Far field of binary phase gratings with errors in the height of the strips

Diffraction gratings are not always ideal but, due to the fabrication process, several errors can be produced. In this work we show that when the strips of a binary phase diffraction grating present certain randomness in their height, the intensity of the diffraction orders varies with respect to that obtained with a perfect grating. To show this, we perform an analysis of the mutual coherence function and then, the intensity distribution at the far field is obtained. In addition to the far field diffraction orders, a "halo" that surrounds the diffraction order is found, which is due to the randomness of the strips height.

Binary gratings with random heights

We analyze the far-field intensity distribution of binary phase gratings whose strips present certain randomness in their height. A statistical analysis based on the mutual coherence function is done in the plane just after the grating. Then, the mutual coherence function is propagated to the far field and the intensity distribution is obtained. Generally, the intensity of the diffraction orders decreases in comparison to that of the ideal perfect grating. Several important limit cases, such as low- and high-randomness perturbed gratings, are analyzed. In the high-randomness limit, the phase grating is equivalent to an amplitude grating plus a “halo.” Although these structures are not purely periodic, they behave approximately as a diffraction grating.

Structure-function Relationships Using the Cirrus Spectral Domain Optical Coherence Tomograph and Standard Automated Perimetry

Purpose: To evaluate the relationship between glaucomatous structural damage assessed by the Cirrus Spectral Domain OCT (SDOCT) and functional loss as measured by standard automated perimetry (SAP). Methods: Four hundred twenty-two eyes (78 healthy, 210 suspects, 134 glaucomatous) of 250 patients were recruited from the longitudinal Diagnostic Innovations in Glaucoma Study and from the African Descent and Glaucoma Evaluation Study. All eyes underwent testing with the Cirrus SDOCT and SAP within a 6-month period. The relationship between parapapillary retinal nerve fiber layer thickness (RNFL) sectors and corresponding topographic SAP locations was evaluated using locally weighted scatterplot smoothing and regression analysis. SAP sensitivity values were evaluated using both linear as well as logarithmic scales. We also tested the fit of a model (Hood) for structure-function relationship in glaucoma. Results: Structure was significantly related to function for all but the nasal thickness sector. The relationship was strongest for superotemporal RNFL thickness and inferonasal sensitivity (R(2) = 0.314, P < 0.001). The Hood model fitted the data relatively well with 88% of the eyes inside the 95% confidence interval predicted by the model. Conclusions: RNFL thinning measured by the Cirrus SDOCT was associated with correspondent visual field loss in glaucoma.

Coherence imaging by use of a Newton rings sampling function

We show that, with suitable optics in the arm of a Michelson interferometer, orthogonal galvo-scanning mirrors build a sampling function in the form of Newton rings when the two interferometer arms are matched. Using a low-coherence source, one can obtain transversal depth-resolved images. A fast display procedure using a storage oscilloscope was devised based on this method.

Coherence imaging by use of a Newton rings sampling function

We show that, with suitable optics in the arm of a Michelson interferometer, orthogonal galvo-scanning mirrors build a sampling function in the form of Newton rings when the two interferometer arms are matched. Using a low-coherence source, one can obtain transversal depth-resolved images. A fast display procedure using a storage oscilloscope was devised based on this method.

Comparison of Fourier-Domain and Time-Domain Optical Coherence Tomography in the Detection of Band Atrophy of the Optic Nerve

PURPOSE: To compare the ability of Fourier-domain (FD) optical coherence tomography (3D OCT-1000; Top, con, Tokyo, Japan) and time domain (TD) OCT (Stratus; Carl Zeiss Meditec Inc, Dublin, California, USA) to detect axonal loss in eyes with band atrophy (BA) of the optic nerve. DESIGN: Cross-sectional study. METHODS: Thirty-six eyes from 36 patients with BA and temporal visual field (VF) defect from chiasmal compression and 36 normal eyes were studied. Subjects were submitted to standard automated perimetry and macular and retinal nerve fiber layer (RNFL) measurements were taken using 3D OCT-1000 and Stratus OCT. Receiver operating characteristic (ROC) curves were calculated for each parameter. Spearman correlation coefficients were obtained to evaluate the relationship between RNFL and macular thickness parameters and severity of VF loss. Measurements from the two devices were compared. RESULTS: Regardless of OCT device, all RNFL and macular thickness parameters were significantly lower in eyes with BA compared with normal eyes, but no statistically significant difference was found with regard to the area under the ROC curve. Structure-function relationships were also similar for the two devices. In both groups, RNFL and macular thickness measurements were generally and in some cases significantly smaller with 3D OCT-1000 than with Stratus OCT. CONCLUSIONS: The introduction of FD technology did not lead to better discrimination ability for detecting BA of the optic nerve compared with TD technology when using the software currently provided by the manufacturer. 3D OCT-1000 FD OCT RNFL and macular measurements were generally smaller than TD Stratus OCT measurements. Investigators should be aware of this fact when comparing measurements obtained with these two devices. (Am J Oplathalmol 2009;147: 56-63. (c) 2009 by Elsevier Inc. All rights reserved.)

Relationship between Optical Coherence Tomography, Pattern Electroretinogram and Automated Perimetry in Eyes with Temporal Hemianopia from Chiasmal Compression

PURPOSE. To evaluate the relationship between pattern electroretinogram (PERG) amplitude, macular and retinal nerve fiber layer (RNFL) thickness by optical coherence tomography (OCT), and visual field (VF) loss on standard automated perimetry (SAP) in eyes with temporal hemianopia from chiasmal compression. METHODS. Forty-one eyes from 41 patients with permanent temporal VF defects from chiasmal compression and 41 healthy subjects underwent transient full-field and hemifield (temporal or nasal) stimulation PERG, SAP and time domain-OCT macular and RNFL thickness measurements. Comparisons were made using Student`s t-test. Deviation from normal VF sensitivity for the central 18 of VF was expressed in 1/Lambert units. Correlations between measurements were verified by linear regression analysis. RESULTS. PERG and OCT measurements were significantly lower in eyes with temporal hemianopia than in normal eyes. A significant correlation was found between VF sensitivity loss and fullfield or nasal, but not temporal, hemifield PERG amplitude. Likewise a significant correlation was found between VF sensitivity loss and most OCT parameters. No significant correlation was observed between OCT and PERG parameters, except for nasal hemifield amplitude. A significant correlation was observed between several macular and RNFL thickness parameters. CONCLUSIONS. In patients with chiasmal compression, PERG amplitude and OCT thickness measurements were significant related to VF loss, but not to each other. OCT and PERG quantify neuronal loss differently, but both technologies are useful in understanding structure-function relationship in patients with chiasmal compression. (ClinicalTrials.gov number, NCT00553761.) (Invest Ophthalmol Vis Sci. 2009; 50: 3535-3541) DOI:10.1167/iovs.08-3093

Phase sensitive pumping and coherence of superposition states

The continuous parametric pumping of a superconducting lossy QED cavity supporting a field prepared initially as a superposition of coherent states is discussed. In contrast to classical pumping, we verify that the phase sensitivity of the parametric pumping makes the asymptotic behaviour of the cavity field state strongly dependent on the phase theta of the coherent state \ alpha > = \ alpha \e(i theta)>. Here we consider theta = pi /4, -pi /4 and we analyse the evolution of the purity of the superposition states with the help of the linear entropy and fidelity functions. We also analyse the decoherence process quantitatively through the Wigner function, for both states, verifying that the decay is slightly modified when compared to the free decoherence case: for theta = -pi /4 the process is accelerated while for theta = pi /4 it is delayed.

Atom lasers, coherent states, and coherence II. Maximally robust ensembles of pure states

As discussed in the preceding paper [Wiseman and Vaccaro, preceding paper, Phys. Rev. A 65, 043605 (2002)], the stationary state of an optical or atom laser far above threshold is a mixture of coherent field states with random phase, or, equivalently, a Poissonian mixture of number states. We are interested in which, if either, of these descriptions of rho(ss) as a stationary ensemble of pure states, is more natural. In the preceding paper we concentrated upon the question of whether descriptions such as these are physically realizable (PR). In this paper we investigate another relevant aspect of these ensembles, their robustness. A robust ensemble is one for which the pure states that comprise it survive relatively unchanged for a long time under the system evolution. We determine numerically the most robust ensembles as a function of the parameters in the laser model: the self-energy chi of the bosons in the laser mode, and the excess phase noise nu. We find that these most robust ensembles are PR ensembles, or similar to PR ensembles, for all values of these parameters. In the ideal laser limit (nu=chi=0), the most robust states are coherent states. As the phase noise or phase dispersion is increased through nu or the self-interaction of the bosons chi, respectively, the most robust states become more and more amplitude squeezed. We find scaling laws for these states, and give analytical derivations for them. As the phase diffusion or dispersion becomes so large that the laser output is no longer quantum coherent, the most robust states become so squeezed that they cease to have a well-defined coherent amplitude. That is, the quantum coherence of the laser output is manifest in the most robust PR ensemble being an ensemble of states with a well-defined coherent amplitude. This lends support to our approach of regarding robust PR ensembles as the most natural description of the state of the laser mode. It also has interesting implications for atom lasers in particular, for which phase dispersion due to self-interactions is expected to be large.

Atom lasers, coherent states, and coherence. I. Physically realizable ensembles of pure states

A laser, be it an optical laser or an atom laser, is an open quantum system that produces a coherent beam of bosons (photons or atoms, respectively). Far above threshold, the stationary state rho(ss) of the laser mode is a mixture of coherent-field states with random phase, or, equivalently, a Poissonian mixture of number states. This paper answers the question: can descriptions such as these, of rho(ss) as a stationary ensemble of pure states, be physically realized? Here physical realization is as defined previously by us [H. M. Wiseman and J. A. Vaccaro, Phys. Lett. A 250, 241 (1998)]: an ensemble of pure states for a particular system can be physically realized if, without changing the dynamics of the system, an experimenter can (in principle) know at any time that the system is in one of the pure-state members of the ensemble. Such knowledge can be obtained by monitoring the baths to which the system is coupled, provided that coupling is describable by a Markovian master equation. Using a family of master equations for the (atom) laser, we solve for the physically realizable (PR) ensembles. We find that for any finite self-energy chi of the bosons in the laser mode, the coherent-state ensemble is not PR; the closest one can come to it is an ensemble of squeezed states. This is particularly relevant for atom lasers, where the self-energy arising from elastic collisions is expected to be large. By contrast, the number-state ensemble is always PR. As the self-energy chi increases, the states in the PR ensemble closest to the coherent-state ensemble become increasingly squeezed. Nevertheless, there are values of chi for which states with well-defined coherent amplitudes are PR, even though the atom laser is not coherent (in the sense of having a Bose-degenerate output). We discuss the physical significance of this anomaly in terms of conditional coherence (and hence conditional Bose degeneracy).