This experiment had a number of aims. One of them was to create an optical path that would produce vignetting. The second was to show that the use of flat fields would compensate for the vignetting. The equipment used was a low cost, poorly colour corrected, 102mm f/4.5 ED achromat that is motor-focus modified. It is possible to avoid vignetting by using a 2" adapter, but on this occasion a 1.2" adapter was used in a 1.25" star diagonal in order to create vignetting.
The SV405CC was fitted with an SVBONY 1.25" IR/UV cut filter and was placed in the star diagonal of the scope. An SVBONY 165 guide scope fitted with a QHY-5II-M camera was used for pulse auto-guiding with PHD2. AstroDMx Capture was used to capture 22 x 3min FITS exposures of the Markarian Chain of galaxies with matching dark frames. Also 20 flat-fields were captured to compensate for vignetting in the optical setup used.
Click on an image to get a closer view
Screenshot of AstroDMx Capture saving FITS data on the Markarian chain. The screenshot clearly shows the vignetting where the centre of the image is brighter than the regions of the image towards the edges.
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Screenshot showing AstroDMx Capture saving FITS flat-field images
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The vignetting is very clear in this screenshot of flat-field capture.
Let us consider for a moment how flat-fields work. If the imaging system was perfect, the flat-fields would be a uniform brightness across the field of view (and would not be needed). There are a number of reasons why the illumination might not be equal across the field. The most obvious that is seen here is vignetting, where less light reaches the outer regions of the sensor than reaches the middle of the sensor. In this case, the vignetting is due to the geometry of the optical path caused by using a 1.25" adapter rather than a 2" adapter. Another reason might be that the sensitivity of all of the pixels over the sensor is not the same. Such a situation can arise as a sensor ages for example. Parts of the sensor might be dirty and so in those regions light is to an extent obscured. Dust rings can be seen on images if dust has fallen onto the sensor or onto the optical window in front of the sensor. It is not always easy to remove such dust. The dust rings produce circular donut-like regions where less light is falling onto the sensor. It is all of these causes of uneven illumination that flat-fields are designed to correct.
How flat fields work
The exact details of flat-fielding can vary a little, but basically flat-fields work like this:
A number of flat-fields are captured and an average flat field image is produced. Then the brightness of every pixel is measured and the pixels can be ordered from brightest to dimmest. The middle pixel in this ordered list of brightness is the median pixel. Alternatively, the brightness of all of the pixels can be averaged and this average or mean pixel brightness will be very similar to the median brightness. Whether the median or the mean pixel brightness is used is a matter of choice, but my preference is for the median as it, unlike the mean, is robust as a measure of central location against the effects of outliers.
The brightness of each pixel should be divided into the brightness of the median (or mean) pixel to produce a correction value for that pixel. Then the brightness of that pixel should be multiplied by its correction value. In this way, the brighter parts of the image will be dimmed a little and the darker parts will be brightened a little.
Remember that a flat-field in a perfect system would have perfectly even brightness across the entire field. Let use use a small numerical example to illustrate the principle. Suppose that the brightness of the median pixel is 10, the brightness of the brightest pixel is 20 and the brightness of the dimmest pixel is 5. If we divide the brightness of the median pixel by the brightness of the brightest pixel we get a correction factor of 10/20 = 0.5. Similarly, if we divide the brightness of the median pixel by the brightness of the dimmest pixel we get a correction factor of 10/5 = 2. Lastly if we divide the brightness of the median pixel by the brightness of the median pixel we get a correction value of 10/10 = 1.
We now need to multiply the brightness of each pixel by its correction factor. Thus the brightness of the three pixels become 20 x 0.5 =10; 10 x 1 = 10 and 5 x 2 = 10. We have achieved our aim of removing the inequalities in brightness due to the various defects previously mentioned.
Every pixel in every image is corrected in this way and the effects of the defects in the system are compensated for and the effects disappear.
Stacking software such as Deep Sky Stacker can do flat-field correction as well as dark-frame correction etc.
Processing the data
Deep sky Stacker was used to dark-frame and flat-field correct the images and then register and stack them. The resulting image was post processed in the Gimp 2.10, Fitswork 4 and Neat Image.
The Markarian chain of galaxies
The SV405CC camera is proving to be a versatile and competent imaging device with a variety of telescopes and with AstroDMx Capture.
AstroDMx Capture can be downloaded HERE.
AstroDMx Capture is available for Windows, macOS, Linux including Raspberry Pi OS and ChromeOS.
