Deconvolution Processing

The regular image processing filters in MaxIm DL are convolution filters.  In essence, a convolution kernel is multiplied by the original image to create a new filtered image.  If you imagine that the distorting effects of atmospheric seeing, tracking errors, and optical misalignment act like filters that distort an ideal image, you can envision a deconvolution filter that works in reverse to remove the distortion.  A deconvolution filters works by comparing the shape of a point spread function (PSF) from the image with an ideal PSF.  The point spread function describes the shape of a star in the image.  The deconvolution routine compares the actual PSF to an ideal PSF and deconvolves the image to make the actual PSF approximate the ideal PSF.

In other words, the deconvolution process undistorts distorted star images.  There is a limit to how well it can work, and it cannot make a bad image great, but it can make a mediocre image good, and it can make a good image even better.

Point Spread Function

The PSF is a three-dimensional profile of the intensity of a star image.  In ideal PSF from a telescope system should be a Gaussian profile.  Below is a cross section of a PSF from an image with undistorted round stars.  This is the standard Gaussian profile shape.

Above:  Profile of a star image.

Now, have a look at an image with less than ideal stars.  The image below of M13 was taken with a telescope that was slightly out of collimation (optical alignment).

Below is a close up of the upper left corner of the image showing slightly distorted stars.  Note the small flares coming off the lower right side of the stars, indicating optical misalignment.

Now, compare the PSF from a distorted star in this image versus the optimal PSF shown above.

Above:  PSF of a distorted star image.  Note the asymmetrical appearance.

The Deconvolution Filter

The deconvolution routine analyzes the actual PSF from the image and tries to restore it to an ideal PSF.  Deconvolution routines are iterative, meaning they run several approximations which successively approach the ideal solution.  The reason for this is that unlike convolution filters, which multiply the image by a filter function, deconvolution filters divide the image by a function.  This means the possibility of division by zero, which leads to a nonsense result, or division by an extremely small number, which results in huge amounts of noise being generated.  Instead, the deconvolution routine makes an estimate of the solution based on the PSF data and information about the noise within the image and runs several iterations, each getting closer to the desired result.

In MaxIm DL, the Deconvolution routine needs a model of the noise in the image, which is easily extracted automatically.  Then it needs to know the shape of the actual PSF, which is also easily extracted, although this is sometimes done manually.  Finally, the routine runs several iterations to produce a final result that is (hopefully) an improvement on the original.

Begin by selecting Filter > Deconvolve to open the Deconvolve window.

Noise Model

In the Noise Model tab of the Deconvolve window, select Auto-Extract.  This will determine the noise level automatically, which is almost always sufficient.  Next, click on the PSF Model tab.

PSF Model

Next, you need to determine the point spread function for the image.  For an image with an asymmetrical distortion, such as this one, it is best to select a star directly from the image to determine the PSF.  Ideally, you want to select a star that is representative of the overall distortion in the image.  For example, in the cropped image of M13 above, you can see most of the bright stars have small flares pointing to the lower right.  Some of the fainter stars, especially those near the lower right corner of the cropped image (closest to the star cluster itself) appear less distorted.  It would be best to select one of the brighter stars that shows a noticeable flare because the deconvolution filter will then attempt to correct for this.

Select the From Image radio button and then click on the Select From Image button.  Then move the cursor to an appropriate star and click on it to select it as the PSF model.  Next, click on the Deconvolve tab.

Deconvolve

You have the choice of two different deconvolution routines, Maximum Entropy and Lucy-Richardson.  Maximum Entropy tends to work best on images that are symmetrically blurred such as by seeing conditions or focus issues.  The Lucy-Richardson algorithm works better for images with asymmetrical distortion such as from tracking/guiding errors or from collimation, as is the case with this example.

Determining the number of iterations can take some experience and some test runs.  In general, you want as few iterations as necessary to achieve the desired results.  3 is a good number to start with.

If you have a large image and/or a slower computer, you can select a subframe within the image to run a test of the filter settings using the Operate On function.  This is a good way to determine how many iterations to run.  Once you see the desired results, set this to Full Image to deconvolve the whole image.

Once the settings are made, click Go and get comfortable.  Running 3 iterations on a 3-megapixel ST-10XME image took 4 minutes 40 seconds using a computer with a 2.5 GHz Pentium IV and 512 MB of RAM.

Final Image

Above:  The M13 image after deconvolution.  Note how much more round the star images are compared to the original image.

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