The cables that connect the IRAC Cryogenic Assembly (the detectors) to the Warm Electronics Assembly (the readout electronics) had a characteristic time constant similar to the rate at which individual pixels were read. As a result, all pixels had an “echo” or ghost in the following readout pixel (Figure 5.6). Since the pixels were contained in four readout channels, the “next” pixel was actually four pixels to the right. The first pixel read out in an IRAC image was the first data byte in the image, and was situated in the lower left corner in most astronomical display software. This effect was corrected for by using the known readout order of the pixels. Starting at the first pixel, we corrected the following pixel, and so on.
Figure 5.6: Correction of cable-induced bandwidth error by iracebwc. The illustrated data show a cosmic ray hit.
An additional wrinkle was that the time required to go from the end of one row to the beginning of the next was slightly longer (by 75%) than the time to go from one column to the next in the same row. As a result, a slightly different coefficient had to be applied. The task was simplified by two things. First, the effect was so small that it was only necessary to correct the following pixel, as the next echo was below 10–5 times the original in intensity. Second, the time of the effect was much faster than the echo decay time. Thus, the problem needed only to be solved in one direction. The current bandwidth coefficients are given in Table 5.1. They are applied using
where A is the pixel intensity in DN and κ is the correction coefficient for a given readout channel (of 4). A different value of κ was used for correcting the first four pixels in a row, based on the pixel values of the last four pixels of the previous row.
5.1.10 Dark Subtraction I: ffcorr (“first frame effect” correction) and labdarksub (labdark subtraction)
The true dark current in the IRAC detectors was actually very low - the most notable dark current features were the electronic glows seen in the Si:As arrays (channels 3 & 4). However, the IRAC arrays experienced considerable pedestal offsets which were commonly of the order of tens of DN. These offsets were dependent on the Fowler sampling, exposure time, and operation history of the arrays, and were thought to be due to very small thermal changes in the internal IRAC cold electronics. The most significant of these offsets was the first frame effect: the laboratory measurements showed that the dark patterns and DC levels changed as a function of the time elapsed between the end of the previous frame and the start of the current frame (called “delay time”). The first frame in a series of exposures was most affected, and therefore this effect is called the first frame effect. During cryogenic operations, channel 1 had very significant variations in offset, compared to the low background in that channel. Channel 2 had very small variations in offset. Channel 4 has significant variations, though they are very small compared to the background. The most significant first frame effect by far is in channel 3. Figure 5.7 shows how the DC levels of darks changed as a function of delay time.
In a sequence of images with the same frame time and Fowler number, the variation from one image to the next consists principally of a uniform change over the whole image. To a much smaller extent, there is also a change in the relative offsets on each of the four outputs of an array (pinstriping) and a small spatial gradient across the image. True dark current and multiplexer glow carry with them the usual shot noise in the number of charges collected at the integrating node, but the rest of the Fowler bias (effective bias due to read strategy) presumably is due to relaxation in the multiplexer and temperature changes. The noise in pixels with low dark current and low glow is the same as the read noise from the multiplexer, so the dark offset variations do not add to the pixel noise. In general, the first frame of any sequence of images tends to have a different offset from the others, because it tends to have an interval, frame time, or Fowler number different from its preceding image. The largest dark offsets occur when a frame is taken with a very short interval from the preceding image, which occurs when multiple frames are commanded at once (using “repeats”).
In the warm mission, the “first-frame effect” is less pronounced in total offset in both arrays. At 3.6 μm, the average offset is 40 DN compared to 80 DN in the cryogenic mission for delay intervals of 7 to 40 seconds. For both arrays, a gradient in the “first-frame effect” has been noted. These residuals will mainly affect measurements of diffuse low surface brightness sources.
Due to the decision not to use the shutter on IRAC for dark and flat measurements, we had a somewhat sophisticated dark subtraction procedure. There were two steps for the dark subtraction, one using a dark from the ground-based laboratory measurements (called “labdarks”), and another using a delta dark which was the difference between the labdark and the skydark measured in a low zodiacal light region.
In the first step of dark subtraction, we subtracted a calibrated labdark from the data. This labdark subtraction occurred before the linearization of the array, so that we could linearize the data as well as possible. The labdark subtraction was handled by a combination of modules including labdarksub and ffcorr, depending on which kind of labdark data were needed. In some observing modes (subarray mode, shortest frames within the HDR mode, and the first frame of an observation or AOR), not enough data were available to construct delay time dependent darks. In such cases, a single mean dark has been computed using 30 seconds as a delay time, and it was used as a labdark. The labdarksub module subtracted this mean labdark. The correction of the first-frame effect for all other frames was handled by the ffcorr module, which interpolated the library of labdarks taken at different exposure times with different delay times, and created a labdark corresponding to the particular delay time of the frame being calibrated. These delay time dependent darks were then subtracted from the iracebwc-processed frame. Therefore, ffcorr required a number of different labdarks taken with different delay times to calibrate properly. These were taken pre-launch and were loaded into the calibration database. Note that as there were no prelaunch labdarks for warm mission operating temperatures, labdarks were not used in the warm mission pipeline. IRAC pipeline determined the delay time (header keyword INTRFRDLY), and the labdark file (header keyword LBDRKFLE) that was subtracted, and placed these within the header keywords of the BCD.
Figure 5.7: First frame effect: dark counts as a function of interval between frames. Each symbol is the mean dark signal in one output of each array, averaged over a box near the center of the array. The dashed curves are multiple exponential fits to the means in the set of 48 images, with the first image excluded. The lower portion of each panel shows the residuals, in electrons, between the data and the fitted curves. This figure is for a 30 second frame time.
The second step of the dark subtraction used a delta-dark found in the skydarksub module described below. This skydark, described in Section 4.1, was subtracted from the IRAC image after the linearization, and should have removed any additional dark features that were not present in the labdarks, but existed in the flight data. Note that the delta-dark included the sky background around the low-zody region.