The final step is to find weighting factors, W, that will correct all three standard star images to the same value. Designating the highest of the signals as Smax, divide each filter signal level by this value:

These weight factors correct for filter transmittance and detector quantum efficiency. With most filters and CCDs, the weight factors will be something like 1.00:0.93:0.78, that is, reasonably close to ideal values of 1.00:1.00:1.00.

• Tip: AIP4Win's Color Calculator Tool makes it easy to use G2V stars for white balance. You can load these images, measure the stars and enter the altitudes at the time you made the images, and the tool will compensate for atmospheric extinction and compute suitably adjusted weighting factors for you.

Correct Images for Extinction. Now the filtered images can be white-balanced and corrected for atmospheric extinction. The images of the celestial object were attenuated in the same way that the images of the white standard were:

where Z is the object's zenith distance when the image was made, and AR , AG, and Ab are the atmospheric transmittance in the R, G, and B passbands.

Finally, we are ready to apply atmosphere and white-balance corrections to each of the filtered images to obtain corrected signals:



If there is a residual sky background component in the images, then applying these corrections will alter the sky component of the signal, but this does not matter because you can subtract the sky background as part of the process of generating a color image.

• Tip: Given a set of weighting factors, AIP4Win s Process RGB Tool will adjust a set of filtered images to the correct color balance. After they have been adjusted, the images are said to be "G2V color balanced "

20.3.3 Create the Color Image

In displaying the image, the goal is to convert corrected images into display inputs. Displays usually accept an 8-bit input for the red, green, and blue primaries, so each color can be displayed in 256 levels of intensity. The three color-channel signals going to the display device, (DR, DG, DB), are called an RGB triad.

The output floor is the smallest display value, (0, 0, 0), which appears black; the output ceiling is the greatest display value, (255, 255, 255), which is white. An input of (100, 100, 100) appears as a medium shade of gray, and an input of (192, 128, 64) displays as a light yellowish-orange. An 8-bit display is capable of producing 256 = 16,777,216 colors—more than the human visual system can distinguish as separate colors.

Given that a color image contains an average sky background that should appear as black (0, 0, 0) or a very dark shade of gray, such as (5, 5, 5), and highlights that should display as bright white (255, 255, 255), the task of the display stage is to convert the pixel values in the corrected images to display values.

Creating the display begins with determining two quantities in each image:

• S'R ,S'G , and S'B , the pixel value of any residual sky


background. This should be measured in a star-free region well away from any celestial objects in the image.

• S'R , S'rT , and S'R , a pixel value representing the

brightest significant region or detail in the celestial object. This choice is subjective—it might be the pixel value of the brightest stars in the images, of the core of a globular cluster, of a galactic nucleus, or the brightest knots in an emission nebula.

The next step is to determine which image has the greatest range, Rrgb , between the maximum value and the sky brightness:

The conversion to 8-bit display values then proceeds as follows:

where y (gamma) is a constant that corrects the nonlinear relationship between the pixel value sent to the display device and its light output. For computer monitors, the value of y is usually close to 1.8. In some computers, the graphics display card automatically compensates for monitor gamma.

The image displayed on the screen will have a black sky background; stars will show soft colors corresponding to their spectral types, and sun-like stars will appear white. Given a good set of filters, accurate measurement of G2V stars, and a good display, nebulae and galaxies appear in the precise colors they would have if you had observed them at the zenith. As a general rule, astronomical images made as described above show rather delicate colors and have an extraordinarily "natural" appearance.

20.3.4 Summary: White-Balance Using G2V Stars

It is possible to construct color images by making images through red, green, and blue color filters. The images can be corrected to accurate white balance by shooting auxiliary images of standard sun-like class G2V stars through the same filters.

1. In preparation, make short-exposure images of one or more G2V stars through the same color filters you plan to use for color imaging. Use the same exposure time for the filtered images, or always use the same exposure ratios among the filter exposures. Note the elevation angle of the G2V star(s) when you make their images.

2. Measure the total pixel value in the filtered star images, and compute the weighting factors, WR, WG, and WB, for the filter set you are using. AIP4Wii7's Color Calculator Tool makes this easy. These weight factors will remain valid until you change the filters, CCD camera, or telescope.

3. Take filtered image sets. The exposure times for the filters should either be the same or have the same ratio as the G2V exposures. Note the elevation angle of the object when you take the images. Take appropriate dark frames and flat fields. Calibrate and stack to produce a high-quality image of the subject through each filter.

4. If a sky background gradient is present in the filtered images, correct the gradient. One of AIP4Witf s Gradient Tools can do this for you.

5. Register the three filtered images to sub-pixel accuracy, and then correct each of the filtered images using its sky background value, elevation angle, and weight factors. AIP4Witfs Process RGB Tool carries out these operations.

6. Create a color image from the three corrected color channels. You can use AIP4Witfs RGB->Color function or the Join Colors Tool to meld the color channels into a single color image.

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