Preparing Red‐Green‐Blue Images from CCD Data

One of the reasons that our forebears were drawn to astronomy was the sheer drama and beauty of the night sky. When photography became a standard astronomical technique, it was natural to combine images taken in different bands to produce spectacular colored images of the night sky (e.g., Malin 1992, and references therein).

When CCD detectors were introduced into astronomy 25 years ago, and especially when large‐format cameras became common, astronomers were once again motivated to generate three‐color composites. CCDs are approximately linear, unlike the roughly logarithmic sensitivity curve of photographic plates, so the natural way to produce an image was to map the logarithm of the pixel intensities to the red, green, and blue brightnesses in the final image (see, e.g., Villard & Levay 2002). This algorithm produces pictures that look rather like those produced from photographs, but unfortunately it also discards a lot of information.

Let us consider CCD data taken in three bands, which we call b, g, and r (e.g., B, R, and I); we assume that these data have been background‐subtracted, if necessary linearized, flat‐fielded, and scaled appropriately. This scaling is to some extent arbitrary, as different astronomers prefer different color balances, but we have found that a conversion to f_ν (in practice to an AB scale; Oke & Gunn 1983) works well.

We desire a mapping to the range [0, 1] for each of three colors, red (R), green (G), and blue (B). The usual algorithm is

where

and where m is the minimum value to display and M is the maximum; these are chosen to bring out favored details. As mentioned in the introduction, a common choice is logarithmic (F≡ln ), but linear or square‐root stretches are also popular. The actual implementation, at least for integer input data, often uses a lookup table.

This style of mapping simulates one of the unfortunate features of photographic plates, namely that all pixels for which r, g, and b are ≥M appear white in the final image. In a photograph this white color corresponds to a lack of information, but for a CCD it is a choice made by the astronomer. In fact, for any nonlinear function F, an object's color in the composite image depends on its brightness, even if none of r, g, or b exceed M.

Fortunately, we can easily avoid these problems. Defining I≡(r + g + b)/3,⁵ set

If max _RGB ≡max (R,G,B)>1, set R≡R/ max _RGB, G≡G/ max _RGB, and B≡B/ max _RGB; if I≡0, set R = G = B = 0. In other words, the intensity is clipped at unity, but the color is correct.⁶ Additionally, it is possible to choose a more flexible functional form for F. Following Lupton, Gunn, & Szalay 1999, we take F(x)≡arcsinh(x/β), where the softening parameter β is chosen to bring out desired details; it determines the point at which we change from a linear to a logarithmic transformation— arcsinh(x)∼x for x≪1, arcsinh(x)∼ln (2x) for x≫1.⁷ The linear part is used to show faint features in the data, while the logarithmic part enables us to simultaneously illustrate structures such as spiral arms or the cores of star clusters that are significantly brighter. As an additional trick, we find that sometimes an arcsinh^1/2 stretch brings out the details of dust lanes in spiral galaxies; here, as before, the arcsinh is used to control the dynamic range.

The results of this simple change are dramatic; a given color (i.e., value of g−b and r−g) is now mapped to a unique color in the RGB image. Figure 1 shows a Sloan Digital Sky Survey (SDSS; York et al. 2000) gri composite of the galaxies NGC 6976, NGC 6977, and NGC 6978. The reader will notice that the stars, rather than all being white, show a variety of red, yellow, and bluish tints; that the spiral bulges (and the group of ellipticals to the lower right of NGC 6977) are a uniform yellowish color, while the spiral disks are blue ([O iii] and Hα appear in B and R, respectively). Furthermore, it is evident that star formation activity in the disks (as indicated by the distinctive bluish color) decreases from left to right.

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We can use the well‐known color composite of the Hubble Deep Field (HDF; Williams et al. 1996), shown in Figure 2, as a pedagogical example.

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The top row of images were prepared using equation (1), while the bottom row used equation (2). The top left panel shows the familiar STScI color image. The bottom left panel uses an arcsinh stretch and is our preferred representation of the HDF. The top middle panel is our best match to the STScI image and uses a logarithmic stretch; the middle bottom panel uses the same logarithmic function (i.e., identical values of m and M). The right‐hand pair of panels share a hard linear stretch (it is identical to the linear part of the arcsinh stretch of the bottom left panel).

Interestingly, the bottom set of panels are pretty similar, with the main difference being that the spiral arms in the lower left corner are rather better defined in the leftmost panel. It is clear that much of the morphological information is carried in the color rather than the intensity.

The bands (f450, f606, and f814) used in Figure 2 are not quite the same as those used in the SDSS composites (g, r, and i), but the astrophysical palette is similar, in the sense that the larger HDF galaxies have colors similar to those seen in Figure 1, with blue disks and yellowish bulges. The fainter objects, however, look unlike anything seen in SDSS imaging, with bright red (K‐corrected) bulges and, in some cases, bluish disks, which must be due to active star formation and the emission of far‐UV light.

Figure 3 shows the globular cluster NGC 2419. Figure 4 shows a color‐magnitude diagram of point sources in a 0.6 deg² region surrounding the cluster. The points in this diagram have the same color as the corresponding objects in the image; the cluster horizontal and giant branches stand out.

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Finally, this technique is not restricted to optical data; Figure 5 shows a Chandra X‐ray image of the supernova remnant Cas A.

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Although CCDs are wonderful detectors, they are not perfect. The SDSS data‐processing pipeline (Lupton et al. 2001) interpolates over saturation trails, which accounts for their absence from these images. Unfortunately, it is not able to correctly recover the counts in the cores of saturated stars, but we do know which pixels were involved.⁸

Equation (2) means that every pixel in the image preserves its color, even in the saturated cores of stars. We can avoid undesirable artifacts in the final picture by finding connected pixels that were saturated in at least one band and replacing them with the average color of the pixels touching the saturated region. Because we do not wish to average over the long bleed trails produced by bright stars, we only apply this procedure to saturated pixels with intensities above M. An obvious example of a bright star is seen at the bottom right of Figure 3. In this case we treated all pixels with at least 10,000 counts in any band as "saturated."

The original implementation of these algorithms was included in the SDSS image‐processing code, but fortunately stand‐alone versions are also available.⁹

Color images have traditionally been considered a luxury, but with the techniques espoused in this paper, we have found that they convey an enormous amount of information. For example, star‐forming regions have a distinctive color, and it is very clear, looking at images of spiral galaxies, how much the star formation rate varies. We encourage the reader to visit the Web page listed here,¹⁰ where, among other objects, all of the NGC galaxies in the SDSS DR1 (Abazajian et al. 2003) are presented.