Compensation of Vignetting

Especially noticeable in astro photography is the brightness decrease from the center of the image to the edge called vignetting. Even the best and otherwise perfect lenses suffer from this phenomenon. It's cause is a simple geometric effect. Light that enters an objective lens along the axis and that later ends up in the center of the image 'sees' a projected cross section of the lens in the shape of a circle. A ray of light that enters under an angle and that will form an element at the edge of the image 'sees' a shortened projected cross section of the entrance lens, an ellipse. The ellipse of course has a smaller area than the circle and accordingly less light hits the film at the corresponding location in the picture and the picture becomes dimmer. In taking picture of astronomical objects any brightness variation of this background is especially apparent, as we expect the sky background to be nice and homogenous. In most 'real life' telescopes additional effects like obstructions from off axis guiders and the off axis light drop due to insufficient secondary mirror diameter add to the overall effect worsening it further. The following picture illustrates this in an example picture taken with a 135mm lens of comet Hyakutake.

The brightness drop towards the edge of the field is plainly visible. Plus a brightening in the lower left corner of the field due to light from the horizon. In making an effort to subtract this background illumination from the image the first choice to model the distribution of intensity is very difficult to achieve due to the many unknowns involved in it. It is however possible to extract the distribution from the image itself and then subtract it from the actual image. This has to be done in the three color channels separately. The background intensity distribution is interpolated from a number of points that are manually identified to be without stars or parts of the object. Those points are selected using the computer mouse on the screen and result in a table of data points (x,y coordinate and red, green and blue color values). A computer software uses two dimensional splines to create a smooth interpolated surface function representing the brightness distribution. Only about 20 points in the image background are needed. The following picture shows the interpolated brightness function.

The difference in the three color channels is obvious and shows that it is necessary to treat the three channels independently. It is interesting to display the background brightness as a color image. The following image shows the brightness modulation.

In the image above even the colored brightening in the lower left corner due to horizon light is visible. Accordingly it can be assumed that the image background will be compensated to a 'flat' neutral background. The result is shown in the following image. The background is neutral black an the vignetting is almost completely gone. In a few areas some 'clouds' are artifacts of the operation. This results from the fact that the background is interpolated from a few points and that the interpolation has slight inaccuracies with respect to the original image. If the choice of the points is inaccurate i.e. there is a faint star or part of a nebula then the background function will not correctly mimic the original image. Accordingly the subtraction is not perfect and a small modulation is visible in the image. If the points are chosen carefully the resultant image should show a clear improvement  over the original.

The main effort has now been completed. Some small further enhancements can be made by stretching the brightness range of the image back to the full range of 256 and applying a Gamma correction (i.e. 1.7) which is shown in the following image.

The above example is from a picture taken with a 135mm tele lens.

In the next sequence the same procedures are applied to an original picture that was taken with a 13 inch f4 Newtonian telescope. The image is of the Cirrus nebula in Cygnus. Due to the slower f-number (f4) compared with the f2.8 for the tele lens the vignetting effect is not as well pronounced. With the small angle of the image on the sky a modulation due to horizon brightening is also not present. There is however a small brightening in the center of the image that is noticeable as a slight blue hue.

The next step shows the extracted background function. It is smoother than that from the 135mm lens but still shows a central bulge.

From the interpolation function a background image can be computed and is shown here.

The following image shows the result of the subtraction, stretch and gamma (1.6) correction of the image. Still a small gain in image quality is visible. The first image on the top of this sequence was treated the same way but without the subtraction step. An improvement is visible.

(Images an processing: G. Gottschalk)

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