* Stars fainter than mv~ 8.0 for white balance with large-aperture telescopes.

nebula-free field or to make an educated guess based on the observer's experience with similar images.

When a sky gradient is present, the values of SR ,SG , and SB vary


from place to place in the image. If the sky and the subject are clearly separated, the observer can apply a gradient correction (a function that is equal in magnitude but opposite in sign from the sky background) to the image.

• Tip: Use AIP4Win's gradient correction tools to correct sky brightness gradients in your images. These tools produce satisfactory "flat" sky from a variety of different types of sky background gradient.

As a practical matter, it is okay to defer subtracting a uniform sky background until the next step, when the corrected images are converted into display values. However, image gradients must be "flattened" before attempting to make a color image.

Section 20.3: Red/Green/Blue Tri-Color Imaging Color Balance with G2V Stars

To make accurate color images, the signal, S, must be proportional only to the flux from celestial object, f, in each passband. However, an earthbound observer can only capture signals that have been multiplied by the extraneous filter and atmospheric factors.

A reliable way to accomplish color balance is to obtain filter images of a standard object of known color. In television, photography, and digital imaging, this is accomplished by adjusting the red, green, and blue signals so that gray and white objects have the same red, green, and blue pixel value—a process known as "white balancing." Standard display devices—computer monitors and printers— are designed so that when a display receives equal color channel values, it generates gray or white on the screen or on the printed page.

In astronomical imaging, we can use main-sequence stars like our Sun, members of spectral class G2V, as white standards. Just as noontime sunlight is the accepted terrestrial standard of white light, class G2V stars comprise an astronomical standard for whiteness. Tables 20.4 and 20.5 list stars that can serve as standards for white balance.

To complete image capture, obtain images of a white standard through the same filters used for the filtered images of the astronomical object. The signal levels from a G2V white standard are:

You can see that the "balanced" stellar flux is altered by the same multiplicative factors that compromise a set of color images: the atmospheric transmit-tances, ax, the filter transmittances, tx, and the detector's quantum efficiency, qx, to yield the three signal levels: sr , sgg2v> and sb . Note that standard techniques used in stellar photometry automatically subtract the sky background from star image signal.

The filter transmittances and detector quantum efficiencies do not change from image to image and night to night. However, because atmospheric transmit-tance depends on the angular distance of the object from the zenith at the time the images are made, in theory each image requires a different atmospheric correction. In practice, however, we can model the atmospheric transmission and compensate knowing the altitude at the time when the color images were made.

Extinction Dims G2V Stars. On several nights with skies that are typical of your observing site, you make images of standard G2V stars using the same telescope, filters, and CCD camera that you normally do, noting as you do, the zenith distance (90° - elevation angle) when you make the images. Because the G2V stars are bright, the exposure times can be quite short, and you can make these im ages on a Moonlight night.

Next, measure the S/?G2V, ^gG2V> and SbG2V signals produced by each G2V star. Because these measurements are made through the atmosphere, blue light will be more strongly attenuated than green, and green more strongly than red. Thus a "white" standard appears yellow or reddish relative to the color it would appear if it had been directly overhead in the sky.

The atmospheric transmittance in each passband is:

where ZG2V is the angular distance between the standard star and the zenith, and kR , kG, and kB, are the extinction coefficients for each passband. In this formulation the atmospheric transmittance is 100% at the zenith.

Although it is possible to determine extinction coefficients for these passbands, it is entirely adequate to use typical values for the extinction coefficients and to read the atmospheric transmittances from a table.

Typical extinction values for moist, low-altitude observing sites are: kR = 0.13 , kG = 0.20 , and kB = 0.29 .

Typical extinction values for dry, high-altitude observing sites are: kR = 0.07 , kG = 0.12 , and kB = 0.22 .

To recover the signal levels that a G2V star would have had if you had observed it at the zenith, divide each observed signal by the corresponding atmospheric transmittance:

The atmospheric extinction terms cancel, leaving a signal that is the product of the G2V flux, the filter transmittances, and the sensor's quantum efficiencies. Since the relative fluxes for a G2V star are, by definition, identical to white light, the flux terms also drop out:

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