Each SCS consists of two coaxial surfaces: a peripheral scleral-type surface described by the equation of a sphere with 12 mm of radii of curvature, and a biconic corneal surface14 described by Eq. (1).

Eq. (1). Bi-conic equation employed to model the corneal 3-D printed surface.14

Where Cvx=1/Rx (Rx is the curvature radii of the x axis); Cvy=1/Ry (Ry is the curvature radii of the y axis); ccx is the conic constant in the x axis and ccy the conic constant in the y axis.

This equation was entered in a custom-built MATLAB Application (App) for the generation of the surfaces (see Fig. 2). The inputs of corneal radii (Rcx for x-axis and Rcy for y-axis), conic constant (ccx and ccy), corneal diameter (DTx and DTy), scleral radii (Rsx and Rsy), scleral diameter (DTsx and DTsy) and the total points for generating the surface (Nx) must be entered to generate the representation (Fig. 1. “3D button”). For creating the 3D model, the stereolithography file was generated with 2 mm of thickness (“Stlwrite” button).

Fig. 2.

A section of the designed Matlab R2020b App for creating the SCSs. Rcx, Rcy: Corneal radii for x-axis and y-axis (mm). ccx, ccy: Corneal conic constants (mm). DTx, DTy: Total corneal diameters (mm). LTotalx, LTotaly: Total length of the base (mm). Rsx, Rsy=Scleral radii (mm). DTsx, DTsy=Total scleral diameters (mm). Nx=Number of points for representing and generating the surface.

The parameters entered in the MATLAB App to define the surfaces (SCS1 and SCS2) are detailed in Table 1.

The convex astigmatic geometries SCS1 and SCS2 were selected to exhibit approximately 2 and 4 diopters of corneal equivalent astigmatism, respectively, and to encompass a broad range of curvature and conic constant values. Both surfaces were used during the experiment in the nominal and x-y transposed position.

For 3-D printing, in contrast to Zhao’s work,12 stereolithography technology was chosen for the manufacture of SCSs given its high spatial resolution and surface printing quality.15,16

The 3-D printing of the SCSs included the following three-step procedure:

• Step#1: Stereo-lithography file; a “Standard Template Library” (.stl) file contains the information of the SCSs which was generated with the MATLAB App specifically in the “Stlwrite” button (Fig. 2). Supports were added for each model to ensure proper support with the program Chitubox64_V1.9.0 (Chitu Systems Inc., China, 2023).

• Step#2: Printing parametrization; the slicing of the generated SCSs models was carried out using the program Ultimaker Cura_V.4.13.0 (Ultimaker B.V., Netherlands, 2023) obtaining a final machine code file (.gcode) with layer height of 0.06 mm and a transversal diameter resolution of 0.02 mm. Finally, the file was then sent for 3-D printing.

• Step#3: Printing process; the fabrication of the SCSs was carried out using the Peopoly Moai 130 3-D resin printer (Peopoly, China, 2018) which uses blue scanning laser technology (wavelength 405 nm) to induce cross-linking of the functional groups composing the resin.17–19 A UV curable acrylate-based resin developed by Peopoly specifically for SLA printers was used.20 A post washing and curing process was applied to remove the partially cured resin.21

Two different kinds of fluorescein patterns were used in this study. Theoretical Fluorescein Patterns and Experimental Fluorescein Patterns. Calculating the TFP required knowledge of the 3-D printed SCS shape and the nominal geometry of the CLs back surface (see Table 2). Obtaining the EFP required the application of fluorescein solution between the SCS and the CLs, along with blue light illumination and a digital camera equipped with a yellow filter. To increase the diversity of synthetic fluorescein patterns, both 3-D printed surfaces were also used with a 90° of rotation in both experimental and theoretical methods.

To generate both types of fluorescein patterns, the parameters of the CLs back surface used are detailed in Table 2. These lenses were made of Polycon II, a RGP material commonly used in CL manufacturing. All possible combinations between CLs and rotated and unrotated SCSs were used to generate a set of 12 fluorescein patterns of each method.

The geometrical characterization of the 3-D printed SCSs were performed using the Eye Surface Profiler (ESP), a novel clinical topographer that employs Fourier-domain profilometry with a dual blue-light projection system and a yellow-filtered camera.22,23 To obtain topographical SCS information, the device uses the green-yellow fluorescence emitted by a thin fluorescein layer ideally aligned parallel to the measured surface.24

Following height data acquisition, a nonlinear regression was performed to characterize the central region of the 3-D printed height data. The geometric characterization involved fitting the measured data to a biconic model over a 9.5 mm aperture diameter, the same as the CLs used in this work. The nonlinear regression was carried out using MATLAB’s “lsqnonlin” function. Moreover, the root mean square error (RMSE) between the data and the model was calculated as a measure of the goodness of fit. To enable a more detailed surface analysis, the differences between the biconic model and each experimental corneal surface were expressed via normalized Zernike polynomials using the ANSI/ISO single-index scheme (Noll ordering) up to radial order 10.25 Then, the relative contributions of low (radial order≤2) and high-order (radial order>2) polynomials were quantified as percentages. Because only corneal CLs were employed in this work, no attempt was made to characterize the scleral surface.

TFPs were calculated using a custom-built MATLAB App (see Fig. 3), following the guidelines from Contact Lens Optics and Lens Design.14 In order to do that, the SCS parameters obtained from the corneal biconic fittings and the nominal back surface geometry of 3 tricurve spherical RGP CLs (Table 2) were used. Fig. 3 highlights the section of the developed App where the theoretical fluorescein pattern was computed using these parameter data. To increase the diversity of synthetic fluorescein patterns, the SCS1 and SCS2 biconic models were also used with 90° of rotation.

Fig. 3.

Section of the MATLAB App used to compute theoretical fluorescein patterns. A linear green scale was applied, where 0 mm tear height corresponds to black. Corneal and scleral radii (Rcx, Rcy, Rsx, Rsy), corneal conic constants (ccx, ccy), corneal and scleral diameters (DTx, DTy, DTsx, DTsy), Nx indicates the number of surface points used for generation, CLs base curves and diameters (R1–R3x/y, DT1–DT3x/y) and CLs conic constants (ccx, ccy).

To generate the corresponding 12 experimental fluorescein patterns, the 3 Spherical CLs (Table 2) were fitted onto the SCSs in normal and 90 degrees rotated positions. To visualize the fluorescein pattern, a solution was prepared by adding 0.04 g of fluorescein sodium to every 10 mL of Systane Lubricant Eye Drops (Alcon Inc., Ginebra, Suiza; 2024). This mixture helped maintain a uniform tear film for a longer period of time. The CLs were properly centered on the corneal surface.

Fluorescein pattern images were captured using the main camera of an iPhone 14 Pro (Apple, Cupertino, CA, USA) equipped with a yellow filter (ROSCO, e-Colour± Filter #104 Deep Amber, ROSCO Laboratories, Inc., USA). Images were illuminated using a modified Burton lamp, originally a handheld magnifier (AURIOL, Model No Z29376, Milomex Ltd., UK), in which the original ring of white LEDs were replaced with 470 nm blue LEDs (TG Blue LED, Toyoda Gosei Co., Ltd., Japan). Experimental fluorograms were obtained using the mode where only four LEDs of the ring were illuminated.

Following image acquisition, contrast was uniformly adjusted using the “Contrast” function in the Photos app integrated in iOS (version 17.5.1). This adjustment operates non-linearly on image luminance, minimally affecting color perception. The app’s contrast scale ranges from −100 (maximum reduction) to ±100 (maximum enhancement), with 0 indicating no adjustment. A value of ±20 was applied to all images, selected by one of the authors (D. Gargallo) to achieve maximal visual similarity with the experimental fluorescein patterns as perceived during capture. Finally, all images were cropped to an 800 × 800 pixel square for analysis.

In order to evaluate the feasibility and reliability of the EFP, those were compared against the TFP through a structured questionnaire-based assessment consisting of 6 questions (single answer multiple-choice test). A total of 22 optometrists with experience in CLs fitting participated in this study answering the questionnaire.

In the questionnaire, each question showed a main fluorescein pattern generated using either experimental or theoretical method. Additionally, four alternative fluorescein patterns were shown, generated using the other method. The optometrists had to identify which of the four patterns corresponded to the same CL and SCS parameters as the main fluorescein pattern. (Further information can be found in Appendix A).

All participants completed the questionnaire using the same laptop model (ASUS ROG Strix G513ICHN004W), same display settings 1920×1080 resolution, IPS panel, 144 Hz refresh rate and 100 % sRGB color coverage and the same surrounding lighting conditions (736 lx).

Data analysis involved evaluating the percentage of optometrists’ answers (pp) for each question. To assess the uncertainty associated with each proportion, a 95 % confidence interval (CI) was calculated using Eq. (2), with a sample size of N = 22.

Eq. (2). Calculation of the CI proposed by Agresti and Caffo.26

In order to assess the statistical significance of the most prevalent response, the CIs for the most prevalent response option were compared with those of the second most prevalent respectively for each question. If the CIs of these options overlapped, this suggested that the optometrists may have had difficulty distinguishing between them, potentially leading to a random choice. In contrast, non-overlapping CIs indicated that the most prevalent answer was more likely selected intentionally, rather than by chance. Nevertheless, the proportion of optometrists selecting the correct answer for each question was quantified as well. All the calculations and the graphics were carried out using Microsoft Excel.

To enhance the analysis, the similarity between each response and its corresponding reference fluorescein image was quantified using the Structural Similarity Index (SSIM). SSIM is a widely used metric that assesses image similarity through a perceptual comparison of quality. It evaluates three key aspects of image appearance: luminance, contrast, and structural information.27 The SSIM index ranges from 0 to 1, where 1 indicates perfect structural similarity, and lower values reflect increasing dissimilarity. In practice, values near 0 indicate very low similarity, while values closer to 1 represent highly similar images in terms of the three evaluated components.

Table 3 summarizes the main parameters obtained from fitting a biconic model to the central region (9.50 mm diameter) of the 3-D printed corneal surfaces. The root mean square difference (RMS_Dif) between the fitted biconic model and the corneal height data obtained from topography was approximately 10.50 µm for both printed surfaces.

The results of the percentage of optometrists who chose each answer option in each question and its CI are shown in Table 4A), the results corresponding to correct answers are written in bold numbers and marked with an asterisk (*). As shown in Table 4A), for all questions, the correct answer was also the most prevalent in relation to the second more frequently selected option. Considering CI overlapping, this higher prevalence of the correct answers was not due to chance p < 0.05.

The SSIM of each possible answer was calculated relative to the reference image used for comparison. The SSIM values for the correct answers ranged from 0.83 to 0.88, with a mean of 0.83 and a standard deviation of 0.02. In contrast, the incorrect answers showed SSIM values ranging from 0.73 to 0.84, with a mean of 0.77 and a standard deviation of 0.08. Correct responses consistently exhibited higher SSIM values than incorrect ones. The overall SSIM results are presented in Table 4B).

The percentages of optometrists who selected the correct and the second most frequently selected answer for each question are represented in Fig. 4. The results for the correct answer correspond to the bold numbers of Table 4A) and the black bars of the figure. The mean percentage of correct answers across all questions was 84.67 % with a standard deviation of 10.07 % and a range interval from 77 to 95 %. For questions number 1, 3, 5 more of the 90 % of the optometrists chose the correct answer.

Fig. 4.

Percentage of optometrists who chose the correct (black bar) and the second more frequently selected answer (white bar). Correct results correspond to the bold numbers shown in Table 4A). Confidence intervals were calculated following Agresti and Caffo.26.

While our findings point out the potential of 3-D printed SCSs as a valuable tool for simulating RGP CL fitting, certain aspects require further investigation to fully establish the scope and applicability of this approach. A critical assessment of the strengths and limitations of our methodology is essential to guide future research and improvements.

One of the strengths of this study is the novelty of the proposed method to simulate rigid CL fittings. Unlike previous studies, our approach includes the characterization of the 3-D printed SCS using an optical topographer, ensuring a more significant evaluation. Additionally, the surface quality of the printed models was sufficient to generate fluor patterns without requiring additional mechanical processing, allowing for a better comparison with the theoretical fluorescein patterns. Another strength of this work is the statistical significance analysis performed, which reinforces the reliability of our findings.

However, due to its pioneering nature, this study has some limitations as well. The most significant is the limited range of corneal surfaces and contact lenses analyzed. A more comprehensive study is needed to determine the limitations of this new approach. Additionally, the analysis method based on digital pictures can be also considered a limitation because more information can be obtained with a real time observation of fluorescein patterns over SCS. In this work, due to the difficulty in standardizing participant interaction with the experimental setup, it was considered that a comparison between digital images provides clearer information about the influence of the proposed method on the appearance of the fluorescein pattern.

Furthermore, the lack of uniformity in the difficulty level of some questions represents a limitation that should be addressed in future studies. Ensuring a more consistent level of difficulty across items is expected to enhance the robustness and comparability of the results.