Астигматизм – один из видов аметропии. Диагностка и коррекция линзами и очками » Лахта Клиника

Астигматизм

О строении человеческого глаза, основных понятиях и клинических нарушениях его оптической системы – рекомендуем более подробный материал «Глаз. Зрение. Рефракция. Аметропия».

Нарушения рефракции, т.е. преломления света внутриглазными оптическими средами с последующей проекцией наблюдаемого образа на сетчатку, носят собирательное название аметропия. Некоторые разновидности аметропии, – такие, например, как анизометропия или анизейкония, – известны, в основном, узким специалистам. Другие распространены настолько широко, что с детства и до глубокой старости вокруг нас (а со временем и в наш персональный адрес) слышны слова «близорукость» и/или «дальнозоркость».

Если усреднить все эпидемиологические оценки, публикуемые в мировой специальной литературе по отдельным видам аметропии, а потом эти оценки сложить, – то вполне вероятно, что суммарная доля намного превысит 100% населения земного шара (в математике такое, конечно, невозможно, однако в реальной жизни, мы понимаем, случается всякое, особенно на выборах). Причина в том, что множество людей страдает комбинированными формами аметропии, а заболеваемость в значительной степени зависит от региона проживания, возраста, профессии, генетики, этнической принадлежности и множества других факторов, к тому же нередко взаимосвязанных. Соответственно, все эти факторы влияют на результаты медико-статистических исследований, сами исследования очень затруднены, а в глобальном масштабе едва ли осуществимы, – по крайней мере, сегодня трудно представить себе всемирный скрининг с достаточной репрезентативностью и достоверностью результатов.

Астигматизм – один из видов аметропии. Более того, это самый распространенный ее вариант, который, как полагают, встречается гораздо чаще близорукости и дальнозоркости, вместе взятых. Однако суть этого нарушения внутриглазной рефракции нельзя сформулировать так же просто, как при гиперметропии («Плохо вижу вблизи») или миопии («Плохо вижу вдаль»). Астигматизм – это «Плохо вижу вообще».

В древнегреческом языке слово «стигма» было многозначным и употреблялось в зависимости от контекста: так могли назвать клеймо, точку, пятно и т.д. Многозначен этот корень и в современной науке. В социальной психиатрии, скажем, термин «стигматизация» означает коллективно-бессознательное предрассудочное отвержение человека на том лишь основании, что он несет на себе «ярлык» психиатрического диагноза; в промышленной оптике под астигматизмом понимают один из искажающих эффектов объектива, и т.д.

Астигматизм в офтальмологическом значении – это принципиальная неспособность оптической системы глаза четко сфокусировать наблюдаемую картину на сетчатке, причем объекты видятся расплывчатыми независимо от того, на каком расстоянии до глаз они находятся. Таким образом, в данном случае «астигматизм» может быть переведен как «отсутствие (фокусной) точки».

Четкость зрительного восприятия – это, прежде всего, четкость границ. Если представить себе, например, черный квадрат на белоснежном листе, то при здоровом зрении граница между фоном и каждой стороной квадрата выглядит как тонкая прямая линия, и чем эта линия тоньше, тем, как говорят фотографы, «резче» изображение. При аметропии граница в нашем примере перестает быть линией и воспринимается как градиент, плавный переход между черным и белым. Но при астигматизме ситуация еще сложней: какие-то участки видятся более-менее отчетливо, а другие расплывчато. Например, горизонтальные стороны квадрата резки, вертикальные размыты; или, скажем, размыты верхний левый и нижний правый углы.

Астигматизм обычно описывается как «несовпадение силы рефракции в различных поперечно-перпендикулярных плоскостях». Но что это означает и почему так происходит? Вспомним: на схемах глазного яблока роговица и хрусталик в разрезе изображаются идеальными, под циркуль, дугами со строго постоянным радиусом. Однако в действительности радиус где-то может отклониться, т.е. в одном участке поверхность оказывается несколько толще, чем в остальных. Упрощенно говоря, астигматизм – это взгляд на мир сквозь линзу с волнистой поверхностью: мало того, что преломляет, так еще и преломляет неравномерно, в разных осях и меридианах по-разному, и вместо одной фокальной плоскости на сетчатку проецируются несколько – отсюда и нечеткость конечного зрительного образа.

Большинство исследований, проводимых в различных странах, свидетельствуют о распространенности астигматизма в пределах от 30% до 60% взрослого населения (речь только о клинически значимом астигматизме, поскольку те или иные колебания формы внутриглазных оптических структур, не сказывающиеся на остроте зрения, встречаются практически у всех людей). Имеет место прямая зависимость частоты встречаемости от среднего возраста исследуемой выборки (чем старше, тем астигматизма больше), однако эта тенденция не абсолютна: астигматизм, в том числе тяжелый и осложненный, может быть выявлен в любом возрасте.

Причины

Из всех предположительных причин астигматической деформации не вызывает сомнений, пожалуй, только определенное (но, опять же, далеко не абсолютное) влияние наследственного фактора. Прочие этиопатогенетические факторы остаются объектом интенсивного изучения, обсуждения и дискуссии. В частности, большинство локализованных на разных языках страниц Википедии называют причины астигматизма «неясными» или «неизвестными».

Приобретенный астигматизм чаще всего связывают с травмами (в т.ч. офтальмохирургическими, где астигматизм может оказаться послеоперационным осложнением), рубцовыми изменениями роговицы вследствие ожогов, инфекционно-воспалительных и дегенеративно-дистрофических процессов, а также с кератоконусом и другими заболеваниями подобного рода.

Симптоматика

Существует несколько классификаций астигматизма, построенных на различных критериях. Так, различают хрусталиковую, корнеальную (роговичную) и сочетанную формы, прямой и обратный астигматизм, врожденный и приобретенный; по степени тяжести выделяют слабую степень (до 3 диоптрий), среднюю (от 3 до 6) и сильную (свыше 6 диоптрий). Во многих случаях астигматизм сочетается с миопией или гиперметропией.
Как показано выше, ощутимых и субъективно дискомфортных нарушений зрения при легком астигматизме может и не быть. Однако подобная ситуация остается достаточно опасной, особенно в раннем детском и школьном возрасте: косвенными проявлениями астигматизма становятся головные боли, астенопия («слабость глаза», т.е. утомляемость, болезненная реакция на зрительные нагрузки и т.д.), тяжесть или «песчаная» резь в глазах. В некоторых случаях отмечается диплопия (двоение), в других нарушается способность к точной оценке расстояния до объектов, отмечается тенденция к никталопии («куриной слепоте»), та или иная степень светобоязни, привычка прищуриваться или наклонять голову под определенным углом, чтобы лучше видеть.

Выраженный астигматизм, особенно комбинированные его формы, в отсутствие коррекции чреват столь же тяжелыми последствиями, как и другие разновидности аметропии: в силу постоянного перенапряжения развиваются амблиопия, косоглазие, снижение прозрачности оптических сред, нарушения в дренажной системе по глаукоматозному типу, дегенерация и отслоение сетчатки вследствие дефицита кровоснабжения, – в конечном счете, любое из перечисленных осложнений может привести к тотальной слепоте.

Диагностика

Астигматизм требует тщательного офтальмоскопического и офтальмометрического обследования. Проводится визометрия (точная оценка остроты зрения с помощью наборов сменных линз, таблиц Сивцева-Головина и др.), рефрактометрия, скиаскопия; по мере необходимости назначаются компьютерная кератотопография (картирование поверхности роговицы), ультразвуковые и другие исследования, необходимые и целесообразные в данном конкретном случае.

Лечение

Оптической коррекции астигматизма (в просторечье – «очки с цилиндрами»), как и офтальмохирургическому его лечению, следует посвятить отдельные статьи, – поскольку это область, в силу сложности самой патологии, в настоящее время активно разрабатывается научно-исследовательским сектором мировой медицины и лидерами индустрии по производству товаров медицинского назначения.

Основными направлениями коррекции астигматизма (что почти всегда исключительно важно и должно делаться как можно раньше) остаются очки и контактные линзы с цилиндрическим компонентом кривизны поверхности. Такая оптика должна изготавливаться строго по индивидуальным показаниям, полученным в ходе самой тщательной диагностики, и нередко обладает очень сложной топологией, – которая, тем не менее, не всегда компенсирует нарушения рефракции полностью. Во избежание неоправданных ожиданий и претензий к врачам следует понимать: в случае выраженной комбинированной рефракционной аномалии, включающей астигматический компонент, обеспечить этим способом четкое и ясное зрение на любой дистанции подчас невозможно физически. Кроме того, пассивная коррекция не способна ни устранить причины астигматизма, ни замедлить его прогрессирование.

Этиопатогенетическим лечением является исправление радиусов кривизны и общей формы поверхности роговицы и/или хрусталика – в тех случаях, когда это возможно, показано и прогностически оправдано. С этой целью производится либо «традиционная» микрохирургическая операция (например, астигматомия, склеропластика и т.д.), либо имплантируется интраокулярная линза, либо осуществляется лазерная коррекция зрения, получившая широкое распространение и признание во всем мире.
Однако и подбор очков, и выбор оптимальной модели контактных линз (которые значительно различаются качеством, назначением, исходной теоретической базой их разработки, материалом изготовления, стратегией и тактикой применения, правилами ухода и гигиены, стоимостью, долговечностью и многими другими параметрами), и планирование радикального вмешательства, – если именно такое решение принято совместно с пациентом, – все это является, повторим и подчеркнем, исключительно индивидуальным лечебно-диагностическим процессом. Ни один метод, ни один способ коррекции в принципе не может стоять «на потоке» и рекомендоваться всем поголовно.

Поэтому первая и главная задача пациента, если возникают проблемы с остротой зрения (или косвенные признаки латентной патологии в этой сфере), – как можно быстрее обратиться к офтальмологу, не растрачивая время и не рискуя потерять зрение при тестировании купленных наугад очков, при самолечении с помощью каких-то брошюр или «советов из интернета», при закапывании или втирании в глаза неизвестно каких субстанций. Астигматизм лечится, но лечится врачами.

90000 Symptoms, Causes, Types, Treatments, Definition 90001 90002 90003 Causes 90004 90003 Types 90004 90003 Correction options 90004 90009 90010 Astigmatism is a type of refractive error caused by the irregularities in the shape of a person’s cornea. The condition is not an eye disease or eye health issue. In this condition, the eye fails to focus the light equally on the retina leading to blurred or distorted vision.It can be present at the time of birth, or can develop gradually in life. 90011 90010 Put simply, Astigmatism is a problem with how the eye focuses light. 90011 90010 Astigmatism is a common eye condition which usually occurs with myopia (nearsightedness) or hyperopia (farsightedness) and can be easily diagnosed with a simple eye exam. 90011 90010 Symptoms of astigmatism include blurred vision or some degree of vision distortion at all distances. Astigmatism can also cause dizziness, eye strain, headaches, squinting and eye irritation.90011 90010 90019 90020 90011 90022 What causes astigmatism? 90023 90010 Astigmatism is usually caused by an irregularly shaped cornea. Instead of the cornea having a symmetrically rounded ball shape, it is shaped more like an egg, with one side (meridians) being significantly more curved than the side perpendicular to it. 90011 90010 (To understand what meridians are, think of the front of the eye like the face of a clock. A line connecting the 12 and 6 is one meridian; a line connecting the 3 and 9 is another.) 90011 90010 The steepest and flattest meridians of an eye with astigmatism are called the principal meridians. 90011 90010 In some cases, the problem is caused by the distortion of shape of the lens inside the eye. This is called lenticular astigmatism, to differentiate it from the more common corneal astigmatism. 90011 90010 Advertisement 90011 90010 FramesDirect.com boasts the largest online selection of top-brand eyewear, selling over 1 million frames since 1996. We use only premium Essilor prescription lenses, and our trained opticians can help you choose the best lens options.Shop online with confidence-find your favorite designer eyewear, and enjoy free shipping and the FramesDirect Price Match Guarantee. 90011 Shop Designer Eyewear 90022 3 types of astigmatism 90023 90010 There are three primary types of astigmatism: 90011 90040 90003 90010 90043 Myopic astigmatism. 90044 90011 90010 One or both principal meridians of the eye are nearsighted. (If both meridians are nearsighted, they are myopic in differing degree.) 90011 90004 90003 90010 90043 Hyperopic astigmatism.90044 90011 90010 One or both principal meridians are farsighted. (If both are farsighted, they are hyperopic in differing degree.) 90011 90004 90003 90010 90043 Mixed astigmatism. 90044 90011 90010 One prinicipal meridian is nearsighted, and the other is farsighted. 90011 90004 90065 90010 Astigmatism is also classified as regular or irregular. In regular astigmatism, the principal meridians are 90 degrees apart (perpendicular to each other). In irregular astigmatism, the principal meridians are not perpendicular.90011 90010 For most, the condition is regular corneal astigmatism, which gives the front surface of the eye an oval shape. 90011 90010 Irregular astigmatism can result from an eye injury that has caused scarring on the cornea, from certain types of eye surgery or from keratoconus, a disease that causes a gradual thinning of the cornea. 90011 90022 Astigmatism in children 90023 90010 It is common for babies to be born with astigmatism, but it usually clears up in the first year or so of the child’s life.The percentage of children with astigmatism decreases significantly as they reach 5 to 9 years of age. 90011 90010 While most children outgrow eye astigmatism, it is more likely to occur in kids who also struggle with either myopia or hyperopia. Like with adults, mild to severe astigmatism in children can be treated with glasses (or contact lenses if they’re old enough). 90011 90010 Babies do not need to wear glasses to treat their astigmatism as they’re likely to outgrow it before it becomes an issue.90011 90010 It’s important to schedule an eye exam for your child to avoid vision problems in school from uncorrected astigmatism. 90011 90010 90043 SEE RELATED: 90044 Vision problems of preschool children 90011 90022 Astigmatism tests 90023 90010 Astigmatism is detected during a routine eye exam with the same instruments and techniques used for the detection of nearsightedness and farsightedness. 90011 90010 Your eye doctor can estimate the amount of the condition you have by shining a light into your eye while manually introducing a series of lenses between the light and your eye.This test is called retinoscopy. 90011 90022 How to correct astigmatism 90023 90010 Options to correct astigmatism can usually be corrected with eyeglasses, contact lenses or refractive surgery. 90011 90010 Refractive surgery is one of the less common astigmatism treatment options, however, since it is a laser procedure that changes the shape of your eyes, it comes with risks associated with most laser surgeries. 90011 90010 Astigmatism should be treated as soon as possible. Once diagnosed, regular visits to an eye doctor are required as astigmatism can fluctuate over time, making it necessary for prescriptions to be modified.90011 90010 90043 WORRIED YOUR CHILD MAY HAVE ASTIGMATISM? 90044 Book an appointment with a children’s eye doctor near you. 90011 90010 Page updated August 20, 2018 90011 .90000 Astigmatism — Optics, Physiology and Management 90001 \ n \ t \ t \ t \ t 90002 2.1. Preparation of dataset for meta-analysis 90003 \ n \ t \ t \ t \ t 90004 The studies used in this meta-analysis were searched on the ScienceDirect in English, the DBpia database, and the KISS (Koreanstudies Information Service System) in Korean . The search keywords used were CLA, weight, health, or fat and the research was limited to the experimental rat studies. About 50 studies were collected and 12 studies were finally selected after omitting some studies with insufficient information, such as no sample variance or no sample size (5, 8-18).90005 \ n \ t \ t \ t \ t 90004 The factors used to investigate the effect of CLA were collected from target studies, if it was studied in at least 2 studies. The selected factors were body fat (%), epididymal fat (g / 100g), fat cell size (μm), final body weight (g), food intake (g / d), leptin (pg / ml), liver-TC (mg / g), liver-TG (mg / g), plasma-TC (mg / dl), plasma-TG (mg / dl), and weight gain (g / d). The unit of each factor was uniformly changed. 90005 \ n \ t \ t \ t \ t 90004 In each study, there were two groups. One group of rats was treated with fat source such as beef tallow, coconut oil, corn oil, fish oil, safflower oil or soybean oil (FR), and the other group of rats was treated with fat source supplemented with CLA (FRC).Because the size of studies after grouping by treated fat source was not enough large, the each fat source has similar effect on obesity. 90005 \ n \ t \ t \ t \ n \ t \ t \ t \ t 90002 2.2. Measure and models for combining 90003 \ n \ t \ t \ t \ t 90004 Since the mean difference between FR and FRC was used for test on anti-obesity effect of CLA, the association measure was decided as the mean difference (MD) of each factor; mean of FRC minus mean of FR. The combined MD of each factor was calculated by the inverse variance method and the mean weighted by inverse variance in the primary studies.If the homogeneity was accepted by Cochran’s Q test, it is assumed that the effect measured in the study population has a single value. The association measure is estimated by using a variation within the studies in the fixed effect model. To reduce the bias caused by heterogeneity, meta-regression models are used to analyze association between treatment effects and study characteristics. The period and amount of CLA supplementation were considered as covariates, and the estimated coefficients of covariates were investigated for possible sources of heterogeneity.If the homogeneity was rejected, the combined MDs of studies were calculated in random effect model in which total variation defined the variation within studies with estimated variation between studies. 90005 \ n \ t \ t \ t \ n \ t \ t \ t \ t 90002 2.3. Identification the publication bias 90003 \ n \ t \ t \ t \ t 90004 The existence of publication bias was checked by using a funnel plot or Egger’s linear regression test. The funnel plot was a scatter plot of the association measure against a inverse of standard error of measure.If the shape of funnel plot about any factor is not funnel or cone around the combined MD, the publication bias was doubtable. Egger’s linear regression test was used to test the null hypothesis that the funnel plot was not asymmetry. Egger’s linear regression is a linear regression of standard normal deviate (defined as association measure over SE) against the inverse of SE, and there may be publication bias if the estimated intercept is significantly different from 0. A positive intercept indicates that more studies are associated with a bigger effect (19).90005 \ n \ t \ t \ t.90000 90001 Telescope astigmatism 90002 90003 90004 90005 telescope 90006 Ѳ 90005 ptics.net 90006 ▪ 90005 90006 90005 90006 ▪ ▪ 90005 90006 ▪ ▪▪▪▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ 90005 90006 CONTENTS 90017 90018 90019 ◄ 4.2. Coma ▐ 4.4. Defocus ► 90017 90021 90022 Similarly to coma, 90023 astigmatism 90024 is an off-axis point wavefront aberration, caused by obliquity of the incident wavefront relative to the optical surface.Astigmatism results simply from the projectional asymmetry arising from wavefront’s inclination to the optical surface. The diameter of wavefront’s projection onto the surface varies from the minimum in the plane of wavefront tilt — determined by the chief (Central) ray and optical axis, hence coinciding with the 90023 tangential plane 90024 — to the maximum in the direction orthogonal to it (90023 sagittal plane 90024), where it equals aperture diameter.90018 90022 As illustration below shows, vertical diameter of the reflected wavefront is smaller than the horizontal due to the effective (projected) diameter in that plane being reduced by a cos 90005 α 90006 factor, 90005 α 90006 being the mirror-to-wavefront axis inclination i.e. field angle in degrees). Since wavefront depth (sagitta) is constant, the shortest diameter (90005 1 90006) will generate the strongest radius, while the longest one (90005 2 90006) generates the weakest radius (profile for 90005 2 90006 is rotated 90 at right).Consequently, the corresponding wavefront sections will focus at two different points, with all other sections focusing in between. Since focal length (I.e. radius of curvature of the wavefront) changes with the square of the diameter for given sagitta depth, wavefront along these two orthogonal diameters focus at the longitudinal separation of (1-cos2α) i, which constitutes longitudinal astigmatism (90041 90005 i 90006 is the image-to-pupil separation, equal to focal length for distant objects).90018 90022 This applies to a lens with the stop at the surface as well, since the basic principle of wavefront transformation by an optical surface applies to both. Convex mirror (or negative lens) would induce astigmatism of opposite sign, with the stronger, shorter vertical line on the surface focusing farther away than the weaker horizontal line. 90018 90022 Another peculiarity of astigmatism is that a cross-section along any wavefront diameter is still spherical, but with the radius of curvature varying with the pupil angle.Thus the wavefront form as a whole deviates from spherical. 90018 90022 For displaced stop — either first optical surface significantly separated from the aperture stop, or secondary and tertiary surfaces (whose stop is formed by a preceding surface) — other surface properties, such as shape, position and conic, also can influence the size of astigmatism. This is due to the displaced stop for these surfaces changing the surface radial asymmetry profile.As illustrated at left, the only configuration that completely corrects for astigmatism is a sphere with the stop at the center of curvature (90005 1 90006). It is apparent from the two axes — that of the wavefront and that of the section of the sphere — coinciding, thus positioning the wavefront symmetrically vs. surface. Any other stop distance will not be fulfilling this condition, reintroducing off-axis aberrations (90005 2 90006). For conic forms other than the sphere, primary astigmatism can be either corrected with appropriate stop position (closer to mirror with smaller — i.e. negative — conics), or only minimized (with conics larger than zero). However, secondary astigmatism, even if low, remains. For a given stop location other than sphere’s center of curvature, the negative conics will generate less astigmatism than the sphere if their shape results in less of a surface vs. wavefront positional asymmetry. On the illustration, that is the case with the stop position 90005 2 90006, as conics toward parabola and hyperbola open wider than the sphere for given radius of curvature (however, as the surface section outlined by the wavefront is not symmetrical about its axis, coma will be generated even if primary astigmatism is cancelled, with one half of the wavefront flatter than the other one).90018 90022 90005 FIG. 43 90006 illustrates the form of astigmatic wavefront deformation for 90005 primary astigmatism 90006, and the resulting geometric (ray) aberration. 90018 90004 90005 90006 90018 90067 FIGURE 43A: 90023 90024 RIGHT: Primary astigmatism on mirror surface, as a result of the projected diameter of the incoming wavefront (90005 W 90006 90005 i 90006) varying with the radial orientation.For the inclination angle shown, the width of vertical, or tangential (with the tangential plane determined by the axis and chief ray) wavefront projection onto the surface, given by cosαD, is at its minimum, gradually increasing with the radial angle around the chief ray to the maximum projection width 90005 D 90006 in the orthogonal (Horizontal, or sagittal) orientation. With the wavefront sagitta (depth) constant, its radius (the focal length) varies with the square of diameter.Being of the smallest diameter, the wavefront section in the tangential (vertical) plane focuses closest, and the wavefront section in 90023 90024 the 90023 90024 sagittal plane farthest away from the mirror 90023. 90024 LEFT: The actual wavefront deviation from the corresponding reference sphere (red dots): for the reference sphere centered at the mid point of defocus 90005 M 90006, and those centered at either sagittal or tangential focus (90005 S 90006 and 90005 T, 90006 respectively; the deviation for the former has cylindrical form oriented vertically, for the latter horizontally).All three spheres coincide at the red dotted line. The P-V error is identical at all three focus locations; however, the deviation averaged over the wavefront (RMS error) is lower at the mid-focus by a factor 0.82, making it the best (diffraction) focus. Solid blue line in the best focus wavefront deviation 90005 (M) 90006 represents the deviation along the central cross-section of the actual wavefront vs. perfect reference sphere centered at the mid-focus point.The dashed blue line is a projection of the deviation along the wavefront edge, indicating saddle-like shape of the wavefront deformation. 90004 90091 43B: Ray geometry of astigmatism is not immediately obvious. It is determined by the inequality of the two perpendicular radii, so that all sections of the wavefront parallel to the shorter radius — the vertical one in this illustration — focus in a horizontal line closer to the objective, and all sections of the wavefront parallel to the perpendicular to the former, longer radius, focus into a vertical line farther away from the objective.This ray geometry produces a round ray spot plot midway between the two line foci. Below are the corresponding wavefront deformations for the three axial focal points. Since the reference sphere for F1 is with the corresponding, shorter radius, wavefront deformation in the vertical direction is zero (since the wavefront maps are for the Zernike aberration form, their color code shows zero deviation for the intersection with zero mean, while in the classical form zero deviation is what is coded red for the two cylindrical deviation forms; for the saddle-like, it is identical to the Zernike form, light blue).90018 90018 90022 Gaussian focus for astigmatic wavefront lies on the Petzval surface of an optical surface, or a system. Balancing defocus aberration for this point — located on the opposite direction from the sagittal focus, and at identical distance from it as the best focus — is zero, and the wavefront error is largest. Between the sagittal and tangential focus, ray disturbance resulting from the astigmatic wavefront deformation takes on rather peculiar form (90005 FIG.44 90006). 90018 90004 90018 90005 90004 FIGURE 44: Geometry of the astigmatic defocus produced by a mirror with the stop at the surface: the wavefront radius at the pupil gradually increases from the minimum in the tangential (vertical) plane to the maximum in the orthogonal to it sagittal plane. Consequently, all wavefront meridians focus at a different length, producing longitudinal defocus, as an axial separation between tangential and sagittal focus.At the sagittal plane focus 90005 S 90006 it forms sagittal line, contained in the tangential plane. And at the tangential plane focus 90005 T 90006 it forms tangential line, laying in the sagittal plane. The lines transform into ellipses of decreasing eccentricity toward the inside of defocus zone. Midway between the two lines is the circle of least confusion (90005 BF 90006), which is the location of best astigmatic focus.90018 90006 90067 Aberration function for primary astigmatism given in Table 4 is for tangential focus, which is identical to that for the sagittal focus, except for the orientation. Neither coincides with the best (diffraction) focus, which is located midway between the two, hence requires correction by defocus. Since for given longitudinal aberration the P-V wavefront error for primary astigmatism equals that for defocus, the defocus added to it equals half the P-V wavefront error of astigmatism.Aberration function for the 90005 wavefront error 90006 of primary (Lower-order) astigmatism at the best focus is given by: 90018 90004 W 90005 a 90006 = A 90005 ρ 90006 90005 2 90006 (cos 90005 2 90006 θ 90005 90006 — 0.5) 90005 90006 (18) 90018 90022 with 90005 A 90006 being the astigmatism peak aberration coefficient, 90005 ρ 90006 the normalized (to 1) height in the pupil, and 90005 θ 90006 the pupil angle.It shows that the wavefront error peaks for ρ = 1 and cos2θ = 1 and 0 (that is, for θ = 0, π / 2, π, 3π / 2 and 2π), which is, every 90 degrees (with the successive peaks being of opposite sign), and orthogonally to the orientations of the minimum wavefront deviation, occurring for cosθ = 90005 √ 90006 0.5 (For θ = π / 4, 3π / 4, 5π / 4 and 7π / 4). It clearly outlines saddle-shaped wavefront deviation, as illustrated on 90005 FIG.43 90006 left. 90018 90022 Note that the maximum wavefront error given by 90005 Eq. 18 90006 — which gives wavefront deviations, not the peak-to-valley error — is one half of the peak aberration coefficient, which equals the P-V error. Numerically, it is identical to the P-V error at either sagittal or tangential focus, W 90005 a 90006 = Aρ2cos2θ, but its RMS value is smaller by a factor of 1/90005 √ 90006 1.5. 90018 90022 When the point of maximum deviation in the tangential (Vertical) plane is closer to the center of reference sphere than its reference sphere point — i.e. when the tangential focus is precedes sagittal in the direction of light travel (or, simply put, is closer to the objective) — the wavefront error of astigmatism is negative. That is the sign of astigmatism in a concave mirror, illustrated on 90005 FIG. 28 90006. There is no difference in appearance between positive and negative Seidel astigmatism, since the pattern is merely rotated by 90, and has an inherent 180-degree rotational symmetry at the best focus location (90005 FIG.30 90006). 90018 90067 The 90005 peak 90006 90005 aberration coefficient 90006 90005 A 90006, which equals the peak-to-valley wavefront error, is given by: 90018 90004 A = aα 90005 2 90006 d 90005 2 90006 = ah 90005 2 90006 / 4F 90005 2 90006 (18.1) 90022 with 90018 a being the astigmatism aberration coefficient (simplified notation for 2 90005 w 90006 22 in Table 4), 90005 h 90006 the point height in image plane, 90005 α 90006 the field angle in radians (with α = h / for object at infinity, 90041 being the focal length) and 90005 d 90006 the pupil (aperture) radius.The 90005 aberration coefficient 90006 90005 a 90006 is, in general form for a single optical surface, given by 90018 90004 a = -0.5n2 [(1 / n’I) — (1 / nO)], 90018 90022 where 90005 I 90006, 90005 O 90006 are the image and object distance, and 90005 n 90006, 90005 n ‘90006 are the refractive index of incidence and refraction or reflection, respectively. 90018 90022 For a concave mirror and stop at the surface, n ‘= — n, I = O / (O-), = R / 2, and the coefficient is given by: 90018 90004 aM 90005 90006 = N / R (18.2) 90022 with 90005 R 90006 being the mirror radius of curvature. For mirror in air oriented to the left, n = 1 and the aberration coefficient is 90005 a 90006 M 90005 = 1 / R 90006. The sign of aberration coefficient indicates the tangential wavefront radius shorter than sagittal, and the sagittal line farther away from the mirror, as shown on 90005 FIG. 43-44 90006. Positive astigmatism has this order reversed. From another perspective, the astigmatism wavefront error is negative when the optical path difference from the point of peak deviation in the tangential plane is smaller than the radius of a perfect reference sphere (the one centered at the mid point between tangential and sagittal focus).90018 90022 So, the direct relation for the P-V wavefront error of the primary astigmatism of a concave mirror can be written as: 90018 90018 90004 W 90005 a 90006 = 90005 α2 90006 d 90005 2 90006 / R = 90005 α2 90006 D / 8F = h 90005 2 90006 / 8fF 90005 2 90006 (18.3) 90022 90005 Shift to the best focus location 90006 is half the longitudinal aberration from either of the two line foci.In terms of the peak aberration coefficient 90005 A 90006, the needed wavefront error of defocus from either tangential or sagittal focus to best focus location is (A / 2). While the P-V error remains unchanged for all three focus locations — sagittal, tangential and midway between these two — the latter has the RMS wavefront error smaller by a factor of 2/90005 √ 90006 6. As a result, this focus location has has the highest peak diffraction intensity, making it the best focus location.90018 90022 The best focus RMS wavefront error in terms of the peak aberration coefficient — or P-V wavefront error — is given by: 90018 90004 90005 ωa 90006 90018 = A / 24 90005 1/2 90006 (19) 90022 Thus the P-V wavefront error of astigmatism corresponding to the diffraction limited RMS of ω = 1/1801/2 is W 90005 a 90006 = (24/180) 1/2 = 0.365, in units of the wavelength. 90018 90022 It should be noted that for astigmatism, and aberrations in general, the point of minimum wavefront deviation does not coincide with the point of PSF maximum, i.e. diffraction focus, when the aberration exceeds certain level. For aberrations in general, significantly over 1/2 wave P-V. Specifically for astigmatism, the PSF peak at the mid focus becomes slightly lower than those at the tangential and sagittal foci — despite the former still retaining lower RMS wavefront error — at 1 wave P-V (Left). With further P-V error increase, the mid focus PSF peak sinks lower vs. tangential / sagittal, down to six times lower intensity at 2 waves P-V (The overall pattern is similar to the longitudinal PSF peak shift with spherical aberration, only with significantly larger maximum-to-mid-focus PSF peak differential).Minimum wavefront error is always for defocus P-V error half that of astigmatism, i.e. at the mid focus, but for errors larger than 1 wave P-V PSF peaks in the proximity of tangential and sagittal focus. PSF peak at the mid focus at 2 waves P-V is identical to that at 3 waves, despite the P-V / RMS error being 50% larger for the latter. Presence of a larger central obstruction alters longitudinal intensity distribution in a way that the shift occurs at somewhat less than 1 wave P-V, with the peak-to-mid-focus differential greater at 1 wave P-V, but smaller at 2 waves.90018 90022 Note that plots are for negative astigmatism, with the tangential focus closer to the objective than sagittal. 90018 90022 The form of the aberration coefficient shows that the astigmatism wavefront error, unlike coma and spherical aberration, does not change with object distance. This is expected consequence of astigmatism of a mirror — as well as that of a lens (contact) objective — being a result of the asymmetry of wavefront projection onto the surface, rather than a product of the wavefront / surface interaction.90018 90022 Astigmatism 90005 ray aberrations 90006 can also be expressed in terms of the peak aberration coefficient 90005 A 90006 as: 90018 L = 8AF 90005 2 90006, 90005 90006 T = 4FA 90005 90006 and 90005 90006 T 90005 a 90006 = 4A / D 90005 90006 (20) 90022 for the 90023 longitudinal 90024, 90023 transverse 90024 and 90023 angular 90024 astigmatism, respectively (the last two as the circle of least confusion diameter).After substituting for 90005 A 90006 and mirror aberration coefficient 90005 a 90006, the mirror transverse aberration — as the circle of least confusion diameter — can be also expressed as T = -Dα2 / 2 = -H3 / 2DF2 for object at infinity, with 90005 h 90006 being the point height in the image plane (Note that aperture 90005 D 90006 needs to be in the metric used for the coefficient calculation, which also becomes the metric of transverse aberration).Since focal lengths of the astigmatic wavefront do not change with the height in the pupil (i.e. the zonal height), transverse astigmatism changes in proportion to the normalized pupil ray height 90005 ρ 90006. With h = α, 90041 being the focal length, angular astigmatism 90005 T 90006 90005 a = T / = 90006 α 90005 2 / 2F 90006, where 90005 F 90006 is the focal ratio number F = / D. Longitudinal astigmatism 90005 L = — 90006 α 90005 2 90006. 90018 90022 There are simple geometric relationships between the 90023 circle of least confusion 90024 diameter and the 90023 sagittal 90024 and 90023 tangential line length 90024, as well as between the three and the 90023 longitudinal aberration 90024.The line length is double the circle diameter, and the longitudinal aberration is numerically greater than either line by a factor of 90005 F 90006 (The focal ratio), as illustrated in 90005 FIG. 44 90006. 90018 90022 The transverse aberration in terms of the RMS wavefront error is 90005 T 90006 90005 a = ω√384 / 2.44 90006, and in terms of the peak-to-valley error 90005 T 90006 90005 a = 4A / 2.44 90006 (for 90005 ω 90006 and 90005 A 90006 in units of the wavelength), both expressed in units of the Airy disc diameter.That makes the astigmatic geometric blur significantly smaller for given amount of wavefront aberration than geometric blur for either spherical aberration or coma (90005 FIG. 45 90006). It is a stark remainder that optical criteria can not be reduced to geometrical considerations; it is the underlying realm of electromagnetic field that determines the properties of the point object image. 90018 90004 90005 FIGURE 45 90006: The ray spot size (top) and actual diffraction patterns for 0.37 wave P-V wavefront error of primary astigmatism (resulting in 0.80 Strehl, thus comparable to 1/4 wave P-V of primary spherical aberration). Perfect diffraction pattern is to the left. Geometric blur diameter at the best focus location (balanced primary astigmatism) is only 0.6 Airy disc diameters. There is no rays outside the Airy disc, yet considerable amount of energy has spread out from the spurious disc — result of the complex wave interference around best focus point (not unexpected, considering that rays focused to a point still produce a pattern).Compared to spherical aberration and coma, the energy spread is concentrated closer to the disc. 90018 90022 As expected due to its uniformly dense geometric blur, the smallest RMS blur radius for astigmatism is at the location of the circle of least confusion. It is given by rRMS = FA 90005 √ 90006 2, or smaller by a factor of 90005 √ 90006 0.5 than the radius of the circle of least confusion. In units of the Airy disc diameter, the RMS blur diameter is RRMS = A 90005 √ 90006 2/1.22, for the peak aberration coefficient 90005 A 90006 in units of the wavelength. 90018 90022 In terms of the RMS wavefront error of astigmatism 90005 ωa 90006, the RMS blur diameter in units of Airy disc diameter is RRMS = 4 90005 √ 90006 3ω 90005 a 90006 /1.22. 90017 90018 90022 90005 EXAMPLE 90006: A 200mm / 5 concave mirror, d = 100, R = -2000, F = 5. Setting θ = 0 and ρ = 1, the 90005 peak wavefront error 90006 at h = 1.4mm off-axis, giving the field angle α = 1.4 / 1000 = 0.0014, is 90005 W 90006 = A / 2 = α2d2 / 2R = -0.0000049mm. The 90005 P-V wavefront error 90006 is twice greater — equal to the peak aberration coefficient — or -0.0000098mm. In units of 550nm (0.00055mm) wavelength, it is 0.0178, or 1/56 wave. Consequently, the 90005 RMS wavefront error 90006 90005 ω 90006 = A / 90005 √ 90006 24 = 0.000002mm or, in units of 550nm wavelength, 1/275 wave. The 90005 transverse astigmatism 90006 (circle of least confusion diameter) is 90005 T 90006 = 4FA = 20α2d2 / R = = 0.000196mm, or 0.03 Airy disc diameters, and 90005 angular astigmatism 90006 90005 Ta 90006 = T / is 0.000000196 radians, or 206.265×0.000000196 = 0.04 arc seconds. 90018 90022 Since both, wavefront error and geometric (ray) aberrations are directly proportional to the aberration coefficient, it implies that they are in a constant proportion themselves. In other words, doubling the wavefront error also doubles the geometric aberration.90018 90022 The RMS blur radius rRMS = FA 90005 √ 90006 2 = 0.0000098mm, and the RMS blur diameter in units of the Airy disc diameter is RRMS = A 90005 √ 90006 2 / 1.22 = 0.0207, for 90005 A 90006 in units of the wavelength. 90018 90022 Aberration coefficient of astigmatism does not change with 90005 object distance 90006. For relatively close objects, transverse astigmatism increases as i /, 90041 90005 i 90006 being the image-to-pupil separation.However, it does not affect the wavefront error: since the wavefront radius is also longer by the same ratio, identical nominal wavefront error results in proportionally greater longitudinal and transverse aberration. 90018 90022 For the 90005 aperture 90006 90005 stop displaced 90006 from mirror surface, the aberration coefficient of astigmatism changes in proportion to Kσ2 + (1-σ) 2, with 90005 σ 90006 being the mirror-to-stop separation (positive in sign) in units of the mirror radius of curvature.The astigmatism aberration coefficient is: 90018 90004 90018 90022 Needed stop separation for zero astigmatism is given by σ = [1 90005 √ 90006 | K |] / (K + 1). Thus, astigmatism is canceled for σ = 0.5 with a paraboloid and σ = 1 with a sphere. The relation is not defined for K = -1 (parabola), but implicates σ = 0.5 limit for 90005 K 90006 approaching -1. For positive values ​​of the conic 90005 K 90006, the aberration coefficient can not be zero regardless of the stop position, since both Kσ2 and (1-σ) 2 are positive.90018 90022 Unlike coma, change in astigmatism caused by displaced aperture stop is independent of object distance. 90018 90022 Aberration coefficient of primary astigmatism for a 90005 lens 90006 with the aperture stop at the surface is identical to the one given for concave mirror (90005 Eq. 19.1 90006), with the radius of curvature 90005 R 90006 replaced by 2 (Eq. 99), 90005 90006 being the lens ‘focal length. For a contact doublet, it gives the peak aberration coefficient as a sum of the aberration coefficients at the first and second lens, respectively, as: 90018 90004 90018 90022 with 90005 α 90006 being the field angle, and 90005 90006 90005 1 90006, 90041 90005 2 90006 the respective lens focal lengths (keep in mind that focal length of a negative lens is numerically negative in the left-to-right Cartesian coordinate system).Change of the stop position results in change of the aberration coefficient only with systems not corrected for spherical aberration, or coma, or both. Since modern refractor objectives commonly are aplanats, their astigmatism is not affected by the stop position. As already mentioned, wavefront error of astigmatism of the contact doublet does not change with object distance. 90018 90022 Strongly curved surfaces give rise to higher order aberrations, and astigmatism is no exception.Although relatively rare in amateur telescopes, 90005 secondary (higher-order) astigmatism 90006 can be significant in systems with sub-aperture correctors, as well as in eyepieces. Unlike the P-V wavefront error of primary astigmatism, which is at either sagittal or tangential focus described with quadratic function (parabola, blue plot on 90005 FIG. 46 90006 left), that of secondary astigmatism, given as W 90005 a 90006 = Aρ4cos2θ, is quartic (4th power) function with a single turning point (red plot on 90005 FIG.46 90006 left). The shape of wavefront deviation is generally similar to that of primary astigmatism, but its near-cylindrical form has larger near-flat middle area and more strongly curved edges. The wavefront shape implies that secondary astigmatism forms longer sagittal / tangential focus lines when unbalanced, or balanced with defocus. 90018 90004 90005 FIGURE 46 90006: The form of wavefront deviation of secondary (higher-order) astigmatism (red) vs.that of primary astigmatism (blue). For given P-V wavefront error, the secondary astigmatism deviation, in its pure form (left), is flatter for central zones, and steeper toward the edges. Balanced with defocus alone, it takes a form similar to balanced primary astigmatism (shaded gray), only the saddle is flatter. It is minimized when balanced w / primary astigmatism 90018 90022 Similarly to that of the primary, the error of secondary astigmatism at either sagittal or tangential focus (left; tangential focus has the same shape simply rotated by 90 about vertex) is reduced by refocusing to the best focus midway between them (right).In either case, the P-V error remains the same, but the RMS error is reduced, and smaller for given P-V error for secondary astigmatism at both focus location. 90018 90022 The more efficient way of minimizing secondary astigmatism is, however, balancing it with the lower-order form of opposite sign. The error is minimized with adding the primary astigmatism with the peak coefficient smaller by 25%, with W 90005 as 90006 = A (ρ4-0.75ρ2) cos2θ, implying that the P-V error of of secondary astigmatism balanced with the lower-order form is smaller by a factor of 0.25 (fourfold) than at either sagittal or tangential focus. The RMS error is smaller than that of balanced primary astigmatism of identical P-V error by a factor 90005 √ 90006 0.6. 90018 90022 However, due to the different rates of aberration increase for the two astigmatism forms (2nd vs. 4th power of field angle for the primary and secondary form, respectively) this optimized balancing is only possible at a narrow field zone.Usually, primary astigmatism is left to be larger initially, with the two forms balancing farther off axis and secondary astigmatism quickly becoming dominant after that. 90018 90004 90017 ◄ 4.2. Coma ▐ 4.4.Defocus ► 90018 90004 Home | Comments 90017 90018 90018 90473 90474.90000 Astigmatism 90001 90002 90003 Astigmatism 90004 is a common vision condition that causes blurred vision. It occurs when the cornea (the clear front cover of the eye) is irregularly shaped or sometimes because of the curvature of the lens inside the eye. 90005 90002 An irregularly shaped cornea or lens prevents light from focusing properly on the retina, the light-sensitive surface at the back of the eye.As a result, vision becomes blurred at any distance. This can lead to eye discomfort and headaches. 90005 90002 Astigmatism frequently occurs with other vision conditions like myopia (nearsightedness) and hyperopia (farsightedness). Together these vision conditions are referred to as refractive errors because they affect how the eyes bend or «refract» light. 90005 90002 There are many causes to astigmatism. It can be hereditary and is usually present from birth. It can decrease or increase over time.90005 90002 A comprehensive optometric examination will include testing for astigmatism. If necessary, your optometrist can provide eyeglasses or contact lenses that correct the astigmatism by altering the way light enters the eyes. 90005 90002 Another option for treating astigmatism is a corneal procedure called orthokeratology (ortho-k). In this painless, noninvasive procedure, the patient wears a series of specially designed rigid contact lenses to gradually reshape the curvature of the cornea.90005 90002 Laser surgery can also treat some types of astigmatism. The laser changes the shape of the cornea by removing a small amount of eye tissue. 90005 90002 90019 90005 90021 What causes astigmatism? 90022 90023 90002 The curvature of the cornea and lens bends the light entering the eye in order to focus it precisely on the retina at the back of the eye. In astigmatism, the surface of the cornea or lens has a somewhat different curvature. 90005 90002 the surface of the cornea is shaped more like a football instead of round like a basketball, the eye is unable to focus light rays to a single point.Vision becomes out of focus at any distance. 90005 90002 In addition, the curvature of the lens inside the eye can change, resulting in an increase or decrease in astigmatism. This change frequently occurs in adulthood and can precede the development of naturally occurring cataracts. 90005 90002 Sometimes astigmatism may develop following an eye injury or eye surgery. 90005 90002 Astigmatism also occurs due to a relatively rare condition called keratoconus in which the cornea becomes progressively thinner and cone-shaped.This results in a large amount of astigmatism, which causes poor vision that can not be clearly corrected with eyeglasses. People with keratoconus usually need contact lenses for clear vision and eventually may need a corneal transplant. 90005 90021 How is astigmatism diagnosed? 90022 90036 90002 An optometrist can diagnose an astigmatism through a comprehensive eye examination. Testing for astigmatism measures how the eyes focus light and determines the power of any optical lenses needed to improve vision.This examination may include: 90005 90039 90040 90003 Visual acuity 90004 -When you read letters on a distance chart, you are measuring your visual acuity. Visual acuity is given as a fraction (for example, 20/40). The top number is the standardized testing distance (20 feet) and the bottom number is the smallest letter size read. A person with 20/40 visual acuity would have to get within 20 feet to read a letter that should be seen clearly at 40 feet. Normal distance visual acuity is 20/20.90043 90040 90003 Keratometry / Topography 90004 -A keratometer is the primary instrument used to measure the curvature of the cornea. By focusing a circle of light on the cornea and measuring its reflection, it is possible to determine the exact curvature of that area of ​​the cornea’s surface. This measurement is particularly critical in determining the proper fit for contact lenses. A corneal topographer, which is gaining use, generates a contour map of the cornea and provides even more detail of the cornea’s shape.90043 90040 90003 Refraction 90004 -Using an instrument called a phoropter, your optometrist places a series of lenses in front of your eyes and measures how they focus light. This is performed using a handheld lighted instrument called a retinoscope or an automated instrument that evaluates the approximate focusing power of the eye. Based on your responses, the power is then refined to determine the lenses that allow the clearest vision. Despite improved technology, patient input remains integral in determining vision needs.90043 90052 90002 With the information from these tests, your optometrist can determine if you have astigmatism. Your optometrist will use these findings, combined with those of other tests performed, to determine the power of any lens correction you need to provide clear, comfortable vision. Once testing is complete, your optometrist can discuss treatment options. 90005 90021 How is astigmatism treated? 90022 90057 90002 People with astigmatism have several options to regain clear vision.They include: 90005 90039 90040 90003 Eyeglasses. 90004 People with astigmatism primarily choose eyeglasses to improve their vision. The eyeglasses contain a special cylindrical lens prescription that compensates for the astigmatism. This provides additional power in specific parts of the lens. 90002 Generally, a single-vision lens is prescribed to provide clear vision at all distances. However, patients over age 40 who have presbyopia may need a bifocal or progressive addition lens.90005 90043 90040 90003 Contact lenses. 90004 Some people will have better vision with contact lenses rather than eyeglasses. Contact lenses may provide clearer vision and a wider field of view. However, since contact lenses are worn directly on the eyes, they require regular cleaning and care to safeguard eye health. 90002 Standard soft lenses may not be effective in correcting astigmatism. However, special toric soft contact lenses can correct for many types of astigmatism. Because rigid gas-permeable contact lenses maintain their regular shape while on the cornea, they can compensate for the cornea’s irregular shape and improve vision for people with astigmatism.90005 90043 90040 90003 Orthokeratology. 90004 Orthokeratology (ortho-k) involves the fitting of a series of rigid contact lenses to reshape the cornea. The patient wears contact lenses for limited periods, such as overnight, and then removes them. People with moderate astigmatism may be able to temporarily obtain clear vision without lenses for most of their daily activities. Orthokeratology does not permanently improve vision. If patients stop wearing the retainer lenses, their vision may return to its original condition.90043 90040 90003 Laser and other refractive surgery procedures. 90004 Astigmatism can also be corrected by reshaping the cornea through LASIK (laser in situ keratomileusis) or PRK (photorefractive keratectomy). PRK removes tissue from the superficial and inner layers of the cornea. LASIK removes tissue only from the inner layer of the cornea. 90043 90052 90002 If you have an astigmatism, you have a wide range of options to correct your vision problem. In consultation with your optometrist, you can select the treatment that best meets your visual and lifestyle needs.90005 .