Effective Refractive Power Research Articles

Novel developments of refractive power measurement techniques in the automotive world

Refractive power measurements serve as the primary quality standard in the automotive glazing industry. In the light of autonomous driving new optical metrics are becoming more and more popular for specifying optical quality requirements for the windshield. Nevertheless, the link between those quantities and the refractive power needs to be established in order to ensure a holistic requirement profile for the windshield. As a consequence, traceable high-resolution refractive power measurements are still required for the glass quality assessment. Standard measurement systems using Moiré patterns for refractive power monitoring in the automotive industry are highly resolution limited, wherefore they are insufficient for evaluating the camera window area. Consequently, there is a need for more sophisticated refractive power measurement systems that provide a higher spatial resolution. In addition, a calibration procedure has to be developed in order to guarantee for the comparability of the measurement results. For increasing the resolution, a measurement setup based on an auto-correlation algorithm is tested in this paper. In order to benchmark the proposed high-resolution refractive power measurement technique, a novel laser-based setup has been realized in the Volkswagen Laser Laboratory as a reference method tuned for high-accuracy measurements. Furthermore, a calibration procedure is established by using a single reference lens with a nominal refractive power of . For the calibration of the entire measurement range of the system, the lens is tilted by an inclination angle orthogonal to the optical axis. The effective refractive power is then given by the Kerkhof model. By adopting the measurement and calibration procedure presented in this paper, glass suppliers in the automotive industry will be able to detect relevant manufacturing defects within the camera window area more accurately paving the way for a holistic quality assurance of the windshield for future advanced driver-assistance system (ADAS) functionalities. Concurrently, the traceability of the measurement results is ensured by establishing a calibration chain based on a single reference lens, which is traced back to international standards.

Unsafe food additive sensing through octagonal-core photonic crystal fibre sensor

To detect food additives, a simple photonic crystal fibre design based on an octagonal hole and hollow circular cladding holes in two layers has been introduced. The numerical study of the design is conducted by simulation in the COMSOL Multiphysics software with the infiltrated test analytes: saccharin, sorbitol, and butyl acetate, operating in the wavelength variation from 1.6 to 4.0 μm. The performance of the proposed sensor is determined by analysing the principal optical parameters: effective refractive index, power fraction, relative sensitivity, confinement loss, chromatic dispersion, propagation constant, V-parameter, spot size, and beam divergence. At the optimal wavelength of 2.0 μm, the sensor design depicts high relative sensitivities of 98.06% for saccharin, 97.05% for sorbitol, 95.81% for butyl acetate, and 3.82 × 10−23 dBm−1 for saccharin, 3.44 × 10−22 dBm−1 for sorbitol, and 1.81 × 10−21 dBm−1 for butyl acetate for confinement loss, which is extremely low. Hence, the proposed food additive sensor is suitable for actual sensing applications based on these obtained results.

Photonic Crystal Fiber Sensor for Detecting Sulfuric Acid in Different Concentrations

A high-performance photonic crystal fiber sensor for sulfuric acid detection is designed and investigated, undertaken through a full vector Finite Element Method on COMSOL Multiphysics software to establish the optical properties of effective refractive index, power fraction, relative sensitivity, confinement loss, chromatic dispersion, and propagation constant. Different aqueous sulfuric acid concentrations of 0%, 10%, 20%, 30%, and 40% were selected as the test analytes. The dimensions of two cladding rings of the hexagon- and circular-shaped air holes and a circular core hole denoted outstanding outcomes of relative sensitivity and confinement loss. At 1.1 µm optimum wavelength, 0%, 10%, 20%, 30%, and 40% sulfuric acid concentrations depict relative sensitivities of 97.08%, 97.67%, 98.06%, 98.39%, and 98.67%, respectively, and confinement losses of 1.32 × 10−12 dB/m, 4.11 × 10−12 dB/m, 1.46 × 10−12 dB/m, 6.34 × 10−12 dB/m, and 2.12 × 10−12 dB/m, respectively.

Prediction of 12 Photonic Crystal Fiber Optical Properties Using MLP in Deep Learning

In this letter, we proposed the use of feed-forward multilayer perceptron in deep learning-based artificial neural network (ANN) to accurately predict 12 optical parameters of silica-based photonic crystal fiber (PCF) within milliseconds using 6 input parameters. The optimized ANN has 3 hidden layers and each layer has 50 neurons. The PCF has several hexagonal-shaped layers with circular air holes, and it uses silica as the cladding and FK51A glass as the core. The PCF parameters that have been successfully predicted include birefringence, chromatic dispersion, effective area, effective refractive index, nonlinear coefficient, numerical aperture, power fraction, relative sensitivity, V-parameter, and loss profiles such as confinement loss, effective material loss, and scattering loss. The prediction has high accuracy with a loss of only 0.00567 and a learning rate of 0.0001. 7-fold validation and batching are used to increase scalability during validation. The proposed ANN is over 99.9% faster than conventional numerical simulation approaches.

Non-degenerate mode power decomposition in optical fiber without prior knowledge

Based on the machine learning methods, a fiber mode decomposition technique is proposed and verified. By employing the principal component analysis and gradient descent algorithm, the effective refractive indexes and mode power weight of the non-degenerate eigenmodes in fiber can be obtained without prior knowledge of the measured fiber. Compared with similar methods such as S2 technique. The decomposition efficiency is increased, and the spurious modes can be also eliminated during the mode structure analysis. This method is applicable for optical fibers, as well as other waveguide structures, whose eigenmodes can be solved under weakly guiding approximation.

Simulation studies of DFB laser longitudinal structures for narrow linewidth emission

Simulation studies targeting high-power narrow-linewidth emission from DFB lasers are presented. The linewidth and output power calculations take into account the mirror losses, including the grating and the facets, as well as spontaneous emission noise, effective refractive index, power and carrier density variations inside the cavity. The longitudinal power and carrier density distributions have been evaluated and their effects on longitudinal spatial hole burning and possible side mode lasing are discussed.

Accuracy of Different Topographic Instruments in Calculating Corneal Power after Myopic Photorefractive Keratectomy.

Purpose:To compare the corneal power measurements obtained using different topographic instruments after myopic photorefractive keratectomy (PRK).Methods:Patients with myopia who were candidates for corneal refractive surgery were sequentially included. Pre-PRK and six months post-PRK corneal powers were measured using Javal manual keratometer, Orbscan II, Galilei, Tomey TMS4, and EyeSys 2000 topographers. Measured values were compared with those obtained using the clinical history method (CHM).Results:This study included 66 eyes of 33 patients. The lowest keratometric measurements were obtained using the Galilei topographer (42.98 ± 1.69 diopters, D) and the highest measurements were obtained using the Javal manual keratometer (43.96 ± 1.54 D) preoperatively. The same order was observed postoperatively. Effective refractive power (EffRP) measured using EyeSys was most similar to the values obtained using CHM (ICC, intraclass correlation coefficient = 0.951), followed by the total corneal power measured using the Galilei system (ICC = 0.943). The values obtained using the adjusted EffRP formula (EffRP – 0.015*Δ Refraction – 0.05) were more consistent with the values obtained using CHM (ICC = 0.954) compared to those obtained with the adjusted average central corneal power formula measured using the Tomey system (ICC = 0.919).Conclusion:Post-PRK corneal powers measured using the adjusted EffRP formula were the most similar to values obtained using CHM.

Correlation of Anterior Corneal Higher-order Aberrations With Age

The aim of this study was to investigate the distribution of higher-order aberrations (HOAs) of the anterior cornea of eyes with cataract in a senior Chinese population and their correlations with age. Four hundred ten Chinese patients (male/female: 196/214; age: 67.9 ± 10.0 years) with cataract were categorized into 5 groups according to their age. The HOAs in the central 6-mm zone of the cornea were measured with an iTrace wavefront analyzer. The correlations between age and total HOA, coma aberration, trefoil aberration, and spherical aberration were assessed using Spearman analysis. The differences in total HOA, coma aberration, trefoil aberration, spherical aberration among various age groups were analyzed using the Kruskal-Wallis H test. The corneal HOA exhibited a nonnormal distribution. A weak correlation was found between age and total HOA, coma aberration (Z3), trefoil aberration (Z3) (P < 0.001 for all). No correlation was found between age and spherical aberration (Z4). Differences in the root mean square of the total HOA, Z3, and Z3 were found among various age groups (P < 0.05). No difference was found in the root mean square of Z4, spherical diopter, corneal curvature, corneal astigmatism, corneal effective refractive power, corneal asphericity Q value and corneal central power across the groups. The distribution of anterior corneal HOAs of eyes with cataract in a senior Chinese population is of the nonnormal type. The total HOA, Z3, and Z3 are correlated to age, unlike Z4 of the anterior cornea.

Comparison of front-surface corneal topography and Bowman membrane specular topography in keratoconus

To define the contribution of the corneal epithelium in corneal topography in keratoconus and discuss the implications regarding combined topography-guided photorefractive keratectomy and corneal collagen crosslinking (CXL). French National Reference Center for Keratoconus, Bordeaux, France. Case series. Specular topographies were performed before and immediately after epithelial removal during conventional CXL surgery in patients with keratoconus. The study included 1 eye with forme fruste keratoconus, 4 eyes in Krumeich stage I, and 3 eyes in stage II. The mean simulated maximum keratometry (K) increased by 2.87 diopters (D) after epithelial removal. The mean effective refractive power increased by a mean of 4.01 D and the astigmatic refractive power, by a mean of 2.17 D. The difference in mean axis deviation was not significant. The mean inferior-superior ratio irregularity index increased 1.51 units. All K and refractive readings except astigmatic refractive axis were significantly increased after epithelial removal. All regularity indices increased significantly without the epithelium. The amplitude of variations in K readings made it difficult to predict the refractive changes after custom laser photoablation based on epithelial-based topography. The astigmatism refractive axis did not change significantly; therefore, this axis could be useful for astigmatic corrections, whereas the spherical component would not be useful. Topographic changes after epithelial removal can be important but not intuitive in keratoconus eyes. This should be considered in custom topography-guided photoablation strategies when attempting to correct refractive errors at the time of CXL.

Characterization of dielectric-coated metallic hollow fiber with subwavelength diameter at terahertz frequency

Dielectric-coated metallic hollow fiber (DMHF) is an increasingly popular fiber for the delivery of terahertz (THz) wave. There is a need for small-diameter fibers in a variety of THz wave applications. Transmission characteristics of DMHF with subwavelength diameter in the THz region are numerically investigated. The effective refractive indices, attenuation constants, and power distributions are presented. The effect of the metal layer on enhancing the modal field confinement is demonstrated by comparing the power distribution of the fiber to that of the polymer tube. Attenuation dependence on the dielectric layer is studied concerning the layer thickness and the refractive index. Both the optimal thickness and the optimal refractive index for the dielectric layer are dependent on the core size. Fiber with a smaller core requires a thicker dielectric layer and lower dielectric refractive index to achieve low attenuation. The results are important to the design of subwavelength diameter DMHF for the transmission of THz waves.

TE surface waves in dielectric slab sandwiched between LHM slabs

In this work, the dispersion relation for TE surface waves has been derived for a slab waveguide constructed from a dielectric material slab sandwiched between two thick layers of left-handed material (LHM). The dispersion relation and the power flow were numerically solved for a given set of parameters: the structural factor, dielectric slab thickness, and the operating frequency on the effective refractive index and power flow. We found that the wave effective refractive index decreases with thickness increase as well as increase in frequency. We found that the effective refractive index increases slightly with increase of structural factor. Also, the power flow increases with thickness and increases with operating frequency.

IOL-Kalkulation nach refraktiver Chirurgie

Cataract surgery is evolving more and more into a refractive procedure with high expectations in terms of visual rehabilitation. Especially patients presenting after previous Excimer laser corneal surgery are used to being independent from glasses. Unfortunately, some of these patients showed unexpected hyperopic surprises after cataract surgery in the past. The changes of corneal radii and keratometer index as well as the inaccurate prediction of the postoperative intraocular lens (IOL) position using different formulas were determined as error sources which led to a reduced IOL power calculation in dioptres. Several methods have been proposed to solve this problem which can be divided in two groups. On the one hand, there are methods that depend on refraction and biometry values before the initial treatment (e. g., clinical history, Feiz-Mannis, double-K, adjusted effective refractive power [EffRadj]-, cornea bypass/Wake Forest methods as well as correction factors to adjust K-values) and on the other hand procedures that only need current pre-cataract surgery measurements (e. g., contact lens method, corneal topography systems, ray tracing, aphakic refraction technique, correction factors to adjust K-values and new formulas including Haigis-L or BESSt and recently a novel pachymetry method). This review describes these procedures and analyses their strengths and weaknesses. The number of presented methods emphasises already that no perfect solution has been determined so far that would be valid for every patient. Some methods do provide a good predictability; however, individual deviations can occur. In general, it is advisable to inform the patient about the higher risk for an inaccurate IOL power calculation. It can be helpful to compare the results of different methods indicating the importance to provide all required individual data by the refractive surgeon already.

Optical coupling between two nanobelts

In this study, we have investigated effective refractive index (ERI) and power confinement factor (PCF) in single nanobelt and coupling between two parallel nanobelts using finite-difference time-domain (FDTD) method. As the width of nanobelt increases, both the effective refractive index (ERI) and power confinement factor (PCF) are increased till the saturation values. The ERI changes linearly with refractive index in our simulation range, while the PCF shows nonlinear characteristic. The coupling length ( L T ) between two nanobelts is much shorter than that in weakly coupled waveguide, which may find applications in solving the cross talk problem. Nanobelt behaves like slab waveguide when the width becomes big enough.

TE Magnetostatic Surface Waves in Symmetric Dielectric Negative Permittivity Material Waveguide

Nonlinear magnetostatic surface wave in a slab waveguide structure has been investigated. The design consisted of dielectric film between two thick nonlinear nonmagnetic negative permittivity material (NPM) layers. A dispersion relation for TE nonlinear Magnetostatic surface waves (NMSSWs) has been derived into the proposed structure and has been numerically investigated. Effective refractive index decreases with thickness and frequency increase have been found. Effective refractive index decrease with optical nonlinearity increase and switching to negative values of effective refractive index at a certain value of optical nonlinearity have been found. This meant that the structure behaved like a left-handed material over certain range. We found that the power flow was changing by changing the operating frequency, the dielectric film thickness, and the optical nonlinearity. Also, the effective refractive index and power flow attained constant values over certain values of dielectric constant values.

Intraocular lens geometry makes a difference: author's reply

Editor, I want to thank Wolfgang Haigis for his comments on the geometry of the intraocular lens (IOL) (Haigis 2004). This issue is important in every method of IOL power calculation. It is true that optic configuration makes a difference in the effective refractive power of the IOL, as it affects the position of the effective lens plane. When Alcon (Fort Worth, TX, USA) changed the optic design of the MA60BM (biconvex 2 : 1 configuration) to that of the MA60AC (biconvex 1 : 1), the effective lens plane was shifted anteriorly, thereby increasing the refractive effect of the IOL and decreasing the A-constant. So much for the A-constant and other fudge factors. However, this does not mean that the physical position of the IOL shifts by a comparable amount. In fact, it is our experience, based on hundreds of ultrasound measurements of postoperative anterior chamber depth (ACD), that the average (measurable) ACD changes surprisingly little in response to optic configuration. By contrast, the ACD does change according to haptics design, and according to whether the IOL is placed within or outside the capsular bag, the type and size of capsulotomy, etc. However, thanks to the standardized capsulorhexis technique, time is running out for ‘personalizing’ IOL power calculations according to surgical technique. Accordingly, my statement that postoperative ACD was 4.74 mm for both IOL types was based on these measurements, assuming that no major error was made (Olsen 2007). Of course, the Olsen formula takes the different optic configurations of the two lenses into account in a separate algorithm, ensuring that the correction of principal planes is carried out according to ‘thick lens’ optics. I agree with Wolfgang Haigis that in theory the ACD of the IOL with the steepest anterior curvature is expected to be the smallest, other things being equal. However, if we had been able to improve our predictions by this small correction, all comparison groups would have been changed by an equal amount, which would not have altered our conclusions. We therefore still believe that our 5-variable method of predicting ACD is more accurate than the Haigis 2-variable method. As we demonstrated in Olsen (2006), lens thickness was ranked third after axial length and preoperative chamber depth in the statistical association of postoperative ACD with the IOL. Unfortunately, lens thickness is not measured with the current version of the Zeiss IOLMaster (Carl Zeiss Meditec AG, Jena, Germany) and therefore must continue to be measured with ultrasound.

Biometry and intraocular lens power calculation

This article surveys the literature of 1 year, between July 2003 and August 2004, on the topic of biometry and intraocular lens power calculation for cataract surgery. There is an increasing demand for low postoperative refractive error with rising patient expectations, especially with patients who have already undergone refractive surgery, and with developing intraocular lens technologies such as multifocal, accommodating, or toric intraocular lenses. Optical biometry has become an invaluable tool for axial length measurement, especially for a setting with a less experienced biometrist. Introduction of ray tracing for power calculation and new methods of dealing with power calculation in eyes that have undergone previous refractive surgery seem promising. New intraocular lens designs that allow adjusting the axial optic position and therefore the effective refractive power of the intraocular lens have been evaluated in animal studies.

Comparison of intraocular lens power calculation methods in eyes that have undergone LASIK

Objective To compare methods of calculating intraocular lens (IOL) power for cataract surgery in eyes that have undergone myopic LASIK. Design Noncomparative case series. Participants Eleven eyes of 8 patients who had previously undergone myopic LASIK (amount of LASIK correction [±standard deviation], −5.50±2.61 diopters [D]; range, −8.78 to −2.38 D) and subsequently phacoemulsification with implantation of the SA60AT IOLs (Alcon Surgical, Inc., Fort Worth, TX) were included (refractive error after cataract surgery, −0.61 ± 0.79 D; range, −2.0 to 1.0 D). Methods We evaluated the accuracy of various combinations of: (1) single-K versus double-K (in which pre-LASIK keratometry is used to estimate effective lens position) versions of the IOL formulas; the Feiz–Mannis method was also evaluated; (2) 4 methods for calculating corneal refractive power (clinical history, contact lens overrefraction, adjusted effective refractive power [EffRP adj], and Maloney methods); and (3) 4 IOL formulas (SRK/T, Hoffer Q, Holladay 1, and Holladay 2). The IOL prediction error was obtained by subtracting the IOL power calculated using various methods from the power of the implanted IOL, and the F test for variances was performed to assess the consistency of the prediction performance by different methods. Main outcome measures Mean arithmetic IOL prediction error, mean absolute IOL prediction error, and variance of the IOL prediction error. Results Compared with double-K formulas, single-K formulas predicted lower IOL powers than the power implanted and would have left patients hyperopic in most cases; the Feiz–Mannis method had the largest variance. For the Hoffer Q and Holladay 1 formulas, the variances for EffRP adj were significantly smaller than those for the clinical history method (0.43 D 2 vs. 1.74 D 2, P = 0.018 for Hoffer Q; 0.75 D 2 vs. 2.35 D 2, P = 0.043 for Holladay 1). The Maloney method consistently underestimated the IOL power but had significantly smaller variances (0.19–0.55 D 2) than those for the clinical history method (1.09–2.35 D 2; P<0.015). There were no significant differences among the variances for the 4 formulas when using each corneal power calculation method. Conclusions The most accurate method was the combination of a double-K formula and corneal values derived from EffRP adj. The variances in IOL prediction error were smaller with the Maloney and EffRP adj methods, and we propose a modified Maloney method and second method using Humphrey data for further evaluation.

Intraocular lens power calculation after incisional and thermal keratorefractive surgery

Purpose: To evaluate the efficacy of corneal topography in determining the central corneal refractive power in intraocular lens (IOL) power calculations after incisional and thermal keratorefractive surgery. Setting: Oregon Eye Institute, Eugene, Oregon, USA. Methods: This retrospective review comprised 20 eyes (14 patients) that had cataract extraction with IOL implantation or refractive lens exchange after radial keratotomy, hexagonal keratotomy, or laser thermal keratoplasty. The effective refractive power (EffRP) of the Holladay Diagnostic Summary on the EyeSys Corneal Analysis System was used to determine the central corneal refractive power, which was input into the Holladay 2 IOL calculation formula. Results: Eighty percent of eyes achieved a postoperative spherical equivalent refraction within ±0.50 diopter of emmetropia. Conclusion: The use of the EffRP increases the likelihood of an acceptable refractive outcome after cataract or refractive lens exchange surgery in eyes with a history of keratorefractive surgery.

Comparison of changes in manifest refraction and corneal power after photorefractive keratectomy

PURPOSE: To determine which corneal curvature values most closely correlate to change in manifest refraction after excimer laser photorefractive keratectomy. METHODS: In a prospective study at the Cullen Eye Institute, excimer laser photorefractive keratectomy was performed on 27 eyes of 27 patients (mean age, 38.07 ± 6.65 years). Preoperative refractive errors ranged from −2.25 diopters to −8.75 diopters (mean, −5.74 ± 2.09 diopters). Preoperatively and 1 month postoperatively, we determined the spherical equivalent of the subjective manifest refraction (corrected for a 12-mm vertex distance) and measured corneal power using standard keratometry (Bausch & Lomb Keratometer; Rochester, New York) and computerized videokeratography (EyeSys Corneal Analysis System; Premier Laser Systems Inc, Houston, Texas). We collected 15 corneal values: standard keratometry and 14 computerized videokeratography values calculated using the axial, instantaneous, and refractive formulas. All calculations were performed with 1.3375 and 1.376 for the refractive index of the cornea. For each of the corneal values, we subtracted the change in corneal power from the change in manifest refraction and calculated for this difference the means, SDs, correlations, and regressions. RESULTS: Mean differences between change in refraction and change in corneal power were lower when for a refractive index of 1.376 than for 1.3375, were lowest for the most central measurement points, and displayed a high SD. A value of 1.408 for the refractive index would be required to optimize the correlation between change in manifest refraction and effective refractive power of the central 3 mm of the cornea. CONCLUSIONS: For individual patients who have undergone photorefractive keratectomy, changes in corneal values determined by computerized videokeratography or by standard keratometry do not reliably predict change in manifest refraction.

Corneal Topography and Postoperative Refraction After Cataract Phacoemulsification Following Radial Keratotomy

We present one case in which phacoemulsification was performed seven years after radial keratotomy (RK). A 55-year-old military police officer had undergone successful bilateral RK for the correction of myopia seven years before he developed a cataract in his left eye. Pre-RK keratometric and refractive data and post-RK myopia reduction were not available. We relied upon corneal topography to measure corneal refractive power. We took the Effective Refractive Power (EffRP) index from EyeSys Holladay's Diagnostic Summary and used SRK-T formula for IOL calculation. A-scan axial length readings were consistent and reliable (AL = 26.0 mm). Aiming at postoperative emmetropia, we implanted a +20D PC IOL (A cost. = 118) was implanted. The lens was expected (SRK-T formula) to give a -1.35D postoperative refraction. After uneventful cataract surgery, corneal topography showed significant corneal instability with central corneal flattening in the first postoperative weeks, mild central corneal steepening at week 6, and return to preoperative corneal curvature at week 23. One year after cataract extraction, the patient's spherical equivalent is +1.12D, showing a prediction error of about 2.5 diopters.