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. Author manuscript; available in PMC: 2009 Nov 1.
Published in final edited form as: Vision Res. 2008 Apr 18;48(26):2615–2624. doi: 10.1016/j.visres.2008.02.012

Spatial Frequencies Used in Landolt C Orientation Judgments: Relation to Inferred Magnocellular and Parvocellular Pathways

J Jason McAnany a, Kenneth R Alexander a,b,c,*
PMCID: PMC2582053  NIHMSID: NIHMS46411  PMID: 18374385

Abstract

The purpose of this study was to define the spatial frequencies that underlie judgments of Landolt C orientation under test conditions designed to favor either the magnocellular (MC) or parvocellular (PC) pathway. Contrast thresholds of two observers were measured for briefly presented Landolt Cs of four sizes, using steady- and pulsed-pedestal paradigms to bias performance toward the MC and PC pathways, respectively. Contrast thresholds were derived from a two-alternative forced-choice orientation judgment task using the QUEST procedure. The Landolt Cs were either low-pass or high-pass Gaussian filtered with a range of cut-off object spatial frequencies (cycles per letter) to limit their frequency content. Center object frequencies were derived from plots of log contrast threshold for orientation judgments vs. log filter cutoff object frequency. The function relating center object frequency to Landolt C angular subtense was nonlinear on log-log coordinates for both the steady- and pulsed-pedestal paradigms, indicating that different object frequencies were used to judge Landolt C orientation at different optotype sizes. However, the function was substantially steeper under the pulsed-pedestal than under the steady-pedestal paradigm, such that a large change in optotype size produced a relatively small change in retinal spatial frequency (cycles per degree). The pattern of results is consistent with previously reported differences between the spatial contrast sensitivity functions of the inferred MC and PC pathways.

Keywords: Contrast, Visual Acuity, Landolt C, Spatial Frequency, Optotype

1. Introduction

The Landolt C optotype is used frequently in the clinical evaluation of visual function. The design of the Landolt C is identical to that of the Sloan letter C, in which the gap width is equal to the stroke width, which in turn is 1/5 the overall optotype size (NAS-NRC, 1980). In vision testing, the Landolt C is presented at one of several orientations, and the observer's task is to judge the location of the gap. Thus, the Landolt C lends itself well to forced-choice psychophysical procedures. The Landolt C is used typically to measure high-contrast visual acuity, which is defined by the threshold gap width in terms of log MAR (minimum angle of resolution), where MAR is 1/5 the angular subtense of the Landolt C. The Landolt C has also been used to measure visual acuity at low contrast (Hiraoka, Okamoto, Ishii, Kakita, & Oshika, 2007) and contrast sensitivity per se (Dennis, Beer, Baldwin, Ivan, Lorusso, & Thompson, 2004; Bühren, Terzi, Bach, Wesemann, & Kohnen, 2006; Bach, 2007), as well as color discrimination (Regan, Reffin, & Mollon, 1994).

A fundamental issue in the use of optotypes such as the Landolt C, or letters in general, is that they contain a broad range of object frequencies (following Parish and Sperling [1991], “object frequency” refers to spatial frequency in cycles per letter [cpl], whereas “retinal frequency” denotes spatial frequency in cycles per degree [cpd]). Visual performance for spatially broad-band optotypes could potentially be based on any of various object frequencies. Nevertheless, it has often been assumed that the identification of letters is governed by a fixed band of object frequencies in the region of 2.5 cpl, regardless of the angular subtense, because there are 5 strokes or 2.5 cycles contained within each letter (e.g., Regan, Raymond, Ginsburg & Murray, 1981). Under this assumption, the MAR value of letters can readily be equated to retinal frequency. For example, a letter with a MAR value of 1 (0 log MAR or 20/20 Snellen equivalent) would correspond to 30 cpd, because the stroke width is 1 arcmin and two strokes comprise a cycle.

However, studies of letter identification have shown that the object frequency region that mediates performance is not constant, but instead varies with optotype size (Alexander, Xie, & Derlacki, 1994; Chung, Legge, & Tjan, 2002; Majaj, Pelli, Kurshan, & Palomares, 2002). Letters of small angular subtense are identified on the basis of their gross strokes (low object frequencies), whereas large letters tend to be identified by their edges (high object frequencies). Thus, there does not appear to be a fixed relationship between log MAR and retinal frequency for the task of letter identification.

Consistent with the results for letters, Bondarko and Danilova (1997) observed that visually normal individuals can discriminate gap widths in the Landolt C that, in terms of equivalent retinal frequency, are higher than the presumed resolution limit. As a consequence, these investigators proposed that individuals base their judgments of Landolt C orientation on an object frequency range centered on 1.3 rather than 2.5 cpl. This theoretical proposal was derived from the observation that 1.3 cpl yields the largest difference in the Fourier spectra for various orientations. This proposal was verified experimentally using band-limited Landolt Cs in a study of the effect of crowding on foveal visual acuity (Hess, Dakin, & Kapoor, 2000). Consequently, as discussed by Bondarko and Danilova (1997), visual acuity for Landolt C optotypes appears to be based on judgments of the shape of the light distribution in an effectively low-pass filtered image, rather than being a resolution task per se. However, it is not apparent whether the same band of object frequencies underlies measurements of contrast sensitivity using Landolt Cs that are larger than the acuity limit.

In addition, there is a potentially important factor that has not been considered previously in studies of the spatial frequency determinants of contrast sensitivity using the Landolt C and other spatially broad-band optotypes. This factor is whether visual performance is mediated by the magnocellular (MC) or the parvocellular (PC) pathway. As demonstrated by Pokorny and Smith (1997), the MC and PC pathways can be targeted psychophysically by using “steady-pedestal” and “pulsed-pedestal” paradigms, respectively. Psychophysical data acquired using these two paradigms have the contrast response properties and temporal integration characteristics associated with the MC and PC pathways described electrophysiologically (Kaplan & Shapley, 1986; Lee, 1996).

It has been observed that the contrast sensitivity function (CSF) obtained under the steady-pedestal paradigm (inferred MC-pathway mediation) is low-pass, whereas the CSF measured using the pulsed-pedestal paradigm (inferred PC-pathway mediation) is band-pass (Leonova, Pokorny, & Smith, 2003). This difference in CSF shape is likely to constrain the range of object frequencies that underlie judgments of Landolt C orientation at different optotype sizes. For example, if the Landolt C is relatively large, then the low object frequency components (which correspond to low retinal frequencies) are potentially useful for judgments of target orientation under test conditions that favor the MC pathway. However, these low frequencies are attenuated and consequently would be less effective under conditions that favor the PC pathway. Thus, the identity of the visual pathway that mediates performance is likely to have a substantial effect on the object frequencies that underlie visual performance using spatially broad-band optotypes such as the Landolt C.

The purpose of the present study was to evaluate this possibility by defining the object frequency region that observers use to judge the orientation of a Landolt C across a range of optotype sizes and under conditions targeting either the MC or the PC pathway. The present study focused on the Landolt C not only because this is a commonly used optotype in vision testing, but also because the Sloan letters differ in their individual contrast sensitivities (Alexander, Xie, & Derlacki, 1997), which makes the study of their spatial frequency components more problematic. Nevertheless, it is likely that our results for Landolt Cs also apply to Sloan letters in general, as discussed in Section 4.3.

Our approach was based on the procedure of Anderson and Thibos (1999). Contrast thresholds were measured for Landolt Cs that were either low-pass or high-pass Gaussian filtered with a range of cutoff object frequencies. The underlying rationale is that, if a particular range of object frequencies does not contribute to orientation judgments, then their removal should have no effect on contrast thresholds. Conversely, the removal of object frequency components that are critical to performance should result in an elevation of the contrast threshold, thus providing an index of the range of object frequencies that are necessary for judgments of Landolt C orientation.

2. Methods

2.1. Observers

Two males, the authors, ages 28 (S1) and 62 (S2) years, with normal best-corrected visual acuity and contrast sensitivity, participated in the study. S1 has normal color vision and S2 has mild deuteranomaly. All experiments were approved by an institutional review board at the University of Illinois at Chicago.

2.2. Stimuli and Apparatus

The test stimuli were Landolt Cs constructed according to standard guidelines (NAS-NRC, 1980). They were always of positive contrast (luminance higher than the surround), and four different sizes were used (0.9, 1.2, 1.5, and 1.8 log MAR, where smaller values of log MAR correspond to smaller letters). In the primary experiment, the Landolt Cs were spatially filtered with either a high-pass or a low-pass two-dimensional Gaussian filter, implemented with standard Matlab filtering functions. Eleven cutoff object frequencies were used, ranging from 0.6 to 10 cpl. Examples of low-pass and high-pass filtered Landolt Cs are given in Figs. 1A and 1B, respectively. In a supplementary experiment investigating contrast sensitivity for band-pass filtered Landolt Cs, the optotypes were spatially filtered using a two-dimensional cosine log filter (Peli, 1990). This filter is symmetrical on a log spatial frequency axis, is torus-shaped in the frequency domain, and has a bandwidth at half-height of one octave. The cosine log filter was centered at an object frequency of 2.5 cpl, which corresponds to the stroke width of the Landolt C optotype. An illustration of this band-pass filtered optotype is given in Fig. 1C.

Fig. 1.

Fig. 1

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Illustrations of a Landolt C that was either low-pass (A) or high-pass (B) Gaussian filtered using the cutoff object frequencies indicated, or band-pass filtered (C) using a cosine log filter with a center object frequency of 2.5 cpl; an unfiltered Landolt C is presented for comparison.

All stimuli were generated by a Macintosh G4 computer and were displayed on an NEC monitor (FE2111SB) with a screen resolution of 1280 × 1024 and a 100-Hz refresh rate, driven by an ATI Radeon video card (9000 Pro) with 10-bit DAC resolution. The monitor, which was the only source of illumination in the room, was viewed monocularly from 1.9 meters through a phoropter with the observer's best refractive correction.

As shown in the center panels in Fig. 2, the test stimuli were presented in the center of a luminance pedestal that subtended 10.4° horizontally and 8.5° vertically. The luminance pedestal was presented in the center of an adapting field that subtended 11.0° horizontally and 8.8° vertically. To aid fixation, four diagonal black lines that extended from the edges of the pedestal to a region just outside of the Landolt C were presented continuously. The pedestal luminance was 30 cd/m2, and it was added to the adapting field, which also had a luminance of 30 cd/m2, so that the luminance of the pedestal plus adapting field was 60 cd/m2. The luminance values used to generate the stimuli were determined by a linearized look-up table, based on calibrations made with a Minolta LS-110 photometer. The test stimulus duration was 30 ms (3 video frames), and the temporal characteristics of the display were confirmed using an oscilloscope and photocell.

Fig. 2.

Fig. 2

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Illustration of the stimulus configurations and temporal sequences (not to scale). For the steady-pedestal paradigm (top), a pedestal square of incremental luminance was presented continuously against an adapting field. The Landolt C target was presented briefly during the test interval. For the pulsed-pedestal paradigm (bottom), the adapting field was presented continuously, and the Landolt C and pedestal square were presented briefly and simultaneously during the test interval. For both paradigms, four fixation guides (diagonal lines) that terminated just outside the region of the test stimulus were shown continuously.

The contrast (C) of the unfiltered Landolt C was defined as Weber contrast:

C=(LT−LP)/LP (1),

where LT is the luminance of the Landolt C, and LP is the pedestal luminance. Because the contrast of complex images is difficult to define (Peli, 1990), a relative definition of contrast was used to characterize the filtered Landolt Cs (cf. Alexander et al., 1994; Chung et al., 2002). That is, the contrast of the filtered Landolt Cs was defined relative to the unfiltered Landolt C target, without rescaling. Thus, for each cut-off frequency, the filtered Landolt C was assigned a contrast of 1.0 when the contrast of the unfiltered C was 1.0, regardless of the actual spatial distribution of the luminance values in the filtered image. When the contrast of the unfiltered Landolt C was reduced by some proportion, then the contrast of the filtered image was considered to have been reduced by the same proportion.

2.3. Procedure

Experiments were written in Matlab using the Psychophysics Toolbox extensions (Brainard, 1997). The two testing paradigms of Leonova et al. (2003) were used, as illustrated in Fig. 2. For the steady-pedestal paradigm (Fig. 2, top), the luminance pedestal was presented continuously in the center of the adapting field. During the test period, the Landolt C was presented briefly in the center of the pedestal. This paradigm is thought to favor the MC pathway, at low to intermediate spatial frequencies and large target sizes, because the test target is presented only briefly. For the pulsed-pedestal paradigm (Fig. 2, bottom), the pedestal and Landolt C were presented briefly and simultaneously. This paradigm is thought to favor the PC pathway because the abrupt onset of the luminance pedestal drives the MC pathway toward saturation.

A 30-s period of adaptation to the adapting field alone (pulsed-pedestal paradigm) or to the adapting field plus pedestal (steady-pedestal paradigm) preceded each session, and a brief warning tone signaled the start of each stimulus presentation. The observer's task was to determine the orientation of the Landolt C by pressing the appropriate button on a gamepad. No feedback was given. The gap in the Landolt C was located randomly either at the top or on the right on each trial (two-alternative forced-choice). The alternatives were limited to these two because left-right and top-bottom judgments of gap location are based on spatial phase rather than on orientation (Bondarko & Danilova, 1997). However, pilot testing indicated that the results would not have been fundamentally different if a four-alternative procedure had been used.

In each testing session, all cutoff object frequencies for both high-pass and low-pass filtered targets were tested for a given size under either the steady-pedestal or the pulsed-pedestal paradigm. The paradigms, sizes, and cutoff object frequencies were selected for testing in a pseudo-random order, and each condition was tested three times, in separate sessions. Contrast thresholds for orientation judgments were obtained using the QUEST procedure (Watson & Pelli, 1983), with the number of trials set to 40 for each condition. Pilot testing had determined that the staircases typically reached an asymptote within approximately 30 trials, but additional trials were added to ensure this was the case. In the following data analyses, curve-fitting was performed using SigmaPlot.

3. Results

3.1. Effect of Gaussian filtering on contrast thresholds for Landolt Cs

Figs. 3 and 4 illustrate the effects of low- and high-pass spatial filtering on contrast thresholds for judging the orientation of a Landolt C with a log MAR value of 1.5, for the steady- and pulsed-pedestal paradigms, respectively. For reference, this log MAR value corresponds approximately to the optotype size used on the Pelli-Robson Contrast Sensitivity Chart. In these and the following figures, the data are plotted separately for S1 and S2. The leftmost and rightmost data points in each plot in Figs. 3 and 4 represent contrast thresholds for Landolt Cs that had the least amount of spatial filtering. The other data points represent the effect of successively changing the cutoff object frequency to remove either the low object frequencies (high-pass filtering, filled symbols) or the high object frequencies (low-pass filtering, unfilled symbols). In general, as the filter cutoff frequency was varied systematically, there was no effect on the contrast threshold until a critical object frequency was reached. Then, the further removal of object frequencies resulted in a systematic elevation of the contrast threshold.

Fig. 3.

Fig. 3

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Log contrast threshold for orientation judgments as a function of log object frequency cutoff of a Gaussian filter for S1 (left) and S2 (right), for low-pass filtered (open symbols) and high-pass filtered (filled symbols) Landolt Cs using the steady-pedestal paradigm. In this and the following figures, data points represent the mean of three measurements, and error bars represent ±1 standard error of the mean (sem), which are omitted when smaller than the data points. The solid lines represent piecewise linear fits to the data as described in the text. The dashed vertical lines indicate the point at which the two functions crossed, which was used as the index of the center object frequency.

Fig. 4.

Fig. 4

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Log contrast threshold for orientation judgments as a function of log object frequency cutoff of a Gaussian filter for S1 (left) and S2 (right), for low-pass filtered (open symbols) and high-pass filtered (filled symbols) Landolt Cs using the pulsed-pedestal paradigm. Other conventions are as in Fig. 3.

To quantify these results, the data in Figs. 3 and 4 were fit piecewise with two linear functions using a least-squares criterion: one region was constrained to have a slope of 0, and the slope of the second region was unconstrained. These functions provided a satisfactory fit to the data. The cutoff object frequency at which the functions crossed (indicated by the vertical dashed lines in Figs. 3 and 4) was taken as the index of the center of the object frequency region required for judgments of Landolt C orientation. This point represents approximately equal elevations of the contrast threshold from those obtained with minimally low- and high-pass-filtered optotypes.

As expected (Pokorny & Smith, 1997), contrast thresholds were higher overall for the pulsed-pedestal paradigm (Fig. 4) than for the steady-pedestal paradigm (Fig. 3). Furthermore, the center object frequency was higher for the pulsed-pedestal paradigm (approximately 4 cpl) than for the steady-pedestal paradigm (approximately 2 cpl). The object frequency bandwidth, defined as the distance between the inflection points in the fitted functions, was approximately 1.5 octaves for both paradigms for both subjects.

3.2. Center frequency as a function of Landolt C log MAR

The analysis illustrated in Figs. 3 and 4 was applied to the data obtained at each of the four log MAR values of Landolt C, except that the piecewise linear fits were performed separately for each of the three data sets obtained for each condition, rather than for the mean results. This yielded three estimates of the center object frequency for each condition for each subject. The center object frequencies derived from this analysis are presented in Fig. 5. This figure plots mean log center object frequency as a function of log reciprocal of MAR for the steady- and pulsed-pedestal paradigms for each of the two observers. The x-axis is plotted as negative log MAR to correspond to the conventional orientation of a CSF, with small optotypes (high spatial frequencies) plotted to the right. For reference, the horizontal dashed line in Fig. 5 represents the assumption that a constant center object frequency of 2.5 cpl governs orientation judgments.

Fig. 5.

Fig. 5

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Log center object frequency as a function of log reciprocal of MAR for four sizes of Landolt C for S1 (left) and S2 (right), with data obtained using either the steady-pedestal (filled squares) or pulsed-pedestal (open triangles) paradigm. The right y-axis indicates the center object frequency in linear units on a log scale. Curves represent the least-squares best fits of Eq. 2. The dashed horizontal line represents an object frequency of 2.5 cpl.

For large Landolt Cs, the center object frequency was markedly higher for the pulsed-pedestal than for the steady-pedestal paradigm. In fact, the separation between the curves exceeded 1 octave (i.e., > 0.3 log unit) for the largest optotype size (leftmost data points). However, as target size decreased, the center object frequencies became more similar for the two paradigms. Thus, there was only a modest change in object frequency as a function of log MAR for the steady-pedestal paradigm (i.e., approximately 0.3 log unit for the change from 0.9 to 1.8 log MAR), but there was a substantial change in the center object frequency for the pulsed-pedestal paradigm (approximately 0.6 log unit) over the same log MAR range. The mean object frequency bandwidth for Landolt Cs, averaged across optotype sizes and subjects, was 1.7 octaves (standard deviation, 0.7 octaves), with no systematic difference between the results for the steady- and pulsed-pedestal paradigms.

The data in Fig. 5 were fit with the log form of the equation:

Foc=Fomin(1+(MARcrit×MAR)) (2),

where Foc indicates the center object frequency, and Fomin and MARcrit are fit parameters controlling the vertical and horizontal positions, respectively, on log-log coordinates. This function transitions between a slope of -1 at large optotype sizes (representing a constant retinal frequency) to a slope of 0 at small optotype sizes (representing a constant object frequency), and it provides a reasonable fit to the data. By this quantitative analysis, there was a substantial difference between the values of MARcrit for the steady- and pulsed-pedestal paradigms (differences of 0.6 and 0.5 log units for S1 and S2, respectively), whereas there was only a small difference in the value of Fomin (differences of -0.06 and -0.05 log units for S1 and S2, respectively). The mean values of Fomin for the two subjects were 1.4 cpl for the steady-pedestal paradigm and 1.2 cpl for the pulsed-pedestal paradigm. These values are consistent with the value of 1.3 cpl proposed by Bondarko and Danilova (1997) on theoretical grounds, and with the value of approximately 1.25 cpl observed experimentally by Hess et al. (2000).

Fig. 6 replots the data and curves of Fig. 5 in terms of center retinal frequency rather than center object frequency. This transformation was based on the relationship:

Fig. 6.

Fig. 6

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Log center retinal frequency as a function of log reciprocal of MAR for S1 (left) and S2 (right). The data points, curves, and dashed line are replotted from Fig. 5. The top x-axis indicates the nominal retinal frequency based on the assumption that 0 log MAR equals 30 cpd; the right y-axis indicates the center retinal frequency in linear units on a log scale. The diagonal dashed line indicates equality between the derived and nominal retinal frequencies.

Fr=12×FoMAR (3),

where Fr is retinal frequency in cpd, Fo is object frequency in cpl, and MAR is 1/5 the angular subtense of the unfiltered Landolt C. The top x-axes in this figure indicate the nominal retinal frequencies corresponding to the log MAR values on the bottom x-axes, assuming that 0 log MAR equals 30 cpd. The diagonal dashed line in Fig. 6, which replots the dashed line of Fig. 5, represents a one-to-one relationship between the nominal retinal frequency and the derived center retinal frequency. That is, data points falling along this line would indicate that Landolt C orientation judgments are governed by a constant region of object frequencies centered on 2.5 cpl for all optotype sizes.

It is evident that the linear relationship depicted by the dashed line in Fig. 6 does not hold for either the steady-pedestal or the pulsed-pedestal paradigm, although the results for the steady-pedestal paradigm lie near the dashed line at large log MAR values. The discrepancy from the dashed line was greatest for large Landolt Cs under the pulsed-pedestal paradigm, where nearly a constant retinal frequency was used regardless of optotype size. For small Landolt Cs, the data approached a slope of 1 for both paradigms, so that log retinal frequency was directly proportional to log MAR. Thus, a nearly constant object frequency was employed for orientation judgments at small optotype sizes. However, the data points for small log MAR values of Landolt C fell below the dashed line. This indicates that the object frequency was lower than 2.5 cpl, consistent with the proposal of Bondarko and Danilova (1997).

4. Discussion

4.1. Object frequencies required for judgments of Landolt C orientation

The aim of this study was to determine the object frequencies that underlie judgments of Landolt C orientation within the context of the inferred MC and PC pathways. The results showed that the object frequency region is not fixed, but depends both on the optotype size and on the visual pathway that is presumed to mediate sensitivity. As shown in Fig. 5, contrast sensitivity for large Landolt Cs was based on object frequencies that were more than 1 octave higher for the pulsed-pedestal paradigm (inferred PC-pathway mediation) than for the steady-pedestal paradigm (inferred MC-pathway mediation). The object frequencies became more similar under the two paradigms when small Landolt Cs were used.

This pattern of results is consistent with the low- and band-pass shapes of the CSFs reported previously for the steady- and pulsed-pedestal paradigms, respectively (Leonova et al 2003). That is, under the steady-pedestal paradigm, there is typically good sensitivity for the low object frequency components (low retinal frequencies) contained in large Landolt Cs, whereas sensitivity is attenuated for these low frequency components under the pulsed-pedestal paradigm. This requires orientation judgments to be based on higher object frequencies under the pulsed-pedestal paradigm than under the steady-pedestal paradigm. For small Landolt Cs, on the other hand, the high object frequency components, which correspond to high retinal frequencies, exceed the limits of the CSFs under both paradigms, requiring that orientation judgments be based on relatively low object frequencies. However, little orientation information is available at object frequencies below approximately 1 cpl (Bondarko & Danilova, 1997). Thus, there is a restricted range of useful object frequencies at small target sizes that is similar for both paradigms.

4.2. Implications for contrast sensitivity functions for the Landolt C

The results shown in Figs. 5 and 6 have important implications for tests of contrast sensitivity that use the Landolt C optotype, as implemented, for example, in the Freiburg Visual Acuity and Contrast Test (FrACT: Bach, 1997; Bach, 2007). To illustrate this, Fig. 7 presents CSFs that were based on judging the orientation of an unfiltered Landolt C optotype, using the steady- and pulsed-pedestal paradigms. In this figure, log contrast sensitivity for orientation judgments is plotted with respect to the nominal log retinal frequency, under the conventional assumption that 0 log MAR equals 30 cpd. The curves in Fig. 7 are the least-squares best fits of the log form of an equation that has been used previously to describe the CSF (Rohaly & Owsley, 1993):

Fig. 7.

Fig. 7

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Mean log contrast sensitivity for orientation judgments using an unfiltered Landolt C as a function of log nominal retinal frequency for S1 (left) and S2 (right). The top x-axis indicates log reciprocal of MAR, and the two x-axes have been scaled such that 0.0 log MAR equals 30 cpd. Curves represent the least-squares best-fits of Eq. 4.

s=AFrne−pFr (4)

where s is the contrast sensitivity at retinal frequency Fr, n is a fit parameter that governs the attenuation of sensitivity at low frequencies, and A and p are fit parameters that control the vertical and horizontal position of the function, respectively, on log-log coordinates.

The CSF for an unfiltered Landolt C (Fig. 7) was low-pass under the steady-pedestal paradigm, as expected (Leonova et al., 2003). However, the CSF under the pulsed-pedestal paradigm was also low-pass, rather than having the low-frequency attenuation associated with this paradigm (Leonova et al., 2003). In fact, these CSFs for an unfiltered Landolt C showed a relatively constant separation of approximately 0.6 log units at low retinal frequencies before converging at high retinal frequencies.

The explanation for the unexpectedly low-pass shape of the CSF for the unfiltered Landolt C under the pulsed-pedestal paradigm is apparent if the data of Fig. 7 are replotted in terms of the actual retinal frequencies that govern performance, as derived from our analysis, rather than in terms of the nominal retinal frequencies. This is illustrated in Fig. 8, in which the data points from Fig. 7 have been replotted according to the actual center retinal frequencies derived from the fitted curves in Fig. 6. For comparison, the dashed curves in Fig. 8 are the solid curves replotted from Fig. 7. For the pulsed-pedestal paradigm, the actual retinal frequency region that governed performance for large Landolt Cs remained nearly constant despite substantial changes in the log MAR values. Thus, the low-pass shape of the CSF for the pulsed-pedestal paradigm, shown in Fig. 7, resulted from the fact that a relatively constant retinal frequency was being tested as Landolt C size was varied. A similar pattern was observed for the steady-pedestal paradigm when using large optotypes, but the deviation from the nominal retinal frequency was less marked than for the pulsed-pedestal paradigm. For small optotypes, the actual retinal frequencies were substantially lower than the nominal retinal frequencies for both paradigms. This resulted in a steep decline in the CSF at small optotype sizes compared to the nominal retinal frequencies, particularly under the steady-pedestal paradigm.

Fig. 8.

Fig. 8

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Mean log contrast sensitivity for orientation judgments using an unfiltered Landolt C as a function of log retinal frequency for S1 (left) and S2 (right). The data points in this figure have been replotted from Fig. 7 in terms of the actual retinal frequencies that were derived from our analysis. The dashed curves replot the solid curves of Fig. 7.

The data shown in Figs. 7 and 8 indicate that the use of a broad-band Landolt C to evaluate contrast sensitivity can lead to inappropriate conclusions about the shape of the CSF, because the object frequency region that governs performance is not constant across target size. A potential solution is to use a Landolt C that has a limited object frequency content, and thus has a predictable relationship between object and retinal frequencies. By way of illustration, Fig. 9 presents CSFs for a Landolt C that was spatially filtered using a cosine log filter to limit the object frequency content to a one-octave range (see Fig. 1C). The CSF for this band-limited Landolt C was low-pass in shape for the steady-pedestal paradigm and band-pass for the pulsed-pedestal paradigm, as expected for targets limited in their frequency content (Leonova, et al, 2003).

Fig. 9.

Fig. 9

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Mean log contrast sensitivity for orientation judgments using a cosine log filtered Landolt C as a function of log retinal frequency for S1 (left) and S2 (right). The top x-axis indicates the retinal frequencies in linear units on a log scale. Curves represent the least-squares best-fits of Eq. 4.

4.3. Relationship to letter identification

Despite the fact that letter identification is a more complex task than judging the location of the gap in a Landolt C, there are striking similarities between the CSFs for Landolt C optotypes and for those obtained previously with the set of 10 Sloan letters (McAnany & Alexander, 2006). First, the shapes of the CSFs for an unfiltered Landolt C shown in Fig. 7 are similar to results reported previously for the Sloan letter set (McAnany & Alexander, 2006). For both categories of optotype, the CSFs were low-pass rather than band-pass for the pulsed-pedestal paradigm. Second, band-pass filtering of Landolt Cs (present study) and Sloan letters (McAnany & Alexander, 2006) resulted in CSFs that had the low-pass and band-pass shapes expected for the inferred MC and PC pathways, respectively (Leonova et al., 2003). Thus, it is likely that the same factors that govern contrast sensitivity for orientation judgments of a Landolt C also constrain contrast sensitivity that is based on the identification of Sloan letters.

4.4. Conclusions

It has been noted previously that the object frequency band that underlies visual performance using spatially broad-band stimuli is not fixed but varies with optotype size (Alexander et al., 1994; Chung et al., 2002; Majaj et al., 2002). The present study demonstrates that the magnitude of this shift in object frequency is highly dependent on whether visual performance is mediated by the inferred MC or PC pathway. As illustrated in Fig. 5, the change in object frequency with Landolt C angular subtense is much more pronounced under conditions that favor the PC pathway. Our findings reinforce the notion that band-pass filtered optotypes are preferable to spatially broadband stimuli in visual function testing. This is particularly the case under conditions that favor the PC pathway, and in individuals with visual system dysfunction that may affect the MC and PC pathways differently (e.g., Alexander, Barnes, Fishman, Pokorny, & Smith, 2004; Alexander, Barnes, & Fishman, 2005).

Acknowledgments

This research was supported by NIH Research Grant EY08301 (KRA), NIH Core Grant EY01792, a research grant from Midwest Eye-Banks, and an unrestricted departmental grant from Research to Prevent Blindness. KRA is a Research to Prevent Blindness Senior Scientific Investigator.

References

  1. Alexander KR, Xie W, Derlacki DJ. Spatial-frequency characteristics of letter identification. Journal of the Optical Society of America A. 1994;11:2375–2382. doi: 10.1364/josaa.11.002375. [DOI] [PubMed] [Google Scholar]
  2. Alexander KR, Xie W, Derlacki DJ. Visual acuity and contrast sensitivity for individual Sloan letters. Vision Research. 1997;37:813–819. doi: 10.1016/s0042-6989(96)00190-3. [DOI] [PubMed] [Google Scholar]
  3. Alexander KR, Barnes CS, Fishman GA, Pokorny J, Smith VC. Contrast processing deficits in melanoma-associated retinopathy (MAR) Investigative Ophthalmology and Visual Science. 2004;45:305–310. doi: 10.1167/iovs.03-0840. [DOI] [PubMed] [Google Scholar]
  4. Alexander KR, Barnes CS, Fishman GA. Characteristics of contrast processing deficits in X-linked retinoschisis. Vision Research. 2005;45:2095–2107. doi: 10.1016/j.visres.2005.01.037. [DOI] [PubMed] [Google Scholar]
  5. Anderson RS, Thibos LN. Sampling limits and critical bandwidth for letter discrimination in peripheral vision. Journal of the Optical Society of America A. 1999;16:2334–2342. doi: 10.1364/josaa.16.002334. [DOI] [PubMed] [Google Scholar]
  6. Bach M. Anti-aliasing and dithering in the “Freiburg Visual Acuity Test’. Spatial Vision. 1997;11:85–89. doi: 10.1163/156856897x00087. [DOI] [PubMed] [Google Scholar]
  7. Bach M. The Freiburg Visual Acuity Test – Variability unchanged by post-hoc re-analysis. Graefe's Archives for Clinical and Experimental Ophthalmology. 2007;245:965–971. doi: 10.1007/s00417-006-0474-4. [DOI] [PubMed] [Google Scholar]
  8. Bondarko VM, Danilova MV. What spatial frequency do we use to detect the orientation of a Landolt C? Vision Research. 1997;37:2153–2156. doi: 10.1016/s0042-6989(97)00024-2. [DOI] [PubMed] [Google Scholar]
  9. Brainard DH. The psychophysics toolbox. Spatial Vision. 1997;10:433–436. [PubMed] [Google Scholar]
  10. Bühren J, Terzi E, Bach M, Wesemann W, Kohnen T. Measuring contrast sensitivity under different lighting conditions: Comparison of three tests. Optometry & Vision Science. 2006;83:290–298. doi: 10.1097/01.opx.0000216100.93302.2d. [DOI] [PubMed] [Google Scholar]
  11. Chung ST, Legge GE, Tjan BS. Spatial-frequency characteristics of letter identification in central and peripheral vision. Vision Research. 2002;42:2137–2152. doi: 10.1016/s0042-6989(02)00092-5. [DOI] [PubMed] [Google Scholar]
  12. Dennis RJ, Beer JM, Baldwin JB, Ivan DJ, Lorusso FJ, Thompson WT. Using the Freiburg Acuity and Contrast Test to measure visual performance in USAF personnel after PRK. Optometry & Vision Science. 2004;81:516–524. doi: 10.1097/00006324-200407000-00013. [DOI] [PubMed] [Google Scholar]
  13. Hess RF, Dakin SC, Kapoor N. The foveal ‘crowding’ effect: physics or physiology? Vision Research. 2000;40:365–370. doi: 10.1016/s0042-6989(99)00193-5. [DOI] [PubMed] [Google Scholar]
  14. Hiraoka T, Okamoto C, Ishii Y, Kakita T, Oshika T. Contrast sensitivity function and ocular higher-order aberrations following overnight orthokeratology. Investigative Ophthalmology & Visual Science. 2007;48:550–556. doi: 10.1167/iovs.06-0914. [DOI] [PubMed] [Google Scholar]
  15. Kaplan E, Shapley RM. The primate retina contains two types of ganglion cells, with high and low contrast sensitivity. Proceedings of the National Academy of Sciences of the United States of America. 1986;83:2755–2757. doi: 10.1073/pnas.83.8.2755. [DOI] [PMC free article] [PubMed] [Google Scholar]
  16. Lee BB. Receptive field structure in the primate retina. Vision Research. 1996;36:631–644. doi: 10.1016/0042-6989(95)00167-0. [DOI] [PubMed] [Google Scholar]
  17. Leonova A, Pokorny J, Smith VC. Spatial frequency processing in inferred PC- and MC-pathways. Vision Research. 2003;43:2133–2139. doi: 10.1016/s0042-6989(03)00333-x. [DOI] [PubMed] [Google Scholar]
  18. Majaj NJ, Pelli DG, Kurshan P, Palomares M. The role of spatial-frequency channels in letter identification. Vision Research. 2002;42:1165–1184. doi: 10.1016/s0042-6989(02)00045-7. [DOI] [PubMed] [Google Scholar]
  19. McAnany JJ, Alexander KR. Contrast sensitivity for letter optotypes vs. gratings under conditions biased toward parvocellular and magnocellular pathways. Vision Research. 2006;46:1574–1584. doi: 10.1016/j.visres.2005.08.019. [DOI] [PubMed] [Google Scholar]
  20. NAS-NRC. Recommended and standard procedures for the clinical measurement and specification of visual acuity: Report of working group 39. Advances in Ophthalmology. 1980;41:103–148. [PubMed] [Google Scholar]
  21. Parish DH, Sperling G. Object spatial frequencies, retinal spatial frequencies, noise, and the efficiency of letter discrimination. Vision Research. 1991;31:1399–1415. doi: 10.1016/0042-6989(91)90060-i. [DOI] [PubMed] [Google Scholar]
  22. Peli E. Contrast in complex images. Journal of the Optical Society of America A. 1990;7:2032–2040. doi: 10.1364/josaa.7.002032. [DOI] [PubMed] [Google Scholar]
  23. Pokorny J, Smith VC. Psychophysical signatures associated with magnocellular and parvocellular pathway contrast gain. Journal of the Optical Society of America A. 1997;14:2477–2486. doi: 10.1364/josaa.14.002477. [DOI] [PubMed] [Google Scholar]
  24. Regan BC, Reffin JP, Mollon JD. Luminance noise and the rapid determination of discrimination ellipses in colour deficiency. Vision Research. 1994;34:1279–1299. doi: 10.1016/0042-6989(94)90203-8. [DOI] [PubMed] [Google Scholar]
  25. Regan D, Raymond J, Ginsburg AP, Murray TJ. Contrast sensitivity, visual acuity and the discrimination of Snellen letters in multiple sclerosis. Brain. 1981;104:333–350. doi: 10.1093/brain/104.2.333. [DOI] [PubMed] [Google Scholar]
  26. Rohaly AM, Owsley C. Modeling the contrast-sensitivity functions of older adults. Journal of the Optical Society of America A. 1993;10:1591–1599. doi: 10.1364/josaa.10.001591. [DOI] [PubMed] [Google Scholar]
  27. Watson AB, Pelli DG. QUEST: a Bayesian adaptive psychometric method. Perception & Psychophysics. 1983;33:113–120. doi: 10.3758/bf03202828. [DOI] [PubMed] [Google Scholar]

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