Citation: Carpena-Torres, C.; Rodríguez-Lafora, M.; Pastrana, C.; Privado-Aroco, A.; Serramito, M.; Batres, L.; Carracedo, G. Cycloplegia Improves the Inter-Optometrist Repeatability of Subjective Refraction. Photonics 2024, 11, 1180. https:// doi.org/10.3390/photonics11121180 Received: 28 October 2024 Revised: 5 December 2024 Accepted: 11 December 2024 Published: 16 December 2024 Copyright: © 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). Article Cycloplegia Improves the Inter-Optometrist Repeatability of Subjective Refraction Carlos Carpena-Torres , Maria Rodríguez-Lafora, Cristina Pastrana , Ana Privado-Aroco , María Serramito , Laura Batres and Gonzalo Carracedo * Ocupharm Research Group, Department of Optometry and Vision, Faculty of Optics and Optometry, Complutense University of Madrid, C/Arcos de Jalón 118, 28037 Madrid, Spain; ccarpena@ucm.es (C.C.-T.); marodr10@ucm.es (M.R.-L.); crispast@ucm.es (C.P.); aprivado@ucm.es (A.P.-A.); mserrami@ucm.es (M.S.); lbatres@ucm.es (L.B.) * Correspondence: jgcarrac@ucm.es Abstract: Background: Since accommodation may be a source of error affecting the inter-optometrist repeatability of subjective refraction, this study investigated whether the use of cycloplegia could improve this repeatability. Methods: A randomized cross-sectional study was conducted on 42 young hyperopes (18.2 ± 7.7 years, range 6 to 31 years). Subjective refraction was performed by two different optometrists in two measurement sessions: one day without cycloplegia and, on a different day, with cycloplegia, in random order. The inter-optometrist repeatability of all refractive variables (M, J0, and J45) was analyzed, selecting one eye randomly, in terms of the 95% confidence interval of repeatability (r). Results: No statistically significant differences were found between the optometrists for any refractive variable, both with and without cycloplegia (p ≥ 0.05). Furthermore, no correlation was found between participants’ age and the refractive differences between optometrists under both cycloplegic conditions (p ≥ 0.05). However, the use of cycloplegia improved the inter-optometrist repeatability of M (r = 0.37 D) compared to the non-cycloplegic measurements (r = 0.62 D). Conclu- sions: These results suggest that accommodation in young hyperopes is likely a primary source of error that could explain the discrepancies in subjective refraction between optometrists. Keywords: repeatability; agreement; subjective refraction; cycloplegia; cyclopentolate; tropicamide 1. Introduction In clinical practice, subjective refraction performed by optometrists allows for the de- termination of a patient’s refractive error considering both optical (objective) and perceptual (subjective) factors of the patient’s visual process. This subjective method, considered the gold standard for measuring refractive errors, is probably the most frequently performed procedure in optometric practice [1]. However, subjective refraction seems not to be highly repeatable when assessed by different optometrists. It is known that differences between optometrists when determining the refractive error of the same patient can reach up to ±0.75 D (95% confidence interval) of the spherical equivalent in some cases, regardless of the patient’s age or the type of refractive error [2–4]. In those patients where accommodation can affect the measurement of refractive error, mainly in children and young hyperopes, cycloplegia is sometimes necessary to paralyze the ciliary muscle. This prevents accommodation spasms and fluctuations that could lead to errors in the refraction process, particularly underestimating the magnitude of hyperopia or overestimating myopia [5,6]. Since accommodation may be a source of error affecting the inter-optometrist repeata- bility of subjective refraction, this study investigated whether the use of cycloplegia could improve this repeatability and the level of agreement between optometrists. The results of this study would help to determine whether the differences found between optometrists Photonics 2024, 11, 1180. https://doi.org/10.3390/photonics11121180 https://www.mdpi.com/journal/photonics https://doi.org/10.3390/photonics11121180 https://doi.org/10.3390/photonics11121180 https://creativecommons.org/ https://creativecommons.org/licenses/by/4.0/ https://creativecommons.org/licenses/by/4.0/ https://www.mdpi.com/journal/photonics https://www.mdpi.com https://orcid.org/0000-0001-9077-3557 https://orcid.org/0000-0003-2395-3106 https://orcid.org/0000-0003-2428-3722 https://orcid.org/0000-0002-2122-675X https://orcid.org/0000-0001-9753-7696 https://orcid.org/0000-0003-0054-1731 https://doi.org/10.3390/photonics11121180 https://www.mdpi.com/journal/photonics https://www.mdpi.com/article/10.3390/photonics11121180?type=check_update&version=1 Photonics 2024, 11, 1180 2 of 8 are due to the influence of the patient’s accommodation or the individual decisions that optometrists make when refining subjective refraction. 2. Materials and Methods 2.1. Study Design and Sample A randomized cross-sectional study was conducted in accordance with Good Clinical Practice guidelines, European institutional regulations, and the Declaration of Helsinki. The study protocol was approved by the ethics committee of the Hospital Clínico San Carlos (code 18/459-R_P; Madrid, Spain), affiliated with the Complutense University of Madrid (UCM). All examinations were carried out at the University Clinic of Optometry of the UCM. Participants voluntarily enrolled after signing written informed consent forms (in the case of minors, this was signed by their legal guardians) with detailed information about all study procedures. Each participant underwent two separate visits: one for subjective refraction measure- ment without cycloplegia and another on a different day of the same week for cycloplegic refraction measurement, both randomly assigned. During each visit, subjective refraction was performed by two optometrists, each with over 10 years of experience, in random order. Neither optometrist had access to the other’s refractive results at any point during the study to avoid measurement bias. Cycloplegia was induced by administering two topical drops of 1% cyclopentolate hydrochloride (Alcon Cusí; Barcelona, Spain), with a 15 min interval between doses. Subjective refraction measurements began 15 min after the last instillation. A total of 42 hyperopic participants were evaluated (18.2 ± 7.7 years, range 6 to 31 years; 32 female and 10 male), with one eye randomly selected for statistical analysis (by coin toss). Inclusion criteria were age between 6 and 35 years (to ensure adequate accommodative function), a cycloplegic spherical equivalent between +0.50 D and +6.00 D, and understanding and signing the informed consent form. Exclusion criteria included clinical history of amblyopia, strabismus, or any other visual dysfunction that could affect accommodation, as well as the presence of ocular disease, trauma, or ocular surgery and the use of systemic or ocular drugs that could affect accommodation. Participants belonged to the University Clinic of Optometry database, having been previously evaluated by other optometrists for vergence and accommodation. 2.2. Subjective Refraction Procedure and Analysis Both optometrists performed the subjective refraction in the same laboratory under photopic conditions using a trial frame and the digital optotype chart VX22 (Visionix; Chartres, France). Retinoscopy was conducted in all cases prior to subjective refraction. Considering the retinoscopy refraction as the reference point, the maximum positive sphere needed to achieve maximum visual acuity was determined with the fogging technique. Next, the cylinder was refined using an astigmatism chart numbered from 1 to 12 (clockwise, in 30◦ increments), followed by adjustments with a ±0.50 D Jackson cross-cylinder to finalize the axis and cylinder power. Lastly, the maximum positive sphere was rechecked. The refraction procedure was standardized for all participants, starting with the right eye, followed by the left. After the procedure for both eyes was completed, binocular balance was achieved using prism dissociation, and the maximum positive sphere was adjusted binocularly to obtain the maximum possible visual acuity. Refractive variables were analyzed in terms of spherical equivalent (M) and the vertical (J0) and oblique (J45) components of astigmatism following the method standardized by Thibos et al. [7]: M = sphere + (cylinder/2) J0 = −(cylinder/2) × cos (2 × axis) J45 = −(cylinder/2) × sin (2 × axis) where enantiomorphism associated with J45 was corrected by changing the sign for the left eye. Photonics 2024, 11, 1180 3 of 8 After completing the refraction procedure, monocular corrected-distance visual acuity (CDVA) was assessed with the high-contrast (100%) Early Treatment Diabetic Retinopathy Study (ETDRS) chart displayed on a VX22 digital screen. 2.3. Statistical Analysis In a recently published study by our research group on the influence of age on the repeatability of subjective refraction, a minimum sample size of 16 participants was esti- mated [4]. For this reason, no new sample size calculation was performed. Statistical analysis was conducted using SPSS Statistics 23 (IBM; Chicago, IL, USA). The inter-optometrist repeatability analysis included the following variables: repeatability (Sr) and its 95% confidence interval (r), the intraclass correlation coefficient (ICC), and the mean difference between optometrists (bias) with its 95% limit of agreement (95% LoA). Sr is mathematically defined as the square root of the mean square within-subject standard deviation, while r is calculated as 2.77 × Sr, representing the value within which 95% of differences between optometrists should lie [8]. The ICC, reflecting the agreement between the two repeated measurements taken by the optometrists, was calculated using a one-way random effects model for single measurements according to the McGraw and Wong convention [9]. Bland–Altman analyses were used to evaluate agreement (bias and 95% LoA) between the two optometrists. In this analysis, 95% LoA is defined as 1.96 × the standard deviation of the mean difference (bias) between optometrists [10]. Since only two refractions were per- formed per participant, the 95% LoA values coincide with those of r which were previously defined. Additionally, the Spearman correlation coefficient (ρ) was calculated to assess the relationship between participant age and the mean difference between optometrists. The normality of the distributions was assessed using the Shapiro–Wilk test, which confirmed normality for all variables. As a result, pairwise comparisons between the two optometrists were performed using the Student’s t-test for paired samples. A statistical significance of 95% (p < 0.05) was set for all statistical analyses. 3. Results Table 1 summarizes the values of all the variables (M, J0, J45, and CDVA) measured by the two optometrists, the statistical comparison between them, and the repeatability results. Additionally, the Bland–Altman plots for the refractive variables, analyzing the agreement between the two optometrists, are shown in Figure 1, while Table 2 presents the results of the intraclass correlation analysis. Regarding the refractive variables (M, J0, and J45), there were no statistically significant differences between the optometrists, either without or with cycloplegia (p ≥ 0.05). Al- though no significant differences were observed, the 95% confidence interval of repeatability (r), which coincides with the 95% limit of agreement (95% LoA) from the Bland–Altman plots, of the spherical equivalent (M) was 0.25 D better with cycloplegia (r = 0.37 D) than without cycloplegia (r = 0.62 D). For the vertical (J0) and oblique (J45) components of astig- matism, this repeatability was similar both with and without cycloplegia, with a difference of just 0.03 D in both cases. The intraclass correlation coefficient (ICC) analysis showed results consistent with the repeatability findings, with slightly better ICCs for M and J0 with cycloplegia, but slightly worse for J45. As for CDVA, statistically significant differences were found between the optometrists, but only when the refraction was performed without cycloplegia. These differences were 0.03 ± 0.07 logMAR (p = 0.004), but they disappeared with the use of cycloplegia (p = 0.729). The repeatability of CDVA measurements was slightly better without cyclople- gia (r = 0.15 logMAR) compared to with cycloplegia (r = 0.18 logMAR). However, the ICC values were slightly better with cycloplegia. Photonics 2024, 11, 1180 4 of 8 Table 1. Inter-optometrist repeatability in terms of repeatability (Sr) and its 95% confidence interval (r) for spherical equivalent (M), cylindrical vectors (J0 and J45), and corrected-distance visual acuity (CDVA). Variable Cycloplegia Optometrist 1 Optometrist 2 p-Value Repeatability (Sr) 95% Confidence Interval (r) M (D) Without 0.93 ± 0.81 1.03 ± 0.84 0.050 0.22 0.62 With 1.53 ± 1.30 1.54 ± 1.28 0.862 0.13 0.37 J0 (D) Without 0.05 ± 0.17 0.07 ± 0.21 0.273 0.09 0.26 With 0.11 ± 0.20 0.09 ± 0.20 0.470 0.08 0.23 J45 (D) Without −0.02 ± 0.18 −0.01 ± 0.19 0.458 0.05 0.15 With −0.01 ± 0.17 −0.01 ± 0.19 0.919 0.06 0.18 CDVA (logMAR) Without −0.12 ± 0.05 −0.16 ± 0.08 0.004 * 0.05 0.15 With −0.11 ± 0.07 −0.12 ± 0.09 0.729 0.06 0.18 * p < 0.05, Student’s t-test for paired samples. Photonics 2024, 11, x FOR PEER REVIEW 4 of 8 0.729). The repeatability of CDVA measurements was slightly better without cycloplegia (r = 0.15 logMAR) compared to with cycloplegia (r = 0.18 logMAR). However, the ICC values were slightly better with cycloplegia. Table 1. Inter-optometrist repeatability in terms of repeatability (Sr) and its 95% confidence interval (r) for spherical equivalent (M), cylindrical vectors (J0 and J45), and corrected-distance visual acuity (CDVA). Variable Cycloplegia Optometrist 1 Optometrist 2 p-Value Repeatability (Sr) 95% Confidence Interval (r) M (D) Without 0.93 ± 0.81 1.03 ± 0.84 0.050 0.22 0.62 With 1.53 ± 1.30 1.54 ± 1.28 0.862 0.13 0.37 J0 (D) Without 0.05 ± 0.17 0.07 ± 0.21 0.273 0.09 0.26 With 0.11 ± 0.20 0.09 ± 0.20 0.470 0.08 0.23 J45 (D) Without −0.02 ± 0.18 −0.01 ± 0.19 0.458 0.05 0.15 With −0.01 ± 0.17 −0.01 ± 0.19 0.919 0.06 0.18 CDVA (logMAR) Without −0.12 ± 0.05 −0.16 ± 0.08 0.004 * 0.05 0.15 With −0.11 ± 0.07 −0.12 ± 0.09 0.729 0.06 0.18 * p < 0.05, Student’s t-test for paired samples. Figure 1. Bland–Altman plots for spherical equivalent (M: upper row, red), vertical cylindrical com- ponent (J0: middle row, green), and oblique cylindrical component (J45: lower row, blue) to assess agreement between the optometrists. The middle line represents the mean difference (bias), while the two dashed lines indicate the 95% limits of agreement (precision). Table 2. Intraclass correlation coefficient (ICC) and its 95% confidence interval for spherical equiva- lent (M), cylindrical vectors (J0 and J45), and corrected-distance visual acuity (CDVA). Figure 1. Bland–Altman plots for spherical equivalent (M: upper row, red), vertical cylindrical component (J0: middle row, green), and oblique cylindrical component (J45: lower row, blue) to assess agreement between the optometrists. The middle line represents the mean difference (bias), while the two dashed lines indicate the 95% limits of agreement (precision). Photonics 2024, 11, 1180 5 of 8 Table 2. Intraclass correlation coefficient (ICC) and its 95% confidence interval for spherical equivalent (M), cylindrical vectors (J0 and J45), and corrected-distance visual acuity (CDVA). Cycloplegia Intraclass Correlation Coefficient [95% Confidence Interval] M J0 J45 CDVA Without 0.926 [0.868, 0.960] 0.754 [0.588, 0.860] 0.911 [0.842, 0.951] 0.290 [−0.010, 0.542] With 0.989 [0.980, 0.994] 0.838 [0.720, 0.909] 0.876 [0.782, 0.931] 0.394 [0.108, 0.620] Lastly, to analyze whether there was a relationship between the participants’ age and the differences found between the optometrists for the refractive variables (M, J0, and J45), Figure 2 shows the scatter plots and linear correlations. No statistically significant differ- ences were found for these parameters, as analyzed by Spearman’s correlation coefficients, either with or without cycloplegia (p ≥ 0.05). Photonics 2024, 11, x FOR PEER REVIEW 5 of 8 Cycloplegia Intraclass Correlation Coefficient [95% Confidence Interval] M J0 J45 CDVA Without 0.926 [0.868, 0.960] 0.754 [0.588, 0.860] 0.911 [0.842, 0.951] 0.290 [−0.010, 0.542] With 0.989 [0.980, 0.994] 0.838 [0.720, 0.909] 0.876 [0.782, 0.931] 0.394 [0.108, 0.620] Lastly, to analyze whether there was a relationship between the participants’ age and the differences found between the optometrists for the refractive variables (M, J0, and J45), Figure 2 shows the scatter plots and linear correlations. No statistically significant differ- ences were found for these parameters, as analyzed by Spearman’s correlation coeffi- cients, either with or without cycloplegia (p ≥ 0.05). Figure 2. Scatter plots and linear correlations between the age of participants and the mean differ- ence between the optometrists for spherical equivalent (M) and cylindrical components (J0 and J45). The analysis of Spearman’s correlation coefficients (ρ) did not show statistically significant correla- tions between these variables (p ≥ 0.05). 4. Discussion As far as we know, this is the first study to evaluate the influence of cycloplegia on the repeatability of subjective refraction. Although it might seem intuitive that, since cy- cloplegia prevents spasms and fluctuations in accommodation [5,6], its use would reduce the expected differences between optometrists, no prior scientific evidence has supported Figure 2. Scatter plots and linear correlations between the age of participants and the mean difference between the optometrists for spherical equivalent (M) and cylindrical components (J0 and J45). The analysis of Spearman’s correlation coefficients (ρ) did not show statistically significant correlations between these variables (p ≥ 0.05). Photonics 2024, 11, 1180 6 of 8 4. Discussion As far as we know, this is the first study to evaluate the influence of cycloplegia on the repeatability of subjective refraction. Although it might seem intuitive that, since cycloplegia prevents spasms and fluctuations in accommodation [5,6], its use would reduce the expected differences between optometrists, no prior scientific evidence has supported this assumption. In this regard, the current study found that, despite the lack of significant differences in any of the refractive variables between the two optometrists, the use of cycloplegia did improve the repeatability of the spherical equivalent (M), as expected. The improvement in the 95% confidence interval of repeatability (r) of M with cy- cloplegia was 0.25 D compared to the non-cycloplegic procedure, which was considered clinically relevant since 0.25 D is the minimum dioptric value that an optometrist can modify in refraction. The fact that this repeatability improved with cycloplegia suggests that accommodation is a source of error in subjective refraction, though not the only one. The Bland–Altman analysis showed that, with cycloplegia, the expected differences in M fell within a range of ±0.25 D, although two participants had differences of 0.50 D and 0.63 D. In these cases, since both optometrists followed an identical protocol, the differences could be attributed to the individual optometrists’ judgment in refining the refraction or variability in patient responses [1]. Additionally, it is noteworthy that the differences in M, both with and without cycloplegia, were independent of the participants’ age. This finding is corroborated by a recent study from our research group which evaluated the repeatability of subjective refraction across different age groups, involving a larger sample under no cycloplegia [4]. Thus, while the current study is not the first to evaluate the inter-optometrist repeata- bility of subjective refraction, it is the only one that uses cycloplegia. When considering studies where optometrists were masked and unaware of the refractive results obtained by others, only three publications exist in the scientific literature. In the 1990s, two studies by Zadnik et al. [2] and Bullimore et al. [3] reported the 95% confidence interval of repeatability (r) of M without cycloplegia, with values of 0.63 D in a sample of 40 non-presbyopic adults and 0.78 D in 86 subjects aged 11 to 60 years, respectively. In line with these findings, a recent study by our research group found similar repeatability of M (r = 0.70 D) in a general population of 86 subjects aged 8 to 69 years [4]. Despite the current study’s sample consist- ing of young hyperopes, the use of cycloplegia was also found to improve inter-optometrist repeatability compared to the results of these earlier studies [2–4]. On the other hand, there are additional publications evaluating the repeatability of subjective refraction, but their results are not comparable to ours, either because they did not follow a masked protocol (introducing bias) [11,12] or because they assessed the repeatability of a single optometrist across different sessions [13,14]. Regarding astigmatism, contradictory results were found. Under cycloplegia, the 95% confidence interval of repeatability (r) of J0 improved, while that of J45 worsened. However, for both variables, the differences in repeatability with and without cycloplegia were 0.03 D, which were not considered clinically relevant. Furthermore, there were no significant differences between optometrists under either condition. Since the contribution of the lens to the total astigmatism of the eye is minimal compared to that of the cornea [15], it is logical that repeatability was not improved with the use of cycloplegia. However, it should be noted that these conclusions are limited by the fact that the study participants presented low astigmatism values. Some evidence of the influence that the magnitude of astigmatism may have on the repeatability of J0 and J45 can be found in the study by Bullimore et al. [3], where, in a sample with higher astigmatism values, the inter-optometrist repeatability of J0 and J45 (r = 0.38 D and 0.31 D, respectively) was worse than that in the current study. CDVA was the only variable with significant differences between the optometrists, but only when measured without cycloplegia. This finding would be methodologically relevant for studies involving different investigators in CDVA measurements, as it could introduce biases that may affect the conclusions. This idea is further supported by the results of a re- cent study from our research group which similarly found differences between optometrists Photonics 2024, 11, 1180 7 of 8 of up to 0.05 logMAR in CDVA without cycloplegia in a group of non-presbyopic adults [4]. However, it should be noted that these differences disappeared with the use of cycloplegia. Finally, several key limitations of this study should be highlighted. First, a limitation to consider is that the measurements were performed by only two optometrists using the same subjective refraction protocol. While this establishes controlled experimental condi- tions, it may not be fully generalized to clinical practice, where protocols and refraction technologies vary widely depending on individual optometrist preferences or resources [1]. Additionally, only the influence of one cycloplegic agent (1% cyclopentolate hydrochloride) was evaluated under a specific posology (two topical instillations, one every 15 min), with how other cycloplegic drugs (e.g., tropicamide) might affect the results remaining unknown. Furthermore, despite the insights provided by this research, the findings may not have direct clinical applicability, as in most cases, subjective refraction under cycloplegia is often unnecessary, since autorefractors can provide similar accuracy and precision under cycloplegia in a much shorter time [5,6]. 5. Conclusions In this study, no significant differences were found between the two optometrists for any of the refractive variables, either with or without cycloplegia. However, the use of cycloplegia improved the inter-optometrist repeatability of the spherical equivalent (M) by 0.25 D, which was considered clinically relevant. These results suggest that accommodation in young hyperopes is likely a primary source of error that could explain the discrepancies found in subjective refraction between optometrists. Supplementary Materials: The following supporting information can be downloaded at: https://www. mdpi.com/article/10.3390/photonics11121180/s1, Table S1: Raw data used for the statistical analysis. Author Contributions: Conceptualization, C.C.-T. and G.C.; methodology, C.C.-T. and G.C.; investiga- tion, M.R.-L. and C.P.; resources, A.P.-A., M.S., and L.B.; writing—original draft preparation, C.C.-T.; writing—review and editing, M.R.-L., C.P., A.P.-A., M.S., L.B. and G.C.; supervision, G.C.; project administration, G.C. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Institutional Review Board Statement: The study was conducted in accordance with Good Clinical Practice guidelines, European institutional regulations, and the Declaration of Helsinki. The protocol was approved by the ethics committee of the Hospital Clínico San Carlos (code 18/459-R_P; date of approval: 16 November 2018), affiliated with the Complutense University of Madrid (Spain). Informed Consent Statement: Informed consent was obtained from all subjects involved in the study. Data Availability Statement: The original contributions presented in the study are included in the Supplementary Materials; further inquiries can be directed to the corresponding author. Conflicts of Interest: The authors declare no conflicts of interest. References 1. Elliott, D.B. What is the appropriate gold standard test for refractive error? Ophthalmic. Physiol. Opt. 2017, 37, 115–117. [CrossRef] 2. Zadnik, K.; Mutti, D.O.; Adams, A.J. The repeatability of measurement of the ocular components. Investig. Ophthalmol. Vis. Sci. 1992, 33, 2325–2333. 3. Bullimore, M.A.; Fusaro, R.E.; Adams, C.W. The repeatability of automated and clinician refraction. Optom. Vis. Sci. 1998, 75, 617–622. [CrossRef] [PubMed] 4. Carpena-Torres, C.; Batres, L.; Serramito, M.; Carracedo, G. Repeatability of Subjective Refraction in Different Age Groups. Photonics 2024, 11, 634. [CrossRef] 5. Yazdani, N.; Sadeghi, R.; Momeni-Moghaddam, H.; Zarifmahmoudi, L.; Ehsaei, A. Comparison of cyclopentolate versus tropicamide cycloplegia: A systematic review and meta-analysis. J. Optom. 2018, 11, 135–143. [CrossRef] [PubMed] 6. Wilson, S.; Ctori, I.; Shah, R.; Suttle, C.; Conway, M.L. Systematic review and meta-analysis on the agreement of non-cycloplegic and cycloplegic refraction in children. Ophthalmic. Physiol. Opt. 2022, 42, 1276–1288. [CrossRef] [PubMed] 7. Thibos, L.N.; Wheeler, W.; Horner, D. Power vectors: An application of Fourier analysis to the description and statistical analysis of refractive error. Optom. Vis. Sci. 1997, 74, 367–375. [CrossRef] [PubMed] https://www.mdpi.com/article/10.3390/photonics11121180/s1 https://www.mdpi.com/article/10.3390/photonics11121180/s1 https://doi.org/10.1111/opo.12360 https://doi.org/10.1097/00006324-199808000-00028 https://www.ncbi.nlm.nih.gov/pubmed/9734807 https://doi.org/10.3390/photonics11070634 https://doi.org/10.1016/j.optom.2017.09.001 https://www.ncbi.nlm.nih.gov/pubmed/29132914 https://doi.org/10.1111/opo.13022 https://www.ncbi.nlm.nih.gov/pubmed/35913773 https://doi.org/10.1097/00006324-199706000-00019 https://www.ncbi.nlm.nih.gov/pubmed/9255814 Photonics 2024, 11, 1180 8 of 8 8. McAlinden, C.; Khadka, J.; Pesudovs, K. Precision (repeatability and reproducibility) studies and sample-size calculation. J. Cataract Refract. Surg. 2015, 41, 2598–2604. [CrossRef] [PubMed] 9. McGraw, K.O.; Wong, S.P. Forming interferences about some intraclass correlation coefficients. Psychol. Methods 1996, 1, 30–46. [CrossRef] 10. Bland, J.M.; Altman, D.G. Measuring agreement in method comparison studies. Stat. Methods Med. Res. 1999, 8, 135–160. [CrossRef] [PubMed] 11. Perrigin, J.; Perrigin, D.; Grosvenor, T. A comparison of clinical refractive data obtained by three examiners. Am. J. Optom. Physiol. Opt. 1982, 59, 515–519. [CrossRef] 12. Goss, D.A.; Grosvenor, T. Reliability of refraction—A literature review. J. Am. Optom. Assoc. 1996, 67, 619–630. [PubMed] 13. Rosenfield, M.; Chiu, N.N. Repeatability of subjective and objective refraction. Optom. Vis. Sci. 1995, 72, 577–579. [CrossRef] [PubMed] 14. Raasch, T.W.; Schechtman, K.B.; Davis, L.J.; Zadnik, K. Repeatability of subjective refraction in myopic and keratoconic subjects: Results of vector analysis. Ophthalmic Physiol. Opt. 2001, 21, 376–383. [CrossRef] [PubMed] 15. Nagra, M.; Dashrathi, R.; Senthan, E.; Jahan, T.; Campbell, P. Characterisation of internal, refractive, and corneal astigmatism in a UK university student population. Cont. Lens Anterior Eye 2020, 43, 333–337. 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MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. https://doi.org/10.1016/j.jcrs.2015.06.029 https://www.ncbi.nlm.nih.gov/pubmed/26796439 https://doi.org/10.1037/1082-989X.1.1.30 https://doi.org/10.1177/096228029900800204 https://www.ncbi.nlm.nih.gov/pubmed/10501650 https://doi.org/10.1097/00006324-198206000-00012 https://www.ncbi.nlm.nih.gov/pubmed/8942135 https://doi.org/10.1097/00006324-199508000-00007 https://www.ncbi.nlm.nih.gov/pubmed/8539026 https://doi.org/10.1046/j.1475-1313.2001.00596.x https://www.ncbi.nlm.nih.gov/pubmed/11563425 https://doi.org/10.1016/j.clae.2020.02.007 Introduction Materials and Methods Study Design and Sample Subjective Refraction Procedure and Analysis Statistical Analysis Results Discussion Conclusions References