We first need to quantify the varying amounts of habitual optical aberrations experienced by each observer before establishing that we can fully correct all optical aberrations to a similar level in both healthy and KC eyes. In total, 10 KC patients with mild-to-severe optical aberrations and 14 age-matched control observers with healthy eyes were tested monocularly (see 'Materials and methods' and Table 1). Habitual optical quality for the tested eye was estimated using our AO system (Figure 2A and 'Materials and methods') by collecting multiple wavefront measurements for each observer wearing their own, everyday optical corrective method, if any. Wavefront maps were fitted with Zernike polynomials to compute the total root mean square (total RMS; all optical aberrations) and higher-order RMS (hRMS+; HOAs only) for a 6-mm pupil (Figure 2B and 'Materials and methods'). Relative to the optical quality in age-matched control (CTRL) observers (mean total RMS 0.84 ± 0.26 µm, range 0.58–1.42), habitual optical quality in KC eyes (mean total RMS 3.18 ± 2.09 µm, range 1.36–7.84) remained suboptimal despite their own optical corrections (CTRL-vs-KC total RMS: Mann–Whitney U-test, U = 1, p<0.001, r = 0.99). Specifically, KC eyes were subject to a substantial amount of uncorrected HOAs (mean hRMS+ 1.91 ± 1.27 µm, range 0.33–4.55), much more than the healthy eyes of control observers (mean hRMS+ 0.37 ± 0.11 µm, range 0.22–0.55) (CTRL-vs-KC hRMS+: Welch’s t-test, t = 3.83, p=0.004, d = 1.71). As previously reported (Pantanelli et al., 2007), KC eyes were particularly affected by large amounts of vertical coma (mean absolute Z₇ coefficient 1.38 ± 0.96 µm, range 0.03–2.89), much more than in typical, healthy eyes (0.12 ± 0.11 µm, range 0.02–0.34) (CTRL-vs-KC absolute Z₇ coefficient: Welch’s t-test, t = 4.11, p=0.003, d = 1.84). The onset of KC in our patients was around their twenties and varied in its progression, as typically observed in this disease (Vazirani and Basu, 2013). As a result, the amount of habitual optical aberrations did not correlate with participant’s age (Pearson correlation with habitual RMS r=+0.29, p=0.169; with habitual hRMS+ r=+0.30, p=0.155).

Consistent with previous studies from our lab (e.g., Sabesan et al., 2007; Sabesan et al., 2017; Sabesan and Yoon, 2009; Sabesan et al., 2012; Zheleznyak et al., 2016), our AO system allowed us to measure visual performance while effectively maintaining aberration-free optical quality, even in severe KC eyes (Figure 2C). To maximize AO correction during stimulus presentation, observers were trained to blink between trials and to pause if the perceptual quality got unstably poor during testing (see 'Materials and methods'). Continuous closed-loop AO correction during visual testing resulted in a residual wavefront RMS that remained not significantly different from 0.055 µm for both healthy eyes (mean 0.051 ± 0.011 µm, range 0.033–0.067; Student t-test: t = 1.49, p=0.161, d = 0.4) and KC eyes (mean 0.059 ± 0.014 µm, range 0.046–0.083; Wilcoxon signed-rank test: Z = 31, p=0.770, r = 0.13). More importantly, aberration-free optical quality under AO correction was similar between CTRL and KC observers (Wilcoxon rank-sum test, U = 50, p=0.259, r = 0.29), with no relation between the individual AO-corrected residual RMS and the amount of habitual optical aberrations without AO correction (Pearson correlation with habitual RMS r=+0.30, p=0.155; with habitual hRMS+ r=+0.33, p=0.120).

The modulation transfer function (MTF) of the eye’s optics characterizes the reduction in signal contrast of individual SF contents imaged on the retina (Figure 2D, E). The reduction in contrast is pronounced at mid-to-high SFs, particularly in KC eyes due to the atypical levels of uncorrected blur (Figure 2D). Importantly, AO correction allowed us to correct all optical aberrations and maintain similar, diffraction-limited optical quality in all participants (Figure 2E). Thus, online AO correction effectively and continuously provided nearly perfect optical quality during visual testing, allowing us to bypass optical factors and assess differences in neural transfer function between CTRL with healthy eyes and KC patients chronically exposed to atypical amounts of optical aberrations.

First, we assessed the CSF in both KC patients (N=10) and age-matched control observers (N=14) under aberration-free conditions. Observers performed an orientation discrimination task at fixation (Figure 3A) in which they reported the orientation of ±45°-tilted Gabor patches varying in both contrast and SF (in cycles per degree [cpd]). To optimize data collection, we used the quick CSF method (Hou et al., 2010; Hou et al., 2016; Lesmes et al., 2010), which combines Bayesian adaptive inference with a trial-by-trial information gain strategy to estimate the observer’s CSF as a truncated log-parabola with four parameters (Figure 3B and 'Materials and methods'): (1) peak sensitivity, CSmax; (2) peak frequency, SFpeak; (3) bandwidth, β; and (4) low-SF truncation level, δ. The low-SF truncation level determines sensitivity at low SFs (CSlow). We also estimated the high-SF cutoff (SFcutoff) from qCSF fits – a measure of VA. The qCSF method has been used to characterize CSF in both neurotypical and diverse clinical populations (Hou et al., 2010; Hou et al., 2016; Lesmes et al., 2010; Thurman et al., 2016; Yan et al., 2017).

Under similar, aberration-free optical quality, KC observers exhibited altered CSF relative to control observers (Figure 4A), showing impairments for high SFs (for SFs ≥ 8.13 cpd) but also improvements for low SFs (for SFs ≤ 0.92 cpd). In other words, even when both groups had matched retinal image quality, there were still substantial differences in contrast sensitivity. This pattern of gains and losses changed the shape of the CSF, revealing both impaired sensitivity at high SFs (SFcutoff; CTRL: 37.5 cpd [35.1–40.3; 95% CI]; KC 29.0 cpd [27.7–31.2]; p<0.001) and better sensitivity at low SF (CSlow; CTRL 4.60 [3.74–5.46]; KC 7.41 [5.82–8.62]; p<0.001). Improved sensitivity at low SFs reflected a reduction in the low-SF truncation level in KC (δ; CTRL +0.063 [+0.034 +0.101]; KC –0.021 [–0.055 +0.028]; p=0.0025). Moreover, the impairment in high-SF cutoff was marginally correlated with the reduction in low-SF truncation across observers (r=+0.38, p=0.0675). The overall result was a shift in peak SF toward lower SFs in KC (SFpeak; CTRL 3.36 cpd [3.25–3.72]; KC 2.70 cpd [2.54–2.91]; p<0.001). Notably, these CSF changes were roughly balanced, resulting in the area under the CSF (AUCSF) being similar between groups (CTRL 2.63 [2.60–2.73]; KC 2.66 [2.60–2.73]; p=0.461). This is also consistent with the fact that we observed no significant changes in amplitude (CSmax; CTRL 67.00 [63.1–80.3]; KC 72.5 [63.8–83.5]; p=0.349) or bandwidth (β; CTRL 2.82 [2.62–2.92]; KC 2.75 [2.60–2.89]; p=0.390).

Critically, both gains and losses in contrast sensitivity under aberration-free conditions were more pronounced in KC patients who experienced large amounts of optical aberrations in their everyday life (Figure 4B and Figure 4—figure supplement 1). Note that KC patients were split based on their habitual optical aberrations only for illustration purposes. Changes in qCSF parameters under full AO correction correlated with the amount of habitual aberrations each observer experienced in their everyday life (Figure 4C; Pearson correlation coefficients using hRMS+; SFpeak: r=−0.72, p<0.001; SFcutoff: r=−0.61, p=0.002; δ: r=−0.75, p<0.001; CSlow: r=+0.57, p=0.003). No correlation was observed for other qCSF parameters (i.e., CSmax,  β, or AUCSF). A similar pattern was observed using the total RMS as an index of habitual optical quality (Figure 4C). Moreover, the age at disease onset in our patients was around their twenties, as typically observed in KC (Vazirani and Basu, 2013). Participant’s age is therefore a good proxy for the exposure duration to the optical aberrations caused by KC. Yet, none of the changes in CSF observed in KC patients actually correlated with participant’s age (Figure 4—figure supplement 2). There was a tendency for the AUCSF and amplitude (CSmax) to decrease with participant's age, consistent with the overall reduction in sensitivity with age (e.g., Yan et al., 2017). Note that substantial changes in visual processing with age are typically observed in much older (>60 years old) observers (e.g., Derefeldt et al., 1979; Elliott et al., 1995; Yan et al., 2017).

VA measurements using high-contrast Snellen E letters (Figure 5A and 'Materials and methods') showed that both groups had better than 20/20 vision when tested under full AO correction, as expected. However, KC patients (15.6 ± 1.9 Snellen VA, range 13.4–18.5) had poorer VA than control observers (12.6 ± 1.3 Snellen VA, range 10.6–15.5) (Figure 5B; CTRL-vs-KC logMAR VA: t = 4.68, p<0.001, d = 1.94). This deficit in high-contrast VA under full AO correction is consistent with previous findings (Sabesan and Yoon, 2009) and correlated with the participant’s amount of habitual aberrations experienced outside the AO (Figure 5C; total RMS: r=+0.74, p<0.001; hRMS+: r=+0.79, p<0.001), but not with participant’s age (Figure 5—figure supplement 1; r=+0.24, p=0.250). Moreover, VA deficits under AO correction correlated with the changes in qCSF parameters (Figure 5D), such as peak SF (r = −0.73, p<0.001), high-SF cutoff (r = −0.74, p<0.001), and notably low-SF truncation (r = −0.66, p<0.001) and low-SF sensitivity (r=+0.42, p=0.039). That is, poorer VA in KC under AO correction was predicted by both impaired high-SF sensitivity as well as improved low-SF sensitivity. Altogether, these findings indicate that long-term exposure to severe optical defects alters the CSF in a way that results in impaired fine spatial vision, but also in better sensitivity to coarser spatial information that is less affected by the eye’s optics. This pattern of results is suggestive of a functional reallocation of sensory processing resources across a broad range of SFs that is expected to optimize visual processing of severely aberrated retinal images, but limits perceptual quality under fully-corrected optical quality.

To better understand how long-term exposure to optical defects alters visual processing across SFs, we used an equivalent noise paradigm (Bejjanki et al., 2014; Burgess et al., 1981; Dosher and Lu, 1998; Lu and Dosher, 1999; Lu and Dosher, 2008; Park et al., 2017) in which we measured perceptual thresholds as a function of varying external noise levels (see 'Materials and methods'). Six KC patients and eight age-matched control observers (see 'Materials and methods' and Table 1) performed an orientation discrimination task under varying levels of dynamic white noise added to the stimuli (Figure 6A), judging whether a foveally presented grating was tilted ±45° from vertical. Five different SFs (0.5, 1, 3, 9, and 16 cpd) were tested across different experimental sessions. Stimulus presentation was controlled using the FAST method (Vul et al., 2010), an advanced adaptive psychophysical technique that allowed us to estimate relevant model parameters in just 480 trials per stimulus SF and per observer. Changes in perceptual thresholds with external noise result in a characteristic threshold-versus-noise (TvN) function, which can be fitted with the PTM (Dosher and Lu, 1998; Lu and Dosher, 1999; Lu and Dosher, 2008) to quantify the effects of noise on perception (Figure 6). The PTM is a computational model of visual processing that had been successfully used to identify the mechanisms underlying perceptual differences for a wide range of brain functions, such as attention (Dosher and Lu, 2000; Lu and Dosher, 1998) and perceptual learning (Dosher and Lu, 1998), as well as between specific populations, such as in amblyopia (Levi and Klein, 2003), autism (Park et al., 2017), dyslexia (Sperling et al., 2005), and cortical blindness (Cavanaugh et al., 2015).

The PTM considers that the differences in perceptual performance between groups can result from changes in three separate mechanisms (Figure 6): (1) signal enhancement, (2) signal selectivity, or (3) gain control (nonlinearity change). Each signal processing mechanism is implemented within the PTM observer model by changes in one of three possible sources of noise: (1) internal additive noise (Aadd), (2) external noise filtering (Aext), and (3) multiplicative internal noise (Amul). Signal enhancement improves the ratio of the signal relative to the internal additive noise. Elevated internal additive noise indicates impaired signal enhancement mechanisms and leads to worse perceptual thresholds at low external noise levels (Figure 6C, upper left). No difference is observed when high external noise is the primary limiting factor as both the signal and the external noise in the stimulus are amplified. Signal selectivity (tuning) determines the capacity of the perceptual template to filter out external noise, which affects performance only at high external noise levels (Figure 6C, upper right). A combined effect of higher internal additive noise and poorer external noise filtering elevates thresholds at all external noise levels, similarly across difficulty levels, which suggests channel reweighting (Figure 6C, lower left). Finally, higher multiplicative internal noise (Amul) would also impair thresholds at all external noise levels, but via a non-uniform shift in TvN functions across difficulty levels (Figure 6C, lower right). The magnitude of multiplicative internal noise is proportional to stimulus contrast: Higher Amul results in greater elevation in internal noise with higher signal contrast, acting similarly to a gain control mechanism (i.e., compressive response at higher contrasts).

First, we analyzed the data using the conventional PTM (Dosher and Lu, 1998; Lu and Dosher, 1999; Lu and Dosher, 2008) to characterize the relative difference in noise-limiting factors between the CTRL and KC groups (see 'Materials and methods'). To do so, contrast thresholds were estimated for each observer as a function of external noise, difficulty level, and stimulus SF. Then, we fitted the data with the PTM in a conventional manner using a least-squares procedure (Figure 7). Given the large individual variability in KC habitual aberrations and its impact on the CSF, KC participants were split into two groups based on KC severity using a median split (total RMS 3.85 µm; hRMS+ 2.24 µm), resulting in three groups based on habitual optical quality: age-matched controls with healthy eyes (N = 8; total RMS 0.88 ± 0.28 µm; hRMS+ 0.34 ± 0.12 µm), mild/moderate KC (N = 3; total RMS 2.19 ± 0.87 µm; hRMS+ 1.25 ± 0.46 µm), and severe KC (N = 3; total RMS 5.82 ± 1.76 µm; hRMS+ 3.51 ± 0.91 µm). All the data from all five SFs were included in the analysis, with the model estimating separate TvNs for each group, each SF, and each difficulty levels (see 'Materials and methods'). The resulting TvN curves estimated by the PTM exhibited characteristic nonlinear patterns (Figure 7).

To assess the mechanisms underlying the differences in contrast sensitivity between groups, several variants of the PTM were fit to the data: no group difference (null model), changes in internal additive noise (A_add), external noise filtering (A_ext), or multiplicative internal noise (A_mul), mixtures of them (A_add + A_mul; A_add + A_ext; A_mul + A_ext), and a full model assuming changes in all three mechanisms (A_add + A_ext + A_mul). To account for the large differences in the number of free parameters across models, we computed the Bayesian information criterion (BIC) evidence that determines which model best fits the data while penalizing for a greater number of free parameters. Figure 7A shows the results of the best model (see Figure 7—figure supplements 1–4 for the results from each of the eight possible variants of the PTM). Overall, the differences in contrast thresholds between groups were best explained by a simple model assuming solely SF-dependent changes in internal additive noise (Figure 7B; A_add; r² = 94.02), followed by mixture models that included internal additive noise as one of the free parameters, and then by the full model. Other models that did not allow changes in internal additive noise (A_add) could not account for the differences between groups. Relative to the control observers, severe KC patients showed a reduction in internal additive noise (A_add) by −49.2% and −53.1% at 0.5 and 1 cpd, respectively. Mild/moderate KC patients did not show such benefits at low SFs, but rather a slight elevation in internal noise by +20.4% and +5.7% at 0.5 and 1 cpd, respectively. At 3 cpd, mild/moderate KC observers showed a negligible difference in internal additive noise (+1.1%) relative to control observers, whereas severe KC patients still showed a slight reduction in internal additive noise (−18.7%). At high SFs, all KC observers exhibited poorer thresholds due to large elevations in internal additive noise, by +21.2% and +110.8% at 9 and 16 cpd for mild/moderate KCs, and by +158.4% and +165% at 9 and 16 cpd for severe KC patients.

Additional PTM analyses, separately for low and high SFs (Figure 7—figure supplements 5 and 6), further supported SF-specific changes in internal additive noise as the primary mechanism underlying altered CSF following long-term exposure to poor optical quality. Furthermore, these results replicate the pattern of gains and losses in contrast sensitivity found in experiment 1 (Figure 7—figure supplement 7), despite differences between the two experiments (e.g., high uncertainty regarding the SF of the upcoming target stimulus on a given trial in experiment 1, whereas there was no uncertainty in experiment 3). When almost no external noise was added to the target stimuli, observers with severe KC showed higher contrast sensitivity for low SFs and impaired sensitivity for high SFs. This pattern was less pronounced in mild/moderate KC participants. At high external noise levels, contrast sensitivity was more comparable across groups, consistent with the predictions of the internal additive noise model (Figure 6C). Note that the differences at high SFs under high external noise (Figure 7—figure supplement 7) are likely due to the fact that the nonlinearity characteristic of TvN curves was not well captured and internal additive noise remained the main limiting factor even at the highest external noise level. Altogether, these results strongly support changes in internal additive noise (i.g., signal enhancement) as the primary mechanism underlying the differences in contrast sensitivity at both low SFs and high SFs in KC patients.

To better assess individual differences in the underlying sources of altered visual processing across SFs and relate them to each observer’s habitual optical quality, we estimated TvN curves and parameter estimates for each individual participant using a hierarchical Bayesian model (see 'Materials and methods'). By assuming that the variability between participants follows a population-level distribution, this method allowed us to estimate group-level ‘traits’ in terms of signal processing given the presence of external noise. We then tested whether the level of internal additive noise, as well as other individual PTM estimates, correlated with the amount of habitual optical aberrations experienced by each participant (Figure 8). Consistent with the SF-specific changes in sensitivity observed in KC patients, poorer habitual RMS was associated with reduced individual internal additive noise levels at low SFs (0.5 and 1 cpd) (Figure 8A; total RMS: r = −0.65, p=0.011; hRMS+: r = −0.63, p=0.016). At high SFs, individual noise estimates were more variable, particularly at 16 cpd where we could not reliably estimate the nonlinear segment of individual TvN curves. Thus, we restricted this analysis to individual noise estimates from the 9 cpd condition. We found that poorer habitual optical quality was positively correlated with elevated individual internal additive noise levels at high SFs (Figure 8A; total RMS: r=+0.65, p=0.012; hRMS+: r=+0.70, p=0.005). No correlation was found at low or high SFs with either multiplicative internal noise or external noise filtering (Figure 8B, C), supporting the finding that SF-specific changes in internal additive noise alone can account for the impact of long-term exposure to poor optical quality on visual processing.

Taken together, the present results reveal that long-term exposure to severe optical defects causes a broad functional reallocation of sensory processing resources across a wide range of SFs, which is mediated by SF-specific changes in signal enhancement mechanisms of SF-selective neurons.

A total of 10 keratoconus patients (KC1–9; mean age 34.7 ± 12.4, range 22–55) and 14 age-matched control observers with healthy eyes (CTRL1–14; mean age 33.6 ± 12.3, range 21–57) participated in this study (see Table 1 for demographic information). Six of the KC patients (mean age 35.8 ± 14.5, range 24–55) and eight of the age-matched control observers (mean age 37.5 ± 12.7, range 21–57) participated in experiment 3. Participants were cyclopleged with tropicamide (1%) to dilate the pupil and paralyze accommodation during visual testing. All participants were screened prior to the study by one of our ophthalmologists, providing standard information (e.g., corneal curvature, refractive error) and ensuring that dilation was safe. An additional screening session was performed to ensure we could obtain good quality wavefront measurements and reach stable aberration-free condition under AO correction. Three potential KC patients and one control observer did not pass this second screening stage and were not tested further along. All control observers were emmetropes or low myopes/hyperopes, with well-corrected optical quality in both eyes and no specific issues that may have affected their optical quality in their daily life (e.g., uncorrected or high myopia, dry eye). All KC patients included in the present study had been diagnosed with KC at least 12 months before testing, with a reported onset of the disease around their twenties. Importantly, all patients had been wearing the same habitual corrective method and did not report substantial changes in their vision for at least 12 months before testing. The eye of KC patients with the most severe habitual optical aberrations was selected for monocular testing under AO (except for KC2 due to the presence of scaring in the untested eye). A qualitative description of the optical quality of the untested eye based on the screening performed by the ophthalmologist is provided in Table 1. The Research Subjects Review Board at the University of Rochester Medical Center approved all experimental protocols, which were conducted according to the guidelines of the Declaration of Helsinki. Informed written consent was obtained from all subjects prior to participation. Participants were compensated $12/hr.

An adaptive optics vision simulator (AOVS) allowed us to bypass any optical factors during psychophysical testing by measuring and correcting all monochromatic and polychromatic aberrations. As illustrated in a simplified schematic (Figure 2A; see also Figure 2—figure supplement 1), the AOVS consisted of a custom-built Shack–Hartmann wavefront sensor to measure the wavefront aberrations, a deformable mirror (ALPAO DM97, Montbonnot, France) to correct subjects’ wavefront aberrations, an artificial pupil set to 5.8 mm, and a calibrated visual display for psychophysical measurements. Wavefront aberrations were measured for a 6-mm pupil at fovea using an infrared (840 ± 20 nm) superluminescent diode. The AOVS was operated in continuous closed loop (~8 Hz), allowing to fully correct all aberrations over a 6-mm pupil using the deformable mirror. Visual testing was performed at fovea under white light conditions using a modified digital light processor display (Sharp XR-10X, Abeno-ku, Osaka, Japan) operating at 8 bits with 1024 × 768 (60 Hz) resolution, sustending 3.56 × 2.67 degrees of visual angle (dva). The display was calibrated with a PR-650 SpectraScan Colorimeter (Photo Research, Chatsworth, CA), and luminance precision was increased to 10.7 bits using the bitstealing technique. A dental impression bite bar mounted to motorized translation stages (x, y, z) with adjustable lateral headrests was used to stabilize head position and maintain pupil alignment during visual testing (Figure 2—figure supplement 1).

Wavefront measurements were collected for each observer using their everyday correction method, if any, to estimate each participant’s habitual optical quality (Figure 2B). Wavefront aberrations were fitted to individual Zernike polynomials up to the 10th order, with 65 Zernike coefficients. The square root of the sum of Zernike coefficients was used to estimate the overall RMS error (total RMS: all Zernike coefficients) and the higher-order aberration (HOAs) RMS error (hRMS+: 6–65th Zernike coefficients), reported in microns (µm). Wavefront measurements were also collected during visual testing to estimate the quality and stability of the AO correction (Figure 2C). The MTF was computed for each participant under their habitual optical quality (Figure 2D) and under full AO correction (Figure 2E). Specifically, we computed the optical transfer function (OTF) from the individual subject’s aberrations at a center wavelength of 555 nm and for a pupil diameter of 6 mm. The MTF was calculated as the absolute value of the OTF, which was averaged radially. Full correction of all Zernike coefficients was applied for the entire duration of each testing session, with the exception of defocus for which appropriate defocus values were used to correct axial chromatic aberrations. Subjective defocus values were determined for all participants by asking them to adjust defocus using a motorized Badal prism to make a high-contrast Snellen letter ‘E’ as sharp as possible, while correcting all other aberrations using AO. Then, through-focus high-contrast VA measurements were used to objectively verify that the subjective defocus value applied during AO correction resulted in a very focused, perceived image and maximal VA performance. After this initial session, each experimental session started with VA measurements to ensure the quality and stability of the AO correction before data collection. To maximize AO correction during stimulus presentation, participants were trained to blinks between trials and to stop if the perceptual quality got unstable and/or poor quality. To minimize the influence of blinks when estimating the residual RMS under AO correction, the median RMS was computed across time for each measurement (Figure 2—figure supplement 2 and Figure 2—video 1). Then, the average residual RMS was computed for each participant from multiple wavefront measurements collected under AO correction (Figure 2C). As detailed and demonstrated in previous work (e.g., Ghosh et al., 2017; Ng et al., 2021; Sabesan et al., 2017; Sabesan and Yoon, 2009; Sabesan et al., 2012; Zheleznyak et al., 2016), our AOVS provided stable, aberration-free optical quality during visual testing in both typical and severely aberrated eyes. Statistical analyses indicated a violation of normality for the habitual total RMS of control and KC groups, as well as for the AO-corrected residual RMS of KC observers (Shapiro–Wilk test, p<0.05). A Mann–Whitney U test was therefore used to compare control and KC groups for these variables, with the effect size given by the rank biserial correlation. Welch’s t-tests were used to compare the amount of habitual hRMS+ and vertical coma between groups due to unequal variance between groups (Levene’s test, p<0.05), with the effect size given by Cohen’s d.

The CSF of each participant was measured using a 2-AFC orientation discrimination task (Figure 3A). Each trial began with a dynamic fixation point. After a blank screen, a Gabor stimulus (Gaussian envelope SD 0.75 dva; SF range 0.25–30 cpd with 12 equal log-step values) oriented ±45° was presented at fovea. A 500-ms temporal Gaussian envelope was used to blend stimuli into the background and avoid onset/offset transients, and a brief tone signaled stimulus onset to reduce temporal uncertainty. Participants were asked to report whether the stimulus was tilted clockwise or counterclockwise. Auditory feedback was provided for both correct and incorrect responses. We used the qCSF method (Hou et al., 2010; Hou et al., 2016; Lesmes et al., 2010) to estimate 81%-correct contrast thresholds over a broad SF range. The qCSF method is a Bayesian adaptive strategy using a priori knowledge about the CSF's general form to obtain reasonably accurate estimates of sensitivity across SFs with as little as 100 trials. The qCSF method describes the CSF as a truncated log-parabola with four parameters (Figure 3B): (1) the peak sensitivity (amplitude) CSmax, (2) the peak frequency SFpeak, (3) the bandwidth β (full width in octaves at half maximum), and (4) the truncation level (plateau) at low SF δ. Without truncation, the CSF is defined as a function of the stimulus frequency (f) in decimal log as a log-parabola CS´(f):(1)CS′(f)=log10(CSmax)− log10(2)(log10(f)−log10(SFpeak)log10(2β)/2)2

This log-parabola is then truncated at SF below the peak SF with the truncation parameter δ, which determines contrast sensitivity at low SF (CSlow):(2)CS(f)= CS′(f),f≥SFpeak,CSlow(f)=log10(CSmax)− δ,f<SFpeak and CS′(f)< CSmax−δ

In addition, the high-SF cutoff (SFcutoff) was estimated from the qCSF fits, corresponding to the frequency at which CSSFcutoff=0  (i.e., 100% contrast). The test procedure was similar to that described in previous studies (e.g., Hou et al., 2010; Lesmes et al., 2010). Briefly, the stimulus space consisted of gratings with contrasts ranging from 0.1% to 99% in steps of 1.5 dB and SF from 0.25 to 30 cpd. After familiarization with the task, participants performed around 7 qCSF runs of 100 trials each (mean number of runs: 7±4 for CTRLs, 7±3 for KCs), which were then combined to compute individual qCSF functions using all trials. Confidence intervals (95% CIs) and p-values were computed from bootstrapping. Specifically, individual trials were randomly resampled with replacement to generate a resampled trial sequence, which was refitted using the qCSF procedure. We repeated this procedure of resampling and refitting 10,000 times to generate bootstrap distributions of the fitted parameters, along with associated confidence intervals. To assess statistical significance for differences in qCSF parameters and SF sensitivity estimates between groups, we computed the difference from the 10,000 random pairs of values from the bootstrap distributions of the two groups, and defined p-values as the proportion of samples that 'crossed' zero. Note that for all of the key comparisons significant p-values also correspond to non-overlapping confidence intervals. For group comparisons at each of the 12 SF levels, p-values were corrected for multiple comparisons using Bonferroni correction by dividing the alpha value level (*p < 0.05; **p < 0.01; ***p < 0.001) by the number of SF levels (i.e., 12).

VA thresholds were measured using a 4-AFC letter orientation task (Figure 5), in which observers judged whether a high-contrast Snellen ‘E’ letter presented for 250 ms at fixation was oriented upward, downward, leftward, or rightward. Stimuli were black letters presented on a white background. The size of each Snellen E letter was adjusted from trial to trial using the QUEST staircase method (Watson and Pelli, 1983) to estimate 62.5%-correct VA thresholds (in logMAR), with 40 trials per staircase. Multiple VA thresholds were collected under AO correction for each participant (mean number of runs: 7 ± 4 for CTRLs, 12 ± 7 for KCs). Each experimental session also started with VA testing to ensure the quality and stability of the AO correction before starting data collection.

We used an equivalent noise paradigm (Bejjanki et al., 2014; Burgess et al., 1981; Dosher and Lu, 1998; Lu and Dosher, 2008; Park et al., 2017) where perceptual thresholds are measured as a function of varying external noise levels added to the stimuli. Contrast thresholds were measured using a 2-AFC orientation discrimination task for various amounts of external noise (Figure 6A). Each trial began with a dynamic fixation point. After a blank screen, a ±45° oriented Gabor signal (cosine envelope diameter 2 dva) embedded in different intensity levels of dynamic white noise (eight levels, from 0 to 0.33 SD; check size 0.06°) was presented at fovea for 100 ms (six noise frames). Participants were asked to report the orientation (±45° from the vertical) of the Gabor patch presented on each trial. Each stimulus was accompanied with a brief tone to reduce temporal uncertainty, and auditory feedback was provided for both correct and incorrect responses. Stimulus presentation was controlled using the FAST method (Vul et al., 2010), an advanced adaptive psychophysical technique used to accurately estimate relevant model parameters in just 480 trials per participant for each SF. This allowed us to estimate contrast thresholds as a function of external noise contrast levels for both 70.71%-correct and 79.37%-correct difficulty levels, similar to previous studies (Bejjanki et al., 2014; Dosher and Lu, 1998; Lu and Dosher, 2008; Park et al., 2017). Five different SFs (0.5, 1, 3, 9, and 16 cpd) were tested across different experimental sessions of 480 trials each (divided into four blocks of 120 trials), for a total of 2400 trials per observer. Data from the equivalent noise experiment were pooled from the FAST structures to estimate psychophysical thresholds for each participant at each of the external noise levels (60 trials per level). This approach yielded independent, albeit noisy, contrast threshold estimates at each noise level. Thresholds were estimated by fitting a Weibull function at each external noise level independently:(3)Pc= 1-1-0.5*2-log⁡(c)αηwhere P denotes percent correct, c is stimulus contrast, α is contrast threshold at 75%-correct performance level, and η is the slope of the function. Similar to Park and colleagues (2017), we used a Bayesian model fitting method implementing a Markov Chain Monte Carlo (MCMC) technique to estimate the two free parameters of the Weibull function (η and α). Specifically, we sampled the posterior distributions of the parameters using JAGS software (http://mcmc-jags.sourceforge.net). We assumed a broad uniform prior on each parameter with a range that includes all practically possible values. Maximum a posteriori (the mode of the posterior) were used as the best estimates of the model parameters. We discarded the first 15,000 samples as a burn-in period and thinned the samples to reduce correlations by only selecting every 200 samples. A total of 10 chains were run in parallel, resulting in 1000 posterior samples per chain. Thresholds at 70.71% and 79.37% were then computed from the estimated Weibull functions.

The PTM model (Dosher and Lu, 1998; Lu and Dosher, 2008) was used to estimate the sources of signal-to-noise changes responsible for performance differences between KC and age-matched control observers. Contrast thresholds for two difficulty levels (70.71% and 79.37%) and across external noise levels were fitted with the PTM to quantify the effects of noise on contrast perception. The PTM consists of five main components (Figure 6B): a perceptual template tuned to the signal, a nonlinear transducer function, a multiplicative internal noise source (N_mul), an additive internal noise source (N_add), and a decision process. The output of the perceptual template is processed by two pathways: the signal pathway in which the output is processed by an expansive nonlinear transducer function, and the multiplicative internal noise pathway in which the output is processed by a rectified nonlinear transducer function. Multiplicative noise is an independent noise source whose amplitude is proportional to the (average) amplitude of the output from the perceptual template, acting as a gain control mechanism. Additive internal noise is another noise source whose amplitude does not vary with signal strength and is related to the gain of the perceptual template. Both multiplicative and additive noise sources are added to the output from template matching, and the noisy signal is submitted to a decision process. Here, contrast thresholds (Cτ) are characterized by(4)Cτ= 1β [(1+Nmul2) Next2γ + Nadd2 (1/d′2−Nmul2)]12γwhere the input (signal + external noise Next) is filtered through a perceptual template, resulting in the amplification of the signal via a gain factor β. The output of the filter is then transformed through a nonlinear transducer function that amplifies the inputs to the γth power, with both internal additive noise (Nadd) and multiplicative internal noise (Nmul) being added to the output. Nadd remains constant across signal levels, while Nmul is proportional to the signal strength. Next is manipulated by the experimenter along with the input signal. Finally, a decision process determines the contrast threshold at a specific performance level (d´). The PTM (Dosher and Lu, 1998; Dosher and Lu, 2000; Lu and Dosher, 2008) considers that performance differences result from changes in three possible sources of inefficiency (Figure 6B, C): (1) changes in internal additive noise (A_add), equivalent to changes in signal enhancement (amplification) of the perceptual template; (2) changes in external noise filtering (A_ext), corresponding to changes in signal selectivity (tuning) of the perceptual template; and (3) changes in multiplicative internal noise (A_mul), acting as a gain control mechanism compressing the perceptual template’s responses to signal contrast (nonlinearity change). Group averages of the independently estimated thresholds were used to fit the conventional PTM across SFs. To characterize group differences between CTRL and KC observers at each SF, the PTM introduces three coefficient indices (A_mul(SF,group), A_add(SF,group), and A_ext(SF,group)) to Equation (4):(5)Cτ= 1β [(1+(Am(SF,group)∗Nmul(SF))2)(Ae(SF,group)∗Next)2γ+(Aa(SF,group)∗Nadd(SF))2(1/d′2−(Am(SF,group)∗Nmul(SF))2)]12γ

The coefficient indices for CTRL are fixed to 1 (A_mul(CTRL) = A_add(CTRL) = A_ext(CTRL) = 1). N_add(SF) and N_mul(SF) did not vary across groups, only across SFs to reflect differences in contrast thresholds related to stimulus SF. To estimate whether and how these three types of noise could account for group differences in KC group(s), we computed the relative differences in the effects of each source of noise between the groups. Elevated sources of noise in KC relative to CTRL would correspond to A_mul(KC), A_add(KC), and/or A_ext(KC) estimates being higher than 1 (i.e., CTRL group), and to poorer contrast thresholds. Conversely, reduced sources of noise in KC relative to CTRL would correspond to estimates lower than 1, and to better contrast thresholds. These three coefficient indices for each KC group could be restricted, either varying or fixed at 1. We compared the results obtained by fitting the eight possible variants of the PTM (Figure 7, Figure 7—figure supplements 1–4), ranging from no change in any of the three noise reduction mechanisms to the full model with changes in all three noise-reduction mechanisms. We compared the control group to two groups of KC participants (mild/moderate and severe) at five different SFs. The full model consisted of 12 shared parameters across groups (β, γ, N_mul(SF1-5), N_add(SF1-5)), and 15 noise parameters (A_mul(SF1-5), A_add(SF1-5), A_ext(SF1-5)) for each of the two KC groups, for a total of 42 parameters. Model fitting was carried out using a least-square method, and goodness of fit (r2) for each candidate model was computed as follows:(6)r2= 1− ∑ [log⁡(Cτpredicted)−log(Cτ)]2∑ [log⁡(Cτ)−mean(log⁡(Cτ))]2where ∑ and mean were computed across groups, SFs, external noise levels, and difficulty levels. Given the large differences in the number of free parameters across models, we computed the Bayesian Information Criterion (BIC) as a criterion for model selection. The BIC selects the best model while correcting for overfitting by introducing a penalty term for the number of free parameters in the model:(7)BIC= n*log⁡RSSn+k*log⁡(n) where n is the number of predicted data points, RSS is the residual sum of squares of the model, and k is the number of parameters of the model. BIC approximates a transformation of a model's posterior probability. We then computed ∆BIC as(8)ΔBICk=BICk−BICk∗where k* corresponds to the model with the lowest BIC value (i.e., the best model).

To better assess the link between habitual optical quality and individual variability in the PTM noise estimates, we used a hierarchical Bayesian modeling technique to fit the PTM to each participant. This technique assumes that each participant is drawn from a population distribution (CTRL or KC), which increases statistical power. Importantly, this technique allows estimation of PTM parameters for each participant within a population, providing a better understanding of individual variability. We assumed that an individual’s response for a given trial is drawn from a Bernoulli distribution (i.e., responseijk ~ Bernoulli(θijk)), where i is the difficulty level, j is the external noise level (Next), and k is the trial number. θijk corresponds to the probability of making a correct response:(9)θijk=1−(1−0.5)∗e(mi log(xijk)log(Cτij))ηwhere x corresponds to the stimulus contrast, η to the slope, Cτij to the contrast threshold, and mi to(10)mi=−log⁡(1−qi1−0.5)1η

The parameter qi corresponds to the difficulty level (i.e., either 70.71% or 79.37%). The PTM defined the contrast threshold Cτij as(11)Cτij=1β[ (1+Nmul2)(wext Nextij )2γ+ Nadd2(1/di′2−Nmul2)]12γ

Equation (11) is the same as Equation (4), except for the fact that a coefficient for external noise (wext ) is added here to characterize the impact of external noise on individual’s contrast thresholds. For each participant, we estimated three parameters Nmul , Nadd, and wext . We assumed a fixed β (1.25) and γ (2) for all participants to simplify the model, which was within a reasonable range reported in previous studies (e.g., Dosher and Lu, 1998; Lu and Dosher, 2008; Park et al., 2017). Note that similar results were observed using other values of β and γ. Similar to the Weibull fitting procedure, an MCMC technique was used to sample from the posterior distributions and estimate the free parameters. Here, we assumed hierarchical priors on each of the model parameters, meaning that each model parameter that characterized an individual participant was assumed to be drawn from an independent Gaussian population distribution with a mean and SD that characterized each group (CTRL or KC). Priors for population means and SDs were set to broad uniform distributions. Maximum a posteriori were used as the best parameter estimates for both individual and population parameters. We used 15,000 iterations for burn-in and only selected every 200 samples for thinning. Ten chains were run in parallel, each of which sampled 2000 posterior samples.