NIRC Timing Patterns and TINT

The effective integration time of an exposure depends on a number of factors, including the timing pattern, the array or subarray size and location, and various overheads. The minimum integration time available follows the functional form

T(min) = a0+a1*C*Nx*Ny+a2*Nx*Ny+a3*Ny+a4*X0*Ny+a5*Y0

where C is the length of the timing pattern (CDS_LEN), Nx and Ny are the subarray sizes in x and y, and X0 and Y0 are the starting corner of the subarray. Note that lower left subarrays start at X0 = Y0 = 0.

The coefficients of this formula (ai) can either be determined from an exhaustive analysis of the logic in the DSP code, or can be empirically measured using the frame pulses from images using various settings. It was found that the formula in use previous to 27 April 1998 is incorrect, hence an empirical analysis of frame-to-frame timing measurements was performed, using a wide variety of subarray settings. The resulting formulae showed the following discrepancies in minimum integration times for various common subarrays and timing patterns. Note that the difference in the minimum integration times (rightmost column) remains the same for a given subarray but different tint values. Hence if your integration times (per coadd, not per total image if you have coadd more than one) are long, say 20 sec, there is relatively little error in using the old formulae. However, in cases like 3-5 micron imaging, where the subarrays can be small and the integration times the minimum allowed, there can be large errors; up to 200%!
Pattern
Mode
Pattern
length
X0
NX
Y0
NY
Old
Formula
(msec)
New
Formula
(msec)
Error
(msec)
patslow
full frame
242
0
256
0
256
422.59
409.52
13.07
subll 128
242
0
128
0
128
106.03
102.94
3.09
subll 64
242
0
64
0
64
26.71
26.06
0.65
subll 32
242
0
32
0
32
6.78
6.71
0.06
subc 128
242
64
128
64
128
117.95
106.28
11.67
subc 64
242
96
64
96
64
35.98
28.89
7.08
subc 32
242
112
32
112
32
12.58
8.76
3.82
pat4xa
full frame
75
0
256
0
256
148.98
137.01
11.97
subll 128
75
0
128
0
128
37.63
34.81
2.82
subll 64
75
0
64
0
64
9.60
9.02
0.58
subll 32
75
0
32
0
32
2.50
2.46
0.05
subc 128
75
64
128
64
128
49.55
38.15
11.40
subc 64
75
96
64
96
64
18.88
11.86
7.02
subc 32
75
112
32
112
32
8.31
4.50
3.80
max12ur
full frame
28
0
256
0
256
29.37
25.02
4.36
subll 128
28
0
128
0
128
7.73
6.84
0.89
subll 64
28
0
64
0
64
2.13
2.04
0.09
subll 32
28
0
32
0
32
0.63
0.72
-0.08
subc 128
28
64
128
64
128
19.65
9.73
9.47
subc 64
28
96
64
96
64
11.40
4.21
6.52
subc 32
28
112
32
112
32
6.44
1.99
3.67

For those who would like the formulae, we compare old and new using two different types of timing patterns: rolled and unrolled. The only unrolled timing pattern in common use is currently max12ur; unrolled patterns have the keyword URMODE = 1. All units below are nanoseconds.
Normal (rolled) Patterns
Unrolled Patterns
(currently only max12ur)
Coefficient
Old formula
New formula
Old formula
New formula
a0
10,900
108,544.6
10,900
113,076.3
a1
25
24.9
12.5
12.49
a2
375
192.2
75
0
a3
5900
7471.7
5900
7752.4
a4
1400
353.3
1400
353.3
a5
7000
6962.3
7000
6962.3

Note that in the empirical fit for the new formulae, we have kept one more significant figure. If the numbers in the above table are rounded to the nearest integer, the RMS deviation from the unrolled fit increases from 0.18% to 0.38%. While this is likely to be of little consequence, we also see little point in rounding the numbers.

Also note that some parameters are very similar in the old and new formulae, while others are quite different.

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