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J. Eur. Opt. Society-Rapid Publ. 21, 10( 2025)
Figure 2.( Left) Flap and( Right) Lenticule geometry to characterize as equation 7. FT and FD stand for the flap thickness and dimeter while CT, LT, CD and LD refer to the cap( lenticule) thickness and dimeter. The bed and hing cuts( for flaps and lenticules) are shown as the gray lines.
Figure
3.( Left) – Raw images of Figure 1.( Right) – The proposed image processing pipeline segments intrastromal lenticule and flap cuts by first enhancing the structures( a, b), then applying a segmentation algorithm to identify corneas( c, d) and consequently the domains of cuts( e, f). Panels in( e) illustrate the presence of sideband noise and its removal to achieve the correct flap geometry. Panel( f) demonstrates the optimization process for detecting the correct posterior( lenticule) cut( orange dots) using Algorithm 1.
Numerically, the transition zone is determined as the region where the posterior curvature shifts from convex to concave. This definition corresponds to a sign change in the second-order gradient of the posterior fits( P( x i, y i) asshownin Fig. 2).
The same rationale can be applied to flap cuts for determining edge cut angles. However, this method necessitates continuous and complete flap cuts to ensure a high-quality fit. To estimate the edge cut angle, peaks within a certain window surrounding a boundary can be selected. Then, two vectors pointing from the boundary point towards the most left( A ~) andright(~ B) peaks are formed. Thus, an inner product determines the inner angle as follows,
h ¼ arcosin
~ A ~ B jAjjBj
!; ð8Þ
where || is the norm of vectors. The deviation may root back to monomial fits that always retrieve a smoother edge compared to practical( planned) sharp edges. Thus, a widening is to account for.
Moreover, the proposed characterization approach enables scanning the lenticule thickness profile. The thickness profile can be described with a parabolic equation which determines the lenticule extraction curvature( R).
Given the refractive indices of air and porcine eyes, the lenticule power( LP) formulates as
LP ¼ ðdnÞ 1 R: ð9Þ
The outlined steps form the proposed numerical pipeline for characterizing intrastromal substructures with a high level of morphological detail.
3 Results
Figures 3a and 3b illustrate the denoising of the OCT scans( corresponding to Fig. 1). By initial use of the peakfinder algorithm, the corneal segment was recognized as shown in Figures 3c and 3d. For flap cases, the intrastromal peaks identified with the PPC may often lead to wider boundary detections. Applying the point-density routine would exclude the sideband peaks as illustrated in Figure 3e.
In Figure 3f, through approximately 8 iterations of Algorithm 1, the optimized posterior( orange line) was obtained. The MSE of Algorithm 1 typically decreases by an order of magnitude after the first four iterations and then continues to decrease monotonically. Additionally, the same point-density scan routine, as Figure 3e, was applied to the lenticule cuts for filtering out falsely detected intrastromal peaks. The point-density scan determines the extent of anterior cuts but may also extend the posterior boundaries. Consequently, the BO( Bayesian optimization)