The LITE instrument operates at a distance above the Earth (referenced to a geoid model of the Earth) given by Shuttle Altitude. At each laser pulse, a backscatter profile is digitized for each channel (wavelength). The digitization does not begin immediately after the laser pulse, but is delayed by a time given by the Digitizer-on Delay. The Digitizer-on Delay begins with the 10 Hz Clock pulse, which precedes the laser pulse by 200.26 microseconds for laser A, and 200.28 microseconds for laser B. The time between the rising edge of the 10 Hz clock pulse and the initiation of the laser light (either 200.26 or 200.28 microseconds) is referred to as laser time delay.
The LITE Level 1 data profiles consists of 3000 data samples for all three channels. Each sample in the backscatter profile is related to backscatter from a particular altitude. Thus, for a given value of i, H(i) is the altitude (above the geoid) from which the signal S(i) was backscattered. In addition to being dependent upon the altitude, the backscatter signal is also a function of the distance from the lidar to the scattering volume, called the Range, R(i). Successive data samples, S(i) and S(i+1), correspond to measurements that were made at times separated by 0.1 microseconds.
The Range Calculation
The distance from the Shuttle to the Earth is the vertical component distance from the Shuttle to the scattering volume plus the distance from the scattering volume to the Earth.
Shuttle Altitude = H(i) + R(i) * cos(off-nadir angle)
H(i) - the distance from the scattering volume to the Earth (using reference geoid model.)
R(i) - the range
off-nadir angle - the pointing direction of LITE relative to nadir. The off-nadir angle is approximately 5 degrees. The calculation of off-nadir angle is performed using the Space Shuttle Attitude Vector (pitch, roll, and yaw). Nadir is along the line normal to the surface of the reference geoid. The normal to the surface is the direction that a plumb bob would hang were it not for local anomalies in the Earth's gravitational field.
The previous equation can be rewritten to determine the Range:
R(i) = ( Shuttle Altitude - H(i) ) / cos(off-nadir angle)
(The height and range values, H(i), Shuttle Altitude, R(i), are in units of kilometers, and the off-nadir angel is in units of degrees.)