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Phase-sensitive amplification for imaging resolution improvement and plasma interferometry

Zun Huang

Published Jan 1, 2009• 0 citations

Abstract

The Rayleigh criterion sets a classical limit on the resolution of optical imaging systems, which brings challenges in remote sensing of spatial information. According to the Rayleigh criterion, only a limited control of resolution can be accomplished by adjusting the optical wavelength or aperture diameter. The resolvability of optical imaging systems can also be represented in terms of the signal-to-noise ratio (SNR). The optical parametric amplier (OPA) is a common nonlinear device used in a variety of applications, such as imaging, quantum information, and ultrafast laser science. It has been shown that when the OPA is operated as a phase-sensitive amplifier (PSA), no quantum noise is added thus preserving the SNR. In this thesis, the hypothesis testing from the classical information theory has been applied to the problem of distinguishing distant point sources. It is numerically demonstrated that an improvement of resolution beyond the classical limit and SNR enhancement could be achieved by utilizing the PSA operated in spatial domain. Plasma diagnostics deducts information of important parameters (such as temperature, plasma density and confinement) in magnetic confinement fusion (MCF) reactions. Interferometer can be used to measure the refractive index of plasma which is correlated with the plasma density. A Mach-Zehnder type interferometer enhanced by the PSA is studied. It has been found that the effect of the PSA is to increase the minimum resolvable interference fringe shift caused by plasma density perturbation so that a better resolution of the interferogram can be obtained. This method may enable significant improvement in plasma density measurement.

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The Rayleigh criterion sets a classical limit on the resolution of optical imaging systems, which brings challenges in remote sensing of spatial information. According to the Rayleigh criterion, only a limited control of resolution can be accomplished by adjusting the optical wavelength or aperture diameter. The resolvability of optical imaging systems can also be represented in terms of the signal-to-noise ratio (SNR). The optical parametric amplier (OPA) is a common nonlinear device used in a variety of applications, such as imaging, quantum information, and ultrafast laser science. It has been shown that when the OPA is operated as a phase-sensitive amplifier (PSA), no quantum noise is added thus preserving the SNR. In this thesis, the hypothesis testing from the classical information theory has been applied to the problem of distinguishing distant point sources. It is numerically demonstrated that an improvement of resolution beyond the classical limit and SNR enhancement could be achieved by utilizing the PSA operated in spatial domain. Plasma diagnostics deducts information of important parameters (such as temperature, plasma density and confinement) in magnetic confinement fusion (MCF) reactions. Interferometer can be used to measure the refractive index of plasma which is correlated with the plasma density. A Mach-Zehnder type interferometer enhanced by the PSA is studied. It has been found that the effect of the PSA is to increase the minimum resolvable interference fringe shift caused by plasma density perturbation so that a better resolution of the interferogram can be obtained. This method may enable significant improvement in plasma density measurement.

Classical information theory can be used to quantify the resolution performance of optical imaging systems. When an optical parametric amplifier (OPA) operated as a phase-sensitive amplifier (PSA) in the transverse spatial domain is used for point source imaging, the angular resolution improvement can approach the de Broglie resolution (i.e. Heisenberg limit). In this paper, classical information theory is employed to quantify the signal-to-noise ratio (SNR) improvement for both an ideal and a realistic multimode PSA applied to the problem of sub-Rayleigh imaging. When only considering the noise originating from the detector, the SNR improvement is found to scale quadratically as a function of the PSA gain, in the limit of noise power comparable to signal power. Differences in performance of an ideal PSA and a realistic PSA are discussed.

A novel quantum phase amplification (QPA) technique is proposed to enhance the spatial resolution of passive imaging systems, without the commensurate increase of the aperture size. The key component of this approach is the production of phase-amplified light, a squeezed state of the electromagnetic field that can be generated in phase-sensitive three-wave mixing (PSTWM). We have established the theoretical basis for QPA using PSTWM and theoretically derived the conditions for the operation of the ubiquitous PSTWM realized by using standard laser technology. In our approach sub-Rayleigh imaging can be explored to perform the super-resolution enhancement of remotely sensed data. We applied the PSTWM to improve the distinguishability of two point sources in several scenarios. In addition, detector segmentation was modeled to optimize the signal-to-noise ratio.

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.

A nonlinear interferometer uses nonlinear elements as beam splitters to split and to recombine optical waves for interference. As a result, the interference fringe size has a nonlinear dependence on the intensity of the field for phase sensing and leads to an enhanced phase signal. In this paper, a practical scheme of nonlinear interferometry for precision phase measurement is analyzed with parametric amplifiers as the nonlinear beam splitters. It is found that the signal due to phase shift is enhanced by a factor of the amplification gain as compared to a linear interferometer with the same phase-sensing light intensity while the quantum noise is kept at the vacuum level, thus, effectively increasing the signal-to-noise ratio (SNR) beyond the standard quantum limit. Furthermore, the scheme is not as sensitive to the detection loss as the linear scheme with a squeezed state for noise reduction. However, losses inside the interferometer limit the enhancement factor in SNR. We apply the concept to a Michelson interferometer but with parametric amplifiers involved for gravitational-wave detection. We find that effective power is increased by the gain of the amplifiers without actually increasing the cycling power inside the interferometer. Furthermore, the full benefits with squeezed input and variational output or the combination of a quantum nondemolition interferometer for sensitivity beyond the standard quantum limit apply here with even better results. Such a nonlinear interferometer will find wide applications in precision measurements.