Best-fit Sphere Research Articles

Three-dimensional assessment of subchondral arc and hip joint coverage angles in the asymptomatic young adult hip.

The primary objective of this study was to develop a custom algorithm to assess three-dimensional (3D) acetabular coverage of the femoral head based on surface models generated from computed tomography (CT) imaging. The secondary objective was to apply this algorithm to asymptomatic young adult hip joints to assess the regional 3D acetabular coverage variability and understand how these novel 3D metrics relate to traditional two-dimensional (2D) radiographic measurements of coverage. The algorithm developed automatically identifies the lateral- and medial-most edges of the acetabular lunate at one-degree intervals around the acetabular rim based on local radius of curvature. The acetabular edges and the center of a best-fit sphere to the femoral head are then used to compute the mean 3D subchondral arc angles and hip joint coverage angles in five acetabular octants. This algorithm was applied to hip models generated from pelvis/hip CT imaging or abdomen/pelvis CT angiograms of 50 patients between 17 and 25 years of age who had no history of congenital or developmental hip pathology, neuromuscular conditions, or bilateral pelvic and/or femoral fractures. Corresponding 2D acetabular coverage measures of lateral center edge angle (LCEA) and acetabular arc angle (AAA) were assessed on the patients' clinical or digitally reconstructed radiographs. The 3D subchondral arc angle in the superior region (58.0 [54.6-64.8] degrees) was significantly higher (p < 0.001) than all other acetabular subregions. The 3D hip joint coverage angle in the superior region (26.2 [20.7-28.5] degrees) was also significantly higher (p < 0.001) than all other acetabular subregions. 3D superior hip joint coverage angle demonstrated the strongest correlation with 2D LCEA (r = 0.649, p < 0.001), while 3D superior-anterior subchondral arc angle demonstrated the strongest correlation with 2D AAA (r = 0.718, p < 0.001). The 3D coverage metrics in the remaining acetabular regions did not strongly correlate with typical 2D radiographic measures. The discrepancy between standard 2D measures of radiographic acetabular coverage and actual 3D coverage identified on advanced imaging indicates potential discord between anatomic coverage and the standard clinical measures of coverage on 2D imaging. As 2D measurement of acetabular coverage is increasingly used to guide surgical decision-making to address acetabular deformities, this work would suggest that 3D measures of acetabular coverage may be important to help discriminate local coverage deficiencies, avoid inconsistencies resulting from differences in radiographic measurement techniques, and provide a better understanding of acetabular coverage in the hip joint, potentially altering surgical planning and guiding surgical technique.

Predicting the Shape of Corneas from Clinical Data with Machine Learning Models

ObjectiveIn ophthalmology, there is a need to explore the relationships between clinical parameters of the cornea and the corneal shape. This study explores the paradigm of machine learning with nonlinear regression methods to verify whether corneal shapes can effectively be predicted from clinical data only, in an attempt to better assess and visualize their effects on the corneal shape. MethodsThe dimensionality of a database of normal anterior corneal surfaces was first reduced by Zernike modeling into short vectors of 12 to 20 coefficients used as targets. The associated structural, refractive and demographic corneal parameters were used as predictors. The nonlinear regression methods were borrowed from the scikit-learn library. All possible regression models (method + predictors + targets) were pre-tested in an exploratory step and those that performed better than linear regression were fully tested with 10-fold validation. The best model was selected based on mean RMSE scores measuring the distance between the predicted corneal surfaces of a model and the raw (non-modeled) true surfaces. The quality of the best model's predictions was visually assessed thanks to atlases of average elevation maps that displayed the centroids of the predicted and true surfaces on a number of clinical variables. ResultsThe best model identified was gradient boosting regression using all available clinical parameters to predict 16 Zernike coefficients. The predicted and true corneal surfaces represented in average elevation maps were remarkably similar. The most explicative predictor was the radius of the best-fit sphere, and departures from that sphere were mostly explained by the eye side and by refractive parameters (axis and cylinder). ConclusionIt is possible to make a reasonably good prediction of the normal corneal shape solely from a set of clinical parameters. In so doing, one can visualize their effects on the corneal shape and identify its most important contributors.

Spatial targeted delivery of riboflavin with a controlled corneal iontophoresis delivery system in theranostic-guided UV-A light photo-therapy.

Seven human donor eye globes underwent corneal cross-linking using theranostic UV-A device with accessory corneal iontophoresis system for patterned delivery of a 0.22% riboflavin solution. Theranostic-guided UV-A light illumination assessed riboflavin distribution and treated corneas at 10 mW/cm2 for 9 min with a 5.0-mm beam size. Corneal topography maps were taken at baseline and 2-h post-treatment. Analysis utilized corneal topography elevation data, with results showing controlled riboflavin delivery led to a consistent gradient, with 40% higher levels centrally (248 ± 79 μg/cm3) than peripherally (180 ± 72 μg/cm3 at ±2.5 mm from the center). Theranostic-guided UV-A light irradiation resulted in significant changes in corneal topography, with a decrease in best-fit sphere value (-0.7 ± 0.2 D; p < 0.001) and consistent downward shift in corneal elevation map (-11.7 ± 3.7 μm). The coefficient of variation was 2.5%, indicating high procedure performance in achieving significant and reliable corneal flattening.

A scapular statistical shape model can reliably predict premorbid glenoid morphology in conditions of severe glenoid bone loss

Knowledge of premorbid glenoid parameters at the time of shoulder arthroplasty, such as inclination, version, joint line position, height, and width, can assist with implant selection, implant positioning, metal augment sizing, and/or bone graft dimensions. The objective of this study was to validate a scapular statistical shape model (SSM) in predicting patient-specific glenoid morphology in scapulae with clinically relevant glenoid erosion patterns. Computed tomography scans of 30 healthy scapulae were obtained and used as the control group. Each scapula was then virtually eroded to create 7 erosion patterns (Walch A1, A2, B2, B3, D, Favard E2, and E3). This resulted in 210 uniquely eroded glenoid models, forming the eroded glenoid group. A scapular SSM, created from a different database of 85 healthy scapulae, was then applied to each eroded scapula to predict the premorbid glenoid morphology. The premorbid glenoid inclination, version, height, width, radius of best-fit sphere, and glenoid joint line position were automatically calculated for each of the 210 eroded glenoids. The mean values for all outcome variables were compared across all erosion types between the healthy, eroded, and SSM-predicted groups using a 2-way repeated measures analysis of variance. The SSM was able to predict the mean premorbid glenoid parameters of the eroded glenoids with a mean absolute difference of 3°±2° for inclination, 3°±2° for version, 2 ± 1 mm for glenoid height, 2 ± 1 mm for glenoid width, 5 ± 4 mm for radius of best-fit sphere, and 1 ± 1 mm for glenoid joint line. The mean SSM-predicted values for inclination, version, height, width, and radius were not significantly different than the control group (P>.05). An SSM has been developed that can reliably predict premorbid glenoid morphology and glenoid indices in patients with common glenoid erosion patterns. This technology can serve as a useful template to visually represent the premorbid healthy glenoid in patients with severe glenoid bony erosions. Knowledge of the premorbid glenoid preoperatively can assist with implant selection, positioning, and sizing.

Corneal densitometry changes after femtosecond laser-assisted intracorneal ring segments implantation in keratoconus.

Intrastromal corneal ring segments are commonly implanted in the corneas of eyes with mild-to-moderate keratoconus; however, changes in corneal densitometry (CD) after implantation are a matter of debate in the current literature. We evaluated the changes in CD 1 and 3 months after femtosecond laser-assisted Keraring implantation. This retrospective, non-comparative, multicenter, case series study included patients with keratoconus who underwent femtosecond laser-assisted implantation of double segments with 90° and 160° arc lengths or two 160° arc length Keraring segments. Demographic and baseline clinical ophthalmic data were recorded. Corneal topography and tomography data acquired using a Pentacam HR Scheimpflug tomography system (Pentacam High Resolution; Oculus, Wetzlar, Germany) with a best-fit sphere were used as a reference surface. Using the Pentacam HR, CD measurements were acquired over a corneal area of 12 mm in total and at four concentric zones (0-2, 2-6, 6-10, and 10-12 mm) of three corneal stromal depths: 120 μm of the anterior corneal stromal layer, 60 μm of the posterior corneal stromal layer, and the central layer of stroma lying between these two layers. We included 40 eyes of 40 patients, including 8 (20%) male and 32 (80%) female individuals, with a mean (standard deviation) age of 21.0 (6.4) years. We observed a significant improvement in the topographic values of steep keratometry (K), flat K, maximum K, and corneal astigmatism (all P < 0.05), but not in the mean K, thinnest corneal pachymetry, corneal thickness at the apex, back elevation, or front elevation (all P > 0.05). The mean total anterior, central, and posterior CD differed significantly among the time points, with a significant increase from the preoperative to the 1-month and 3-month postoperative visits (all P < 0.05) and no difference between those of the 1-month and 3-month postoperative visits (all P > 0.05). The mean CD for the anterior layer in the central, paracentral, and mid-peripheral zones, and the central layer in all four zones, differed significantly among time points, with a significant increase from the preoperative to the 1-month and 3-month postoperative visits (all P < 0.05), which remained unchanged from the 1-month to the 3-month postoperative visit (all P < 0.05), except for the central 2-6-mm zone, which decreased significantly from the 1-month to the 3-month postoperative visit (P < 0.001). The CD of the central 10-12-mm zone did not differ significantly in each pairwise comparison (all P > 0.05). In contrast, CD for the posterior layer in the paracentral zone decreased significantly from the preoperative to the 1-month and 3-month postoperative visits but increased, to a lesser extent, from the 1-month to the 3-month postoperative visit (all P < 0.05). Femtosecond laser-assisted Keraring implantation significantly changes CD, with improvement in most topography parameters. Further longitudinal studies with larger sample sizes are required to verify these preliminary findings.

Acute Corneal Hydrops in Keratoconus Coinciding With COVID-19 Infection.

To the Editor: Acute corneal hydrops (AH), characterized by corneal stromal edema after a Descemet membrane rupture that allows aqueous humor entry, is observed in cases of keratoconus. Patients typically present with rapidly deteriorating visual acuity, photophobia, and pain. A timely diagnosis and management are essential to ruling out other vision-threatening pathologies such as corneal edema, infectious keratitis, uveitis, Fuchs endothelial dystrophy, postoperative edema, and acute transplant rejection. Here we describe a case of AH in a patient with keratoconus coinciding with coronavirus disease 2019 (COVID-19) infection and emphasize the importance of patient education in the context-restricted face-to-face consultations. A 20-year-old healthy man was evaluated regularly every 3 months for keratoconus using visual acuity and refraction assessments and anterior segment optical coherence tomography imaging. He wore corneal rigid gas-permeable contact lenses in both eyes. He also had a mild ocular allergy but no atopy or habit of eye-rubbing. There was no family history of keratoconus. A year earlier, he had an episode of AH in his left eye. While his left eye stabilized after pressure patching, the keratoconus progressed in his right eye. Examination findings at his last visit before the COVID-19 diagnosis included: corrected distance visual acuity with a gas-permeable contact lens of 20/30 (right) and 20/16 (left), anterior keratometry of 66.4 D (right) and 43.5 D (left), the thinnest corneal thickness of 264 mm (right) and 468 mm (left), and posterior “best-fit sphere” 9-mm radius values of 4.88 (right) and 6.46 mm (left). Approximately 2 months after the last follow-up, he developed flu-like symptoms (sore throat and fever) and was diagnosed the next day with COVID-19 on polymerase chain reaction. Two days after symptom onset, he noticed sudden deterioration of vision in his right eye and called our hospital. The cornea specialist in the ophthalmology department made a tentative phone diagnosis of AH based on his ocular history and instructed him to apply a pressure patch with ophthalmic ointment. He was examined at our hospital after 10 days of quarantine. The corrected distance visual acuity of the right eye was 20/2000, while a slitlamp examination revealed corneal protrusion and marked corneal epithelial as well as stromal edema in the right eye. Fluorescein corneal observation showed no epithelial abnormality, and a definitive AH diagnosis was made. Optical coherence tomography imaging revealed a break in Descemet membrane with overlying corneal edema (Supplemental Digital Content Fig. 1, https://links.lww.com/APJO/A179). No abnormality was noted in the left eye. He had received the second COVID-19 vaccine dose 1 month before the viral infection and reported experiencing no vaccine-related complications. On examination a month later, the AH in the right eye had remarkably improved. Various ophthalmic management and care delivery experiences have been reported during the COVID-19 pandemic. Perspectives in corneal crosslinking were reported relating to keratoconus in particular.1,2 To the best of our knowledge, our case is the first of AH with concomitant keratoconus and COVID-19 infection, although it was not possible to demonstrate a clear association among them. A previous history of AH in either eye is a predisposing risk factor for AH.3 This case underscores the importance of informing patients of their disease status and the need to undergo regular examinations. However, patients with COVID-19 may not be able to receive a timely ophthalmic examination. This patient was distressed until the postquarantine ophthalmic examination was performed; however, his previous experience with AH including successful pressure patching was helpful for the clinician and patient, who was better able to understand the extent of his condition and follow the provided instructions. In the absence of a clinical history of keratoconus, effectively managing AH before a face-to-face examination could be performed would have been challenging. Here are summary points of consideration when educating a patient with an acute event during a pandemic setting: Recognize the patient’s distress due to being in isolation during the acute event. Provide clear information about the disease and instructions for its independent management during quarantine. Strict hand hygiene should be thoroughly practiced while applying the pressure patch and patients should keep unwashed hands away from their face at times. Remote management may require conservative management methods. This requires careful consideration, particularly in acute ophthalmic cases. Although keratoconus was previously considered a noninflammatory ectatic corneal disease, recent evidence shows a relationship between its pathogenesis and chronic inflammatory events.4,5 Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection is known to cause a proinflammatory state.6 There are several reports of corneal graft rejection in patients infected with COVID-19.6–8 Large population-based case-control studies are needed to investigate the possible association between AH in keratoconus and the SARS-CoV-2 cytokine response. Shizuka Koh, MD, PhD*† Takeshi Soma, MD, PhD† Vishal Jhanji, MD‡ Kohji Nishida, MD, PhD†

Relationship between Diurnal Variation in Intraocular Pressure and Central Corneal Power.

Relationship between intraocular pressure (IOP) change and central corneal curvature is complicated by measurement techniques and corneal biomechanical parameters. Findings from this study indicate that it is worthwhile to observe the association between diurnal change in IOP and corneal power. This study aimed to investigate the relationship between the diurnal change in IOP and central corneal power among eyes with and without myopia. Sixty healthy eyes of 24 emmetropes and 36 myopes were recruited for this cross-sectional study. Both anterior and posterior central corneal powers of the steep (Ks), flat (Kf), mean meridian (Km), best-fit spheres, and central corneal thickness were recorded followed by the IOP (Goldmann-correlated IOP [IOPg] and corneal-compensated IOP) and corneal biomechanics (corneal hysteresis and corneal resistance factor). Measurements were obtained every 3 hours from 9.30 am to 6.30 pm . Linear-mixed model was used to determine the relationship between the change in IOP and the associated change in corneal measurements (adjusted for age, sex, refractive error, central corneal thickness, and biomechanics) among the myopic and nonmyopic eyes. Group mean, amplitude of change, and the diurnal change in IOPg were (mean ± standard deviation) 15.14 ± 2.50, 3.33 ± 1.44, and 1.81 ± 1.25 mmHg, respectively. Overall, an IOP increase was associated with a decrease in the adjusted anterior corneal powers. Myopic eyes were associated with a decrease of 0.04 D (95% confidence interval [CI], 0.07 to 0.01 D; P = .02) in Ks and 0.03 D (95% CI, 0.06 to 0.001 D; P = .047) in Kf per mmHg increase in IOP, whereas for emmetropes, per mmHg increase in IOP only flattened the Kf by 0.03 D (95% CI, 0.06 to 0.004 D; P = .02). Change in anterior corneal power was inversely related to the change in IOPg, with myopic and nonmyopic eyes reporting a significant but differential impact of IOP. Clinicians must keep in mind the impact of large IOP fluctuation on the anterior corneal power.

Wavefront optical spacing of freeform surfaces and its measurement using CGH interferometry

For optical surfaces, the distance between the wavefront at ideal design position and that at real surface testing position along the wavefront propagation direction is an important parameter. It determines the on-axis curvature deviation and best-fit sphere radius of the surface under testing, and thus, affects the optical distance, effective focal length, and tolerance design of the optical system. We define the distance as wavefront optical spacing (WOS or spacing d). The analytical form of the WOS can be utilised in critical tolerance balancing, and its test results can aid in optical system redesign. Aiming at a computer-generated hologram (CGH) interferometric test, in this study, we propose the WOS concept and deduce the coupling relation between the surface error and spacing d, particularly in freeform surface conditions. A cat-eye CGH interferometric method was presented to test the spacing error within a precision of several microns. The simulation and error budget demonstrate that this method can measure the WOS of freeform surfaces. The experimental results indicate that the metrology accuracy is 10.2 ± 4.3 μm (P = 95%) (absolute accuracy), 4.5 μm (repeatability), and 2.1 ppm (relative accuracy).

Angle κ and its effect on the corneal elevation maps in refractive surgery candidates.

To assess the associations of angle κ and Pentacam decentration indices with elevation maps in normal refractive surgery candidates. Salouti Cornea Research Center, Salouti Eye Clinic, Shiraz, Iran. Retrospective observational study. In this research, the right eyes of 173 refractive surgery candidates were assessed. Data of front and back corneal elevation maps, keratometric data, decentration indices, and corneal astigmatism obtained by Pentacam HR system and angle κ obtained by Orbscan IIz were extracted. Maximum elevation (or depression) for each of the 4 quadrants was recorded. Correlations of elevation values with angle κ, Pentacam decentration indices, keratometry, and astigmatism were examined by Pearson correlation coefficient. 148 age- and sex-matched cases with keratoconus grade 1 were selected as a positive control group, and Pentacam variables were compared between the groups. Overall, data from 173 eyes of 173 normal refractive surgery candidates and 148 eyes of 148 patients with keratoconus were recorded and analyzed. In normal refractive surgery candidates, the mean of angle κ was 5.32 ± 1.36 (SD) degrees. Angle κ had a positive correlation with front and back temporal elevations based on a best-fit sphere (BFS) ( r = 0.339, P = .001; r = 0.300, P < .001, respectively). Front and back keratometric astigmatisms were positively correlated with front and back nasal and temporal elevations ( r ≥ 0.543, P < .001) and negatively correlated with superior and inferior elevations ( r ≤ -0.547, P < .001). These associations no longer existed when using best-fit toric ellipse (BFTE) for calculating elevation data. The thinnest point to vertex decentration was significantly associated with the back temporal elevation (based on the BFTE) in both normal ( r = 0.311, P < .001) and keratoconus ( r = 0.190, P = .021) eyes. This study showed that elevation maps obtained by the Pentacam system using BFS might be affected by both the large angle κ and corneal astigmatism, confounding the preoperative assessment of refractive surgery candidates. Using BFTE as a reference for calculating elevation data should eliminate most diagnostic issues and thus is encouraged in this context.

Anterior segment characteristics in normal and keratoconus eyes evaluated with a new type of swept-source optical coherence tomography.

This study aimed to evaluate and compare the discriminating ability of corneal elevation maps generated using a swept-source optical coherence tomography (SS-OCT) (SS-OCT ANTERION, Heidelberg Engineering, Heidelberg, Germany), which was estimated with different reference surfaces, to distinguish normal corneas from those with keratoconus and keratoconus suspect. A total of 126 eyes of patients, which comprised 43, 37, and 46 keratoconus, keratoconus suspects, and normal controls, respectively, were included in this study. The anterior and posterior elevations at the thinnest point under the best-fit sphere (BFS) and toric-ellipsoid (BFT), respectively, and other corneal parameters were measured using the SS-OCT. In addition, the receiver operating characteristic (ROC) curve analysis and cut-off value were calculated to evaluate the diagnostic ability of the corneal elevation values in differentiating keratoconus and keratoconus suspects from normal eyes. The mean total keratometric and corneal elevation values were significantly higher in the keratoconus group than in the other groups. Pachymetric parameters exhibited the lowest values for keratoconus. In addition, ROC curve analyses showed a high accuracy of the thinnest point anterior and posterior BFT for both keratoconus and keratoconus suspects and normal controls (area under the ROC were 0.969 and 0.961, respectively). Furthermore, the optimal cut-off point of the posterior elevation at the thinnest point under BFT was 16.44 μm (sensitivity and specificity of 86% and 98%, respectively) for differentiating keratoconus from normal and keratoconus suspect eyes. The elevation map using the BFS and BFT references measured with the anterior segment SS-OCT is considered an effective indicator for keratoconus diagnosis. Therefore, the anterior segment SS-OCT can effectively differentiate keratoconus from suspected keratoconus and normal corneas by measuring parameters such as posterior and anterior elevations, pachymetry, and keratometry.

ACCURACY INVESTIGATIONS OF HAND-HELD SCANNING SYSTEMS USING DIFFERENT DUMBBELL ARTEFACTS

Abstract. The use of hand-held 3D scanning systems is becoming increasingly widespread in both the industrial and cultural sectors, and, particularly in the cultural sector, the systems are sometimes used by non-specialists. At the same time, the surface of cultural objects has a wide variety of textural properties. It is therefore of great importance that the measuring systems meet qualitative standards. For this purpose, the Creaform GO!Scan, Artec Eva and Artec Spider are compared in absolute terms of accuracy using a calibrated textured spherical dumbbell in accordance with the VDI 2634 guidelines. Both GO!Scan (sphere spacing error SD = 0.03 mm) and Eva (SD = 0.03 mm) meet the expected accuracy, while the Spider (SD = 0.3 mm) does not. Furthermore, a relative comparison is made with dumbbell bars with different texture properties. The probing error form (maximum range of residuals to the best-fit sphere) was able to reveal the effects of different texture properties on surface noise for both the Artec Eva and the Artec Spider. The Spider had larger margins for the metal sphere, while the Eva had larger margins for the textured sphere. In the case of the GO!Scan, texture properties did not matter. Furthermore, the scanners were tested on a cultural reference object. The quality standards of the VDI examination were achieved on average for every scan system, but this cannot be guaranteed for complex object areas.

High-Precision Ion Beam Figuring of X-Ray Plane Mirrors for the Bendable KB Focusing System

Two trapezoidal plane mirrors of 240 mm in length were fabricated by ion beam figuring (IBF) technology for application in a bendable KB focusing system. The correction of surface height and slope errors in different spatial frequency ranges of the mirrors was studied systematically. After one to two iterations of IBF, the figure height errors of the vertical focusing mirror (VFM) and horizontal focusing mirror (HFM) were improved from 32.4 and 65.4 nm to 2.7 and 7.2 nm (RMS), respectively. If the best-fit sphere of the surface profile was subtracted, the residual two-dimensional height errors were only 1.1 and 1.2 nm (RMS). The slope errors in the low spatial frequency range were corrected much faster than the middle frequency ones (f = ∼1 mm−1), which make the low-frequency slope error much smaller. After IBF, the two-dimensional slope errors of the two mirrors calculated with a spatial interval of 1 and 10 mm were reduced to approximately 0.29 and 0.08 μrad, respectively. Full spatial frequency characterization of the VFM before and after IBF showed that the low-frequency figure errors (f &amp;lt; 1 mm−1) were significantly reduced while the middle- and high-frequency morphologies (f &amp;gt; 1–2 mm−1) remain almost the same as before figuring. The fabricated plane mirrors were applied in the hard X-ray micro-focusing beamline in the Shanghai Synchrotron Radiation Facility (SSRF), which realized a focal spot of 2.4 μm × 2.8 μm at 10 keV.

Comparison of Chemical and Mechanical Surface Treatments on Metallic Precision Spheres for Using as Optical Reference Artifacts.

The improvement of industrial manufacturing processes requires measurement procedures and part inspection tasks to be faster and faster while remaining effective. In this sense, the capabilities of noncontact measuring systems are of great help, not only because of the great amount of data they provide but also for the ease of the integration of these systems as well as their automation, minimising the impact on the industry. This work presents a comparative study on the influence of two surface treatments performed on low-cost, high-precision metallic spheres on the suitability of these spheres to be used as artefacts for the calibration of optical sensors, specifically laser triangulation sensors. The first surface treatment is sandblasting (a mechanical process), whose effect has been studied and presented in previous work. The second treatment focused on in this paper is acid etching (a chemical process). The comparison has been performed by evaluating the same metrological characteristics on two identical groups of spheres of similar type (diameter and accuracy), each of which was subjected to a different treatment. It was necessary to obtain the reference values of the metrological parameters with high accuracy, which involved measuring the spheres with a coordinate measuring machine (CMM) by contact probing. Likewise, spheres were scanned by a laser triangulation sensor mounted on the same CMM. The results derived from both the contact and laser measurements and before and after treating the surfaces were used to compare four parameters: point density, sphere diameter, sphere form deviation, and standard deviation of the best-fit sphere to the corresponding point cloud. This research has revealed that acid etching produces better optical qualities on the surfaces than the mirror-like original ones, thus enhancing the laser sensor capturing ability. However, such chemical etching has affected the metrological characteristics of the spheres to a greater extent than that produced by sandblasting. This difference is due to the variability of the chemical etching, caused by the high aggressiveness of the acid, which makes the process very sensitive to the time of exposure to the acid and the orientations of the spheres in the bath.

Analysis and comparison of monofocal, extended depth of focus and trifocal intraocular lens profiles

To test the feasibility of using profilometers to extract information about IOL surfaces design. A standard monofocal IOL (Tecnis 1), a monofocal IOL that provided some depth of focus (Eyhance), an extended depth of focus IOL based on refractive optics (Mini Well) and a trifocal IOL based on diffractive optics were used in this study (Tecnis Synergy). The surface topography of the IOLs was measured by using a multimode optical profilometer. Posterior surface of Tecnis 1 IOL was spherical and the anterior surface aspherical. In the Eyhance IOL, posterior surface was spherical and anterior surface did not fit to any of our reference surfaces, indicating a higher order aspheric surface design. In the Mini Well Ready IOL, a best-fit sphere surface was obtained for the second surface and a high order aspherical surface design was deduced for the first surface. The anterior surface of the Synergy IOL was aspherical and the base curve of the diffractive structure fitted very well to a spherical surface. To consider an aspheric surface as possible best-fit surface provided more information than if only best-fit spherical surface was considered. The high order aspheric surface designs employed in the IOLs studied presented differences, regarding best-fit asphere surface, higher than 1 micron. These differences were correlated with the generation of spherical aberration complex profiles (with Zernike terms higher than 4th order) and with the production of distinct amounts of depth of focus. This method was also useful to deduce the base curve of diffractive surfaces.

Three-Dimensional Quantification of Cam Resection Using MRI Bone Models: A Comparison of 2 Techniques.

Background:The current clinical standard for the evaluation of cam deformity in femoroacetabular impingement syndrome is based on radiographic measurements, which limit the ability to quantify the complex 3-dimensional (3D) morphology of the proximal femur.Purpose:To compare magnetic resonance imaging (MRI)–based metrics for the quantification of cam resection as derived using a best-fit sphere alpha angle (BFS-AA) method and using 3D preoperative-postoperative surface model subtraction (PP-SMS).Study Design:Descriptive laboratory study.Methods:Seven cadaveric hemipelvises underwent 1.5-T MRI before and after arthroscopic femoral osteochondroplasty, and 3D bone models of the proximal femur were reconstructed from the MRI scans. The alpha angles were measured radially along clockfaces using a BFS-AA method from the literature and plotted as continuous curves for the pre- and postoperative models. The difference between the areas under the curve for the pre- and postoperative models was then introduced in the current study as the BFS-AA–based metric to quantify the cam resection. The cam resection was also quantified using a 3D PP-SMS method, previously described in the literature using the metrics of surface area (FSA), volume (FV), and height (maximum [FHmax] and mean [FHmean]). Bivariate correlation analyses were performed to compare the metrics quantifying the cam resection as derived from the BFS-AA and PP-SMS methods.Results:The mean ± standard deviation maximum pre- and postoperative alpha angle measurements were 59.73° ± 15.38° and 48.02° ± 13.14°, respectively. The mean for each metric quantifying the cam resection with the PP-SMS method was as follows: FSA, 540.9 ± 150.7 mm2; FV, 1019.2 ± 486.2 mm3; FHmax , 3.6 ± 1.0 mm; and FHmean, 1.8 ± 0.5 mm. Bivariate correlations between the BFS-AA–based and PP-SMS–based metrics were strong: FSA (r = 0.817, P = .012), FV (r = 0.888, P = .004), FHmax (r = 0.786, P = .018), and FHmean (r = 0.679, P = .047).Conclusion:Strong positive correlations were appreciated between the BFS-AA and PP-SMS methods quantifying the cam resection.Clinical Relevance:The utility of the BFS-AA technique is primarily during preoperative planning. The utility of the PP-SMS technique is in the postoperative setting when evaluating the adequacy of resection or in patients with persistent hip pain with suspected residual impingement. In combination, the techniques allow surgeons to develop a planned resection while providing a means to evaluate the depth of resection postoperatively.

Posterior Corneal Curvature Changes After Pre-Descemet's Endothelial Keratoplasty: A Prospective Analysis.

To assess the changes in the posterior corneal curvature after pre-Descemet's endothelial keratoplasty (PDEK) and correlate with the visual outcomes. Eyes with pseudophakic bullous keratopathy, aphakic bullous keratopathy, and Fuchs dystrophy undergoing PDEK were included. The main outcome measures were the topography (OrbscanIIz, Bausch and Lomb) indices-total corneal power (TCP) in diopters (D), radius of the posterior curvature (mm), and best-fit sphere of the posterior corneal surface (BFS in D) at preoperative and postoperative 1 month, 3 months, and 6 months. Overall, 43 eyes of 43 patients with a mean age of 68 ± 9.6 years were studied. The mean preoperative TCP 43.1 D ± 2.3 reduced to 42.4 D ± 2.6 at 3 months (P < 0.010). There was a statistically significant decrease in the mean posterior corneal curvature at 1 month and 3 months postoperatively (P = 0.002). There was no significant change in the TCP and posterior corneal curvature at 6 months (P > 0.05). The mean BFS showed an increase at 1 month (53.45 ± 5.2 D) and 3 months (52.95 ± 5.1 D) and decrease at 6 months (51.90 ± 5.3 D). The overall change in BFS (P > 0.05) was not significant. There was significant improvement in visual acuity (P < 0.05). The best-corrected visual acuity was ≥20/40 in 79.07% and ≥20/60 in 100% at 6 months. There was no statistically significant correlation between the change in the best-corrected visual acuity and TCP, posterior corneal curvature, or BFS. Although there was immediate postoperative change in the posterior curvature, no significant change was induced by PDEK.

Agreement and Repeatability of Corneal Thickness and Radius among Three Different Corneal Measurement Devices.

Corneal refractive surgery screening, orthokeratology, and contact lens fitting require accurate estimation of the corneal thickness and curvature. We found that any of the imaging devices used in this study can be used to image a healthy myopic cornea, which is essential to screen for corneal ectasia. This study aimed to compare agreement and repeatability of corneal thickness and radius measurements obtained using Scheimpflug imaging (Pentacam HR), swept-source optical coherence tomography (Casia SS-1000), and Placido-Scheimpflug tomography (Topographic Modeling System, version 5 [TMS-5]). Sixty eyes of 60 subjects with myopia were measured with Casia, TMS-5, and Pentacam for their central corneal thickness (CCT), thinnest corneal thickness, central corneal radius of the steep meridian (Ks), central corneal radius of the flat meridian (Kf), mean central corneal radius (Km), and anterior and posterior best-fit spheres. Two readings were obtained from each instrument. Central corneal thickness was also measured with ultrasound pachymetry. Intraclass correlation coefficient, repeatability coefficient, and coefficient of variation were calculated. Repeatability coefficient, coefficient of variation, and intraclass correlation coefficient of CCT among the instruments ranged between 2.48 and 12.79, 0.17 and 0.86, and 0.98 and 1.00, respectively. Mean CCT measurements were similar between Casia, TMS-5, Pentacam, and ultrasound pachymetry (P = .13). Intraclass range of correlation for agreement was 0.95 to 0.99 for CCT among instruments. The range of 95% limits of agreement (LoAs) for ultrasound CCT was narrowest with Casia (31.94 μm). Casia-TMS-5 displayed a narrow range of 95% LoA for CCT (12.14 to -12.44), thinnest corneal thickness (12.31 to -11.31), and Ks (0.56 to -0.53), whereas Casia-Pentacam showed a narrow range of 95% LoA for Kf (0.56 to -0.42), Km (0.41 to -0.27), and anterior best-fit sphere (0.03 to -0.07). A significant difference in posterior best-fit sphere measurements was noted among all instruments (P = .01). Casia, TMS-5, and Pentacam can be used interchangeably to measure corneal thickness and radius measurement in healthy eyes. Casia had the best agreement with ultrasound pachymeter CCT and exhibited the highest repeatability.

Validation of the sandblasting process in the manufacturing of precision spheres for non-contact metrology

In order to ensure the measurements that can be made with non-contact metrology technologies, it is necessary to use verification and calibration procedures using precision artefacts as reference elements. In this environment, the need for increasingly accurate but also more cost-effective calibration artefacts is a clear demand in industry. The aim of this work is to demonstrate the feasibility of using low-cost precision spheres as reference artefacts in calibration and verification procedures of non-contact metrological equipment. Specifically, low-cost precision stainless steel spheres are used as reference artefacts. Obviously, in order for such spheres to be used as standard artefacts, it is necessary to change their optical behaviour by removing their high brightness. For this purpose, the spheres are subjected to a manual sandblasting process, which is also a very low-cost process. The equipment used to validate the experiment is a laser triangulation sensor mounted on a Coordinate Measuring Machine (CMM). The CMM touch probe, which is much more accurate, will be used as a device for measuring the influence of sandblasting on the spheres. Subsequently, the influence of this post-processing is also checked with the laser triangulation sensor. Ultimately, the improvement in the quality of the point clouds captured by the laser sensor will be tested after removing the brightness, which distorts and reduces the quantity of points as well as the quality of the point clouds. In addition to the number of points obtained, the parameters used to study the effect of sandblasting on each sphere, both in contact probing and laser scanning, are the measured diameter form error, as well as the standard deviation of the point cloud regarding the best-fit sphere.

Pose-varied swing arm profilometer test for off-axis aspheric surfaces with strong asphericity.

The swing arm profilometer (SAP) has been widely used to test large aspheric optics by measuring the asphericity from its best-fitting sphere (BFS). To further improve the test accuracy, we propose a pose-varied test mode for the SAP with a shorter-range probe to measure off-axis aspheric surfaces with stronger asphericity. In contrast to the classical SAP mode in which the air-table is fixed in a stationary position during measurement, we adjust the pose of each scan arc to match the local BFS and the measurement range of the probe decreases to half that of the global asphericity. To verify the effectiveness, we conduct experiments on an off-axis asphere with a diameter of 3 and 2 m. Compared with a classical SAP mode, it achieved an improved performance of 50% higher repeatability and 32% higher accuracy.

Simulation and measurement of systematic errors of stitching interferometry for high precision X-ray mirrors with large radius of curvature.

To accurately measure the surface figure of curved mirrors with large radius of curvature (RoC) using stitching interferometry methods, three types of measurement errors are systematically studied, including retrace error, defocusing error within a single subaperture, and stitching angle error among different subapertures. It was found that part of the retrace error caused by the mismatch between the reference wavefront and reflected wavefront has little effect, while the overall retrace error, including the influence of the imperfect optical elements, will cause an error of 1-2 nm RMS within a single subaperture. Defocusing error will enlarge the error due to amplification of optical path error caused by the deviation of the position of the CCD. Because the error is mainly in the edge area, a slope threshold, which controls the maximum surface slope of each subaperture, can be optimized to reduce the effect of the defocus on stitching measurement error. Constant angle error among neighboring subapertures has the biggest accumulation effect on the final stitched figure. For the spherical mirror with RoC of 100 m of 80mm×40mm, the error of the one-dimensional residual profile is 4.67 nm PV, assuming a constant angle error of 2×10-7rad. For the elliptical mirror with RoC of 60-140 m, it is more than 15 nm peak-to-valley (PV). It is because the profile difference caused by constant angle error is closer to a circle, which can be mostly removed after subtraction of a best-fit sphere. Based on the above error analysis, the developed algorithm-based stitching method was used to measure an elliptical cylindrical mirror of 74mm×40mm with RoC of 60-140 m, and the result was compared with a slope measurement instrument from the Beijing Synchrotron Radiation Facility. After removing the best fitting ellipse profile, the one-dimensional difference between the two results is only 0.77 nm RMS, which demonstrated good measurement accuracy.