Dynamic refraction and anterior segment OCT biometry during accommodation

Accommodation is the process by which the eye changes focus. These changes are the result of changes to the shape of the crystalline lens. Few prior studies have quantified the relation between lens shape and ocular accommodation, primarily at discrete static accommodation states. We present an instrument that enables measurements of the relation between changes in lens shape and changes in optical power continuously during accommodation. The system combines an autorefractor to measure ocular power, a visual fixation target to stimulate accommodation, and an optical coherence tomography (OCT) system to image the anterior segment and measure ocular distances. Measurements of ocular dimensions and refraction acquired dynamically on three human subjects are presented. The individual accommodative responses are analyzed to correlate the ocular power changes with changes in ocular dimensions.


Introduction
Accommodation is the process by which the optical power of the eye changes in order to shift focus from far to near.These changes in ocular power are the result of changes to the shape of the crystalline lens in response to contraction of the ciliary muscle [1].With increasing age, accommodative function diminishes until it is completely lost around the age of 50-55, a condition known as presbyopia.The inability to see near objects has a negative impact on quality of life [2,3].There are currently several treatments under development to restore the accommodative function observed in early age, including accommodating intraocular lenses, laser treatments, and pharmacological approaches [4][5][6].In order to evaluate the true efficacy of these emerging solutions, an approach is needed to objectively measure both the optical and mechanical changes with accommodation [7].
Most of the prior work on quantifying the accommodative response has characterized the optical response statically or dynamically, with commercial or custom-built autorefractors [8][9][10].There are fewer studies on the changes in lens shape and ocular dimensions during accommodation.Changes in lens shape during accommodation have been studied using MRI [11,12], Scheimpflug imaging [13,14], ultrasound [15][16][17][18], and more recently with OCT [19][20][21][22][23][24][25][26][27][28][29][30][31].Most biometry studies quantified the lens shape at discrete static steady-state accommodative demands.Only a few studies have quantified the changes in lens shape dynamically either at fixed accommodation or in response to step stimuli [19,21,25,26,28,32].Dynamic continuous measurements can provide insight on the lens mechanical characteristics [32].Another advantage of dynamic recordings is that the relation between optical and biometric changes can be characterized in a single continuous acquisition and with higher dioptric resolution than with static recordings at discrete accommodative states.
In addition, most prior studies characterize the changes in lens shape with respect to accommodative demand (i.e., the amplitude of the stimulus in diopters), but do not quantify the accompanying accommodative response (i.e., the dioptric change in focus of the eye).Due to the presence of accommodative lag (or less frequently, accommodative lead), the accommodative response is generally different from the accommodative demand and the response elicited by a given demand is highly variable across individuals [15].To eliminate these confounding effects and find the true dynamic relationship between optical and anatomical accommodative changes, ocular biometry must be studied with respect to accommodative response, instead of accommodative demand.The challenge is that these measurements require custom-built devices that integrate dynamic optical biometry and refraction with an approach to produce controlled accommodation demands.
Among the studies that have quantified the relation of biometry changes to accommodative response [15][16][17][18]20,22,[33][34][35], only one study presents dynamic recordings of the optical and biometric changes during accommodation [32].Biometry was acquired with ultrasound biomicroscopy (UBM) which enables fast and high precision measurements of lens thickness, but requires contact with the eye, which makes measurements less comfortable to the patient and prevents simultaneous optical and biometric measurements of the same eye.
In this manuscript, we describe an optical instrument for non-contact, dynamic studies of the optical and biometric changes during accommodation.This device combines a wavefront-based autorefractor, a visual fixation target, and an OCT system to measure the crystalline lens shape and other key ocular dimensions.In the current implementation, refraction and biometry are recorded sequentially.A preliminary study on three human subjects demonstrates the feasibility of acquiring dynamic biometry during accommodation.

Overall system
The custom-built device combines a Shack-Hartmann ocular aberrometer using a commercial wavefront sensor, a fixation target providing a step or ramp accommodation stimulus, and a custom-built whole eye-OCT system (Fig. 1).In the current implementation, the OCT and refraction measurements are optically coupled with the fixation target using a removable dichroic mirror.OCT images and refraction measurement are acquired sequentially by respectively removing and inserting the dichroic mirror.The aberrometer, fixation target and OCT beam delivery unit are assembled together on a breadboard that is mounted on an adjustable slit-lamp base with a forehead chin-rest to ensure correct subject positioning and facilitate measurements.Detailed descriptions of each module are provided below.

Wavefront-based autorefraction
The wavefront-based refractor is based on a standard Shack-Hartmann (SH) configuration using a 4f-relay system that images the subject's pupil onto the lenslet array.The system utilizes a commercial Shack-Hartmann wavefront sensor (WFS20-5C, Thorlabs, New Jersey, USA).The 4f-relay system uses two achromats (L1, L2) of focal length 150 mm (AC254-150-AB, Thorlabs, New Jersey, USA).The lenses were selected to provide a working distance that matches that of the OCT system.The light source was a fiber-coupled 830 nm superluminescent diode (D830, Superlum Diodes, Moscow, Russia).A fiber-optic collimator (PAF-X-2-B, Thorlabs, New Jersey, USA) produces a beam with a calculated diameter of 0.42 mm (1/e 2 ) that was directed to the subject's eye through a 45:55 pellicle beamsplitter (BS1) (CM1-BP145B2, Thorlabs, New Jersey,

Pupil camera
To facilitate proper alignment of the device with the subject's eye, a pupil imaging system is included in the wavefront-sensor channel.The pupil imaging system consists of a CMOS camera (Firefly MV FMVU-03MTM, FLIR Systems, British Columbia, Canada) and an achromatic lens pair with focal length f = 50 mm (L3) and f = 150 mm (L1), providing a magnification of 1/3.The distal lens of the pupil imaging system (L1) is shared with the 4frelay system of the SH aberrometer.The pupil imaging system is coupled to the 4f-relay with an 8:92 pellicle beamsplitter, BS2 (CM1-BP108, Thorlabs, New Jersey, USA).A ring of infrared LEDs is employed to ensure illumination of the iris during pupil camera alignment.

Ramp and step accommodation stimulus
A two-channel accommodation stimulus was developed to provide either step or ramp accommodative demands.Both the step and ramp stimuli can produce vergences ranging from -20 D to +10 D. The range was selected to provide a 10 D accommodation stimulus in subjects with spherical refractive error ranging from -10 D to +10 D.
To achieve this vergence range, a modified version of a two-channel Badal system using three lenses in each channel (near channel: L1, L4, L5; far channel: L1, L6, L7) was implemented [36].The Badal system presents a visual stimulus that is a letter E printed on paper and illuminated with a white LED.The equivalent spatial frequency of the letter in the vertical direction is 3.8 cycles/degree, corresponding to 20/180 visual acuity.The optotype 'E' is a target that most subjects are familiar with and can easily focus on, and it has a range of frequency components needed to stimulate accommodation.The illuminance produced by the fixation target at the corneal plane was 0.027 lux, corresponding to a luminance of 21 cd/m 2 .
The vergence of the ramp accommodation stimulus is changed by changing the distance between the lenses of the Badal system.For the ramp stimulus, a hollow roof prism mirror (M2) (HR1015-P01, Thorlabs, NJ) is mounted on a motorized linear stage (X-LSM235B, Zaber Technologies, British Columbia, Canada).The stage has 235 mm of travel distance with a maximum velocity of 104 mm/s, which corresponds to a maximum rate of change in vergence of 9.5 D/s.Each millimeter of displacement corresponds to 0.1 D change in vergence.The USA).The power delivered to the eye was 0.195 mW, below the exposure limit calculated using the ANSI Z80.36-2016 standard for our beam geometry.

Pupil camera
To facilitate proper alignment of the device with the subject's eye, a pupil imaging system is included in the wavefront-sensor channel.The pupil imaging system consists of a CMOS camera (Firefly MV FMVU-03MTM, FLIR Systems, British Columbia, Canada) and an achromatic lens pair with focal length f = 50 mm (L3) and f = 150 mm (L1), providing a magnification of 1/3.The distal lens of the pupil imaging system (L1) is shared with the 4f-relay system of the SH aberrometer.The pupil imaging system is coupled to the 4f-relay with an 8:92 pellicle beamsplitter, BS2 (CM1-BP108, Thorlabs, New Jersey, USA).A ring of infrared LEDs is employed to ensure illumination of the iris during pupil camera alignment.

Ramp and step accommodation stimulus
A two-channel accommodation stimulus was developed to provide either step or ramp accommodative demands.Both the step and ramp stimuli can produce vergences ranging from -20 D to +10 D. The range was selected to provide a 10 D accommodation stimulus in subjects with spherical refractive error ranging from -10 D to +10 D.
To achieve this vergence range, a modified version of a two-channel Badal system using three lenses in each channel (near channel: L1, L4, L5; far channel: L1, L6, L7) was implemented [36].The Badal system presents a visual stimulus that is a letter E printed on paper and illuminated with a white LED.The equivalent spatial frequency of the letter in the vertical direction is 3.8 cycles/degree, corresponding to 20/180 visual acuity.The optotype 'E' is a target that most subjects are familiar with and can easily focus on, and it has a range of frequency components needed to stimulate accommodation.The illuminance produced by the fixation target at the corneal plane was 0.027 lux, corresponding to a luminance of 21 cd/m 2 .
The vergence of the ramp accommodation stimulus is changed by changing the distance between the lenses of the Badal system.For the ramp stimulus, a hollow roof prism mirror (M2) (HR1015-P01, Thorlabs, NJ) is mounted on a motorized linear stage (X-LSM235B, Zaber Technologies, British Columbia, Canada).The stage has 235 mm of travel distance with a maximum velocity of 104 mm/s, which corresponds to a maximum rate of change in vergence of 9.5 D/s.Each millimeter of displacement corresponds to 0.1 D change in vergence.The accommodation stimulus is coupled to the wavefront sensor with a 45°hot mirror (DM2) (64468, Edmund Optics, New Jersey, USA).The distal lens of the Badal system (L1) is shared with the 4f-relay of the wavefront sensor.
In the ramp accommodation mode, the far channel is turned off and only the near channel is used.The channel is adjusted to distance refraction by moving the motorized stage until the subject perceives the target is in focus.The ramp stimulus is produced by moving the motorized stage.The entire system is controlled with a LabVIEW program which has a user interface that allows the operator to adjust the type, amplitude, and speed of the accommodation stimulus.
Step accommodation is also a capability of the system and is achieved by first turning on the LED in the far channel and turning off the LED in the near channel.Next, the far channel is adjusted to distance refraction by moving the motorized stage until the subject perceives that the target is in focus.Then, the auxiliary lens in the near channel (L4) is moved to a predetermined position based on the desired accommodative demand.The step stimulus is produced by simultaneously turning off the LED in the far channel and turning on the LED in the near channel.This process is controlled electronically and is precisely synchronized with the acquisition of refraction or OCT (see details in [25]).

OCT system and image analysis
The combined system described above was coupled with a previously developed whole-eye OCT system with wavelength of 840 nm [25,26,37].The OCT has an axial resolution (in air) of 8 µm and an axial range (in air) of 10.5 mm and can acquires B-scans of the anterior segment at a rate of 13 Hz.The power delivered to the eye by the OCT is 0.75 mW [25].The OCT is coupled to the aberrometer system with a dichroic mirror (DM1) (FF749-SDi01-25 × 36 × 3.0, Semrock, New York, USA) mounted on a stage with rotational and lateral adjustment (see details in [26]).OCT images were processed using a semi-automatic segmentation software to determine the curvatures (anterior cornea, posterior cornea, anterior lens, posterior lens) and thicknesses (central corneal thickness, anterior chamber depth, lens thickness, and vitreous depth) of the various ocular components as they change with accommodation [26,38].

Software control and synchronization
A LabVIEW software was developed for subject imaging to display, control, and record the data from the custom device.The software allows the operator to adjust the parameters of the wavefront sensor (acquisition speed and optical zone diameter) and accommodation stimulus (ramp or step, ramp speed, amplitude).For refraction measurements, the operator aligns the imaging system using the real-time display of the pupil camera and wavefront sensor for guidance.The refraction measurements are recorded as the motorized stage follows a pre-programmed displacement routine, synchronized with the computer's internal clock.On the other hand, the OCT acquisition and accommodation stimulus is synchronized with a custom-built electronic trigger.The OCT device outputs a signal when acquisition starts that is detected by the electronic circuit and the motorized stage is triggered to move according to its pre-programmed displacement routine.

Calibration using an eye model
The wavefront-based autorefractor was first calibrated using an eye model.The eye model consists of an achromatic lens with a focal length of 30 mm (ACN127-030-B, Thorlabs, New Jersey, USA) and a diffuse-reflecting port plug from an integrating sphere mounted on a linear translation stage.The refraction of the eye model can be varied by adjusting the position of the translation stage.For calibration, the exit pupil of the eye model must be positioned in the plane conjugate to the lenslet array (reference plane).For this purpose, the calibration was performed in two steps.A first calibration curve was recorded with the lens of the eye model located at the estimated position of the focal plane of lens L1.This calibration curve was fitted with the theoretical paraxial formula relating stage position and eye model refraction, using the position error with respect to the reference plane as an additional fitting parameter.The value of the positioning error obtained from the fit was used to correct the position of the eye model.A final calibration curve was then recorded with the eye model positioned in the reference plane.Wavefront measurements were taken for eye model refractions ranging from -20 D to +10 D with an exposure time set to 1.5 ms and measurement pupil diameter set to 2 mm.The error between measured and predicted sphere is shown in Fig. 2. The relationship between predicted and measured sphere was found to be linear, with a slope of 1.01 D/D and an intercept of 0.03 D. The error between fit and measurements was less than ±0.12 D along the entire range with larger deviation in the hyperopic (> 5 D) range, most likely due to a non-linearity of the eye model calibration which was not corrected (Fig. 2).Wavefront measurements were taken for eye model refractions ranging from -20 D to +10 D with an exposure time set to 1.5 ms and measurement pupil diameter set to 2 mm.The error between measured and predicted sphere is shown in Fig. 2. The relationship between predicted and measured sphere was found to be linear, with a slope of 1.01 D/D and an intercept of 0.03 D. The error between fit and measurements was less than ±0.12 D along the entire range with larger deviation in the hyperopic (> 5 D) range, most likely due to a non-linearity of the eye model calibration which was not corrected (Fig. 2).Inclusion criteria for our study is subjects who are 16 years of age or older with a natural lens.

Intra-and inter-session repeatability on human eyes
Intra-and intersession repeatability tests were performed on 3 human subjects to test reliability of the measurements within the same session and over multiple sessions.In an Institutional Review Board approved study, three subjects, ages 25, 31, 33 years with baseline spherical error of -9.50 D, 0.0 D, -3.75 D and cylinder of -0.75 D, -1.5 D, 0 D respectively were enrolled.Inclusion criteria for our study is subjects who are 16 years of age or older with a natural lens.Exclusion criteria include those unable to provide informed consent as well as any history of macular degeneration or edema, retinal detachment, glaucoma, corneal disease, corneal surgery, and amblyopia.Subjects were instructed to not wear contact lenses on imaging days.The right eyes were imaged ten times on three separate occasions with the SH-aberrometer with an acquisition speed set to 20 Hz and measurement pupil diameter set to 2 mm.Sphere, cylinder, and axis values were converted to power vectors (M, J0, J45) [39].Subjects were imaged without correction.
Standard deviations of the intra-and inter-session repeated measurements were within 0.46 D, 0.27 D and 0.17 D for M, J0 and J45, respectively, or equivalently, within 0.5 D and 0.15 D for sphere and cylinder, respectively.Test-Intraclass Correlation Coefficients (ICC) and their 95% confident intervals were calculated using SPSS statistical package version 23 (SPSS Inc, Chicago, IL, USA) for M, J0, and J45 for both intra-and inter-session results and found to be above 0.988 for M, 0.988 J0 and above 0.935 for J45 (Table 1).ICC values between 0.75 and 0.9 indicate good reliability, and values greater than 0.90 indicate excellent reliability [40].

Calibration on human eyes
The accuracy of wavefront measurements obtained with the SH-aberrometer system was evaluated on 12 subjects in the same IRB approved protocol as above by comparing to a commercial autorefractor (RM-800, Topcon).Twenty-three eyes of 12 subjects (age: 21-70 years, mean: 36.1 years) were included.The subjects' baseline refraction measured with the commercial device at the spectacle plane ranged from -9.25 D to +2.25 D for sphere, with cylinder ranging from 0 D to 2.25 D. Both eyes of all subjects were measured without correction, except for one eye of one subject that did not meet inclusion criteria.Five measurements were acquired on each eye without cyclopegia with an acquisition speed of 20 Hz and a measurement pupil diameter set to 2 mm.The refraction measurements from the commercial system were converted from the spectacle plane to the pupil plane, assumed to be 3 mm from the corneal plane, using the standard effectivity equation so that the reference plane for the measurements is the same for both devices.Bland Altman analysis revealed that there is good agreement between the two devices for the M, J0 and J45 terms as shown in Fig. 3.The mean difference of M, J0, and J45 was -0.02 D, -0.03 D, and -0.09D, respectively, with a 95% confidence interval of 0.91 D, 0.45 D, and 0.25 D, respectively.Except for two subjects (ages 21 and 33 years), all mean spherical equivalent refraction values were within +/-1 D. Overall, the agreement is comparable to the agreement obtained in other studies comparing commercial and prototype devices [41].The subjects with greater than 1 D error could have been accommodating during the measurements as cyclopegia is not used.

Human subject imaging protocol
Proof-of-principle study to evaluate the ability of the system to record accommodative response to continuous ramp stimulus was conducted on three human subjects.The right eyes of three subjects, ages 21, 27, 31 years with baseline spherical error of -0.38 D, 0.38 D, -3.63 D and less than 0.5 D of cylinder were enrolled with informed consent following the IRB-approved protocol described above.The optical and biometric accommodative responses to a set of different stimuli were recorded sequentially using the following protocol.Subjects were seated in front of the device and the optical accommodative response was recorded with the autorefractor (beam splitter removed).For this measurement, the operator adjusted the position of the instrument until the pupil was in focus.In all measurements, the pupil was decentered on the wavefront sensor by approximately 0.5 mm in the vertical and horizontal directions to avoid interference of the central corneal reflection.Once the subject was positioned, the ramp accommodation target is adjusted to distance refraction by moving the motorized stage until the subject perceives the target is in focus and then 0.25 D hyperopic fog is applied.Finally, the wavefront acquisition was started.Responses were acquired in triplicate for three magnitudes, 2, 4, and 8 D, of ramp stimuli with a speed of 0.25 D/s.Preliminary tests with speeds ranging from 0.25 D/s to 8 D/s showed the 0.25 D/s ramp provided reproducible accommodative responses.Each recording session lasted for the duration of the ramp stimulus (12 to 36 s).Between each measurement, the subject was instructed to relax and remove their head from the chin rest.After the wavefront measurements were completed, the operator placed the dichroic mirror in the system to begin the OCT imaging of the subjects.The OCT system was aligned by observing a live image.Recordings were started once the pupil was seen to be horizontal and centered and the corneal reflection was visible in the image.With these conditions, the OCT is aligned approximately with the pupillary axis.Responses were acquired in the same sequence using the same protocol as for the wavefront recordings.For each instrument, a total of three experimental runs were performed for each type of stimulus.

Accommodation data analysis
For each run, baseline sphere values were calculated by averaging the first 15 sphere measurements from the wavefront sensor.Accommodative response was then calculated by subtracting the baseline sphere from the sphere measurement.OCT images were processed with previously custom-made semi-automated segmentation and distortion correction software [42] that provided values of the anterior and posterior cornea curvature, central corneal thickness, anterior chamber depth, anterior and posterior lens curvature, and vitreous depth.Optical and biometric measurements were plotted as a function of time and accommodative demand.Biometry versus accommodative response curves were then generated by using values recorded at the same accommodative demand.The wavefront sensor was set to record data at 20 Hz and the OCT system acquired images at a rate of 8.7 whole eye frames per second.To account for the different acquisition rates, wavefront measurements were interpolated using the OCT acquisition time scale.
To compare the responses of the 8 D ramp stimuli, changes in lens thickness, anterior chamber depth, vitreous depth, and lens anterior and posterior radius of all three runs were plotted against stimulus and against accommodation response for each subject.Linear fits were performed to obtain lens thickness and curvature versus accommodation stimulus and response.

Accommodation study results
Responses could be recorded successfully in all subjects.The accommodative responses had a similar behavior in all subjects, with a latency followed by a linear response with time or accommodative demand, up to maximal accommodation.Once the ramp accommodation stimulus begins, there is a latency of up to about 4 seconds (e.g., 1 D at 0.25 D/s) before the accommodation or biometric values begin to change.This latency reflects in part the reaction time and the subjective depth of focus of the subjects.Lens thickness, anterior chamber depth, vitreous depth, and lens anterior and posterior radius to the 2, 4, and 8 D stimuli of all three subjects were plotted against time to show the time trace of the responses (Fig. 4).To evaluate

Discussion
In this manuscript, we describe an instrument that combines an autorefractor, ramp accommodation target and OCT system to measure the optical and biometric changes that occur in accommodation dynamically.The calibration experiments on a model eye and human subjects demonstrate that the wavefront sensor can accurately measure changes in refraction.
Proof of concept accommodation studies on three human subjects demonstrate the feasibility of acquiring measurements with the combined system.In this study we acquire dynamic refraction and biometry measurements on the same subjects in response to ramp accommodation stimuli to quantify the relationship between biometry and refractive change.
Prior studies have also studied relationship between optics and biometry [16][17][18]22,23], but some of these are limited to measuring the contralateral eye which may not provide the same relationship.This system enables continuous measurements during dynamic accommodative responses to controlled stimuli.The ability to acquire measurements continuously provides the responses of the 8 D ramp stimuli, changes in lens thickness, anterior chamber depth, vitreous depth, and lens anterior and posterior radius of all three runs were plotted against stimulus and against accommodation response for each subject (Fig. 5).Change in biometry was calculated by adjusting the values to a pre-stimulus baseline which was the average of the first 15 values.The biometric responses (lens thickness and curvature, ocular distances) of all three subjects were plotted versus accommodation response and accommodation stimuli.The average slopes of each of these corresponding values are presented in Tables 2 and 3 in units of D/mm.

Discussion
In this manuscript, we describe an instrument that combines an autorefractor, ramp accommodation target and OCT system to measure the optical and biometric changes that occur in accommodation dynamically.The calibration experiments on a model eye and human subjects demonstrate that the wavefront sensor can accurately measure changes in refraction.Proof of concept accommodation studies on three human subjects demonstrate the feasibility of acquiring measurements with the combined system.In this study we acquire dynamic refraction and biometry measurements on the same subjects in response to ramp accommodation stimuli to quantify the relationship between biometry and refractive change.Prior studies have also studied relationship between optics and biometry [16][17][18]22,23], but some of these are limited to measuring the contralateral eye which may not provide the same relationship.This system enables continuous measurements during dynamic accommodative responses to controlled stimuli.The ability to acquire measurements continuously provides insight into the dynamics of the accommodative response that cannot be obtained from static measurements acquired at discrete accommodative demands.For instance, the continuous recordings allow us to quantify the initial latency in the first few seconds of the response with much higher precision.Another advantage of continuous acquisition of dynamic responses is that the entire accommodative response from the relaxed state to maximal acquisition can be acquired in a single recording.Studies relying on static measurements require a separate recording for each individual accommodative demand, which typically limits these studies to measurements at few accommodative states in 1 D or 2 D step increments.Being able to evaluate the dynamics of accommodation can be useful in understanding the closed-loop system that drives ciliary muscle contraction based on retinal image cues [43].The system can be programmed to present accommodation stimuli other than ramp and step types, including rectangular or sinusoidal stimuli.
Ideally, OCT and wavefront should be acquired simultaneously.In this study, we acquired OCT and wavefront measurements sequentially.After completion of wavefront measurements, the light source of the wavefront sensor is turned off and a dichroic mirror reflecting the OCT beam and transmitting the illumination from the fixation target is inserted to enable OCT image acquisition.This sequential approach was required because the wavefront sensor and OCT system use similar central wavelengths (830 nm and 840 nm) and the use of a conventional beam splitter to combine the system would produce excessive power losses.Wavefront and OCT images can be acquired simultaneously by choosing a longer wavelength for either OCT imaging or aberrometry with the appropriate dichroic mirror at the location of DM1 in Fig. 1.The optical radiation of both the OCT and autorefractor modules would need to be analyzed to ensure it is below the safety exposure levels during simultaneous use of both light sources.Alternatively, our group presented a single-beam implementation that enabled interlaced acquisition of dynamic OCT and wavefront data [44].
The speed of the ramp stimulus (0.25 D/s) was selected based on initial feasibility testing of a 31 year old subject.The subject's accommodative response was recorded to an 8 D ramp stimulus presented at seven different ramp speeds: 0.25, 0.50, 1, 2, 4, 6, and 8 D/s.We found that the gain (response to stimulus) was significantly lower at speeds above 1 D/s and that the highest accommodation was observed at 0.25 D/s.The 0.25 D/s ramp stimulus provided us with many sample points across the accommodative response that allowed us the sensitivity to evaluate the dynamic accommodative response.More extensive studies will need to be performed to evaluate the effect of stimulus speed on accommodative response, including any age-dependent relationship that may exist.Finally, the system design allows us to easily change the visual fixation target in order to study the psychophysical elements that contribute to accommodative response, such as aberrations, blur, spectrum, and contrast.
The latency of approximately 4 seconds that we observed before the accommodation or biometric values began to change corresponds to 1 D lag before an accommodative response is elicited, within the range observed when accommodation is assessed using subjective techniques [45,46].It may also be attributable to the removal of a number of cues for accommodation such as size, contrast, parallax, overlapping contours due to the Badal optics and the choice of target, as well as the lack of binocular cues such as retinal disparity.The removal of these cues is a limitation of the system.A more natural response would be produced with an open-field design that includes convergence.We purposefully chose a monocular stimulus that eliminates convergence to facilitate the quantitative analysis of the OCT images.Convergence would produce a tilt of the OCT images that would increase as the eye accommodates.This tilt would require the implementation of more complex distortion correction algorithms to accurately quantify ocular distances and the shape of the ocular surfaces.Although the monocular stimulus may alter the accommodative response (e.g., accommodative response versus demand), we expect that the relation between biometry and response (i.e., change in ocular power versus change in ocular dimensions) will not be affected significantly.
After this lag, the accommodative response in the 21, 27, and 31 year old subjects was 0.71, 0.79, 0.99 D/D, respectively.Our results for refractive change versus anterior chamber depth and lens thickness are consistent with prior studies.For instance, Ramasubramanian and Glasser [17] found on average −0.055 mm/D and 0.076 mm/D for anterior chamber depth and lens thickness, respectively, in a study on 26 young subjects.For these parameters we found an average change of -0.062 mm/D for anterior chamber depth and 0.070 mm/D for lens thickness [18], a difference on the order of 10% which may reflect in part the difference in sample size and age distribution.
We found that the response to different stimulus amplitudes is reproducible within each subject (Fig. 4), except for one response of the 21 year old to one of the 8 D stimuli.In general, the variability in the biometry reflects variability in the latency, which shifts the curves.During the accommodative phase, the slopes in mm/D or D/D are consistent across sessions for each subject.This observation reinforces the benefits of continuous dynamic recordings in reducing measurement variability by helping to focus the analysis on the linear phase of the responses.
We find a measurement variability of +/-0.032mm for anterior chamber depth, +/-0.028mm for lens thickness and +/-0.020mm for vitreous depth, quantified by calculating the RMS error between the data and the linear fit during the linear phase.This variability is within the typical precision of ocular biometry devices using OCT and comparable to the variability that we measured in prior studies at steady-state accommodation [47].This variability primarily reflects variability of the segmentation algorithm in detecting the ocular surface boundaries.It reflects the larger uncertainty in quantifying radius of curvature, particularly when surfaces are flatter.The use of a 3-D image acquisition and segmentation algorithm may help reduce the variability of the lens radii measurements.However, a higher imaging speed will be required for dynamic imaging in 3-D.
The combined system presented in this manuscript can dynamically measure the refraction and biometry changes that occur in accommodation.An effective accommodation restoration technique will need to be evaluated dynamically in natural accommodation [43].For instance, dynamic imaging studies of accommodating IOLs (aIOL) demonstrated the lack of interaction of the ciliary muscle with the aIOL to induce accommodation.Understanding the closed-feedback loop of natural accommodation will be required when measuring the effectiveness of restoration techniques that aim to use the existing ciliary muscle contraction and lens capsule anatomy to induce an optical change (laser and pharmaceutical lens softening).Understanding the direct relationship between optical power and biometric changes that occur in accommodation will provide insights to the mechanism of accommodation as well as an objective measure to evaluate emerging treatments of presbyopia.

Fig. 2 .
Fig. 2. Model eye calibration results.(left) correlation and (right) error of nominal versus measured sphere (D). in two steps.A first calibration curve was recorded with the lens of the eye model located at the estimated position of the focal plane of lens L1.This calibration curve was fitted with the theoretical paraxial formula relating stage position and eye model refraction, using the position error with respect to the reference plane as an additional fitting parameter.The value of the positioning error obtained from the fit was used to correct the position of the eye model.A final calibration curve was then recorded with the eye model positioned in the reference plane.
Intra-and intersession repeatability tests were performed on 3 human subjects to test reliability of the measurements within the same session and over multiple sessions.In an Institutional Review Board approved study, three subjects, ages 25, 31, 33 years with baseline spherical error of -9.50 D, 0.0 D, -3.75 D and cylinder of -0.75 D, -1.5 D, 0 D respectively were enrolled.
commercial autorefractor (RM-800, Topcon).Twenty-three eyes of 12 subjects (age: 21-70 years, mean: 36.1 years) were included.The subjects' baseline refraction measured with the commercial device at the spectacle plane ranged from -9.25 D to +2.25 D for sphere, with cylinder ranging from 0 D to 2.25 D. Both eyes of all subjects were measured without correction, except for one eye of one subject that did not meet inclusion criteria.Five measurements were acquired on each eye without cyclopegia with an acquisition speed of 20 Hz and a measurement pupil diameter set to 2 mm.

Fig. 4 .
Fig. 4. Accommodative response (ACC) (D), lens thickness (LT) (mm), anterior chamber depth (ACD) (mm), vitreous depth (VD) (mm), anterior lens curvature (ALR) (mm), and posterior lens curvature (PLR) (mm) versus time (s) of 21, 27, and 31 year old subjects to 2, 4, and 8 D ramp accommodation stimuli at 0.25 D/s.Vertical dotted lines indicate the start and end of the ramp stimuli as indicated in the legend.A representative run is shown for each subject.