|4. Color-image composition||3.|
|4.3||Assigning red, green, and blue|
|4.4||Setting the white point|
|4.5||Cutoffs, gamma, saturation|
We took pictures of galaxies for this catalog in 2 (for 82 galaxies) or 3 (for 31 galaxies) passbands. We can determine what portion of the spectrum of the galaxy is recorded on the individual frames taking into account the transmission characteristics of the atmosphere, how the aluminized mirrors reflect light, the transmission function of the filter in use, and the sensitivity of the CCD device to electromagnetic radiation at various wavelengths. In this respect the individual frames hold scientific value. On the other hand, converting a set of frames taken using different filters to a color-composite picture is not a "scientific" process. Since the human eye is not sensitive to color at very low light levels, and observers are not looking through eyepieces at large telescopes regularly when observing extragalactic objects nowadays, and because the color sensitivity of various CCD devices, photographic emulsions, and the human eye differ significantly, it is very difficult to construct a color picture "similar" to what a human observer would see by looking through a very large telescope (collecting enough light to stimulate his or her color vision). Furthermore: the Lowell data is available only in 2 bands; the Palomar data is taken in g (green), r (red), and i (infrared) bands; the Lowell data was not calibrated through standard-star observations; and foreground stars were removed (a process that leaves colored-residuals in images). This said, we outline our attempt to create a useful set of color images using our data in the paragraphs below.
It is very important to align the 3 (or 2) images that will constitute one color image. We looked at the original images (those before the step of foreground-star-removal), interactively identified a handful of stars that were not saturated and had narrow point-spread-functions, and fitted three parameters: the required rotation and the required shifts in x and y directions for the images to be aligned. In the case of the Palomar images we kept the g image unchanged and modified the r and i bands to match the g image. In the case of the Lowell images we modified the R frame to match the J picture. An overhelming majority of the fits yielded close to zero rotation. Some of the required shifts were significant, and in one case (NGC 3556) resulted in an image cropped to such a degree that considerable portions of the galaxy are not visible in the color-composite image. We used sync interpolation to rotate and to shift images.
In case of the Palomar images, where three bands are available, we assigned the bluest image (g) to blue, the medium-wavelength image (r) to green, and the reddest image (i) to red. The effective wavelengths of the g, r, and i filters are 493nm, 655nm, and 820nm, respectively. The system transmission functions are plotted in the previous section of this User Guide. These do not match closely the wavelengths we usually associate with blue, green, and red (approximately 400nm, 510nm, and 650nm) and are also far from peak sensitivities of the three cones in the human eye used in photopic (color) vision at low, intermediate, and high wavelengths (which are 430nm, 530nm, and 560nm). Nevertheless, if there are no abrupt jumps in spectra of galaxies, if spectra do not turn over in the range of 400-800 nm, the above assignments will give us useful color information. If a galaxy emits relatively more light toward short wavelengths, this galaxy will be blue with our choice of colors; similarly, if a spectrum is relatively stronger toward longer (redder) wavelengths, this galaxy in our picture will be red, or at least redder than the blue galaxy just mentioned.
Our task is a bit more difficult with the Lowell galaxies. Only two images were taken, one in the band designated as J (or sometimes as B_J, to avoid confusion with the infrared J band of the Johnson system, since this filter is "blue") and the other in the band called R. The J filter has an effective wavelength of 450nm, while R has an effective wavelength of 650nm. The system transmission functions are also plotted in the previous section. We chose to assign J as blue, the average of J and R as green, and R as red. Since we had to generate the green images using the two available pictures, these color-composite images will show less color variations than those constructed from three independent images.
Proper scaling of the individual images is necessary before the above assignments. We calibrated almost all images in our catalog (recorded how many counts would represent zero magnitude in a given image). The Palomar data was calibrated using standard stars observed during the night we spent on the mountain, but the first part of the night was not photometric. At Lowell standard-star data was not available. We constructed color-color relationships using representative galaxy spectra (see Frei and Gunn: "Generating colors and k-corrections from existing catalog data," in the Astronomical Journal, vol. 108, p. 1476, 1994). Using these tables and published B magnitudes and B-V colors for our galaxies, we could estimate the g, r, and i magnitudes of the Palomar galaxies and the J and R magnitudes of the Lowell galaxies. For the Lowell galaxies, this is the only calibration information we had; for the Palomar galaxies, this information complements the standard-star data.
One of the Palomar galaxies (NGC 4498) had no published B-V color in the literature, so the standard-star data is the only way of calibrating this galaxy. Moreover, we compared the two methods (our color-color tables and the standard-star method) of calibration in the above paper and showed 0.1-0.2 magnitude (systematic) differences between the colors obtained. To avoid this much error in the case of the Palomar galaxies we decided to use the standard-star data for calibration for all but three galaxies (NGC 3031, NGC 3198, and NGC 3319). These three galaxies were observed during the first half of the night when conditions may not have been photometric and the magnitudes obtained with the two methods may have differed significantly. Accepting the magnitudes obtained from the standard-star observations for the rest of the 28 Palomar galaxies solves the problem of NGC 4498, where color-color tables are useless in the absence of a published B-V value.
Nine of the Lowell galaxies had no published B-V colors, and since there are no standard-star magnitudes, we had to estimate the colors of these galaxies. All nine galaxies (NGC 3596, NGC 3675, NGC 3893, NGC 4030, NGC 4136, NGC 4487, NGC 4593, NGC 5334, and NGC 5669) are spirals with numerical Hubble types in the range of 3-6. Since previous studies showed that galaxy-spectra form a one-parameter sequence as the function of the Hubble type, assigning the mean color of the same Hubble type to the galaxies with unpublished data is a possible solution. We calculated the mean of B-V colors of our spirals in the catalog for numerical Hubble types 3-6. For Type=3: B-V=0.85, T=4: B-V=0.69, T=5: B-V=0.60 and for T=6: B-V=0.56. These numbers confirm the smooth behavior of the B-V vs. T relationship.
Since the effective wavelengths of our filters are different form the conventional red, green, and blue wavelengths, and are even different for the two sets of images (Palomar and Lowell), we decided to use the convention many people adopt while constructing color images: adjusting colors so that the Sun would appear white, or a shade of grey, depending on the brightness. All we had to figure out were the g-r, r-i, and J-R colors of the Sun, in order to scale are R, G, and B frames. Since we did not find published data, we had to calculate the would-be colors of the Sun ourselves. We followed an algorithm similar to the one in the paper we mentioned above. First, we obtained the filter transmission curves, combined them with the optics and CCD system efficiencies, the absorption properties of the atmosphere, and two reflections from aluminum. We obtained spectra of four spectrophotometric standard stars, multiplied the system transmission curves with these spectra, and integrated the light to obtain "instrumental magnitudes." These magnitudes differ from the magnitudes published in the literature for the same standard stars, since the zero-points of the photometric systems are usually set arbitrarily (making one's favorite standard star white and zero magnitude, to mention one method). Comparing our "instrumental magnitudes" and those values from the literature, we obtained offsets for each band. These offsets, added to the instrumental magnitudes, now provide real magnitudes.
We entered the solar spectrum from Allen: "Astrophysical Quantities" (The Athlore Press, 3rd edition, reprinted in 1983, page 172). We multiplied this spectrum with all the transmission curves of our systems (g, r, i, J, and R) and also with the standard Johnson B and V filters. After integrating, we added the instrumental offsets and subtracted magnitudes to obtain the required colors. g-r turned out to be 0.09, r-i is 0.02, and J-R is 0.87 for the Sun. We calculated B-V as well, to check our method, and recovered the quantity (0.65) well known from the literature. We scaled our frames according to these colors. This way we tied the Palomar and Lowell colors together, and unfortunately ensured to have a very pale looking set of color images.
Galaxy images represent a wide dynamic range of intensities, and CCD devices record this information much better than non-linear photographic emulsions did in the past. The central regions of galaxies can be extremely bright, with the outskirts of galaxies very faint in comparison (only slightly brighter than the background sky), however, linear CCD devices are still capable of recording useful information all over the galaxy. It is difficult to represent all this information in one single image. We gamma-corrected our images (using gamma=2.2) in order to show more detail in faint regions of the galaxy and still not saturate the bright center significantly. See the section 2 for more information on gamma correction.
We assigned a minimum and maximum threshold to each image. Counts below the minimum were set to zero, and show as black pixels in the image. Counts above the maximum were set to the maximum value, and show as much red, green, or blue (or the required combination of these three), as possible. The lower cutoff is usually the sky plus 0.7 times sigma (of the sky). This is enough to set almost all pixels belonging to the background sky to zero (black), but the faint portions of the galaxy are still visible. The upper cutoff is set to half the maximum brightness in the galaxy, that is, the sky plus 50 times sigma, whichever is lower. For all but the faintest galaxies this meant that the cutoff is actually the sky plus 50 times sigma, and in the case of some faint galaxies the cutoff was half the maximum value.
We used gamma correction between the minimum and maximum thresholds, and assigned 8 bits to all R, G, and B, forming a 24-bit color image. We saved a "ppm" (portable pixmap) file and converted that file to JPEG setting the quality index to 80 percent. This method results in a very good quality but still small, easy-to-download file.
We increased color saturation somewhat to improve the appeal of these pictures. Galaxies show up very uninteresting if colors are set correctly. Galaxies usually appear unsaturated and most probably would look similar to the human observer at low light levels to those yellowish-green pictures presented in Wray: "The Color Atlas of Galaxies" (Cambridge University Press, 1988). In order to show more color we enhanced the blue/green and red/green ratios according to:
red = red * (red/green)**1.8,
blue = blue * (blue/green)**1.8
where the power was set to 1.8 after some experimentation with different values. This is a rather strong extrapolation toward the red and the blue, but pictures are still reasonable (not oversaturated) and show observable color variations at the same time.
Some pixels around the center of galaxies usually saturate to white, making the overall level of the image bright enough to see detail in the faint regions. In seven cases (NGC 2403, NGC 2541, NGC 3031, NGC 3675, NGC 4242, NGC 4571, and NGC 5204) the sky was too bright and noisy. To solve this problem we set the lower cutoff to a higher value (sky plus 1.5-2.0 times sigma) and decreased gamma (to 1.9).
Inherent to the nature of the algorithms described above we introduce some problems to our color images. The most apparent three are cropping, noisy residuals where stars were subtracted, and some strong blue or green dots - again an artifact of star subtraction.
Copyright © 1999 by
Princeton University Press.|
Created by Zsolt Frei and James E. Gunn. Email remarks to email@example.com
This page was last updated on June 16, 1999.