Applying the mathematics of quantum information to a Poisson semiclassical photodetection model, we derive fundamental limits to parameter estimation and hypothesis testing with any measurement of weak incoherent optical sources via linear optics and photon counting. Connections with our recent work on superresolution imaging are highlighted.
KEYWORDS: LIDAR, Sensors, Speckle, Homodyne detection, Reflectivity, Ranging, Signal to noise ratio, Photodetectors, Target detection, Monte Carlo methods
Theory has shown [1] that the quantum enhancements afforded by squeezed-vacuum injection (SVI) and phasesensitive
amplification (PSA) can improve the spatial resolution of a soft-aperture, homodyne-detection laserradar
(ladar) system. Here we show they can improve the range resolution of such a ladar system. In particular,
because an experimental PSA-enhanced system is being built whose slow photodetectors imply multi-pulse
integration, we develop range-measurement theory that encompasses its processing architecture. We allow the
target to have an arbitrary mixture of specular and speckle components, and present computer simulation results
demonstrating the range-resolution improvement that accrues from quantum enhancement with PSA.
Phase-sensitive amplification (PSA) can enhance the signal-to-noise ratio (SNR) of an optical measurement suffering
from detection inefficiency. Previously, we showed that this increased SNR improves LADAR-imaging
spatial resolution when infinite spatial-bandwidth PSA is employed. Here, we evaluate the resolution enhancement
for realistic, finite spatial-bandwidth amplification. PSA spatial bandwidth is characterized by numerically
calculating the input and output spatial modes and their associated phase-sensitive gains under focused-beam
pumping. We then compare the spatial resolution of a baseline homodyne-detection LADAR system with homodyne
LADAR systems that have been augmented by pre-detection PSA with infinite or finite spatial bandwidth.
The spatial resolution of each system is quantified by its ability to distinguish between the presence of 1 point
target versus 2 closely-spaced point targets when minimum error-probability decisions are made from quantum
limited measurements. At low (5-10 dB) SNR, we find that a PSA system with a 2.5kWatts pump focused to
25μm × 400μm achieves the same spatial resolution as a baseline system having 5.5 dB higher SNR. This SNR
gain is very close to the 6 dB SNR improvement possible with ideal (infinite bandwidth, infinite gain) PSA at
our simulated system detection efficiency (0.25). At higher SNRs, we have identified a novel regime in which
finite spatial-bandwidth PSA outperforms its infinite spatial-bandwidth counterpart. We show that this performance
crossover is due to the focused pump system's input-to-output spatial-mode transformation converting
the LADAR measurement statistics from homodyne to heterodyne performance.
We demonstrate a balanced-homodyne LADAR receiver employing a phase-sensitive amplifier (PSA) to raise the
effective photon detection efficiency (PDE) to nearly 100%. Since typical LADAR receivers suffer from losses in the
receive optical train that routinely limit overall PDE to less than 50% thus degrading SNR, PSA can provide significant
improvement through amplification with noise figure near 0 dB. Receiver inefficiencies arise from sub-unity quantum
efficiency, array fill factors, signal-local oscillator mixing efficiency (in coherent receivers), etc. The quantum-enhanced
LADAR receiver described herein is employed in target discrimination scenarios as well as in imaging applications. We
present results showing the improvement in detection performance achieved with a PSA, and discuss the performance
advantage when compared to the use of a phase-insensitive amplifier, which cannot amplify noiselessly.
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