**Purpose.**:
The qCSF method is a novel procedure for rapid measurement of spatial contrast sensitivity functions (CSFs). It combines Bayesian adaptive inference with a trial-to-trial information gain strategy, to directly estimate four parameters defining the observer's CSF. In the present study, the suitability of the qCSF method for clinical application was examined.

**Methods.**:
The qCSF method was applied to rapidly assess spatial CSFs in 10 normal and 8 amblyopic participants. The qCSF was evaluated for accuracy, precision, test–retest reliability, suitability of CSF model assumptions, and accuracy of amblyopia screening.

**Results.**:
qCSF estimates obtained with as few as 50 trials matched those obtained with 300 Ψ trials. The precision of qCSF estimates obtained with 120 and 130 trials, in normal subjects and amblyopes, matched the precision of 300 Ψ trials. For both groups and both methods, test–retest sensitivity estimates were well matched (all *R* > 0.94). The qCSF model assumptions were valid for 8 of 10 normal participants and all amblyopic participants. Measures of the area under log CSF (AULCSF) and the cutoff spatial frequency (cutSF) were lower in the amblyopia group; these differences were captured within 50 qCSF trials. Amblyopia was detected at an approximately 80% correct rate in 50 trials, when a logistic regression model was used with AULCSF and cutSF as predictors.

**Conclusions.**:
The qCSF method is sufficiently rapid, accurate, and precise in measuring CSFs in normal and amblyopic persons. It has great potential for clinical practice.

^{ 1,2 }It affects 2% to 4% of the general population

^{ 2 }and is the most common cause of uniocular blindness in adults.

^{ 3 }In the United States, 750,000 preschoolers are at risk for amblyopia, and roughly half of those may not be identified before school age.

^{ 4 }In China, it is believed that there are tens of millions of children affected by the visual disorder.

^{ 5 }Amblyopia has become a serious social and economic challenge.

^{ 6 }

^{ 7,8 }contour integration,

^{ 9–11 }and global motion perception.

^{ 12,13 }Of these functions, it is letter acuity, measured rapidly with a chart and easy to understand, that is widely used in screening, early intervention, and treatment evaluation of amblyopia. However, it has been suggested that the contrast sensitivity function (CSF), which describes how visual sensitivity varies as a function of grating spatial frequency, characterizes amblyopia's spatial vision deficits better than does letter acuity.

^{ 14–25 }For example, contrast sensitivity at high spatial frequencies is still abnormal in amblyopes who are deemed “treated” based on the criterion of remediated visual acuity.

^{ 26 }CSF testing could improve screening, diagnosis, and evaluation of treatment outcomes of amblyopia.

^{ 27,28 }and the CVS-1000 series chart (VectorVision, Greenville, OH). Although chart tests are convenient in clinical use, their limited number of contrast levels greatly limits the range and resolution of the test grating stimuli.

^{ 29–33 }In addition, charts using broadband letters as stimuli (e.g., the Pelli-Robson chart), are typically insensitive to frequency-specific deficits.

^{ 34 }In contrast, the CSF can be measured with higher precision and accuracy in laboratory psychophysical tests. However, even with adaptive methods such as the QUEST

^{ 35 }or Ψ method,

^{ 36 }a reasonable threshold estimate at a single spatial frequency usually takes 50 to 100 trials. Consequently, a CSF measurement obtained with conventional adaptive methods, sampling at seven different spatial frequencies, requires up to 700 trials, can take 1 hour, and is therefore too time-consuming, making it unsuitable for clinical use.

^{ 37 }recently developed a novel adaptive psychophysical procedure, the qCSF method, which estimates the full CSF rapidly (∼5–10 minutes) with reasonable precision (2–3 dB). (In this paper, 1 dB = 0.05 log units, 12%; but in the clinical definition of decibels [1 dB = 0.1 log units], the precision and bias were half of the corresponding estimates.) The method applies a Bayesian adaptive test strategy, first developed to estimate the threshold and slope of psychometric functions,

^{ 36,38 }to directly estimate CSF parameters. The CSF form assumed by the qCSF is the truncated log-parabola,

^{ 39,40 }which is specified by four parameters: (1) the peak gain (sensitivity), γ

_{max}; (2) the peak spatial frequency ƒ

_{max}; (3) the bandwidth β, which describes the function's full-width at half-maximum (in octaves); and (4) δ, the low-frequency truncation level (Fig. 1). Lesmes et al.

^{ 37 }validated the qCSF method with a psychophysical experiment, using an orientation identification task in three normal subjects. Combined with simulation results, they demonstrated that 50 to 100 qCSF trials provided accurate CSF estimates.

^{ 41–43 }are fixed. After defining a probability distribution over the four CSF parameters, a one-step-ahead search of the stimulus space (over dimensions of spatial frequency and contrast) is used to choose stimuli that maximize the information gained over the CSF parameter space.

^{ 36,38,44,45 }After the Bayesian update of the probability distribution following each trial, a CSF estimate can be calculated from the expected values of the four parameters.

^{ 36 }Such an independent assessment was critical for evaluating the relative accuracy of qCSF estimates, in addition to the accuracy of several model assumptions: (1) Individual CSFs can be well described with a specific functional form; and (2) the slopes of psychometric functions at different spatial frequencies are the same. These assumptions, which allow CSF task performance to be modeled as a relatively simple psychometric surface (Fig. 1), have support in the empiric literature on CSFs in the normal population.

^{ 39,40,46 }However, they must be re-evaluated in clinical populations.

No. | Sex | Age (y) | Eye | Type of Amblyopia | Eye Alignment | Correction | Acuity | Test-Retest Interval (d) | Experienced |
---|---|---|---|---|---|---|---|---|---|

1 | M | 20 | AE | Anisometropia | None | 1.50DC×90 | 2.5 | 1 | Yes |

FE | −1.50DS:0.75DC×180° | 1.0 | |||||||

2 | M | 25 | AE | Strabismus/anisometropia | RXT 10Δ | 0.75DS | 10.0 | 5 | Yes |

FE | −5.00DS | 1.3 | |||||||

3 | F | 20 | AE | Anisometropia | None | +3.00DS:+1.00DC×15° | 2.0 | 12 | Yes |

FE | +0.50DS:+0.50DC×160° | 1.3 | |||||||

4 | F | 22 | AE | Anisometropia | None | +2.50DS | 2.0 | 15 | Yes |

FE | Plano | 1.0 | |||||||

5 | M | 31 | AE/LE/Measured | Anisometropia | None | +4.00DS | 2.5 | 4 | No |

AE/RE | None | +5.00DS | 2.0 | ||||||

6 | M | 22 | AE/RE/Measured | Anisometropia | None | +6.00DS | 4.0 | 3 | Yes |

AE/LE | None | +3.00DS | 1.3 | ||||||

7 | M | 21 | AE | Strabismus/anisometropia | LET 10Δ | +1.25DS:+0.50DC×180° | 5.0 | 12 | Yes |

FE | +1.00DS | 0.67 | |||||||

8 | M | 25 | AE | Strabismus/anisometropia | LET 18Δ | 6.50DS:+1.00DC×80° | 5.0 | 7 | No |

FE | 5.50DS | 1.3 |

^{2}. A special circuit was used to achieve 14-bit grayscale resolution.

^{ 47 }Stimuli were generated on the fly by a technical computing software (MatLab 7.1.0.14; The MathWorks Corp., Natick, MA) and Psychtoolbox subroutines.

^{ 48,49 }Participants viewed the stimuli monocularly at a distance of 2.4 m. A chin–forehead-rest was used to minimize head movements during the experiment.

_{max}; (2) the peak spatial frequency ƒ

_{max}; (3) the bandwidth β, which describes the function's full-width at half-maximum (in octaves), and (4) δ, the low-frequency truncation level. The possible CSFs considered for Bayesian inference were represented by a probability distribution over a gridded parameter space, T

_{ν→}, where ν→ = (γ

_{max},

*f*

_{max}, β, δ). The stimulus space, T

_{x→}, where

*x→*= (

*c*,

*f*), represents all possible grating stimuli with contrast

*c*and spatial frequency

*f*. The goal of the qCSF method is to efficiently search the stimulus space to gain information in the parameter space. See 1 for a more detailed description of the qCSF algorithm.

*x→*= (

*c*,

*f*) comprises gratings that vary in contrast (from 0.1%–99% in 1.5-dB steps) and spatial frequency (from 0.5 to 16 cycles per degree [cpd] in 3-dB steps). One exception was observer A1, who was tested at spatial frequencies that varied from 0.5 to 12 cpd in 3-dB steps, based on practice results. For the Ψ method, stimulus contrast

*c*was sampled from 0.1% to 99% in 1-dB steps; contrast thresholds were measured independently at 0.69, 1.29, 2.42, 4.54, 8.52, and 16.00 cpd for all subjects except A1. For subject A1, thresholds were measured at 0.67, 1.19, 2.12, 3.78, 6.73, and 12.00 cpd.

^{ 35 }The Discussion section presents simulation results that demonstrate that matching the assumed slope and the observer's slope is not critical for threshold estimation.) For the qCSF, the threshold variable, τ, was defined by the CSF model. For the Ψ method, τ was estimated independently at each spatial frequency.

^{ 36 }contrast thresholds were estimated independently at six spatial frequencies with 50 trials for each spatial frequency and a total of 300 trials. A qCSF run encompassed 300 trials. To compare the results from the qCSF and Ψ methods, contrast thresholds obtained with the qCSF method were calculated at the six spatial frequencies used in the Ψ method. All participants completed two sessions of 600 trials, with 300 qCSF trials randomly intermixed with 300 Ψ trials. Because of scheduling conflicts, the interval between the two sessions ranged from 1 to 15 days across subjects (see Table 1 for details).

^{ 50 }based on 500 simulated repetitions of full experimental runs of 300 qCSF and 300 Ψ trials. For each participant, the slope of the psychometric functions was assumed to be the slope of the best-fitting single-slope Weibull function (see Assumptions Check). For each observer, the precision in a qCSF or Ψ run was characterized by the standard deviation of the distribution of resampled threshold estimates: where

*k*indexes spatial frequency,

*i*indexes repetition, and τ

^{k}is the mean threshold of

*N*repetitions in the

*k*th spatial frequency condition.

*P*> 0.10, paired

*t*-test], but for all trials of the normal group [

*P*> 0.05; paired

*t*-test]). The averaged precision of the qCSF method over participants and sessions for both the normal and amblyopia groups are shown in Figure 3 as a function of the number of trials. The average precision of the normal group was 3.86 ± 0.91, 2.63 ± 0.83, and 1.41 ± 0.59 dB after 50, 100, and 300 qCSF trials, respectively. The average precision of the amblyopia group was 4.71 ± 0.74, 3.23 ± 0.77, and 1.73 ± 0.48 dB after 50, 100, and 300 qCSF trials. The standard deviations in the amblyopia group were larger than those in the normal group until the 110th trial (for any trial before 110,

*P*< 0.05;

*t*-test). The average precision of the Ψ method for the normal and amblyopia groups was 2.40 ± 0.80 and 2.70 ± 0.55 dB, respectively, in 300 trials. The precision achieved with ∼120 qCSF trials matched that obtained with 300 Ψ trials in the normal group. The precision achieved with ∼130 qCSF trials matched that obtained with 300 Ψ trials in the amblyopia group.

*k*indexes spatial frequency, and log(τ

_{Ψ}

^{k}) is the average threshold from the two sessions.

*P*> 0.10; paired

*t*-test). The average bias over the two sessions is plotted as a function of the number of trials for the normal and amblyopia groups in Figure 4. Averaged over sessions, the mean bias of the qCSF method after 50, 100, and 300 trials was 0.32, −0.03, and −0.16 dB in the normal group, and −1.38, −0.78, and −0.24 dB in the amblyopia group. For both groups, these biases were not significantly different from 0 (

*P*> 0.10;

*t*-test).

*P*< 0.001) for the normal and amblyopia groups, respectively (Fig. 5). Linear regression was also applied to analyze thresholds obtained from both groups. The slope for the Ψ method was 0.837 (confidence interval [CI]: 0.761–0.914), with

*r*

^{2}= 0.892 in the normal group, and 0.977 (CI: 0.893–1.06), with

*r*

^{2}= 0.922 in the amblyopia group.

*P*< 0.001), respectively. For the amblyopia group, the correlations were 0.924, 0.951, and 0.945 (all

*P*< 0.001). For thresholds measured in 50 qCSF trials, the slope of the linear regression between the first and second sessions was 0.717 (CI: 0.627–0.806,

*r*

^{2}= 0.815) in the normal group, and 1.12 (CI: 0.983–1.26,

*r*

^{2}= 0.855) in the amblyopia group. After 100 qCSF trials, the slopes in the normal and amblyopia groups were 0.765 (CI: 0.683–0.847,

*r*

^{2}= 0.858) and 1.078 (CI: 0.975–1.18,

*r*

^{2}= 0.905). After 300 qCSF trials, the slopes in the normal and amblyopia groups were 0.820 (CI: 0.750–0.891,

*r*

^{2}= 0.903) and 1.095 (CI: 0.983–1.21,

*r*

^{2}= 0.893), respectively.

*r*

^{2}was 0.983 ± 0.014 in the first session and 0.968 ± 0.034 in the second session. In the amblyopia group, the mean

*r*

^{2}was 0.955 ± 0.018 and 0.965 ± 0.021 in the first and second sessions, respectively. Consistent with previous reports,

^{ 39 }the truncated log-parabolic model provided an excellent description of the CSFs in the normal group. Our results also suggest that the same functional form can be used to describe CSFs in amblyopic vision.

^{ 46,51 }:

*c*′ = log10(contrast) − log10(τ), where τ is the threshold.

^{52,53}where

*i*indexes the contrast condition,

*N*

_{i}and

*K*

_{i}are the number of total and correct trials, and

*P*

_{i}is the percentage correct predicted by the Weibull function. A full model with six independent slopes at six different spatial frequencies and a reduced model with a single slope across six different spatial frequencies were compared by using the χ

^{2}statistic

^{52,53}where

*df*=

*k*

_{full}−

*k*

_{reduced}, and

*k*is the number of parameters in each model.

*P*> 0.1). For these subjects, the slope invariance assumption is correct. Averaged over subjects, the best-fitting slope of the reduced model is 1.70 ± 0.53 in the normal group and 1.36 ± 0.32 in the amblyopia group, with no significant difference (

*t*

_{15}= 1.69,

*P*> 0.10). The average slope over the two groups is 1.55 ± 0.47.

^{ 29,37,54–57 }whereas the spatial frequency cutoff (cutSF) characterizes the high-frequency resolution of the visual system.

^{ 26,58 }To characterize the contrast sensitivity differences between the normal and amblyopic participants, we calculated AULCSF and cutSF for each subject. The AULCSF was calculated as the integration from 0.5 cpd to the root of the log-parabola in the high-spatial-frequency range. The cutSF was defined as the spatial frequency at which contrast sensitivity is 2.0 (threshold = 0.5).

*P*-values from the

*t*-test. The AULCSF differences between the groups became significant after approximately 40 trials (2.29 ± 0.36 vs. 2.53 ± 0.46,

*t*

_{34}= −1.70,

*P*< 0.05). After 39 trials, the cutoff frequency of the amblyopia group also became significantly lower than that of the normal group (19.4 ± 12.1 vs. 37.4 ± 26.5,

*t*

_{34}= −2.51,

*P*< 0.01). After 50 trials, the significance level of both differences remained high (

*P*< 0.01).

*r*= −0.426,

*P*< 0.01). The correlation between the final cutSF and visual acuity was also significant (

*r*= −0.374,

*P*< 0.05). These analyses confirm a relationship between CSF metrics provided by the qCSF and visual acuity (the predominant clinical vision measure). The correlations are not significant if we restrict the analysis to the amblyopia group, perhaps due to the relatively small sample size. Although the CSF correlates with visual acuity, the two parameters may provide different measures of spatial vision.

^{ 59 }analysis based on the AULCSF and cutSF was used to predict membership in the two groups where

*P*(amb) is the probability of a subject's having amblyopia, area represents AULCSF,

*sf*represents cutSF, and βs are the coefficients.

_{0}= 7.41, β

_{1}= 5.85, and β

_{2}= −1.22 (Hosmer and Lemeshow goodness-of fit-test, χ

^{2}

_{7}= 5.00,

*P*= 0.661). There was no significant difference between the predicted and the observed values.

*P*> 0.5 was categorized as an amblyope. The hit rate, false alarm rate, and percentage of correct classifications after each qCSF trial in the two sessions were averaged and plotted as functions of the number of trials (Fig. 10). The mean accuracy of the prediction was 77.8% after 50 trials with a low false alarm rate of 10%. The accuracy of the prediction was 88.9% in 300 trials. This result shows the potential of the qCSF method in screening amblyopia.

_{max,}ƒ

_{max}, β, and δ). AULCSF and cutSF were calculated from the best-fitting parameters. Noting that the Ψ CSF data were composed by thresholds at six spatial frequencies, each prediction of the running analysis was based on multiples of six trials. The hit, false alarm, and percentage correct as functions of trials are plotted in Figure 10. The accuracy of the Ψ prediction was 72.2% in 54 trials. The accuracy of the Ψ method was lower than that of qCSF until ∼170 trials. After 180 trials, the predictions from both methods are almost the same. The percentage correct of final prediction by the Ψ method is 88.9%, the same as the prediction of the qCSF with 300 trials.

^{ 37 }and Ψ

^{ 36 }methods. The precision, accuracy, and test–retest reliability of the qCSF method were evaluated. Our analysis validated the assumptions of the qCSF method in observers with normal and amblyopic vision. The method's CSF model (truncated log-parabola) can well describe individual CSF data, and the psychometric slope is constant across different spatial frequencies for most subjects. Moreover, additional analyses showed that approximately 50 qCSF trials could capture the differences in CSF features (AULCSF and cutSF) between the normal and amblyopia groups. By adopting a logistic regression, we demonstrated the potential of qCSF for screening amblyopia with an accuracy of 77.8% in 50 trials. Taken together, our results demonstrate the potential of the qCSF method, an accurate and precise method of measuring CSFs in both normal people and amblyopes, as a tool for clinical practice.

^{ 35 }However, the mean estimated value of slopes (1.55 ± 0.47) for all participants was much less than 3.5. To examine the effects of this parameter mismatch on our results, we simulated CSF measurements on an observer whose underlying psychometric functions have a slope of 1.55, with both the qCSF and Ψ methods that assume four different predefined slopes (1, 1.55, 2, and 3.5). The simulation had 500 iterations, each of which consisted of 300 qCSF trials and 50 × 6 Ψ trials.

^{ 37 }

*P*> 0.10;

*t*-test). For 94% of the trials, the bias with slope 1.55 did not differ from 0 (for these trials,

*P*> 0.1;

*t*-test). Taken together with the results of the previous analysis, we conclude that the steep slope value predefined in the qCSF program did not appreciably affect our results.

^{ 60,61 }In these experiments, novices improved substantially after training, but participants who were highly practiced did not. This phenomenon raises another important question: how to minimize effects of practice during measurement. There is plenty of evidence that even a single testing session can introduce learning effects,

^{ 62 }and overexposure to certain tasks could lead to performance decrements.

^{ 63,64 }With these considerations, the fewer trials a measurement takes, the less effect it may have on the results. On the other hand, a sufficient number of trials are necessary to achieve the desirable precision. The qCSF method may be one of the solutions to this dilemma in CSF measurement.

^{ 8 }There are also critical problems of binocular combination that underlie the disorder.

^{ 65 }Combining the results of qCSF with other binocular metrics may improve the diagnosis of amblyopia.

^{ 66,67 }equidetectable elliptical contours in color space,

^{ 45 }threshold versus external noise contrast (TvC) functions,

^{ 68 }the spatiotemporal contrast sensitivity surface,

^{ 69 }neural input–output relationships,

^{ 70–72 }and the discrimination of memory-retention models.

^{ 73,74 }These methods provide a powerful testing approach that is potentially important for many clinical applications. The present study provides a sample application.

^{ 37 }we validated the method for larger groups of observers with normal and abnormal vision. With 50 to 100 qCSF trials, which require only 2 to 6 minutes to complete, the CSF of a patient could be measured with acceptable precision and classified with logistic regression. We believe that with improvements in computing power and more powerful statistical tools, the qCSF method will be appropriate for use in screening amblyopia and other visual impairments.

*p*

_{0}(ν→), representing our knowledge about the tested CSF, was constructed with hyperbolic secants.

^{75}A conditional probability lookup table

*p*(

*correct*|x→,ν→) was initialized by calculating all the probabilities of correct response for all possible stimulus conditions T

_{x→}and all possible parameters T

_{ν→}. As prescribed by Kontsevich and Tyler,

^{36}before the

*t*+1th trial began, the qCSF program calculated:

Precision (dB) | Bias (dB) | |||||||
---|---|---|---|---|---|---|---|---|

OS 1 | OS 1.55 | OS 2.5 | OS 3.5 | OS 1 | OS 1.55 | OS 2.5 | OS 3.5 | |

MS 1 | 3.19 | 2.45 | 2.04 | 1.90 | 0.04 | 0.63 | 1.23 | 1.44 |

MS 1.55 | 3.10 | 2.21 | 1.77 | 1.61 | −0.35 | 0.09 | 0.44 | 0.63 |

MS 2.5 | 3.27 | 2.24 | 1.65 | 1.48 | −0.14 | −0.12 | 0.02 | 0.18 |

MS 3.5 | 3.56 | 2.34 | 1.67 | 1.37 | 0.26 | −0.06 | −0.01 | 0.04 |

Precision (dB) | Bias (dB) | |||||||
---|---|---|---|---|---|---|---|---|

OS 1 | OS 1.55 | OS 2.5 | OS 3.5 | OS 1 | OS 1.55 | OS 2.5 | OS 3.5 | |

50 Trials | ||||||||

MS 1 | 4.10 | 3.62 | 3.02 | 3.15 | −0.28 | −0.03 | 0.26 | 0.09 |

MS 1.55 | 4.20 | 3.70 | 3.42 | 3.85 | −0.24 | −0.36 | −0.37 | −0.41 |

MS 2.5 | 4.61 | 4.63 | 3.03 | 2.89 | −0.08 | −0.31 | −0.45 | −0.29 |

MS 3.5 | 4.85 | 4.01 | 3.15 | 2.62 | 0.13 | 0.16 | 0.00 | −0.20 |

100 Trials | ||||||||

MS 1 | 3.06 | 2.57 | 2.16 | 2.05 | −0.78 | −0.01 | 0.58 | 0.69 |

MS 1.55 | 3.16 | 2.54 | 2.07 | 1.79 | −0.70 | −0.53 | −0.10 | 0.12 |

MS 2.5 | 3.35 | 2.57 | 1.86 | 1.52 | −0.50 | −0.37 | −0.30 | −0.09 |

MS 3.5 | 3.44 | 2.79 | 1.89 | 1.46 | −0.44 | −0.29 | −0.29 | −0.14 |

300 Trials | ||||||||

MS 1 | 1.83 | 1.32 | 1.01 | 0.96 | −0.41 | 0.80 | 1.67 | 2.06 |

MS 1.55 | 1.73 | 1.14 | 0.91 | 0.75 | −1.07 | −0.21 | 0.62 | 1.18 |

MS 2.5 | 1.99 | 1.24 | 0.56 | 0.30 | −1.14 | −0.69 | −0.08 | 0.02 |

MS 3.5 | 2.10 | 1.41 | 0.84 | 0.26 | −1.02 | −0.75 | −0.29 | 0.01 |

*Amblyopia: Basic and Clinical Aspects*: London: Butterworth-Heinemann; 1991:10–14.

*Vision Res*. 2009;49:2535–2539. [CrossRef] [PubMed]

*Eur J Neurosci*. 2009;29:1064–1070. [CrossRef] [PubMed]

*Am J Ophthalmol*. 2006;141:175–184. [CrossRef] [PubMed]

*Chin J Ophthalmol*. 2003;39:4.

*J AAPOS*. 2007;11:76. [CrossRef]

*Amblyopia: Basic and Clinical Aspects*. London: Butterworth-Heinemann; 1991:78–93.

*J Vis*. 2003;3:380–405. [CrossRef] [PubMed]

*Vision Res*. 1997;37:3145–3161. [CrossRef] [PubMed]

*Vision Res*. 1998;38:889–894. [CrossRef] [PubMed]

*Vis Neurosci*. 2003;20:577–588. [CrossRef] [PubMed]

*Vision Res*. 2003;43:729–738. [CrossRef] [PubMed]

*Vision Res*. 2005;45:449–460. [CrossRef] [PubMed]

*Br J Ophthalmol*. 1985;69:136–142. [CrossRef] [PubMed]

*Trans Ophthalmol Soc UK*. 1979;99:391–397. [PubMed]

*Vision Res*. 1977;17:1049–1055. [CrossRef] [PubMed]

*J Cataract Refract Surg*. 1989;15:141–148. [CrossRef] [PubMed]

*Ann Ophthalmol*. 1981;13:1069–1071. [PubMed]

*Br J Ophthalmol*. 1986;70:553–559. [CrossRef] [PubMed]

*Ophthalmology*. 1988;95:139–143. [CrossRef] [PubMed]

*Doc Ophthalmol*. 2001;103:175–186. [CrossRef] [PubMed]

*Int Ophthalmol*. 2008;28:407–412. [CrossRef] [PubMed]

*Ophthalmology*. 1980;87:1140–1149. [CrossRef] [PubMed]

*Acta Ophthalmol*. 1981;59:35–37. [CrossRef]

*Eye*. 2007;21:218–223. [CrossRef] [PubMed]

*Vision Res*. 2007;47:22–34. [CrossRef] [PubMed]

*Clin Vision Sci*. 1988;2:187–199.

*Optom Vis Sci*. 1993;70:969–975. [CrossRef] [PubMed]

*J Cataract Refract Surg*. 2009;35:47–56. [CrossRef] [PubMed]

*Br J Ophthalmol*. 2004;88:11–16. [CrossRef] [PubMed]

*Graefes Arch Clin Exp Ophthalmol*. 2007;245:1805–1814. [CrossRef] [PubMed]

*Optom Vis Sci*. 2006;83:290–298. [CrossRef] [PubMed]

*Ophthalmic Physiol Opt*. 1991;11:218–226. [CrossRef] [PubMed]

*Int Ophthalmol Clin*. 2003;43:5–15. [CrossRef] [PubMed]

*Percept Psychophys*. 1983;33:113–120. [CrossRef] [PubMed]

*Vision Res*. 1999;39:2729–2737. [CrossRef] [PubMed]

*J Vis*.

*An Adaptive Method for Estimating Multiple Parameters of a Psychometric Function*. Presented at the 29th Annual Meeting of the Society for Mathematical Psychology. Chapel Hill, NC: University of North Carolina,; 1996.

*J Vis*. 2005;5:717–740. [CrossRef] [PubMed]

*J Opt Soc Am*. 1993;10:1591–1599. [CrossRef]

*Percept Psychophys*. 2001;63:1293–1313. [CrossRef] [PubMed]

*Percept Psychophys*. 1992;51:409–422. [CrossRef] [PubMed]

*J Acoust Soc Am*. 1995;97:3749–3760. [CrossRef] [PubMed]

*Percept Psychophys*. 1997;59:989–1003. [CrossRef] [PubMed]

*J Math Psychol*. 2006;50:369–389. [CrossRef]

*Percept Psychophys*. 2001;63:1356–1376. [CrossRef] [PubMed]

*J Neurosci Methods*. 2003;130:9–18. [CrossRef] [PubMed]

*Spat Vis*. 1997;10:437–442. [CrossRef] [PubMed]

*Percept Psychophys*. 2001;63:1314–1329. [CrossRef] [PubMed]

*Percept Psychophys*. 2001;63:1348–1355. [CrossRef] [PubMed]

*J Vis*. 2002;2:312–323. [CrossRef] [PubMed]

*Ophthalmology*. 2006;113:1807–1812. [CrossRef] [PubMed]

*Invest Ophthalmol Vis Sci*. 1999;40:1351–1355. [PubMed]

*J Refract Surg*. 1998;14:397–407. [PubMed]

*J Refract Surg*. 2000;16:507–514. [PubMed]

*Vision Res*. 2006;46:739–750. [CrossRef] [PubMed]

*Applied Logistic Regression*. New York: Wiley; 1989.

*Proc Natl Academy Sci U S A*. 1996;93:6830–6834. [CrossRef]

*Invest Ophthalmol Vis Sci*. 1997;38:1493–1510. [PubMed]

*J Vis*. 2002;2:190–203. [PubMed]

*Vision Res*. 2006;46:4071–4074. [CrossRef] [PubMed]

*Vision Res*. 2007;47:1094–1102. [CrossRef] [PubMed]

*J Vis*. 2009;9:1–16.

*Percept Psychophys*. 2007;69:311–323. [CrossRef] [PubMed]

*Vision Research*. 2006;46:3160–3176. [CrossRef] [PubMed]

*J Vis*. 2009;9:696. [CrossRef]

*Adv Neural Inform Process Syst*. 2007;19:857.

*Neural Comput*. 2009;21:619–687. [CrossRef] [PubMed]

*Neural Comput*. 2005;17:1480–1507. [CrossRef] [PubMed]

*Psychol Rev*. 2009;116:48–518. [CrossRef]

*Neural Comput*. 2010;22:887–905. [CrossRef] [PubMed]

*Vision Res*. 1997;37:1595–1604. [CrossRef] [PubMed]