1. Introduction

The optics of the eye initiate the visual process by the formation of an image on the retina. As in any optical apparatus, the wave aberration function at the exit pupil plane can be recovered to quantify its response to a point-source by the point spread function (PSF) at the image plane [1,2]. The eye as a nearly aplanatic biological optical system is prone to mismatches in ocular dimensions and affected by refractive errors that cause monochromatic aberrations which blur the retinal image. Other key components that impact visual quality include chromatic aberrations, scattering, or diffraction [3]. Adjusting a probe beam with high numerical aperture (NA) to the fully dilated pupil for high resolution retinal imaging will be affected by the aberrations of the eyeś imperfect optics preventing near-diffraction-limited resolution. With adaptive optics (AO), a technique adopted from astronomy to correct for the effects of atmospheric turbulence [4], wavefront error (WFE) detection and its correction have been implemented in the field of ocular imaging to overcome this limitation by improving the resolution required to visualize ocular pathologies at the cellular level [5]. In AO, incoming wavefronts are detected by a wavefront sensor (WFS) that communicates in a closed feedback loop with programmable liquid-crystal spatial phase modulators or deformable mirrors to correct for aberrations. The Shack-Hartmann wavefront sensor (SH-WFS) is the most widely used sensor, whereby a lenslet array samples the pupil field to generate a spot pattern at a sensor array plane positioned in the focal plane. The array registers spot displacements that are measures of the discrete local phase gradients of the incident wave [6,7].

Currently, optical coherence tomography (OCT) is the most successful diagnostic imaging modality in ophthalmology due to its ability to non-invasively generate in real time tissue cross-sections with micrometer resolution [8,9]. OCT as an interferometric technique has also lent itself for combined application with AO for 3-D in-vivo cellular isotropic resolution, by virtue of having axial resolution decoupled from transversal resolution—the former being only governed by spectral bandwidth and center wavelength of the light source [10]. Spectral domain OCT and recently also Swept source OCT (SS-OCT) has resulted in a paradigmatic shift in ocular imaging, owing to substantially increased imaging speed along with a marked increase in sensitivity [11]. This has paved the way for volumetric retinal imaging with high lateral resolution.

More recently, the possibility to obliviate the need for sensors by means of digital adaptive optics (DAO) has been a re-occurring topic of interest. As a coherent imaging technique, OCT intrinsically yields the full complex-valued signal of the light field including amplitude and phase information, similar to holography [12]. To enhance transverse resolution with DAO for imaging, different techniques such as the optimization of image sharpness metrics [13,14], the guide-star based approach [15], or the split-aperture DAO technique as a digital-scene- equivalent to SH-WFS [16] have been proposed. Recently, a guide star-based DAO algorithm for retinal imaging has been presented using a point scanning SS-OCT setup [17]. This technique uses a digital lateral shearing (DLS) technique to extract the WFE. DLS-DAO does not require a priori knowledge of the systems parameters and is independent of the intensity distribution at the image plane. Thereby, it has been shown that the WFE can be non-iteratively fitted with Zernike modes at a comparatively low computational burden.

The use of wavefront sensing to objectively assess ocular visual performance has also enabled researchers and clinicians to investigate monochromatic ocular lower and higher order aberrations (HOA), which has improved our understanding of the human eye [18–21]. At the turn of the millennium, ocular aberrometry was moved from laboratory into the clinics and came to be an essential technique for visual performance analysis, refractive surgery planning, assessing pathologies that affect the optical performance of the eye, or for wavefront-shaped customized intraocular lenses [22–24]. Consequently, although SH-WFS remains the most popular method, its commercialization has sparked several other hardware-based techniques such as ray tracing, the Tschernig approach, or automated retinoscopy.

In this work, a phase-sensitive single-mode fiber based point-scanning SS-OCT setup at a B-scan rate of >1 kHz is reconfigured in a de-scanning geometry to be employed for ocular optical coherence aberrometry (OCA) with the guide star-based DLS-DAO technique. Hereby, the ocular PSF field, including amplitude and phase information, is volumetrically de-scanned in a single pass configuration for DAO-based post-processing. By doing so, apart from being unaffected by the ambiguous localization from which retinal layer(s) the light is back-reflected from, this approach enables retinal image quality assessment along with digital WFE computation from the complex-valued PSF field. By virtue of having the ability to numerically refocus the in depth selected aberrated en face image in post-processing, this uniquely opens up the possibility to validify straightaway how close the computed WFE is to the ground-truth. We validate the approach first on a model eye showing defocus and astigmatism experiments. Subsequently we demonstrate in-vivo aberrometry on 2 subjects at a B-scan rate of >1 kHz in accordance with established standards for reporting ophthalmic aberrations.

2. Methods

2.1 Experimental setup

The schematic of the fiber-based SS-OCT setup in de-scanning configuration with a static illumination spot is shown in Fig. 1. An akinetic swept source laser (SSL) (Insight Photonic Solutions, Inc., Lafayette, Colorado, USA) at a center wavelength of λo = 1032 nm with an internal k-clock for linear k-space sampling is used. The SSL has an output power of 40 mW, a unidirectional sweep rate of 450 kHz, and a bandwidth of Δλ = 22 nm which translates to an axial resolution of δz = 22 µm in air. Additionally, a pupil camera is employed for pupil and illumination beam entry position alignment. A 50:50 fiber coupler is used to split light from the SSL into a separate illumination channel via fiber-coupled collimator C1 and the reference arm via fiber-coupled collimator C4. In the illumination channel, a narrow collimated coherent beam of 0.6 mm in diameter is directed via a 90/10 beam splitter (BS) (90% transmission; 10% reflection) into the eye (artificial/real) to diminish significant aberrations of the ocular optics and to serve as guide star. Based on the le Grand eye model [25], this translates to a theoretically ideal diffraction-limited focused spot of 37 µm diameter on the retina. Using a variable optical attenuator (VOA), the incident sample power measured at the pupil plane is set to 600 µW, which is well below the maximum permissible exposure (MPE) at λo = 1032 nm for a spot size of 37 µm according to the European laser safety standard [26]. The back-reflected light from the illuminated retinal spot area propagates through the ocular media and full pupil of the eye into the detection arm via the 90/10 BS. In the detection arm, the light first traverses the achromatic doublets L1 (f = 100) and L2 (f = 30) that form telescope T1. The telescope induces a ∼3.3-fold de-magnification preceding the two-axis galvanometric scanner (Cambridge Technologies) to avoid clipping by the 3 mm clear aperture size of the scanning mirrors. After passing through the galvo scanner, the light beam is re-magnified by the second telescope T2 (L3, f = 30; L4, f = 100) and focused on the tip of the single-mode detection fiber by the collimator C2 (f = 34 mm). In the reference arm, the light is first reflected by a reference mirror (RM) that can be displaced along the z-axis for coherence gate adjustment, before being coupled via collimator C3 into the single-mode fiber at the interferometer exit. The interference signal is detected by the dual balance detector (DBD) (PDB130C, Thorlabs Inc., NJ, USA).

 

Fig. 1. Schematic of the fiber-based SS OCT system configured for ocular aberrometry to generate a volumetric PSF scan. BS, beam splitter; C1-4, fiber-coupled collimators; DBD, dual-balance detector; FC, 50:50 fiber-coupler; PP, polarization paddles; RM, reference mirror, SSL, swept source laser at λ0 = 1032 nm; T1 and T2, telescopes; VOA, variable optical attenuator; XY GS, dual axis galvanometer scanner.

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2.2 Volumetric point spread function scanning

In previous work, we demonstrated wavefront error reconstruction and correction for a retinal OCT imaging system [27]. In that case, the sample arm was a double pass system (same illumination and detection path both affected by aberrations of the eye) and galvo scanners scanned the illumination beam across the retina. A photoreceptor, representing an approximate PSF within the imaged field-of-view (FOV), was selected as a guide star and subaperture-DAO was applied to calculate the WFE at the pupil plane. Note that in such setup the lateral OCT imaging PSF is the square of the single pass PSF, which also results in the pupil field being auto-convoluted [28]. Hence, the WFE obtained with this configuration does not represent the single pass WFE associated with ocular visual performance.

In this work, as illustrated in Fig. 2, the cardinal difference to a conventional OCT configuration is that the spot formed on retina by a narrow illumination beam via a separate channel is stationary, while its image representing the PSF is de-scanned at the detection fiber plane using XY galvo scanners. By having the pupil of the eye optically conjugated with the Fourier/focal plane of the collimator lens C2 that couples the back reflected light into the detection fiber in the sample arm, the focused illumination spot effectively renders the PSF of the eyeś optics assuming that the optical components of the sample arm introduce a negligible amount of optical aberrations. For an aberration free eye this translates to a width size of ∼74 µm at the detection fiber plane. The PSF profile is laterally translated by the GS over the single mode fiber tip with the mode field diameter of 5 µm. As the PSF is laterally de-scanned and sampled, the light that couples into the detection fiber is combined with the reference light from collimator C3 in the 50/50 coupler. To avoid phase wrapping and ambiguous velocity readings for DAO-based processing, motion-induced phase shifts should not exceed 2π for phase error estimation [29,30]. To remain within this unambiguous range and avoid phase decorrelation in post-processing, the basic premise hereby was to use a single-mode fiber SS OCT setup with a fast enough tomogram rate. This enables an adequate lateral correlation of the signal phase in order to assume that any phase difference between B-scans is solely due to in-vivo ocular bulk motion. A 3-D OCT dataset of $150(x )\times 150(y )\times 1024\; (k )$ voxels is generated at an effective B-scan rate of 1.5 kHz and a volume rate of 10 Hz. At that speed, any major lateral eye motion is avoided, and the bulk phase shift due to the axial motion of the eye can be numerically corrected. Since a true single pass configuration is not possible in the human eye, the low NA for the illumination path with an input beam diameter of 0.6 mm and the high NA for the detection path in the sample arm limited by the full pupil size of 6–7 mm are used to break the double-pass symmetry [31]. The narrow entrance pupil given by the narrow illumination beam creates unequal entrance and exit pupil sizes [32]. This effectively mimics the single pass commonly used in SH-WFS based aberrometry, by which the created guide star acts as an outcoming point source and yields the PSF that captures the ocular aberration only along the single pass [33]. The back-reflected retinal image is thereby volumetrically scanned with the galvo scanners. As the lateral 2-D raster scan of the PSF with the galvo scanner is complete, a 3-D OCT dataset of the ocular PSF is acquired. The detected interference signal with frequency (k) sweep of the SSL is subsequently digitized by a 12 Bit waveform digitizer (Alazartech Technologies, Inc., Canada, ATS9360) at a rate of 400 M samples/s excluding invalid data points of the akinetic laser sweep [34,35]. LabVIEW (National Instruments, Austin, TX) is used for signal recording, processing, and synchronization. A 1-D fast Fourier transform calculation along the spectral dimension (along wavenumber k) yields the complex-valued depth resolved volumetric PSF. Finally, an en face PSF slice is selected for post-processing.

 

Fig. 2. Simplified schematic of SS-OCT-based depth-resolved PSF scanning in a single pass configuration. Light from the SSL is split into the reference arm and a separate illumination channel. A narrow coherent pencil beam is projected and focused on the fovea to create a diffraction-limited guide star. The pupil plane of the eye is optically conjugated with the front Fourier plane of the single mode fiber detection plane. The back-reflected light passes through the full pupil of the eye into the interferometers’ sample arm. The two-axis galvanometer scanner laterally raster scans the ocular PSF across the detection fiber. OCT-based interferometry at the detection plane enables depth resolved complex-valued signal acquisition of the aberrated ocular PSF. For post-processing, an en face PSF slice is selected from the volume.

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2.3 Digital wavefront sensing

The WFE is computed offline in Matlab (MATLAB R2017b, The MathWorks Inc., Natick, MA, USA) by employing a non-iterative guide star-based DAO technique as a digital equivalent of lateral shearing of wavefronts (DLS-DAO) shown in Fig. 3. Equations and a comprehensive discussion regarding the sensitivity and dynamic range of DLS-DAO have been presented in previous work [17]. In brief, first a 2-D FFT of the selected complex valued en face aberrated PSF frame is calculated to obtain the pupil plane field data. Note, that in order to obtain a well delineated pupil without any aliasing, the sampling step size for the PSF profile along the lateral dimension should satisfy the Nyquist criterion, which ultimately depends on the size of the lateral FOV covering the PSF profile scanned by the galvo scanner and the number of pixels in the FOV. Digital replicas of the original pupil field are generated, which are shifted by a unit pixel along the lateral x and y dimension. Based on the pixel-by-pixel phase difference between the original and the laterally shifted digital copies of the pupil field, the per pixel slope of the WFE is computed. The unit pixel shift along lateral x and y dimensions provides the maximum detectable slope of the WFE along x and y, which also means the maximum dynamic range for WFE detection. Furthermore, the unit pixel shift yields the maximum number of slope data points within the pupil, which can provide a WFE map with slope data per pixel. At the unit pixel shift, the minimum detectable WFE slope that determines the sensitivity, is limited by the standard deviation of the phase noise. Once the slope data is generated, the WFE can be calculated based on modal or zonal reconstruction using Zernike polynomial fitting. Thereafter, the obtained phase error can be digitally phase conjugated with the pupil field of the aberrated PSF, which upon 2-D inverse FFT provides the aberration-free PSF field. The processing time of DLS-DAO (MATLAB on CPU @ 3.1 GHz, 16 GB RAM) to calculate the WFE from an en face PSF image of size 150 × 150 pixels with a pupil diameter size of 85 pixels is 0.17 seconds.

 

Fig. 3. Schematic of the DLS-DAO algorithm. The wavefront error is calculated from the aberrated complex-valued image field via digital lateral shearing of the computed pupil field.

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With the de-scanning configuration of the SS-OCT setup in this work, the narrow beam illumination of 0.6 mm forms a diffraction limited spot on the retina which acts as a pseudo point source or a guide star, and the back-reflected light passing through the full pupil of the eye is imaged at the detection fiber plane of the sample arm. The galvo scanner is positioned in the sample arm such that it receives only the outcoming light (single pass) and translates the image of the spot at the detection fiber plane, while the illuminated spot on the retina remains stationary. Thereby, the sampled single pass PSF pertains to the description of monochromatic ocular aberrations and refractive error computation. Lower order Zernike coefficients can be converted with known formulae [36,37] to refractive power vector form [M, J₀, J₄₅] from which the spherocylindrical refractive error can be computed as expressed in the Appendix A. Since an OCT setup is used to perform ocular aberrometry, it will be referred to as optical coherence aberrometry (OCA). For confirmatory proof of principle experiments, an artificial model eye, used to calibrate autorefractors, was employed [38]. It consists of an achromatic lens (focal length f = 32mm) with a curved shell that can be displaced along the optical axis to alter f, a switchable diaphragm wheel to select the pupil size (2 to 8 mm), as well as a diffusive layer serving as a synthetic retinal plane. A slot with axis orientation markings adjacent to its lens further accommodates trial lenses. The model eye was fixed on a kinematic platform mount, and the camera unit was employed to ensure proper placement along x-y-z of its optical axis with respect to the beam probe, whilst verifying that the two reflexes of front and back side of its lens were co-incidental to avoid tip/tilt. In a first step, OCA with the DLS-DAO algorithm was validated ex-vivo by introducing aberration and by numerically refocusing the original image. Repeatability and accuracy of the results was assessed. In a subsequent step, defocus was quantified by introducing in the trial lens slot adjacent to the model eyes’ entrance aperture spherical lenses of nominal diopter (D). They serve as aberrating plates at scaled ± 0.5 D in/decrements up to 3 D. For each of the introduced aberrations, volumes were acquired. The same procedure was performed with cylindrical lenses [39]: astigmatism was induced at scaled 0.5 D increments up to 3 D in line with the axis orientations of the slot at 90°, 0/180°, and 45/135°. Since orthogonal astigmatism was evaluated both vertically and horizontally, oblique astigmatism was evaluated twice, and volumes were acquired for each of the introduced aberrations.

To subsequently demonstrate the potential of the method, two healthy subjects were measured unilaterally on their right eyes in order retrieve the ocular WFE with corresponding standard deviations (SDs) across 3 consecutive measurements in comparison with a commercially available aberrometer.

3. Experimental results

3.1 Ex-vivo model eye

The pupil plane of the model eye (Skia/Retinoscope Trainer, Heine Optotechnik GmbH; Herrsching, Germany) was adjusted to be optically conjugated with the front Fourier plane of C2 that couples the light into the detection fiber. By steering the shell wheel of the model eye to continuously vary defocus, the broadening of the PSF width was visualized in real-time via the live B-scan (in x and z) to ensure proper positioning. At the focused position, a collimated Gaussian beam at λ_o = 1032 nm with 0.6 mm entrance pupil diameter translates to a calculated beam waist of ∼71 µm at the image plane. To confirm this experimentally, a volume was acquired at the focused position with a 6 mm aperture and was selected as the aberration-free baseline. In post-processing, the en face image of the layer corresponding to the synthetic retinal plane was selected. The residual root mean square wavefront error value calculated using DLS-DAO was 0.078 µm, which is very close to the Marechal’s criterion of 0.074 µm for a diffraction limited performance. Thereafter, for an initial confirmatory validation an arbitrary amount of mixed defocus and astigmatism was induced via ophthalmic trial lenses in the model eyeś slot. A second volume was acquired, and the induced aberration was refocused via the DLS-DAO algorithm. Figure 4(a) shows longitudinal B-scans of the focused PSF (left) matching the theoretical beam waist of ∼71 µm and the aberrated PSF (right) after introducing aberrating trial lenses, respectively. Figs. 4(b) and (c) show the aberrated en face image and the numerically corrected image at the depth indicated by the red arrow in (a), respectively. In Figs. 4(d) and (e) the corresponding estimated Zernike coefficients and phase error map are shown. Figure 4(f) shows radially averaged profile plots of the aberrated and numerically corrected PSFs of (b) and (c) and how they match that of the optically focused PSF. Figure 5 shows a profile plot of the reconstructed wave aberration error map indicating the average and standard deviations over 5 consecutive measurements for the model eye without realignment and a 6 mm aperture. The SD of ±0.03 µm demonstrates both a high repeatability as well as accuracy of WFE estimation.

 

Fig. 4. Procedure of WFE computation and numerical refocusing of the de-scanned aberrated ocular PSF. (a) Side-by-side longitudinal B-scans adjusted in depth of the focused PSF (left) and the aberrated PSF (right). The red arrow indicates the selected depth for post-processing. (b) Original aberrated en face image with combined defocus and astigmatism. (c) Numerically refocused image. (d) and (e) are Zernike coefficients and phase error map in microns, respectively. (f) Radially averaged profile of the PSF, with optical focus (dashed purple line) being matched after the aberrated PSF (red line) is numerically refocused (blue line). Scale bars indicate 50 µm.

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Fig. 5. Cross-section of the detected phase error map at the pupil plane of the model eye with a 6 mm aperture. Error bars are ± SD across 5 consecutive measurements.

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Measurements to evaluate the accuracy of sphere and cylinder error are shown over the range of theoretical input values as a defocus curve and an astigmatic double angle plot [J₀, J₄₅] [40] in Fig. 6(a) and Fig. 6(b), respectively. Figure 6(a) shows defocus on the x axis plotted against the nominal value on the y axis with correlation of R²= 0.9985 (y = 1.006x – 0.0065). Figure 6(b) shows astigmatic terms from the Zernike expansion plotted as a double-angle plot of astigmatic power vector components [J₀, J₄₅] with a correlation in measured magnitude across measurements for all meridians of R²= 0.9959 (y = 0.9959x – 0.0016). Figures 6(c), (d), (e), and (f), (g), (h) show exemplary en face PSFs, WFE maps, and digitally refocused PSFs for 3 D defocus and 1.5 D astigmatism, respectively.

The mean absolute discrepancies from nominal values across the measured dynamic range were 0.06 D and 0.05 D for sphere and cylinder, with the measurement error never exceeding 0.14 D. As seen in Fig. 5 the discrepancy between repeated measurements without realignment being lower and thus reflective of the instrument noise during the experiments, we can reasonably assume this to be the upper bound error and that the deviations are primarily attributable to manufacturing alterations of ophthalmic trial lenses.

 

Fig. 6. (a) Defocus curve at scaled 0.5 D increments from −3.0 to +3.0 D. (b) Double angle plot (J₀ and J₄₅) of induced astigmatism at 90°, 45/135°and 0/180°. Each circle represents 0.5 D. Inner ring: 0.5 D; Outer ring: 3 D. (c), (d) and (e) are the blurring of an en-face PSF with an induced defocus of 3 D sphere error, the corresponding WFE map in µm, and the refocused en-face PSF, respectively. (f), (g), and (h) are the smearing of an en-face PSF in concordance with the magnitude and axis orientation of the induced refractive astigmatism error of 1.5 D at 45/135°, the corresponding WFE map, and the refocused en-face PSF, respectively. Scale bars indicate 50 µm.

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The sensitivity and dynamic range of OCA is inevitably dependent on the shot noise limited performance of the system in use. Therefore, the signal to noise ratio (SNR) as a function of induced refractive error was evaluated.

Figure 7(a) and (b) show the loss in SNR with increasing level of sphere and cylinder error, respectively. Although currently limited by the phase noise and rather small FOV, by virtue of being able to reliably detect the PSF and the phase error properly for a SNR >20 dB, we were still able to demonstrate a dynamic range of −3 to +3 D for defocus and 3 D in magnitude for astigmatism with unaveraged data without dynamic refocusing. It is worth noting that the loss for cylinder error had an earlier flattening of the curve than for sphere error, whereby from 0.5 to 3 D the former had a less pronounced SNR drop (∼9 dB). Since from thereon the astigmatic smearing of the PSF would exceed the chosen FOV, we empirically increased it to $200(x )\times 200(y )$ for an additional measurement with a 4 D cylinder trial lens. Figs. 7(c), (d), and (e) show the smeared en-face PSF, the WFE map, and the refocused en-face PSF, respectively. While no longer the case for defocus, the cylinder error SNR in this case was still above 20 dB (∼21 dB). Converted to cylinder error with negative annotation, the estimated cylinder error was −3.96 D. This quantitatively demonstrates that if we expand the FOV at the expense of the rapid B-scan rate that in-vivo DAO requires, an even higher astigmatism dynamic range is possible.

 

Fig. 7. SNR loss as a function of induced refractive error. (a) and (b) are the SNR loss of sphere (red) and astigmatism error (blue) in 0.5 D steps. (c) is the en face PSF for an induced cylinder of 4 D after having extended the FOV to 200(x) × 200(y). (d) and (e) are respectively the corresponding WFE map in µm and the digitally refocused PSF yielding an estimated cylinder error of −3.96 D. Scale bars indicate 50 µm.

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3.2 In vivo ocular aberrometry

For a pilot proof of principle, 2 healthy subjects with low refractive error were studied unilaterally on their right eyes after explaining the nature and purpose of the experiments: subject (A) (ER, female, 32 years old, −1.25 D sphere), and subject (B) (MN, male, 32 years old, −0.75 D sphere, – 1 D astigmatism). In-vivo measurements were performed in accordance with the protocols approved by the ethics committee of the Medical University of Vienna. Measurements with the experimentally modified setup were compared with a commercially available aberrometer (Discovery System; Innovative Visual Systems, Elmhurst, Illinois), which uses a super luminescent diode (SLD) source (λ_o = 830 nm) and a digital Hartmann-screen for wavefront sensing (H-WFS). The aberrometer enables the direct export of aberration data for research/analysis purposes and has been validated in comparison with autorefractometry, internal wavefront aberrometry, as well as within the framework of cataract surgery [41–43]. By virtue of being able to directly export Zernike coefficients from the systemś software (v. 1.63), the H-WFS served as a validating reference. Aberrometry with the H-WFS was performed unilaterally in the same dark ambient room as the OCT setup by one operator under uniform conditions. After pharmacologically induced mydriasis (tropicamide 0.5%, Mydriaticum, Agepha), the subjects were positioned on the aberrometers head-mount and were instructed to fixate on the internal fixation target while keeping their eyes wide open during the measurement procedure. Three consecutive measurements were performed by instructing volunteers to blink twice before each measurement to avoid tear-film break up. Subsequently, aberrometric data was extracted from the H-WFŚ software scaled to the wavelength of 555 nm to account for longitudinal chromatic aberration and match the relative photopic spectral sensitivity peak of the human eye.

 

Fig. 8. B-scan of PRL and NFL layer of subject (A).

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For the measurement procedure with the experimental SS-OCA system, subjects were first instructed to familiarize and adequately position themselves with their chin and forehead on a three-axis head-mount. As recommended by the ANSI standard for reporting ocular aberrations (Z80.28), the beam was referenced to the entrance pupil center (line from fixation at infinity in object space to the center of the entrance pupil, and the center of the exit pupil to the foveal point of fixation). After activating the voltage for the SSL and the galvo scanner, the same operator ensured via the camera unit that the pupil was properly centered, and the adequate positioning of each subject’s eye was reconfirmed by direct visualization of the live B-scan. The remaining measurement procedure was analogous to the one with the clinical aberrometer. Figure 8 shows that with the axial resolution of the setup, depth resolved interferometric full complex-valued signal acquisition of the PSF was obtained from the nerve fiber layer (NFL) and the photoreceptor layer (PRL).

Succeeding standard in-vivo OCT post-processing analogous to the ex-vivo experiments in section 3.1, bulk phase correction was performed as outlined by Shemonski et al. to correct the axial ocular bulk motion [44]. For each of the subjects, the en face PSF corresponding to the PRL was selected as being close to the presumed subjective focal plane of the eye (plane of vision) for post-processing. To compare both instruments, the 4^th Zernike polynomial order was chosen as the cut-off value to extract the ocular WFE map (excluding piston and tilt) for the largest common pupil size in each of the subjects, and adjusted for chromatic defocus for the operating wavelength of 1032 nm [45].

We observed a mean loss of ∼12 dB for in-vivo measurements compared to the static model eye, which we attribute to the lower reflectivity of the human retina combined with residual head movements. Nevertheless, for the chosen sampling step size and FOV, we were able to represent ocular aberrations over a pupil with an average diameter of ∼86 pixels which corresponds to ∼4.7 mm with >5000 generated local slope data samples. Figure 9(a) shows the comparison for an ametropic subject (A) for a 4.7 mm pupil with predominantly myopic defocus as seen in the more focused PSF for the infrared wavelength and the corresponding WFE maps for H-WFS and SS-OCA, respectively. Figure 9(b) shows measurements performed on a myopic subject with a clinically relevant amount of astigmatism (B) for a 4.9 mm pupil. Figs. 9(c) and (d) show correspondingly the mean value of Zernike coefficients with SDs of 3 consecutive measurements in each subject for both devices. For subject (A) the estimated Zernike coefficients of lower order aberrations are in concordance with an offset for Zernike coefficients for the 3^rd and 4^th order between both instruments. Converted to spherical equivalent error (M) for the quasi exclusively myopic subject, the averaged values were −1.68 D and −1.48 D for H-WFS and SS-OCA, respectively. For subject (B) Zernike bar graphs for $Z_2^0,Z_2^{ - 2}$ and $Z_2^2$ are matching, with an offset for $Z_3^1$ and $Z_4^0$. Converted to sphero-cylinder prescription form for this subject with a moderate amount of astigmatism, the averaged values were −1.00 D S, −1.01 D C @ 113° and −0.96 D S, −0.99 D C @ 113° for H-WFS and SS-OCA, respectively. Figs. 9(e) and (f) show the normalized profile plots of the PSFs, whereby after DLS-DAO-based refocusing the profile matches closely with the theoretical diffraction limit of 37 µm spot size for each of the subjects.

 

Fig. 9. In-vivo aberrometry with H-WFS (yellow margins) and SS-OCA (blue margins) on subjects A and B. (a) and (b) are a side-by-side comparison of H-WFS spot diagrams (upper left) with corresponding WFE maps in µm (middle left), and unaveraged en-face PSF images matched in orientation (upper-right), corresponding WFE maps in µm (middle right), and the refocused PSF (bottom right) for each subject, respectively. Scale bars for the scanned PSFs indicate 50 microns. (c) and (d) are Zernike bar graphs (OSA standard) plotted by clinical convention with modes on the x axis against coefficient magnitude on y axis through the 4^th radial order. Yellow and blue bars indicate estimated referential H-WFS and SS-OCA values, respectively. Vertical black bars on top of Zernike coefficient magnitude indicate SD. (e) and (f) are radially averaged profile plots of the scanned PSFs before (red) and after correction (blue) for subjects A and B, respectively.

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4. Discussion and conclusion

The feasibility of the sub-aperture DAO algorithm has been recently demonstrated for in vivo 3-D retinal cellular-level resolution of human cone photoreceptors with a line-field OCT setup [16,29]. More recently, guide-star based DLS-DAO for point-scanning SS-OCT has shown to be within the Marechaĺs criterion of a diffraction-limited performance for >12^th order wavefront errors, yielding an adequate computational speed for a 512×512-pixel image (>260 k slope data points) for a 6^th order Zernike fit, which was experimentally substantiated in terms of resolution and SNR enhancement of image quality [17]. This paper demonstrates the proof of principle how a SS-OCT setup can be modified to perform ocular aberrometry by employing the guide star-based DLS-DAO technique. In section 3.1 ex-vivo lower order aberration estimation was assessed, whereby Fig. 6(a) and Fig. 6(b) show well-corresponding defocus and astigmatism values with linear regression correlation coefficients of above 0.99 and slopes close to 1. Although we currently limited ourselves to a rather small FOV, by virtue of being able to reliably detect the PSF and the phase error for a SNR >20 dB, a dynamic range of ±3 D for defocus and 3 D for astigmatism with unaveraged data without dynamic refocusing could be demonstrated as seen in Figs. 7(a) and (b). By extending the FOV at the expense of the effective B-scan rate, the accuracy of WFE estimation for 4 D astigmatism was also substantiated as seen in Figs. 7(c), (d), and (e).

In section 3.2 in-vivo SS-OCA via DLS-DAO was compared with a commercially available aberrometer. The representation of ocular aberrations for a 4.7 mm pupil field generated >5000 local slope data samples and provided a resolution that is serviceable for the digital description of ocular aberrations. It is worth highlighting that while we were able to reproducibly detect 2^nd order aberrations in concordance with referential H-WFS values and did not detect spurious HOA, we did not empirically evaluate the latter as is the case for factory calibrated aberrometers. The offset in HOA Zernike terms for the 2 measured subjects is most likely due to a loss in SNR with the current configuration, speckle noise, and/or the impact of motion which can corrupt the measured phase. This would call for a state-of-the-art calibration and forthcoming investigations to measure repeatedly their accuracy, since the 6^th polynomial order is canonically deemed to be sufficient for the description of all meaningful ocular aberrations [46].

Generally, ocular aberrometry as a technique is influenced by several factors that can affect its precision. For the presented approach these would include a) residual aberrations present in the system, b) the phase jitter of the system as seen in Fig. 5 which ultimately can be affected by vibrations of the optical components, c) the residual chromatic aberration uncertainty interval by the bandwidth of the SSL, d) the error in DAO-based WFE estimation in post-processing, and as mentioned earlier, e) speckle noise. Factors a) and b) can be addressed with a calibration procedure and factory-based mounting for future experiments. For factor c), the chromatic focus difference of the spectral width in the infrared range is known to be considerably smaller than the same spectral width in the visible range [45]. With respect to the defocus uncertainty introduced by the finite bandwidth of the SSL (Δλ = 22 nm at a center wavelength of 1032 nm) employed in our experiments, this can be considered very modest for in vivo aberrometry as it is below published data of the already minor longitudinal chromatic aberration inter-subject variability (<0.10 D) [47]. Nevertheless, careful experimental investigations with depth resolved PSF scanning at infrared wavelength in relation to psychophysical assessments would warrant future investigations. The reason being is that conventional aberrometry measuring at near infrared or infrared, accounts for the stronger reflection from deeper retinal layers with a fixed offset to shift the plane of reflection to the subjective focal plane [48]. This is necessary to account for the uncertainty interval by the diffusion in the choroid, whereas with the proposed method in this paper, we select the retinal layer of interest in depth from the volume to compute the ocular WFE. We expect factor d) to be of minor significance, as the DAO algorithm employed in this work has shown to yield a negligible residual root mean square WFE standard deviation for retinal imaging throughout the range of aberration orders relevant for clinical aberrometry [17]. Lastly, factor e) would need to be addressed by employing a suitable averaging scheme. While the computation of 2^nd order terms was possible in the 2 measured subjects, the en face PSF image fields and the calculated pupil fields were affected by speckle noise as seen in sections 3.1 and 3.2 of the results. Note, that technical specifications/methods for speckle reduction such as low pass filtering and incoherent averaging employed by commercial aberrometry techniques [49] affect the phase of the signal and may not be suitable for DAO-based processing. Although the use of coherent averaging may be employed to enhance the SNR, it has shown to have little effect on speckle reduction [50]. Therefore, an averaging scheme to mitigate speckle noise that can preserve the phase of the signal needs to be investigated in the future, for example by averaging slope data derived via DAO from consecutively acquired PSF volumes.

Another influence to be considered when it comes to more aberrant PSFs, is the drop in SNR for measurement precision. This can be however relaxed by pre-compensating part of the defocus error, which common commercial aberrometer employ to remove a defocus offset before the aberrated wave enters the sensor. Nevertheless, based on our experiments, currently the main limiting factor for the dynamic range is the small FOV. This is due to the limitation imposed by the phase stability required to enable a high-volume rate for in vivo measurements, which in turn is limited by a) the sweep rate of the SSL in use and b) the galvo scanner frequency. Because the dynamic range with unaveraged data and the setup and power on the sample in use will be currently more limited under in-vivo conditions, future steps could involve the implementation of foveal tracking to not only potentially diminish measurement variability, but to also consolidate vision on the line of sight for reliable averaging and increasing of SNR. With DAO not presupposing a priori knowledge of system parameters such as focus distance, wavelength, or refractive index, it could in principle be applied in any phase sensitive point scanning or full and line field interferometric system. Therefore, the use of a faster SSL with an A-scan rate of >1 MHz [51] along with scanning mirrors at higher frequency could be contemplated in the future, in order to increase the FOV. This could improve the dynamic range and facilitate phase stability for subjects with stronger ocular motion.

Some additional limitations of our experiments are worth mentioning. First, ensuring the exact axial location of each eyeś pupil plane at micrometer precision would require an additional auxiliary system, since pupil plane alignment and vertex distance considerations can become important for eyes with higher WFEs than the ones studied in our experiments. Second, while a camera was used to monitor the centration of the incoming beam probe, an established automated pupil centering algorithm should be preferably utilized for in-vivo measurements with respect to lateral and/or angular pupil positioning. Third, although we chose the SSL for its rapid sweep rate, establishing an optimal trade-off between bandwidth of the SSL and chromatic defocus interval could be desirable, as depth resolved PSF scanning could further benefit from a light source with a broader bandwidth to consistently obtain the signal from different retinal layers. These aforementioned considerations would need to be addressed, in order to enable a rigorous examination akin to commercially available devices [52]. Nevertheless, we experimentally demonstrate the feasibility of the technique as seen in Fig. 9, whereby for the two measured subjects the outcome of the presented method was substantiated via numerical refocusing, which prompted the retrieval of the respective corrected images. Moreover, for the computed refractive values, the difference between SS-OCA and the referential H-WFS are within published 95% limits of agreement of the latter [41], as well as within the accuracy that subjective refraction can be measured (<0.25 D).

In general, one of the reasons as to why direct wavefront sensors such as SH-WFS have gained widespread and continuous use in vision science and ophthalmology [53,54], is that they circumvent elaborate phase retrieval algorithms and obliviate the need for a reference arm or phase stability. With OCT being firmly established as the most successful imaging modality in ophthalmology, future developments of ocular aberrometry via DAO can be insofar interesting, because it offers the ability to select in depth the aberrated ocular PSF from the retinal layer of interest. This could improve our understanding how the optics of the eye initiate the visual process. Whereas pupil plane metrics remain to be yet fully established in everyday clinical practice, it has been shown how optimized image computations with neural weighting are superior predictors for visual quality [55,56], and along with convolved Snellen optotypes, usually also intrinsically intuitive for both patients and clinical personnel. In clinical ophthalmology, and in particular for procedures aiming at altering the refractive state of the eye, the clinicians’ goal is ultimately to improve/restore the quality of the retinal image. One potential advantage of the proposed approach is that it does not require center of mass algorithms, nor does it exclusively rely on the pupil field to compute the retinal image. When it comes to computing the ocular WFE with current methods, one reoccurring topic of discussion is the mutual orthogonality between low and higher order modes of the Zernike polynomial decomposition—adapted from optical metrology for clinical ophthalmology—as it has shown to fail modelling all the information that influences ocular visual performance in more aberrant eyes [57]. Being associated with an unpredictable loss of visually significant information with erroneous retinal image and contrast sensitivity predictions, alternative polynomial decompositions for ocular wavefront analysis have recently been proposed [58]. The ability to validate straightaway how well the aberrated image can be numerically refocused to the diffraction limit could therefore enable the assessment how different WFE reconstruction methods relate to the ground truth. Moreover, with the increased use of presbyopia-correcting intraocular lenses based on optical technologies associated with postoperative photic phenomena, the presented approach could also call for potential future investigations [59]. In this growing class of patients, these lenses often employ optics that induce discontinuous phase profiles and pose a challenge to spatially sample the optical field at the exit pupil [60]. This makes the utility of reliable ocular aberrometry and improved wavefront acquisition currently more pertinent [61]. With the technique presented in this paper we have immediate depth resolved access to the PSF including amplitude and phase information, and show with a modified SS-OCT setup as to how the ocular wave aberration can be retrieved via DAO instead of vice-versa [62–64].

In summary, we show in this paper for the first time to our knowledge, how an optical coherence tomography setup can be modified to perform ocular aberrometry by non-iteratively computing the wave aberration from the de-scanned PSF in the image plane. Except for an additional collimator and beam-splitter no additional hardware was implemented, nor did digital adaptive optics cause significant computational burden for the description of ocular aberrations. Since the limitations of our setup in its current state are in part related to the seamless reconfiguration from retinal imaging to ocular aberrometry, future investigations will involve the enhancement of phase stability along with a state-of-the-art calibration and the implementation of additional components typically employed for ocular wavefront sensing.