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Objective depth-of-focus is different from subjective depth-of-focus and correlated with accommodative microfluctuations
Vision Research 50 (2010) 1266–1273
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Objective depth-of-focus is different from subjective depth-of-focus and correlated with accommodative microfluctuations Peijun Yao a, Huiling Lin b, Jia Huang a, Renyuan Chu a, Bai-chuan Jiang a,c,* a
Fudan University, Eye and ENT Hospital, 83 Fenyang Road, Shanghai 200031, PR China Wenzhou Medical College, School of Optometry and Ophthalmology, 82 Xueyuan Road, Wenzhou, Zhejiang 325003, PR China c Nova Southeastern University, College of Optometry, 3200 S. University Drive, Ft. Lauderdale, FL 33322, USA b
a r t i c l e
i n f o
Article history: Received 27 July 2009 Received in revised form 11 March 2010
Keywords: Depth-of-focus Accommodation Microfluctuations Blur sensitivity
a b s t r a c t In this study, we investigated whether the objective depth-of-focus (DOF) is different from the subjective DOF and whether it correlates to accommodative microfluctuations (AMF). The objective DOF and subjective DOF at 1.5 D accommodative stimulus (AS) level were compared in the same group of subjects. The objective DOF and magnitude of AMF were measured at 5 AS levels from 0 D to 4 D. Results showed that there was a significant difference and no correlation between the objective DOF and the subjective DOF. The objective DOF was correlated to the magnitude of AMF. The results suggest that objective DOF and subjective DOF represent the blur sensitivity of two different systems. AMF are correlated with the blur sensitivity of the accommodative system. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction Retinal defocus serves as an important visual input to various visual processes such as accommodation, depth perception, and emmetropization of the eye (Fisher & Ciuffreda, 1988, 1989; Hung, Ciuffreda, Khosroyani, & Jiang, 2002; Mather, 1996, 1997; Norton & Siegwart, 1995; Rabin, van Sluyters, & Malach, 1981). Constant retinal defocus has been suggested as leading to axial elongation of the eye (Gilmartin, 1998; Goss & Wickham, 1995; Hung & Ciuffreda, 1999; Hung et al., 2002; Ong & Ciuffreda, 1995; Rosenfield & Gilmartin, 1998). The visual system can tolerate a certain amount of optical defocus without detection of blur (Legge, Mullen, Woo, & Campbell, 1987). This blur tolerance has been defined as blur threshold (Campbell, 1957), blur detection threshold (Jiang & Morse, 1999; Rosenfield & Abraham-Cohen, 1999), and depth-offocus (DOF) (Millodot, 2004) in different studies with basically the same concept. Campbell (1957) first defined blur threshold, half the extent (±DD), as the smallest amount of retinal defocus that could cause a detectable deterioration in the quality of retinal image. In this paper, we use the term DOF to refer to the blur detection threshold. Blur threshold of the visual system is related to two central neural systems that detect and respond to the visual stimulus. The perceptual system is responsible for subjective cognition of image sharpness, while the accommodative system alters the refractive * Corresponding author at: Nova Southeastern University, College of Optometry, 3200 S. University Drive, Ft. Lauderdale, FL 33322, USA. Fax: +1 954 262 1818. E-mail address: [email protected] (B.-c. Jiang). 0042-6989/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.visres.2010.04.011
power of the eye to improve the sharpness of the retinal image based on the defocused stimulus. Kotulak and Schor (1986a) defined perceptual threshold and sensorimotor threshold to distinguish the difference in blur threshold between the perceptual and accommodative systems. Numerous studies have investigated the blur threshold of the visual system in the past half century. Most of these studies concentrated on the cognitive aspect of blur. The DOF measured by psychophysical methods has also been called perceptual DOF (Campbell, 1957). The perceptual DOF was found to increase with age and was influenced by visual acuity and image quality (Green, Powers, & Banks, 1980; Layton & Siegel, 1982; Legge et al., 1987; Mordi & Ciuffreda, 1998). Myopes are also reported to have higher blur detection threshold than emmetropes (Rosenfield & Abraham-Cohen, 1999). They attributed the larger accommodative lag in myopes to the observed reduction in blur sensitivity. In the accommodative-control system, retinal defocus, as the error signal of the accommodative system, is detected by the sensory component before stimulating the motor controller to produce accommodative response (AR) (Hung & Semmlow, 1980; Jiang, 1997). Studies show that AR changes with a small amount of change in stimulus even when the subject does not perceive blurring of the stimulus (Ludlam, Witenberg, Gigio, & Rosenberg, 1968). This suggests that the ability of the accommodative system to detect blur is different from that of the perceptual system. In a previous study, the blur sensitivity of the accommodative system was assessed by measuring the smallest change in the accommodative stimulus (AS) that causes a detectable change in the AR (Kotulak & Schor, 1986; Ludlam et al., 1968; Mordi & Ciuffreda, 1998; Vasudevan, Ciuffreda, & Wang, 2006a). Jiang (2000) defined
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this smallest change in AS as accommodative stimulus/response (S/R) threshold. Since the threshold is measured using an objective method, it is also called as the objective DOF. In previous studies, investigators obtained various values of DOF due to different target and test conditions, such as spatial frequency, luminance and baseline vergence of target as well as pupil size (Atchison & Smith, 2002). Objective DOF was smaller in value than subjective DOF in most studies, while both had a wide range of values, from ±0.1 D to ±0.81 D for objective DOF (Ludlam et al., 1968; Kotulak & Schor, 1986a; Mordi & Ciuffreda, 1998; Vasudevan, Ciuffreda, & Wang, 2006a, 2006b) and from ±0.02 D to ±1.75 D for subjective DOF (Ciuffreda, 1991, 1998). Few studies have compared the objective and subjective DOF in the same cohort. Kotulak and Schor (1986a) found the objective DOF to be smaller than the subjective DOF using a power spectrum technique in three subjects. Mordi and Ciuffreda (1998) got similar results using direct measurement of AR changes in 30 subjects. However, Marcos, Moreno, and Navarro (1999) measured the quality of retinal image in three subjects and found that the subjective DOF was in most cases smaller than the objective DOF. Recently, Vasudevan, Ciuffreda, and Wang (2007) found no difference between the objective DOF measured in free space and the subjective DOF measured with a Badal system. Inconsistency of criterion and target conditions in the above studies is probably responsible for the variation in the results (Jacobs, Smith, & Chan, 1989). As we mentioned above, the objective DOF represents the sensitivity of the accommodative system to blur. Even when a subject views a stationary target, there are variations of AR about the mean level. These variations are known as accommodative microfluctuations (AMF) (Campbell, Robson, & Westheimer, 1959; Collins, 1937; Charman & Heron, 1988; Denieul, 1982; Kotulak & Schor, 1986b; Winn, Pugh, Gilmartin, & Owens, 1990a). The amplitude of AMF is reported to be about 0.10 D–0.50 D. They depend upon many factors such as pupil size (Campbell et al., 1959; Gray, Winn, & Gilmartin, 1993a; Stark & Atchison, 1997), luminance (Gray, Winn, & Gilmartin, 1993b), contrast (Denieul & Corno-Martin, 1994) and spatial frequency of the target (Niwa & Tokoro, 1998). These are the same factors that affect the DOF of the eye (Atchison & Smith, 2002). We hypothesize that the AMF cause rapid and small changes in retinal defocus which are detected by the sensory component of the accommodative-control system and provide negative feedback information to maintain the AR level. This suggests a possible relationship between the magnitude of AMF and the DOF of the eye. Previous studies have found that the magnitude of AMF increases with increasing AS (Day, Strang, Seidel, Gray, & Mallen, 2006). They attributed the change of AMF to the effect of accommodation response-induced zonular relaxation and increased noise of the accommodative plant at higher AS levels. If the AMF are related to the objective DOF, one would expect to observe an increase in objective DOF at higher AS levels. In this study, we conducted two experiments. In the first experiment, objective DOF and subjective DOF were measured and compared for the same group of subjects. In both measurements, we used targets with the same spatial frequency and contrast and at the same AS level. In the second experiment, we investigated whether the objective DOF changes with AS level and whether that change correlates to the change in AMF.
2. Methods 2.1. Experiment 1 The purpose of this experiment was to compare the objective DOF with the subjective DOF obtained from same individuals under the same viewing conditions.
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2.1.1. Subjects Twelve emmetropic optometry students in NOVA Southeastern University, 20–38 years old (mean ± SD, 25.7 ± 4.7 years) including 3 males and 9 females, participated in this experiment. Subjective binocular refraction was performed before the experiment. The inclusion criteria was that the refractive error in spherical equivalent (SE) was within ±0.50 D with astigmatism no more than 0.50 D. The average SE of the twelve subjects was 0.07 ± 0.17 D (mean ± SD). None of the subjects had ocular disease or anisometropia (i.e. more than 1.00 D differences in SE between the eyes). They all had visual acuity of 20/20 or better and normal binocular vision. Only the right eyes were tested in this experiment. Informed consent was obtained from each subject after the nature and possible consequences of the study were explained. The research followed the tenets of the Declaration of Helsinki and was approved by Nova Southeastern University’s Committee for the Protection of Human Subjects. The subjects in Experiment 2 experienced a similar procedure regarding the informed consent. 2.1.2. Measurement of the subjective DOF In the measurement of subjective DOF, the subject’s right eye viewed two identical targets through a two-channel Badal system when his/her left eye was occluded (Legge et al., 1987; Jiang & Morse, 1999) (Fig. 1). The eye was positioned at the focal point of the +5.0 D Badal lens. A beam splitter with a silver coating over half its surface was positioned between the Badal lens and the targets. The standard target was aligned with the Badal lens at an optical distance of 1.5 D and could be viewed through the transparent part of the beam splitter. The testing target was positioned at the side and aligned with the reflective part of the beam splitter. Thus, when viewed through the beam splitter, each of the two targets occupied half of the visual field. The vergence of the testing target could be changed by adjusting the distance of the target relative to the Badal lens. The luminance, proximal effect and size cues were constant in this system. Each target consisted of a high contrast square-wave grating (high precision Ronchi Rulings) with 17.2 c/deg subtending a visual angle of 7.28°. The luminance of the targets was 180 cd/m2. Light sources were positioned at a distance of twice the focal length from the Badal lens so that the details of the light source would not be the cue for AR. During the measurement, the subject was instructed to maintain focus on the standard target so that the AR was controlled by this fixed target. The testing target was initially placed at the same vergence distance as the standard target. Then the subject moved the testing target away from the Badal lens, thus reducing the vergence of the target. When the subject detected the just noticeable blur of the testing target, a measurement was taken. The dioptric difference DD between the positions of the two targets was defined as the subjective DOF (±DD). During the experiment, the subject’s pupil size was recorded by a digital camera positioned far from the eye. A ruler was placed beneath the eye as a reference. 2.1.3. Measurement of the objective DOF In the measurement of the objective DOF, the subject was instructed to look at the target with the right eye through a Badal stimulator so that changes in vergence of the target (i.e., AS) by 0.1 D steps did not change the luminance or size of the target (Crane & Cornsweet, 1970). The Badal stimulator contained a Badal lens and an auxiliary imaging lens (Fig. 2). The target was a high contrast 17.2 c/deg square-wave grating presented by a computer screen (NEC AccuSync 72vx). The luminance of the target was 180 cd/m2. The target was positioned 2 m from the auxiliary lens and subtended a visual angle of 7.28°. The effective stimulus for accommodation was determined by the auxiliary lens in the Badal system. By moving the auxiliary imaging lens, the whole system
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Fig. 1. Top view of the two-channel Badal system used to measure subjective DOF in Experiment 1. RE, the subject’s right eye; L, +5.0 D Badal lens; BS, beam splitter, ST, standard target; TT, testing target; LS, light source; f, focal length of the Badal lens (20 cm). Arrow near TT indicates the movement of the testing target. The additional figure (TT/SS) shows the front view of the two targets through the Badal lens and the beam splitter.
Fig. 2. Top view of the apparatus used to measure objective DOF in Experiments 1 and 2. RE, the subject’s right eye; AutoRef, open-field autorefractor; L, +5.0 D Badal lens; f, focal length of the Badal lens (20 cm); ML, moveable auxiliary lens with +5.0 D; T, computer screen.
presented different AS to the subject’s right eye. Thus the spatial frequency, visual angle and luminance of the targets were consistent between the measurements of the subjective DOF and the objective DOF. The refractive error was measured using a Canon Autoref R-1 with a resolution of 0.125 D. This autorefractor was aligned with the Badal stimulator and the target. The refractive error was converted into SE value and then was used to calculate the AR. A digital camera was used to record the image of the eye displayed on the monitor of the autorefractor for measuring the pupil size during the experiment. The alignment circle (6 mm in diameter) in the monitor of autorefractor was used as a reference. The objective DOF was determined as the difference between two AS levels when the AR showed a significant change. During the measurement, the subjects were instructed to look at the target and keep it clear through the whole procedure. The AS was changed by the Badal stimulator from 0.9 D to 2.1 D by 0.1 D in each step. At each AS level, 20 readings of the autorefractor were recorded and then converted into AR. The ARs at each AS level were compared with the ARs at the 1.5 D AS level using the t-test. The tvalues of the nine steps were plotted against the AS values and fitted by a third order polynomial curve. The critical t-value for onetailed test, t[19] = ±1.686, corresponds to a Type I error rate of 0.05 at a freedom of 19. It was used as the criterion for achieving a statistically significant difference between the measured ARs, and in
turn the threshold for the change in AS. The mean difference between the upper and lower AS values was calculated and presented as ±DD, which was regarded as the objective DOF at the 1.5 D AS level (Tao, Jiang, & Morse, 1998). 2.1.4. Data analysis The values of objective DOF and subjective DOF were compared using the paired t-test. The correlation between the two DOFs and the correlation between the DOFs and accommodative error (AE) were analyzed using Pearson analysis. AE was calculated as the difference between the AR and the corresponding AS. The pupil sizes under these two experimental conditions were also compared using the paired t-test. 2.2. Experiment 2 The purpose of this experiment was to investigate whether there was a correlation between the objective DOF and the magnitude of accommodative microfluctuations. 2.2.1. Subjects Fifteen myopic optometry student in NOVA Southeastern University, 23–30-year old (25.6 ± 2.0 years, mean ± SD) including 7 males and 8 females, participated in the second experiment. The
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inclusion criterion was that the refractive error in SE was between 0.50 D and 6.00 D with astigmatism no more than 0.50 D. The average SE of the fifteen subjects in this experiment was 3.20 ± 1.72 D (mean ± SD). The onset age of myopia was 8– 15 years old (11.1 ± 2.7 years, mean ± SD). According to their self reports, the refractive errors were stable or changed no more than 0.25 D in the past year. None of the subjects had ocular disease or anisometropia (i.e. had less than 1.00 D differences in SE between the eyes). All the subjects had corrected visual acuity of 20/20 or better and normal binocular visual functions. Only the right eyes were tested in the experiment. All subjects used soft contact lenses to correct their refractive errors. Subjective refraction was repeated with the contact lenses in situ to ensure the refractive error was corrected within ±0.25 D.
one before and one after points in the data were also deleted. Then, the remaining data were used to calculate the mean value and root mean square (RMS) value of AR at that AS level. The RMS value of AR was defined as the magnitude of AMF in this study (Day et al., 2006). At 1 D and 4 D AS levels, after the measurement of AMF, the objective DOF was measured in the same way as in Experiment 1 except that the order of AS presentation was in two directions. At each AS level, the AR to the initial AS was measured and then the ascending and descending parts of measurement were performed in a random order. The ascending and descending parts both contained four 0.1 D steps in AS. The objective DOFs at 1 D and 4 D AS levels were calculated by using the same methods described in Experiment 1.
2.2.2. Apparatus AR was measured by an open-field infrared autorefractor (WAM-5500, Grand Seiko Co., Ltd., Hiroshima, Japan). The reference plane was set at the corneal plane and the reported resolution of this device was 0.01 D. In hi-speed mode, the instrument sampled the refractive error data every 0.2 s. The refractive error reading was converted into SE value and exported to a computer by using a software program (WCS-1). Mean SE value was used to calculate the AR. The chinrest of the autorefractor was modified to enable the vertical and horizontal adjustment. A 4 mm artificial pupil made of an infra-red filter was placed 14 mm in front of the corneal apex. A Badal stimulator similar to the set-up used in Experiment 1 was used to provide the AS (Fig. 2). A computer screen (NEC AccuSync 72vx) located 4.4 m from the auxiliary lens was used to present the target. The target was a 3 3 array of high contrast Snellen E letters with spatial frequency of 12 c/deg (logMAR 0.4). It subtended a visual field of 2°. The measured luminance was 77 cd/m2.
2.2.4. Analysis The RMS values at five AS levels were analyzed using one-way ANOVA. The independent variable in this analysis was the AS levels. The dependent variable was the RMS values. The objective DOFs at 1 D and 4 D levels were compared using the paired t-test. Correlation between the RMS value and the objective DOF was analyzed at 1 D and 4 D AS levels.
2.2.3. Procedures The subject’s right eye was aligned with the autorefractor, the Badal system, and the target. The left eye was occluded during the experiment. The subjects were instructed to look at the center of the target and keep it clear. To measure the AMF, the ARs for each AS level (0–4 D) were measured continuously for 20 s in hispeed mode, respectively. During the intervals between different AS levels, the subject was instructed to close his eyes and rest. Meanwhile, the investigator adjusted the target by moving the auxiliary lens quietly. Since image size maintained constant in the Badal system, the subject was not able to detect either the direction or the magnitude of the change in the AS. The missing data caused by eye closure or blink were deleted. To avoid bias,
3. Results 3.1. Experiment 1 In this experiment, the objective DOF and the subjective DOF were measured at an AS level of 1.5 D using targets of the same spatial frequency, contrast and luminance in the same group of subjects. Fig. 3 shows an individual accommodative stimulus response curve obtained at the 1.5 D AS level and the plot of AS versus t-values. All the curves obtained were well fitted and were used to calculate the objective DOF. The mean objective DOF of the 12 subjects was ±0.09 ±0.03 D. The mean subjective DOF was ±0.52, ±0.30 D. The paired t-test showed that the difference between the objective and subjective DOFs was significant (t = 5.309, P < 0.001) (Fig. 4). Correlation between the objective DOF and subjective DOF was not significant (P > 0.05). The mean pupil size was not significantly different (t = 1.374, P = 0.098) during the measurements for objective DOF (5.82 ± 0.94 mm) and subjective DOF (5.42 ± 1.49 mm). 3.2. Experiment 2 In this experiment, 15 subjects’ objective DOFs and the magnitude of AMF were measured under the same target conditions. As
Fig. 3. The measurement of objective DOF based on the data of an individual subject (# 2). Panel A is the subject’s accommodative response curve obtained at 1.5 D AS level. The error bar shows one standard deviation of the mean value. Panel B is the plot of AS against the t-values obtained by comparing the AR at each AS level to the AR at the 1.5 D level. A third order polynomial curve is smoothly fitted to the data. The two dashed lines indicate the critical t-values with statistically significant difference (a = 0.05) and corresponding AS values. The range in AS axis indicates the objective DOF and is presented as ±DD.
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Fig. 4. Comparison of subjective DOF and objective DOF at 1.5 D AS level in 12 emmetropes. The open circles are the individual subjective DOFs. The filled circles are the individual objective DOFs. The points farthest to the right represent the corresponding mean value of DOF of these subjects. The error bar shows one standard deviation of the mean value.
an example, recorded accommodative microfluctuations of an individual (subject #14) are shown in Fig. 5. The mean RMS values of AR at different AS levels are shown in Fig. 6. There was a significant increase in RMS value with increasing AS level (F = 17.025, P < 0.001). Post hoc tests showed that RMS values for each AS level was significantly different from those of other AS levels except that there was no difference in the RMS values between 0 D and 1 D AS levels, and between 3 D and 4 D AS levels. The objective DOFs at 1 D and 4 D AS levels are shown in Fig. 7. The paired t-test showed that objective DOF at 4 D AS level (±0.092, ±0.023 D) was significantly larger than that at 1 D AS level (±0.055, ±0.018 D) (t = 5.276, P < 0.001). The objective DOF showed a strong correlation with the RMS value of the microfluctuations at 1 D and 4 D AS levels, respectively (Fig. 8). 4. Discussion The main findings of this study are that the objective DOF is less than the subjective DOF, and that they are not correlated with each other. The objective DOF varies at different AS levels and is highly correlated to the magnitude of AMF.
Fig. 5. Accommodative microfluctuations at 0–4 D AS levels for an individual subject (#14).
4.1. The measurement of objective DOF In this study, the objective DOF is defined as the smallest change in AS which can cause a just detectable change in AR. In previous studies, the objective DOF was measured by monitoring the change in the AR while changing the AS (Ludlam et al., 1968; Kotulak & Schor, 1986a; Mordi & Ciuffreda, 1998; Vasudevan et al., 2006a). In those studies, the AS was presented using a Badal system so that proximal effects and size cues were eliminated. Thus the observed AR was induced only by retinal defocus. The present study used the same method of target presentation and AR measurement but applied a different criterion of detectable change in AR which was first suggested by Tao et al. (1998). Different criterions of just detectable change in AR may result in varied values of objective DOF. Kotulak and Schor (1986a) used a sine wave grating with a temporal frequency of 1 Hz as AS. The ARs were analyzed in a signal-detection format. They found the objective DOF to be ±0.12 D to ±0.14 D at 2.5 mm pupil diameter in three subjects. This method successfully eliminated the influence of system noise. Later, Vasudevan, Ciuffreda, and Wang (2006a) reported the objective DOF to be ±0.46 D to ±0.81 D by monitoring the AR to a slowly varying AS. The criterion used to determine the change point was when the change in AR was larger than 0.25 D and remained at the new steady-state level for at least 2 s. But they changed the AS with a velocity of 0.10–0.15 D/s. Thus there would be a
Fig. 6. The average RMS values of accommodative microfluctuations are plotted against the AS levels for 15 subjects. The error bar shows one standard deviation of the mean value.
0.20–0.30 D of change in AS during the 2 s which was required to determine a consistent change of 0.25 D in AR. In addition, the microfluctuations in AR might cause judgment error. These factors might cause their results to be larger than the true value. The present study used statistical criterion instead of subjective inspection by the investigator. Therefore, the bias caused by human error was
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Fig. 7. Comparison of objective DOF at 1 D and 4 D AS levels in 15 subjects. The filled squares are the individual objective DOFs at 1 D AS level. The open squares are the individual objective DOFs at 4 D AS level. The squares farthest to the right represent the mean value of objective DOF at each corresponding level. The error bar shows one standard deviation of the mean value.
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Besides, the 4 mm pupil diameter used in the present study is larger than that used by Kotulak and Schor, which may also contribute to the relatively smaller value of DOF measured in the present study. Within this study, the pupil diameter was not different between the objective and the subjective DOF measurements in Experiment 1. Phillips, Winn and Gilmartin (1992) have proved that the blur-driven accommodation only does not induce the pupil near response. Thus the accommodation induced by the Badal stimulator in this study, should not cause much change in pupil size. Concerning the identified artificial pupil diameter used in Experiment 2, the tiny change in pupil size during the accommodation should have little influence on the measurement of AR or DOF. But our estimation of the objective DOF is a relative value. It is dependent on the number of data points used for statistics comparison (t-test). If we use a larger number of data points, the estimation would become smaller. 4.2. The measurement of subjective DOF The accommodative response was not monitored during the measurement of subjective DOFs, the measured DOF might be a little bit inflated. But since the standard target in Experiment 1 represented an accommodative stimulus around the tonic level of accommodative system, the fluctuations of accommodation should be at least amount and the DOF was reported to be symmetric around the tonic level. Therefore, the accommodative response to the standard target should be quite stable and the measured range of AS should be adequate to represent subjective DOF. In previous studies, the reported subject DOF ranges from ±0.02 D to ±1.75 D (Jacobs et al., 1989; Atchison, Charman, & Woods, 1997; Rosenfield & Abraham-Cohen, 1999; Ciuffreda 1991, 1998; Schmid, Iskander, & Edwards, 2002; Wang & Ciuffreda, 2004). The discrepancy in these results may be due to different experimental conditions. The subjective DOF obtained in this study, is similar with the subjective DOF for 4 mm pupil size reported by Atchison et al. (1997). The experimental methods in the two studies are similar except Atchison et al. measured the subject’s DOF under cyclopedia condition. The individual differences in the AMF might have effect on the perceptual judgment of DOF. In addition, larger AE at higher AS levels means larger retinal defocus. Under such defocus conditions, the subject’s just noticeable blur range (i.e., DOF) may increase, which can be predicted by the non-linear fall-off in MTF with defocus. However, in this study, the objective DOF was measured around the tonic accommodative level. The effect of AE and AMF should be reduced to the minimum. 4.3. The objective DOF and subjective DOF
Fig. 8. Correlation between the objective DOF and the RMS value of accommodative microfluctuations. Panel A is the data at 1 D AS level. Panel B is the data at 4 D AS level.
eliminated and the results should be more reliable. The objective DOFs measured in Experiment 1 were just a little less than the Autoref’s resolution of 0.125 D. This situation was better in the Experiment 2 with a higher resolution autorefractor. Because the objective DOF is very small, we believe that the high resolution is better for the measurement.
The results in the first experiment of this study showed that the objective DOF was smaller than the subjective DOF when they were measured under the same target conditions and compared within the same individuals. No correlation was found between the two DOFs. This is consistent with the findings in previous studies (Kotulak & Schor, 1986a; Marcos et al., 1999; Mordi & Ciuffreda, 2004). When Ludlam et al. (1968) measured the objective DOF, they found that change in defocus stimulus as small as 0.1 D could induce a constant change in AR when the subject was not able to perceive the blurring of the target. Later, Kotulak and Schor (1986a) also found that a blur stimulus smaller than the perceptual DOF of the eye could cause a change in the AR. They suggested that there are dual thresholds, sensorimotor and perceptual. Our results support their findings and suggest that the objective DOF and subjective DOF represent the blur sensitivity of two different systems. The two DOFs are different in magnitude and have different underlying mechanisms. This is supported by the finding that the subjec-
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tive DOF increased at a rate of 0.027 D/year but objective DOF did not change with age (Mordi & Ciuffreda, 1998). The objective DOF, which is determined by measuring the changes in AR, depends on the function of both the sensory and motor components of the accommodative system. The accommodative system responds to a defocused stimulus continuously and rapidly in order to minimize the retinal defocus, so as to maintain the optimal image quality. The accommodative system is controlled by the midbrain-oculomotor nucleus complex/Edinger-Westphal nucleus, which is in lower levels than the parieto-temporal areas in the visual cortex (Jaeger & Benevento, 1980; Judge & Cummings, 1986; Jampel, 1959). This may explain why the reaction of the accommodative system is not recognized by the perceptual system. The widely used term, ‘‘the DOF of the eye”, refers to the smallest amount of defocus that causes a just noticeable blur. During the measurement of subjective DOF in most previous studies, the accommodation was paralyzed by a cycloplegic agent or stabilized by fixating on a reference target (Atchison et al., 1997; Campbell, 1957; Walsh & Charman, 1988; Rosenfield & Abraham-Cohen, 1999; Ciuffreda, Wang, & Wong, 2005). Thus the subjective DOF is independent of the accommodative system and is related to the blur sensitivity of the perceptual system. In this study, the accommodation was not paralyzed but was stabilized by staying focused on the fixation target. Comparison between the objective and subjective DOFs in this study indicates that the accommodative system is more sensitive to defocus stimulus than the perceptual system. As long as the retinal defocus is within the range of subjective DOF, the subject regards the image as clear and well focused. Although little is known of higher-center processing of accommodation signals, we speculate that small defocus signal might be inhibited in the perceptual system. This mechanism helps to ensure that the perceptual system is not disturbed by images with small amounts of defocus. 4.4. The objective DOF and microfluctuations In Experiment 2, the AR at each AS level was recorded continuously for 20 s with a sampling rate of 5 Hz. The sampling rate was not high enough for power spectrum analysis but was higher than the reported peak frequency of 2 Hz in AMF (Charman & Heron, 1988). In this study, we used the average RMS value of the AR to represent the magnitude of AMF. Day et al. (2006) used power spectrum analysis to evaluate the frequency components of AMF. They also used the RMS value of the AR to represent the magnitude of AMF. In this study, the RMS value was found to be correlated to the objective DOF at both 1 D and 4 D levels. This adds support to the suggestion by Jiang (2000) that objective DOF may be related to the AMF. One controversy in terms of the mechanism and significance of AMF is whether they represent simply an inevitable instability of AR as background noise in the accommodative plant or are they regulated by the neural controller and therefore play an active role in guiding and maintaining AR. Charman (1983) found that a reduction in pupil size led to increasing slower oscillations of accommodation, which was consistent with the changes of the DOF of the eye. Other studies also found the same pattern in the change of the low frequency of microfluctuations and the DOF with various target luminance, form and pupil size (Hung, Semmlow, & Ciuffreda, 1982; Charman & Heron, 1988; Winn, Charman, Pugh, Heron, & Eadie, 1989; Winn, Pugh, Gilmartin, & Owens, 1989; Winn, Pugh, Gilmartin, & Owens, 1990a, 1990b; Winn & Gilmartin, 1992; Gray, Winn, & Gilmartin, 1993a, 1993b; van der Heijde, Beer, & Dubbelman, 1996; Stark & Atchison, 1997). This indicates that low frequency microfluctuations may play an important role in maintaining steady-state AR. This is confirmed by the high correlation between the AMF and the objective DOF found in this study.
Since the objective DOF represents the sensitivity of the accommodative system to defocus, this result indicates that microfluctuations are part of the instantaneous adjustment of the AR instead of merely representing the instability of accommodative system. In the results of Experiment 2, the RMS value of AMF was larger than the objective DOF for each subject. We have to mention that the objective DOF represents the defocus threshold in AS, and the RMS of AMF represent the average change of AR in a short period. This result suggests that when the magnitude of AMF exceeds the blur threshold of accommodative system, the accommodative-control system could detect the temporal defocused image and then adjust the AR back to its baseline level. This supports the theory proposed by previous researchers (Alpern, 1958; Fender, 1964; Charman & Tucker, 1978; Hung et al., 1982; Kotulak & Schor, 1986c) that small fluctuations of accommodation provide the error signal to the accommodative-control system to maintain a steady response. Since the detection of these error signals depends on the sensitivity of the accommodative system to blur stimulus, i.e. objective DOF, in addition to the intrinsic mechanical instability of the accommodative system, the AMF may also be regulated by the objective DOF. In Experiment 2, only myopes were included because accommodative abnormality is considered to be important in myopia development. The influence of AMF on blur sensitivity of accommodative system needs to be studied with a larger range of subjects with different refractive status, such as emmetropes and progressing myopes, in the future. 4.5. The effect of the accommodative stimulus In this study, we found that the RMS value of AMF increases with the increasing AS level from 0 D to 4 D. Association between the magnitude of AMF and AR was reported by previous studies (Krueger, 1978; Denieul, 1982; Kotulak & Schor, 1986c; Miege & Denieul, 1988; Heron & Schor, 1995; Stark & Atchison, 1997). Kotulak and Schor (1986c) reported that the microfluctuations over the AS range of 1–4 D was smallest at the 1 D AS level. Miege and Denieul (1988) reported the amplitude of microfluctuations was largest at 3 D when measuring from 1 D to 4 D levels. Previous authors attributed the increase of the microfluctuations to the decrease of zonular tension and consequently less constrained natural vibrations of lens and its support system with the increasing AR level. Recently, Day et al. (2006) tried to associate the change of the magnitude of microfluctuations with the neurological controller demonstrated above but they simply assumed the DOF was constant at different AS levels. They attributed the microfluctuations to the physical property of the accommodative system noise. However, our study has shown that the magnitude of microfluctuations is correlated to the objective DOF at both 1 D and 4 D AS levels. This correlation suggests that accommodative microfluctuation might be regulated by the objective DOF as a result of the feedback accommodative-control system. The true function of AMF needs to be revealed in further studies. Acknowledgments This work was supported by NSU PFRDG #335441, NSU HPD Grant #335230, and NSFC Grant #30530770. Dr. Peijun Yao was supported by the State Scholarship Fund from the China Scholarship Council. The authors thank Dr. Ken Seger for helpful comments on the manuscript. References Alpern, M. (1958). Variability of accommodation during steady fixation at various levels of illuminance. Journal of the Optical Society of America, 48, 193–197.
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Vision Research journal homepage: www.elsevier.com/locate/visres
Objective depth-of-focus is different from subjective depth-of-focus and correlated with accommodative microfluctuations Peijun Yao a, Huiling Lin b, Jia Huang a, Renyuan Chu a, Bai-chuan Jiang a,c,* a
Fudan University, Eye and ENT Hospital, 83 Fenyang Road, Shanghai 200031, PR China Wenzhou Medical College, School of Optometry and Ophthalmology, 82 Xueyuan Road, Wenzhou, Zhejiang 325003, PR China c Nova Southeastern University, College of Optometry, 3200 S. University Drive, Ft. Lauderdale, FL 33322, USA b
a r t i c l e
i n f o
Article history: Received 27 July 2009 Received in revised form 11 March 2010
Keywords: Depth-of-focus Accommodation Microfluctuations Blur sensitivity
a b s t r a c t In this study, we investigated whether the objective depth-of-focus (DOF) is different from the subjective DOF and whether it correlates to accommodative microfluctuations (AMF). The objective DOF and subjective DOF at 1.5 D accommodative stimulus (AS) level were compared in the same group of subjects. The objective DOF and magnitude of AMF were measured at 5 AS levels from 0 D to 4 D. Results showed that there was a significant difference and no correlation between the objective DOF and the subjective DOF. The objective DOF was correlated to the magnitude of AMF. The results suggest that objective DOF and subjective DOF represent the blur sensitivity of two different systems. AMF are correlated with the blur sensitivity of the accommodative system. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction Retinal defocus serves as an important visual input to various visual processes such as accommodation, depth perception, and emmetropization of the eye (Fisher & Ciuffreda, 1988, 1989; Hung, Ciuffreda, Khosroyani, & Jiang, 2002; Mather, 1996, 1997; Norton & Siegwart, 1995; Rabin, van Sluyters, & Malach, 1981). Constant retinal defocus has been suggested as leading to axial elongation of the eye (Gilmartin, 1998; Goss & Wickham, 1995; Hung & Ciuffreda, 1999; Hung et al., 2002; Ong & Ciuffreda, 1995; Rosenfield & Gilmartin, 1998). The visual system can tolerate a certain amount of optical defocus without detection of blur (Legge, Mullen, Woo, & Campbell, 1987). This blur tolerance has been defined as blur threshold (Campbell, 1957), blur detection threshold (Jiang & Morse, 1999; Rosenfield & Abraham-Cohen, 1999), and depth-offocus (DOF) (Millodot, 2004) in different studies with basically the same concept. Campbell (1957) first defined blur threshold, half the extent (±DD), as the smallest amount of retinal defocus that could cause a detectable deterioration in the quality of retinal image. In this paper, we use the term DOF to refer to the blur detection threshold. Blur threshold of the visual system is related to two central neural systems that detect and respond to the visual stimulus. The perceptual system is responsible for subjective cognition of image sharpness, while the accommodative system alters the refractive * Corresponding author at: Nova Southeastern University, College of Optometry, 3200 S. University Drive, Ft. Lauderdale, FL 33322, USA. Fax: +1 954 262 1818. E-mail address: [email protected] (B.-c. Jiang). 0042-6989/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.visres.2010.04.011
power of the eye to improve the sharpness of the retinal image based on the defocused stimulus. Kotulak and Schor (1986a) defined perceptual threshold and sensorimotor threshold to distinguish the difference in blur threshold between the perceptual and accommodative systems. Numerous studies have investigated the blur threshold of the visual system in the past half century. Most of these studies concentrated on the cognitive aspect of blur. The DOF measured by psychophysical methods has also been called perceptual DOF (Campbell, 1957). The perceptual DOF was found to increase with age and was influenced by visual acuity and image quality (Green, Powers, & Banks, 1980; Layton & Siegel, 1982; Legge et al., 1987; Mordi & Ciuffreda, 1998). Myopes are also reported to have higher blur detection threshold than emmetropes (Rosenfield & Abraham-Cohen, 1999). They attributed the larger accommodative lag in myopes to the observed reduction in blur sensitivity. In the accommodative-control system, retinal defocus, as the error signal of the accommodative system, is detected by the sensory component before stimulating the motor controller to produce accommodative response (AR) (Hung & Semmlow, 1980; Jiang, 1997). Studies show that AR changes with a small amount of change in stimulus even when the subject does not perceive blurring of the stimulus (Ludlam, Witenberg, Gigio, & Rosenberg, 1968). This suggests that the ability of the accommodative system to detect blur is different from that of the perceptual system. In a previous study, the blur sensitivity of the accommodative system was assessed by measuring the smallest change in the accommodative stimulus (AS) that causes a detectable change in the AR (Kotulak & Schor, 1986; Ludlam et al., 1968; Mordi & Ciuffreda, 1998; Vasudevan, Ciuffreda, & Wang, 2006a). Jiang (2000) defined
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this smallest change in AS as accommodative stimulus/response (S/R) threshold. Since the threshold is measured using an objective method, it is also called as the objective DOF. In previous studies, investigators obtained various values of DOF due to different target and test conditions, such as spatial frequency, luminance and baseline vergence of target as well as pupil size (Atchison & Smith, 2002). Objective DOF was smaller in value than subjective DOF in most studies, while both had a wide range of values, from ±0.1 D to ±0.81 D for objective DOF (Ludlam et al., 1968; Kotulak & Schor, 1986a; Mordi & Ciuffreda, 1998; Vasudevan, Ciuffreda, & Wang, 2006a, 2006b) and from ±0.02 D to ±1.75 D for subjective DOF (Ciuffreda, 1991, 1998). Few studies have compared the objective and subjective DOF in the same cohort. Kotulak and Schor (1986a) found the objective DOF to be smaller than the subjective DOF using a power spectrum technique in three subjects. Mordi and Ciuffreda (1998) got similar results using direct measurement of AR changes in 30 subjects. However, Marcos, Moreno, and Navarro (1999) measured the quality of retinal image in three subjects and found that the subjective DOF was in most cases smaller than the objective DOF. Recently, Vasudevan, Ciuffreda, and Wang (2007) found no difference between the objective DOF measured in free space and the subjective DOF measured with a Badal system. Inconsistency of criterion and target conditions in the above studies is probably responsible for the variation in the results (Jacobs, Smith, & Chan, 1989). As we mentioned above, the objective DOF represents the sensitivity of the accommodative system to blur. Even when a subject views a stationary target, there are variations of AR about the mean level. These variations are known as accommodative microfluctuations (AMF) (Campbell, Robson, & Westheimer, 1959; Collins, 1937; Charman & Heron, 1988; Denieul, 1982; Kotulak & Schor, 1986b; Winn, Pugh, Gilmartin, & Owens, 1990a). The amplitude of AMF is reported to be about 0.10 D–0.50 D. They depend upon many factors such as pupil size (Campbell et al., 1959; Gray, Winn, & Gilmartin, 1993a; Stark & Atchison, 1997), luminance (Gray, Winn, & Gilmartin, 1993b), contrast (Denieul & Corno-Martin, 1994) and spatial frequency of the target (Niwa & Tokoro, 1998). These are the same factors that affect the DOF of the eye (Atchison & Smith, 2002). We hypothesize that the AMF cause rapid and small changes in retinal defocus which are detected by the sensory component of the accommodative-control system and provide negative feedback information to maintain the AR level. This suggests a possible relationship between the magnitude of AMF and the DOF of the eye. Previous studies have found that the magnitude of AMF increases with increasing AS (Day, Strang, Seidel, Gray, & Mallen, 2006). They attributed the change of AMF to the effect of accommodation response-induced zonular relaxation and increased noise of the accommodative plant at higher AS levels. If the AMF are related to the objective DOF, one would expect to observe an increase in objective DOF at higher AS levels. In this study, we conducted two experiments. In the first experiment, objective DOF and subjective DOF were measured and compared for the same group of subjects. In both measurements, we used targets with the same spatial frequency and contrast and at the same AS level. In the second experiment, we investigated whether the objective DOF changes with AS level and whether that change correlates to the change in AMF.
2. Methods 2.1. Experiment 1 The purpose of this experiment was to compare the objective DOF with the subjective DOF obtained from same individuals under the same viewing conditions.
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2.1.1. Subjects Twelve emmetropic optometry students in NOVA Southeastern University, 20–38 years old (mean ± SD, 25.7 ± 4.7 years) including 3 males and 9 females, participated in this experiment. Subjective binocular refraction was performed before the experiment. The inclusion criteria was that the refractive error in spherical equivalent (SE) was within ±0.50 D with astigmatism no more than 0.50 D. The average SE of the twelve subjects was 0.07 ± 0.17 D (mean ± SD). None of the subjects had ocular disease or anisometropia (i.e. more than 1.00 D differences in SE between the eyes). They all had visual acuity of 20/20 or better and normal binocular vision. Only the right eyes were tested in this experiment. Informed consent was obtained from each subject after the nature and possible consequences of the study were explained. The research followed the tenets of the Declaration of Helsinki and was approved by Nova Southeastern University’s Committee for the Protection of Human Subjects. The subjects in Experiment 2 experienced a similar procedure regarding the informed consent. 2.1.2. Measurement of the subjective DOF In the measurement of subjective DOF, the subject’s right eye viewed two identical targets through a two-channel Badal system when his/her left eye was occluded (Legge et al., 1987; Jiang & Morse, 1999) (Fig. 1). The eye was positioned at the focal point of the +5.0 D Badal lens. A beam splitter with a silver coating over half its surface was positioned between the Badal lens and the targets. The standard target was aligned with the Badal lens at an optical distance of 1.5 D and could be viewed through the transparent part of the beam splitter. The testing target was positioned at the side and aligned with the reflective part of the beam splitter. Thus, when viewed through the beam splitter, each of the two targets occupied half of the visual field. The vergence of the testing target could be changed by adjusting the distance of the target relative to the Badal lens. The luminance, proximal effect and size cues were constant in this system. Each target consisted of a high contrast square-wave grating (high precision Ronchi Rulings) with 17.2 c/deg subtending a visual angle of 7.28°. The luminance of the targets was 180 cd/m2. Light sources were positioned at a distance of twice the focal length from the Badal lens so that the details of the light source would not be the cue for AR. During the measurement, the subject was instructed to maintain focus on the standard target so that the AR was controlled by this fixed target. The testing target was initially placed at the same vergence distance as the standard target. Then the subject moved the testing target away from the Badal lens, thus reducing the vergence of the target. When the subject detected the just noticeable blur of the testing target, a measurement was taken. The dioptric difference DD between the positions of the two targets was defined as the subjective DOF (±DD). During the experiment, the subject’s pupil size was recorded by a digital camera positioned far from the eye. A ruler was placed beneath the eye as a reference. 2.1.3. Measurement of the objective DOF In the measurement of the objective DOF, the subject was instructed to look at the target with the right eye through a Badal stimulator so that changes in vergence of the target (i.e., AS) by 0.1 D steps did not change the luminance or size of the target (Crane & Cornsweet, 1970). The Badal stimulator contained a Badal lens and an auxiliary imaging lens (Fig. 2). The target was a high contrast 17.2 c/deg square-wave grating presented by a computer screen (NEC AccuSync 72vx). The luminance of the target was 180 cd/m2. The target was positioned 2 m from the auxiliary lens and subtended a visual angle of 7.28°. The effective stimulus for accommodation was determined by the auxiliary lens in the Badal system. By moving the auxiliary imaging lens, the whole system
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Fig. 1. Top view of the two-channel Badal system used to measure subjective DOF in Experiment 1. RE, the subject’s right eye; L, +5.0 D Badal lens; BS, beam splitter, ST, standard target; TT, testing target; LS, light source; f, focal length of the Badal lens (20 cm). Arrow near TT indicates the movement of the testing target. The additional figure (TT/SS) shows the front view of the two targets through the Badal lens and the beam splitter.
Fig. 2. Top view of the apparatus used to measure objective DOF in Experiments 1 and 2. RE, the subject’s right eye; AutoRef, open-field autorefractor; L, +5.0 D Badal lens; f, focal length of the Badal lens (20 cm); ML, moveable auxiliary lens with +5.0 D; T, computer screen.
presented different AS to the subject’s right eye. Thus the spatial frequency, visual angle and luminance of the targets were consistent between the measurements of the subjective DOF and the objective DOF. The refractive error was measured using a Canon Autoref R-1 with a resolution of 0.125 D. This autorefractor was aligned with the Badal stimulator and the target. The refractive error was converted into SE value and then was used to calculate the AR. A digital camera was used to record the image of the eye displayed on the monitor of the autorefractor for measuring the pupil size during the experiment. The alignment circle (6 mm in diameter) in the monitor of autorefractor was used as a reference. The objective DOF was determined as the difference between two AS levels when the AR showed a significant change. During the measurement, the subjects were instructed to look at the target and keep it clear through the whole procedure. The AS was changed by the Badal stimulator from 0.9 D to 2.1 D by 0.1 D in each step. At each AS level, 20 readings of the autorefractor were recorded and then converted into AR. The ARs at each AS level were compared with the ARs at the 1.5 D AS level using the t-test. The tvalues of the nine steps were plotted against the AS values and fitted by a third order polynomial curve. The critical t-value for onetailed test, t[19] = ±1.686, corresponds to a Type I error rate of 0.05 at a freedom of 19. It was used as the criterion for achieving a statistically significant difference between the measured ARs, and in
turn the threshold for the change in AS. The mean difference between the upper and lower AS values was calculated and presented as ±DD, which was regarded as the objective DOF at the 1.5 D AS level (Tao, Jiang, & Morse, 1998). 2.1.4. Data analysis The values of objective DOF and subjective DOF were compared using the paired t-test. The correlation between the two DOFs and the correlation between the DOFs and accommodative error (AE) were analyzed using Pearson analysis. AE was calculated as the difference between the AR and the corresponding AS. The pupil sizes under these two experimental conditions were also compared using the paired t-test. 2.2. Experiment 2 The purpose of this experiment was to investigate whether there was a correlation between the objective DOF and the magnitude of accommodative microfluctuations. 2.2.1. Subjects Fifteen myopic optometry student in NOVA Southeastern University, 23–30-year old (25.6 ± 2.0 years, mean ± SD) including 7 males and 8 females, participated in the second experiment. The
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inclusion criterion was that the refractive error in SE was between 0.50 D and 6.00 D with astigmatism no more than 0.50 D. The average SE of the fifteen subjects in this experiment was 3.20 ± 1.72 D (mean ± SD). The onset age of myopia was 8– 15 years old (11.1 ± 2.7 years, mean ± SD). According to their self reports, the refractive errors were stable or changed no more than 0.25 D in the past year. None of the subjects had ocular disease or anisometropia (i.e. had less than 1.00 D differences in SE between the eyes). All the subjects had corrected visual acuity of 20/20 or better and normal binocular visual functions. Only the right eyes were tested in the experiment. All subjects used soft contact lenses to correct their refractive errors. Subjective refraction was repeated with the contact lenses in situ to ensure the refractive error was corrected within ±0.25 D.
one before and one after points in the data were also deleted. Then, the remaining data were used to calculate the mean value and root mean square (RMS) value of AR at that AS level. The RMS value of AR was defined as the magnitude of AMF in this study (Day et al., 2006). At 1 D and 4 D AS levels, after the measurement of AMF, the objective DOF was measured in the same way as in Experiment 1 except that the order of AS presentation was in two directions. At each AS level, the AR to the initial AS was measured and then the ascending and descending parts of measurement were performed in a random order. The ascending and descending parts both contained four 0.1 D steps in AS. The objective DOFs at 1 D and 4 D AS levels were calculated by using the same methods described in Experiment 1.
2.2.2. Apparatus AR was measured by an open-field infrared autorefractor (WAM-5500, Grand Seiko Co., Ltd., Hiroshima, Japan). The reference plane was set at the corneal plane and the reported resolution of this device was 0.01 D. In hi-speed mode, the instrument sampled the refractive error data every 0.2 s. The refractive error reading was converted into SE value and exported to a computer by using a software program (WCS-1). Mean SE value was used to calculate the AR. The chinrest of the autorefractor was modified to enable the vertical and horizontal adjustment. A 4 mm artificial pupil made of an infra-red filter was placed 14 mm in front of the corneal apex. A Badal stimulator similar to the set-up used in Experiment 1 was used to provide the AS (Fig. 2). A computer screen (NEC AccuSync 72vx) located 4.4 m from the auxiliary lens was used to present the target. The target was a 3 3 array of high contrast Snellen E letters with spatial frequency of 12 c/deg (logMAR 0.4). It subtended a visual field of 2°. The measured luminance was 77 cd/m2.
2.2.4. Analysis The RMS values at five AS levels were analyzed using one-way ANOVA. The independent variable in this analysis was the AS levels. The dependent variable was the RMS values. The objective DOFs at 1 D and 4 D levels were compared using the paired t-test. Correlation between the RMS value and the objective DOF was analyzed at 1 D and 4 D AS levels.
2.2.3. Procedures The subject’s right eye was aligned with the autorefractor, the Badal system, and the target. The left eye was occluded during the experiment. The subjects were instructed to look at the center of the target and keep it clear. To measure the AMF, the ARs for each AS level (0–4 D) were measured continuously for 20 s in hispeed mode, respectively. During the intervals between different AS levels, the subject was instructed to close his eyes and rest. Meanwhile, the investigator adjusted the target by moving the auxiliary lens quietly. Since image size maintained constant in the Badal system, the subject was not able to detect either the direction or the magnitude of the change in the AS. The missing data caused by eye closure or blink were deleted. To avoid bias,
3. Results 3.1. Experiment 1 In this experiment, the objective DOF and the subjective DOF were measured at an AS level of 1.5 D using targets of the same spatial frequency, contrast and luminance in the same group of subjects. Fig. 3 shows an individual accommodative stimulus response curve obtained at the 1.5 D AS level and the plot of AS versus t-values. All the curves obtained were well fitted and were used to calculate the objective DOF. The mean objective DOF of the 12 subjects was ±0.09 ±0.03 D. The mean subjective DOF was ±0.52, ±0.30 D. The paired t-test showed that the difference between the objective and subjective DOFs was significant (t = 5.309, P < 0.001) (Fig. 4). Correlation between the objective DOF and subjective DOF was not significant (P > 0.05). The mean pupil size was not significantly different (t = 1.374, P = 0.098) during the measurements for objective DOF (5.82 ± 0.94 mm) and subjective DOF (5.42 ± 1.49 mm). 3.2. Experiment 2 In this experiment, 15 subjects’ objective DOFs and the magnitude of AMF were measured under the same target conditions. As
Fig. 3. The measurement of objective DOF based on the data of an individual subject (# 2). Panel A is the subject’s accommodative response curve obtained at 1.5 D AS level. The error bar shows one standard deviation of the mean value. Panel B is the plot of AS against the t-values obtained by comparing the AR at each AS level to the AR at the 1.5 D level. A third order polynomial curve is smoothly fitted to the data. The two dashed lines indicate the critical t-values with statistically significant difference (a = 0.05) and corresponding AS values. The range in AS axis indicates the objective DOF and is presented as ±DD.
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Fig. 4. Comparison of subjective DOF and objective DOF at 1.5 D AS level in 12 emmetropes. The open circles are the individual subjective DOFs. The filled circles are the individual objective DOFs. The points farthest to the right represent the corresponding mean value of DOF of these subjects. The error bar shows one standard deviation of the mean value.
an example, recorded accommodative microfluctuations of an individual (subject #14) are shown in Fig. 5. The mean RMS values of AR at different AS levels are shown in Fig. 6. There was a significant increase in RMS value with increasing AS level (F = 17.025, P < 0.001). Post hoc tests showed that RMS values for each AS level was significantly different from those of other AS levels except that there was no difference in the RMS values between 0 D and 1 D AS levels, and between 3 D and 4 D AS levels. The objective DOFs at 1 D and 4 D AS levels are shown in Fig. 7. The paired t-test showed that objective DOF at 4 D AS level (±0.092, ±0.023 D) was significantly larger than that at 1 D AS level (±0.055, ±0.018 D) (t = 5.276, P < 0.001). The objective DOF showed a strong correlation with the RMS value of the microfluctuations at 1 D and 4 D AS levels, respectively (Fig. 8). 4. Discussion The main findings of this study are that the objective DOF is less than the subjective DOF, and that they are not correlated with each other. The objective DOF varies at different AS levels and is highly correlated to the magnitude of AMF.
Fig. 5. Accommodative microfluctuations at 0–4 D AS levels for an individual subject (#14).
4.1. The measurement of objective DOF In this study, the objective DOF is defined as the smallest change in AS which can cause a just detectable change in AR. In previous studies, the objective DOF was measured by monitoring the change in the AR while changing the AS (Ludlam et al., 1968; Kotulak & Schor, 1986a; Mordi & Ciuffreda, 1998; Vasudevan et al., 2006a). In those studies, the AS was presented using a Badal system so that proximal effects and size cues were eliminated. Thus the observed AR was induced only by retinal defocus. The present study used the same method of target presentation and AR measurement but applied a different criterion of detectable change in AR which was first suggested by Tao et al. (1998). Different criterions of just detectable change in AR may result in varied values of objective DOF. Kotulak and Schor (1986a) used a sine wave grating with a temporal frequency of 1 Hz as AS. The ARs were analyzed in a signal-detection format. They found the objective DOF to be ±0.12 D to ±0.14 D at 2.5 mm pupil diameter in three subjects. This method successfully eliminated the influence of system noise. Later, Vasudevan, Ciuffreda, and Wang (2006a) reported the objective DOF to be ±0.46 D to ±0.81 D by monitoring the AR to a slowly varying AS. The criterion used to determine the change point was when the change in AR was larger than 0.25 D and remained at the new steady-state level for at least 2 s. But they changed the AS with a velocity of 0.10–0.15 D/s. Thus there would be a
Fig. 6. The average RMS values of accommodative microfluctuations are plotted against the AS levels for 15 subjects. The error bar shows one standard deviation of the mean value.
0.20–0.30 D of change in AS during the 2 s which was required to determine a consistent change of 0.25 D in AR. In addition, the microfluctuations in AR might cause judgment error. These factors might cause their results to be larger than the true value. The present study used statistical criterion instead of subjective inspection by the investigator. Therefore, the bias caused by human error was
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Fig. 7. Comparison of objective DOF at 1 D and 4 D AS levels in 15 subjects. The filled squares are the individual objective DOFs at 1 D AS level. The open squares are the individual objective DOFs at 4 D AS level. The squares farthest to the right represent the mean value of objective DOF at each corresponding level. The error bar shows one standard deviation of the mean value.
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Besides, the 4 mm pupil diameter used in the present study is larger than that used by Kotulak and Schor, which may also contribute to the relatively smaller value of DOF measured in the present study. Within this study, the pupil diameter was not different between the objective and the subjective DOF measurements in Experiment 1. Phillips, Winn and Gilmartin (1992) have proved that the blur-driven accommodation only does not induce the pupil near response. Thus the accommodation induced by the Badal stimulator in this study, should not cause much change in pupil size. Concerning the identified artificial pupil diameter used in Experiment 2, the tiny change in pupil size during the accommodation should have little influence on the measurement of AR or DOF. But our estimation of the objective DOF is a relative value. It is dependent on the number of data points used for statistics comparison (t-test). If we use a larger number of data points, the estimation would become smaller. 4.2. The measurement of subjective DOF The accommodative response was not monitored during the measurement of subjective DOFs, the measured DOF might be a little bit inflated. But since the standard target in Experiment 1 represented an accommodative stimulus around the tonic level of accommodative system, the fluctuations of accommodation should be at least amount and the DOF was reported to be symmetric around the tonic level. Therefore, the accommodative response to the standard target should be quite stable and the measured range of AS should be adequate to represent subjective DOF. In previous studies, the reported subject DOF ranges from ±0.02 D to ±1.75 D (Jacobs et al., 1989; Atchison, Charman, & Woods, 1997; Rosenfield & Abraham-Cohen, 1999; Ciuffreda 1991, 1998; Schmid, Iskander, & Edwards, 2002; Wang & Ciuffreda, 2004). The discrepancy in these results may be due to different experimental conditions. The subjective DOF obtained in this study, is similar with the subjective DOF for 4 mm pupil size reported by Atchison et al. (1997). The experimental methods in the two studies are similar except Atchison et al. measured the subject’s DOF under cyclopedia condition. The individual differences in the AMF might have effect on the perceptual judgment of DOF. In addition, larger AE at higher AS levels means larger retinal defocus. Under such defocus conditions, the subject’s just noticeable blur range (i.e., DOF) may increase, which can be predicted by the non-linear fall-off in MTF with defocus. However, in this study, the objective DOF was measured around the tonic accommodative level. The effect of AE and AMF should be reduced to the minimum. 4.3. The objective DOF and subjective DOF
Fig. 8. Correlation between the objective DOF and the RMS value of accommodative microfluctuations. Panel A is the data at 1 D AS level. Panel B is the data at 4 D AS level.
eliminated and the results should be more reliable. The objective DOFs measured in Experiment 1 were just a little less than the Autoref’s resolution of 0.125 D. This situation was better in the Experiment 2 with a higher resolution autorefractor. Because the objective DOF is very small, we believe that the high resolution is better for the measurement.
The results in the first experiment of this study showed that the objective DOF was smaller than the subjective DOF when they were measured under the same target conditions and compared within the same individuals. No correlation was found between the two DOFs. This is consistent with the findings in previous studies (Kotulak & Schor, 1986a; Marcos et al., 1999; Mordi & Ciuffreda, 2004). When Ludlam et al. (1968) measured the objective DOF, they found that change in defocus stimulus as small as 0.1 D could induce a constant change in AR when the subject was not able to perceive the blurring of the target. Later, Kotulak and Schor (1986a) also found that a blur stimulus smaller than the perceptual DOF of the eye could cause a change in the AR. They suggested that there are dual thresholds, sensorimotor and perceptual. Our results support their findings and suggest that the objective DOF and subjective DOF represent the blur sensitivity of two different systems. The two DOFs are different in magnitude and have different underlying mechanisms. This is supported by the finding that the subjec-
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tive DOF increased at a rate of 0.027 D/year but objective DOF did not change with age (Mordi & Ciuffreda, 1998). The objective DOF, which is determined by measuring the changes in AR, depends on the function of both the sensory and motor components of the accommodative system. The accommodative system responds to a defocused stimulus continuously and rapidly in order to minimize the retinal defocus, so as to maintain the optimal image quality. The accommodative system is controlled by the midbrain-oculomotor nucleus complex/Edinger-Westphal nucleus, which is in lower levels than the parieto-temporal areas in the visual cortex (Jaeger & Benevento, 1980; Judge & Cummings, 1986; Jampel, 1959). This may explain why the reaction of the accommodative system is not recognized by the perceptual system. The widely used term, ‘‘the DOF of the eye”, refers to the smallest amount of defocus that causes a just noticeable blur. During the measurement of subjective DOF in most previous studies, the accommodation was paralyzed by a cycloplegic agent or stabilized by fixating on a reference target (Atchison et al., 1997; Campbell, 1957; Walsh & Charman, 1988; Rosenfield & Abraham-Cohen, 1999; Ciuffreda, Wang, & Wong, 2005). Thus the subjective DOF is independent of the accommodative system and is related to the blur sensitivity of the perceptual system. In this study, the accommodation was not paralyzed but was stabilized by staying focused on the fixation target. Comparison between the objective and subjective DOFs in this study indicates that the accommodative system is more sensitive to defocus stimulus than the perceptual system. As long as the retinal defocus is within the range of subjective DOF, the subject regards the image as clear and well focused. Although little is known of higher-center processing of accommodation signals, we speculate that small defocus signal might be inhibited in the perceptual system. This mechanism helps to ensure that the perceptual system is not disturbed by images with small amounts of defocus. 4.4. The objective DOF and microfluctuations In Experiment 2, the AR at each AS level was recorded continuously for 20 s with a sampling rate of 5 Hz. The sampling rate was not high enough for power spectrum analysis but was higher than the reported peak frequency of 2 Hz in AMF (Charman & Heron, 1988). In this study, we used the average RMS value of the AR to represent the magnitude of AMF. Day et al. (2006) used power spectrum analysis to evaluate the frequency components of AMF. They also used the RMS value of the AR to represent the magnitude of AMF. In this study, the RMS value was found to be correlated to the objective DOF at both 1 D and 4 D levels. This adds support to the suggestion by Jiang (2000) that objective DOF may be related to the AMF. One controversy in terms of the mechanism and significance of AMF is whether they represent simply an inevitable instability of AR as background noise in the accommodative plant or are they regulated by the neural controller and therefore play an active role in guiding and maintaining AR. Charman (1983) found that a reduction in pupil size led to increasing slower oscillations of accommodation, which was consistent with the changes of the DOF of the eye. Other studies also found the same pattern in the change of the low frequency of microfluctuations and the DOF with various target luminance, form and pupil size (Hung, Semmlow, & Ciuffreda, 1982; Charman & Heron, 1988; Winn, Charman, Pugh, Heron, & Eadie, 1989; Winn, Pugh, Gilmartin, & Owens, 1989; Winn, Pugh, Gilmartin, & Owens, 1990a, 1990b; Winn & Gilmartin, 1992; Gray, Winn, & Gilmartin, 1993a, 1993b; van der Heijde, Beer, & Dubbelman, 1996; Stark & Atchison, 1997). This indicates that low frequency microfluctuations may play an important role in maintaining steady-state AR. This is confirmed by the high correlation between the AMF and the objective DOF found in this study.
Since the objective DOF represents the sensitivity of the accommodative system to defocus, this result indicates that microfluctuations are part of the instantaneous adjustment of the AR instead of merely representing the instability of accommodative system. In the results of Experiment 2, the RMS value of AMF was larger than the objective DOF for each subject. We have to mention that the objective DOF represents the defocus threshold in AS, and the RMS of AMF represent the average change of AR in a short period. This result suggests that when the magnitude of AMF exceeds the blur threshold of accommodative system, the accommodative-control system could detect the temporal defocused image and then adjust the AR back to its baseline level. This supports the theory proposed by previous researchers (Alpern, 1958; Fender, 1964; Charman & Tucker, 1978; Hung et al., 1982; Kotulak & Schor, 1986c) that small fluctuations of accommodation provide the error signal to the accommodative-control system to maintain a steady response. Since the detection of these error signals depends on the sensitivity of the accommodative system to blur stimulus, i.e. objective DOF, in addition to the intrinsic mechanical instability of the accommodative system, the AMF may also be regulated by the objective DOF. In Experiment 2, only myopes were included because accommodative abnormality is considered to be important in myopia development. The influence of AMF on blur sensitivity of accommodative system needs to be studied with a larger range of subjects with different refractive status, such as emmetropes and progressing myopes, in the future. 4.5. The effect of the accommodative stimulus In this study, we found that the RMS value of AMF increases with the increasing AS level from 0 D to 4 D. Association between the magnitude of AMF and AR was reported by previous studies (Krueger, 1978; Denieul, 1982; Kotulak & Schor, 1986c; Miege & Denieul, 1988; Heron & Schor, 1995; Stark & Atchison, 1997). Kotulak and Schor (1986c) reported that the microfluctuations over the AS range of 1–4 D was smallest at the 1 D AS level. Miege and Denieul (1988) reported the amplitude of microfluctuations was largest at 3 D when measuring from 1 D to 4 D levels. Previous authors attributed the increase of the microfluctuations to the decrease of zonular tension and consequently less constrained natural vibrations of lens and its support system with the increasing AR level. Recently, Day et al. (2006) tried to associate the change of the magnitude of microfluctuations with the neurological controller demonstrated above but they simply assumed the DOF was constant at different AS levels. They attributed the microfluctuations to the physical property of the accommodative system noise. However, our study has shown that the magnitude of microfluctuations is correlated to the objective DOF at both 1 D and 4 D AS levels. This correlation suggests that accommodative microfluctuation might be regulated by the objective DOF as a result of the feedback accommodative-control system. The true function of AMF needs to be revealed in further studies. Acknowledgments This work was supported by NSU PFRDG #335441, NSU HPD Grant #335230, and NSFC Grant #30530770. Dr. Peijun Yao was supported by the State Scholarship Fund from the China Scholarship Council. The authors thank Dr. Ken Seger for helpful comments on the manuscript. References Alpern, M. (1958). Variability of accommodation during steady fixation at various levels of illuminance. Journal of the Optical Society of America, 48, 193–197.
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