High-speed video

The high-speed video timing was calibrated in a way similar to that originally used for the normal-speed video: with an LED in the field of view. The LED was connected through a resistor to the GPS-based binary coded decimal (BCD) 100 ms bit. The LED would be on during odd hundred millisecond intervals and off for even intervals. The time of a sprite event within the normal-speed video was used to determine which odd or even 100 ms block was being observed in the high-speed video sequence.

Sub-frame accuracy timing was obtained by examining the brightness of the LED during an on/off transition and comparing this brightness with that when it was on for an entire frame. An LED which was observed to be relatively dim during an on$\Rightarrow$off transition must have changed state during the earlier part of the frame interval. However, a relatively dim LED during an off$\Rightarrow$on transition indicates that the LED turned on in the latter part of the frame interval, etc.

Figure B.3: Both the off$\Rightarrow$on LED transition as well as the subsequent on$\Rightarrow$off LED transition are shown for a 2000 frame-per-second sequence. The exact time of the transition within a frame can be estimated by comparing the relative brightness of the LED to when it was on throughout the frame. The horizontal white lines denote block boundaries and hence separate regions with different start and end times of integration.

In order to calculate the time of the transitions, an average LED intensity was determined before, during, and after an LED transition. This procedure was complicated by the fact that the high-speed video frame is not light-integrated simultaneously. Instead, the high-speed video frame is integrated in blocks starting from the top, as explained in Section A.1. Any measurement of intensity had to be confined to within the same block.

Table B.1: The high-speed video timing calibration procedure is shown here for the LED transitions in Figure B.3. The LED intensities are 9$\times$9 pixel averages of the 8-bit grayscale intensities within the respective LED regions. The time offset corresponds to the time elapsed for the LED transition relative to the start of light integration for the top block at index 0 during the LED transition frame.

Timing calculation for Figure B.3
	Block	LED	LED intensity [0-255]				Time
Transition	index	region	Before	During	After	Calculation	Offset
	4	top	33.2	60.7	106.2	$0.5(\frac{4}{6}+\frac{106.2-60.7}{106.2-33.2}) =$	.645 ms
off$\Rightarrow$on	5	center	31.3	89.5	139.6	$0.5(\frac{5}{6}+\frac{139.6-89.5}{139.6-31.3})$ =	.648 ms
	4	top	87.2	61.8	36.0	$0.5(\frac{4}{6}+\frac{61.8-36.0}{87.2-36.0}) =$	.585 ms
on$\Rightarrow$off	5	center	97.8	53.6	34.3	$0.5(\frac{5}{6}+\frac{53.6-34.3}{97.8-34.3}) =$	.569 ms
Average time offset: .612$\pm$.041 ms

Table B.1 shows the timing calibration procedure which was used for the 4:37:05 UT sprite event on October 6, 1997. The sprite event occurred between the LED transitions shown in Figure B.3. Calculations were performed for both the off$\Rightarrow$on and on$\Rightarrow$off transitions since the 8-bit grayscale in the digitized image may not have been linearly proportional to actual light intensity. By using both transitions, any systematic error in the intensity estimate was minimized.

The timing calibration procedure was also performed for all other high speed video sequences shown in this dissertation.