FSO Acquisition and Tracking
Stare acquisition probability, raster scan lines and time over the 3σ uncertainty cone, beacon margin and the quadrant-detector tracking error for a free-space optical terminal.
Stare acquisition probability
4.40 %
target inside the FOV without scanning
Raster scan
10 lines, 0.573 s
the 2U square holds 99.46 % of targets
Beacon margin
10.0 dB
above sensitivity
Tracking SNR (voltage)
10.0 (20.0 dB)
P_beacon / (NEP·√B)
Quadrant-detector NEA (rms per axis)
0.913 µrad
(3π/16)(λ/D)/SNR, point source
Diffraction angle λ/D
15.5 µrad
spot size on the quadrant cell
Stare probability and raster scan time vs FOV
Stare: with a circular Gaussian pointing error (σ = U/3 per axis), the target falls inside a FOV of full angle Θ with probability 1 − exp(−(Θ/2)²/2σ²). Raster: lines spaced by Θ sweep a square of side 2U, so N = ⌈2U/Θ⌉ lines take N·2U/ω, with no turnaround, overlap or dwell time.
Tracking: a quadrant detector locates a diffraction-limited spot to (3π/16)(λ/D)/SNR rms, SNR being the voltage SNR of the four quadrants summed (Tyler and Fried, 1982). These are first estimates for sizing a terminal, not a simulation of an acquisition sequence.
Model and references
Illustrative. A simplified model that shows trends and orders of magnitude. Don't use its numbers for design. About the tiers
Circular Gaussian pointing error; raster without turnaround, overlap or dwell; quadrant-cell NEA (3π/16)(λ/D)/SNR for a point source. A sizing estimate, not an acquisition-sequence simulation.
- Tyler G. A., Fried D. L. (1982). Image-position error associated with a quadrant detector. J. Opt. Soc. Am. 72(6), 804–808. RMS error π√((3/16)² + (n/8)²)(λ/D)/SNR, n = 0 for a point source. doi:10.1364/JOSA.72.000804