Free
Article  |   January 2015
Spatial summation across the central visual field: Implications for visual field testing
Author Affiliations
  • Sieu K. Khuu
    The School of Optometry and Vision Science, UNSW Australia, Sydney, New South Wales, Australia
    s.khuu@unsw.edu.au
  • Michael Kalloniatis
    The School of Optometry and Vision Science, UNSW Australia, Sydney, New South Wales
    Centre for Eye Health, UNSW Australia, Sydney, New South Wales, Australia
    MKalloniatis@cfeh.com.au
Journal of Vision January 2015, Vol.15, 6. doi:10.1167/15.1.6
  • Views
  • PDF
  • Share
  • Tools
    • Alerts
      ×
      This feature is available to Subscribers Only
      Sign In or Create an Account ×
    • Get Citation

      Sieu K. Khuu, Michael Kalloniatis; Spatial summation across the central visual field: Implications for visual field testing. Journal of Vision 2015;15(1):6. doi: 10.1167/15.1.6.

      Download citation file:


      © ARVO (1962-2015); The Authors (2016-present)

      ×
  • Supplements
Abstract

In the present study, we measured the extent of spatial summation in the detection of image contrast within the central 40° visual field. Contrast detection thresholds (in 28 observers) were measured for a spot of light of 10 different sizes [area: 0.03–1.92(°)2] at different retinal meridians (0°, 45°, 90°, 135°, 180°, 225°, 270°, and 315°) and eccentricities (0°, 5°, 10°, 15°, and 20°). Contrast detection thresholds were significantly affected by the size of the stimulus with sensitivity improving with stimulus size consistent with Ricco's law. Summation curves were similar across different spatial meridians, but the extent of spatial summation increased with retinal eccentricity consistent with previous reports. The size of the stimulus was also shown to affect contrast detection thresholds in the periphery. In particular, contrast detection thresholds decreased more rapidly with increasing eccentricity for a smaller target than a larger one. This difference in performance is accounted for by the accompanying change in Ac with eccentricity. In Experiment 2, we show that spatial uncertainty affected contrast detection, particularly at eccentric locations greater than 5°, such that cueing the location of the stimulus improved contrast thresholds. Spatial uncertainty improved overall performance but did not affect the estimates of the critical areas of summation. The results of the present study indicate that, due to spatial summation, detection performance is highly dependent on the size of the stimulus, its eccentric location, and spatial uncertainty. Future perimetric methodologies must consider these factors to improve detection sensitivity.

Introduction
A primary function of the human visual system is to detect contrast variations in an image (e.g., Kelly, 1977; Marr, 1983). Contrast steps in an image provide a cue to the contrast of important objects and features and are the primary basis for their recognition and the determination of a scene's spatial layout. The detection of contrast is thought to be mediated by neuronal channels that function by pooling or summing the light energy falling within their receptive field (Barlow, 1958; Hallet, 1963). This process of spatial summation has been well established to be dependent on both the size and temporal duration of the stimulus as both are important factors in determining the amount of light energy available to the visual system (e.g., Hecht, Shlaer, & Pirenne, 1942; Owen, 1971; Weale, 1958). In the present study, we sought to determine the extent of spatial summation at multiple locations within the central 40° visual field. 
Ricco's law (after Ricco, 1877), which characterizes the process of spatial summation in the detection of luminance contrast, states that the contrast detection threshold monotonically decreases (traditionally assumed as a slope of −1 in log-log coordinates) with stimulus size to a critical area (Ac), beyond which Piper's law (slope of −0.5) or less is observed. Within the Ac, an equal reciprocal relationship exists between the luminance of the stimulus (required for detection) and its size, such that stimulus detection occurs once the product of the luminance and the area of the stimulus is the same or greater than a constant value. This relationship changes for sizes greater than the Ac with partial dependency on stimulus area (Piper's law), such that contrast sensitivity improves with the square root of the stimulus area. Previous research has indicated that Piper's law might reflect a process in which limiting noise affects the spatial summation process (see Meese, 2010; Meese & Summers, 2012; Tyler & Chen, 2000). Indeed, a number of proposals have been made to account for partial summation in which either the limiting noise affects processing before or after summation and whether the signal transducer is linear or nonlinear (e.g., following a square root law, see Meese & Summers, 2012, for a review). Such models provide a better characterization for partial summation over traditional assumptions that attribute this process to probability summation. However, the neural mechanism/process that precisely accounts for partial summation remains a focus of research. Spatial summation is no longer observed once the size of the stimulus has far exceeded the pooling regions critical to the detection of contrast. Typically, spatial summation is expressed as L×Ak = C, where L is the luminance of the stimulus, A is the stimulus area, k is the summation coefficient, and C is a constant. The degree of summation is reflected in k with complete summation equal to 1 while partial summation is less than this value. No summation is given by a k of 0. 
Previous studies have well demonstrated the robustness of Ricco's law, and in particular, the size of the Ac has been shown to be dependent on the luminance of the background, color, and retinal eccentricity (Davson, 1980; Johnson, Keltner, & Balestrery, 1978; Sloan, 1961; Wilson, 1970). Although the neural mechanism responsible for spatial summation remains at present unclear, previous investigations have provided neurophysiological correlates in the receptive field size (e.g., Dacey, 2000; Dacey & Petersen, 1992) and density of retinal ganglion cells and the degree to which they pool information over the visual field (Barlow, 1958; Garway-Heath et al., 2002; Hallet, 1963; R. Harweth et al., 2010; R. S. Harwerth, Carter-Dawson, Shen, Smith, & Crawford, 1999). Previous research has also implicated a cortical locus for spatial summation (e.g., Adesnik, Bruns, Taniguchi, Huang, & Scanziani, 2012; Kapadia, Westheimer, & Gilbert, 1999; Sceniak, Ringach, Hawken, & Shapley, 1999), and the process of spatial summation has been modeled in terms of a population response of neurons working as a network to sum light over localized regions of the visual field (see Dumoulin & Wandell, 2008; Kendrick, Winawer, Mezer, & Wandell, 2013). Indeed, Pan and Swanson (2006) have proposed a model in which perimetric stimuli (circular spots) might be coded by cortical pooling in the primary visual cortex. They noted that a summation model in which receptive fields resembled those of orientation-tuned simple cells in the primary visual cortex well predicted behavioral data that characterized contrast sensitivity changes with stimulus size. 
The observation that the detection of contrast is mediated by a process of spatial summation has direct implications for current perimetric technologies that attempt to map the visual field by determining the contrast sensitivity (of a spot of light) at discrete spatial locations (see Anderson, 2006; Heijl, Lindgren, & Olsoon, 1987; Johnson, Wall, & Thompson, 2011; Katz & Sommer, 1986). For example, white-on-white standard automated perimetry (SAP), which is recognized as the gold standard in the assessment of ocular disease, typically measures the contrast detection threshold of a Goldmann size III (presented at relatively low photopic light levels at a duration of 100–300 ms to foveal and peripheral locations; see Johnson et al., 2011). However, as indicated by Ricco's law, contrast detection is dependent upon the size of the stimulus with the Ac scaling with retinal eccentricity (e.g., Flanagan, Wild, & Wood, 1988; Sloan, 1961; Wild, Wood, & Flanagan, 1987; Wilson, 1970). For example, Wilson (1970), Sloan (1961), and Johnson et al. (1978) have measured the spatial summation curves for eccentricities up to 55°. In particular, they have noted that, although the shape of the summation curves does not change, the Ac monotonically increases in size with retinal eccentricity. This indicates greater spatial summation at peripheral locations than at the fovea, perhaps reflecting larger receptive fields (and/or density, e.g., Garway-Heath et al., 2002) of peripheral cells responsible for the detection of light information (Dacey & Petersen, 1992). 
It has been well demonstrated that contrast thresholds are location-specific (e.g., Baldwin, Meese, & Baker, 2012; Pointer & Hess, 1989), and in the present study, we examine the degree to which contrast detection reflects an interdependence of the stimulus size and eccentricity. In particular at larger retinal eccentricities, the size of the test stimulus might be smaller than the Ac, and elevated thresholds reflect spatial summation (e.g., Anderson, 2006; Sloan, 1961). Indeed, the interdependence of stimulus size, contrast, and retinal location on detection performance has been well recognized in the literature as a major factor in limiting the sensitivity of existing visual field technologies (e.g., Anderson, 2006; Johnson et al., 2011; Redmond, Garway-Heath, Zlatkova, & Anderson, 2010; Wall, Doyle, Eden, Zamba, & Johnson, 2013). This is especially noteworthy given that the Ac has been shown to change in ocular disease (such as glaucoma, see Fellman, Lynn, Starita, & Swanson, 1989; Redmond et al., 2010), which limits the effective use of current perimetric technologies in their diagnosis. 
Previous studies have acknowledged the importance of the size of the test stimulus in perimetric testing and whether it might be used to improve the detection of visual loss. For example, Anderson (2006) noted that, based on the findings of Wilson (1970), a Goldmann size III stimulus at peripheral locations falls outside spatial summation within the central 30° radius but is within spatial summation for eccentric locations of 40° and greater. Accordingly, contrast detection thresholds are not equated across the visual field in conventional visual field testing, and scaling the size to ensure equal summation might provide a more effective method of visual field testing. This has been acknowledged by Redmond et al. (2010), who noted that in glaucoma the Ac is larger in size relative to age-matched normals, and they proposed that future perimetric procedures might change the test size during testing (to equate contrast detection thresholds) to increase group differences between normal and disease populations. The adoption of a different test size stimulus for the detection of visual function in eye disease has also been proposed by Wall et al. (2013). Here the observation is made that a large test stimulus size (e.g., Goldmann V target) might be more effective in detecting glaucomatous loss (as evidenced by a difference in mean deviation) than a smaller size III target. Accordingly, the recommendation is made to use perimetric procedures that modify the stimulus test size, such as size threshold perimetry (STP) in which the contrast of a target is kept constant, but its size is modulated to obtain a “size threshold.” Indeed, it has been reported that STP is more effective in detecting glaucomatous visual field loss than standard procedures that use a fixed stimulus size (Wall et al., 2013). Other perimetric technologies, such as the Heidelberg edge perimetry, which scales target size with eccentricity, have been shown to be effective in detecting early glaucomatous loss (e.g., Mulak, Szummy, Sieja-Bujewska, & Kubrak, 2012). However, the effectiveness and validity of these perimetric procedures remain the focus of much research. 
Although a number of methods have been proposed that seek to improve measurement sensitivity by modifying and using different test stimulus sizes, the success of such proposals are contingent on understanding and quantifying the extent of spatial summation across the visual field. As mentioned, previous studies have characterized the change in Ac as a function of retinal eccentricity. However, it is important to note that, although these studies have been informative in characterizing the extent of spatial summation in the visual field, they are limited in that they only characterized contrast detection performance using a small number of test sizes along the horizontal and or vertical meridian, usually at one eccentricity, and drawn from a small number of observers (e.g., Sloan, 1961; Wilson, 1970). Interestingly, no data has been provided that characterizes the extent of spatial summation at other meridians. The lack of data at other angular meridians and the small pool of observers limit their use as “normative” data for comparison with current visual field technologies that map performance across the entire visual field and not just to cardinal meridians. As mentioned, ocular diseases, such as glaucoma, shows pattern loss of contrast sensitivity (see Redmond et al., 2010) that is diffuse across the visual field, and thus providing normative data regarding how the Ac changes across the visual field is an important first step in accurately characterizing loss in this eye disease. This was the primary goal of the present study. 
Experiment 1: Determining the extent of spatial summation across the central 40° visual field
In Experiment 1, we measured spatial summation curves at eight angular meridians at retinal locations of 0°, 5°, 10°, 15°, and 20° of eccentricity using a standard testing paradigm. In a pool of 28 observers, we provide data on how the Ac changes with retinal location and whether differences exist along different angular meridians. 
Methods
Participants
Twenty-eight participants (mean age: 20 years) acted as observers in the present study. They were experienced observers but were naïve to the aims of the study. All had normal or corrected-to-normal visual acuity and underwent ophthalmic assessment to rule out any pathology and abnormalities. Corrective lenses were worn during the experiment. Participants gave their informed consent prior to participating in the present study. 
Stimulus and apparatus
Stimuli were white circular spots of light presented on a white-gray background (10 cd/m2) for 200 ms (see Figure 1). This duration ensured that the stimulus pulse was outside Bloch's law, and the presentation time did not affect contrast detection thresholds (see Barlow, 1958). There were 10 different stimulus sizes with areas of 0.03, 0.06, 0.12, 0.24, 0.36, 0.48, 0.72, 0.96, and 1.92(°)2 (note that these stimulus sizes do not correspond to standard Goldmann test sizes). For foveal conditions, an additional test size of 0.01(°)2 was included in testing. These stimuli were presented at meridians (from right horizontal and in a counterclockwise direction) of 0°, 45°, 90°, 135°, 180°, 225°, 270°, and 315° and at eccentricities of 0°, 5°, 10°, 15°, and 20° of eccentricity (see Figure 1). This visual field region was chosen as most visual field testing approaches primarily encompass this region (see Heijl et al., 1987; Schiefer et al., 2010). A black fixation mark (0.06° × 0.06°, Weber Contrast −0.2) was placed at the center of the stimulus, on which the participant was instructed to fixate at the beginning of each stimulus presentation. Note that for foveal presentations the fixation mark disappeared 150 ms before the presentation of the stimulus less it overlaps and interferes with contrast detection (see Summers & Meese, 2009). For eccentric locations, the fixation mark was present throughout the duration of the trial, but it did not overlap with the stimulus. Stimuli were presented on a linearized CRT (Mitsubishi Diamond Pro 27-in.) monitor that was driven at a frame rate of 100 Hz. A head and chin rest was used to ensure a constant viewing distance of 40 cm. Stimuli were generated on a MacBook Pro computer using custom written software in MATLAB (Mathworks, version 7). 
Figure 1
 
A schematic of the experimental stimulus and procedure (A), and a representation of stimulus locations tested in the present study (B).
Figure 1
 
A schematic of the experimental stimulus and procedure (A), and a representation of stimulus locations tested in the present study (B).
Procedure
The abovementioned stimuli were briefly presented to the observer randomly at one of the eight angular meridians and at one of the five eccentricities. Participants were instructed to maintain central fixation, and after a period of 400 ms, the stimulus was flashed on the screen for a period of 200 ms. A high-frequency beep (duration 50 ms) was sounded 100 ms prior to the onset of the stimulus so that the participants were aware of the subsequent stimulus presentation. The task of the observers was to indicate whether they saw the stimulus or whether no stimulus was present. They indicated their response by pressing keys on a computer keyboard. This also signaled the beginning of the next trial. An adaptive staircase procedure (71% correct performance level) was used to modify the contrast of the stimulus. Initially, the staircase had a starting Weber (contrast level) that was randomly chosen from a range of 0.2–0.15. The step size of the stimulus was initially 0.02, and this was halved after the first and subsequent reversal. After the fourth reversal, the step size was 0.0025 and remained at this level until the end of the staircase. The “bit stealing” algorithm of Tyler (1997) was used to increase the gray scale level of the monitor to 12 bits (i.e., 4,096 levels). The staircase lasted for six reversals, and the average of the last four reversals provided a measure of the contrast detection threshold. 
Contrast detection thresholds using the abovementioned staircase procedure were measured for each of the 10 stimulus sizes at the eight different angular meridians and at eccentricities of 0°, 5°, 10°, 15°, and 20° in a randomized order. Note that at 0° the target spot was only presented centrally. Additionally, locations coinciding with the blind spot were not tested. Observers performed these trials once in five blocks, in which one eccentricity was examined per block. The block order (i.e., the order in which participants were tested at different eccentricities) was randomized within the block and between participants. Within a block of trials, the presentation order of the 10 different test stimulus sizes and locations were randomized, and their staircases were interleaved. Participants performed this task monocularly with their left eye (with natural pupils) and with their right eye patched. Our reason for the methods and procedures used in Experiment 1 is that it is similar to SAP testing approaches, in which observers subjectively responded to a seen spot of light (by pressing a button) that is presented to random locations on the screen without spatial cueing. This allows for a degree of comparison and application to standard perimetric testing procedures used in previous studies and in clinical settings to measure contrast sensitivity. 
Results and discussion
In Figure 2, average contrast detection thresholds (expressed as log ΔL/L, where ΔL is the minimum luminance difference required for detection from background L) are plotted as a function of the area of the test stimulus (log deg2) and for different retinal eccentricities (different symbols). To provide a gauge of the variability of observers, in Figure 2, error bars represent 1 SD of the mean. In addition, for a particular stimulus condition, the observer data was examined as a frequency distribution, and a Gaussian function was fitted to the data (using GraphPad Prism 6). This was performed for 40 different conditions randomly chosen from the over 330 different combinations of test stimulus sizes, meridian angles, and eccentricities. This analysis revealed that, on average, the data of the 28 observers were normally distributed and well approximated by a Gaussian distribution (mean R2 = 0.771). However, this analysis also noted and included data from observers that deviated by 2 SD or more from the mean. 
Figure 2
 
Contrast thresholds plotted as a function of the size of the stimulus. Within each plot, data from different eccentricities are plotted as different symbols. Data for the different meridians (see schematic diagrams in each panel) are arrayed around the central panel, which shows data for foveal conditions. Error bars represent 1 SD from the mean.
Figure 2
 
Contrast thresholds plotted as a function of the size of the stimulus. Within each plot, data from different eccentricities are plotted as different symbols. Data for the different meridians (see schematic diagrams in each panel) are arrayed around the central panel, which shows data for foveal conditions. Error bars represent 1 SD from the mean.
Note also that vertical lines are indicative of Goldmann test sizes ranging from I to V. The central panel provides data for foveal conditions, and data for different spatial locations are arrayed around the central plot, coinciding with their meridian angle in a counterclockwise direction. Accordingly, angles of 0° and 180° represented the horizontal meridian, and 90° and 270° represented top and bottom vertical axes, respectively. Note that for meridians of 0° and 180° the data represents the average of eight participants who were separate from the 28 whose data are represented in the other plots. Evident in Figure 2 are Ricco-like summation curves: As the size of the stimulus was increased, there was a monotonic decrease in contrast detection thresholds to a critical value beyond which thresholds reflected partial summation (Piper's law) or there is no or minimal improvement. This pattern of data was observed at other meridians and retinal eccentricities. To approximate the contrast detection curves for each eccentricity in each panel and to estimate the degree of spatial summation change with retinal eccentricity, two-segment linear regression analyses (least-squares regression) were performed on these data using GraphPad Prism 6. As it was our goal to estimate the area of critical summation (Ac), this analysis was constrained such that the slope of the first line was fixed to a constant traditionally considered to be −1 (Ricco, 1877), and the second line (representing partial summation) was allowed to vary with the fit. The curves of best fit (average R2 = 0.88) are also shown in Figure 2. The Ac values from these curve fits were separately shown in Figure 4 (see below for a discussion). 
A repeated-measures two-way ANOVA conducted separately for each of the eight meridians confirmed that both changing test stimulus size and eccentricity had a significant effect (with ps < 0.0001 for both factors across the eight meridians) on contrast detection thresholds. However, a significant interaction effect was also observed for all eight meridian angles (with ps < 0.0001), which indicated that the summation curves were dependent on retinal eccentricity. For nonfoveal locations, contrast detection curves systematically shift to the right, indicating an increase in the area of spatial summation with retinal eccentricity. 
As discussed above and noted previously (see Flanagan et al., 1988; Sloan, 1961; Wild et al., 1987; Wilson, 1970), sensitivity to contrast is dependent on both the size of the stimulus and its retinal location. To provide an indication of this change across the meridians assessed in the present study, in Figure 3 the contrast sensitivity (as log ΔL/L) is plotted for six different target sizes as a function of retinal eccentricity. Different panels represents data for the horizontal (0°–180° axis, Figure 3A), vertical (90°–270° axis, Figure 3B), and the two oblique axes of 45°–225° (Figure 3C) and 135°–315° (Figure 3D). A two-way repeated-measures ANOVA performed separately for each meridian axis revealed a main effect of stimulus size (ps < 0.0001) and eccentricity (ps < 0.0001) but also significant interaction effects (ps < 0.0001) between retinal eccentricity and test size. A number of findings present themselves. First, the size of the test stimulus significantly affected contrast detection thresholds; increasing the test stimulus size significantly improved overall detection performance. Thus, the visual system is more sensitive to larger- than smaller-sized targets. Second, contrast detection thresholds monotonically increased with retinal eccentricity, highlighting superior performance for foveal presentations compared to peripheral locations. However, the rate at which contrast detection thresholds change with eccentricity is clearly dependent on the size of the stimulus. Note that this threshold change was greatest for the smallest target but became progressively smaller for larger targets. The largest target thresholds were relatively unchanged over the range of eccentricities used in the present study. 
Figure 3
 
Contrast thresholds (log ΔL/L) plotted as a function of eccentricity for six different test sizes. Error bars represent 95% confidence limits. Different plots (A–D) plot data along different meridian axes: A, horizontal axis; B, vertical axis; C and D, oblique axes (see schematic representation in each figure).
Figure 3
 
Contrast thresholds (log ΔL/L) plotted as a function of eccentricity for six different test sizes. Error bars represent 95% confidence limits. Different plots (A–D) plot data along different meridian axes: A, horizontal axis; B, vertical axis; C and D, oblique axes (see schematic representation in each figure).
Figure 4
 
Derived Ac values plotted in linear polar coordinates. Error bars signify 95% confidence limits. Different symbols represent the Ac obtained at different retinal eccentricities, which are plotted along their respective meridian angle. Dashed circles represent the size of Goldmann I–III targets.
Figure 4
 
Derived Ac values plotted in linear polar coordinates. Error bars signify 95% confidence limits. Different symbols represent the Ac obtained at different retinal eccentricities, which are plotted along their respective meridian angle. Dashed circles represent the size of Goldmann I–III targets.
These results are in agreement with Sloan (1961), who originally characterized the dependency of contrast sensitivity on target location and size. Importantly, the present study extends this observation to other angular meridians, allowing extrapolation to clinical visual field testing. A comparison of the data in Figure 3 for each test stimulus size at different meridians did not observe a main effect of meridian angle (with ps > 0.1421). This suggests that for a particular test stimulus size the change in contrast detection with retinal eccentricity is approximately the same for the eight angular meridians examined in the present study. As the plots in Figure 3 are representative of the minimum contrast required for detection at different eccentricities, they provide a comparable description of the “Hill of Vision” for different test stimulus sizes. As indicated in Figure 3, the shape of the hill of vision is dependent on the test stimulus size, and its “kurtotic” form is largely determined by whether the stimulus test size falls within or outside the Ac of Ricco's law. Accordingly, existing testing strategies that use a fixed test size might provide a measure of performance that is confounded with spatial summation (see Anderson, 2006). 
As it was the goal of the present study to determine the spatial extent of summation across the visual field, we provide in Figure 4 estimates of the Ac values for different eccentric locations, which correspond to the inflection point of the segmental line fit shown in Figure 2. Ac values are plotted in polar coordinates as linear ΔL/L along their respective meridians; the Ac values for different eccentricities are denoted by different symbols. Error bars represent 95% confidence intervals to facilitate comparison between different Acs. Figure 4 clearly shows that the Ac systematically increases with retinal eccentricity. For reference, Goldmann sizes I–III are shown in Figure 4 as dashed circles. A number of findings present themselves. The data in the present study indicates that, for foveal locations, a size I is smaller than the Ac, but test sizes II and III are outside the area of spatial summation but within regions corresponding to partial summation (Piper's law) or complete summation. At eccentricities between 5° and 15°, test sizes smaller than and including size II are within the Ac, and at 20°, a size III target falls close to the Ac although there is a degree of variability along different meridians. As mentioned in the Introduction, SAP employs a fixed-size target to map contrast sensitivity across the visual field. Because Ac increases with retinal eccentricity as indicated here and in the literature (e.g., Sloan, 1961; Wilson, 1970), this confirms that a Goldmann size III stimulus (in white-on-white perimetry) will fall within or outside the Ac depending on the retinal eccentricity of the stimulus. 
Experiment 2: The role of spatial uncertainty in the detection of contrast and its affect on spatial summation
As noted in Experiment 1, observers were required to detect a spot of light target (of different sizes) presented to random locations in the visual field. As mentioned, we adopted this testing procedure as it accords with SAP testing protocols in which the stimulus location is not cued and observers subjectively respond only to the presence of the stimulus. However, this method might mean that observer responses are influenced by both criterion bias and spatial uncertainty in detecting uncued targets. 
Previous studies have examined the issue of spatial uncertainty in the detection of contrast. For example, Carrasco, Penpeci-Talgar, and Eckstein (2000) measured the contrast sensitivity function using peripherally presented targets in which the location of the stimulus was cued or uncued. They reported that when the spatial position of the stimulus was cued and measured objectively using a forced-choice procedure, contrast detection performance was superior to when it was not cued and observers were uncertain about the position of the stimulus (see also Lee, Koch, & Braun, 1997; Lu & Dosher, 1998). However, the improvement in contrast sensitivity was uniform across all spatial frequencies, which suggests that reducing spatial uncertainty might improve overall detectability due to the general allocation of spatial attention. 
Due to the testing methods adopted in Experiment 1, contrast detection thresholds reported in Figure 2 might be influenced by spatial uncertainty and criterion bias, and the degree to which these factors might influence the extent of spatial summation remains unclear. In Experiment 2, we examined this issue by measuring spatial summation curves in two separate conditions in which the location of the target was uncued (using the methods of Experiment 1) or cued and measured objectively using a two-interval forced choice (2IFC) procedure. This issue is additionally noteworthy because uncertainty in location of elements is inherent to SAP, and it remains to be established whether and how performance in perimetric testing might be ameliorated by observers not knowing the position of the target. 
Methods
Observers
Five observers participated in the present study. All had normal or corrected-to-normal visual acuity with no history of any visual disorders. One observer (SKK) was an author of the study, and the others were experienced observers who were naïve to the aims of the experiment. Observers gave their informed consent before participating in this experiment. 
Stimulus and procedures
The stimulus and procedures were similar to that employed in Experiment 1. However, we measured spatial summation curves at only eight points along the horizontal meridian at: −20°, −15°, −10°, −5°, 0°, 5°, 10°, and 20° using the right eye (the left eye was patched) with the spatial location coinciding with the blind spot not tested. We measured spatial summation curves at different eccentricities because, as noted in Experiment 1, the change in Ac was dependent on eccentric location but not on the meridian angle (see Figure 4). At each eccentric location, contrast sensitivity was measured for six test stimulus sizes of 0.03, 0.06, 0.12, 0.24, 0.48, and 0.72(°)2. Note that for foveal conditions, a smaller test size of 0.01(°)2 was used, and 0.48(°)2 was omitted from the range of sizes tested. For uncued conditions, testing procedures were similar to those employed in Experiment 1. While maintaining central fixation, observers were presented a spot of light (of a particular size, cued by an auditory beep) to one of the eight spatial locations with the testing location randomized from trial to trial. Thus, there was uncertainty in the location of the stimulus as there was a one in eight chance that the stimulus would be presented to each location. This is analogous to Experiment 1 in which the stimulus location was presented to one of eight angular meridians for a particular retinal eccentricity. As in Experiment 1, observers were required to indicate (on the keyboard) whether they saw the stimulus. 
For cued conditions, the testing procedure was similar, but the spatial location of the stimulus was cued by the presentation of two vertical black lines (length: 1°, width: 0.125°, Weber contrast −0.2) placed 1° above and below the target location to be tested. These lines were briefly presented for 150 ms and disappeared from the display 150 ms before the onset of the stimulus position. As noted above, a limitation of the uncued task adopted in Experiment 1 is that observers are required to subjectively respond “yes/no” to whether they saw the stimulus. Accordingly, this subjective task might mean that thresholds are additionally affected by criterion bias. To address this, in cued conditions, contrast detection thresholds were measured using an objective 2IFC procedure. In both intervals, the spatial location of the stimulus was cued, but the stimulus was only presented in one interval. The interval containing the stimulus was randomized from trial to trial. The task of the observers was to judge the interval in which the stimulus was presented, and they did so by pressing the corresponding keys on a keyboard. 
In both cued and uncued conditions, contrast detection thresholds were concurrently measured for the six different stimulus test sizes at the eight different eccentric locations with the staircases (corresponding to the 71% correct performance level) randomly interleaved. Sufficient breaks were given to ensure observer vigilance and avoid fatigue. This was repeated at least five times, and the results averaged for the different test size conditions at each spatial location. 
Results and discussion
The results (average of the five observers) of Experiment 2 are shown in Figure 5. In Figure 5, spatial summation curves for cued and uncued conditions are plotted (as square and circle symbols, respectively) for different retinal eccentricities. Error bars here are representative of 1 SD to provide an indication of the variability between observers. Two-line fits (as in Experiment 1 and shown in Figure 5 as solid lines) to these data provide an estimate of the Ac for cued and uncued conditions and for different retinal eccentricities. These Ac values are plotted in Figure 6 as a function of eccentricity; to facilitate comparison between the two different cueing conditions, error bars are indicative of 1 SEM
Figure 5
 
Contrast detection thresholds (n = 5) plotted as a function of stimulus area for targets presented at different eccentricities along the horizontal meridian (different panels). Error bars represent 1 SD. Results for conditions in which the stimulus was cued and uncued are represented by squares and circles, respectively. In the framed panel, the average difference between cued and uncued conditions collapsed across the six different test sizes is plotted as a function of eccentricity.
Figure 5
 
Contrast detection thresholds (n = 5) plotted as a function of stimulus area for targets presented at different eccentricities along the horizontal meridian (different panels). Error bars represent 1 SD. Results for conditions in which the stimulus was cued and uncued are represented by squares and circles, respectively. In the framed panel, the average difference between cued and uncued conditions collapsed across the six different test sizes is plotted as a function of eccentricity.
Figure 6
 
The Ac plotted as a function of retinal eccentricity for cued and uncued conditions (represented by circles and squares, respectively). The average log difference in Ac between the two conditions is shown as diamonds. Error bars denote ±1 SEM.
Figure 6
 
The Ac plotted as a function of retinal eccentricity for cued and uncued conditions (represented by circles and squares, respectively). The average log difference in Ac between the two conditions is shown as diamonds. Error bars denote ±1 SEM.
A two-way repeated-measures ANOVA, which examined the effect of stimulus size (factor 1, six levels) and cueing (factor 2, uncued vs. cued) on contrast thresholds were performed separately for the eight different retinal eccentricities. For all eccentric locations, a main effect of stimulus size was observed (ps < 0.0001), such that increasing stimulus size improved contrast detection performance. This is consistent with spatial summation as noted in Experiment 1 and in previous studies (e.g., Sloan, 1961; Wilson, 1970). In addition, no significant interaction effect was observed (ps > 0.3011), which indicated that the effect of changing stimulus size on contrast detection in both cued and uncued conditions was the same. 
A main effect of spatial cueing was observed, but only at peripheral eccentricities greater than 5° of eccentricity in both nasal and temporal directions. At these eccentricities, contrast detection thresholds were significantly lower (ps < 0.0154) when the target location was cued and contrast detection objectively measured using a 2IFC procedure. For the central and −5° and 5° locations, there was no significant difference between cued and uncued conditions (ps > 0.1078). No effect of cueing at these eccentricities might be accounted for by the fact that observers were instructed to fixate centrally, and the proximity of the target at these locations might mean that they were immediately obvious and detectable. In summary, for the observers who participated in Experiment 2, there was no advantage to cueing the location of the stimulus or employing more objective procedures to quantify thresholds when the stimulus was located close to fixation. 
The difference between cued and uncued conditions is summarized in the boxed panel shown in Figure 5. Here, the difference between uncued and cued conditions is collapsed across different test sizes (as there was no significant interaction effect) and plotted as a function of the spatial position of the target stimulus. Positive values indicate that detection thresholds from cued conditions were lower than uncued conditions. Error bars represent 1 SEM. As shown in this plot, the difference between cued and uncued conditions significantly increased, one-way ANOVA: F(7, 32) = 2.757, p = 0.0233, with retinal eccentricity, such that cueing the stimulus resulted in lower contrast detection thresholds. 
Although spatial cueing had an effect on overall contrast detection at peripheral locations, it did not affect the extent of spatial summation (see Figure 6). For the data shown in Figure 6, a two-way repeated-measures ANOVA was performed to examine the effect of stimulus location (factor 1, eight levels) and spatial cueing (factor 2, uncued vs. cued) on the Ac. This analysis revealed a main effect of stimulus location, F(7, 64) = 5.64, p < 0.0001, such that the Ac increased with eccentricity. This is consistent with the findings of Experiment 1 (see Figure 4). Additionally, there was no significant interaction effect, F(7, 64) = 0.17, p = 0.9896, which indicated that the change in Ac with retinal eccentricity was the same for both cueing conditions. However, no effect of spatial cueing was observed, F(1, 64) = 0.12, p = 0.7324, which indicated that there was no significant difference in the Ac between cued and uncued conditions. Indeed, the difference between the uncued and cued conditions plotted in Figure 6 (denoted by diamond symbols) is approximately zero across the range of eccentricities examined. The implications of these findings are that while the results of Experiment 1 might be influenced by spatial uncertainty and the subjective method by which data was collected, the Acs reported in Figure 4 inherently reflect the manner in which the neural mechanisms spatially summate light information within their receptive fields. 
General discussion
In the present study, we provided data characterizing spatial summation profiles at discrete spatial locations across the visual field within a 20° radius of central vision. We confirm that spatial summation increased with retinal eccentricity, and this change was uniform across different spatial meridians (see Figure 4). Such an increase is likely to reflect the number of ganglion cells that contribute to spatial pooling (e.g., Harwerth et al., 1999; Garway-Heath et al., 2002). We also confirmed across different spatial meridians that the increase in Ac largely accounts for the change in contrast sensitivity profiles with targets of different spatial sizes. Notably large targets are easily perceptible, and contrast detection thresholds do not appreciably change with retinal eccentricity (at least up to 20°). Smaller targets are, however, dependent on retinal eccentricity with contrast thresholds demonstrating greater change with retinal eccentricity. The degree of change with eccentricity simply reflects whether the tested stimulus size falls within or outside the Ac (see Figure 3). 
In Experiment 2, we note that the spatial uncertainty affected overall contrast detection performance but not the extent of spatial summation. The Ac for conditions in which the stimulus location was cued or uncued remained the same despite contrast detection improving under cued conditions. This finding has implications for perimetric approaches that present targets to multiple locations without cueing their location. In particular, spatial uncertainty might affect contrast detection thresholds for targets presented at eccentric locations, and this has consequences for the use and interpretation of the visual field as a means of assessing eye disease and its progression. In addition, the results of Experiment 2 indicate that the shape of the hill of vision at eccentric locations, as noted in Experiment 1 (Figure 3) and in previous studies using visual fields, might be affected by spatial uncertainty. This is certainly consistent with previous observations by Heijl et al. (1987) that peripheral contrast thresholds are more variable than central locations. Given the findings of the present study, this variability might be attributed to spatial uncertainty, and this might be a contributing factor in determining the rate at which contrast sensitivity decreases with eccentricity. Future studies that compare and contrast detection performance (across the entire visual field) between cued and uncued conditions using SAP and with different test sizes would be highly informative. Current perimetric protocols have no ability to cue the spatial location of targets unless custom protocols are used in which testing is undertaken at a small number of locations. Thus, our results indicate that it is not possible to use normative database values to compare data from custom protocols employing a few test points. Finally, it should be noted that the importance of cueing the location of targets is not just limited to visual field testing, but other functional measures of vision, such as letter and word acuity across the visual field. For example, Battista and Kalloniatis (2002) have demonstrated that a right field bias in recognizing words in the periphery was eliminated if the location of the stimulus was cued. Given the general impact of spatial uncertainty on perception, future studies might cue the location of the stimulus to control for perceptual biases and noise. 
Our results largely agree with previous studies that originally measured spatial summation curves and their change in the periphery (e.g., Sloan, 1961, Sloan & Brown, 1962; Wilson, 1970). It should be noted that the Ac is commonly an estimate derived from the curve fit applied to data, and no convention exists as to which provides the best fit. Consequently, the approximation of the Ac is largely dependent on the number of test sizes examined as well as the number of observers. Unfortunately, previous studies have characterized performance only with a small number of observers (e.g., one to two observers in Wilson, 1970, and Sloan, 1961) or have only used a few test sizes corresponding to Goldmann sizes 0–V (e.g., Sloan, 1961; Sloan & Brown, 1962), which limits the accuracy in approximating the Ac and estimating the coefficient of summation. These methodological factors might provide an account of the degree of variability in the reported Acs between studies. The present study best avoided these issues as it comprehensively examined spatial summation in a large number of observers using a large number of stimulus sizes and mapped the Ac along cardinal as well as oblique meridians in the visual field. Thus, these data are an important first step in providing a normative database for use in clinical visual field testing and the development of new methodologies to improve task sensitivity by using stimuli always within total spatial summation (Anderson, 2006), thus allowing for improved detection of eye disease. 
Previous studies examining spatial summation have attempted to quantify the extent of summation by fitting an exponential function to data to derive a single spatial summation coefficient (k) (e.g., Sloan, 1961; Sloan & Brown, 1962). This method might be limited because the coefficient is derived from a fit over the entire range of stimulus sizes tested (frequently Goldmann sizes 0–V). This is problematic for a number of reasons. First, such a fit would span Ricco's and Piper's areas, which are thought to be subserved by separate physiological mechanisms with different summation profiles. Second, because of the uniform fit, it does not provide a direct measure of the Ac nor take into consideration that the Ac changes with retinal eccentricity. In regards to the latter, it has been reported that the summation coefficient is larger for a small target but is smaller for a larger one, and the coefficient increases with retinal eccentricity. Significantly, Sloan and Brown (1962) argued that the summation coefficient is less than 0.8 for the central field and is greater than this value in the far periphery. However, this coefficient change might simply reflect the increase in Ac with eccentricity. That is, for a given test stimulus size, the summation coefficient increases with eccentricity as it falls further within Ricco's (or Piper's) area. This possibility has not been considered by previous investigations that have attempted to map retinal ganglion density with contrast sensitivity (e.g., Garway-Heath et al., 2002). Here, it is assumed that the relationship between the coefficient and its change with eccentricity arises because of a change in ganglion cell density and not a change in the Ac itself. Accordingly, a two-line fit (or three-line fit) would be preferential to provide a more valid estimation of spatial summation by separately estimating the Ricco's and Piper's areas of summation and pinpointing the Ac. Note that the present study employed such a fit with a large number of target sizes, and we were able to well characterize Ricco's law and the Ac at various points in the visual field. 
As mentioned in the Introduction, it has been recommended that the size of the test stimulus should be scaled with retinal eccentricity such that the test size is the same or greater than the Ac (see Anderson, 2006; Redmond et al., 2010, Sloan, 1961) to avoid spatial summation. Note that although this procedure would ensure good stimulus detectability (as contrast thresholds are lower at and outside the Ac), it might be impractical to measure for clinical purposes as it is derived by measuring contrast sensitivity with multiple target sizes and at multiple locations. Thus, this is potentially time-consuming and inefficient. More importantly, though, determining and testing close to the Ac does not necessarily improve task sensitivity in detecting visual loss due to eye disease. Note that eye disease is usually accompanied by a loss in retinal cells contributing to spatial summation (Malik et al., 2012; Redmond et al., 2010). However, a larger test size (or one scaled to the Ac) would activate more cells, contributing to the summation process, and therefore would compensate for any loss arising from retinal damage. For example, Redmond et al. (2010) measured spatial summation curves in a glaucoma and an age-matched normal group. They reported that participants with glaucoma had generally poorer contrast sensitivity and larger Acs than age-matched normals. However, the largest group difference in performance occurred for test sizes less than the Ac. For sizes larger than the Ac, the difference in contrast sensitivity between the two groups was minimal presumably because the size of the stimulus activated more cells and compensated for the loss of cells due to glaucoma. Accordingly, using a test stimulus size scaled to the Ac or larger will therefore be a poor group discriminator as both groups will be equally effective in detecting the stimulus. 
Future recommendations might employ a test size smaller than the Ac and within Ricco's law, with which group differences in contrast sensitivity are more pronounced. As noted by Sloan and Brown (1962), the summation profiles in eye diseases, such as macular degeneration and optic neuritis, typically exhibit “photometric harmony” (i.e., elevated thresholds across all test stimulus sizes) but also “photometric dysharmony” (see Weekers, 1959) in which thresholds are more elevated in the diseased eye, especially at small sizes, due to spatial summation differences. Dubois-Poulsen, Magis, Ben-Mansour, and Lanneau (1959) reported that kinetic perimetry isopter changes did not follow expected contraction with dimmer/smaller test size reduction in glaucoma patients. They reported markedly constricted visual fields with smaller/dimmer targets in glaucoma patients, thus identifying a more severe visual field deficit. The failure of kinetic isopters to follow expected changes in patients with ocular disease led Dubois-Poulsen et al. (1959) to coin the term “photometric dysharmony.” The now classic studies of Sloan (1961), Sloan and Brown (1962), and Wilson (1970) specifically investigated spatial summation in normal and a range of eye diseases to better characterize the effect of spatial summation on the amount of threshold elevation in ocular disease. These studies partially mapped Ricco's law but, more importantly, found many patients with whom smaller test stimuli (within Ricco's law) displayed a larger deficit compared to the use of larger test stimuli. These findings demonstrate that at smaller sizes contrast thresholds between the normal and the diseased eye might be more obvious, and therefore, the use of a small test stimulus size might present a better means of discriminating group differences and detecting visual field loss. This is despite the known optical effects and aberrations that might limit and change the image resolution of a small target on the retina. In this study, threshold values of small test stimuli always fell within the slope of −1 indicating that, despite the image degradation, all the light fell within the area delineated by complete spatial summation. However, the basis of any future recommendations to scale the test size stimulus with eccentricity to increase test sensitivity must be based on data that extensively characterize the spatial summation across the entire visual field and allow a comparable unit of measure when using different test sizes. Although the present study has made an important first step to address this paucity in knowledge, at present, this has not been entirely realized in the literature. 
Acknowledgments
We thank the observers who participated in the study and the editor and two anonymous reviewers for their help and constructive comments. This research was supported by an Australian Research Council (ARC) Discovery Project grant (grant number: DP110104713) to S. Khuu. The work was supported by the National Health and Medical Research Council of Australia (NHMRC #1033224). The Centre for Eye Health is an initiative between UNSW Australia and Guide Dogs NSW/ACT. Guide Dogs NSW/ACT are also a partner on the NHMRC grant. 
Commercial relationships: The following work is applicable to the following Patent: “Structure-function in retinal disease.” Inventors: Kalloniatis, M., Khuu, S. K., & Alsaleem, N. (2012). Australian Provisional Patent: 2012905587. 
Corresponding author: Sieu Khuu. 
Email: s.khuu@unsw.edu.au. 
Address: The School of Optometry and Vision Science, UNSW Australia, Sydney, New South Wales, Australia 
References
Adesnik H. Bruns W. Taniguchi H. Huang Z. J. Scanziani M. (2012). A neural circuit for spatial summation in visual cortex. Nature, 490, 226–231. [CrossRef] [PubMed]
Anderson R. S. (2006). The psychophysics of glaucoma: Improving the structure/function relationship. Progress in Retinal and Eye Research, 25, 79–97. [CrossRef] [PubMed]
Baldwin A. S. Meese T. S. Baker D. H. (2012). The attenuation surface of contrast sensitivity has the form of a witch's hat within the central visual field. Journal of Vision, 12 (11): 23, 1–17, http://www.journalofvision.org/content/12/11/23, doi:10.1167/12.11.23. [PubMed] [Article]
Barlow H. (1958). Temporal and spatial summation in human vision at different background intensities. The Journal of Physiology, 141, 337–350. [CrossRef] [PubMed]
Battista J. Kalloniatis M. (2002). Left-right word recognition asymmetries in central and peripheral vision. Vision Research, 42, 1583–1592. [CrossRef] [PubMed]
Carrasco M. Penpeci-Talgar C. Eckstein M. (2000). Spatial attention increases contrast sensitivity across the CSF: Support for signal enhancement. Vision Research, 40, 1203–1215. [CrossRef] [PubMed]
Dacey D. M. (2000). Parallel pathways for spectral coding in primate retina. Annual Review of Neuroscience, 23, 743–775. [CrossRef] [PubMed]
Dacey D. M. Petersen M. R. (1992). Dendritic field size and morphology of midget and parasol ganglion cells of the human retina. Proceedings of the National Academy of Sciences, USA, 89, 9666–9670. [CrossRef]
Davson H. (1980). Physiology of the eye (4th ed.). New York: Academic Press.
Dubois-Poulsen A. Magis C. L. Ben-Mansour, Lanneau, . (1959). La dysharmonie photometrique dans le champ visuel des glaucomateux [Translation: Photometric dysharmony in the visual field of glaucoma patients]. Documenta Ophthalmologica, 13, 286. [CrossRef] [PubMed]
Dumoulin S. O. Wandell B. A. (2008). Population receptive field estimates in human visual cortex. Neuroimage, 15, 647–660. [CrossRef]
Fellman R. L. Lynn J. R. Starita R. J. Swanson W. H. (1989). Clinical importance of spatial summation in glaucoma. In: Heijl A. (Ed.), Perimetry update, 1988/89, vol. 1989 (pp. 313–324). The Hague, Netherlands: Berkeley: Kugler & Ghedini.
Flanagan J. G. Wild J. M. Wood J. M. (1988). Stimulus configuration and the format of the normal sensitivity gradient. Documenta Ophthalmologica, 69, 371–383. [CrossRef] [PubMed]
Garway-Heath D. F. Holder G. E. Fitzke F. W. Hitchings R. A. (2002). Relationship between electrophysiological, psychophysical and anatomical measurements in glaucoma. Investigative Ophthalmology and Visual Science, 43, 2213–2220. [PubMed]
Hallet P. (1963). Spatial summation. Vision Research, 3, 9–24. [CrossRef]
Harwerth R. S. Carter-Dawson L. Shen F. Smith E. L. Crawford M. L. (1999). Ganglion cell losses underlying visual field defects from experimental glaucoma. Investigative Ophthalmology and Visual Science, 40 (10), 2242–2250, http://www.iovs.org/content/40/10/2242. [PubMed] [Article] [PubMed]
Harweth T. Wheat J. Fredette M. J., & Anderson D. R. (2010). Linking structure and function in glaucoma. Progress in Retinal and Eye Research, 29, 249–271. [CrossRef] [PubMed]
Hecht S. Shlaer S. Pirenne M. H. (1942). Energy, quanta, and vision. The Journal of General Physiology, 25, 819–840. [CrossRef] [PubMed]
Heijl A. Lindgren G. Olsoon J. (1987). Normal variability of static perimetric threshold values across the central visual field. Archives of Ophthalmology, 105, 1544. [CrossRef] [PubMed]
Johnson C. A. Keltner J. L. Balestrery F. (1978). Effects of target size and eccentricity on visual detection and resolution. Vision Research, 18, 1217–1222. [CrossRef] [PubMed]
Johnson C. A. Wall M. Thompson H. S. (2011). A history of perimetry and visual field testing. Optometry & Vision Science, 88, E8–E15.
Kapadia M. K. Westheimer G. Gilbert C. D. (1999). Dynamics of spatial summation in primary visual cortex of alert monkeys. Proceedings of the National Academy of Sciences, USA, 96, 12073–12078. [CrossRef]
Katz J. Sommer A. (1986). Asymmetry and variation in the normal hill of vision. Archives of Ophthalmology, 104, 65–88. [CrossRef]
Kelly D. (1977). Visual contrast sensitivity. Journal of Modern Optics, 24, 107–129.
Kendrick N. K. Winawer J. Mezer A. Wandell B. A. (2013). Compressive spatial summation in human visual cortex. Journal of Neurophysiology, 110, 481–494. [CrossRef]
Lee D. K. Koch C. Braun J. (1997). Spatial vision thresholds in the near absence of attention. Vision Research, 37 (17), 2409–2418. [CrossRef]
Lu Z. Dosher B. A. (1998). External noise distinguishes attention mechanisms. Vision Research, 38, 1183–1198. [CrossRef]
Malik R. Swanson W. H. Garway-Heath D. F. (2012). The ‘structure-function’ relationship in glaucoma - past thinking and current concepts. Clinical Experimental Ophthalmology, 40, 369–380. [CrossRef]
Marr D. (1983). Vision: A computational investigation into the human representation and processing of visual information. New York: W.H. Freeman and Company.
Meese T. S. (2010). Spatially extensive summation of contrast-energy is revealed by contrast detection of micro-pattern textures. Journal of Vision, 10 (8): 14, 1–21, http://www.journalofvision.org/content/10/8/14, doi:10.1167/10.8.14. [PubMed] [Article]
Meese T. S. Summers R. J. (2012). Theory and data for area summation of contrast with and without uncertainty: Evidence for a noisy energy model. Journal of Vision, 12 (11): 9, 1–28 , http://www.journalofvision.org/content/12/11/9, doi:10.1167/12.11.9. [PubMed] [Article]
Mulak M. Szummy D. Sieja-Bujewska A. Kubrak M. (2012). Heidelberg edge perimeter employment in glaucoma diagnosis – Prelimnary report. Advances in Clinical Experimental Medicine, 21, 665–670.
Owen W. G. (1971). Spatio-temporal integration in the human peripheral retina. Vision Research, 12, 1011–1026. [CrossRef]
Pan F. Swanson W. H. (2006). A cortical pooling model of spatial summation for perimetric stimuli. Journal of Vision, 6 (11): 2, 1159–1171, http://www.journalofvision.org/content/6/11/2, doi:10.1167/6.11.2. [PubMed] [Article]
Pointer J. S. Hess R. F. (1989). The contrast sensitivity gradient across the human visual field: With emphasis on the low spatial frequency range. Vision Research, 29, 1133–1151. [CrossRef]
Redmond T. Garway-Heath D. F. Zlatkova M. B. Anderson R. S. (2010). Sensitivity loss in early glaucoma can be mapped to an enlargement of the area of complete spatial summation. Investigative Ophthalmology & Visual Science, 51 (12), 6540–6548, http://www.iovs.org/content/51/12/6540. [PubMed] [Article]
Ricco A. (1877). Relazione fra il minimo angolo visuale et l'intensita luminosaluminosa [Translation: Relationship between the minimum visual angle and intensity of light]. Annali di Ottalmologia, 6, 373–479.
Sceniak M. P. Ringach D. L. Hawken M. J. Shapley R. (1999). Contrast's effect on spatial summation by macaque V1 neurons. Nature Neuroscience, 2, 733–739.
Schiefer U. Papageorgiou E. Sample P. A. Pascual J. P. Selig B. Krapp E., & Paetzold J. (2010). Spatial pattern of glaucomatous visual field loss obtained with regionally condensed stimulus arrangements. Investigative Ophthalmology and Visual Science, 51 (11), 5685–5689, http://www.iovs.org/content/51/11/5685. [PubMed] [Article]
Sloan L. (1961). Area and luminance of test object as variables in examination of the visual field by projection perimetry. Vision Research, 1, 121–138.
Sloan L. Brown D. J. (1962). Area and luminance of test object as variables in projection perimetry, Clinical studies of photometric dysharmony. Vision Research, 2, 527–541.
Summers R. J. Meese T. S. (2009). The influence of fixation points on contrast detection and discrimination of patches of grating: Masking and facilitation. Vision Research, 49, 1894–1900.
Tyler C. W. (1997). Colour bit-stealing to enhance the luminance resolution of digital displays on a single pixel basis. Spatial Vision, 10, 369–377. [CrossRef]
Tyler C. W. Chen C. C. (2000). Signal detection theory in the 2AFC paradigm: Attention, channel uncertainty and probability summation. Vision Research, 40, 3121–3144. [CrossRef]
Wall M. Doyle C. K. Eden T. Zamba K. D. Johnson C. A. (2013). Size threshold perimetry performs as well as conventional automated perimetry with stimulus sizes III, V, and VI for glaucomatous loss. Investigative Ophthalmology and Visual Science, 54 (6), 3975–3983, http://www.iovs.org/content/54/6/3975. [PubMed] [Article] [CrossRef]
Wang F. R. Zhou X. D. Zhou S. A. (1994). A CT study of the relation between ocular axial biometry and refraction. Zhonghua Yan Ke Za Zhi, 30 (1), 39–40.
Weale R. (1958). Retinal summation and human visual thresholds. Nature, 181, 154. [CrossRef]
Weekers R. (1959). Discussion of papers presented at symposium on glaucoma. Documents in Ophthalmology, 13, 333. [CrossRef]
Wild J. M. Wood J. M. Flanagan J. G. (1987). Spatial summation and the cortical magnification of perimetric profiles. Opthalmologica, Basel, 195, 88–96. [CrossRef]
Wilson M. (1970). Invariant features of spatial summation with changing locus in the visual field. The Journal of Physiology, 207, 611–622. [CrossRef]
Figure 1
 
A schematic of the experimental stimulus and procedure (A), and a representation of stimulus locations tested in the present study (B).
Figure 1
 
A schematic of the experimental stimulus and procedure (A), and a representation of stimulus locations tested in the present study (B).
Figure 2
 
Contrast thresholds plotted as a function of the size of the stimulus. Within each plot, data from different eccentricities are plotted as different symbols. Data for the different meridians (see schematic diagrams in each panel) are arrayed around the central panel, which shows data for foveal conditions. Error bars represent 1 SD from the mean.
Figure 2
 
Contrast thresholds plotted as a function of the size of the stimulus. Within each plot, data from different eccentricities are plotted as different symbols. Data for the different meridians (see schematic diagrams in each panel) are arrayed around the central panel, which shows data for foveal conditions. Error bars represent 1 SD from the mean.
Figure 3
 
Contrast thresholds (log ΔL/L) plotted as a function of eccentricity for six different test sizes. Error bars represent 95% confidence limits. Different plots (A–D) plot data along different meridian axes: A, horizontal axis; B, vertical axis; C and D, oblique axes (see schematic representation in each figure).
Figure 3
 
Contrast thresholds (log ΔL/L) plotted as a function of eccentricity for six different test sizes. Error bars represent 95% confidence limits. Different plots (A–D) plot data along different meridian axes: A, horizontal axis; B, vertical axis; C and D, oblique axes (see schematic representation in each figure).
Figure 4
 
Derived Ac values plotted in linear polar coordinates. Error bars signify 95% confidence limits. Different symbols represent the Ac obtained at different retinal eccentricities, which are plotted along their respective meridian angle. Dashed circles represent the size of Goldmann I–III targets.
Figure 4
 
Derived Ac values plotted in linear polar coordinates. Error bars signify 95% confidence limits. Different symbols represent the Ac obtained at different retinal eccentricities, which are plotted along their respective meridian angle. Dashed circles represent the size of Goldmann I–III targets.
Figure 5
 
Contrast detection thresholds (n = 5) plotted as a function of stimulus area for targets presented at different eccentricities along the horizontal meridian (different panels). Error bars represent 1 SD. Results for conditions in which the stimulus was cued and uncued are represented by squares and circles, respectively. In the framed panel, the average difference between cued and uncued conditions collapsed across the six different test sizes is plotted as a function of eccentricity.
Figure 5
 
Contrast detection thresholds (n = 5) plotted as a function of stimulus area for targets presented at different eccentricities along the horizontal meridian (different panels). Error bars represent 1 SD. Results for conditions in which the stimulus was cued and uncued are represented by squares and circles, respectively. In the framed panel, the average difference between cued and uncued conditions collapsed across the six different test sizes is plotted as a function of eccentricity.
Figure 6
 
The Ac plotted as a function of retinal eccentricity for cued and uncued conditions (represented by circles and squares, respectively). The average log difference in Ac between the two conditions is shown as diamonds. Error bars denote ±1 SEM.
Figure 6
 
The Ac plotted as a function of retinal eccentricity for cued and uncued conditions (represented by circles and squares, respectively). The average log difference in Ac between the two conditions is shown as diamonds. Error bars denote ±1 SEM.
×
×

This PDF is available to Subscribers Only

Sign in or purchase a subscription to access this content. ×

You must be signed into an individual account to use this feature.

×