Intensity Correlation Measurements Research Articles

Super-resolving interference without intensity-correlation measurement

The high-order intensity correlation function of $N$-photon interference with thermal light observed in a recent experiment [S. Oppel, T. B\"uttner, P. Kok, and J. von Zanthier, Phys. Rev. Lett. 109, 233603 (2012)] is analyzed. The terms in the expansion of the $N\mathrm{th}$-order correlation function are put into three groups. One group contributes a homogeneous background. Both of the other two contribute $(N\ensuremath{-}1)$-fold super-resolving fringes. In principle they correspond to coherent and incoherent superpositions of classical optical fields, respectively. Therefore similar super-resolving fringes can be obtained without intensity-correlation measurements. We report the experimental results of the coherent and incoherent super-resolving diffraction fringes, which are observed directly in the intensity distribution. The $N\ensuremath{-}1$ sources in both the coherent and incoherent cases are set in certain definite positions. In the coherent case, moreover, the phase difference between two adjacent source fields is $\ensuremath{\pi}$. The fringe visibility is unity in the incoherent case, while it decreases as $N$ increases in the incoherent case.

Extracting the phase information from atomic memory by intensity correlation measurement.

We demonstrate experimentally controlled storage and retrieval of the optical phase information in a higher-order interference scheme based on Raman process in (87)Rb atomic vapor cells. An interference pattern is observed in intensity correlation measurement between the write Stokes field and the delayed read Stokes field as the phase of the Raman write field is scanned. This result implies that the phase information of the Raman write field can be written into the atomic spin wave via Raman process in a high gain regime and subsequently read out via a spin-wave enhanced Raman process, thus achieving optical storage of phase information. This technique should find applications in optical phase image storage, holography and information processing.

Sub-Rayleigh limit imaging via intensity correlation measurements**Project supported by the National Major Scientific Instruments Development Project of China (Grant No. 2013YQ030595), the Hi-Tech Research and Development Program of China (Grant No. 2011AA120102), and the National Natural Science Foundation of China (Grant No. 11275024).

We demonstrate sub-Rayleigh limit imaging of an object via intensity correlation measurements. The image completely unaffected by the disturbance of diffraction-limit is achieved under the condition that the imaging system has an appropriate field of view. The resolution of this sub-Rayleigh limit imaging system is only tied to the lateral resolution of the illumination light.

X-Band Interferometric SAR Observations of Baltic Fast Ice

Detailed mapping of fast-ice deformation can be used to characterize the rheological behavior of fast ice and subsequently improve sea ice modeling. This study uses interferometric synthetic aperture radar to map fast-ice deformation with unprecedented spatial resolution (meter range) and sensitivity (cm-mm range). Two interferometric acquisitions, each with a temporal baseline of 24 h, were performed by the X-band SAR satellite constellation Cosmo-SkyMed over the northeast Bay of Bothnia in the middle of the 2012 ice season. The first interferogram shows deformation of the fast ice due to force from impinging drift ice, and the normal strain within the fast ice is measured. Complementary intensity correlation measurements reveal a slow movement of the drift ice toward the fast ice. The second interferogram exhibits a low fringe rate over the fast ice with fringes being aligned along the coastline. Deformation appears to be stronger around leads, skerries, and grounded ice ridges. It is also observed that the coherence images provide information that is complementary to the information in the backscatter images.

Quantitative phase-contrast imaging through a scattering media.

We report a new technique for the recovery of quantitative phase and amplitude information of an object hidden behind a scattering medium. Two-point intensity correlation measurement together with digital holography principles are utilized for this purpose. The hologram information of the object and a reference beam is scrambled by the presence of a scattering medium in its path. A direct digital holographic recording of this scattered light does not lead to the reconstruction of actual object information. We propose the idea of recovering this hologram information from the spatially fluctuating field of a laser speckle pattern using the intensity correlation, and subsequently apply digital reconstruction of the hologram for recovery of quantitative phase and amplitude information of objects hidden by a random diffuser.

Intensity interferometry of single x-ray pulses from a synchrotron storage ring.

We report on measurements of second-order intensity correlations at the high-brilliance storage ring PETRA III using a prototype of the newly developed adaptive gain integrating pixel detector. The detector records individual synchrotron radiation pulses with an x-ray photon energy of 14.4keV and repetition rate of about 5MHz. The second-order intensity correlation function is measured simultaneously at different spatial separations, which allows us to determine the transverse coherence length at these x-ray energies. The measured values are in a good agreement with theoretical simulations based on the Gaussian Schell model.

Lensless imaging based on coherent backscattering in random media

We studied lensless imaging due to coherent backscattering in random media both theoretically and experimentally. The point spread function of the lensless imaging system was derived. Parameters such as the volume fraction of the scatterer in the random scattering medium, the diameter of the scatterer, the distance between the object to be imaged and the surface of the random scattering medium were optimized to improve the image contrast and resolution. Moreover, for complicated objects, high contrast and quality images were achieved through the high-order intensity correlation measurement on the image plane, which may propel this imaging technique to practical applications.

Third-order optical intensity correlation measurements of pseudo-thermal light

Third-order Hanbrury Brown—Twiss and double-slit interference experiments with a pseudo-thermal light are performed by recording intensities in single, double and triple optical paths, respectively. The experimental results verifies the theoretical prediction that the indispensable condition for achieving a interference pattern or ghost image in Nth-order intensity correlation measurements is the synchronous detection of the same light field by each reference detector, no matter the intensities recorded in one, or two, or N optical paths. It is shown that, when the reference detectors are scanned in the opposite directions, the visibility and resolution of the third-order spatial correlation function of thermal light is much better than that scanned in the same direction, but it is no use for obtaining the Nth-order interference pattern or ghost image in the thermal Nth-order interference or ghost imaging.

Pattern recognition based on the correlated intensity fluctuations of thermal light.

Here we present a pattern recognition scheme based on the intensity correlation of thermal light. We prove theoretically that under spatially incoherent illumination the matched filtering technique can be realized in the ghost imaging field. Using the matched filtering technique, it is possible to distinguish an object from a preestablished set of objects through their ghost images, which are extracted by means of intensity correlation measurement. According to the pattern recognition scheme, we present a numerical simulation in which we can easily identify the character inserted into the object arm from a set of two characters through the position of the autocorrelation peak. This pattern recognition scheme opens up the possibility of performing coherent optical processing under spatially incoherent illumination.

Polarimetry by classical ghost diffraction

We present a technique for studying the polarimetric properties of a birefringent object by means of classical ghost diffraction. The standard ghost diffraction setup is modified to include polarizers for controlling the state of polarization of the beam in various places. The object is characterized by a Jones matrix and the absolute values of the Fourier transforms of its individual elements are measured. From these measurements the original complex-valued functions can be retrieved through iterative methods resulting in the full Jones matrix of the object. We present two different placements of the polarizers and show that one of them leads to better polarimetric quality, while the other placement offers the possibility to perform polarimetry without controlling the source’s state of polarization. The concept of an effective source is introduced to simplify the calculations. Ghost polarimetry enables the assessment of polarization properties as a function of position within the object through simple intensity correlation measurements.

Unbalanced lensless ghost imaging with thermal light

Lensless ghost imaging (LGI) with thermal light requires an equal length between the test and reference arms. When this condition is not met, the image becomes blurred. Here we propose an experimental scheme of LGI where the lengths of the two arms are not equal. Our experiment shows that when a glass rod is inserted into a longer arm, the clear image can be formed in the intensity correlation measurement of the two arms. The theoretical analysis can well explain the experimental results. The unbalanced LGI may provide an alternative scheme in practical application.

Recovery of complex valued objects from two-point intensity correlation measurement

We propose and experimentally demonstrate a technique for the recovery of the wavefront from spatially fluctuating fields using the two point intensity correlation, i.e., fourth order correlation. Assuming spatial ergodicity and Gaussian statistics for the speckle field, we connect the fourth order correlation to the modulus of the corresponding second order correlation. The idea is to retrieve the complex coherence function and consequently the wavefront using the off-axis holography. Application of this technique is demonstrated in the reconstruction of complex field of the object lying behind a weak scatterer. Experimental results of recovery of the complex field of phase objects “vortices” with three values of topological charges are presented.

Resolving microstructures in Z pinches with intensity interferometry

Nearly 60 years ago, Hanbury Brown and Twiss [R. Hanbury Brown and R. Q. Twiss, Nature 178, 1046 (1956)] succeeded in measuring the 30 nrad angular diameter of Sirius using a new type of interferometry that exploited the interference of photons independently emitted from different regions of the stellar disk. Its basis was the measurement of intensity correlations as a function of detector spacing, with no beam splitting or preservation of phase information needed. Applied to Z pinches, X pinches, or laser-produced plasmas, this method could potentially provide spatial resolution under one micron. A quantitative analysis based on the work of Purcell [E. M. Purcell, Nature 178, 1449 (1956)] reveals that obtaining adequate statistics from x-ray interferometry of a Z-pinch microstructure would require using the highest-current generators available. However, using visible light interferometry would reduce the needed photon count and could enable its use on sub-MA machines.

Intensity interferometry with more than two detectors?

The original intensity interferometers were instruments built in the 1950s and 1960s by Hanbury Brown and collaborators, achieving milliarcsec resolutions in visible light without optical-quality mirrors. They exploited a then-novel physical effect, nowadays known as HBT correlation after the experiments of Hanbury Brown and Twiss, and considered fundamental in quantum optics. Now a new generation of intensity interferometers is being designed, raising the possibility of measuring intensity correlations with three or more detectors. Quantum optics predicts two interesting features in many-detector HBT: (i) the signal contains spatial information about the source (such as the bispectrum or closure phase) not present in standard HBT and (ii) correlation increases combinatorially with the number of detectors. The signal-to-noise ratio (SNR) depends crucially on the number of photons – in practice always ≪1 – detected per coherence time. A simple SNR formula is derived for thermal sources, indicating that three-detector HBT is feasible for bright stars. The many-detector enhancement of HBT would be much more difficult to measure, but seems plausible for bright masers.

Second-order Lau effect with pseudo-thermal light

Lau effect is a self-imaging formed in the far field of a pair of gratings illuminated by spatially incoherent light. We report the experimental demonstration of the second-order Lau effect with incoherently pseudo-thermal light. Spatially periodic structures were nonlocally superposed giving rise to interference patterns in intensity correlation measurement. The experimental results are in agreement with the theoretical analysis. The second-order Lau effect can be well understood by the unfolded version of the experimental setup where the bucket detection can be thought as the incoherent illumination in classical Lau effect.

Hanbury Brown–Twiss Interferometry at a Free-Electron Laser

We present measurements of second- and higher-order intensity correlation functions (so-called Hanbury Brown-Twiss experiment) performed at the free-electron laser (FEL) FLASH in the non-linear regime of its operation. We demonstrate the high transverse coherence properties of the FEL beam with a degree of transverse coherence of about 80% and degeneracy parameter of the order 10(9) that makes it similar to laser sources. Intensity correlation measurements in spatial and frequency domain gave an estimate of the FEL average pulse duration of 50 fs. Our measurements of the higher-order correlation functions indicate that FEL radiation obeys Gaussian statistics, which is characteristic to chaotic sources.

Optimizing the use of detector arrays for measuring intensity correlations of photon pairs

Intensity correlation measurements form the basis of many experiments based on spontaneous parametric down-conversion. In the most common situation, two single-photon avalanche diodes and coincidence electronics are used in the detection of the photon pairs, and the coincidence count distributions are measured by making use of some scanning procedure. Here we analyse the measurement of intensity correlations using multi-element detector arrays. By considering the detector parameters such as the detection and noise probabilities, we found that the mean number of detected photons that maximises the visibility of the two photon correlations is approximately equal to the mean number of noise events in the detector array. We provide expressions predicting the strength of the measured intensity correlations as a function of the detector parameters and on the mean number of detected photons. We experimentally test our predictions by measuring far-field intensity correlations of spontaneous parametric down-conversion with an electron multiplying CCD camera, finding excellent agreement with the theoretical analysis.

Optical control of a quantum rotor

The possibility to coherently control a quantum rotor is investigated theoretically. The rotor is realized by an antiferromagnetic spin-1 Bose-Einstein condensate, trapped in the optical field of a Fabry-P\'erot resonator. By tuning the pumping field of the resonator, coherent control over the rotor is achieved. The technique is illustrated by the numerical simulation of a protocol that transforms the rotor's ground state into a squeezed state. The detection of the squeezed state via measurement of intensity correlations of the cavity field is proposed.

Nonuniversal Intensity Correlations in a Two-Dimensional Anderson-Localizing Random Medium

Complex dielectric media often appear opaque because light traveling through them is scattered multiple times. Although the light scattering is a random process, different paths through the medium can be correlated encoding information about the medium. Here, we present spectroscopic measurements of nonuniversal intensity correlations that emerge when embedding quantum emitters inside a disordered photonic crystal that is found to Anderson-localize light. The emitters probe in situ the microscopic details of the medium, and imprint such near-field properties onto the far-field correlations. Our findings provide new ways of enhancing light-matter interaction for quantum electrodynamics and energy harvesting, and may find applications in subwavelength diffuse-wave spectroscopy for biophotonics.

Localization of photon bunching with thermal light

We propose an experimental scheme in which two orthogonally polarized thermal light beams with antisymmetrical wavefronts are overlapped. The experimental results demonstrate that this setup can focus the beam in two-photon and multiphoton correlation measurements. The focused ``two-photon'' spot possesses subwavelength resolution, surpassing the classical diffraction limit. Since the experimental setup consists of only two right-angle-mirror devices without the help of lenses, the two-photon focusing effect does not apparently rely on the beam focusing. Physically, the phenomenon signifies that the photon bunching can be localized within a very small region through two-photon interference in contrast to the conventional Hanbury Brown\char21{}Twiss effect of thermal light. In the higher-order intensity correlation measurement, the multiphoton bunching can be limited within a very small central region while the background is greatly suppressed.