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I examined the effect of pupil size directly through simulations performed by my new vision model using the σave = 0.10 and δρave = 0.0025 average neural parameters. In this way, a personalized simulation for one specific pupil diameter can be accomplished in ∼15 minutes for any subject whose wavefront aberration has been measured before. I swept the pupil diameter from 2 mm to 6 mm with 1 mm increment. Since the wavefront profile of the 10 subjects presented in Section 3.3 had been measured before, I used their data for my investigation again. As before, though all data for the subjects’ both eyes were available, I considered only their right eyes (OD) in my analysis, because the two eyes of a person are often strongly correlated [55], [97], [114].
The significance of the effect of pupil size on visual quality can be clearly illustrated by examining the optical PSF, an example for which is shown in Figure 35.
Figure 35. The variation of the optical point spread function with respect to ocular pupil diameter for subject S. T.’s OD eye in the common 2…6 mm diameter range.
To present a more comprehensive analysis by taking advantage of my complex visual acuity simulations (see Chapter 6), I examined not only the change in the acuity value, but also the alteration of the psychometric function of vision, described by Eqs. (20) and (21), with respect to the d pupil diameter. A representative result consisting of the psychometric functions of subject S.
T.’s OD eye corresponding to all examined pupil sizes is illustrated in Figure 36.
Figure 36. The effect of pupil size on the psychometric function of vision based on simulations performed by the personalized model of subject S. T.’s OD eye with different pupil diameters.
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The figure clearly shows the significant impact of the pupil size. However, from the point of view of clinical applicability the numerical acuity value is more important. Therefore, I determined V according to Eq. (22). The acuity values derived from the performed analyses are presented in Table 20 for all 10 subjects examined.
Subject V [logMAR]
d [mm] 2 3 4 5 6
Ku. Ma. −0.43 −0.41 −0.35 −0.31 −0.29
G. A. −0.36 −0.31 −0.22 −0.21 −0.18
M. T. −0.35 −0.26 −0.24 −0.22 −0.19
P. B. −0.31 −0.29 −0.23 −0.18 −0.17
S. T. −0.37 −0.30 −0.24 −0.21 −0.19
U. F. −0.41 −0.36 −0.29 −0.27 −0.25
R. I. −0.41 −0.34 −0.29 −0.26 −0.25
Kl. Mi. −0.17 −0.13 −0.10 −0.09 −0.07
S. O. −0.38 −0.31 −0.27 −0.25 −0.22
G. T. −0.40 −0.34 −0.27 −0.24 −0.21
Table 20. Results of the individual acuity simulations performed with different pupil diameters in the common 2…6 mm range.
Based on these results, one can see that 1 mm alteration in the pupil diameter can cause 0.02…0.07 logMAR change in the visual acuity value. The effect is more significant in case of smaller pupil sizes, which is in good agreement with the fact that pupil contraction cuts off the edge of high-order aberrations [22]. Further comprehensive analysis of the simulation results is presented in the next section.
7.4. Discussion of ophthalmologic relevance
In order to formulate a general statement for subjects with normal and supernormal vision, I made statistics on the individual results of the examined subject group. I determined the average visual acuity value and its standard deviation over the subjects for each tested pupil size. Then, by applying linear regression to the data, I determined the direct relationship between the d pupil diameter and the Vave average visual acuity value of healthy subjects in the common 2…6 mm diameter range:
43 . 0 04 . 0 )
(d d
Vave . (35)
The average visual acuity value and its standard deviation with respect to pupil diameter is depicted in Figure 37 together with the fitted Vave(d) linear function and relations derived based on the literature [64], [112].
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Figure 37. The average change of the visual acuity value with respect to pupil size in the 2…6 mm diameter range. The black dash-dotted line represents the average curve corresponding to standard
90 cd/m2 chart illumination presented in the literature by Rabbetts [112], while the green dashed line illustrates the “Historical Reference” dataset presented by Holladay et al. [64].
In order to confirm the validity of my simulations, I compared my results describing healthy young subjects with normal vision to the observations presented in the literature [64], [112]. Since the direct influence of pupil diameter on visual acuity over such specific subject group has not been studied yet, I estimated it through its relation with background illumination [27], [53], [128], and also compared it to the “Historical Reference” tabulated by Holladay et al. [64]. Despite both results are a combination of independent measurements performed under different conditions with different subjects, the outcomes nicely correlate with my direct simulations (see Figure 37).
The slope of Vave(d) that describes the average alteration of visual acuity with respect to pupil diameter (i.e. 0.04 logMAR/mm) is in good agreement with the numerical values presented in the literature for subjects with no or only a small amount of defocus or astigmatism (i.e. 0…0.75 D spherical equivalent: 0.027…0.071 logMAR/mm) [58], [70].
The thoughtful reader may notice that the acuity value suddenly drops at d = 2 mm entrance pupil diameter according to the “Historical Reference” data [64], see green dashed line in Figure 37. As based on both measurements and diffraction analyses [28], [70], [143] visual acuity deteriorates quickly only below 2 mm entrance pupil diameter—which is consistent with my simulations—the credibility of Holladay et al.’s results at d = 2 mm is doubtful.
Moreover, it has to be noted, that there is a small systematic offset between my simulation results and the observations presented in the literature, which may arise from multiple causes.
While my vision model has been calibrated based on my special laboratory experiments performed in a darkened room (see Section 3.3), the measurement conditions of the results presented in the literature are unknown. The effect of environmental conditions is well illustrated by the difference between the two curves derived from distinct references [64], [112]. Besides, the offset of the
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simulation results may be caused by the small size of the subject group, as the simulations were performed only for 10 subjects. This consideration is supported by the observation, that both the offset and the standard deviation of my results halves in case of excluding Kl. Mi., the only subject with −0.5 D refractive error. Nevertheless, the systematic offset is smaller than the standard deviation of my results, which verifies the applicability of my vision simulations.
7.5. Conclusions
In order to determine the direct influence of pupil size on visual acuity without any external intervention that may disturb the tested subject, I performed personalized acuity simulations by my neuro-physiological vision model presented in Chapter 6. Based on my results, I approximated the average visual acuity of healthy subjects with normal vision in the 2…6 mm diameter range by a linear formula to examine its tendency. My results are well supported by clinical experience presented in the literature [28], [58], [64], [70], [112].
Due to its significant influence compared to other environmental conditions (see Table 1), I suggest that it would be fairly important to keep the surrounding illumination of the examination room at a standard level. Furthermore, in order to take into account subject-specific pupil adaptation, the entrance pupil diameter should be recorded beside the measured visual acuity value with at least 0.5 mm spatial accuracy by using a measuring system similar to that presented in Chapter 5. Beyond the direct clinical relevance, these results well confirm the applicability of my vision model for vision analysis purposes.
Corresponding thesis: T6
I determined the direct relationship between the d pupil diameter and the Vave average visual acuity value of healthy subjects with normal vision in the common 2…6 mm diameter range by analyzing the results of visual acuity simulations performed using my new vision model. The obtained 0.04 logMAR/mm slope of Vave(d) is in good agreement with observations presented in the literature. Based on the results, I concluded that for the sake of comparability of acuity values, the pupil diameter has to be measured too with at least 0.5 mm spatial accuracy during visual acuity tests. [P4], [P6], [P7]
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