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PubMed1981

A system matrix for astigmatic optical systems: II. Corrected systems including an astigmatic eye.

The 4 x 4 system matrix is applied to corrected astigmatic systems including a schematic eye in which each surface is astigmatic at a different axis. In addition to representing the eye, the 4 x 4 system generates 2 x 2 magnification matrices which describe the meridional magnifications that occur in the presence of astigmatism including the magnifications that occur with bitoric eikonic correcting lenses, or other meridional magnifying systems.

Astigmatism↗
PubMed2006

Paraxial propagation of astigmatic wavefronts through noncoaxial astigmatic optical systems.

PURPOSE: The paraxial propagation of astigmatic wavefronts through a noncoaxial system is described. METHODS: The augmented stepalong method (ASAM) for vergences is extended to tilted and decentered elements. RESULTS: Equations for the case of tilted and decentered elements are presented in the framework of vergence calculations. All effects according to the perturbation of a centered system can be derived from the vergences provided by the calculations for the unperturbed system. In particular, the shift in image space rendered by the pertubation is simply the sum of additional decenter and tilt terms to the unperturbed system. CONCLUSIONS: Previous work on the description of the propagation of astigmatic wavefronts has been generalized to noncoaxial systems. This completes the wavefront picture built on the paraxial augmented stepalong method.

Astigmatism↗
PubMed2004

Corneal and lenticular components of total astigmatism in a preschool sample.

PURPOSE: To examine the contribution of corneal and lenticular components to total astigmatism in preschool low and high astigmats to determine whether there was any compensation for high astigmatism by the lenticular component. METHODS: Cycloplegic refractive and keratometric measures using the Retinomax K-Plus (Nikon Inc., Melville, NY) were conducted on 129 children (mean age, 51.1 +/- 8.4 mo) in Oxford County, Canada. We divided the sample into high astigmats (total cylinder > or =1 D; mean, 1.38 +/- 0.43 D; n = 29) and normal astigmats (total cylinder < or =0.75 D; mean, 0.22 +/- 0.20 D; n = 100). Measures of total and corneal cylinder were transposed into J0 and J45 components, where positive and negative J0 values quantified with-the-rule (WTR) and against-the-rule astigmatisms, respectively, and J45 quantified oblique astigmatism. RESULTS: WTR astigmatism was dominant in both the high and normal astigmatic group. J0 and J45 components of corneal astigmatism were highly correlated with total astigmatism in high astigmats, whereas only J0 was significantly correlated with total astigmatism in normal astigmats. Although the magnitude of total and corneal cylinder was significantly greater in high astigmats, overall lenticular cylinder was similar in both groups. However, the Fourier transforms showed high astigmats to have significantly lower lenticular J0 and higher lenticular J45 than the normal astigmats. CONCLUSIONS: Astigmatism in 3- to 5-year-old children is primarily corneal. In preschool children, the lens does not vary in response to high amounts of corneal WTR astigmatism, and in fact, it increases the oblique astigmatism component when the corneal component is high. In high astigmats, lenticular astigmatism contributes to both J0 and J45 components, whereas the corneal contribution is primarily J0.

Astigmatism↗
PubMed2002

An analysis of the astigmatic changes induced by accelerated orthokeratology.

PURPOSE: The change in corneal astigmatism induced by reverse geometry lenses for orthokeratology has not been described previously. This study examines the efficacy of accelerated orthokeratology for reducing astigmatism and whether this varies with the degree of pre-existing astigmatism. METHOD: Twenty-three randomly chosen eyes exhibiting 0.50 D to 1.75 D pre-fitting with-the-rule astigmatism were retrospectively analysed. Astigmatism was measured by simulated keratometry and corneal topography before and at the completion of a course of orthokeratology. The change in astigmatism measured by keratometry was calculated by two vector analysis techniques: the Bailey-Carney method, which was designed for contact lens-induced corneal shape changes, and the Alpins method, which was designed for surgically-induced corneal shape changes. The change in astigmatism measured by corneal topography was calculated by the EyeSys Version 3.2 software. RESULTS: Most patients (20/23) had some reduction of astigmatism but orthokeratology is incapable of a total elimination of pre-fit astigmatism. Alpins vector analysis showed that an increased efficacy of 60 to 80 per cent would be required to eliminate astigmatism. All three methods found a 50 per cent mean reduction in astigmatism from the pre-fit level. Topographical analysis indicates that the reduction in astigmatism occurs mainly over the central 2.00 mm chord. There is a very poor correlation between the pre-and post-wear corneal astigmatism at the 2.00 mm chord (R(2) = 0.11, p = 0.04) and the predictability of the final astigmatic axis is also poor (angle of error = 1.22 +/- 27.35). CONCLUSIONS: Accelerated orthokeratology seems more successful than conventional orthokeratology at reducing with-the-rule astigmatism. However, it reduces pre-existing astigmatism by an average of only 50 per cent and it does not do so reliably either for magnitude or direction. These results provide two useful patient selection criteria for orthokeratology. They are: assuming 0.50 D to 0.75 D of astigmatism is a satisfactory outcome, orthokeratology can be expected to be successful for pre-fitting astigmatism of up to 1.00 D to 1.50 D; and the greater the pre-existing astigmatism, the less likely orthokeratology is to be successful.

Astigmatism↗
PubMedDate not supplied

Photorefractive keratectomy for hyperopic and mixed astigmatism.

BACKGROUND: The correction of astigmatism with photorefractive keratectomy has been recommended in simple and myopic astigmatism. Therefore in this study the excimer laser was used to correct compound hyperopic and mixed astigmatism. METHODS: We present a prospective clinical study of photorefractive keratectomy in 30 eyes of 24 patients with compound hyperopic astigmatism with a mean spherical equivalent of +4.30 D and mean astigmatism of 2.33 D (group I) and in 17 eyes of 15 patients with mixed astigmatism with a mean spherical equivalent refraction of +0.46 D and mean astigmatism of 4.75 D (group II). The excimer laser used in this study was an MEL 60 (Aesculap-Meditec). In both groups an 18-month follow-up study was performed. RESULTS: In the compound hyperopic astigmatism group after 18 months, 14 of 17 treated eyes (82.3%) were within +/-1.00 D, and 11 (64.7%) were within 60.50 D of the intended correction. In the mixed astigmatism group after 18 months, 10 of 11 eyes (90.9%) were within +/-1.00 D, 8 eyes (72.7%) were within +/-0.50 D of the intended correction. In regard to the stability the 1 year regression of spherical equivalent in the compound hyperopic astigmatism group is 0.78 D and in the mixed astigmatism group 0.37 D. At 18 months, spectacle corrected visual acuity in the compound hyperopic astigmatism group was unchanged or improved in 14 eyes (87.5%); 2 eyes (12.5%) had lost one line. In the mixed astigmatism group at 18 months, spectacle corrected visual acuity was unchanged or improved in 9 eyes (81.8 %); 2 eyes (18.1%) lost one line. Preoperatively, the mean uncorrected visual acuity was 20/100 in the compound hyperopic astigmatism group and the mixed astigmatism group. At 18 months, 14 eyes (93.3%) in the compound hyperopic astigmatism group had an uncorrected visual acuity of 20/40 or better; 4 (26.6%) eyes had an uncorrected visual acuity of 20/20 or better. In the mixed astigmatism group, 9 (81.8%) eyes had an uncorrected visual acuity of 20/40 or better; 4 (36.3%) eyes had an uncorrected visual acuity of 20/20 or better. CONCLUSION: Photorefractive keratectomy is an efficient and relatively safe procedure for reducing or eliminating compound hyperopic and mixed astigmatism up to 6.00 D.

Adult↗
PubMed1997

Astigmatism and visual recovery after 'large incision' extracapsular cataract surgery and 'small' incisions for phakoemulsification.

PURPOSE: This study compares the change over time of the astigmatism caused by "large" incision extracapsular cataract extraction (ECCE) and three smaller incisions for phakoemulsification. Based on this data, a mathematical model that predicts the course of astigmatism after a superior incision of length 3 to 12 mm has been developed. The relationship of axial length and preoperative astigmatism to induced post-operative astigmatism, the recovery of visual acuity, and the rate of YAG laser capsulotomy after each procedure also are documented. METHODS: Induced astigmatic change was calculated using a simple method of vector analysis. The change in induced astigmatism was calculated for 8 years after ECCE (n = 144), for 3 years after 6 mm superior incisions (6SUP) (n = 93), for 2 years after 3 mm superior incisions (3SUP) (n = 120), and for 18 months after 3 mm temporal incisions (3Temp) (n = 65). Plotted semi-logarithmically, the astigmatic change in each group may be represented mathematically. RESULTS: Two weeks after ECCE the mean induced cylinder was +3.47 D, which decayed to about -1.25 D after 6 months. Induced cylinder increased gradually to about -1.6 D after 8 years, although this further change was not significantly different than that at 6 months after surgery. For the phako groups, the net induced cylinder on the first post-operative day was: +1.23 D (6SUP), +0.49 D (3Sup), and -0.19 D (3Temp). After 6Sup the wound was astigmatically stable after approximately 3 months, and 3 years after surgery net induced cylinder was -0.66 D. After 3Sup the wound was astigmatically stable after about 6 weeks, and after 18 months net induced cylinder was -0.35 D. No significant change in astigmatism was detected at any time after 3Temp. Maximum visual acuity was reached after a mean of approximately 6 weeks after ECCE, 2 weeks after 6Sup, and between 1 day and 1 week after 3Sup and 3Temp. The rate of YAG laser capsulotomy was higher after ECCE than after any of the phakoemulsification procedures. No relationship of axial length or preoperative astigmatism to astigmatic change was detected. CONCLUSIONS: Incision size and location affect post-operative astigmatism. Induced astigmatism decreases with wound size, and only the 3 mm temporal incision is astigmatically neutral. The time for visual recovery increases with wound size. There appears to be less need for laser capsulotomy after phakoemulsification with capsulorrhexis than after ECCE. Axial length does not affect induced astigmatism after any of the 4 incisions, and preoperative astigmatism does not affect astigmatic change after ECCE and 6Sup.

Aged↗
PubMed2004

The prevalence of astigmatism in Taiwan schoolchildren.

PURPOSE: To understand the prevalence and distribution of astigmatism in schoolchildren in Taiwan, we analyzed and compared the nationwide survey data in 1995 and 2000. METHODS: A total of 11,175 students were enrolled in 1995, and 10,878 students were enrolled in 2000. The refractive status of each student was measured with an autorefractor during cycloplegia and rechecked with retinoscopy. RESULTS: About half of schoolchildren (57.5% in 1995 and 49.0% in 2000) had no astigmatism (<0.5 D). About one third of schoolchildren's astigmatism was <1 D (27.9% vs. 32.6%). Eleven percent of schoolchildren in 1995 and 13% in 2000 had astigmatism between 1.0 and 2.0 D. Less than 2% of students had astigmatism >3.0 D (1.3% in 1995 and 1.8% in 2000). Most astigmatism was with-the-rule: 83.3% in 1995 and 89.9% in 2000. Only 16.6% of children in 1995 and 9.7% in 2000 had against-the-rule astigmatism. Very little astigmatism was oblique (0.1% in 1995 and 0.4% in 2000). The rate of myopic astigmatism increased with age. In contrast, the rate of hyperopic and mixed astigmatism decreased with age. In addition, the rate of with-the-rule astigmatism increased and the rate of against-the-rule decreased with respect to age, but oblique astigmatism was rather stable with age. CONCLUSIONS: Most schoolchildren had little or no astigmatism. In Taiwan, most astigmatism is <1 D and is myopic with-the-rule astigmatism. There was more myopic astigmatism and with-the-rule astigmatism in 2000 than in 1995.

Adolescent↗
PubMed1995

[The relations of corneal, lenticular and total astigmatism].

PURPOSE: To determine the relations of corneal, lenticular and total astigmatism and the changes of the astigmatism with age. METHOD: Out-patients with refractive errors were refracted with retinoscope after using cycloplegic drops and measured the radii of anterior corneal curvature. RESULT: One hundred and ninety-four cases (382 eyes) with refractive errors were studied. Of the eyes 67.9% had regular corneal astigmatism, 68.1% irregular lenticular astigmatism and 60.7% regular total astigmatism, 88.5% of the corneal astigmatism has the same quality as the total astigmatism. The total astigmatism in 46% of the eyes included the summation of corneal and lenticular astigmatism, but in 41.3% of the eyes irregular lenticular astigmatism corrected the regular corneal astigmatism. The astigmatism of cornea, lens and total astigmatism changed from regular to irregular with the increase of age. The linear correlation analysis showed a positive correlation between the power of horizontal corneal refraction and age, and a negative corrlation between the power of vertical corneal refraction and age. CONCLUSION: The shape of cornea was the major cause of total astigmatism. The influence of lens on the total astigmatism was different. The reasons for the change of the total astigmatism from regular to irregular with the increase of age were the changes of the power of corneal refraction, particularly the increase of the power of horizontal corneal refraction and lenticular irregular astigmatism.

Adolescent↗
PubMed1997

[Choice of the site of incision for cataract surgery without suture according to preoperative astigmatism].

PURPOSE: To compare surgically induced astigmatism, postoperative astigmatism and uncorrected visual acuity after cataract surgery depending on the site of a 4 mm sutureless incision (superior scleral or corneal temporal) and on the preoperative astigmatism. METHODS: According to preoperative astigmatism and to the site of incision 4 groups have been distinguished. Group I: with-the-rule preoperative astigmatism and superior scleral incision, group II: with-the-rule preoperative astigmatism and corneal temporal incision, group III: against-the-rule preoperative astigmatism and superior scleral incision, group IV: against-the-rule preoperative astigmatism and temporal incision. The patients had a preoperative and postoperative (Day 1, 8, 30, 180, 360) keratometry. Surgically induced astigmatism, preoperative and postoperative astigmatism have been expressed according to Naeser method. The uncorrected visual acuity at Day 30 has been compared in each group. RESULTS: Preoperative astigmatism was similar in the four groups. Surgically induced astigmatism was -0.18 diopter (D) at day 30 and -0.41 D at day 360 for the scleral incisions and +0.60 D at day 30 and +0.33 D at day 360 for the temporal incisions. The postoperative astigmatism was +0.5 D at day 30 and +0.27 at day 360 for the group I and +1.22 D at day 30 and +0.95 D at day 360 for group II. There was no statistical difference in the uncorrected visual acuity. Postoperative astigmatism was -0.8 D at day 30 and -1.03 D at day 360 in group III and -0.04 D at day 30 and -0.31 D at day 360 in group IV. The visual acuity was significantly better in group IV than in group III. CONCLUSION: In cases of preoperative with-the-rule astigmatism < or = 0.75 D the two sites of incisions are possible. In cases of WTR astigmatism over 0.75 D we perform a superior scleral approach. In cases of against-the-rule astigmatism the temporal incision is the only one to consider.

Aged↗
PubMed2001

Astigmatism analysis by the Alpins method.

PURPOSE: To determine the effectiveness of correcting astigmatism by laser refractive surgery by a vectorial astigmatism outcome analysis that uses 3 fundamental vectors: target induced astigmatism vector (TIA), surgically induced astigmatism vector, and difference vector, as described by the Alpins method. METHODS: A data set of 100 eyes that had laser in situ keratomileusis to correct myopia and astigmatism (minimum preoperative refractive astigmatism 0.75 diopter) was analyzed. The data included preoperative and 3 month postoperative values for manifest refraction and standard keratometry. Using the ASSORT or VectrAK analysis program, individual and aggregate data analyses were performed using simple, polar, and vector analysis of astigmatism and an analysis of spherical change. Statistical analysis of the results was used for means and confidence limits, as well as to examine the differences between corneal and refractive astigmatism outcomes. RESULTS: At an individual patient level, the angle of error was found to be significant, suggesting variable factors at work, such as healing or alignment. A systematic error of undercorrection of astigmatism is prevalent in the treatment of these 100 patients by a factor of between 15% and 30%, depending on whether refractive or corneal values are examined. Spherical correction showed systematic undercorrection of 11%, and parallel indices demonstrated it to be more effective than the astigmatic correction. CONCLUSION: This method of astigmatism analysis enables the examination of results of astigmatism treatment measured by both refractive and corneal measurements using vector analysis. By examining individual vector relationships to the TIA (ie, the correction index, index of success, and flattening index), a comprehensive astigmatism analysis is completed. Each index provides information necessary for understanding any astigmatic change. Astigmatic outcome parameters are more favorable when measured by subjective refractive than objective corneal methods.

Astigmatism↗