|Figure 4: A raw image from a 34-second exposure of echelle position 2 of Ori. The faint stripes of brighter intensity are caused by electrical interference, described in §7.2. The blotches result from variations in sensitivity (of order 50%) caused by damage to the photocathode (§6.1.3). One blotch that is darker than the others (3/4 of the way from left to right, 2/3 of the way from top to bottom) is caused by a ``hole'' in the CCD dark current, i.e., a small circular patch where the level is lower than normal. It is eliminated when a dark current pattern (at an appropriate temperature) is subtracted (§7.3). A prominent dead column is responsible for the top-to-bottom black line, and another bad column (not so obvious) extends below the short, black, vertical line near the top right of the image. Defective individual pixels or small groups of pixels (§7.4) can also be seen in the picture.|
A classical way to remove uniform vertical stripes added by some instrumental effect is to subtract each column's mean or median from all of its pixels. No harm is done to the scientific data, unless the original, correct image itself has long, vertical features. This process almost works for the IMAPS spectra, except for the fact that photocathode blotches and the strongest features in the brightest orders influence entire columns and vertical ripples are then introduced.
In a Fourier transform of a picture (Fig. 5), the electrical interference that must be removed has all of its energy at the y frequency equal to 0 and is mostly distributed over moderate and large x frequencies. By contrast, the useful image information lacks this extreme concentration and has most of its power at low x and y frequencies. Thus, to remove the electrical interference, we completely suppressed all amplitudes associated with frequency components on the y=0 line above 40 cycles per frame. For lower frequencies, we multiplied the amplitudes in the line by a Hanning window function so that there was a smooth transition from no attenuation at zero frequency to full attenuation at 40 cycles. A reverse transform after this microsurgery produces a picture of the spectrum that is completely free of the vertical lines (except for the two bad columns) but is otherwise unchanged.
Figure 5: An image with intensities proportional to the logarithm of the Fourier transform (times its complex conjugate) of the exposure shown in Fig. 4. The origin has been shifted to the center of the picture, to make it easier to see important structures near zero frequency in x or y. Practically all of the energy in the horizontal line (y frequency = 0) is caused by the electrical interference discussed in §7.2. The patches above and below the center (x frequency equal to 0 and a y frequency of about 50 cycles per frame plus a weak 2nd harmonic) are caused by the echelle orders.