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arXiv:1412.3207 · Physical Review A

Accurate multipixel phase measurement with classical-light interferometry

Mandeep Singh, Kedar Khare, Anand K. Jha, Shashi Prabhakar, Ravindra Pratap Singh

Published Feb 12, 2015• 38 citations
arXivHTMLPDF

Abstract

We demonstrate accurate phase measurement from experimental low photon level interferograms using a constrained optimization method that takes into account the expected redundancy in the unknown phase function. This approach is shown to have significant noise advantage over traditional methods, such as balanced homodyning or phase shifting, that treat individual pixels in the interference data as independent of each other. Our interference experiments comparing the optimization method with the traditional phase-shifting method show that when the same photon resources are used, the optimization method provides phase recoveries with tighter error bars. In particular, rms phase error performance of the optimization method for low photon number data (10 photons per pixel) shows a $>5\ifmmode\times\else\texttimes\fi{}$ noise gain over the phase-shifting method. In our experiments where a laser light source is used for illumination, the results imply phase measurement with an accuracy better than the conventional single-pixel-based shot-noise limit that assumes independent phases at individual pixels. The constrained optimization approach presented here is independent of the nature of the light source and may further enhance the accuracy of phase detection when a nonclassical-light source is used.

DOI
10.1103/physreva.91.021802

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We demonstrate accurate phase measurement from experimental low photon level interferograms using a constrained optimization method that takes into account the expected redundancy in the unknown phase function. This approach is shown to have significant noise advantage over traditional methods, such as balanced homodyning or phase shifting, that treat individual pixels in the interference data as independent of each other. Our interference experiments comparing the optimization method with the traditional phase-shifting method show that when the same photon resources are used, the optimization method provides phase recoveries with tighter error bars. In particular, rms phase error performance of the optimization method for low photon number data (10 photons per pixel) shows a >5\ifmmode×\else\texttimes\fi>5\ifmmode\times\else\texttimes\fi{}>5\ifmmode×\else\texttimes\fi noise gain over the phase-shifting method. In our experiments where a laser light source is used for illumination, the results imply phase measurement with an accuracy better than the conventional single-pixel-based shot-noise limit that assumes independent phases at individual pixels. The constrained optimization approach presented here is independent of the nature of the light source and may further enhance the accuracy of phase detection when a nonclassical-light source is used.
The use of phase-shifting interferometry (PSI) in the ultra-low-light region would open the way for important applications, such as imaging of phototoxic substances and sensing of ultrafast phenomena. In the ultra-low-light region, the statistical nature of photons can be a dominant source of noise compared with other noise caused by experimental instruments. Here we theoretically derive the precision limit determined by the statistical nature of photons for simultaneously measuring the transmittance and phase of a sample with PSI. We show that the precision of PSI depends on the phase and transmittance themselves. We also show a trade-off relation between transmittance and phase. Then we compare PSI with sequential optimal measurements in which the transmittance and phase of a sample are separately measured for each corresponding optimal measurement. We also discuss the case where the input number of photons fluctuates with a Poisson distribution and show that the fluctuation affects both the transmittance and phase precision for PSI.
Optical phase determination using just a few photons is crucial for applications in biological imaging and quantum information processing, yet is hampered by shot noise from the source and readout noise from the sensor. Employing a skipper CCD, which can arbitrarily decrease readout noise, the authors investigate these noise sources individually and demonstrate a significant improvement in detection fidelity with reduced detector noise. With fewer than three photons per pixel, the accuracy of phase estimation suffers, regardless of detection noise. This insight highlights the skipper CCD's potential to enhance high-fidelity phase detection in ultralow-light scenarios.
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Closure phase enables imaging with ground-based interferometric arrays by canceling telescope-dependent phase errors due to atmospheric fluctuations. It can be obtained by measuring fringe phases on individual baselines forming a triangle and summing them. We show that closure phases can be measured more accurately with fewer photons by performing joint measurements on multiple photons. We first establish that at least three photons from the same atmospheric temporal phase-stability window are required for closure-phase information to survive the unknown telescope-dependent phase noise, and show that joint three-photon measurements already provide an advantage over single-photon measurements in the minimal three-telescope setting. We then turn to large arrays and consider estimating all bispectra---complex quantities whose phases are the closure phases---under a global mean-square error criterion. Although an mmm-telescope array contains Θ(m2)Θ(m^2)Θ(m2) independent triangle bispectra, we show that physical constraints on the visibilities make the total information content grow only nearly linearly with mmm at fixed accuracy. Exploiting this structure, we construct an efficient protocol using at most three-photon joint measurements with photon cost O~(m)\tilde{O}(m)O~(m), whereas any sequential single-photon protocol requires Ω(m2)Ω(m^2)Ω(m2) photons. When the number of detected photons per temporal stability window scales linearly with the array size, this allows the required exposure time to remain independent of mmm up to logarithmic factors. We further analyze the complementary high-precision regime using multiparameter quantum metrology and find a similar advantage for collective measurements. Overall, our results show that quantum information processing techniques can substantially improve the sensitivity and robustness of optical interferometry.
Optimizing the sensitivity for interferometric measurement of optical phase involves maximizing the intensity of the illuminating light source and minimizing any noise sources. Limits to the light source intensity may arise from the availability of a stable high-power laser or from damage to the system being measured. For example, we describe here a scanning confocal polarization microscope designed to image the dynamics of nerve networks. In this case the light intensity limit is set by several factors, including the scanning rate, the required response time and damage limits of the biological system. Assuming a stable experimental configuration for the interferometer and light source, the limiting noise source for visible light interferometry is shot-noise associated with the quantum state of the light inputs to the interferometer. Shot-noise can be thought of as arising from vacuum fluctuations entering the dark input port of the interferometer.(1) These vacuum field fluctuations combine with the light entering the other port to cause shot-noise in the detected photocurrent at the output ports of the interferometer. This shot-noise current normally limits the measured phase variance Δϕ to a value of 1/N where N is the average number of photons detected in a measurement interval. We describe an experiment which demonstrates that this shot-noise limit can be improved by injecting squeezed vacuum into the normally dark input port.(2) In this case the phase variance is reduced below the 1/N limit by the degree of squeezing. In contrast to early experiments,(2) we are now operating the interferometer in a dark fringe mode(3–5) in order to avoid setting a limit to the light level caused by detector saturation (near 1 mW).