Spaceborne Laser Radar

Terry Flom

doi:10.1364/AO.11.000291

Applied Optics
Vol. 11,
Issue 2,
pp. 291-299
(1972)
•https://doi.org/10.1364/AO.11.000291

Spaceborne Laser Radar

Terry Flom

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Terry Flom, "Spaceborne Laser Radar," Appl. Opt. 11, 291-299 (1972)

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Abstract

Laser radar systems are being developed to acquire and track targets in applications such as the rendezvous and docking of two spacecraft. To search effectively for and locate a target using a narrow laser beam, a scanning system is needed. This paper describes a scan technique whereby a narrow laser beam is synchronously scanned with an equally narrow receiver field-of-view without the aid of mechanical gimbals. Equations are developed in order to examine the maximum acquisition and tracking rates, and the maximum target range for a scanning laser radar system. A recently built prototype of a small, lightweight, low-power-consuming scanning laser radar is described.

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COMPONENT	COOPERATIVE TARGET	NON-COOPERATIVE TARGET
τ₁ (electrical-to-optical conversion efficiency)	Hardware Constant	Hardware Constant
τ₂ (transmitter optical transmittance)	Hardware Constant	Hardware Constant
τ₃ (transmittance of propagation medium)	e⁻² ^α ^R	e⁻² ^α ^R
τ₄ (fraction of target subtended by trans. beam)	$\frac{Ω_{cc}}{Ω_{tb}} \approx \frac{\frac{π}{4} d_{cc}^{2} / R^{2}}{θ_{tb}^{2}}$	$\frac{Ω_{T}}{Ω_{tb}} \approx \frac{A_{T} / R^{2}}{θ_{tb}^{2}}$
τ₅ (target reflectance)	Hardware Constant	Hardware Constant
τ₆ (=τ₃)	e⁻² ^α ^R	e⁻² ^α ^R
τ₇ (fraction of receiver aperture subtended by return beam)	$\frac{Ω_{iFOV}}{Ω_{rb}} \approx \frac{\frac{π}{4} d_{R}^{2} / R^{2}}{d_{cc}^{2} / {(K_{cc} λ)}^{2}}$	$\frac{Ω_{iFOV}}{Ω_{rb}} \approx \frac{\frac{π}{4} d_{R}^{2} / R^{2}}{π}$
τ₈ (receiver optical transmittance	Hardware Constant	Hardware Constant
P_MDS (minimum detectable signal)	$\frac{Δ t I_{MDS}}{t_{d} s_{λ}}$	$\frac{Δ t I_{MDS}}{t_{d} s_{λ}}$

J_BS	Backscatter radiant intensity (w/ster)
Ω_iFOV	Receiver instantaneous field-of-view (ster.)
Θ_iFOV	Receiver Instantaneous field-of view (rad.)
S_λ	Receiver sensitivity at wavelength λ(a/w)
H_λs	Solar irradiance at wavelength λ(w/m². Å)
Δλ	Optical bandwidth (meters)
λ	Laser wavelength (meters)
A_T	Area of radar target (m²)
Ω_R	Solid angle subtended by receiver (ster.)
Ω _π	Solid angle for target reflection off lambertian surface (ster.)
N_B	Radiance of sunlit cloud background (w/cm². ster. μm)
A_R	Area of receiver collector (m²)
d_R	Diameter of receiver collector (meters)
I_dc/A	Dark current noise of detector (a/cm²)
k	Boltzmann’s constant (1.38 × 10⁻²³ joules/K)
T	Temperature (K)
ΔF	Electrical bandwidth (Hz)
R_L	Load Resistor (ohms)
L	Atmospheric Attenuation Coefficient
R	Line-of-sight range to target (m)
Ω_cc	Beam spread due to diffraction at corner cube (ster.)
Ω_tb	Transmitter beamwidth (ster.)
Θ_tb	Transmitter beamwidth (rad.)
d_cc	Diameter of corner cube reflector (meters)
Ω_T	Solid angle subtended by target (ster.)
Θ_rb	Beam spread of reflected beam off target (rad.)
K_cc	(1.22) Factor introduced by examining the central maximum to the first null of the diffraction pattern from an optical corner cube reflector.
G	photomultiplier gain
Δt	Laser pulse width (sec)
t_d	Period or dwell time between successive pulses

RANGE
MAXIMUM RANGE	94 km (=50 MILES)
RANGE ACCURACY	±0.02* OR ±10 cm (WHICHEVER IS>)
RANGE-RATE COVERAGE	0-1 km/SEC
RANGE-RATE ACCURACY	±1.0% OR ±0.5 cm/SEC (WHICHEVER IS>)
ANGLE
ANGLE COVERAGE (WITHOUT GIMBALS)
PITCH & YAW	±15° × ±15°
ANGLE ACCURACY
PITCH & YAW	+0.02° (0.35 mRAD)
MAXIMUM ANGULAR ACQUISITION VELOCITY
PITCH & YAW
WORST CASE	0.04 DEGREE/SECOND (FOR 1 KHZ SCAN RATE)
BEST CASE	0.3 DEGREE/SECOND (FOR 1 KHZ SCAN RATE)
MAXIMUM ANGULAR TRACKING VELOCITY
PITCH & YAW	1.10 DEGREE/SECOND (FOR 1 KHZ SCAN RATE)
ANGLE-RATE RESOLUTION
PITCH & YAW	±1.0% OR ±0.01 DEGREE/SECOND (WHICHEVER IS >)
ACQUISITION TIME	0–140 SECONDS

	XMTR - RCVR	ELECTRONICS

SIZE	6″ × 9″ × 21″	9″ × 9″ × 9″

WEIGHT	30 POUNDS	10 POUNDS

INPUT POWER @28 VDC	40 WATTS TOTAL

COMPONENT	COOPERATIVE TARGET	NON-COOPERATIVE TARGET
τ₁ (electrical-to-optical conversion efficiency)	Hardware Constant	Hardware Constant
τ₂ (transmitter optical transmittance)	Hardware Constant	Hardware Constant
τ₃ (transmittance of propagation medium)	e⁻² ^α ^R	e⁻² ^α ^R
τ₄ (fraction of target subtended by trans. beam)	$\frac{Ω_{cc}}{Ω_{tb}} \approx \frac{\frac{π}{4} d_{cc}^{2} / R^{2}}{θ_{tb}^{2}}$	$\frac{Ω_{T}}{Ω_{tb}} \approx \frac{A_{T} / R^{2}}{θ_{tb}^{2}}$
τ₅ (target reflectance)	Hardware Constant	Hardware Constant
τ₆ (=τ₃)	e⁻² ^α ^R	e⁻² ^α ^R
τ₇ (fraction of receiver aperture subtended by return beam)	$\frac{Ω_{iFOV}}{Ω_{rb}} \approx \frac{\frac{π}{4} d_{R}^{2} / R^{2}}{d_{cc}^{2} / {(K_{cc} λ)}^{2}}$	$\frac{Ω_{iFOV}}{Ω_{rb}} \approx \frac{\frac{π}{4} d_{R}^{2} / R^{2}}{π}$
τ₈ (receiver optical transmittance	Hardware Constant	Hardware Constant
P_MDS (minimum detectable signal)	$\frac{Δ t I_{MDS}}{t_{d} s_{λ}}$	$\frac{Δ t I_{MDS}}{t_{d} s_{λ}}$

J_BS	Backscatter radiant intensity (w/ster)
Ω_iFOV	Receiver instantaneous field-of-view (ster.)
Θ_iFOV	Receiver Instantaneous field-of view (rad.)
S_λ	Receiver sensitivity at wavelength λ(a/w)
H_λs	Solar irradiance at wavelength λ(w/m². Å)
Δλ	Optical bandwidth (meters)
λ	Laser wavelength (meters)
A_T	Area of radar target (m²)
Ω_R	Solid angle subtended by receiver (ster.)
Ω _π	Solid angle for target reflection off lambertian surface (ster.)
N_B	Radiance of sunlit cloud background (w/cm². ster. μm)
A_R	Area of receiver collector (m²)
d_R	Diameter of receiver collector (meters)
I_dc/A	Dark current noise of detector (a/cm²)
k	Boltzmann’s constant (1.38 × 10⁻²³ joules/K)
T	Temperature (K)
ΔF	Electrical bandwidth (Hz)
R_L	Load Resistor (ohms)
L	Atmospheric Attenuation Coefficient
R	Line-of-sight range to target (m)
Ω_cc	Beam spread due to diffraction at corner cube (ster.)
Ω_tb	Transmitter beamwidth (ster.)
Θ_tb	Transmitter beamwidth (rad.)
d_cc	Diameter of corner cube reflector (meters)
Ω_T	Solid angle subtended by target (ster.)
Θ_rb	Beam spread of reflected beam off target (rad.)
K_cc	(1.22) Factor introduced by examining the central maximum to the first null of the diffraction pattern from an optical corner cube reflector.
G	photomultiplier gain
Δt	Laser pulse width (sec)
t_d	Period or dwell time between successive pulses

Abstract

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Figures (10)

Tables (3)

Equations (10)

Applied Optics