Attenuation and diffusion produced by small-radius curvatures in POFs.

Our aim is to characterize curvatures using a methodology previously applied to other localized disturbances in plastic optical fibers (POFs). The effects of several curvature radii and turn angles have been analyzed, so that for each condition, angular dependent attenuation and diffusion are obtained from experimental measurements to construct a matrix that accounts for the global effects of power loss and mode mixing introduced by the curvature over the angular power distribution. Power loss as a function of bend radius was calculated using the characteristic matrices and compared to experimental results to validate the model. This curvature model can be a useful tool to predict the impact of bends on transmission properties as is demonstrated in the example of a small network in a domestic environment.

POF misalignment model based on the calculation of the radiation pattern using the Hankel transform.

Here, we propose a method to estimate misalignment losses that is based on the calculation of the radiated angular power distribution as light propagates through space using the fiber far field pattern (FFP) and simplifying and speeding calculations with the Hankel transform. This method gives good estimates for combined transversal and longitudinal losses at short, intermediate and long offset distances. In addition, the same methodology can be adapted to describe not only scalar loss but also its angular dependence caused by misalignments. We show that this approach can be applied to upgrade a connector matrix included in a propagation model that is integrated into simulation software. This way, we assess the effects of misalignments at different points in the link and are able to predict the performance of different layouts at system level.

Coastal zone management with stochastic multi-criteria analysis.

The methodology for coastal management proposed in this study takes into account the physical processes of the coastal system and the stochastic nature of forcing agents. Simulation techniques are used to assess the uncertainty in the performance of a set of predefined management strategies based on different criteria representing the main concerns of interest groups. This statistical information as well as the distribution function that characterizes the uncertainty regarding the preferences of the decision makers is fed into a stochastic multi-criteria acceptability analysis that provides the probability of alternatives obtaining certain ranks and also calculates the preferences of a typical decision maker who supports an alternative. This methodology was applied as a management solution for Playa Granada in the Guadalfeo River Delta (Granada, Spain), where the construction of a dam in the river basin is causing severe erosion. The analysis of shoreline evolution took into account the coupled action of atmosphere, ocean, and land agents and their intrinsic stochastic character. This study considered five different management strategies. The criteria selected for the analysis were the economic benefits for three interest groups: (i) indirect beneficiaries of tourist activities; (ii) beach homeowners; and (iii) the administration. The strategies were ranked according to their effectiveness, and the relative importance given to each criterion was obtained.

Frequency response in step index plastic optical fibers obtained from the generalized power flow equation.

We present a method to obtain the frequency response of step index (SI) plastic optical fibers (POFs) based on the power flow equation generalized to incorporate the temporal dimension where the fibre diffusion and attenuation are functions of the propagation angle. To solve this equation we propose a fast implementation of the finite-difference method in matrix form. Our method is validated by comparing model predictions to experimental data. In addition, the model provides the space-time evolution of the angular power distribution when it is transmitted throughout the fibre which gives a detailed picture of the POFs capabilities for information transmission. Model predictions show that angular diffusion has a strong impact on temporal pulse widening with propagation.

The spatial tuning of color and luminance peripheral vision measured with notch filtered noise masking.

We have measured the spatial bandwidths of the bandpass red-green chromatic and luminance mechanisms at four locations in the nasal visual field (0, 10, 20 and 30 degrees) using a method of notch filtered noise masking which effectively removes the artifact of off-frequency looking for our stimuli. Detection thresholds were measured for luminance or isoluminant red-green Gaussian enveloped test gratings of 0.5 cpd embedded in 1/f noise. Firstly, thresholds were obtained as a function of increasing noise spectral density and were fitted using a standard noise masking model. These results support the existence across the visual field of independent, red-green chromatic and luminance mechanisms with similar sampling efficiencies. Secondly, we measured thresholds in notch filtered noise as a function of notch width and derived the spatial bandwidth of the detection mechanism. We find both color and luminance mechanisms have similar bandwidths which remain virtually constant across eccentricity. These results indicate strong overall similarities between the early processing of color and luminance vision, and lend support to the role of color as an 'intrinsic image' in spatial vision. The results are discussed in the light of the anchored channel and shifting channel models of peripheral contrast sensitivity and pattern detection.

Objective measurement of the off-axis longitudinal chromatic aberration in the human eye.

Longitudinal chromatic aberration (LCA) of the human eye has been studied repeatedly, but only at the fovea. Poor visual acuity prevents its subjective determination beyond a few degrees eccentricity. Consequently, we have used an objective approach, similar to that of Charman and Jennings [(1976). Vision Research 16, 999-1005], to measure ocular LCA across the visual field. To determine the validity of our double-pass approach, a direct comparison between objective and subjective results was established where possible, namely at the fovea and parafoveally (2.5 deg). In both cases we focused a monochromatic point source at four different wavelengths (458, 501.8, 543.5 and 632.8 nm). At the fovea, for a 3 mm pupil, we found a close match between subjective and objective results. However, as the subjective task became harder (off-axis or larger pupils), subjective results tended to yield slightly more myopic eyes than the results for objective refraction. In all cases, the offset was virtually independent of the wavelength used. Therefore, we have not found evidence of any biased estimates of the LCA, as determined objectively. Our foveal results show reasonable agreement with previous findings, except for slightly smaller amounts of LCA. Starting at the fovea, LCA tends to gradually increase with eccentricity, up to 40 deg, although such an increase is small, just approaching statistical significance. Computation of the LCA using a model eye predicts a slightly smaller increase with eccentricity.

Aberrations and relative efficiency of light pencils in the living human eye.

We propose a new method for ray tracing in the living human eye. It consists of delivering a narrow light pencil from an unexpanded laser beam and recording the integrated energy and position of the aerial image formed by the outgoing beam (after reflection off the retina and passage through the fully open pupil of the eye and camera lens). The lateral displacement of the aerial image is proportional to the geometrical aberration (displacement) of the incoming ray at the retina. In addition, its integrated energy is proportional to retinal reflectance that is highly directional [related to the Stiles-Crawford (SC) effect and to the effective pupil transmittance]. This method permits us, by delivering rays through different equispaced positions at the pupil plane, to sample the complex pupil function: its magnitude is a measure of the effective pupil transmission and its phase is the wave aberration. Experimental results, aberrations, and reflectometric directionality for four subjects are consistent with previous findings.

Absence of linear subthreshold summation between red-green and luminance mechanisms over a wide range of spatio-temporal conditions.

We have tested the independence of red-green chromatic and luminance mechanisms at detection threshold using a method of subthreshold summation. Stimuli were isoluminant red-green gratings and yellow-black luminance gratings that uniquely activate the red-green color and luminance mechanisms, respectively. Stimuli were Gaussian enveloped 0.25, 1 or 4 cpd sinewave gratings, counter-phase flickered at 0, 5 or 9 Hz. The threshold detection of red-green color contrast was measured in the presence of a subthreshold amount of luminance contrast, and vice versa. The results allow a model of linear summation between the color and luminance mechanisms to be rejected, but are well fitted by a model, assuming that these mechanisms are independent but combine to determine detection by probability summation, with a high summation index (median value = 4). We conclude that there are independent red-green chromatic mechanism and luminance detection mechanisms over this range of spatio-temporal conditions.

Shape of stars and optical quality of the human eye.

Star images are entoptic phenomena that most people can perceive when looking at bright point sources in darkness. Diffraction and/or ocular aberrations seem to be a plausible cause for the star patterns, but to our knowledge no objective recordings of retinal optical images showing these characteristic patterns have been reported before. We have projected a small Gaussian spot of light onto the retina and registered the aerial image formed externally through a fully dilated pupil [one-and-a-half-pass method [J. Opt. Soc. Am. A 12, 2385 (1995)]]. We have verified that, for fully dilated pupils (> 9 mm), the blur caused by the finite size of the Gaussian spot is small. Consequently, these aerial images are a reasonably good approximation of the (inverted) optical point-spread function of the eye. These objectively recorded images displayed the distinctive radiating patterns of star images, which were compared with subjective patterns sketched out by the same observers. A strikingly close match was found between the objective and the subjective patterns of the same eyes. In addition, we computed the diffraction patterns produced by a simple schematic model of the suture lines of the anterior lens surface, also obtaining star-shaped images. These results support the commonly accepted hypothesis of a purely optical origin of subjective star images.

Phase transfer and point-spread function of the human eye determined by a new asymmetric double-pass method.

A recent study has shown that the double-pass method provides a good estimate of the ocular modulation transfer function (MTF) but that it does not yield the phase transfer function (PTF) [J. Opt. Soc. Am. A 12, 195 (1995)]. Therefore, one cannot recover the true retinal point-spread function (PSF). We present a modification of the double-pass method to overcome this problem. The key is to break the symmetry between the two passes. By using an unexpanded Gaussian input beam, we produce a diffraction-limited PSF for the first passes. Then, by using a large exit pupil, we get an aberrated PSF for the second pass. The double-pass aerial image is the cross correlation of both PSF's, so that the Fourier transform of such an aerial image directly provides the true retinal PTF, up to the cutoff frequency of the effective (small), diffraction-limited entrance pupil. The resulting double-pass aerial image is a blurred version of the true retinal PSF. Thus it shows the effect not only of even symmetric aberrations but also of odd and irregular aberrations such as coma. We have explored two different ways to retrieve the true retinal PSF: (a) deblurring of the aerial image and (b) PSF reconstruction combining PTF data with conventional double-pass MTF. We present promising initial results with both artificial and real eyes.

Color and luminance spatial tuning estimated by noise masking in the absence of off-frequency looking.

We assessed the contribution of off-frequency looking for pattern detection and obtained bandwidths for chromatic and luminance mechanisms in conditions free from this effect. We used a simultaneous spatial masking technique with Gaussian enveloped sinusoidal test stimuli (0.5 cycle/deg) and filtered one-dimensional static-noise masks whose spectral power was uniformly distributed per octave. Stimuli were modulated in the chromatic (isoluminant red-green) or the luminance (yellow-black) domain. Color and luminance detection thresholds were compared for low-pass, high-pass, and notch- (band-stopped) filtered noise. We obtained the following results: (1) at high-noise spectral densities, masking by notched noise is greater than the summed masking of the high- and low-pass noise, indicating the presence of off-frequency looking for both color and luminance detection. There is no evidence for off-frequency looking at lower power densities. (2) Using notch-filtered noise, which avoids the problem of off-frequency looking, we found that color processing is subserved by bandpass channels with bandwidths similar to those revealed for luminance processing. (3) Both color and luminance mechanisms appear to have bandwidths proportional to their center frequency (constant in octaves). (4) The lower and upper sides of the color and luminance tuning functions were estimated individually by use of high-pass and low-pass noise of a low power density and are revealed to be asymmetric, with the lower side declining more steeply than the upper side.

Evidence for separate pathways for color and luminance detection mechanisms.

We measure threshold versus contrast (TvC) functions for chromatic (red-green) and luminance sine-wave-grating stimuli for (1) the detection of luminance in the presence of color contrast and (2) the detection of color in the presence of luminance contrast. We find that, although these crossed TvC functions both display a dipperlike shape, their facilitation differs from that found for standard uncrossed dipper functions (luminance on luminance or color on color contrast). Their facilitation disappears (cross condition 1) or is reduced (cross condition 2) by randomized presentation of the phase of the test and the mask, and the remaining facilitation (cross condition 2) displays no spatial tuning. We argue that these crossed facilitatory interactions cannot be explained by detection mechanisms with common inputs from color and luminance contrast (a nonindependence of transduction), and we present evidence that instead they reflect the use of local cues in the stimuli. We also measure the luminance-luminance TvC function in the presence of a fixed suprathreshold color contrast. The results demonstrate that, even when the color contrast produces a masking of the luminance thresholds, luminance-luminance facilitation still occurs. Thus the opposing effects of masking and facilitation can occur simultaneously. Furthermore, while luminance-luminance facilitation occurs independently of color contrast, masking can be produced by either contrast. This suggests that masking and facilitation have different underlying origins. Similar results are found for the color detection thresholds in the presence of a luminance pedestal. We conclude that there are separate pathways for the detection of color and luminance contrast, each with no input from the other contrast. We suggest that the cross masking reflects divisive interactions between these pathways that is restricted to high contrasts.

The spatial tuning of chromatic mechanisms identified by simultaneous masking.

We have investigated the spatial transfer characteristics of the mechanisms sensitive to color in the human visual system using a method of simultaneous spatial masking with isoluminant chromatic stimuli. The test stimuli were Gaussian enveloped red-green gratings of three spatial frequencies in the lowpass region of the color domain (0.25, 0.5 and 1 c/deg). The masking stimuli were red-green gratings at the orientation and phase of the test, presented at the same spatial frequency, and at +/- 1, and +/- 2 octaves from its spatial frequency. We obtained test contrast threshold as a function of mask contrast for a wide range of mask contrasts (TvC functions). Tuning functions were derived from linear fits of the masking data, by taking the mask contrast that doubled the minimum test threshold at each spatial frequency. Chromatic tuning functions show bandpass characteristics for all test spatial frequencies examined with an average full bandwidth at half-height of 2.6 octaves, which is similar to the luminance bandwidths obtained under comparable conditions. Thus, our results suggest that the color contrast sensitivity function is the upper envelope of a range of bandpass mechanisms whose peaks extend to very low spatial frequencies.

Relative contributions of optical and neural limitations to human contrast sensitivity at different luminance levels.

The relative contributions of optical and neural constraints on human contrast sensitivity as a function of spatial frequency were assessed for a range of luminances. First, the overall two-dimensional contrast sensitivity function (CSF) was obtained for three eyes at three luminances (0.05, 0.5 and 20 cd/m2) using a standard two-alternative forced-choice procedure. Second, the two-dimensional modulation transfer function (MTF) of the optics was measured for the same eyes and pupil sizes using a hybrid optical-digital method. The two-dimensional neural transfer function (NTF) was obtained as the ratio between the CSF and the MTF. Minor factors, such as the effect of cone aperture, were also considered in the computations. Our results show that at all luminances, the fall off in contrast sensitivity at high spatial frequencies is mainly due to optical factors. The losses in contrast sensitivity with decreasing luminance are, however, primarily due to noise limitations.