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Abstract
This study compared on-axis and peripheral detection acuities measured with interference fringes, that bypass eye optics, and with screen-based Gabor gratings combined with an adaptive optics system. Gabor gratings are sinusoidal gratings incorporated with a Gaussian envelope that attenuate spatial frequency broadening that occur at the window edge. The magnitude of the attenuation was varied. Peripheral detection acuities were always higher for interference fringes than for Gabor gratings. Less attenuated Gabors (with sharper edges) had higher acuities than more attenuated Gabors (with less sharp edges). Theoretical investigations indicated that the spatial frequency broadening occurring due to the sharp edge of the less attenuated Gabors contribute little to high detection grating acuity in the periphery, but that the lower attenuation provides a greater number of visible cycles which is of more benefit to detection than is the case on-axis.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Peripheral vision is important in many tasks such as driving and general mobility. Patients with central field loss rely on their peripheral vision to perform day-to-day activities. Hence it is of interest to understand factors affecting the peripheral vision.
To evaluate the optical and neural limitations of peripheral vision, studies have evaluated detection and resolution acuities in the horizontal peripheral field [1–6]. Acuities varied considerably between studies. One reason might be the use of different targets. Sinusoidal interference fringes are projected directly on the retina to “bypass” the optics of the eye while acuities of screen-based gratings are affected by the eye optics including higher-order aberrations. The interference fringes have sharp edges. Screen-based gratings can have sharp edges (i.e., are sinusoidal across the grating) or have Gabor attenuation in which the contrast between bright and dark bars reduces from the center outwards according to a Gaussian envelop. The Gabor envelope is specified by its standard deviation σ, the angle from the center of the grating by which contrast reduces to 60.7% (e−0.5) of its central contrast.
Gabor functions have been used to determine peripheral visual performance in several studies, examples of which are 1° [6], 0.6° [7] and 1.6° [5]. Venkataraman et al. [5] found lower detection acuities than studies using interference fringes [2,4,8,9], which they attributed to the visibility of grating edges in the other studies. When an edge is added, a mixture of higher and lower spatial frequencies is created. This is shown in Fig. 1.
Fig. 1. Effects of field and edge effects on distribution of spatial frequency components. Spatial frequency for all figures is 1 cpd. Top left shows an unattenuated sine wave grating of field size 5.0°, and the top right shows its spatial frequency pattern; there is little spatial broadening. The middle row is as for the top, except now the field size is 2.5 degrees; there is considerable spatial broadening. The bottom row is as for the middle row, but now there is Gabor standard deviation of 1° applied to the grating. The spatial broadening has been reduced.
This study consisted of three parts. Firstly we determined whether peripheral detection acuities of interference fringes were similar or not to screen-based gratings with sharp edges. For the latter, full adaptive optics correction was used to eliminate aberrations of the eye and the optical system. Secondly, we compare horizontal and vertical gratings. Thirdly, we determined the effects of the number of visible gratings in the periphery, such as can occur by varying the field size (field effect), and the sharpness of the edge of screen gratings (edge effect) on thresholds.
2. Methods
2.1 Participants
Three male participants, aged 28-30 years, in good health and with normal visual functions with corrected visual acuities of 6/6 or better, were recruited. Participants 1 and 2 were emmetropes and participant 3 had refraction −1.00 DS/−1.25 DC x 180. Right eyes were tested and left eyes were occluded. The study complied with the declaration of the Treaty of Helsinki, approval was obtained from the University Human Research Ethics Committee, and informed written consent was obtained from all participants after procedures were explained. Experiment duration was approximately 20 hours per participant. A session lasted up to 2 hours, and breaks were given every 5 minutes or as required.
2.2 Experiment 1: Lotmar Visometer and interference fringes
A Lotmar Visometer (Haag-Streit, Bern, Switzerland) was used in which two white light point sources were imaged at the pupil to interfere on the retina as high-contrast sinusoidal fringes. A 550 nm (10 nm full width at half maximum) interference filter (65098 Edmund Scientific, Barrington, NJ) provided monochromatic light.
The Visometer was mounted on a gimbal arrangement so that the stimulus could be rotated along a range of meridians out to 90° eccentricity. For on-axis testing, the participants looked at the gratings, but for off-axis testing the participants viewed a red light. For the on-axis and off-axis measurements, the field size was set to 1.5° and 2.5°, respectively. A white cardboard was placed around the Visometer to unclutter the background; its luminance was approximately 1.0 cd/m2.
The point sources produced by the instrument were in focus 50 mm from the instrument and remained stationary as the stimulus was rotated. Participants were stabilized using the bite bar mounted on an adjustable XYZ mount. The participants were aligned longitudinally so that the cornea (3 mm from the pupil plane) was 47 mm from the instrument. Correct alignment horizontally and vertically was determined by finding the center of the positions for which the stimulus disappeared in horizontal and vertical directions.
Spatial frequencies were set well above expected detection limit and participants were instructed to rotate the spatial frequency knob slowly to lower frequencies until contrast could be perceived. Detection acuities were measured for horizontal and vertical gratings at 0°, ± 20° and ±30° in the horizontal visual field. Each measurement was repeated 3 times; averages were reported. Because the point sources were always well within the pupil and results are not affected by accommodation, pupils were not dilated [10].
The participants were naive to performing peripheral field detection tasks. Hence, they underwent 5 practice sessions of about 2 hours to become familiar with the procedure and adept at identifying contrast before starting the experiment proper.
2.3 Adaptive optics system and Gabor fringes
The setup has been explained by Jaisankar et al. [11], so not all details are provided. Detection acuities were measured with full correction of monochromatic aberrations using an adaptive optics setup (Fig. 2). One drop of 1% cyclopentolate was instilled 30 minutes prior to measurements. Experimentation began after full dilation was obtained (≥ 7 mm).
Fig. 2. Adaptive optics setup to correct on-axis and peripheral aberration. LD - Red laser diode (λ = 635 nm), L1 to 8 - achromatic lenses, S1 to 4 - apertures (S1 - Laser diode luminance controller, S2 - corneal reflection controller, S3 - stop, S4 - field size controller), M1 - plane mirror, BS1 to BS3 - beam splitters, FT - peripheral fixation LED targets (±30° and ±20°), DM - deformable mirror, HSWS - Hartmann-Shack wavefront sensor, F1 - Monochromatic filter (λ = 532 nm), P - pupil conjugate plane, R - retinal conjugate plane.
An illumination arm consisted of a red laser diode (Thorlabs, KLS635, Newton, NJ) placed at the focal point of lens L1 and a circular aperture S1 controlling the beam diameter. Beam splitter B1 directed the collimated laser beam to enter the eye and focus on the retina.
A wavefront sensor arm contained a series of lenses (L2 to L5) to ensured that the deformable mirror DM (ALPAO, DM 69-15 Montbonnot, France) and the lenslet array of the Hartman-Shack wavefront sensor (HSWS) were conjugated to the entrance pupil of the eye, and beam splitters (BS1 to BSS3) ensured that the light coming out of the eye reached the DM and the reflected light from the DM reached the HSWS. The wavefront of the light, determined using the HSWS, was corrected by adjusting the shape of DM. Aberrations were corrected over the entire DM surface (pupil conjugate) which had an aperture (S3) of 10.5 mm diameter. This acted as a 7 mm pupil stop because of 1.5x magnification between the DM and the eye.
For a stimulus arm, Gabor gratings of 100% central contrast were generated by an adaptive psychophysics program in MATLAB 2019b and displayed on an OLED microdisplay (EMA-100311-01 SVGA Rev 3 Monochrome Green OLED-XL, eMagin, Sydney, NSW, Australia) using an adaptive psychophysics program. The light was reflected at BS2 onto the deformable mirror, which provided the aberration correction as imaged on the retina (path S3 to R). Lenses L2, L3, L6, L7, L8 ensured that the display was conjugated to the retina. Aperture S4 controlled the field size of the target on the OLED screen during the experiment (1.5° for on-axis and 2.5° for off-axis to match the fields for the Lotmar Visometer). A filter of wavelength 532 nm (10 nm full width at half maximum), in front of the OLED display, provided pseudo-monochromatic light.
Detection acuities were assessed at the fovea and at ±20° and ±30° eccentricities along the horizontal meridian. Red light emitting diodes (LEDs) off the optical axis of the system provided fixation targets; we were not able to monitor fixation, but occasionally reminded the participants fixate accurately. Due to restrictions of the optical setup, the peripheral targets were placed close to the eye (in planes 60-80 mm from the corneal plane). Considering that the eye rotates about the center-of-rotation, approximately 13.5 mm behind the corneal apex, to view the targets, the visual field angles were overestimated. For a distance x in mm from the corneal apex to the target plane, the true angle θ ‘ was related to the nominal angle θ by
The true angles were ±16.5° (not ±20°) and ±26.3° (not ±30°).
2.4 Stimulus luminance
As described by Jaisankar et al. [11], the luminances of the Visometer and OLED display were determined to be 23 cd/m2 and 22 cd/m2, respectively.
2.5 Psychophysical method
Detection acuities with the adaptive optics system were assessed by an adaptive psychophysical procedure using a customized program [7]. Further details were provided by Jaisankar et al. [11] who used it to determine contrast sensitivity, but here it was used to determine detection acuities.
2.6 Experimental procedure
The experimental procedures were similar to those used by Jaisankar et al. [11]. These included obtaining the best possible peripheral refraction corrections. The instrument was operated in static mode (open-loop) with the aberration-corrected DM shape and subjective best focus.
Horizontal and vertical grating acuities were determined separately. The order of test grating orientation was selected randomly. The two-interval forced choice method was used to determine detection acuity. One of the intervals contain the grating and the other interval contained a blank field. The participants were asked to indicate which of the two intervals contained the grating by pressing one of the assigned buttons in a keypad. The stimulus in both intervals was cued by sound with a delay of 200 ms and each interval was presented for 500 ms. The participants underwent 10 practice sessions of about 2 hours each before starting the experiment proper.
Standard deviations of Gabor gratings on-axis were 1000° (effectively no attenuation), 1.0°, 0.5° and 0.2°, and all were combined with a 1.5° window size. Standard deviations of Gabor gratings for peripheral angles were 1000°, 1.6°, 1.0° and 0.5°, and all were combined with a 2.5° window size.
2.7 Calculating the size of the visible Gabor patch from estimated visual acuities
There are two factors which could cause the size of a Gabor patch to influence acuity: 1) an increased number of visible gratings, and 2) edge effects that broaden the spatial frequencies of the presented Gabors. For an edge effect to be present, the perceived size must be larger than the aperture. The edge effect will be considered in section 2.8. Anderson [17] found that increasing the number of visible cycles increased acuity, up to a limit of six visible cycles. The rule of thumb of six cycles is still used, e.g. [5]. Anderson varied window size, whereas nowadays the size of Gabor patches is controlled by setting the standard deviation of its attenuation. The relation between the standard deviation of the Gabor patch and the number of visible cycles was studied by Fredericksen [12]. We followed a similar method when determining the number of visible cycles.
To calculate a Gabor patch’s perceived size, we inferred the neural contrast sensitivity function to find out at which size contrast decreases below the detection threshold using the following steps:
- 1. Peak contrast sensitivity csp and the corresponding spatial frequency sfp at different eccentricities were taken from a previous study [13]. The values are 0°: 110 and 3.0 c/deg; 20°: 68 and 1.6 c/deg; 30° 27 and 1.3 c/deg.
- 2. The cutoff frequency sfc for each eccentricity were taken as the acuity for the interference fringes in this study.
- 3. A linear interpolation in logarithm space determined the log neural contrast function, with log contrast sensitivity log(cs) at any spatial frequency sf given by (Fig. 3):
- 4. The neural contrast sensitivity for sf calculated from in the above equation. For this, sf was taken as the average result for horizontal and vertical gratings.
- 5. The neural contrast sensitivity was inverted to get the perceived contrast c.
- 6. The diameter at which c occurred is given by [12] where σ is the Gabor standard deviation.
- 7. The number of visible cycles is calculated by multiplying sf and D. We calculated each eccentricity separately and took the average of horizontal and vertical acuities for all subjects.
2.8 FWHM of the spatial frequency band (edge effect)
To estimate the edge effect on the spatial frequency distribution, we calculated the full width at half maximum (FWHM) of the frequency distribution of the image of Gabors both with and without edge truncation. Figure 4 shows an example.
Fig. 4. Determining the influence of a sharp edge on the FWHM of Gabor patches. The top left shows a Gabor patch of standard deviation 1°C and spatial frequency, corresponding to the visual acuity at 20°C nasal field and with a sharp edge corresponding to 2.5°C diameter. The top right shows the same, but without the edge. The bottom shows the fast Fourier transforms corresponding to the top left figure. The FWHMs are 0.59 and 0.38 with and without the edge, respectively.
3. Results
3.1 Acuities for interference fringes vs viewing an AO corrected OLED screen without Gabor attenuation
These two cases had the same aperture sizes (1.5° on-axis, 2.5° off-axis), and the same comparison cases (identical participants, both horizontal and vertical gratings). They differed in actual angles in the periphery (20° and 30° fringes, 16.5° and 26.3° AO, expected to result in higher acuity for AO), and psychophysical method (method of adjustment for fringes, two interval forced choice for AO, expected to result in higher acuity for AO).
Figure 5 shows results. Except for on-axis, and despite the methodological differences expected to result in higher acuities for AO, acuity was consistently higher for interference fringes. For example, at 30° temporal field and vertical gratings, the average fringe and AO acuities were 10.4 cycles per degree (cpd) and 7.4 cpd, respectively.
Fig. 5. Grating acuities for interference fringes and AO corrected OLED screen without Gabor attenuation. Error bars represent standard deviations of the participants.
An Anderson-Darling normality test of the peripheral data did not reject normality (p = 0.10). Accordingly, for statistical analysis a four-way ANOVA interaction analysis was conducted modeling main effects and interaction effects simultaneously, with factors of type (interference fringes or AO), field eccentricity, orientation, and participant as effects, with participant treated as a random effect and the other factors as fixed effects. We found that interference fringes and AO differed significantly (p = 0.045). Unsurprisingly, eccentricity had a significant effect (p < 0.001). Orientation had a significant effect (p = 0.001), but participant did not. Interaction effects were significant except for orientation with subject and orientation with eccentricity.
3.2 Acuities for horizontal vs vertical gratings
For the comparison, the interference fringes and all grating sizes were included. Participants were treated as random effects. The ANOVA analysis was performed separately for each eccentricity, since grating sizes for on-axis were different than for off-axis.
Figure 6 shows results. The trend at all eccentricities was for horizontal gratings to give higher acuities than vertical gratings. On-axis, the trend did not reach significance (p = 0.051). For 20° nasal and 20° temporal, there was a significant effect of grating orientation (p = 0.027 and 0.009, respectively), but when doing multiple comparisons none of the individual Gabor sizes or interference fringes showed significant differences. For 30° nasal and 30° temporal, there was significant effect of orientation (p = 0.002 and 0.010, respectively), as well as significance for the individual comparisons at interference fringes and full size AO but not for the smaller Gabor sizes.
Fig. 6. Grating acuities for interference fringes and Gabors of different SDs. Error bars represents standard deviations of the group. Points are shown for each participant.
3.3 Sizes of the visible Gabor patches
The visible sizes of the Gabor patches exceeded the diameter of the aperture for all peripheral cases except for 0.5° standard deviation, where it barely fell below (Fig. 7). Thus, for nearly all of these realistic Gabor patches, window effects did not affect the results.
3.4 FWHM of the spatial frequency band
Table 1 shows results. Compared with the Gabor acuities, the FWHMs are small. They exceed 1 cpd only on-axis . The difference between the with and without edge effects was 1.0 to 1.5 cpd on-axis, but in the periphery they were ≤0.5 cpd.
Table 1. FWHM for Gabors with and without edge effect
4. Discussion
This study compared on-axis and peripheral detection acuity measured with interference fringes and with Gabor gratings of different standard deviations. Interference fringes were generated using a Lotmar Visometer and Gabor gratings were created on an OLED screen and imaged with an adaptive optics system.
Three main factors must be considered in interpreting the results. First, the measurement angles of interference fringes and Gabors were different, since the fixation targets of Gabors were close to the eye (60-80 mm) and no compensation was made for the center-of-rotation being behind the front of the eye. Thus, the Gabor fixation angles were smaller than the interference fixation to the eye by 12% to 18%. If the screen targets had been further out, the acuities with Gabor patches would have been lower, although one exception to this might be 20° temporal visual field, which was approximately 16.5° for the Gabors and would be influenced by the blind spot. Second, the psychophysics methods used were different for interference fringes (method of adjustment) and for Gabor (adaptive psychophysical procedure). The method of adjustment does not have a constant step size nor a time limit for detecting the fringes, but in general returns lower sensitivities because participants do not have to give an affirmative response until they are comfortable do so, unlike the forced choice of the other method [14]. Third, any residual defocus and aberrations after adaptive optics correction may have reduced acuity.
The on-axis detection acuities did not show significant differences between interference fringes and Gabors until the standard deviation was reduced to 0.2°. Conversely, the peripheral detection acuities with Gabor patches were lower than for interference fringes at all standard deviations, even with no attenuation. The smallest difference between Gabor patches and interference fringes occurred for the case with no attenuation. This indicates that, while for on-axis tasks it is sufficient to exceed a relatively modest standard deviation to reach similar results, in the periphery measurements need to be made with identical Gabor standard deviations to be comparable. Anderson et al. [15] reported a window size effect in which acuity increased on-axis and in the periphery as the field (window) size increased until there were approximately 6 cycles in the window. In our data, acuity continued increasing as the attenuation was lowered, even when the 6 visible cycles were exceeded. For example, in the 20 degrees nasal field with a standard deviation of 1.0 degrees, 16 cycles were visible, and reducing the attenuation to a standard deviation of 1.6 degrees still increased acuity from 6.4 to 8.8 cpd. The increase in acuity seen with less attenuation cannot be explained by the spatial frequency broadening of the edge effect. In the example above, the FWHM was only 0.6 degrees.
The consequence of the above findings is that it is more important for peripheral vision than for foveal vision that sizes of Gabor patches are matched. Furthermore, it seems that integration of peripheral vision happens over a larger area than is the case in on-axis vision. The extent of that area, i.e., at how many visible cycles this plateaus, is still an open question needing further investigation.
Off-axis, detection acuities for horizontal gratings were consistently higher (significant p value noted with paired t-test) than for vertical gratings. The average horizontal grating/vertical grating acuity ratios were 1.20 ± 0.07. This “meridional effect” is consistent with previous studies finding radially orientated gratings having higher acuities than circumferentially orientated gratings [5,16–18].
There are considerable differences in peripheral detection acuities in the literature. Table 1 compares studies, and includes factors which might be responsible for differences in detection acuities. Some results are plotted in Fig. 8. The peripheral detection acuities with interference fringes in the current study were lower than those of Zhu et al. [4] at all eccentricities. The detection acuities with Gabors (0.5° for on-axis and 1° for peripheral eccentricities) in the current study were similar to acuities in Atchison et al. [6] for on-axis and nasal eccentricities and slightly lower than acuities in Atchison et al. for temporal eccentricities (note the other study had only one participant). At 20° nasal eccentricity, the detection acuity with 1.6° Gabor in the current study was similar to that in Venkataraman et al. [5]. Considerable differences in detection acuity at 20° nasal eccentricity occurred between the current study with 0.5° Gabor and the study by Rosén et al. [7] with 0.6° Gabor, with Rosén et al. showing higher detection acuity. The small differences in Gabor standard deviations should not cause the acuity difference between the studies. Another difference is the peripheral field size, which in the current study was 2.5° and in the Rosén et al. study was 9°.
The average luminance in the current study was 23 cd/m2 which was considerably lower than luminances in previous studies (Table 2). Further studies on the effect of luminance on detection acuity are recommended.
Table 2. Detection acuities for different studies.
5. Conclusion
Peripheral detection acuities with less attenuated were more closely matched than the more attenuated Gabors to the acuities of interference fringes. Unlike on-axis vision, there was no plateau after which acuities remained the same. We do not believe spatial frequency broadening caused by the edge effect to be a major factor causing this.
Acknowledgements
Durgasri Jaisankar was a recipient of a Queensland University of Technology Postgraduate Research Award.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are available in Dataset 1, Ref. [19].
References
1. L. Frisen and A. Glansholm, “Optical and neural resolution in peripheral vision,” Invest. Ophthalmol. Vis. Sci. 14, 528–536 (1975).
2. Y.-Z. Wang, L. N. Thibos, and A. Bradley, “Effects of refractive error on detection acuity and resolution acuity in peripheral vision,” Invest. Ophthalmol. Vis. Sci. 38, 2134–2143 (1997).
3. L. Thibos, F. Cheney, and D. Walsh, “Retinal limits to the detection and resolution of gratings,” J. Opt. Soc. Am. A 4(8), 1524–1529 (1987). [CrossRef]
4. H.-F. Zhu, A. J. Zele, M. Suheimat, A. J. Lambert, and D. A. Atchison, “Peripheral detection and resolution with mid-/long-wavelength and short-wavelength sensitive cone systems,” J. Vis. 16(10), 21 (2016). [CrossRef]
5. A. P. Venkataraman, S. Winter, R. Rosén, and L. Lundström, “Choice of grating orientation for evaluation of peripheral vision,” Optom. Vis. Sci. 93(6), 567–574 (2016). [CrossRef]
6. D. A. Atchison, A. Mathur, and S. R. Varnas, “Visual performance with lenses correcting peripheral refractive errors,” Optom. Vis. Sci. 90(11), 1304–1311 (2013). [CrossRef]
7. R. Rosén, L. Lundström, and P. Unsbo, “Influence of optical defocus on peripheral vision,” Invest. Ophthalmol. Visual Sci. 52(1), 318–323 (2011). [CrossRef]
8. L. N. Thibos, D. L. Still, and A. Bradley, “Characterization of spatial aliasing and contrast sensitivity in peripheral vision,” Vision Res. 36(2), 249–258 (1996). [CrossRef]
9. T. Y. Chui, M. K. Yap, H. H. Chan, and L. N. Thibos, “Retinal stretching limits peripheral visual acuity in myopia,” Vision Res. 45(5), 593–605 (2005). [CrossRef]
10. L. N. Thibos, “Optical limitations of the Maxwellian view interferometer,” Appl. Opt. 29(10), 1411–1419 (1990). [CrossRef]
11. D. Jaisankar, M. Suheimat, R. Rosén, and D. A. Atchison, “Defocused contrast sensitivity function in peripheral vision,” Ophthalmic Physiol. Opt. 42(2), 384–392 (2022). [CrossRef]
12. R. Fredericksen, P. J. Bex, and F. A. Verstraten, “How big is a Gabor patch, and why should we care?” J. Opt. Soc. Am. A 14(1), 1–12 (1997). [CrossRef]
13. R. Rosén, L. Lundström, A. P. Venkataraman, S. Winter, and P. Unsbo, “Quick contrast sensitivity measurements in the periphery,” J. Vis. 14(8), 3 (2014). [CrossRef]
14. C. C. Wier, W. Jesteadt, and D. M. Green, “A comparison of method-of-adjustment and forced-choice procedures in frequency discrimination,” Atten. Percept. Psychophys. 19(1), 75–79 (1976). [CrossRef]
15. R. S. Anderson, D. W. Evans, and L. N. Thibos, “Effect of window size on detection acuity and resolution acuity for sinusoidal gratings in central and peripheral vision,” J. Opt. Soc. Am. A 13(4), 697–706 (1996). [CrossRef]
16. R. Anderson, M. Wilkinson, and L. Thibos, “Psychophysical localization of the human visual streak,” Optom. Vis. Sci. 69(3), 171–174 (1992). [CrossRef]
17. J. Rovamo, V. Virsu, P. Laurinen, and L. Hyvärinen, “Resolution of gratings oriented along and across meridians in peripheral vision,” Invest. Ophthalmol. Vis. Sci. 23, 666–670 (1982).
18. L. A. Temme, L. Malcus, and W. K. Noell, “Peripheral visual field is radially organized,” Am. J. Optom. Physiol. Opt. 62(8), 545–554 (1985). [CrossRef]
19. D. Jaisankar, M. Suheimat, R. Rosén, and D. A. Atchison, “Dataset for paper” figshare (2022), https://doi.org/10.6084/m9.figshare.21299586.
