Gamma

Many terms used in planetary imaging are already in frequent use by nonas-tronomers. The digital camera era has plunged many otherwise sane and normal people into the world of image-processing jargon. However, the term gamma is rarely understood and it is so crucial to planetary imaging that an explanation is required. At first glance it would appear that increasing the gamma of an image makes it brighter and reducing the gamma of an image makes it dimmer. However, it is a lot more subtle than that. Play around with the gamma function

Figure 8.6. The color dispersion on a low-altitude (20 degrees) Mars is obvious in this image by the author, taken in August 2003. A red/yellow fringe to the south (top) and a blue/violet fringe to the north (bottom) reduce the achievable resolution. Image: Martin Mobberley.

Figure 8.7. Mars (from top) in infra-red, red, green, and blue light (these are sharpened images.) The final image is an LRGB composite employing the clean luminance data from the infra-red image and the colors from the low-res, noisy, red, green, and blue images. Image: Martin Mobberley.

Figure 8.8. Saturn, in near-perfect seeing, imaged through red, green, and blue filters with a Celestron 9.25 SCT at f/40 and an ATiK 1HS webcam. The blue image is the noisiest. Image: Damian Peach.

on any image-processing package like Photoshop or Paint Shop Pro and you will notice that the brightest and darkest parts of the image stay the same, whereas the mid-range brightness varies considerably. The gamma function makes use of an interesting property of numbers between zero and one, raised to a certain power. In PC image processing, one way of representing brightness is by regarding jet black as zero, brilliant white as 1.0, and the mid-range brightness as 0.5.

As a slight digression, inside the computer's processor the brightness of a pixel might be represented by 8 bits (0-255) or 16 bits (0-65,535). As an example of an 8-bit number, imagine the binary number 00010000. The right-most digits in 00010000 that represent 1, 2, 4, and 8 are all zero as are the left-most digits representing 32, 64, and 128. However, the digit representing 16 is one, so 16 in decimal = 00010000 in binary. The full range of pixel brightnesses (from 00000000 to 11111111 in binary) are equal to 0 to 255 in decimal. But, as far as gamma is concerned, 0 = 0, but 255 = 1. Everthing is scaled down such that black is 0 and white is 1.

Figure 8.9. The LRGB tool in Maxim DL. In the example, an LRGB image of a low-altitude Jupiter is being created using infrared as red, blue as blue, a simulated green (red plus blue averaged), and an infrared luminance with a 50% weighting. In other words, the end result is a sharp tri-color Jupiter using just two filters!

Figure 8.9. The LRGB tool in Maxim DL. In the example, an LRGB image of a low-altitude Jupiter is being created using infrared as red, blue as blue, a simulated green (red plus blue averaged), and an infrared luminance with a 50% weighting. In other words, the end result is a sharp tri-color Jupiter using just two filters!

Anyway, back to the plot. The clever bit is that numbers between 0 and 1, whatever power they are raised to, stay between 0 and 1. This is the essence of the gamma function. In addition, 0 raised to any power stays at 0 and 1 raised to any power stays at 1.

The gamma function is generally represented by the following formula: final pixel brightness = original pixel brightness raised to the power 1/gamma, where the original pixel Brightness is between 0 and 1. Or, FPB = OPB1/y. If gamma (y) is set to 1, then FPB = OPB, i.e., there is no change in brightness. However, if gamma is less than 1, the mid-range brightness will be dimmer than before; if gamma is more than 1, the mid-range brightness will be brighter than before.

Using real numbers, with the original mid-range brightness of 0.5: With a gamma of 0.7, FPB = 0.51/07 = 0.37, i.e., brightness has dropped from 50% to 37%. With a Gamma of 1.3, FPB = 0.51/13 = 0.59, i.e., brightness has increased from 50% to 59%. But in each case, the minimum, 0%, and maximum, 100%, brightness will not change.

At this point, the reader may wonder why I am laboring this mathematical point so much, especially as the brightness variations in my example appear so trivial. However, when you see the effects of a gamma variation on a planetary image your opinion may well change! Spherical planetary objects with subtle features can show significant improvement when the gamma is reduced. The effect is especially noticeable with Jupiter, where it is advisable to set the webcam's own gamma very low to start with. While it is advantageous to retain the darkest and brightest (e.g., Jupiter's equatorial zone) features on a planet at their original values, reducing the brightness of the mid-tones reveals substantial details in Jupiter's brighter regions; details that, with a high gamma setting, would seem over-bright and washed out. The advantage of a gamma reduction (combined with unsharp mask/wavelet processing) means that the maximum fine-detail contrast can be achieved without the planetary limb disappearing or the planetary equator whiting out. Registax has a built-in gamma function tool for adjusting the gamma of the final image (Figure 8.10).

Altering the gamma on Saturn can enable fine gradations in the polar regions to be captured, while not saturating the equatorial region and maintaining a good brightness to the rings. In the era of photography, two of the biggest planetary hassles were preventing Jupiter's limb regions from darkening and disappearing and stopping Saturn's rings from doing the same. With careful tweaking of brightness, contrast, and gamma in Registax, both features can be saved from disappearing into the blackness, and a nice, punchy, high-contrast image can be preserved, too.

Figure 8.10. Clicking the Gamma tab in Registax brings up a useful graph showing how much the mid-range brightness of the final image is being altered.

Preserving the Jovian limb is essential when trying to measure the positions of features on the globe.

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