Analytical first order comparison of amplitude and phase noise in single and dual Mach-Zehnder interferometer detection schemes for DQPSK transmission systems

An analytical first order calculation of the impact of Gaussian white noise on a novel single Mach-Zehnder Interferometer demodulation scheme for DQPSK reveals a constant Q factor ratio to the conventional scheme.

Theoretical evaluation of the cataract extraction-refraction-implantation techniques for intraocular lens power calculation

PURPOSE: To evaluate theoretically three previously published formulae that use intra-operative aphakic refractive error to calculate intraocular lens (IOL) power, not necessitating pre-operative biometry. The formulae are as follows: IOL power (D) = Aphakic refraction x 2.01 [Ianchulev et al., J. Cataract Refract. Surg.31 (2005) 1530]; IOL power (D) = Aphakic refraction x 1.75 [Mackool et al., J. Cataract Refract. Surg.32 (2006) 435]; IOL power (D) = 0.07x(2) + 1.27x + 1.22, where x = aphakic refraction [Leccisotti, Graefes Arch. Clin. Exp. Ophthalmol.246 (2008) 729]. METHODS: Gaussian first order calculations were used to determine the relationship between intra-operative aphakic refractive error and the IOL power required for emmetropia in a series of schematic eyes incorporating varying corneal powers, pre-operative crystalline lens powers, axial lengths and post-operative IOL positions. The three previously published formulae, based on empirical data, were then compared in terms of IOL power errors that arose in the same schematic eye variants. RESULTS: An inverse relationship exists between theoretical ratio and axial length. Corneal power and initial lens power have little effect on calculated ratios, whilst final IOL position has a significant impact. None of the three empirically derived formulae are universally accurate but each is able to predict IOL power precisely in certain theoretical scenarios. The formulae derived by Ianchulev et al. and Leccisotti are most accurate for posterior IOL positions, whereas the Mackool et al. formula is most reliable when the IOL is located more anteriorly. CONCLUSION: Final IOL position was found to be the chief determinant of IOL power errors. Although the A-constants of IOLs are known and may be accurate, a variety of factors can still influence the final IOL position and lead to undesirable refractive errors. Optimum results using these novel formulae would be achieved in myopic eyes.

Linear binocular combination of responses to contrast modulation:contrast-weighted summation in first- and second-order vision

Binocular combination for first-order (luminancedefined) stimuli has been widely studied, but we know rather little about this binocular process for spatial modulations of contrast (second-order stimuli). We used phase-matching and amplitude-matching tasks to assess binocular combination of second-order phase and modulation depth simultaneously. With fixed modulation in one eye, we found that binocularly perceived phase was shifted, and perceived amplitude increased almost linearly as modulation depth in the other eye increased. At larger disparities, the phase shift was larger and the amplitude change was smaller. The degree of interocular correlation of the carriers had no influence. These results can be explained by an initial extraction of the contrast envelopes before binocular combination (consistent with the lack of dependence on carrier correlation) followed by a weighted linear summation of second-order modulations in which the weights (gains) for each eye are driven by the first-order carrier contrasts as previously found for first-order binocular combination. Perceived modulation depth fell markedly with increasing phase disparity unlike previous findings that perceived first-order contrast was almost independent of phase disparity. We present a simple revision to a widely used interocular gain-control theory that unifies first- and second-order binocular summation with a single principle-contrast-weighted summation-and we further elaborate the model for first-order combination. Conclusion: Second-order combination is controlled by first-order contrast.

Calculation of mutual information for nonlinear communication channel at large signal-to-noise ratio

Using the path-integral technique we examine the mutual information for the communication channel modeled by the nonlinear Schrödinger equation with additive Gaussian noise. The nonlinear Schrödinger equation is one of the fundamental models in nonlinear physics, and it has a broad range of applications, including fiber optical communications - the backbone of the internet. At large signal-to-noise ratio we present the mutual information through the path-integral, which is convenient for the perturbative expansion in nonlinearity. In the limit of small noise and small nonlinearity we derive analytically the first nonzero nonlinear correction to the mutual information for the channel.