Sub-Rayleigh imaging via N-photon detection

The Rayleigh diffraction bound sets the minimum separation for two point objects to be distinguishable in a conventional imaging system. We demonstrate sub-Rayleigh resolution by scanning a focused beam--in an arbitrary, object-covering pattern that is unknown to the imager--and using N-photon photodetection implemented with a single-photon avalanche detector array. Experiments show resolution improvement by a factor ～(N-N(max))(?) beyond the Rayleigh bound, where N(max) is the maximum average detected photon number in the image, in good agreement with theory.     

Sub-Rayleigh imaging via undersampling scanning based on sparsity constraints

We demonstrate that, by undersampling scanning object with a reconstruction algorithm related to compressed sensing, an image with the resolution exceeding the finest resolution defined by the numerical aperture of the system can be obtained. Experimental results show that the measurements needed to achieve sub-Rayleigh resolution enhancement can be less than 10% of the pixels of the object. This method offers a general approach applicable to point-by-point illumination super-resolution techniques.     

Sub-Rayleigh ghost imaging via sparsity constraints based on a digital micro-mirror device

In a diffraction-limited system, the imaging resolution limit is given by Rayleigh criterion. When both the image?s sparsity and the point spread function determined by the optical system?s Rayleigh diffraction limit are taken as popular a priori, sub-Rayleigh ghost imaging, which is backed up by numerical simulation and experiments, is achieved by modulating the thermal light with a digital micro-mirror device (DMD). The differences between this approach and former ghost imaging without considering the optical system?s point spread function are also discussed.     

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.     

Light intensity correlation measurements in the presence of multiple scattering

We discuss the results of a model calculation of the intensity correlation function for multiply scattered light and compare our analytic predictions with experiments.     

Performance of third-order ghost imaging with second-order intensity correlation

The third-order ghost imaging with the second-order intensity correlation is theoretically and experimentally demonstrated.The resolution and visibility of the reconstructed image are discussed,and the relationship between resolution and visibility is analyzed.The theoretical results show that a tradeoff exists between the visibility and resolution of the reconstructed image;the better the image resolution,the worse the image visibility.Numerical simulations are carried out to verify this theory,and a ghost...     

Probability theory of intensity correlation in ghost imaging with thermal light

To well reveal the imaging mechanism of ghost imaging (GI) with thermal light, we propose a probability theory using more general assumptions than existing theoretical explanations that the reference patterns obey an arbitrary identical distribution and the objects are of grayscale. It is not limited to a specific correlation function, even multi-functional variants of reference patterns can be used in correlation calculation. We have proven in both theory and experiments that the reconstruction means are linear transformations of original object's gray values and the probabilities of recovered pixel values in the pixel region of the same original gray value follow a Gaussian distribution, whose variance explains the appearance of reconstruction noise. We also derive the relationship between pattern variance and contrast-to-noise ratio under noisy conditions, which will be instructive for better pattern construction. This work will deepen the understanding of GI and enrich intensity correlation forms.     

Optical authentication via photon-synthesized ghost imaging using optical nonlinear correlation

We present a method for optical authentication via photon-synthesized ghost imaging using optical nonlinear correlation. In ghost imaging, multiple series of photons recorded at the object beam arm can be arbitrarily controlled for the generation of synthesized objects. Ghost imaging with sparse reference intensity patterns provides a channel to effectively modulate the noise-like synthesized objects during the recovery, and the reconstructed (noise-like) objects, i.e., added or subtracted information, can be further authenticated by optical nonlinear correlation algorithm. It is expected that the proposed method can provide an effective and promising alternative for ghost-imaging-based optical processing.     

Low-coherence interferometry by intensity correlation

‘Low-coherence interferometry’ is an old technique which has had a wide development recently, and is based on the fact that interference with a path difference much longer that the coherence length gives rise to a ‘channeled spectrum’, which can be detected either by a dispersive spectroscope or by a second interferometer with a variable delay. We have tested an alternative way to detect path differences in this kind of interferometry, by analyzing the output intensity fluctuation correlations by a radiofrequency spectrum analyzer, and Fourier transforming the data. This method is suitable for very long path differences. The experiments have been performed with different lengths of single-mode fibre, in Mach–Zehnder and Fabry–Pérot configurations. Received: 30 March 2000 / Revised version: 17 Juli 2000 / Published online: 20 September 2000     

The accuracy of signal intensity measurements in magnetic resonance imaging as evaluated within the knee.

Quantitative signal intensity measurements are being utilized in both clinical and research magnetic resonance imaging protocols. This paper addresses three questions in quantitative MRI measurements as evaluated within the knee: 1) the accuracy of quantitative measurements; 2) improvement of accuracy by phantom normalization; and 3) the amount of signal change that is clinically significant. Seven normal subjects were imaged on three different days within a 1-wk period. Test-tube phantoms of manganous chloride (MnCl2) were imaged posterior to the knee and were used to normalize each image. The variation in signal intensity within the same subject averaged 20% for both the anterior cruciate ligament (ACL) and the posterior cruciate ligament (PCL). The phantom variation was approximately 18%. Signal intensity normalization by background subtraction, background division, phantom division, or a combination of subtraction and division did not significantly improve either the phantom variation or the ligament variation. Given that an individual ligament intensity will be measured with standard errors of +/- 20% of its value, we calculated the minimum increase in signal intensity to be considered abnormal relative to a normal ligament. A relative signal increase of 46% can be considered pathologic with 95% confidence. These findings emphasize that quantitative measurements must be carefully assessed when being applied in clinical settings.     

Near-field acoustic intensity measurements using an accelerometer-based underwater intensity vector sensor

An accelerometer-based underwater acoustic intensity vector sensor is used to measure the acoustic nearfield of a single spherical source, and a pair of sources that vibrate in or out of phase with each other. The intensity sensor consists of co-located pressure and inertial sensors within a neutrally buoyant probe body. The design of this probe has been published previously. The measurements were performed in a large tank at a frequency of 5 kHz for two sources of different sizes, corresponding to ka values of 0.7 and 1.2 respectively, where k is acoustic wavenumber and a is the source radius. By way of validation, the acoustic intensity field from two closely spaced, interacting spherical radiators is predicted using the exact theory of the translational addition theorem for spherical wave functions. The predictions using this theory compare favorably well with the measured intensity field. Beam pattern and calibration data obtained for the intensity sensor suggest that underwater acoustic intensity generated by simple and complex sources can be measured to an accuracy of ±1 dB provided that ka is less than approximately 0.2.     

The impact of light polarization on imaging visibility of Nth-order intensity correlation with thermal light

The relationship between the imaging visibility of arbitrary Nth-order intensity correlation with thermal light and light’s degree of polarization is investigated. It is shown that for the same order correlation, the value of visibility with partially polarized light is greater than that with natural light but smaller than that with completely polarized light, and the visibility in all three cases is remarkably enhanced as N increases.     

Space-time correlation function of spatially and temporally integrated laser speckle intensity in a two-lens imaging optical system

An analytical form of the cross correlation function in a two-lens imaging optical system has been obtained by calculating the integrated speckle intensity with a gaussian profile approximation for the transmittance of the detection area and the weight function of the sampling time. Adapting the results to a speckle velocimeter, the experimental conditions of the sampling time and the optimal relation between the speckle size and the detection area have been discussed.     

An acoustic chamber for sound intensity measurements

The construction and performance of an acoustic chamber suitable for sound intensity measurements is described. The walls and the ceiling of the room are treated with glass wool sheets, air gap and pleated carpet in that order for sound absorption. The final testing of the room shows that good sound absorption is obtained down to low frequencies. The sound absorption coefficient for the room varies between 0.83 and 0.91 for different frequencies.     

Equilibrium time correlation functions in the low-density limit

We consider a system of hard spheres in thermal equilibrium. Using Lanford's result about the convergence of the solutions of the BBGKY hierarchy to the solutions of the Boltzmann hierarchy, we show that in the low-density limit (Boltzmann-Grad limit): (i) the total time correlation function is governed by the linearized Boltzmann equation (proved to be valid for short times), (ii) the self time correlation function, equivalently the distribution of a tagged particle in an equilibrium fluid, is governed by the Rayleigh-Boltzmann equation (proved to be valid for all times). In the latter case the fluid (not including the tagged particle) is to zeroth order in thermal equilibrium and to first order its distribution is governed by a combination of the Rayleigh-Boltzmann equation and the linearized Boltzmann equation (proved to be valid for short times).Supported in part by NSF Grant PHY 78-22302.     

The classical limit for quantum mechanical correlation functions

For quantum systems of finitely many particles as well as for boson quantum field theories, the classical limit of the expectation values of products of Weyl operators, translated in time by the quantum mechanical Hamiltonian and taken in coherent states centered inx- andp-space around? ^?1/2 (coordinates of a point in classical phase space) are shown to become the exponentials of coordinate functions of the classical orbit in phase space. In the same sense,? ^?1/2 [(quantum operator) (t) — (classical function) (t)] converges to the solution of the linear quantum mechanical system, which is obtained by linearizing the non-linear Heisenberg equations of motion around the classical orbit.