IlluminatedZoom: spatially varying magnified vision using periodically zooming eyeglasses and a high-speed projector.

Spatial zooming and magnification, which control the size of only a portion of a scene while maintaining its context, is an essential interaction technique in augmented reality (AR) systems. It has been applied in various AR applications including surgical navigation, visual search support, and human behavior control. However, spatial zooming has been implemented only on video see-through displays and not been supported by optical see-through displays. It is not trivial to achieve spatial zooming of an observed real scene using near-eye optics. This paper presents the first optical see-through spatial zooming glasses which enables interactive control of the perceived sizes of real-world appearances in a spatially varying manner. The key to our technique is the combination of periodically fast zooming eyeglasses and a synchronized high-speed projector. We stack two electrically focus-tunable lenses (ETLs) for each eyeglass and sweep their focal lengths to modulate the magnification periodically from one (unmagnified) to higher (magnified) at 60 Hz in a manner that prevents a user from perceiving the modulation. We use a 1,000 fps high-speed projector to provide high-resolution spatial illumination for the real scene around the user. A portion of the scene that is to appear magnified is illuminated by the projector when the magnification is greater than one, while the other part is illuminated when the magnification is equal to one. Through experiments, we demonstrate the spatial zooming results of up to 30% magnification using a prototype system. Our technique has the potential to expand the application field of spatial zooming interaction in optical see-through AR.

Indicators for Assessing the Quality of Refractive Error Care.

SIGNIFICANCE: Quality refractive error care is essential for reducing vision impairment. Quality indicators and standardized approaches for assessing the quality of refractive error care need to be established. PURPOSE: This study aimed to develop a set of indicators for assessing the quality of refractive error care and test their applicability in a real-world setting using unannounced standardized patients (USPs). METHODS: Patient outcomes and three quality of refractive error care (Q.REC) indicators (1, optimally prescribed spectacles; 2, adequately prescribed spectacles; 3, vector dioptric distance) were developed using existing literature, refraction training standards, and consulting educators. Twenty-one USPs with various refractive errors were trained to visit optical stores across Vietnam to have a refraction, observe techniques, and order spectacles. Spectacles were assessed against each Q.REC indicator and tested for associations with vision and comfort. RESULTS: Overall, 44.1% (184/417) of spectacles provided good vision and comfort. Of the spectacles that met Q.REC indicators 1 and 2, 62.5 and 54.9%, respectively, provided both good vision and comfort. Optimally prescribed spectacles (indicator 1) were significantly more likely to provide good vision and comfort independently compared with spectacles that did not meet any indicator (good vision: 94.6 vs. 85.0%, P = .01; comfortable: 66.1 vs. 36.3%, P < .01). Adequately prescribed spectacles (indicator 2) were more likely to provide good comfort compared with spectacles not meeting any indicator (57.7 vs. 36.3%, P < .01); however, vision outcomes were not significantly different (85.9 vs. 85.0%, P = .90). Good vision was associated with a lower mean vector dioptric distance (P < .01) but not with comfort (P = .52). CONCLUSIONS: The optimally prescribed spectacles indicator is a promising approach for assessing the quality of refractive error care without additional assessments of vision and comfort. Using USPs is a practical approach and could be used as a standardized method for evaluating the quality of refractive error care.

Technical Report: Solar Ultraviolet Protection from Sunglasses.

SIGNIFICANCE: There is substantial scientific uncertainty about the necessary levels of protection in sunglasses to avoid delayed health effects from solar ultraviolet radiation in the ultraviolet A (UV-A) band. The longer-wavelength limit for UV-A and the inclusion of the spectral effectiveness function in the calculation of solar UV-A transmittance are questionable. PURPOSE: There has been a wide range of informed opinion with regard to the level-or even need for-near-ultraviolet filtration (by absorption or reflection) in sunglasses. Many current sunglass filter lenses transmit very little near-ultraviolet radiant energy, whereas others transmit a significant fraction. There also are opposing commercial interests that argue either for strong filtration or for minimal protection. We review the evidence for potential risks and the challenge for the designer of any sunglass lens. It is shown that current standards are not at all cautious in their requirements for near-ultraviolet protection and do not meet a philosophical approach of minimizing needless exposure to optical energy that does not benefit vision. METHODS: The arguments for and against various factors in eye protection from ultraviolet radiation are discussed. The solar UV-A transmittance of some sunglass and clear spectacle lens materials has been calculated using the formulae and methods used in the International Standards Organization sunglass standard. The Annex gives results of the calculations both with and without the S(λ) erythemal weighting function and up to 380 or 400 nm. RESULTS: The solar UV-A transmittance calculated with the S(λ) function and only up to 380 nm gives numerical results that are lower than taking either the upper limit for UV-A as 400 nm or without the S(λ) function. CONCLUSIONS: Most sunglass lenses will still pass the requirements with the more stringent requirements, but some spectacle lens materials will need extra treatment.

Technical Support by Smart Glasses During a Mass Casualty Incident: A Randomized Controlled Simulation Trial on Technically Assisted Triage and Telemedical App Use in Disaster Medicine.

BACKGROUND: To treat many patients despite lacking personnel resources, triage is important in disaster medicine. Various triage algorithms help but often are used incorrectly or not at all. One potential problem-solving approach is to support triage with Smart Glasses. OBJECTIVE: In this study, augmented reality was used to display a triage algorithm and telemedicine assistance was enabled to compare the duration and quality of triage with a conventional one. METHODS: A specific Android app was designed for use with Smart Glasses, which added information in terms of augmented reality with two different methods-through the display of a triage algorithm in data glasses and a telemedical connection to a senior emergency physician realized by the integrated camera. A scenario was created (ie, randomized simulation study) in which 31 paramedics carried out a triage of 12 patients in 3 groups as follows: without technical support (control group), with a triage algorithm display, and with telemedical contact. RESULTS: A total of 362 assessments were performed. The accuracy in the control group was only 58%, but the assessments were quicker (on average 16.6 seconds). In contrast, an accuracy of 92% (P=.04) was achieved when using technical support by displaying the triage algorithm. This triaging took an average of 37.0 seconds. The triage group wearing data glasses and being telemedically connected achieved 90% accuracy (P=.01) in 35.0 seconds. CONCLUSIONS: Triage with data glasses required markedly more time. While only a tally was recorded in the control group, Smart Glasses led to digital capture of the triage results, which have many tactical advantages. We expect a high potential in the application of Smart Glasses in disaster scenarios when using telemedicine and augmented reality features to improve the quality of triage.

Reliability Testing of Augmented Reality Glasses Technology: Establishing the Evidence Base for Telewound Care.

PURPOSE: To test the fidelity and feasibility of using augmented reality glass (ARG) telehealth technology for comprehensive wound, ostomy, and continence (WOC) service delivery to underserved rural practice settings. DESIGN: Intrarater reliability design focusing on treatment integrity. SAMPLE AND SETTING: Adult patients in a tertiary care hospital and a rural long-term care setting who were scheduled for routine wound care consults. METHODS: Intra- and interrater reliability were assessed using a documentation-based wound assessment tool comprising 6 discrete assessment points. The wound teleassessment was first conducted by the telehealth "hub" WOC nurse remotely in collaboration with a bedside nurse wearing the ARG. The same hub WOC nurse then conducted an assessment at the bedside. Initial assessment points and treatment plans were compared to establish assessment and treatment intrarater reliability. A different WOC nurse, blinded to the first assessment, also conducted a bedside assessment and provided treatment recommendations, which were then compared to the hub WOC nurse's initial remotely ARG-generated treatment plan to establish treatment interrater reliability. RESULTS: Sixteen patients with 21 wounds were assessed. Six wound assessment components were included, yielding a total of 126 total observation points. Intrarater assessment reliability was 98%. Treatment plan interrater reliability was 100%. CONCLUSIONS: Results support further evaluation of ARG technology as a tool to enhance the delivery of wound care services in remote underserved settings. Implementation and evaluation of this technology on clinical and financial outcomes in multiple wound care delivery environments should be determined moving forward. Successful implementation should serve as a template to expand evidence-based WOC nursing care across the globe.

[Spectacle Glasses - an Overview]. / Brillengläser ­ eine Übersicht.

This paper will give some support to choose the right spectacle lens. The question "what is the proper spectacle lens" cannot be answered exactly, the answer depends on many parameters. Depending on the visual task, the right spectacle lens is a compromise between lens properties. These properties are pointed out in the paper.

[Glasses as Relevant Factor in Expert Opinions]. / Die Brille als Bewertungsfaktor im Gutachten.

Optical correction is an independent factor in expert opinions. It is outlined how this should be considered in different legal areas.

Smart-Glasses: Exposing and Elucidating the Ethical Issues.

The objective of this study is to provide an overview over the ethical issues relevant to the assessment, implementation, and use of smart-glasses. The purpose of the overview is to facilitate deliberation, decision making, and the formation of knowledge and norms for this emerging technology. An axiological question-based method for human cognitive enhancement including an extensive literature search on smart-glasses is used to identify relevant ethical issues. The search is supplemented with relevant ethical issues identified in the literature on human cognitive enhancement (in general) and in the study of the technical aspects of smart-glasses. Identified papers were subject to traditional content analysis: 739 references were identified of which 247 were regarded as relevant for full text examinations, and 155 were included in the study. A wide variety of ethical issues with smart-glasses have been identified, such as issues related to privacy, safety, justice, change in human agency, accountability, responsibility, social interaction, power and ideology. Smart-glasses are envisioned to change individual human identity and behavior as well as social interaction. Taking these issues into account appears to be relevant when developing, deliberating, deciding on, implementing, and using smart-glasses.

Equivalence between solar irradiance and solar simulators in aging tests of sunglasses.

BACKGROUND: This work is part of a broader research that focuses on ocular health. Three outlines are the basis of the pyramid that comprehend the research as a whole: authors' previous work, which has provided the public to self-check their own sunglasses regarding the ultraviolet protection compatible to their category; Brazilian national survey in order to improve nationalization of sunglasses standards; and studies conducted on revisiting requirements of worldwide sunglasses standards, in which this work is inserted. It is still controversial on the literature the ultraviolet (UV) radiation effects on the ocular media, but the World Health Organization has established safe limits on the exposure of eyes to UV radiation based on the studies reported in literature. Sunglasses play an important role in providing safety, and their lenses should provide adequate UV filters. Regarding UV protection for ocular media, the resistance-to-irradiance test for sunglasses under many national standards requires irradiating lenses for 50 uninterrupted hours with a 450 W solar simulator. This artificial aging test may provide a corresponding evaluation of exposure to the sun. METHODS: Calculating the direct and diffuse solar irradiance at a vertical surface and the corresponding radiant exposure for the entire year, we compare the latter with the 50-h radiant exposure of a 450 W xenon arc lamp from a solar simulator required by national standards. RESULTS: Our calculations indicate that this stress test is ineffective in its present form. CONCLUSIONS: We provide evidence of the need to re-evaluate the parameters of the tests to establish appropriate safe limits for UV irradiance. SIGNIFICANCE: This work is potentially significant for scientists and legislators in the field of sunglasses standards to improve the requirements of sunglasses quality and safety.

A Comparison of Spectacles Purchased Online and in UK Optometry Practice.

PURPOSE: To compare spectacles bought online with spectacles from optometry practices. METHODS: Thirty-three participants consisting of single vision spectacle wearers with either a low (N = 12, mean age 34 ± 14 years) or high prescription (N = 11, mean age 28 ± 9 years) and 10 presbyopic participants (mean age 59 ± 4 years) wearing progressive addition lenses (PALs) purchased 154 pairs of spectacles online and 154 from UK optometry practices. The spectacles were compared via participant-reported preference, acceptability, and safety; the assessment of lens, frame, and fit quality; and the accuracy of the lens prescriptions to international standard ISO 21987:2009. RESULTS: Participants preferred the practice spectacles (median ranking 4th, IQR 1-6) more than online (6th, IQR 4-8; Mann-Whitney U = 7345, p < 0.001) and practice PALs (median ranking 2nd, IQR 1-4) were particularly preferred (online 6.5th, IQR 4-9, Mann-Whitney U = 455, p < 0.001). Of those deemed unacceptable and unsafe, significantly more were bought online (unacceptable: online 43/154 vs. practice 15/154, Fisher's exact p = 0.0001; unsafe: online 14/154 vs. practice 5/154, Fisher's exact p = 0.03). CONCLUSIONS: Participants preferred spectacles from optometry practice rather than those bought online, despite lens quality and prescription accuracy being similar. A greater number of online spectacles were deemed unsafe or unacceptable because of poor spectacle frame fit, poor cosmetic appearance, and inaccurate optical centration. This seems particularly pertinent to PAL lenses, which are known to increase falls risk. Recommendations are made to improve both forms of spectacle provision.

Sphero-cylindrical error for oblique gaze as a function of the position of the centre of rotation of the eye.

PURPOSE: New designs of ophthalmic lenses customised for particular wearing conditions (e.g., vertex distance or wrap tilt angle) have emerged during the last few years. However, there is limited information about the extent of any improvement in visual quality of these products. The aim of this work was to determine whether customisation according to the centre of rotation of the eye (CRE) improves visual quality for oblique gaze in monofocal spherical lenses. METHODS: Conventional spherical lenses were designed by numerical ray tracing with back vertex powers (BVP) ranging from +8 to -8 dioptres (D) and base curves from 0 to 8 D. The wavefront error at oblique gaze (40°) was computed for each design with CRE positions from 20 to 35 mm. Sphero-cylindrical (SC) error was calculated using wavefront Zernike coefficients, considering only monochromatic aberrations. Visual acuity in logMAR was estimated following the Raasch empirical regression model. RESULTS: SC error and visual acuity maps were calculated for each BVP as a function of base curves and CRE in a graded colour scale. From SC error maps maximum spherical and cylindrical errors (MSE and MCE) of 1.49 D and -1.24 D respectively were found for BVP from 0 to -2 D, 2.27 D and -1.90 D for BVP from -2 D to -4 D, 2.59 D and -2.20 D for lenses from -4 D to -6 D and 2.63 D and -2.28 D for lenses from -6 D to -8 D. Concerning positive lenses, we obtained MSE and MCE of 0.37 D and -1.35 D respectively for lenses from 0 D to +2 D, 0.39 D and -2.23 D for lenses from +2 D to +4 D and 0.36 D and -2.73 D for lenses from +4 D to +6 D. Regarding visual acuity maps for 40° oblique gaze, significant loss of visual acuity (>0.30 logMAR, Snellen 6/12, 20/40, decimal 0.50) was found for BVP as low as -2 D. Clinically negligible high order aberration levels (equivalent spherical power <0.25 D) were found for all cases. CONCLUSIONS: We calculated SC error and visual acuity maps as a function of base curves and CRE position for a set of spherical lenses at oblique gaze. These maps could be useful as a clinical guide to select the best base as a function of CRE and BVP for each patient. It was found that negative lenses with low BVP provided high SC error when they were designed with low bases. However, high BVP negative lenses with low SC error were found for medium bases and low CRE or for low bases and high CRE positions. In the case of positive lenses, the dependence of SC error with CRE position was less noticeable. Finally, high order aberrations did not have a significant influence over visual quality.

Photochromic dynamics of ophthalmic lenses.

We describe and characterize a straightforward test setup for characterizing temporal and spectral dynamics of photochromic spectacle materials. Three measurement examples of contemporary silicate and organic photochromic spectacles are provided. The setup showed a good absolute accuracy of ≤5% of the luminous transmittance (τ(v)) and repeatability of better than 3%. The samples showed different fading times. The sample with the highest dynamic range was the slowest and showed a noticeable change in the transmission spectra during deactivation. The silicate had the lowest dynamic range but also the most homogeneous transmission spectra throughout activation and deactivation. The proposed test device provided accurate results for spectral and temporal dynamics of photochromic materials under realistic conditions.

Scoring of progressive power lenses by means of user power maps.

PURPOSE: A progressive power lens (PPL) has a relatively complex power distribution, with regions for far, intermediate, and near vision, and also regions affected by aberrations, mainly astigmatism and defocus. Scoring techniques (Sheedy, Optom Vis Sci 2004;81:350-61) have been proposed to mark and classify PPLs according to their optical performance at each region. The objective of this study is to show that although scoring is useful to compare different lens designs, its outcome is highly dependent on the way power is defined and/or computed. METHODS: To demonstrate this, the progressive surfaces of many different current designs have been measured with a profiler. From these measurements and by means of exact ray tracing techniques, we obtain both the power maps that we would measure with a focimeter or a typical lens mapper and the power maps that the user perceives at the actual position of use. The scoring technique from Sheedy has then been applied to both types of maps. RESULTS: It is shown that the parameters that define the characteristics of a PPL when the power map is measured with a standard mapper are not significantly associated with the actual performance of the lens when it is fitted. In a similar way, it is shown that two lenses that have been optimized according to the same target power distribution may get completely different marks depending on the definition of power that has been used in the optimization process. We also propose a graphical method to easily grasp the overall PPL performance by simultaneously presenting four-dimensional information from the scoring technique. CONCLUSIONS: Although in general Sheedy's test is an important tool to compare different PPL designs, it cannot be used to compare those designs optimized for improving user power from classical front side designs when power has been measured for both types of designs with a standard focimeter.

Many ready-made reading spectacles fail the required standards.

PURPOSE: To determine whether the optical quality of near-vision ready-made spectacles (RMS) reaches the quality assurance levels required by the international standard ISO 16034:2002. METHODS: A total of 322 near-vision RMS of powers +2.50, +3.00, and +3.50 DS were randomly selected from high street stores in North East England. Assessments of the optical quality of the RMS were made, and the results were compared against the standards included in ISO 16034:2002 and the more lenient standards used to assess RMS in low-resource countries. RESULTS: Forty-eight percent of the 322 near-vision RMS failed to provide the optical quality required by international standards, with 62% of the +3.50 DS spectacles failing the requirements. This was principally due to a high prevalence of induced horizontal (60%) and vertical prism (32%) beyond the tolerance levels stipulated in ISO 16034:2002. The figures were similar when the more lenient standards used to assess RMS in low-resource countries were used due to RMS centration distances that were too large. CONCLUSIONS: There is a large prevalence of significant amounts of induced horizontal and vertical prism in higher powered near-vision RMS such as +3.50 DS. Given that the need for high-powered RMS indicates the presence of hyperopia and/or age-related eye disease in addition to presbyopia, it may be appropriate to restrict the sale of RMS to optical powers of +1.00 to +2.50 DS, which would contain much fewer errors. We also strongly recommend that manufacturers use a centration distance for near-vision RMS that is similar to an average near (and not distance) interpupillary distance.

Driving with bioptic telescopes: organizing a research agenda.

Being a licensed driver in the United States and many other countries facilitates health and well-being. Based on the vision standards in most states, individuals with worse than 20/40 visual acuity who desire licensure are denied through the usual licensure application process. However, >40 states have bioptic telescope licensing programs where applicants can gain licensure contingent on meeting specific requirements. Despite the existence of the bioptic telescope and these licensing programs since the 1970s, there has been little rigorous scientific study of this topic. Here, I offer an organizing perspective for a research agenda on driving with bioptic telescopes, with the long-term practical goal being to provide an evidence basis for licensure policies and training programs.

Axial length and proliferative diabetic retinopathy.

PURPOSE: To determine the correlation between axial length and diabetic retinopathy (DR) in patients with diabetes mellitus for 10 years or more. METHODS: This study was a prospective, observational, cross-sectional study. Patients with diabetes for 10 years or more were included. We excluded eyes with any other significant ocular disease or any prior intraocular surgery, except uncomplicated cataract surgery. Only one eye of each patient was included as the study eye. The severity of DR was graded as no DR, non-proliferative DR (NPDR), or proliferative DR (PDR). Axial length was measured by A-scan ultrasound (10 MHz Transducer, AL-2000 Biometer/Pachymeter; Tomey, Phoenix, AZ). Univariate logistic regression models were used to evaluate the relationship between the dependent variables (any DR, PDR) and all potential risk factors. Axial length and other factors with p value <0.1 were included in multivariate logistic regression models. Backward selection based on the likelihood ratio statistic was used to select the final models. RESULTS: We included 166 eyes from 166 patients (93 female and 73 male; mean age, 68.8 years). The mean diabetes duration was 15.4 years. Fifty-four (32.5%) eyes had no DR, 72 (43.4%) eyes had NPDR, and 40 (24.1%) eyes had PDR. In univariate analysis, hypertension (p = 0.009), renal impairment (p = 0.079), and insulin use (p = 0.009) were associated with developing any DR. Hypertension (p = 0.042), renal impairment (p = 0.014), insulin use (p = 0.040), pseudophakia (p = 0.019), and axial length (p = 0.076) were associated with developing PDR. In multivariate analysis, hypertension (p = 0.005) and insulin use (p = 0.010) were associated with developing any DR. Hypertension (p = 0.020), renal impairment (p = 0.025), pseudophakia (p = 0.006), and axial length (p = 0.024) were associated with developing PDR. CONCLUSIONS: This observational study suggests an inverse relationship between axial length and the development of PDR in patients with diabetes for 10 years or more. No relationship was found between axial length and the development of any DR.

The interpupillary distance in adult Caucasian subjects, with reference to 'readymade' reading spectacle centration.

PURPOSE: The magnitude of the far interpupillary distance (FIPD) has recognized significance within and beyond clinical optometry. Quantitative information regarding the lesser-reported near parameter (NIPD) would similarly be of interest, and could be of relevance with regard to the visual comfort obtained with 'readymade' reading spectacles. METHODS: Mensuration statistics relating to the FIPD and NIPD are presented, as collated from the spectacle dispensing records of n = 1354 healthy Caucasian presbyopic subjects. The FIPD data were partitioned across 4 age bands (by decade, 41-80 years of age): the NIPD data were distributed across seven nominal reading powers (in 0.50 D steps, +1.00 to +4.00 D). The results of these analyses are considered here, along with their potential application. RESULTS: Consistent gender (male > female) and classification (far > near) differences in IPD (both of approximately 3 mm) were confirmed throughout these data. The magnitude of the adult FIPD is in accord with previously published results; this dimension is now supplemented by NIPD values, whose relationship with total near power is also described. CONCLUSIONS: This new anthropometric survey indicates that inter- and intra-gender interocular facial measurement stability is a characteristic of presbyopic subjects. It is suggested that across the anticipated range of age and total reading power requirement of Caucasian (White Northern European) wearers of 'readymade' reading spectacles, adoption of a standard optical centration distance of 61 mm would be universally appropriate.

Determining spherical lens correction for astronaut training underwater.

PURPOSE: To develop a model that will accurately predict the distance spherical lens correction needed to be worn by National Aeronautics and Space Administration astronauts while training underwater. The replica space suit's helmet contains curved visors that induce refractive power when submersed in water. METHODS: Anterior surface powers and thicknesses were measured for the helmet's protective and inside visors. The impact of each visor on the helmet's refractive power in water was analyzed using thick lens calculations and Zemax optical design software. Using geometrical optics approximations, a model was developed to determine the optimal distance spherical power needed to be worn underwater based on the helmet's total induced spherical power underwater and the astronaut's manifest spectacle plane correction in air. The validity of the model was tested using data from both eyes of 10 astronauts who trained underwater. RESULTS: The helmet's visors induced a total power of -2.737 D when placed underwater. The required underwater spherical correction (FW) was linearly related to the spectacle plane spherical correction in air (FAir): FW = FAir + 2.356 D. The mean magnitude of the difference between the actual correction worn underwater and the calculated underwater correction was 0.20 ± 0.11 D. The actual and calculated values were highly correlated (r = 0.971) with 70% of eyes having a difference in magnitude of <0.25 D between values. CONCLUSIONS: We devised a model to calculate the spherical spectacle lens correction needed to be worn underwater by National Aeronautics and Space Administration astronauts. The model accurately predicts the actual values worn underwater and can be applied (more generally) to determine a suitable spectacle lens correction to be worn behind other types of masks when submerged underwater.

Fifth-order theory of astigmatism of thin spherical spectacle lenses.

PURPOSE: To demonstrate and analyze the fifth-order theory of oblique astigmatism of a thin spherical spectacle lens and make a comparison with the third-order theory and exact ray tracing. METHODS: Fifth-order equations were derived and used for analysis of oblique astigmatism of a spherical spectacle lens to calculate analytically the shape of the lens with corrected oblique astigmatism for large angles of field of view. These results were compared with those of finite ray tracing and the third-order aberration theory. RESULTS: Formulas for the calculation of oblique astigmatism of a thin spherical spectacle lens were derived. These formulas analytically express oblique astigmatism of the third and fifth order. The theory presented generalizes the third-order description of astigmatism of the spherical spectacle lens and derived equations enable calculation of the shape of the spectacle lens with corrected astigmatism even for a large field of view. The fifth-order solution is compared with the third-order theory and the exact solution found by ray tracing. Differences between the third- and fifth-order theory are <0.05 D for spherical lenses, which is negligible clinically. CONCLUSIONS: The presented fifth-order equations, which are a generalization of the third-order formulas for the description of oblique astigmatism, can be used for the analytical expression of the fifth-order astigmatism of the spherical lens. They can simply be applied for the initial design of lenses with corrected astigmatism for large angles of view, something not possible using the third-order theory. We conclude that astigmatism of the fifth order has little effect on the image quality of the spectacle lens, and the third-order theory is satisfactory for practical calculations in optometry.