of the line connecting them (cf
Figure 1):
A diagram of the 2MASS frame data cycle appears as Figure 1. The READ1 and READ2 readouts for each pixel occur at the two vertical dotted lines, at times t1 and t2 with respect to the pixel reset at t = 0. The dotted horizontal line, at a data number (DN) of about 8300 in the figure, represents the "offset", O, a quantity which is highly variable from camera to camera, frame to frame and pixel to pixel. The solid sloping line just above O is the dark signal as a function of time; the slope is exaggerted to make it more visible.
In the absence of a sky signal, the data value at READ1 time t1, is O+TD1, where TD1 is the "true dark" at t1. The implication of the term "true dark" is that the true dark would be 0 at time t = 0, and proportional to time thereafter (even in the dark), while the "true offset" O is constant throughout the frame, and equal to the pixel value at t = 0. Since it takes ~50 msec to read out a frame, quatities at t = 0 are really not directly experimentally accessible; yet still might affect the pixel saturation; see below. Similary, O+TD2 is the dark value of READ2 at t2. In the equations below, the symbols R1, R2, D1, and D represent the standard pipeline quantities READ1, READ2, DARK1, and DARK.
Since the slope of the dark line is exaggerated (the offset O is correct in order-of- magnitude), it is clear that what we normally call "DARK1" in the pipeline processing is really mostly offset. DARK1 is formed as an average over a few score of dark frames by the DARKS subsystem. Assuming the true dark is reasonably stable, we can describe DARK1 as
where the mean dark offset <O> is the average of O as computed by DARKS, and TD1 is the very small "true dark" correction to <O> at t1 (cf Figure 1). Similarly, the READ2 dark D2 (never actually used alone in pipeline processing) would be
The difference (DARK2-DARK1), known as DARK in the pipeline, would then be
Thus the pipeline DARK is almost entirely TD2, except for a small contribution by TD1. In fact, DARK is of the order of a few hundred DN, and not strictly positive, though its frame median generally seems to be > 0.
For the saturation analysis, a priori we do not know precisely the extent to which the saturation is an array property in the pixels, a property of the amplifiers, or some mixture of the two. That the pixel threshold histograms are often broad, and that the threshold images often show little sign of the quad boundaries, hints that the effect is mostly in the pixels rather than in the amplifiers, but this still needs to be better substantiated and quantified. However, it does seem likely that R2-O is the pixel signal that will organize the thresholds most effectively. The original version of the saturation analysis was based on
as the variable of interest. Based on the above considerations, the analysis has been revised to allow
to be studied instead.
Based on the foregoing, we can then compute all the quantities we need.
For any frame and pixel, given READ2 and READ1, we can estimate
O using the slope of the line connecting them (cf
Figure 1):
t1
where the slope is
=
(R2-R1)/(t2-t1).
So if
= t1/(t2 -
t1),
we have
,
so long as READ2 is below saturation.
The mean dark offset <O> is similarly
| <O> | = | D1 - Dt1
|
| = | D1 - D
|
using
D =
(D2 - D1)/(t2-t1).
Using all this we then get for the pixel value:
]
= (R2-R1)(1+) .
or if
= f ,
then
.
Thus (R2-R1) f is what we use
for the y value in the revised saturation fits at low light levels.
However, a problem arises with the foregoing when R2 saturates.
Then (R2-R1) f , instead of tending
to an asymptotic value as READ2 alone does,
eventually begins to drop because R1 continues to rise
slowly after R2 has saturated, so (R2-R1) decreases.
(Note that for really extreme saturation levels,
even READ2 alone does actually
drop with increasing light, rather than remaining at the maximum value.
This is a separate effect, far out of the range of interest here.)
Because we are studying the behavior in the soft saturation region, this effect
must be present even before the maximum, and so distort the resulting shape of
the saturation curve.
Therefore at high light levels we use R2 - <O>, since
<O> is a constant and involves only the darks.
The changeover from (R2-R1) f
to R2 - <O> is by interpolation between the two in the mid-range of
light levels.
A somewhat similar issue arises for the light variable x ,
discussed below, and is treated in the same way.
In order to make the control inputs and output plots directly and conveniently comparable to what has been done before, in most of the human interfaces in the revised analysis, y values have been corrected by the mean dark offset, <O> . This returns us to something close to the READ2 in the original analysis, while still removing the effect of variations in O from the thresholds. This is the meaning of the phrase "READ2 EQUIV" in some of the plot labels.
For the saturation analysis we want to plot the output pixel signal y vs the light level x. In the original analysis, READ1-DARK1 was used as an approximation to the light level, since it is unaffected by saturation in this context. However, it does suffer from the problem that it contains O, which is highly variable. This is mainly a problem at low light levels, when the variation in O may be comparable to the signal. What we really want for x, at least at low light levels, is
and using our expression above for O this is
| R1 - O - TD1 | = | t1 - TD1
|
| = | [(R2 - R1)/(t2 - t1)] t 1 - [t1/(t2 - t1)] D. | |
| = | (R2 - R1 - D) . |
This is fine at low light levels, but fails at high levels, when once again R2 saturates. The solution adopted is again to use
at low light levels, and
(which was used everywhere originally) at high levels, and interpolate smoothly between them in the mid-range.
In general the data with the new variables look similar to the older READ2 vs READ1-DARK1 set. The main exception is the histogram of the intercepts of the linear fit, which is much narrower, because the effect of the variation in O over the array has been removed.
NOTES:
