image Deconvolution Methods

Astra Image performs three different kinds of deconvolution:

• Maximum Entropy - A good choice for noisy images. If you have an underexposed image, or if you just didn't have a lot of frames in the stack, try maximum entropy first.

• Lucy Richardson - More aggressive than Maximum Entropy and it does not deal with noise as well if you use a high number of iterations. The algorithm does run faster than Maximum Entropy.

• Van Cittert - Most aggressive - best for high signal-to-noise images.

Each is an iterative process that is performed several times to improve the image in small steps.

Deconvolution Adjustments

Figure 1 - Astra Image Deconvolution Interface

Each deconvolution dialog box in Astra Image has three main sections:

1. Point Spread Function Type (Figure 1, Number 1) - The point spread function type selects the type of error to be corrected. Most of the time we will be using Gaussian, but experiment to see what works best for a particular image.

   • Gaussian is good for removing atmospheric turbulence (bad seeing).

   • Exponential is good for correcting lens and focus problems.

   • Cauchy is good for general all-purpose use.

   • Moffat gives fine control over the "wings" of the PSF curve, allowing a sharper peak in the point spread function.

2. Settings (Figure 1, Number 2)- Adjustment parameters

   • PSF Size - Adjusts the size of the point spread function. A blurry image will usually require a larger PSF.

   • PSF Wing Adjustment - Adjusts the peak of the PSF.

   • Iterations - Sets the number of times the deconvolution function is run on the image. 10 to 20 is usually a good number to start with.

3. Preview (Figure 1, Number 3) - Click the Preview button to apply the setting to the small section of the image in the preview window. The left window shows the deconvolution, and right window shows the original image. Click and drag the left preview window to move the image around and to reset the preview. Applying the deconvolution to just a small section of the image allows much quicker previews.

Processing

The different deconvolution types are accessed under the Process pull-down menu. All work pretty much the same way.

Start with a Gaussian PSF and a relatively low setting for the PSF size of about 1.0. Set the number of initial iterations between 10 and 20.

Click the preview button to see the result. If the result in the preview is unsatisfactory, change the PSF size. Try different PSF sizes. Once you have a PSF size that seems to give good results, try increasing the number of iterations. You can also try reducing the PSF size a little bit and using more iterations.

Maximum entropy is a complex algorithm and can take a long time to complete, especially if a large number of iterations are used. Maximum entropy can also be used to reduce noise while sharpening the image.

Lucy Richardson has an "Aggressive" setting. When checked, it will have a more powerful effect with less iterations. Noise, however, will become more aggravated more quickly also. For the aggressive setting, 10 and 20 iterations is a good starting point. If the aggressive setting is not used, then usually more than 20 iterations are needed.

Van Cittert method is the most aggressive deconvolution method offered by Astra Image. It should be used for high signal-to-noise images such as those of the Sun, Moon and planets that were stacked with a lot of frames. Because Van Cittert is the most aggressive algorithm, noise will quickly become the limiting factor. Van Cittert is also the fastest deconvolution method.

Hold your mouse cursor over the image to see a comparison between the original stacked image and one with a Lucy Richardson deconvolution applied to it. A PSF of 0.5 was used with 10 aggressive iterations. This image of Copernicus was shot with a C11 working at f/10 and Live View capture by Images Plus through a Canon T2i (550D). Frames were stacked in AviStack with multi-point alignment.

Wavelets

Details in an image exist on different scales, from the smallest, such as craterlets on the Moon, to the largest, such as Lunar Mare.

Wavelets transform details in an image into frequency information. This way, details at different scales can be sharpened independently. Hold your mouse cursor over the image to see a comparison between the original stacked image and one with wavelet sharpening applied to it. This image of Saturn was shot with a C11 working at f/20 and 640 x 480 Movie Crop Mode recorded in a Canon T2i (550D). Sliders in the Wavelets panel are used to adjust features in the image at different scales. If noise is present in the image, it is usually on a small scale, so using the Very Small Detail slider may make it worse.

Astra Image Wavelets Panel

This tutorial was done with Astra Image 3.0SI version 3.0.6.0.