Astigmatism
Blur from astigmatic lens at different distances
SpecialtyOphthalmology, optometry
SymptomsDistorted or blurred vision at all distances, eyestrain, headaches[1]
ComplicationsAmblyopia[2]
CausesUnclear[3]
Diagnostic methodEye exam[1]
TreatmentGlasses, contact lenses, surgery[1]
Frequency30% to 60% of adults (Europe, Asia)[4]

Astigmatism is a type of refractive error due to rotational asymmetry in the eye's refractive power. This results in distorted or blurred vision at any distance.[1] Other symptoms can include eyestrain, headaches, and trouble driving at night.[1] Astigmatism often occurs at birth and can change or develop later in life.[5] If it occurs in early life and is left untreated, it may result in amblyopia.[2]

The cause of astigmatism is unclear; however, it is believed to be partly related to genetic factors.[3][4] The underlying mechanism involves an irregular curvature of the cornea and protective reaction changes in the lens of the eye, called lens astigmatism, that has the same mechanism as spasm of accommodation.[1][3] Diagnosis is by an eye examination called autorefractor keratometry (objective, allows to see lens and cornea components of astigmatism) and subjective refraction.

Three treatment options are available: glasses, contact lenses, and surgery.[1] Glasses are the simplest.[1] Contact lenses can provide a wider field of vision and fewer artifacts than even double aspheric lenses.[1] Refractive surgery permanently changes the shape of the eye and thereby cures astigmatism.[1]

In Europe and Asia, astigmatism affects between 30% and 60% of adults.[4] People of all ages can be affected by astigmatism.[1] Astigmatism was first reported by Thomas Young in 1801.[3][6]

Signs and symptoms

Although astigmatism may be asymptomatic, higher degrees of astigmatism may cause symptoms such as blurred vision, double vision, squinting, eye strain, fatigue, or headaches.[7] Some research has pointed to the link between astigmatism and higher prevalence of migraine headaches.[8]

Complications

While astigmatism by itself is not a life-threatening condition, it can be an indirect cause of serious trauma or death if a vehicle driver refrains from wearing corrective lenses while driving, especially at night or in poor weather conditions.

Causes

Congenital

The cause of congenital astigmatism is unclear; however, it is believed to be partly related to genetic factors.[3] Genetics, based on twin studies, appear to play only a small role in astigmatism as of 2007.[9]

Genome-wide association studies (GWAS) have been used to investigate the genetic foundation of astigmatism. Although no conclusive result has been shown, various candidates have been identified. In a study conducted in 2011 on various Asian populations, variants in the PDGFRA gene on chromosome 4q12 were identified to be associated with corneal astigmatism.[10] A follow-up study in 2013 on the European population, however, found no variant significantly associated with corneal astigmatism at the genome-wide level (single-nucleotide polymorphism rs7677751 at PDGFRA).[11] Facing the inconsistency, a study by Shah and colleagues in 2018 included both populations with Asian and Northern European ancestry. They successfully replicated the previously identified genome-wide significant locus for corneal astigmatism near the PDGFRA gene, with a further success of identifying three novel candidate genes: CLDN7, ACP2, and TNFAIP8L3.[12] Other GWAS studies also provided inconclusive results: Lopes and colleagues identified a susceptibility locus with lead single nucleotide polymorphism rs3771395 on chromosome 2p13.3 in the VAX2 gene (VAX2 plays an important role in the development of the dorsoventral axis of the eye);[13] Li and associates, however, found no consistent or strong genetic signals for refractive astigmatism while suggesting a possibility of widespread genetic co-susceptibility for spherical and astigmatic refractive errors. They also found that the TOX gene region previously identified for spherical equivalent refractive error was the second most strongly associated region.[14] Another recent follow-up study again had identified four novel loci for corneal astigmatism, with two also being novel loci for astigmatism: ZC3H11B (associated with axial length), NPLOC4 (associated with myopia), LINC00340 (associated with spherical equivalent refractive error) and HERC2 (associated with eye color).[12]

Acquired

Astigmatism may also occur following a cataract surgery or a corneal injury.[15] Contraction of the scar due to wound or cataract extraction causes astigmatism due to flattening of the cornea in one direction.[15] In keratoconus, progressive thinning and steepening of the cornea cause irregular astigmatism.[16]

Pathophysiology

Illustration of astigmatism

Axis of the principal meridian

  • Regular astigmatism – principal meridians are perpendicular. (The steepest and flattest meridians of the eye are called principal meridians.)
    • With-the-rule astigmatism – the vertical meridian is steepest (a rugby ball or American football lying on its side).[17]
    • Against-the-rule astigmatism – the horizontal meridian is steepest (a rugby ball or American football standing on its end).[17]
    • Oblique astigmatism – the steepest curve lies in between 120 and 150 degrees and 30 and 60 degrees.[17]
  • Irregular astigmatism – principal meridians are not perpendicular.

In with-the-rule astigmatism, the eye has too much "plus" cylinder in the horizontal axis relative to the vertical axis (i.e., the eye is too "steep" along the vertical meridian relative to the horizontal meridian). Vertical beams of light focus in front (anterior) to horizontal beams of light, in the eye. This problem may be corrected using spectacles which have a "minus" cylinder placed on this horizontal axis. The effect of this will be that when a vertical beam of light in the distance travels towards the eye, the "minus" cylinder (which is placed with its axis lying horizontally – meaning in line with the patient's horizontal meridian relative to the excessively steep vertical meridian) will cause this vertical beam of light to slightly "diverge", or "spread out vertically", before it reaches the eye. This compensates for the fact that the patient's eye converges light more powerfully in the vertical meridian than the horizontal meridian. Hopefully, after this, the eye will focus all light on the same location at the retina, and the patient's vision will be less blurred.

In against-the-rule astigmatism, a plus cylinder is added in the horizontal axis (or a minus cylinder in the vertical axis).[18]

Axis is always recorded as an angle in degrees, between 0 and 180 degrees in a counter-clockwise direction. Both 0 and 180 degrees lie on a horizontal line at the level of the center of the pupil, and as seen by an observer, 0 lies on the right of both the eyes.

Irregular astigmatism, which is often associated with prior ocular surgery or trauma, is also a common naturally occurring condition.[19] The two steep hemimeridians of the cornea, 180° apart in regular astigmatism, may be separated by less than 180° in irregular astigmatism (called nonorthogonal irregular astigmatism); and/or the two steep hemimeridians may be asymmetrically steep—that is, one may be significantly steeper than the other (called asymmetric irregular astigmatism). Irregular astigmatism is quantified by a vector calculation called topographic disparity.[20]

Focus of the principal meridian

With accommodation relaxed:

  • Simple astigmatism
    • Simple hyperopic astigmatism – first focal line is on the retina, while the second is located behind the retina.
    • Simple myopic astigmatism – first focal line is in front of the retina, while the second is on the retina.
  • Compound astigmatism
    • Compound hyperopic astigmatism – both focal lines are located behind the retina.
    • Compound myopic astigmatism – both focal lines are located in front of the retina.
  • Mixed astigmatism – focal lines are on both sides of the retina (straddling the retina).

Throughout the eye

Astigmatism, whether it is regular or irregular, is caused by some combination of external (corneal surface) and internal (posterior corneal surface, human lens, fluids, retina, and eye-brain interface) optical properties. In some people, the external optics may have the greater influence, and in other people, the internal optics may predominate. Importantly, the axes and magnitudes of external and internal astigmatism do not necessarily coincide, but it is the combination of the two that by definition determines the overall optics of the eye. The overall optics of the eye are typically expressed by a person's refraction; the contribution of the external (anterior corneal) astigmatism is measured through the use of techniques such as keratometry and corneal topography. One method analyzes vectors for planning refractive surgery such that the surgery is apportioned optimally between both the refractive and topographic components.[21][22]

Diagnosis

A number of tests are used during eye examinations to determine the presence of astigmatism and to quantify its amount and axis. A Snellen chart or other eye charts may initially reveal reduced visual acuity. A keratometer may be used to measure the curvature of the steepest and flattest meridians in the cornea's front surface.[23] Corneal topography may also be used to obtain a more accurate representation of the cornea's shape.[24] An autorefractor or retinoscopy may provide an objective estimate of the eye's refractive error and the use of Jackson cross cylinders in a phoropter or trial frame may be used to subjectively refine those measurements.[25][26][27] An alternative technique with the phoropter requires the use of a "clock dial" or "sunburst" chart to determine the astigmatic axis and power.[28][29] A keratometer may also be used to estimate astigmatism by finding the difference in power between the two primary meridians of the cornea. Javal's rule can then be used to compute the estimate of astigmatism.

A method of astigmatism analysis by Alpins may be used to determine both how much surgical change of the cornea is needed and after surgery to determine how close treatment was to the goal.[30]

Another rarely used refraction technique involves the use of a stenopaeic slit (a thin slit aperture) where the refraction is determined in specific meridians – this technique is particularly useful in cases where the patient has a high degree of astigmatism or in refracting patients with irregular astigmatism.

Classification

There are three primary types of astigmatism: myopic astigmatism, hyperopic astigmatism, and mixed astigmatism. Cases can be classified further, such as regular or irregular and lenticular or corneal.

Treatment

Astigmatism may be corrected with eyeglasses, contact lenses, or refractive surgery.[1] Glasses are the simplest and safest, although contact lenses can provide a wider field of vision. Refractive surgery can eliminate the need to wear corrective lenses altogether by permanently changing the shape of the eye but, like all elective surgery, comes with both greater risk and expense than the non-invasive options. Various considerations involving eye health, refractive status, and lifestyle determine whether one option may be better than another. In those with keratoconus, certain contact lenses often enable patients to achieve better visual acuity than eyeglasses. Once only available in a rigid, gas-permeable form, toric lenses are now also available as soft lenses.

In older people, astigmatism can also be corrected during cataract surgery. This can either be done by inserting a toric intraocular lens or by performing special incisions (limbal relaxing incisions). Toric intraocular lenses probably provide a better outcome with respect to astigmatism in these cases than limbal relaxing incisions.[31]

Toric intraocular lenses can additionally be used in patients with complex ophthalmic history, such as previous ophthalmic surgery.[32] In such complex cases, toric intraocular lenses seem to be as effective as in non-complex cases for correction of concurrent corneal astigmatism.[32]

Epidemiology

In 2019, the World Health Organization reported that 123.7 million people worldwide were affected by uncorrected refracting errors, including astigmatism. A compilation of many systematic reviews found that there was an 8-62% prevalence of astigmatism among adults, with an estimated prevalence of 40% worldwide.[33] The country with the highest reported prevalence among the compilation of systematic reviews is China at 62%.[33] The prevalence of astigmatism increases with age due to changes in refractive index gradients.[33][34] According to an American study, nearly three in ten children (28.4%) between the ages of five and seventeen have astigmatism.[35] A Brazilian study published in 2005 found that 34% of the students in one city were astigmatic.[36]

Studies have shown that infants in their first few months have a high prevalence of astigmatism due to a steep cornea. The steepest corneas are found in infants with low birth weights and post-conceptional age.[37] By the age of four, the prevalence of astigmatism has reduced as the cornea flattens. The cornea remains mostly stable during adulthood, and then steepens again in older adulthood (40+ years).[37]

Mild astigmatism has a higher prevalence than moderate and significant astigmatisms and increased until the age of 70, while moderate and significant astigmatisms showed an increase in prevalence after the age of 70.[33] Of the levels of astigmatism, mild astigmatism is most prevalent, making up about 82% of the total reported astigmatisms.[33]

With-the-rule astigmatism among the total population has a prevalence range of 4 to 98% globally. The prevalence range for against-the-rule astigmatism is from 1 to 58%. For oblique astigmatism, the prevalence range is from 2 to 61%.[33] With-the-rule astigmatism is more prevalent in young adults, and over time, the prevalence shifts to be mostly against-the-rule astigmatism.[37] A Polish study published in 2005 revealed "with-the-rule astigmatism" may lead to the onset of myopia.[38]

The main cause of astigmatism is changes in the curvature of the cornea.[37] When left untreated, astigmatism causes people to have a lower vision-related quality of life. Some factors that lead to this are a decrease in vision quality and an increase in glare and haloes.[33] People with astigmatism have more difficulty with night driving and can have a decreased productivity due to errors. However, there are many ways to help correct astigmatisms. The use of glasses, contacts, Toric intraocular lenses, Toric implantable Collamer lenses, corneal refractive surgery have been shown to correct astigmatisms.[33]

History

As a student, Thomas Young discovered that he had problems with one eye in 1793.[39] In the following years he did research on his vision problems.[40] He presented his findings in a Bakerian Lecture in 1801.[41]

Independent from Young, George Biddell Airy discovered the phenomenon of astigmatism on his own eye.[42] Airy presented his observations on his own eye in February 1825 at the Cambridge Philosophical Society.[43][44] Airy produced lenses to correct his vision problems by 1825,[42][45] while other sources put this into 1827[46] when Airy obtained cylindrical lenses from an optician from Ipswich.[47] The name for the condition was given by William Whewell.[48][49][50]

By the 1860s astigmatism was a well established concept in ophthalmology,[51] and chapters in books described the discovery of astigmatism.[52][53][54]

In 1849, Irish English physicist and mathematician George Stokes invented Stokes lens to detect astigmatism.[55] In 1887 American ophthalmologist Edward Jackson revised the Stokes lens concept and made a cross cylinder lens to refine power and axis of astigmatism.[56] In 1907 Jackson described determination of the axis of a correcting cylinder in astigmatism using a cross cylinder.[57]

See also

References

  1. 1 2 3 4 5 6 7 8 9 10 11 12 "Facts About Astigmatism". National Eye Institute. National Institutes of Health. Archived from the original on 2 October 2016. Retrieved 16 June 2019.
  2. 1 2 Harvey, EM (June 2009). "Development and treatment of astigmatism-related amblyopia". Optometry and Vision Science. 86 (6): 634–9. doi:10.1097/opx.0b013e3181a6165f. PMC 2706277. PMID 19430327.
  3. 1 2 3 4 5 Read, SA; Collins, MJ; Carney, LG (January 2007). "A review of astigmatism and its possible genesis". Clinical & Experimental Optometry. 90 (1): 5–19. doi:10.1111/j.1444-0938.2007.00112.x. PMID 17177660. S2CID 8876207.
  4. 1 2 3 Mozayan, E; Lee, JK (July 2014). "Update on astigmatism management". Current Opinion in Ophthalmology. 25 (4): 286–90. doi:10.1097/icu.0000000000000068. PMID 24837578. S2CID 40929023.
  5. ↑ "The Ultimate Guide to Astigmatism". Feel Good Contacts.
  6. ↑ "Thomas Young | British physician and physicist". Encyclopædia Britannica. Archived from the original on 29 August 2017. Retrieved 28 August 2017.
  7. ↑ "Astigmatism". MedicineNet. OnHealth.com. Archived from the original on 2 July 2013. Retrieved 8 September 2013.
  8. ↑ Harle, Deacon E.; Evans, Bruce J. W. (2006). "The Correlation Between Migraine Headache and Refractive Errors". Optometry and Vision Science. 83 (2): 82–7. doi:10.1097/01.opx.0000200680.95968.3e. PMID 16501409. S2CID 32019102.
  9. ↑ Read, SA; Collins, MJ; Carney, LG (January 2007). "A review of astigmatism and its possible genesis". Clinical & Experimental Optometry. 90 (1): 5–19. doi:10.1111/j.1444-0938.2007.00112.x. PMID 17177660. S2CID 8876207.
  10. ↑ Fan, Qiao; Zhou, Xin; Khor, Chiea-Chuen; Cheng, Ching-Yu; Goh, Liang-Kee; Sim, Xueling; Tay, Wan-Ting; Li, Yi-Ju; Ong, Rick Twee-Hee; Suo, Chen; Cornes, Belinda (December 2011). "Genome-wide meta-analysis of five Asian cohorts identifies PDGFRA as a susceptibility locus for corneal astigmatism". PLOS Genetics. 7 (12): e1002402. doi:10.1371/journal.pgen.1002402. ISSN 1553-7404. PMC 3228826. PMID 22144915.
  11. ↑ Yazar, Seyhan; Mishra, Aniket; Ang, Wei; Kearns, Lisa S.; Mountain, Jenny A.; Pennell, Craig; Montgomery, Grant W.; Young, Terri L.; Hammond, Christopher J.; Macgregor, Stuart; Mackey, David A. (2013). "Interrogation of the platelet-derived growth factor receptor alpha locus and corneal astigmatism in Australians of Northern European ancestry: results of a genome-wide association study". Molecular Vision. 19: 1238–1246. ISSN 1090-0535. PMC 3675057. PMID 23761726.
  12. 1 2 Shah, Rupal L.; Guggenheim, Jeremy A.; UK Biobank Eye and Vision Consortium (December 2018). "Genome-wide association studies for corneal and refractive astigmatism in UK Biobank demonstrate a shared role for myopia susceptibility loci". Human Genetics. 137 (11–12): 881–896. doi:10.1007/s00439-018-1942-8. ISSN 1432-1203. PMC 6267700. PMID 30306274.
  13. ↑ Lopes, Margarida C.; Hysi, Pirro G.; Verhoeven, Virginie J. M.; Macgregor, Stuart; Hewitt, Alex W.; Montgomery, Grant W.; Cumberland, Phillippa; Vingerling, Johannes R.; Young, Terri L.; van Duijn, Cornelia M.; Oostra, Ben (1 February 2013). "Identification of a candidate gene for astigmatism". Investigative Ophthalmology & Visual Science. 54 (2): 1260–1267. doi:10.1167/iovs.12-10463. ISSN 1552-5783. PMC 3576051. PMID 23322567.
  14. ↑ Li, Qing; Wojciechowski, Robert; Simpson, Claire L.; Hysi, Pirro G.; Verhoeven, Virginie J. M.; Ikram, Mohammad Kamran; Höhn, René; Vitart, Veronique; Hewitt, Alex W.; Oexle, Konrad; Mäkelä, Kari-Matti (February 2015). "Genome-wide association study for refractive astigmatism reveals genetic co-determination with spherical equivalent refractive error: the CREAM consortium". Human Genetics. 134 (2): 131–146. doi:10.1007/s00439-014-1500-y. ISSN 1432-1203. PMC 4291519. PMID 25367360.
  15. 1 2 Ramanjit, Sihota; Tandon, Radhika, eds. (2015). Parsons' diseases of the eye (Twenty-second ed.). New Delhi, India: Reed Elsevier India. p. 76. ISBN 978-81-312-3819-6. OCLC 905915528.
  16. ↑ "Keratoconus - EyeWiki". eyewiki.aao.org. Retrieved 2 May 2022.
  17. 1 2 3 Gilbert Smolin; Charles Stephen Foster; Dimitri T. Azar; Claes H. Dohlman (2005). Smolin and Thoft's The Cornea: Scientific Foundations and Clinical Practice. Lippincott Williams & Wilkins. pp. 173–. ISBN 978-0-7817-4206-1.
  18. ↑ Carlo Cavallotti; Luciano Cerulli (31 May 2008). Age-Related Changes of the Human Eye. Springer Science & Business Media. pp. 49–. ISBN 978-1-59745-507-7.
  19. ↑ Bogan, SJ; Waring III, GO; Ibrahim, O; Drews, C; Curtis, L (1990). "Classification of normal corneal topography based on computer-assisted videokeratography". Archives of Ophthalmology. 108 (7): 945–9. doi:10.1001/archopht.1990.01070090047037. PMID 2369353.
  20. ↑ Alpins, NA (1998). "Treatment of irregular astigmatism". Journal of Cataract and Refractive Surgery. 24 (5): 634–46. doi:10.1016/s0886-3350(98)80258-7. PMID 9610446. S2CID 25181513.
  21. ↑ Alpins, NA (1997). "New method of targeting vectors to treat astigmatism". Journal of Cataract and Refractive Surgery. 23 (1): 65–75. doi:10.1016/s0886-3350(97)80153-8. PMID 9100110. S2CID 13411077.
  22. ↑ Alpins, NA (1997). "Vector analysis of astigmatism changes by flattening, steepening, and torque". Journal of Cataract and Refractive Surgery. 23 (10): 1503–14. doi:10.1016/s0886-3350(97)80021-1. PMID 9456408. S2CID 21814626.
  23. ↑ "Keratometry". St. Luke's Cataract & Laser Institute. Archived from the original on 29 October 2013. Retrieved 8 September 2013.
  24. ↑ Corneal Topography and Imaging at eMedicine
  25. ↑ Graff, T (1962). "Control of the determination of astigmatism with the Jackson cross cylinder". Klinische Monatsblätter für Augenheilkunde und für Augenärztliche Fortbildung. 140: 702–8. PMID 13900989.
  26. ↑ Del Priore, LV; Guyton, DL (1986). "The Jackson cross cylinder. A reappraisal". Ophthalmology. 93 (11): 1461–5. doi:10.1016/s0161-6420(86)33545-0. PMID 3808608.
  27. ↑ Brookman, KE (1993). "The Jackson crossed cylinder: Historical perspective". Journal of the American Optometric Association. 64 (5): 329–31. PMID 8320415.
  28. ↑ "Basic Refraction Procedures". Quantum Optical. Archived from the original on 29 October 2013. Retrieved 8 September 2013.
  29. ↑ "Introduction to Refraction". Nova Southeastern University. Archived from the original on 10 September 1999. Retrieved 8 September 2013.
  30. ↑ Boyd, Benjamin F. (2011). Modern Ophthalmology The Highlights. Panama: Jaypee Brothers Medical Pub. p. 388. ISBN 9789962678168.
  31. ↑ Lake, Jonathan C; Victor, Gustavo; Clare, Gerry; Porfírio, Gustavo JM; Kernohan, Ashleigh; Evans, Jennifer R (17 December 2019). Cochrane Eyes and Vision Group (ed.). "Toric intraocular lens versus limbal relaxing incisions for corneal astigmatism after phacoemulsification". Cochrane Database of Systematic Reviews. 2019 (12): CD012801. doi:10.1002/14651858.CD012801.pub2. PMC 6916141. PMID 31845757.
  32. 1 2 Mustafa, Osama M.; Prescott, Christina; Alsaleh, Fares; Dzhaber, Daliya; Daoud, Yassine J. (2019). "Refractive and Visual Outcomes and Rotational Stability of Toric Intraocular Lenses in Eyes With and Without Previous Ocular Surgeries: A Longitudinal Study". Journal of Refractive Surgery. 35 (12): 781–788. doi:10.3928/1081597x-20191021-03. ISSN 1081-597X. PMID 31830294. S2CID 209341790.
  33. 1 2 3 4 5 6 7 8 Zhang, Jun; Wu, Yifei; Sharma, Bhavna; Gupta, Ritu; Jawla, Shantanu; Bullimore, Mark A. (1 March 2023). "Epidemiology and Burden of Astigmatism: A Systematic Literature Review". Optometry and Vision Science. 100 (3): 218–231. doi:10.1097/OPX.0000000000001998. ISSN 1538-9235. PMC 10045990. PMID 36749017.
  34. ↑ Asano, Kazuko; Nomura, Hideki; Iwano, Makiko; Ando, Fujiko; Niino, Naoakira; Shimokata, Hiroshi; Miyake, Yozo (2005). "Relationship Between Astigmatism and Aging in Middle-aged and Elderly Japanese". Japanese Journal of Ophthalmology. 49 (2): 127–33. doi:10.1007/s10384-004-0152-1. PMID 15838729. S2CID 20925765.
  35. ↑ Kleinstein, R. N.; Jones, LA; Hullett, S; et al. (2003). "Refractive Error and Ethnicity in Children". Archives of Ophthalmology. 121 (8): 1141–7. doi:10.1001/archopht.121.8.1141. PMID 12912692.
  36. ↑ Garcia, Carlos Alexandre de Amorim; Oréfice, Fernando; Nobre, Gabrielle Fernandes Dutra; Souza, Dilene de Brito; Rocha, Marta Liliane Ramalho; Vianna, Raul Navarro Garrido (2005). "Prevalence of refractive errors in students in Northeastern Brazil". Arquivos Brasileiros de Oftalmologia. 68 (3): 321–5. doi:10.1590/S0004-27492005000300009. PMID 16059562.
  37. 1 2 3 4 Read, Scott A.; Collins, Michael J.; Carney, Leo G. (January 2007). "A review of astigmatism and its possible genesis". Clinical & Experimental Optometry. 90 (1): 5–19. doi:10.1111/j.1444-0938.2007.00112.x. ISSN 0816-4622. PMID 17177660. S2CID 8876207.
  38. ↑ Czepita, D; Filipiak, D (2005). "The effect of the type of astigmatism on the incidence of myopia". Klinika Oczna. 107 (1–3): 73–4. PMID 16052807.
  39. ↑ Coggin, David (1893). "Notes on the Centennial Anniversary of the Discovery of Astigmatism". Boston Med Surg J. 128 (6): 136–137. doi:10.1056/NEJM189302091280603.
  40. ↑ Atchison, David A; Charman, W Neil (2011). "Thomas Young's contributions to geometrical optics" (PDF). Clinical and Experimental Optometry. 94 (4): 333–340. doi:10.1111/j.1444-0938.2010.00560.x. PMID 21214628.
  41. ↑ Thomas Young (1801). "II. The Bakerian Lecture. On the mechanism of the eye". Philosophical Transactions of the Royal Society of London. 91: 23–88. Bibcode:1801RSPT...91...23Y. doi:10.1098/rstl.1801.0004.
  42. 1 2 Levene, J. R. (1966). "Sir George Biddell Airy, F.R.S. (1801-1892) and the Discovery and Correction of Astigmatism". Notes and Records of the Royal Society of London. 21 (2): 180–199. doi:10.1098/rsnr.1966.0017. JSTOR 531067. S2CID 72385672.
  43. ↑ Wang, Ming (22 October 2007). Irregular Astigmatism: Diagnosis and Treatment. SLACK Incorporated. ISBN 9781556428395.
  44. ↑ George Biddell Airy (1827). "On a peculiar Defect in the Eye, and a mode of correcting it". Transactions of the Cambridge Philosophical Society.
  45. ↑ Read, Scott A; Collins, Michael J; Carney, Leo G (2007). "A review of astigmatism and its possible genesis". Clinical and Experimental Optometry. 90 (1): 5–19. doi:10.1111/j.1444-0938.2007.00112.x. PMID 17177660. S2CID 8876207.
  46. ↑ Porter, Jason (2006). Adaptive optics for vision science: principles, practices, design, and applications. Wiley. ISBN 9780471679417.
  47. ↑ Wood, Alexander; Oldham, Frank (1954). Thomas Young Natural Philosopher 1773–1829.
  48. ↑ Donders, Franciscus Cornelis (1866). Die Anomalien der Refraction und Accommodation des Auges. Braumüller. p. 381.
  49. ↑ Wang, Ming (22 October 2007). Irregular Astigmatism: Diagnosis and Treatment. SLACK Incorporated. ISBN 9781556428395. Archived from the original on 29 June 2011.
  50. ↑ Snyder, C. (1965). "The Rev. Mr. Goodrich and His Visual Problem". Archives of Ophthalmology. 73 (4): 587–589. doi:10.1001/archopht.1965.00970030589023. PMID 14270148.
  51. ↑ Bumstead, J. F. (1863). "A Few Remarks on Astigmatism". Boston Med Surg J. 69 (14): 280–284. doi:10.1056/NEJM186311050691404.
  52. ↑ Donders, Franciscus C (1862). Astigmatismus und cylindrische Gläser. Peters. p. 129.
  53. ↑ Artal, Pablo; Tabernero, Juan (2010). "Optics of human eye: 400 years of exploration from Galileo's time". Applied Optics. 49 (16): D123–30. Bibcode:2010ApOpt..49G.123A. doi:10.1364/AO.49.00D123. PMID 20517354. S2CID 1539303.
  54. ↑ The Optical Review. Vol. 2. Jewelers' Circular. 1908. pp. 35–37.
  55. ↑ Wunsh, Stuart E. (10 July 2016). "The Cross Cylinder". Ento Key.
  56. ↑ Ferrer-Altabás, Sara; Thibos, Larry; Micó, Vicente (14 March 2022). "Astigmatic Stokes lens revisited". Optics Express. 30 (6): 8974–8990. Bibcode:2022OExpr..30.8974F. doi:10.1364/OE.450062. ISSN 1094-4087. PMID 35299337. S2CID 245785084.
  57. ↑ Newell, F. W. (April 1988). "Edward Jackson, MD--a historical perspective of his contributions to refraction and to ophthalmology". Ophthalmology. 95 (4): 555–558. doi:10.1016/s0161-6420(88)33158-1. ISSN 0161-6420. PMID 3050696.
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