Search

Retinal image light distributions in a standard optical model of a diffraction-limited eye with round pupils are presented for several patterns of amplitude and phase modulation of the light admitted into the eye. Of special interest are circularly symmetrical configurations of truncated Bessel amplitude transmission functions, and of light subjected to axicon deviation. It is shown by several examples that this kind of beam shaping allows generation of retinal imagery, which can be more robust to defocus while maintaining minimal image degradation, and it points to situations of two separate zones simultaneously in sharp focus, several diopters apart.

Analysis of retinal image formation for beams of coherent and incoherent radiation emphasizes the role of the Poynting vector’s inclination with respect to the retinal image plane. Coherent beams interfere and give rise to a single Poynting vector that highlights the unique direction of incidence of energy flow, whereas multiple incoherent beams, especially incoherent extended sources in the pupil, generate electro-magnetic disturbances in the image plane each characterized by Poynting vectors of their own. As a result, the Stiles–Crawford diminution of luminant efficiency adds differently depending on the coherence of the entering light. Two practical considerations follow: first, in performing diffraction calculations for the retinal image from known wavefronts in the pupil plane, apodization terms should not be factored in, and, second, in principle, for perfect imaging in standard target viewing, Stiles–Crawford integration with increasing pupil diameter is not expected.

The third dimension in the reproduction of real scenes in three-dimensional displays is commonly subject to scale changes. The geometry of the situation is laid out, permitting the depth rendition of displays to be characterized and subjected to empirical examination. Psychophysical experiments are presented showing, even when geometrical deformations have been factored out, specific deviations from veridicality in observers’ depth reports for stereograms of simple static patterns devoid of secondary cues.

The classical radiance-luminance parallelism of units for the measurement of emission and reception of flux applies when visual processing is modeled on principles of physics or engineering. “Energy” has a defined meaning in these disciplines: it is the time integral of flux; the time rate of transfer of flux has the dimension of power. Hence energy is appropriate only when light stimuli are delimited in time, else power is the applicable word. To conform to dimensional specifications in physics, energy models in vision would deal with packets of stimuli of fixed duration, not the time rate of excitation, and have magnitudes expressed in the form of the square root of the integrated squared spatial or spatio-temporal distributions.

Psychophysical experiments, with a new paradigm but in broad conformity with classical results on glare, were used to estimate the scattering in the eye. Combining the data with those from a companion experiment [ J. Opt. Soc. Am. A12, 1411– 1416 ( 1995)] using objective double-pass measurements of the retinal image in the same subjects permitted a synthesis of the complete point-spread function. Results were obtained on two young subjects and one older one with more prominent scatter but normal visual acuity. This permitted the derivation of performance parameters of the eyes, such as the Strehl ratio and cumulative light functions. When the scattering was more prominent, we were able to characterize performance losses that manifested themselves in changes in absolute and contrast detection thresholds.

To measure the intrinsic resolving capacity of the retinal and neural levels of vision, we devised a method that creates two lines with controllable contrast on the retina. The line separation can be varied at will, down to values below those achievable with conventional optical techniques. Implementation of the method with use of a He–Ne laser leads to a procedure that permits analysis of the performance of the human visual apparatus.

Psychophysical experiments, with a new paradigm but in broad conformity with classical results on glare, were used to estimate the scattering in the eye. Combining the data with those from a companion experiment [J. Opt. Soc. Am. A 12, 1411–1416 (1995)] using objective double-pass measurements of the retinal image in the same subjects permitted a synthesis of the complete point-spread function. Results were obtained on two young subjects and one older one with more prominent scatter but normal visual acuity. This permitted the derivation of performance parameters of the eyes, such as the Strehl ratio and cumulative light functions. When the scattering was more prominent, we were able to characterize performance losses that manifested themselves in changes in absolute and contrast detection thresholds.

Point-spread functions (PSF’s) of human eyes at medium pupil size (3.5 mm) were derived from double-pass measurements. It was demonstrated that reliable information on PSF shape in the central 7-arcmin radius can be obtained in spite of uncertainty about the height and extent of the tail of the double-pass image. Measurements from some healthy young eyes (of subjects 21–31 years old) and several older eyes (of subjects 63–75 years old) with good acuity revealed little difference in the half-width at half-height of the PSF, but, owing to the higher tail in their PSF’s, the Strehl ratio of the older eyes is much lower. Computation of the modulation transfer functions of the older eyes revealed a more prominent loss at low spatial frequencies.

Psychophysical experiments, with a new paradigm but in broad conformity with classical results on glare, were used to estimate the scattering in the eye. Combining the data with those from a companion experiment [J. Opt. Soc. Am. A 12, 1411–1416 (1995)] using objective double-pass measurements of the retinal image in the same subjects permitted a synthesis of the complete point-spread function. Results were obtained on two young subjects and one older one with more prominent scatter but normal visual acuity. This permitted the derivation of performance parameters of the eyes, such as the Strehl ratio and cumulative light functions. When the scattering was more prominent, we were able to characterize performance losses that manifested themselves in changes in absolute and contrast detection thresholds.

In this paper we describe four experiments concerned with spatial-interval discrimination. The first experiment demonstrates that perturbations in the internal light distribution of two bright bars alter the perceived separation of the bars without influencing the precision of spatial-interval discrimination. Specifically, alterations in the centroid of the luminance distribution of the bars were found to influence their perceived separation systematically. In the second experiment we investigated separation discrimination for (a) a pair of bright lines, (b) a pair of dark lines, and (c) a pair of lines with opposite polarity (a bright–dark pair). For large interline separations, the thresholds for separation discrimination of the three stimuli were equivalent. However, for small separations (<4 arcmin) the thresholds for the opposite-polarity pair were significantly higher than those for either bright or dark lines. The third experiment showed that separation discrimination is also impaired when the direction-of-brightness change of adjacent edges is the same. In the fourth experiment, random luminance perturbations were introduced in the interval between two bright bars separated by 1.5 to 8 arcmin by the addition of a dim line within the interval. The effect of these perturbations was also to alter the perceived separation of the bars with no effect on the precision of spatial-interval discrimination. Increasing the intensity of the perturbating line (to equal that of the outer lines) elevated thresholds for small separations (<4 arcmin) to approximately 6 arcsec but had no effect on the threshold for larger separations. Taken together, these results (1) suggest that large and small separations are processed differently and (2) place strong constraints on models for spatial-interval discrimination.

Binocular summation was studied with two different hyperacuity tests, a bisection test and a vernier-type test. The summation factor differed between the two tests and depended on the test configuration. In the bisection test, binocular summation increased with decreasing line separation, and for the largest separation binocular inhibition was found. In the vernier test summation was essentially more constant for different separations. It is argued that, for a bisection test with a small intertarget distance, the hyperacuity thresholds involve a component of intensity discrimination that is due to overlapping retinal line-spread functions. An additional, unexplained finding was that in a vertically oriented three-dot alignment test the monocularly perceived alignment always occurred while the center dot was displaced toward the nasal side.

A briefly flashed pattern never appears quite sharp, and visual acuity is reduced with short exposures. These observations led to an examination of the effect of exposure duration on sharpness discrimination. A foveally seen edge appears just-discriminably blurred when its edge light distribution is changed from being sharp to conforming to a ramp whose width (increasing from 0% to 100% of maximal luminance) is ~1 arcmin. When the exposure duration is reduced, the ramp width for minimal blur increases, rising by factors of 2–4 for exposures as short as 30 msec. This change is not due to a shortage of light. Threshold blur discrimination is not affected by retinal image motions of up to 1 deg/sec. Temporal combinations of sharp and blurred borders always worsen performance, and multiple brief presentations do not give so good a threshold as a single longer one.

If a pattern requiring orientation discrimination was presented randomly in one of five clearly demarcated time frames 500 ms apart, orientation thresholds were elevated ~20% over their values when the time slot was fixed. For stereoscopic depth discrimination the disparity threshold elevation was ~ 40%.

Because the discriminability of spatial intervals may give a pointer to possible underlying detection mechanisms for hyperacuity, a careful measurement was undertaken of how this function behaves with the width of the spatial intervals in the 6- to 12-min-of-arc range. Data on two subjects failed to produce convincing evidence for significant segmentation in the line-separation discrimination curve.

Thresholds for temporal-order detection of two successively displayed vertical stripes were determined for monocular and binocular stimulation. Thresholds are lower for binocular stimulation by roughly a factor of 1.4 compared with those found under monocular stimulation. This corresponds to quadratic summation. This is found for angular separations of the two stripes amounting to 5 and 40 min of arc.

Experimental findings [J. Opt. Soc. Am. 72, 1367 (1982)] that suggest a segmented nature of the line-separation discrimination curve need to be carefully tested for robustness before they are used as evidence for a fine structure of the processing apparatus for spatial vision.

Experimental findings [ J. Opt. Soc. Am.72, 1367 ( 1982)] that suggest a segmented nature of the line-separation discrimination curve need to be carefully tested for robustness before they are used as evidence for a fine structure of the processing apparatus for spatial vision.