"Нередко зрение обманывает нас, и мы видим то, чего в действительности не существует. Объясняется это оптическими иллюзиями — ошибками зрительного восприятия. Люди с давних пор учились их преодолевать и даже использовать. И, надо сказать, значительно в этом преуспели
Нередко зрение обманывает нас, и мы видим то, чего в действительности не существует. Объясняется это оптическими иллюзиями — ошибками зрительного восприятия"
...или же наш мозг странно реагирует на подобные иллюзии т.о. вводится в заблуждение
т.о. можно с помощью иллюзий влиять на мозг, вводить в гипнотическое состояние, что я с успехом, неожиданным для себя и делал, просто используя физиологию глаза
а индейцы, используя ту же физиологию, могли просто исчезать стоя прямо перед вашими глазами
Слепое пятно в глазу, слышали про такое?
Давно хочу написать об этом диссертацию
иллюзия мак каллоу- одна из сторон которую планирую употребить для иллюстрации, она была продемонстрирована на последней обложке одного из журналов ннаука и жизнь -не иогу найти
3 3 16
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3380664/
Higher-Order Aberrations in Myopic Eyes
Farid Karimian, MD, Sepehr Feizi, MD, and Azade Doozande, MD
Author information ; Article notes ; Copyright and License information ;
This article has been corrected. See J Ophthalmic Vis Res. 2010 July; 5(3): 214.
This article has been cited by other articles in PMC.
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Abstract
Purpose
To evaluate the correlation between refractive error and higher-order aberrations (HOAs) in patients with myopic astigmatism.
Methods
HOAs were measured using the Zywave II aberrometer over a 6 mm pupil. Correlations between HOAs and myopia, astigmatism, and age were analyzed.
Results
One hundred and twenty-six eyes of 63 subjects with mean age of 26.4±5.9 years were studied. Mean spherical equivalent refractive error and refractive astigmatism were ;4.94±1.63 D and 0.96±1.06 D, respectively. The most common higher-order aberration was primary horizontal trefoil with mean value of 0.069±0.152 ;m followed by spherical aberration (;0.064±0.130 ;m) and primary vertical coma (;0.038±0.148 ;m). As the order of aberration increased from third to fifth, its contribution to total HOA decreased: 53.9% for third order, 31.9% for fourth order, and 14.2% for fifth order aberrations. Significant correlations were observed between spherical equivalent refractive error and primary horizontal coma (R=0.231, P=0.022), and root mean square (RMS) of spherical aberration (R=0.213, P=0.031); between astigmatism and RMS of total HOA (R=0.251, P=0.032), RMS of fourth order aberration (R=0.35, P<0.001), and primary horizontal coma (R=0.314, P=0.004). Spherical aberration (R=0.214, P=0.034) and secondary vertical coma (R=0.203, P=0.031) significantly increased with age.
Conclusion
Primary horizontal trefoil, spherical aberration and primary vertical coma are the predominant higher-order aberrations in eyes with myopic astigmatism.
Keywords: Higher-Order Aberrations, Myopia, Zywave Aberrometer, Hartmann-Shack Aberrometer
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INTRODUCTION
Higher-order aberrations (HOAs) are small optical irregularities or imperfections of the eye which cannot be corrected by simple sphere and cylinder corrections. Many authors believe that HOAs are the reason many patients complain of halo, glare and decreased contrast sensitivity after successful corneal refractive surgery.1,2 In the normal eye, 90% of total aberrations are caused by the cornea. New diagnostic technologies enable the detection and correction of ocular aberrations beyond defocus and astigmatism3,4 by applying the root mean square (RMS) of Zernike coefficient polynomials.5,6
The purpose of this study was to measure and evaluate the distribution of HOAs in myopic eyes and to determine any correlation between the degree of refractive error (myopia and astigmatism) and HOAs.
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METHODS
The study included young refractive surgery candidates with a completely normal ocular examination except for myopic refractive error. Exclusion criteria were history of ocular or corneal surgery or trauma, corneal scar, lens or media opacity, pathologic myopia or severe chorioretinal atrophy which could alter vision and wavefront measurements, and best spectacle-corrected visual acuity (BSCVA) of 20/40 or worse. Soft and rigid gas-permeable hard contact lenses were discontinued for at least 2 and 6 weeks, respectively and measurements were taken provided that there was no corneal warpage.
Measurement of HOAs and wavefront analysis were performed across a 6.0 mm pupil using Zywave II aberrometer with Zywave software version 5.2 (Bausch & Lomb, Rochester, NY, USA) in a dark room. The Zywave II aberrometer is a Hartmann-Shack wavefront sensor applying light in the near infrared range (;=785 nm).7 In this aberrometer, the pupil is sampled through a square array of lenslets with a fixed pitch, the number of spots (samples) depends on the chosen pupil diameter. Each measurement consists of five sequential runs; the system computes the average of three best compatible measurements after rejecting the two measurements with higher deviations from the mean.
All measurements were performed by one experienced technician using the same machine and procedure. If the natural scotopic pupil failed to reach 6.0 mm, it was dilated with 2.5% phenylephrine eye drops as recommended by the manufacturer. Aberrometric measurements were performed approximately 30 minutes after instillation of the drop. To avoid instrument accommodation, the eye was fogged approximately 1.00 D during measurements.8
Zernike polynomials up to the fifth order were used for data analysis. All Zernike coefficients were transformed to the standard form as recommended by the Optical Society of America.9 Analyzed parameters included Zernike coefficients from third to fifth orders; RMS of total HOAs from third to fifth orders; RMS of fourth order spherical aberration (square root of the sum of squared coefficients of Z40); RMS of coma-like aberration (square root of the sum of squared coefficients of Z3;1, Z31, Z5;1, and Z51); RMS of trefoil-like aberrations (square root of the sum of squared coefficients of Z3;3, Z33, Z5;3, and Z53); and RMS of third, fourth and fifth order aberrations. Correlations between HOAs and myopia, astigmatism and age were examined using multiple linear regression analysis and Pearson’s correlation coefficient (R) with significance level set at 0.05.
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RESULTS
One hundred and twenty-six eyes of 63 myopic patients including 41 (65%) female and 22 (35%) male subjects with mean age of 26.4±5.9 (range, 18–43) years met the study criteria. Mean spherical equivalent refractive error was ;4.94±1.63 (range, ;1.13 to ;8.50) D and mean astigmatism was 0.96±1.06 (range, 0 to 4.50) D; BSCVA was 20/20 or better in all eyes.
From the mean of total aberrations (RMS) 53.9% were in the third; 31.9% in the fourth; and 14.2% in the fifth orders of aberration (Table 1). Considering the Zernike coefficient of each HOA, primary horizontal trefoil (Z33) had the highest mean followed by spherical aberration (Z40) and primary vertical coma (Z3;1) (Table 2).
Table 1
Table 1
Root mean square (RMS) values for different aberrations
Table 2
Table 2
Coefficient values for each Zernike term from third to fifth order
Multiple linear regression analysis revealed significant correlations between spherical equivalent refractive error and primary horizontal coma (R=0.231, P=0.022), and the RMS of spherical aberration (R=0.213, P=0.031) (Figures 1, ,2).2). No significant correlation was found between spherical equivalent refractive error and the RMS of total HOAs or the RMS of any order of aberrations. A significant direct correlation was also observed between astigmatism and the RMS of total HOA (R=0.251, P=0.032) and the RMS of fourth order aberrations (R=0.35, P<0.001). Considering individual Zernike polynomials, there was a significant correlation between astigmatism and primary horizontal coma (R=0.314, P=0.004) (Figures 3, ,4,4, ,5).5). Furthermore it was noted that spherical aberration (R=0.214, P=0.034) and secondary vertical coma (R=0.203, P=0.031) increased significantly with age (Figures 6, ,77).
Figure 1
Figure 1
Correlation between spherical equivalent refractive error and primary horizontal coma (R=0.231, P=0.022).
Figure 2
Figure 2
Significant correlation between spherical equivalent refractive error and root mean square of spherical aberration (R=0.213, P=0.031).
Figure 3
Figure 3
Significant correlation between astigmatism and root mean square of total higher-order aberrations (R=0.251, P=0.032).
Figure 4
Figure 4
Significant correlation between astigmatism and root mean square of fourth order aberrations (R=0.35, P<0.001).
Figure 5
Figure 5
Significant correlation between astigmatism and Zernike coefficient of primary horizontal coma (R=0.314, P=0.004).
Figure 6
Figure 6
Significant correlation between age and spherical aberration (R=0.214, P=0.034).
Figure 7
Figure 7
Significant correlation between age and secondary vertical coma (R=0.203, P=0.031).
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DISCUSSION
This study explores changes in higher-order aberrations as a function of refractive error (spherical equivalent and astigmatism) and age. Multiple linear regression analysis showed that spherical equivalent refractive error was significantly correlated with primary horizontal coma and the RMS of spherical aberration. These findings are in good accordance with results reported by Applegate10 who found dramatically increased coma and spherical aberrations in myopic eyes using a subjective single-pass aberroscope. Similarly using a Shack-Hartmann aberrometer, Paquin et al11 found that optical quality was worse in myopic eyes and that high amounts of coma were more frequent in high myopia. Using a subjective ray-tracing technique, He et al12 measured aberrations in 146 young adults and found that myopic eyes have slightly higher combined fourth order and higher aberrations as compared to emmetropic eyes. But similar to the current study, they failed to find a significant correlation between total aberrations and spherical equivalent refractive error. Wei et al13 showed that there was no correlation between the degree of myopia and the RMS of total higher order aberrations or third to fifth order RMS. Analyzing individual Zernike coefficients rather than RMS values, they found a slightly significant correlation between myopia and primary horizontal trefoil.
Despite these findings, the correlation between refractive error and HOAs remains a matter of controversy. Collins et al,14 using an objective double-pass aberroscope, reported lower average spherical aberrations in high myopes than emmetropes. Cheng et al15 also concluded that wavefront aberrations were unrelated to refractive error in a population of 200 normal eyes. Maybe, such conflicting conclusions in the aforementioned studies can be attributed to high variability in monochromatic aberrations in myopic eyes. Alternatively, it may be due to lack of a standard method for measurement and interpretation of HOAs. Further studies with larger sample size utilizing a systematic approach are necessary to address this issue.
In concordance with previous reports,16–18 we noted that the contribution of average RMS of higher order aberrations decreased as the order increased: third order aberrations predominated, followed by fourth and fifth order aberrations. Wang et al16 investigated HOAs from third to sixth orders using WaveScan System across a 6.0 mm pupil in 532 eyes with mean WaveScan spherical equivalent of ;3.39±2.84 (range, ;11.56 to +7.60) D and found that spherical aberration was the predominant aberration followed by primary vertical coma. In contrast, we observed that primary horizontal trefoil had the highest mean followed by spherical aberration and primary vertical coma. This difference may be due to the range of refractive errors evaluated in each study; we analyzed HOAs only among myopic eyes while in the aforesaid study, both myopic and hyperopic subjects were evaluated.
We found positive correlations between the amount of astigmatism and the RMS of HOA, the RMS of fourth order aberration, and primary horizontal coma. But, there was no association between astigmatism and vertical coma, vertical trefoil, horizontal trefoil, and spherical aberrations. Other investigators have reported the influence of astigmatism on wavefront aberrations. Slight but significant correlations between astigmatism and primary horizontal coma, and between astigmatism and primary horizontal trefoil were reported by Wei et al.13 Furthermore, Cheng et al15 reported slightly larger total higher-order RMS in astigmatic eyes which supports our findings. Zheng et al19 conducted a study on 226 eyes of 113 patients and evaluated the influence of the amount and axis of astigmatism on HOAs. To evaluate the pure effect of astigmatism on contrast sensitivity function (CSF) and aberration, the investigators only corrected the spherical component of refractive errors and left the astigmatic component uncorrected. By dividing the patients into three groups based on amount of astigmatism, they found that increasing astigmatism was associated with increasing coma aberrations, secondary coma aberrations, third order, fifth order, and total HOAs. However, the fourth order aberration remained constant.
The current study demonstrated statistically significant correlations between age and spherical aberration, and secondary vertical coma which is consistent with previous reports.16,20 Such associations may be due to changes in the cornea or crystalline lens which occur with aging. For example, corneal astigmatism usually shifts from with-the-rule to against-the-rule over time. Furthermore, the crystalline lens starts to demonstrate alterations in refractive index and therefore, changes in aberrations occur due to cataract formation.21–24 Since we measured optical aberrations of the eye as a whole system, we cannot attribute the observed increase in spherical aberration and secondary vertical coma to changes in the cornea or the crystalline lens caused by lenticular astigmatism or aging. Other studies25–27 have reported no correlation between aging and corneal spherical aberration, which implies that the increasing spherical aberration with age is caused by lenticular rather than corneal changes. Furthermore, age range was limited in our study (18 to 43 years), thereby our observations regarding the effect of age on HOAs may not be applicable to other age groups. Further evaluations, particularly longitudinal studies, are required to determine how much alterations in ocular aberrations are attributable to age related changes in the cornea.
Applegate et al28 reported that for an equal amount of RMS error, different coefficients of Zernike polynomials affect visual function to varying degrees. They concluded that aberrations close to the center of the Zernike table (e.g., coma, spherical aberration, secondary astigmatism) cause greater distortion of vision than those located at the periphery of the table. In addition, we demonstrated that the contribution of each higher-order aberration to total HOAs decreases with increasing order. Based on these two observations, one may conclude that lower order and more central aberrations, affect image quality to a greater extent. Therefore, lower-order aberrations including defocus (sphere) and astigmatism remain the most significant contributors to optical system quality and constitute the top priority for correction during refractive surgery. The next priority would be to deal with higher-order aberrations located higher in the Zernike table such as primary coma and those involving central vision like spherical aberration. Later, one can proceed to more inferiorly and peripherally located HOAs. In other words, correcting HOAs without completely eliminating lower-order aberrations may not improve visual performance and meet patients’ expectations.
In summary, we found primary horizontal trefoil to be the predominant HOA in a young myopic population with spherical equivalent refractive error ranging from ;1.13 to ;8.5 D. Spherical and coma-like aberrations are HOAs associated with increasing myopia and age. Astigmatism is significantly correlated with total HOAs, fourth order and coma-like aberrations.
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REFERENCES
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4. Liang J, Williams DR, Miller DT. Supernormal vision and high-resolution retinal imaging through adaptive optics. J Opt Soc Am A Opt Image Sci Vis. 1997;14:2884–2892. [PubMed]
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7. Liang J, Williams DR. Aberrations and retinal image quality of the normal human eye. J Opt Soc Am A Opt Image Sci Vis. 1997;14:2873–2883. [PubMed]
8. Hament WJ, Nabar VA, Nuijts RM. Repeatability and validity of Zywave aberrometer measurements. J Cataract Refract Surg. 2002;28:2135–2141. [PubMed]
9. Thibos LN, Applegate RA, Schwiegerling JT, Webb R. Standards for reporting the optical aberrations of eyes. In: Lakshminarayanan V, editor. Vision science and its applications. TOPS-35. Washington, DC: Optical Society of America; 2000. pp. 232–244.
10. Applegate RA. Noninvasive assessment of the visual system. Vol. 1. Washington, DC: Optical Society of America; 1991. 1991. Monochromatic wavefront aberrations in myopia; pp. 234–237. (Technical Digest Series).
11. Paquin MP, Hamam H, Simonet P. Objective measurement of optical aberrations in myopic eyes. Optom Vis Sci. 2002;79:285–291. [PubMed]
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14. Collins MJ, Wildsoet CF, Atchison DA. Monochromatic aberrations and myopia. Vision Res. 1995;35:1157–1163. [PubMed]
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16. Wang L, Koch DD. Ocular higher-order aberrations in individuals screened for refractive surgery. J Cataract Refract Surg. 2003;29:1896–1903. [PubMed]
17. Carkeet A, Leo SW, Khoo BK, Au Eong KG. Modulation transfer functions in children: pupil size dependence and meridional anisotropy. Invest Ophthalmol Vis Sci. 2003;44:3248–3256. [PubMed]
18. Wang Y, Zhao K, Jin Y, Niu Y, Zuo T. Changes of higher order aberration with various pupil sizes in the myopic eye. J Refract Surg. 2003;19:S270–S274. [PubMed]
19. Zheng GY, Du J, Zhang JS, Liu SB, Nie XL, Zhu XH, et al. Contrast sensitivity and higher-order aberrations in patients with astigmatism. Chin Med J. 2007;120:882–885. [PubMed]
20. McLellan JS, Marcos S, Burns SA. Age-related changes in monochromatic wave aberrations of the human eye. Invest Ophthalmol Vis Sci. 2001;42:1390–1395. [PubMed]
21. Navarro R, Santamaria J, Besc;s J. Accommodation-dependent model of the human eye with aspherics. J Opt Soc Am A. 1985;2:1273–1281. [PubMed]
22. Pallikaris LG, Panagopoulou SI, Siganos CS, Molebny VV. Objective measurement of wavefront aberrations with and without accommodation. J Refract Surg. 2001;17:S602–S607. [PubMed]
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24. Glasser A, Campbell MC. Biometric, optical and physical changes in the isolated human crystalline lens with age in relation to presbyopia. Vision Res. 1999;39:1991–2015. [PubMed]
25. Amano S, Amano Y, Yamagami S, Miyai T, Miyata K, Samejima T, et al. Age-related changes in corneal and ocular higher-order wavefront aberrations. Am J Ophthalmol. 2004;137:988–992. [PubMed]
26. Oshika T, Klyce SD, Applegate RA, Howland HC. Changes in corneal wavefront aberrations with aging. Invest Ophthalmol Vis Sci. 1999;40:1351–1355. [PubMed]
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Articles from Journal of Ophthalmic & Vision Research are provided here courtesy of Medknow Publications
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http://www.carlomasci.it/biblio/aberrazioni_5.pdf
иллюзия мак каллоу на последней обложке наука и жизнь вдохновила меня когда то на написание диссертации но подобные труды уже существуют на польском например
Словно оптическая иллюзия, насмехающаяся тень отрывается все дальше от меня с каждым...
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Main page / Popular articles / Optical aberrations (distortions) of human visual system
Optical aberrations (distortions) of human visual system
Optical aberrationsAs any non-perfect optical system, the human eye is prone to optical defects – aberrations, which downgrade vision quality distorting retinal image. Aberration is an angular deviation of the narrow parallel light beam from the point of the perfect retinal crossing, caused by the whole eye optical system.
In technical optics the quality of the optical system is determined by aberrations of the plane or spherical front of the light wave when the light passes through the system. For example an eye with no aberrations would have a plane wave front and provide the most comprehensive image of a point source on the retina (the so called Airy disc, the size of which depends only on the pupil diameter). But in reality even with 100% vision the optical defects of the light refracting eye surfaces distort the rays and form a wrong wave front, thus creating an image on the retina which is bigger and asymmetrical.
Zernike polynomials sequences
Zernike polynomials sequences
The quantitative characteristic of the image optical quality is the root mean square of deviation errors of real wave front from the ideal. The German mathematician Zernike introduced a mathematical formalism, employing polynomial sequences to describe wave front aberrations. Polynomials of the first and the second (lower) sequences describe the usual for ophthalmologists aberrations – myopia, hyperopia and astigmatism. The polynomials of higher orders are less familiar: the third corresponds to coma – it is a spherical aberration of oblique light beams falling at an angle to the eye optical axis. The base of it is eye optical elements asymmetry, as the corneal centre does not coincide with the crystalline lens centre. The fourth order are spherical aberrations due to unevenness of the clear lens refractive power. The higher orders are known as irregular aberrations.
Wave front measurements
Wave front measurements
Optical system is considered to be good if Zernike coefficients are close to zero, so the mean root square of the errors is less than 1/14 of the light wave length (Marechal criterion). Based on the coefficient data vision acuity may be predicted through modelling of optotypes images on the retina. A special device aberrometer is used for evaluation of the human visual system aberrometry. Excimer Clinics use Wave Scan aberrometer manufactured by VISX Inc (USA).
Eye aberration determination methods
At present a couple of eye aberrations evaluation methods are used, based on different principles.
Eye aberration determination methodsThe first one is retinal imaging aberrometry. Two parallel laser beams of 650 nm wavelength and 0.3 mm diameter are projected on the retina, one falls strictly alongside the optical axis and is the reference while the other is at a given distance from it. Then the degree of the second beam deviation from the reference beam fixation point is registered. This procedure is repeated for each point within the pupil area.
The second principle is the outgoing refraction aberrometry. It has been widely used in astronomy for aberrations compensation in telescopes when light was passing through atmosphere and cosmic space. Using a diode laser with 850 nm wave length a collimated emission beam is directed into the eye, this beam passing through all the eye media is reflected by the retina with all the aberrations in force and is registered by a matrix consisting of 1089 micro-lenses. Each micro-lens collects undistorted rays in its own focal point and the aberrated rays are focused at a certain distance from that point. The collected information is processed by a computer and is presented as an aberrations chart. WaveScan aberrometer is using this procedure..
The third principle is based on the compensating adjustment of the light beam falling on the foveola. Today the method is used as a subjective aberrometer demanding active participation of a patient. A light beam is directed into the eye through a rotating disk with 1 mm holes, the disc is located on the same optical axis as the pupil. When the disc rotates the narrow parallel light beams pass through every point of the pupil and are projected on the foveola where another ray is directed with a reference mark shaped as a cross. If a patient is nearsighted, farsighted or astigmatic or has other aberrations of higher orders, he will notice misalignment of the dots to the cross, and he has to match them using a special unit. The angle of shift describes the aberration degree.
Versatility of ophthalmologic devices created using latest technologies and based on different operating principles ensures quality and quantitative lower and higher order aberration evaluation and determination of factors that may influence them.
The major causes of aberrations in the eye optical system:
Shape and transparency of cornea and clear lens; retinal condition; transparency of intraocular fluid and vitreous bode.
Pupil diameter increase.With the pupild diameter of 5.0 mm aberrations of the 3rd order prevail, increase of the diameter to 8.0 mm leads to aberrations of the 4th order. It has been calculated that the critical pupil diameter for the minimum effect of higher order aberrations is 3.22 mm.
Accommodation. It has been noted that aberrations grow with age and from 30 to 60 aberrations are doubled. Maybe it is due to the fact that the crystalline lens elasticity and transparency deteriorate with age and it seizes to compensate corneal aberrations. This also happens in case of accommodation spasm..
Accommodation spasm is rather frequent and happens in patients of various ages. In ophthalmology the accommodation spasm is a condition when accommodation is too steadily strained because of such a contraction of the ciliary muscle, that it is not released when accommodation is not required anymore. In other words accommodation spasm is a prolonged static overexertion of the eye muscle as a result of e.g. too long time spent at a computer screen and resulting in development of a computer syndrome. Accommodation spasms can develop with all refractions (astigmatism included). Accommodation spasm causes pseudo-myopia or amplify true myopia.
Tear film condition. It has been revealed that tear film damage increases higher order aberrations by 1.44 times. One of tear film disorders is the Dry eye syndrome. Dry eye syndrome develops when the corneal surface goes dry due to interrupted blinking and long staring at the work object. It has been noticed that during computer work and reading one is blinking tree times less than normal. This makes tear film dry out and it cannot get enough time to restore. The usual causes of the dry eye syndrome are: great loads during computer work and reading, dry air inside rooms, wrong nourishment with too less vitamins, air pollution, some medication.
Contact lenses use. Soft contact lenses can cause wave monochrome abberations of higher order while rigid lenses reduce 2nd order aberrations. However aspheric surface of hard contact lenses can produce spherical aberrations. Aspherical contact lenses may cause greater instability of vision acuity than spherical. Multifocal lenses can induce coma-type and 5th order aberrations.
Today there are a procedures for individualized vision correction (Super LASIK, Custom Vue) based on aberrometry that allow to achieve excellent results in practically any complicated cases, compensating all the distortions of the visual system to a maximum.
Read on
https://en.wikipedia.org/wiki/Aberrations_of_the_eye
Aberrations of the eye
From Wikipedia, the free encyclopedia
The eye, like any other optical system, suffers from a number of specific optical aberrations. The optical quality of the eye is limited by optical aberrations, diffraction and scatter.[1] Correction of spherocylindrical refractive errors has been possible for nearly two centuries following Airy's development of method's to measure and correct ocular astigmatism. It has only recently become possible to measure the aberrations of the eye and with the advent of refractive surgery it might be possible to correct certain types of irregular astigmatism.
The appearance of visual complaints such as halos, glare and monocular diplopia after corneal refractive surgery has long been correlated with the induction of optical aberrations. Several mechanisms may explain the increase in the amount of higher-order aberrations with conventional eximer laser refractive procedures: a change in corneal shape toward oblateness or prolateness (after myopic and hyperopic ablations respectively), insufficient optical zone size and imperfect centration. These adverse effects are particularly noticeable when the pupil is large.[2]
Contents [hide]
1 Wavefront approach to aberrations of the eye
2 Aberration of normal eyes
3 Low Order Aberrations
4 High Order Aberrations
5 Assessment and quantitative expression of ocular aberrations
5.1 Assessment
5.2 Quantitative expression
5.2.1 RMS
5.2.2 Zernike Polynomials
6 Management
7 See also
8 References
Wavefront approach to aberrations of the eye[edit]
The flat wavefronts change to spherical wavefronts as they pass through a pinhole
A wavefront is a surface over which an optical disturbance has a constant phase. Rays and wavefronts are two mutually complementary approaches to light propagation. Wavefronts are always normal (perpendicular) to the rays.
For light to converge to a perfect point, the wavefront emerging from the optical system must be a perfect sphere centered on the image point. The distance in micrometers between the actual wavefront and the ideal wavefront is the wavefront aberration, which is the standard method of showing the aberrations of the eye. Therefore, aberrations of the eye are the difference between two surfaces: the ideal and the actual wavefront.
Aberration of normal eyes[edit]
In normal population the dominant aberrations are the ordinary second-order spherocylindrical focus errors, which are called refractive errors. Higher order aberrations are a relatively small component, comprising about 10% of the eye’s total aberrations.[3] High order aberrations increase with age and mirror symmetry exists between the right and the left eyes.[4]
Several studies have reported a compensation of the aberration of the cornea by the aberration of the crystalline lens. The spherical aberration of the cornea is usually positive whereas the young crystalline lens exhibits a negative spherical aberration. Besides, there is strong evidence of compensation for aberrations between the cornea and intraocular optics in cases of astigmatism (horizontal/vertical) and horizontal coma. The balance of corneal and internal aberrations is a typical example of creating two coupling optical systems.[5]
The accommodative response of the eye results in changes to the lens shape and substantially affects the Wavefront aberration pattern. Most eyes show positive spherical aberration when unaccomodated with a trend toward negative spherical aberration on accommodation.[1]
Low Order Aberrations[edit]
Includes Myopia (positive defocus), hyperopia (negative defocus), and regular astigmatism. Other lower-order aberrations are non- visually significant aberrations known as first order aberrations, such as prisms and zero-order aberrations (piston). Low order aberrations account for approximately 90% of the overall wave aberration in the eye.[5][6]
High Order Aberrations[edit]
Spherical aberration. A perfect lens (top) focuses all incoming rays to a point on the Optical axis. In spherical aberration (Bottom) peripheral rays are focused more tightly than central rays.
There are numerous higher-order aberrations, of which only spherical aberration, coma and trefoil are of clinical interest.
Spherical aberration is the cause of night myopia and is commonly increased after myopic LASIK and surface ablation. It results in halos around point images. Spherical aberration exacerbates myopia in low light (night myopia). In brighter conditions, the pupil constricts, blocking the more peripheral rays and minimizing the effect of spherical aberration. As the pupil enlarges, more peripheral rays enter the eye and the focus shifts anteriorly, making the patient slightly more myopic in low-light conditions. In general, the increase in overall wave aberration with pupil size has been reported to increase to approximately the second power of the pupil radius. This is because of the fact that most wave aberration is due to 2nd order aberrations, which have a square radius dependency.[5] The effect of spherical aberration increases as the fourth power of the pupil diameter. Doubling pupil diameter increases spherical aberration 16 times.[7] Thus, a small change in pupil size can cause a significant change in refraction. This possibility should be considered in patients who have fluctuating vision despite well-healed corneas following keratorefractive surgery.
Coma is common in patients with decentred corneal grafts, keratoconus, and decentred laser ablations.
Trefoil produces less degradation in image quality compared with coma of similar RMS magnitude.[6]
Assessment and quantitative expression of ocular aberrations[edit]
Assessment[edit]
Shack Hartmannsystem
Many techniques for measuring the eye’s aberrations have been described, The most common technique is Shack-Hartmann aberrometry. Other methods include Tscherning systems, ray tracing and Skiascopy methods.[2][8]
Quantitative expression[edit]
RMS[edit]
Quantitative comparisons between different eyes and conditions are usually made using RMS (root mean square). To measure RMS for each type of aberration involves squaring the difference between the aberration and mean value and averaging it across the pupil area. Different kinds of aberrations may have equal RMS across the pupil but have different effects on vision, therefore, RMS error is unrelated to visual performance. The majority of eyes have total RMS values less than 0.3 µm.[6]
Zernike Polynomials[edit]
The most common method of classifying the shapes of aberration maps is to consider each map as the sum of fundamental shapes or basis functions. One popular set of basis functions are the Zernike polynomials.[2] Each aberration may be positive or negative in value and induces predictable alterations in the image quality.[9] Because there is no limit to the number of terms that may be used by Zernike polynomials, vision scientists use the first 15 polynomials, based on the fact that they are enough to obtain a highly accurate description of the most common aberrations found in human eye.[10] Among these the most important Zernike coefficients affecting visual quality are coma, spherical aberration, and trefoil.[6]
Zernike polynomials are usually expressed in terms of polar coordinates (;,;), where ; is radial coordinate and ; is the angle. The advantage of expressing the aberrations in terms of these polynomials includes the fact that the polynomials are independent of one another. For each polynomial the mean value of the aberration across the pupil is zero and the value of the coefficient gives the RMS error for that particular aberration (i.e. the coefficients show the relative contribution of each Zernike mode to the total wavefront error in the eye).[4] However these polynomials have the disadvantage that their coefficients are only valid for the particular pupil diameter they are determined for.
In each Zernike polynomial Z^m_n, the subscript n is the order of aberration, all the Zernike polynomials in which n=3 are called third-order aberrations and all the polynomials with n=4, fourth order aberrations and so on. Z^2_4 and Z^{-2}_4 are usually called secondary Astigmatism and should not cause confusion. The superscript m is called the angular frequency and denotes the number of times the Wavefront pattern repeats itself.[4]
List of Zernike modes and their common names:[11]
Plots of Zernike polynomials in the unit disk
Zernike Term Name
Z^0_0 Piston
Z^1_1, Z^{-1}_1 Tilt (Prism)
Z^0_2 Defocus
Z^2_2, Z^{-2}_2 Astigmatism
Z^2_4, Z^{-2}_4 Secondary Astigmatism
Z^0_4 Spherical Aberration
Z^1_3,Z^{-1}_3 Coma
Z^3_3, Z^{-3}_3 Trefoil
Z^4_4, Z^{-4}_4 Quadrafoil
Management[edit]
Low order aberrations (hyperopia, Myopia and regular astigmatism), are correctable by eyeglasses, soft contact lenses and refractive surgery. Neither spectacles nor soft contact lenses nor routine keratorefractive surgery adequately corrects high order aberrations. Significant high order aberration usually requires a rigid gas-permeable contact lens for optimal visual rehabilitation.[6]
Customized Wavefront-guided refractive corneal laser treatments are designed to reduce existing aberrations and to help prevent the creation of new aberrations.[6] The wavefront map of the eye may be transferred to a Lasik system and enable the surgeon to treat the aberration. Perfect alignment of the treatment and the pupil on which the Wavefront is measured is required, which is usually achieved through iris feature detection. An efficient eye tracking system and small spot size laser is necessary for treatment . Wavefront customization of ablation increases the depth of ablation because additional corneal tissue must be ablated to compensate for the high order aberrations.[2] Actual results with Wavefront guided LASIK showed that not only it cannot remove HOA but also the optical aberrations are increased. However, the amount of increase in aberrations are less than conventional Lasik.[12] Corneal optical aberrations after photorefractive keratectomy with a larger ablation zone and a transition zone are less pronounced and more physiologic than those associated with first-generation (5 mm) ablations with no transition zone.[13]
Aspherical intraocular lenses (IOLs) have been used clinically to compensate for positive corneal spherical aberrations. Although Aspherical IOLs may give better contrast sensitivity, it is doubtful, whether they have a beneficial effect on distance visual acuity. Conventional (not Aspherical) IOLs give better depth of focus and better near vision. The reason for improved depth of focus in conventional lenses is linked to residual spherical aberration. The small improvement in depth of focus with the conventional IOLs enhances uncorrected near vision and contribute to reading ability.[14]
Wavefront customized lenses can be used in eyeglasses. Based on Wavefront map of the eye and with the use of laser a lens is shaped to compensate for the aberrations of the eye and then put in the eyeglasses. Ultraviolet Laser can alter the refractive index of curtain lens materials such as epoxy polymer on a point by point basis in order to generate the desired refractive profile.[1]
Wavefront customized contact lenses can theoretically correct HOA. The rotation and decentration reduces the predictability of this method.[1]
See also[edit]
Optical aberrations
Wavefront
Zernike polynomials
References[edit]
Using Wikipedia for research Learn about researching with Wikipedia
^ Jump up to: a b c d Cervi;o, A; Hosking, SL; Montes-Mico, R; Bates, K (Jun 2007). "Clinical ocular wavefront analyzers.". Journal of refractive surgery (Thorofare, N.J. : 1995) 23 (6): 603–16. PMID 17598581.
^ Jump up to: a b c d Dimitri T. Azar , Damien Gatinel, Thang Hoang-Xuan (2007). Refractive surgery (2nd ed.). Philadelphia: Mosby Elsevier. ISBN 978-0-323-03599-6.
Jump up ^ Lawless, MA; Hodge, C (Apr 2005). "Wavefront's role in corneal refractive surgery.". Clinical & experimental ophthalmology 33 (2): 199–209. doi:10.1111/j.1442-9071.2005.00994.x. PMID 15807834.
^ Jump up to: a b c Charman, WN (Jun 2005). "Wavefront technology: past, present and future.". Contact lens & anterior eye : the journal of the British Contact Lens Association 28 (2): 75–92. doi:10.1016/j.clae.2005.02.003. PMID 16318838.
^ Jump up to: a b c Lombardo, M; Lombardo, G (Feb 2010). "Wave aberration of human eyes and new descriptors of image optical quality and visual performance.". Journal of cataract and refractive surgery 36 (2): 313–31. doi:10.1016/j.jcrs.2009.09.026. PMID 20152616.
^ Jump up to: a b c d e f Basic and Clinical Science Course, Section 13: Refractive Surgery (2011-2012. ed.). American Academy of Ophthalmology. 2011–2012. pp. 7–9. ISBN 978-1615251209.
Jump up ^ Basic and Clinical Science Course, Section 3: Clinical Optics (2011-2012 last major rev. 2010-2012. ed.). American Academy of Ophthalmology. 2011–2012. p. 100. ISBN 978-1615251100.
Jump up ^ Myron Yanoff, Jay S. Duker (2009). Ophthalmology (3rd ed.). Mosby Elsevier. p. 104. ISBN 978-0-323-04332-8.
Jump up ^ Applegate, RA; Thibos, LN; Hilmantel, G (Jul 2001). "Optics of aberroscopy and super vision.". Journal of cataract and refractive surgery 27 (7): 1093–107. doi:10.1016/s0886-3350(01)00856-2. PMID 11489582.
Jump up ^ Thibos, LN; Applegate, RA; Schwiegerling, JT; Webb, R (Sep–Oct 2000). "Report from the VSIA taskforce on standards for reporting optical aberrations of the eye.". Journal of refractive surgery (Thorofare, N.J. : 1995) 16 (5): S654–5. PMID 11019893.
Jump up ^ Wyant, James C. "Zernike Polynomials".
Jump up ^ Kohnen, T; B;hren, J; K;hne, C; Mirshahi, A (Dec 2004). "Wavefront-guided LASIK with the Zyoptix 3.1 system for the correction of myopia and compound myopic astigmatism with 1-year follow-up: clinical outcome and change in higher order aberrations.". Ophthalmology 111 (12): 2175–85. doi:10.1016/j.ophtha.2004.06.027. PMID 15582071.
Jump up ^ Endl, MJ; Martinez, CE; Klyce, SD; McDonald, MB; Coorpender, SJ; Applegate, RA; Howland, HC (Aug 2001). "Effect of larger ablation zone and transition zone on corneal optical aberrations after photorefractive keratectomy.". Archives of ophthalmology 119 (8): 1159–64. doi:10.1001/archopht.119.8.1159. PMID 11483083.
Jump up ^ Nanavaty, MA; Spalton, DJ; Boyce, J; Saha, S; Marshall, J (Apr 2009).
"Wavefront aberrations, depth of focus, and contrast sensitivity with aspheric and spherical intraocular lenses: fellow-eye study.". Journal of cataract and refractive surgery 35 (4): 663–71. doi:10.1016/j.jcrs.2008.12.011. PMID 19304086.
Categories: VisionDisorders of ocular muscles, binocular movement, accommodation and refraction
http://www.allaboutvision.com/conditions/aberrations.htm
Higher-Order Aberrations
By Madeleine Vessel; reviewed by Vance Thompson, MD
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Higher-order aberrations or HOAs are more complex vision errors than lower-order aberrations, which have more familiar names such as nearsightedness, farsightedness and astigmatism.
If your eye doctor tells you that you have a higher-order aberration, you may wonder exactly what this condition means and what impact — if any — it has on the quality of your vision.
Higher-order aberrations have relatively unfamiliar names such as coma, spherical aberration and trefoil. These types of aberrations can produce vision errors such as difficulty seeing at night, glare, halos, blurring, starburst patterns or double vision (diplopia).
No eye is perfect, which means that all eyes have at least some degree of higher-order aberrations. If you are diagnosed with higher-order aberrations, you need not be concerned unless they are significant enough to cause vision symptoms.
What Exactly Is a Higher-Order Aberration?
A higher-order aberration is a distortion acquired by a wavefront of light when it passes through an eye with irregularities of its refractive components (tear film, cornea, aqueous humor, crystalline lens and vitreous humor).
Abnormal curvature of the cornea and crystalline lens may contribute to the distortion acquired by a wavefront of light. Serious higher-order aberrations also can occur from scarring of the cornea from eye surgery, trauma or disease.
Cataracts clouding the eye's natural lens also can cause higher-order aberrations. Aberrations also may result when dry eye diminishes your eye's tear film, which helps bend or refract light rays to achieve focus.
Common Wavefront Shapes (Aberrations)
Chart showing wavefront maps of common aberrations in the eye.
This chart reveals more common shapes of aberrations created when a wavefront of light passes through eyes with imperfect vision. A theoretically perfect eye (top) is represented by an aberration-free flat plane known, for reference, as piston. (Image: Alcon Inc.)
How Are Higher-Order Aberrations Diagnosed?
Higher-order aberrations are identified by the types of distortions acquired by a wavefront of light as it passes through your eye. Because light travels in bundles of rays, a common way of describing an individual wavefront involves picturing a bundle of light rays. The tip of each light ray in the bundle has its own point. You create the wavefront or wavefront map by drawing lines perpendicular to each point.
The shape of a wavefront passing through a theoretically perfect eye with no aberrations is a flat plane known, for reference, as piston (see chart). The measure of difference between the actual wavefront shape and the ideal flat shape represents the amount of aberration in the wavefront.
Because no eye is perfect (emmetropic), a wavefront passing through an eye acquires certain three-dimensional, distorted shapes. So far, more than 60 different shapes, or aberrations, have been identified.
Wavefront eye exams can detect significant amounts of aberrations, which create vision problems because they interfere with the eye's ability to see clear and distinct images (focus).
Two categories of aberrations commonly are used to describe vision errors, including:
How smoking harms your vision.
Lower-order aberrations consist primarily of nearsightedness and farsightedness (defocus), as well as astigmatism. They make up about 85 percent of all aberrations in an eye.
Higher-order aberrations comprise many varieties of aberrations. Some of them have names such as coma, trefoil and spherical aberration, but many more of them are identified only by mathematical expressions (Zernike polynomials). They make up about 15 percent of the total number of aberrations in an eye.
Order refers to the complexity of the shape of the wavefront emerging through the pupil — the more complex the shape, the higher the order of aberration.
What Impact Do Higher-Order Aberrations Have on Vision Quality?
The impact of higher-order aberrations on vision quality depends on various factors, including the underlying cause of the aberration.
People with larger pupil sizes generally may have more problems with vision symptoms caused by higher-order aberrations, particularly in low lighting conditions when the pupil opens even wider.
But even people with small or moderate pupils can have significant vision problems when higher-order aberrations are caused by conditions such as scarring of the eye's surface (cornea) or cataracts that cloud the eye's natural lens. Also, specific types and orientation of higher-order aberrations have been found in some studies to affect vision quality of eyes with smaller pupils.
Large amounts of certain higher-order aberrations can have a severe, even disabling, impact on vision quality.
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What Symptoms Are Associated With Higher-Order Aberrations?
An eye usually has several different higher-order aberrations interacting together. Therefore, a correlation between a particular higher-order aberration and a specific symptom cannot easily be drawn. Nevertheless, higher-order aberrations are generally associated with double vision, blurriness, ghosts, halos, starbursts, loss of contrast and poor night vision.
Can Higher-Order Aberrations Be Corrected?
Quite a bit of attention is being focused on higher-order aberrations these days because they finally can be diagnosed by wavefront technology (aberrometry) and because they recently have been identified as sometimes serious side effects of refractive surgery.
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At present, various forms of adaptive optics have been or are being developed to custom correct higher-order aberrations. These include new kinds of spectacles, contact lenses, intraocular lenses and refractive surgery, which modifies the shape of the eye's surface or cornea.
The aim of adaptive optics is to achieve the type of vision correction that can make flatter the shape of the wavefront emerging in the plane of the pupil by offsetting its distortion.
However, adaptive optics may be unable to pinpoint specific physical imperfections of refractive components of the eye that cause these distortions in the first place.
[For more information about vision correction for higher-order aberrations, read about high-definition eyeglass lenses and wavefront or custom LASIK.]
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http://www.telescope-optics.net/eye_aberrations.htm
telescope;ptics.net ; ; ; ; ;;;; ; ; ; ; ; ; ; ; ; CONTENTS
; 13. THE EYE ; 13.4. Monochromatic eye aberrations ;
13.3. EYE ABERRATIONS
PAGE HIGHLIGHTS
• Optical properties • Ophthalmic vs. optical • Schematic eye
• Axes and lines • Off-axis pencils
Considering its biological origin - as opposed to precisely crafted optics - it is not surprising that optical aberrations of the human eye are significant. They include both monochromatic and chromatic aberrations. The former include aberrations typical of conic surfaces of revolution, but also irregular wavefront deformations caused by local deformations of eye surfaces. Eye constitutes the last optical element in the objective-eyepiece-eye train, thus its aberrations affect the final visual image just as those of telescope itself.
One exception is defocus error - either common focusing errors such as myopia (short sight) and hypermetropia (or hyperopia, long sight) - by far the most significant single aberration of the average eye. Low axial defocus error, allowing for "normal" acuity, (usually considered to imply either less than 0.5 diopters, or 1 in terms of visual acuity, i.e. 20/20 vision, or better) is called emmetropia. Luckily, eye defocus error doesn't affect retinal image quality when looking through a telescope, due to its correction by focusing via focuser.
FIGURE 220: The most significant factor causing eye defocus error is a mismatch between the size of eye ball and eye lens' power (left). Eye wavefront aberration are commonly measured by reverse imaging, i.e. analyzing reflection of a point source at the retina.
In general, in reverse imaging, wavefront originating at a point-source at the center of fovea would exit the perfect eye perfectly flat, i.e. as a collimated beam; real eyes are always aberrated, and wavefront originating from retinal reflection (which is the common way of assessing wavefront quality) is not flat.
On the other hand, we normally do not notice appreciable eye color errors, due to perception of color blurring due to eye chromatism being mainly filtered out during brain signal processing. Nevertheless, spread of energy on the retina caused by eye chromatism does lower optical quality of the retinal image just as much as with the color separation fully detectable.
Individual deviations in eye aberration level are quite wide. Main causes are individual deviations in size and shape of eye surfaces involved in image formation, and the efficiency of eye compensatory mechanisms. Integral part of the final (perceived) error level here are the spatial and functional properties of retinal photoreceptors. What separates eye from a non-biological detector is that its neural signal processing non-trivial significance in determining the final outcome.
Basic optical properties of human eye, typical deviations from the idealized schematic eye, main determinants of pupil size and accommodative power, are presented on FIG. 221.
FIGURE 221: (A) Eye aberrations are the result of its optical simplicity, combined with imperfect surface shapes and alignment of its optical components. The single largest aberration, defocus, accounting for about 1/2 of the total aberration of the average eye, is the consequence of a limited range of refocusing (accommodation), mainly a function of the eye (crystalline) lens. Eye's accommodative power - defined as the differential between relaxed (infinity) focus and distance of nearest focus (i.e. 1/d in diopters, with d being the distance of nearest focus in meters) - declines with age, from nearly 15 diopters in early childhood to
1-2 diopters after age 50. Second largest axial aberration, astigmatism (on average about 3 times smaller in magnitude than defocus), mainly originates at a deformed front surface of the cornea. Spherical aberration is minimized by aspheric (prolate) shapes of eye surfaces, as well as by decreasing refractive power of the eye lens toward its edges. Axial coma mainly results from tilt and decenter of the eye lens relative to the visual axis. The later also causes axial lateral color, while axial chromatic defocus, in the form of primary spectrum (i.e. shorter wavelengths focusing closer to the eye lens that longer wavelengths) is due to relatively narrow range of refractive/dispersive powers of eye's optical elements. (B) Eye pupil diameter varies both, with illumination level and individually. For given illumination level, variations in pupil size up to a factor of two are not uncommon (top; smoothed out plots for 250 subjects from Richman et al. 2004). Decrease in illumination causes pupil to increase; it nearly doubles vs. size in average daylight conditions and comes close to its maximum diameter already in twilight illumination. Pupil size steadily declines with age, but individual differences are wide (bottom; 91 subjects from Winn et al. 1994 and 70 subjects from Yang et al. 2002, with the latter only qualifying illuminance level as "photopic" and "mesopic'). The plots are for the average pupil size; individual deviations are in the range of about ±2mm. While older individuals have generally smaller pupil, largest pupils at the old end are still be significantly larger than the smallest pupils at the young end (also, the largest pupils at old age are nearly as large as largest pupils at a young age). Pupil size also changes with object distance, generally being somewhat larger for closer objects.
Most of the refractive power of the eye - about 2/3 - comes from cornea, and in particular from its front surface. This is due to both, strongly curved corneal surface and the refractive index differential being the highest here (1 vs. 1.38). Within the eye, refractive indici vary between 1.33 and 1.41, thus having only secondary effect on the optical power and with it, secondary effect on eye aberrations as well. In general, cornea and eye lens tend to induce errors of opposite sign that partly - and often significantly - offset in the combined wavefront.
Average actual eye focal length ;A is around 23mm; however, since the medium in which the image is formed has refractive index n~1.33, the effective focal length ;E used in the aberration calculation is 23/n, or ~17mm. Due to the effective compression of light waves in its denser medium, the Airy disc formed on the retina is smaller than what it would be in air medium. Since the media in which the eye forms images (vitreous humour) is of refractive index ~1.33, diffraction effect is suppressed compared to that of imaging in air-medium. Thus, the Airy disc diameter, given by 2.44;F/n, n being the refractive index of the imaging media, is smaller by a factor of ~0.75.
More specifically, in a medium slower by a factor 1/n, the wavelength gets "compressed" by the same ratio, and any given linear optical path difference expressed in units of the standard wavelength effectively increases by a factor of n. In other words, the first diffraction minima - as well as all the successive ones - occur at an angular radius smaller by a factor of 1/n. Also, any nominal wavefront deviation results in the phase error greater by the same 1/n ratio (this doesn't mean that a deviant wavefront entering the eye will have its error multiplied by the ~1.33 factor; due to proportionally slower imaging medium, the wavefront formed within it will have its nominal linear error reduced by the same factor, preserving the effective error size unchanged).
Likewise, errors induced by eye lens will be smaller by the same ~0.75 factor compared to those that would be induced should the lens be imaging in air. As a result, the effective wavefront error doesn't change. Physically, diffraction effects - including those induced by aberrations - are reduced in size, but so is the wavelength. As long as eye retina is an over-sampled detector (i.e. with the linear point image larger than photoreceptor by a factor of 2, or more), its conventional linear diffraction cutoff separation ;F would be smaller by a factor ~0.75, due to reduced effective wavelength ;; and so would its nominal angular cutoff angle ;/D. However, general form of the diffraction resolution limit - ;/D - remains unchanged.
Note that, as in the usual telescope optics notation, D here is the aperture diameter. In describing eye aberration, the same symbol is used for one of the basic metrics, diopter. For sake of clarity, this section on eye aberrations uses D for "diopter", while eye pupil diameter is denoted by P.
But calculating wavefront error based on longitudinal aberration requires rescaling the actual eye f.l. ;A so that it corresponds to the actual diffraction pattern, when formed in air. Since the Airy disc formed on the retina is appropriate in size to one produced by the F-number resulting from F=;A/1.33P, not the one given by F=;A/P, the appropriate focal length to use as the basis for calculating defocus error is 23mm/1.33~17mm. It gives a proper match of the longitudinal/transverse errors and the Airy disc size.
Quantifying eye aberrations is a difficult task and, not surprisingly, research results are not always in good agreement. Main reasons, in addition to much more complex function of an active biological optical system, such as the eye, are usually small sample size, prone to significant individual deviations from the average, as well as different methods of measurement, methodologies and/or degree of measurement accuracy. To make result interpretation more difficult, ophthalmological concepts are often different than those used in physical optics, and its overall scientific integrity is probably lower.
Table bellow summarizes some of the main differences in the terminology, concepts and presentation between ophthalmic and (optical) telescope optics.
TELESCOPE OPTICS
OPHTHALMOLOGY
OPTICAL SYSTEM
PASSIVE
ACTIVE
OBJECT DISTANCE
INFINITY
CLOSE/INFINITY
IMAGE MEDIUM
AIR
VITREOUS HUMOUR
ERROR ASSESSMENT LOCATION
IMAGE SPACE
OBJECT SPACE
PRIMARY OPTICAL TOOL
STANDARD ABERRATION FUNCTIONS
ZERNIKE ABERRATION TERMS
ZERNIKE COEFFICIENT FORM
IN UNIT OF WAVELENGTH
MICRONS
FORM OF LONGITUDINAL ABERRATION
STANDARD METRICS
DIOPTERS
OPHTHALMOLOGY-SPECIFIC ABERRATION TERMS:
; REFRACTIVE ERROR: Commonly defocus error, although any eye-generated ray/wavefront aberration is, in fact, refractive error
; LOWER-ORDER ABERRATIONS: Those with Zernike radial order n lower than 3 (tilt, defocus, primary astigmatism)
; HIGHER-ORDER ABERRATIONS: Zernike radial order n of 3 or higher (includes primary coma and spherical aberration)
; TRANSVERSE CHROMATISM: Lateral chromatic magnification (lateral chromatism in telescope optics)
; DEPTH OF FOCUS: Range of defocus with acceptable image deterioration relative to best focus (not necessarily diffraction-limited)
; SPHERE or FOCUS: Defocus (i.e. lens power needed to correct defocus of the eye; some eyeglasses prescription terms, frequently - and inappropriately - are used for naming the aberrations themselves)
; PRISM: Wavefront tilt
; CYLINDER: Astigmatism
; AXIS: Angle between two astigmatic meridians (doesn't have to be 90°)
One needs to keep in mind these important points: unlike the standard eye model, an actual eye is:
(1) an active optical system, with adjustable components and aberrations varying in time,
(2) it is not strictly centered system,
(3) it is not a rotationally symmetrical system, and
(4) final perception is the subject of neural processing.
Consequently, aberration forms of comparable magnitude do not necessarily have identical effect as in a passive optical system, such as telescope and, to a small but not insignificant degree, eye aberrations are random.
Optical system of human eye is usually represented by the schematic eye, which uses average dimensions with idealized, centered and rotationally symmetrical surfaces, in modeling eye imaging and aberrations. As every complex system, eye is described by its entrance and exit pupil and 6 cardinal points: object and image space focal point, first and second principal plane, and first and second nodal point (FIG. 222).
FIGURE 222: LEFT - Illustration of the optical scheme of human eye; there is a number of schemes, from those simplest ones, with a single spherical refractive surface, to those with two lens elements with aspheric surfaces and gradient index. The above nominal values are based on the Gullstrand-Emsley schematic eye, which uses a single corneal refractive surface, but adding the second surface has little effect on the optical parameters shown. Eye pupil is the system's aperture stop; its image by the preceding optical element (cornea) forms the system's entrance pupil - which is the apparent boundary to entering rays from object point - at about 3mm behind the anterior cornea, 13% larger than eye pupil. Image of the aperture stop by the optical element following it in the optical train (eye lens) forms system's exit pupil - the apparent boundary to rays from the image point - only slightly smaller than eye pupil. Eye exit pupil is, for all practical purposes, at the eye pupil (iris). Due to the eye being an unequifocal system, with its object space (anterior) focal length smaller than its image space (posterior) focal length, nodal points are not contained in the principal planes; they are shifted deeper into the eye, straddling the rear surface of eye lens.
RIGHT, TOP - Scheme of image formation by unequifocal system (not to eye's specifications; principal and nodal points are more widely separated, for clarity; also, image plane farther out than posterior focal plane corresponds to accommodated eye). Image of a point-object at the height h in the outer field is determined by two rays originating at the object point, one normal to the 2nd principal plane (normal to the axis at the 2nd principal point P'), and the other passing through through the anterior focal point and turning parallel with the axis at the first principal plane (normal to the axis at the first principal point P). The significance of nodal points is that the ray from object point directed toward 1st nodal point (N) acts as if it follows the axis to the 2nd nodal point (N'), from which it connects to the image point keeping the original ray orientation. In other words, nodal points define the actual incident angle, i.e. actual field of view. Apparent incident angle, and field of view, determined by the ray passing through the center of exit pupil (i.e. intersecting the axis at a point between nodal and principal points) - the chief ray - is smaller than the actual angle and field; for the schematic eye, by a constant factor of about 0.82. RIGHT - BOTTOM: Imaging by human eye often can be sufficiently well modeled with a simplified version of schematic eye, called reduced eye. Shown is Emsley's reduced eye, which assumes a single refractive surface and 60 diopters effective (in air) eye focal length. With aperture stop at the surface, its entrance and exit pupils coincide with it; likewise, its two principal points coincide at the refractive surface (P), and two nodal points coincide at the surface's center of curvature (N). Foveal center is assumed to coincide with the posterior focus, thus optical and visual axis also coincide.
A basic aberration-defining reference line in a general optical system is the chief ray: a ray that passes through the center of aperture stop, determining the reference optical path length against which are measured optical path differences of other rays. For an axial image point, the chief ray coincides with optical axis; for off-axis image points, chief ray is the one passing through the center of the aperture stop. In ophthalmology, on the other hand, it is common to refer to line-of-sight (LOS) as the chief ray equivalent - a concept not compatible with the conventional aberration theory (taking a ray other than one passing though the center of the aperture stop as the reference for optical path difference changes the wavefront aberration form, making symmetrical aberrations asymmetrical).
Optical axis associated with schematic eye is defined same as for any centered system with rotationally symmetrical surfaces, as a line connecting surface vertices. Other relevant axes and lines are illustrated on FIG. 223.
FIGURE 223: Axes and lines associated with the eye. Two of them pass through foveal center: visual axis and line of sight. The former connects fovea with the 2nd nodal point (visual axis in the image plane), and then 1st nodal point with the object point. The latter, also a broken line, connects fovea to the object point through the exit and entrance pupil centers. Pupillary axis is not associated with schematic eye; by definition, it is a normal to the anterior cornea, directed to the entrance pupil center. This is possible only if the corneal surface is deformed, or eye elements misaligned (otherwise, normal to anterior cornea would nearly point at its center of curvature). Finally, fixation axis connects object point and eye's center of rotation.
Visual axis is defined as the line connecting foveal center to the 2nd nodal point. Being parallel to the line connecting the corresponding object point and 1st nodal point, this line defines the actual visual field angle (this is the prevailing definition of visual axis; some authors have a different view, defining visual axis as one connecting fovea with the center of entrance pupil). Due to foveal eccentricity (4°-8° toward temporal, and about 2° toward inferior retina), this line is inclined to the optical axis; temporal inclination angle is usually denoted by ;. A term related to visual axis is achromatic axis, defined by a ray passing through eye's exit pupil and nodal point onto the foveal center with zero lateral color error; according to the Indiana University School of Optometry, real eyes data show that mean angular differential between this axis and visual axis gravitates toward zero, suggesting that the two nearly coincide in the average eye (near-zero lateral color is only a statistical figure, indicating that positive and negative lateral color errors nearly offset each other in the sum of individual errors; according to the same source, average foveal lateral color significantly differs from zero).
Line of sight (LOS) is a broken line connecting object point to the foveal center through the centers of the entrance and exit pupils. As mentioned, it is commonly - and incorrectly - regarded as the chief ray equivalent. In fact, it is not the rays that pass through the centers of entrance and exit pupils that constitute the chief ray: it is the ray that passes through the center of the aperture stop (thus representing the actual central ray of the entering pencil) and appears as if passing through the center of the entrance pupil (from the object point side) and through the center of the exit pupil (from the image point side).
Pupilary axis is defined as a normal to the front corneal surface (hence passing it w/o refraction) directed at the center of the entrance pupil. It is sometimes, too, referred to as the chief-ray-equivalent, which is incorrect, since chief ray passes through the center of the aperture stop. Such axis in schematic eye would always point at the corneal center of curvature. In real eyes, however, this angle (determined by measuring the angle of light reflected from anterior cornea at which it projects back at the entrance pupil center), in general, indicates corneal deformation and/or misalignment in the optical path, the larger its deviation from the visual axis - usually denoted by ; - the more so (this does not necessarily result in significantly higher level of eye aberrations; for instance, larger kappa-angle is associated with higher level of eye's compensatory coma, with both cornea and eye lens generating more of the aberration, but off opposite signs, tending to minimize the total aberration). Another angle associated with pupillary axis is that between it and LOS, usually denoted by ; (some authors use ;, which may be confusing).
Since the main purpose of exploring eye aberrations here is to gain insight into their effect on the telescope image quality, i.e. the interaction between axial and off-axis aberrations of the telescope (including eyepiece) vs. those of the eye, it is important to note that, due to the active nature of eye function, this interaction does not not produce a simple balance of axial and off-axis aberrations of the the two. Specifically, off-axis aberration of the eye are very significant, but their effect on off-axis image quality in a telescope is normally small to negligible (FIG. 224).
FIGURE 224: Reflex eye movements at the eyepiece bring image of selected field object onto the retinal spot with highest acuity - the fovea. This, in turn, requires bringing selected object onto the visual axis, connecting selected object and fovea. If the selected object is an object located in the outer eyepiece field, it effectively becomes a nearly axial object for the eye. In other words, it is primarily foveal aberrations of the eye that interact with telescope aberrations, regardless of the field location of point observed. When optical axes of the eye (right eye, top view, assuming eyepiece exit pupil nearly coinciding with eye pupil) coincides with that of the eyepiece (A), observer is looking at a point somewhat off the field center (the angle is approximated by the discrepancy between eye's optical and visual axis, usually 4-8°). In order to bring field center into foveal area, eye has to rotate clockwise around center of rotation, which nearly coincides with the center of vitreous body, until the visual axis nearly coincides with eyepiece optical axis. The off-axis point H, farther out in the field, is imaged by the eye onto the outer retinal field; it is present in the field of view, but very distorted due to the combined effect of low-resolution photoreceptors in the outer retina, off-axis aberrations of the eyepiece, and off-axis aberrations of the eye. Turning attention to this point causes reflex eye movement - counterclockwise rotation by angle a - bringing it into foveal area; since eye rotation causes eye pupil displacement vs. eyepiece exit pupil, rotation is accompanied with a slight head displacement (s), keeping the two pupils nearly coinciding (B).
Despite eye off-axis aberrations having little or no influence on the quality of telescopic image, they will be also addressed; not only for the completeness of information but, more importantly, as an indicator of possible magnitude of axial eye aberrations caused by excessive deformation and/or misalignment of eye's optical surfaces. One of possible misalignment forms is decenter or despace (or both) of eyepiece pupil with respect to eye pupil; it can induce significant axial aberrations, primarily coma and lateral color.
Eye aberrations will be addressed in four main sections:
(1) monochromatic aberrations, axial 2nd order and off-axis 2nd order,
(2) higher-order monochromatic aberrations,
(3) chromatic aberrations, and
(4) combined eye aberrations.