October 2024
Volume 65, Issue 12
Open Access
Retina  |   October 2024
Critical Impact of Working Distance on OCT Imaging: Correction of Optical Distortion and Its Effects on Measuring Retinal Curvature
Author Affiliations & Notes
  • Yong Woo Kim
    Department of Ophthalmology and Visual Sciences, Dalhousie University and Nova Scotia Health, Halifax, Nova Scotia, Canada
  • Glen P. Sharpe
    Department of Ophthalmology and Visual Sciences, Dalhousie University and Nova Scotia Health, Halifax, Nova Scotia, Canada
  • Julia Siber
    Heidelberg Engineering GmbH, Heidelberg, Germany
  • Ralf Keßler
    Heidelberg Engineering GmbH, Heidelberg, Germany
  • Jörg Fischer
    Heidelberg Engineering GmbH, Heidelberg, Germany
  • Tilman Otto
    Heidelberg Engineering GmbH, Heidelberg, Germany
  • Balwantray C. Chauhan
    Department of Ophthalmology and Visual Sciences, Dalhousie University and Nova Scotia Health, Halifax, Nova Scotia, Canada
  • Correspondence: Balwantray C. Chauhan, Department of Ophthalmology and Visual Sciences, Dalhousie University, 2W Victoria, Room 2035, 1276 South Park St., Halifax, NS B3H 2Y9, Canada; bal@dal.ca
Investigative Ophthalmology & Visual Science October 2024, Vol.65, 10. doi:https://doi.org/10.1167/iovs.65.12.10
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      Yong Woo Kim, Glen P. Sharpe, Julia Siber, Ralf Keßler, Jörg Fischer, Tilman Otto, Balwantray C. Chauhan; Critical Impact of Working Distance on OCT Imaging: Correction of Optical Distortion and Its Effects on Measuring Retinal Curvature. Invest. Ophthalmol. Vis. Sci. 2024;65(12):10. https://doi.org/10.1167/iovs.65.12.10.

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      © ARVO (1962-2015); The Authors (2016-present)

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Abstract

Purpose: To assess the impact of working distance (WD) on optical distortion in optical coherence tomography (OCT) imaging and to evaluate the effectiveness of optical distortion correction in achieving consistent retinal Bruch's membrane (BM) layer curvature, regardless of variations in WD.

Methods: Ten subjects underwent OCT imaging with four serial macular volume scans, each employing distinct WD settings adjusted by balancing the sample and reference arm of the OCT interferometer (eye length settings changed). Either of two types of 30° standard objectives (SOs) was used. A ray tracing model was used to correct optical distortion, and BM layer curvature (represented as the second derivative of the curve) was measured. Linear mixed effects (LME) modeling was used to analyze factors associated with BM layer curvature, both before and after distortion correction.

Results: WD exhibited significant associations with axial length (β = −1.35, P < 0.001), SO type (P < 0.001), and eye length settings (P < 0.001). After optical distortion correction, the mean ± SD BM layer curvature significantly increased from 16.80 ± 10.08 µm–1 to 49.31 ± 7.50 µm–1 (P < 0.001). The LME model showed a significant positive association between BM layer curvature and WD (β = 1.94, P < 0.001). After distortion correction, the percentage change in BM layer curvature due to a 1-mm WD alteration decreased from 9.75% to 0.25%.

Conclusions: Correcting optical distortion in OCT imaging significantly mitigates the influence of WD on BM layer curvature, enabling a more accurate analysis of posterior eye morphology, especially when variations in WD are unavoidable.

Optical coherence tomography (OCT) is a transformative technology offering high-resolution, three-dimensional imaging of the retina and optic nerve head (ONH). OCT has become a valuable tool for identifying and tracking morphological changes in the retina and ONH associated with a wide range of ocular diseases. Researchers have recently begun to use OCT to measure the curvature of retinal layers, sclera, or lamina cribrosa (LC) to gain insights into morphological alterations in diseases such as glaucoma,14 pathological myopia,57 and retinitis pigmentosa (RP).8,9 LC curvature indices have shown promise as diagnostic tools for differentiating between glaucoma and non-glaucomatous optic neuropathies, as well as for distinguishing glaucoma eyes from healthy eyes.10,11 In highly myopic eyes, perineural canal scleral bowing is increased with axial length compared to control eyes.12 In non–highly myopic RP eyes, the steepness of macular curvature has been associated with the degree of photoreceptor degeneration.8 
Despite its many benefits, the accuracy of OCT imaging can be compromised by distortions that affect the precise representation of eyeball shape. One source of distortion lies in the presentation format of A-scans in OCT, which results in a rectangular display of B-scans.13 Unlike ultrasonography, where A-scans conform to a fan shape consistent with the scanning pattern, OCT presents fan-shaped A-scan beams in a rectangular format. In addition, the optical path length (OPL) of the OCT beams through the eye can vary according to working distance (WD), the distance between the apex of the front lens of the OCT standard objective (SO) and the apex of the cornea.14 This leads to alterations in the morphology of B-scans that impact the precision of curvature analysis. Therefore, it is crucial to correct for inherent optical distortions to ensure accurate morphological analysis of the retina. 
We posited that the distortion of OCT B-scans is dependent on WD and that correcting the optical distortion effect results in a constant retinal curvature, regardless of varying WDs. To test this hypothesis, we acquired a series of OCT scans from single subjects and systematically varied the WD. The objective of our study was to determine the impact of WD on optical distortion and retinal morphology of B-scans and to evaluate whether our optical distortion correction algorithm could produce a constant retinal curvature. 
Methods
The present study involved participants who were selected from a longitudinal observational study conducted at the Eye Care Centre of Nova Scotia Health in Halifax, Nova Scotia, Canada. The study adhered to the tenets of the Declaration of Helsinki and was approved by the Nova Scotia Health Ethics Review Board. All participants met the eligibility criteria and provided written consent to participate in the study. Only the right eye of each participant was selected for analysis. 
Study Participants
The study included participants with open-angle glaucoma and healthy individuals. Glaucoma patients had evidence of progressive ONH changes, as well as a positive glaucoma hemifield test (GHT) based on standard automated perimetry using the 24-2 Swedish Interactive Thresholding Algorithm (SITA) program with the Humphrey Field Analyzer (Carl Zeiss Meditec, Dublin, CA, USA). Healthy subjects had a normal eye examination, intraocular pressure below 21 mmHg, and GHT within normal limits. Eyes in either group with refractive error exceeding ±6.00 diopter (D) sphere or ±3.00 D astigmatism were excluded from the study. 
OCT Imaging
The macula was imaged using real-time eye tracking to stabilize the image (SPECTRALIS OCT2; Heidelberg Engineering, Heidelberg, Germany). A raster pattern that spanned 30° horizontally and 25° vertically was used, consisting of 61 horizontal B-scans, each containing 768 A-scans that were averaged nine times (PPoleH, Glaucoma Module Premium Edition software; Heidelberg Engineering). Images were acquired with reference to the fovea to Bruch's membrane opening center (FoBMO) axis with an imaging acquisition protocol (Anatomic Positioning System; Heidelberg Engineering) with which two anatomical landmarks—namely, the fovea and BMO center—are first identified. Four BMO points, 90° apart, were identified and verified by the operator, after which all scans were acquired with reference to the subjects’ own FoBMO axis.15 The corneal curvature and axial length were measured by biometry (IOLMaster; Carl Zeiss Meditec) with the former entered into the SPECTRALIS prior to imaging. 
To obtain B-scan images at different WDs, the macula was scanned serially using four different WDs. The WD was adjusted as follows: The length of the reference arm was changed, by selecting different eye length settings in the acquisition software (short, medium, long, or extra-long). To rebalance the OCT interferometer, the length of the sample arm was then manually adjusted by moving the camera head farther from the eye, thus increasing the WD for longer reference arm settings. If the OCT image of the retina appeared at the same z-position within the OCT frame, the WD was increased exactly by 2.5 mm, which corresponds to the eye length step size in air (nair = 1.00). Because the accuracy of the manual adjustment is usually not perfect, differences in the z-position of the retina (e.g., position of the BM layer at the fovea) within the OCT frames were considered (see Supplementary Fig. S1; further elaboration is provided in the following section). 
With the release of the multicolor imaging mode, the SPECTRALIS was equipped with a modified front lens assembly (standard objective lens 2 [SO2]), which has the same field of view (30°) and highly similar optical properties as the original lens assembly (standard objective lens 1 [SO1]). The purpose of this modification was to improve the confocal suppression of image artifacts due to lens reflections. Although the axial optical resolution in OCT systems is independent of the refractive properties of the focusing lens,16,17 the OPL difference between axial and peripheral beams within a B-scan could be different for the two front lens assemblies and thus introduce slightly different distortions on the apparent retinal curvature. Therefore, the impact of the objective lens (SO2 vs. SO1) was also a subject of this study. 
Equation for OPL Differences
In OCT imaging, the OPL difference (ΔOPL) between an object and a reference arm is measured. The OCT image is displayed within a frame where the upper edge aligns with the OPL of the reflecting mirror in the reference arm, meaning ΔOPL = 0. In normal OCT imaging, such as in non–enhanced depth imaging mode, the plane at ΔOPL = 0 is typically positioned in the vitreous, just in front of the internal limiting membrane, which marks the transition from vitreous to retina. The modulation frequency of the interference signal between the reference arm and the backscattering tissue structure determines the corresponding ΔOPL, which is then converted to geometric distance (GD) by dividing it by the refractive index of the retina (nretina). For the SPECTRALIS software, a refractive index of nretina = 1.36 is assumed, resulting in a specific geometric pixel scaling factor (sf; digital resolution) of sf = 3.87 µm/px. Therefore, the following Equation 1 was established for OCT imaging:  
\begin{eqnarray} OP{L_{TS}} = OP{L_{RA}} + ZPO{S_{TS}}\quad \end{eqnarray}
(1)
 
In Equation 1, OPLTS denotes the OPL within the sample arm from the beam-splitting surface of the interferometer to the position of the backscattering tissue structure (TS). OPLRA refers to the OPL of the reference arm, from the beam-splitting surface of the interferometer to the reflecting mirror in the reference arm. ZPOSTS represents the OPL difference from the virtual position of the reference arm to the backscattering structure visible in the OCT frame. 
The value for ZPOSTS can be determined by measuring the GD from the tissue structure to the upper limit of the frame using the software caliper within the SPECTRALIS viewing module or by calculating the corresponding number of pixels with a standard software tool. To accurately determine this value, it is important to account for the first 16 pixels that are not displayed and saved in SPECTRALIS images due to artifacts from the DC term in the OCT signal intensity expression. These 16 “hidden pixels” contribute to an additional OPL of hPx = #px × sf × nretina = 16 px × 3.87 µm/px × 1.36 = 84.2 µm. Therefore, in Equation 2, ZPOSTS is calculated as  
\begin{eqnarray} ZPO{S_{TS}} = ZPO{S_{BM}} + hPx = G{D_{BM}} \times {n_{retina}} + hPx\quad \end{eqnarray}
(2)
Here, GDBM represents the GD from BM to the upper edge of the OCT frame, calculated as GDBM = #px × sf. Thus, one can establish Equation 3 for the OPL of BM at the fovea:  
\begin{eqnarray} OP{L_{SA,BM}} = OP{L_{RA}} + hPX + ZPO{S_{BM}}\quad \end{eqnarray}
(3)
Equation 3 specifies the OPL of BM at the fovea, incorporating the contribution from hidden pixels and the geometric distance to BM. 
Determining the Working Distance
The WD is defined as the distance between the apex of the SO lens and the apex of the cornea. If the axial length of the examined eye is known, the WD can be determined by comparing the settings of the two interferometer arms and the z-position of the scan within the OCT frame. This is deduced by the following equations. Equation 4 represents the OPL of the sample arm until the BM:  
\begin{eqnarray} OP{L_{SA,BM}} = OP{L_{SA\_cam}} + \Delta OP{L_{refraction}} + WD + OP{L_{eye}}\quad \end{eqnarray}
(4)
 
In this equation, OPLSA_cam is the OPL of the sample arm inside the camera to the apex of the front lens at 0 D, ∆OPLrefraction is the OPL change for the refraction setting, WD is the working distance, and OPLeye is the OPL within the eye from the corneal apex to BM. This refers to the axial length of the eye (from biometry) multiplied by the mean refractive index of ocular tissue, which is 1.336. Because the vitreous represents the largest tissue structure within the eyeball and the refractive indices of the cornea and anterior chamber deviate only slightly from this value, the mean refractive index of ocular tissue was assumed to be that of the vitreous. 
The OPL of the reference arm can be calculated using Equation 5:  
\begin{eqnarray} OP{L_{RA}} = OP{L_{RA\_max}} - Po{s_{RM}}\quad \end{eqnarray}
(5)
In this equation, OPLRA is the OPL of the total reference arm, OPLRA_max is the maximum OPL of the reference arm, and PosRM is the subtracted OPL to obtain the actual length of the reference arm due to the motorized adjustment of the reference arm length. This value is part of the saved metadata of the OCT images. 
By inserting Equations 4 and 5 into Equation 3, we obtain Equation 6:  
\begin{eqnarray} \begin{array}{@{}l@{}} OP{L_{SA\_cam}} + \Delta OP{L_{refraction}} + WD{\rm{\ }} + OP{L_{eye}}\\ = OP{L_{RA\_max}} - {\rm{\ }}Po{s_{RM}} + hPX + Po{s_{BM}} \end{array}\quad \end{eqnarray}
(6)
This can be rearranged to obtain an expression for the WD:  
\begin{eqnarray*} {\rm{WD}} = OP{L_{RA\_max}} - Po{s_{RM}} + hPX + Po{s_{BM}} \\ -\, OP{L_{S{A_{cam}}}} - \Delta OP{L_{refraction}} - OP{L_{eye}} \end{eqnarray*}
We define the SPECTRALIS specific parameter \(X = OP{L_{RA\_max}} - OP{L_{S{A_{cam}}}} + hPX\), and we obtain Equation 7:  
\begin{eqnarray} {\rm{WD}} = X - \Delta OP{L_{refraction}} - OP\ {L_{eye}} - Po{s_{RM}} + Po{s_{BM}} \end{eqnarray}
(7)
 
The values for X are XSO1 = 70.87 mm and XSO2 = 68.71 mm and were provided for this study by Heidelberg Engineering from computer-aided design (CAD) and optical design data. In Supplementary Figure S1, we propose a method to determine the WD independently by measuring the ΔOPL between the reference arm (OPLRA) and the sample arm within the camera (\(OP{L_{S{A_{cam}}}}\)) using a simple tool mounted to the SPECTRALIS objective. 
Estimating the Equal OPL Curvature and B-Scan Correction
The beam propagation in the scanning sample arm was characterized through a ray tracing model simulated using optical design software (OpticStudio; Ansys, Canonsburg, PA, USA). In the simulation, the chief ray, which was modeled for the scanned beam at a particular angular mirror position, was aligned with the A-scan obtained at the same angular position. The Atchinson eye model was employed to represent the human eye, and the ray tracing model incorporated working distance, keratometry, and axial length values.18 Using this ray tracing model, equal OPL curvature (representing the curvature of the actual A-scan paths) was estimated for each subject (refer to Supplementary Fileset S1 for detailed information). To incorporate the influence of the aspherical shape of the eyeball on the OPL, the conic constant was estimated alongside the spherical curvature. This estimation was performed using a merit function within the ray tracing model, adjusting the equal OPL curvature and conic constant for each incident angle. This adjustment was based on Equation 819:  
\begin{eqnarray} z = \frac{{c{r^2}}}{{1 + \sqrt {1 - \left( {1 + k} \right){c^2}{r^2}} }}\quad \end{eqnarray}
(8)
In this equation, z is the z-coordinate of the standard surface, c is the curvature (the reciprocal of the curvature radius), r is the radial coordinate, and k is the conic constant. The equal OPL curvature for a specified incident angle was inferred utilizing the provided z, k, and r values (see Supplementary Fig. S2). The actual B-scan image was warped using the backward transform function with the imager package in R 4.2.3 (R Foundation for Statistical Computing, Vienna, Austria), with adjustments made to account for the equal OPL curvature values, resulting in an optical distortion-corrected B-scan image. Detailed information on image warping is provided in Supplementary Figure S3. This correction was performed only in the plane of the B-scan and not in three dimensions (3D). 
Measurement of BM Layer Curvature
Automated image segmentation was performed using the device software (Heidelberg Eye Explorer 1.10.4.0; Heidelberg Engineering) and manually reviewed and corrected, when necessary, by a trained observer to ensure accuracy. The segmentation data for the BM layer were exported to a CSV file and subsequently imported into R 4.2.3. We utilized the smooth.spline function in R to obtain smoothed segmentation data. The curvature of the BM layer was estimated by combining the first and second derivatives of the segmentation data, as shown in the following Equation 920:  
\begin{eqnarray} C = \frac{{f^{\prime\prime}\left( x \right)}}{{{{(1 + f^{\prime}{{\left( x \right)}^2})}^{\frac{3}{2}}}}}\quad \end{eqnarray}
(9)
In this equation, C represents the curvature of the BM layer, and f(x) represents the function of the BM segmentation layer (see Supplementary Fig. S4). For each horizontal B-scan, we sampled 100 equally spaced points to measure the curvature. To calculate the mean curvature of the BM layer, we averaged the curvature data from all sampled points across 31 B-scans. 
In Silico Analysis
To validate the efficacy of current correction method for optical distortion, 3D-printed model eyes with curvature radii of 12 mm and 14 mm, filled with deionized water, were scanned using SPECTRALIS OCT in accordance with the previously described procedure: serial scanning with four different eye length settings. The raw OCT images and their positional pixel coordinate data were exported and converted into actual length scales. The raw OCT images were corrected using the same method described above, based on the estimated equal OPL curvature. The estimated curvature values for each of the four eye length settings were compared before and after correction for optical distortion. Detailed information for the in silico analysis is provided in Supplementary Figures S5 to S8 and Supplementary Table S1
Data Analysis
The relationship between BM curvature and various ocular parameters was analyzed using linear mixed-effects (LME) models. The response variable was either the uncorrected or corrected BM curvature, and the covariates included age, gender, axial length, WD, type of SO lens, and diagnosis of glaucoma. A random intercept and slope for WD were incorporated to account for the within-subject correlation of repeated measurements. The baseline variables were centered on the mean values of the study subject group to facilitate the interpretation of coefficients. All statistical analyses were performed using the lme4 package in R.21 Statistical significance was assumed for P < 0.05. 
Results
The study included three patients with glaucoma and seven healthy subjects whose demographic data are presented in Table 1. Five subjects each were imaged using the two different objectives, SO1 and SO2. Figure 1 illustrates variations in WD corresponding to different eye length settings of the SPECTRALIS. The LME model indicated a significant association between WD and axial length (β = −1.22, P < 0.001), the type of SO lens (SO2 exhibited a 1.87 mm longer WD than SO1; P < 0.001), and the eye length settings (WD increased with transitions from short to medium to long to extra-long; P < 0.001) (Table 2). 
Table 1.
 
Subject Demographics
Table 1.
 
Subject Demographics
Figure 1.
 
Eye length setting and working distances. The WD significantly increased as the eye length setting was changed to short (S), medium (M), long (L), and extra-long (XL). The solid line indicates the best linear fit.
Figure 1.
 
Eye length setting and working distances. The WD significantly increased as the eye length setting was changed to short (S), medium (M), long (L), and extra-long (XL). The solid line indicates the best linear fit.
Table 2.
 
LME Model for Working Distance
Table 2.
 
LME Model for Working Distance
There was a marked impact of optical distortion correction on BM curvature (Fig. 2). After correction, there was a significant increase in the mean BM layer curvature, from 16.80 ± 10.08 µm–1 to 49.31 ± 7.50 µm–1 (P < 0.001). In silico analysis of two model eyes (curvature radii of 12 mm and 14 mm) also showed a significant restoration of retinal curvature after correction for optical distortion (Fig. 2, Supplementary Table S1). 
Figure 2.
 
Mean BM layer curvature before and after correction for optical distortion. Each subject underwent four serial OCT scans with different eye length settings (short, medium, long, and extra-long). The retinal BM layer curvature was measured on each B-scan of the horizontal volume scans and then averaged. Before correction, the mean BM layer curvature demonstrated a significant positive correlation with the WD. However, this effect was minimized after the correction. M1, model eye with curvature radius of 14 mm; M2, model eye with curvature radius of 12 mm.
Figure 2.
 
Mean BM layer curvature before and after correction for optical distortion. Each subject underwent four serial OCT scans with different eye length settings (short, medium, long, and extra-long). The retinal BM layer curvature was measured on each B-scan of the horizontal volume scans and then averaged. Before correction, the mean BM layer curvature demonstrated a significant positive correlation with the WD. However, this effect was minimized after the correction. M1, model eye with curvature radius of 14 mm; M2, model eye with curvature radius of 12 mm.
The LME model, incorporating BM layer curvature data prior to correction, revealed significant associations between the mean curvature of the BM layer and age (β = −0.33, P = 0.010), WD (β = 1.94, P < 0.001), and the diagnosis of glaucoma (β = −6.79, P = 0.029) (Table 3). According to this model, a 1-mm change in WD led to a 9.75% alteration in the mean BM layer curvature. The LME model utilizing BM layer curvature data after correction indicated significant associations between the mean curvature of the BM layer and age (β = −0.32, P < 0.001), WD (β = −0.13, P = 0.027), and the diagnosis of glaucoma (β = −6.12, P = 0.031). Conversely, in this latter model, a 1-mm change in WD resulted in only a 0.25% alteration in the mean BM layer curvature. 
Table 3.
 
Liner Mixed-Effect Model for Mean BM Layer Curvature
Table 3.
 
Liner Mixed-Effect Model for Mean BM Layer Curvature
The representative OCT B-scans before and after correction for optical distortion at varying working distances are shown in Figure 3 and Supplementary Video S1. These B-scans were obtained from a 53-year-old male with primary open-angle glaucoma. In the absence of optical distortion correction, the BM layer curvature increased as the WD was increased from 20.8 mm to 28.6 mm, yielding BM layer curvatures of 6.8 µm–1 (WD = 20.8 mm), 11.6 µm−1 (WD = 23.1 mm), 17.6 µm−1 (WD = 25.8 mm), and 23.3 µm–1 (WD = 28.6 mm). This effect was mitigated after applying optical distortion correction, resulting in more consistent and stable BM layer curvature: 46.6 µm−1 (WD = 20.8 mm), 46.0 µm−1 (WD = 23.1 mm), 46.0 µm−1 (WD = 25.8 mm), and 45.5 µm−1 (WD = 28.6 mm). 
Figure 3.
 
Representative OCT B-scans before and after correction for optical distortion. Representative B-scans of a 53-year-old male with primary open-angle glaucoma. The left column showcases a series of B-scans captured at four different eye length settings (short, medium, long, and extra-long) prior to the application of optical distortion correction. The right column displays the identical scans after applying correction for optical distortion. Note the progressively increasing curvature of the BM layer as the WD was increased from 20.8 mm to 28.6 mm in the absence of optical distortion correction. However, this phenomenon is substantially reduced following the correction for the optical distortion effect. The back-to-back comparison of the same scan is available in Supplementary Video S1.
Figure 3.
 
Representative OCT B-scans before and after correction for optical distortion. Representative B-scans of a 53-year-old male with primary open-angle glaucoma. The left column showcases a series of B-scans captured at four different eye length settings (short, medium, long, and extra-long) prior to the application of optical distortion correction. The right column displays the identical scans after applying correction for optical distortion. Note the progressively increasing curvature of the BM layer as the WD was increased from 20.8 mm to 28.6 mm in the absence of optical distortion correction. However, this phenomenon is substantially reduced following the correction for the optical distortion effect. The back-to-back comparison of the same scan is available in Supplementary Video S1.
BM layer curvature within the macula is illustrated with a heatmap in Figure 4. Because the volume scans were aligned to each individual's unique FoBMO axis, the heatmap effectively mitigated the impact of ocular torsion during the OCT scan, facilitating the measurement of the consistent curvature at a fixed macular location. Figure 4 shows the BM layer curvature of the same subject featured in Figure 3, both prior to and following correction for optical distortion effects. 
Figure 4.
 
BM layer curvature heatmap before and after correction for optical distortion. The heatmap visualizes the curvature of the BM layer for the same subject in Figure 3. The horizontal green line represents the axis from the fovea to the BM opening, and the white cross denotes the location of the fovea. The upper row displays the heatmaps before applying correction for optical distortion, and the lower row presents the heatmaps after applying the correction. After the optical distortion correction, we observed a significant increase in the mean BM layer curvature. The values transformed from 9.7 µm–1 (WD = 20.8 mm), 14.6 µm–1 (WD = 23.1 mm), 20.5 µm–1 (WD = 25.8 mm), and 25.7 µm–1 (WD = 28.6 mm) to 49.4 µm–1 (WD = 20.8 mm), 48.9 µm–1 (WD = 23.1 mm), 48.8 µm–1 (WD = 25.8 mm), and 47.9 µm–1 (WD = 28.6 mm). This heatmap, referenced to the FoBMO axis, enables the measurement of consistent curvature at a specific macular location, irrespective of any ocular torsion exhibited by subjects during the scan.
Figure 4.
 
BM layer curvature heatmap before and after correction for optical distortion. The heatmap visualizes the curvature of the BM layer for the same subject in Figure 3. The horizontal green line represents the axis from the fovea to the BM opening, and the white cross denotes the location of the fovea. The upper row displays the heatmaps before applying correction for optical distortion, and the lower row presents the heatmaps after applying the correction. After the optical distortion correction, we observed a significant increase in the mean BM layer curvature. The values transformed from 9.7 µm–1 (WD = 20.8 mm), 14.6 µm–1 (WD = 23.1 mm), 20.5 µm–1 (WD = 25.8 mm), and 25.7 µm–1 (WD = 28.6 mm) to 49.4 µm–1 (WD = 20.8 mm), 48.9 µm–1 (WD = 23.1 mm), 48.8 µm–1 (WD = 25.8 mm), and 47.9 µm–1 (WD = 28.6 mm). This heatmap, referenced to the FoBMO axis, enables the measurement of consistent curvature at a specific macular location, irrespective of any ocular torsion exhibited by subjects during the scan.
Discussion
The objective of this study was to examine how WD affects optical distortion and perceived morphological features of the retina in B-scan images of OCT. We found that when left uncorrected, the curvature of the retinal BM layer significantly increased with increasing WD due to the optical distortion effect. However, after applying a ray tracing model to correct the distortion, the curvature of the retinal BM layer increased significantly, which is assumed to be closer to actual morphology.13,22 Moreover, the impact of WD on the curvature reduced significantly after correcting for the distortion. 
Optical distortion in OCT B-scans has been a concern for many researchers, and several attempts have been made to address this issue. Kuo et al.13 were among the first to correct ocular shape using a ray tracing model. Their correction model, which included both numerical and analytical approaches, used the curvature obtained with magnetic resonance imaging (MRI) scans as the reference standard. After correction, they demonstrated that the paired differences between curvatures obtained with OCT and MRI decreased after correction. In their subsequent study, they applied the distortion correction model to 52 subjects and found that the retinal radius of curvature and asphericity measurements obtained from distortion-corrected OCT scans were not statistically different from those obtained from MRI scans.22 McNabb et al.23,24 expanded on this technique by using either swept-source OCT or whole-eye OCT systems to generate posterior topography maps in normal and pathologic eyes, enabling quantitative analysis of retinal curvature. 
A major limitation of current correcting models for optical distortion in OCT is the absence of an adequate reference standard method for measuring retinal curvature. Even if eyes imaged in vivo could be obtained for histological analysis, significant curvature changes can arise from tissue fixation. Although some researchers have used MRI as an alternative method to estimate posterior eye curvature,13,22 the significant difference in resolution between OCT and MRI makes accurate comparisons challenging. We hypothesized that the distortion of OCT B-scans depended on WD and that correction for optical distortion would result in a constant retinal curvature, irrespective of different WDs. This approach can serve as an indirect validation of the appropriateness of the optical distortion correction. As we anticipated, our correction model notably diminished the influence of WD on the curvature of the BM layer. Although the impact of WD remained statistically significant even after the optical distortion correction, the magnitude of this impact was negligible. Prior to correction, each 1-mm change in WD led to a 9.75% change in BM curvature, whereas after correction it was only 0.25%. Correction led to nearly uniform B-scan morphology across different WDs. 
Our study emphasizes the significance of correcting the optical distortion effect for the accurate analysis of posterior eye morphology with OCT. Although it can be argued that the impact of optical distortion would be minimal when analyzing images longitudinally from a single subject with the same OCT settings, variations in working distance during OCT acquisition could still result in fluctuations in retinal curvature. In practice, it is challenging to maintain a constant working distance during OCT acquisition, and WD can also vary depending on the examiner. Therefore, even in longitudinal studies, correcting the optical distortion effect is essential to ensure precise and reliable outcomes. Moreover, it is crucial to exercise caution when interpreting uncorrected curvature data, particularly in studies that compare results among subjects in cross-sectional data. 
Kim and colleagues25 conducted a study to investigate the three-dimensional architecture of the posterior sclera using swept-source OCT. They determined the posterior pole configuration by identifying the deepest point of the eyeball through reconstructed coronal views of the posterior pole scans. Their spatial analysis unveiled the significant role of posterior scleral configuration in influencing optic disc configuration and the rate of visual field progression in myopic eyes with normal-tension glaucoma.2628 Nonetheless, this method faces limitations due to the potential influence of eyeball rotation during OCT image acquisition, which can affect the consistent identification of the deepest point within the eyeball. Variations in subjects’ fixation can lead to shifts in the location of the deepest point, introducing inaccuracies. In contrast, the BM layer curvature heatmap presented in our study offers a distinct advantage by enabling the measurement of consistent curvature at a specific macular location. This improvement enhances precision in the analysis, irrespective of any ocular torsion exhibited by subjects during the scan. Furthermore, it facilitates the identification of specific points of interest, such as areas with the highest BM layer curvature, relative to the positions of the fovea and the BMO center. 
Our study has several limitations. First, our sample size was small and did not cover the entire range of axial lengths, particularly those that encompass high myopia; therefore, the current findings should be validated in highly myopic eyes or pathologic myopic eyes with posterior staphylomas. Nonetheless, because the present study employed the Atchinson eye model, which is widely acknowledged for providing an accurate representation of the optics of myopic eyes for ray tracing simulations, it is expected that this model could be suitable for correcting optical distortion in highly myopic eyes.18 It would also be prudent to investigate the correction effect in hyperopic eyes, a demographic that the current study did not include. Second, due to differences in the OCT devices used and details in the ray tracing models, it is challenging to directly compare our optical distortion correction algorithm with other existing algorithms.13,24,2931 Third, the examiner's influence on variations in WD can vary across different OCT devices. Notably, the SPECTRALIS allows for WD adjustments based on eyeball settings and offers flexibility for the examiner to optimize the image through modifications. However, in the case of other devices, altering or adjusting the WD may be restricted or not possible for the examiner. Nevertheless, even in these cases, WD can still vary among subjects depending on their ocular refraction. Finally, it must be acknowledged that the precise measurement of retinal curvature remains unattainable with the current correction method. Although comparing measurements with other imaging modalities such as MRI or ultrasonography may enhance the objectivity of findings, it is important to recognize that these modalities also entail inherent measurement errors. The in silico analysis with the 3D-printed model eyes showed promising results indicating that the current correction method can restore the retinal curvature to values very close to the actual curvature, although discrepancies persisted possibly due to the inherent limitations of 3D printing. Despite this limitation, our correction method retains utility for longitudinal tracking or for making comparisons between subjects. 
In conclusion, our study illustrates the substantial influence of WD on BM layer curvature in OCT B-scans. Notably, the correction of optical distortion proved highly effective in mitigating WD-related variations, resulting in a relatively consistent BM layer curvature profile across B-scans. These findings underscore the importance of carefully managing optical distortion when performing quantitative morphological analyses. By controlling the impact of WD on optical distortion, we can enhance the accuracy of curvature analysis, thereby ensuring a more precise morphological assessment. 
Acknowledgments
Supported by grants from the Korea Health Technology R&D Project through the Korea Health Industry Development Institute (KHIDI), funded by the Ministry of Health & Welfare, Republic of Korea (HI19C1333), and the Canadian Institutes of Health Research (MOP11357). 
Disclosure: Y.W. Kim, None; G.P. Sharpe, None; J. Siber, Heidelberg Engineering (E); R. Keßler, Heidelberg Engineering (E); J. Fischer, Heidelberg Engineering (E); T. Otto, Heidelberg Engineering (E); B.C. Chauhan, Heidelberg Engineering (F), Revenio (F), Topcon (F) 
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Figure 1.
 
Eye length setting and working distances. The WD significantly increased as the eye length setting was changed to short (S), medium (M), long (L), and extra-long (XL). The solid line indicates the best linear fit.
Figure 1.
 
Eye length setting and working distances. The WD significantly increased as the eye length setting was changed to short (S), medium (M), long (L), and extra-long (XL). The solid line indicates the best linear fit.
Figure 2.
 
Mean BM layer curvature before and after correction for optical distortion. Each subject underwent four serial OCT scans with different eye length settings (short, medium, long, and extra-long). The retinal BM layer curvature was measured on each B-scan of the horizontal volume scans and then averaged. Before correction, the mean BM layer curvature demonstrated a significant positive correlation with the WD. However, this effect was minimized after the correction. M1, model eye with curvature radius of 14 mm; M2, model eye with curvature radius of 12 mm.
Figure 2.
 
Mean BM layer curvature before and after correction for optical distortion. Each subject underwent four serial OCT scans with different eye length settings (short, medium, long, and extra-long). The retinal BM layer curvature was measured on each B-scan of the horizontal volume scans and then averaged. Before correction, the mean BM layer curvature demonstrated a significant positive correlation with the WD. However, this effect was minimized after the correction. M1, model eye with curvature radius of 14 mm; M2, model eye with curvature radius of 12 mm.
Figure 3.
 
Representative OCT B-scans before and after correction for optical distortion. Representative B-scans of a 53-year-old male with primary open-angle glaucoma. The left column showcases a series of B-scans captured at four different eye length settings (short, medium, long, and extra-long) prior to the application of optical distortion correction. The right column displays the identical scans after applying correction for optical distortion. Note the progressively increasing curvature of the BM layer as the WD was increased from 20.8 mm to 28.6 mm in the absence of optical distortion correction. However, this phenomenon is substantially reduced following the correction for the optical distortion effect. The back-to-back comparison of the same scan is available in Supplementary Video S1.
Figure 3.
 
Representative OCT B-scans before and after correction for optical distortion. Representative B-scans of a 53-year-old male with primary open-angle glaucoma. The left column showcases a series of B-scans captured at four different eye length settings (short, medium, long, and extra-long) prior to the application of optical distortion correction. The right column displays the identical scans after applying correction for optical distortion. Note the progressively increasing curvature of the BM layer as the WD was increased from 20.8 mm to 28.6 mm in the absence of optical distortion correction. However, this phenomenon is substantially reduced following the correction for the optical distortion effect. The back-to-back comparison of the same scan is available in Supplementary Video S1.
Figure 4.
 
BM layer curvature heatmap before and after correction for optical distortion. The heatmap visualizes the curvature of the BM layer for the same subject in Figure 3. The horizontal green line represents the axis from the fovea to the BM opening, and the white cross denotes the location of the fovea. The upper row displays the heatmaps before applying correction for optical distortion, and the lower row presents the heatmaps after applying the correction. After the optical distortion correction, we observed a significant increase in the mean BM layer curvature. The values transformed from 9.7 µm–1 (WD = 20.8 mm), 14.6 µm–1 (WD = 23.1 mm), 20.5 µm–1 (WD = 25.8 mm), and 25.7 µm–1 (WD = 28.6 mm) to 49.4 µm–1 (WD = 20.8 mm), 48.9 µm–1 (WD = 23.1 mm), 48.8 µm–1 (WD = 25.8 mm), and 47.9 µm–1 (WD = 28.6 mm). This heatmap, referenced to the FoBMO axis, enables the measurement of consistent curvature at a specific macular location, irrespective of any ocular torsion exhibited by subjects during the scan.
Figure 4.
 
BM layer curvature heatmap before and after correction for optical distortion. The heatmap visualizes the curvature of the BM layer for the same subject in Figure 3. The horizontal green line represents the axis from the fovea to the BM opening, and the white cross denotes the location of the fovea. The upper row displays the heatmaps before applying correction for optical distortion, and the lower row presents the heatmaps after applying the correction. After the optical distortion correction, we observed a significant increase in the mean BM layer curvature. The values transformed from 9.7 µm–1 (WD = 20.8 mm), 14.6 µm–1 (WD = 23.1 mm), 20.5 µm–1 (WD = 25.8 mm), and 25.7 µm–1 (WD = 28.6 mm) to 49.4 µm–1 (WD = 20.8 mm), 48.9 µm–1 (WD = 23.1 mm), 48.8 µm–1 (WD = 25.8 mm), and 47.9 µm–1 (WD = 28.6 mm). This heatmap, referenced to the FoBMO axis, enables the measurement of consistent curvature at a specific macular location, irrespective of any ocular torsion exhibited by subjects during the scan.
Table 1.
 
Subject Demographics
Table 1.
 
Subject Demographics
Table 2.
 
LME Model for Working Distance
Table 2.
 
LME Model for Working Distance
Table 3.
 
Liner Mixed-Effect Model for Mean BM Layer Curvature
Table 3.
 
Liner Mixed-Effect Model for Mean BM Layer Curvature
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