* Transmittance typical of a clear night at a moist, low-altitude observing site.
• Green with wavelengths between 600 nm and 500 nm;
• Blue with wavelengths between 500 nm and 400 nm;
• Ultraviolet consists of all wavelengths shorter than 400 nm.
As we discuss color imaging, we will refer to these spectral regions as the /, R, G, B, and U passbands. With the spectrum partitioned into five passbands, a camera produces a signal that is the sum of the response in each of them:
S = FjAiQj + FrArQr + FgAgQg + FbAbQb + FvA&v (Equ. 20.4)
where S is the output signal from the camera, Fb FR, FG, FB, and Fv are light flux from the object in the five passbands; ah AR, ag, ab, and av are the transmittance of the atmosphere in each passband; and Qb QR, QG, QB, and Qv are the product of the transmittance of the telescope optics and the quantum efficiency of the CCD in each.
Consider next the signal that results when you add a filter:
+ fbtbabqb + futuauqu where tb tr, tg, tb, and tv are the filter transmittances within the subscripted passband. The signal in each passband is the product of the flux from the object, the transmittance of the filter, the transmittance of the atmosphere, and the quantum efficiency of the detector. The signal from the detector is the sum of the signals in each passband.
Now consider making images through a set of red, green and blue filters. An ideal red filter transmits all of the light only in the red passband, and blocks light in all of the other passbands:
The ideal green filter transmits only in the green passband: Tj = 0, Tr = 0, Tg = 1 , Tb = 0, and Tv = 0.
And an ideal blue filter transmits only in the blue passband: Tj = 0, Tr = 0, Tg = 0, Tb = 1 , and Ti; = 0.
Most filters fall short of the ideal, and transmit some light outside the proper passbands. Especially insidious are infrared leaks, because many CCDs reach their peak quantum efficiency in the near infrared, so that even a small leak can generate a large signal. Although filter leakage increases the signal, the signal does not result from light in the correct passband, so the inflated signal leads to inaccurate color. It is important to remember that the more closely the filter set approaches the ideal, the better the color images they will produce.
However, suppose that we do have filters that are reasonably close to the ideal. Upon substituting their transmittances into Equation 20.5, we obtain the following signals from a celestial object:
Skylight Contamination. We have focused on the flux coming from the astronomical source, but in so doing we have neglected an important contribution to the signal level—the light of the night sky background. Even at dark-sky sites, the sky background signal is often as large as or larger than that of huge nebulae, the outer arms of spiral galaxies, and faint clusters of galaxies. Under suburban skies, sky background represents the dominant source of signal in the filtered images. Thus, the actual signal level seen in an astronomical image is:
where SR ,SG , and SB are signals contributed by sky background light.
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