Comparison of higher order aberration profiles between normal and amblyopic eyes in children with idiopathic amblyopia


  • Gaurav Prakash,

    1. Cornea and Refractive Surgery Services, Rajendra Prasad Centre for Ophthalmic Sciences, All India Institute of Medical Sciences, Ansari Nagar, New Delhi, India
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  • Namrata Sharma,

    1. Cornea and Refractive Surgery Services, Rajendra Prasad Centre for Ophthalmic Sciences, All India Institute of Medical Sciences, Ansari Nagar, New Delhi, India
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  • Rohit Saxena,

    1. Strabismus, Amblyopia and Neuro-ophthalmology Services, Rajendra Prasad Centre for Ophthalmic Sciences, All India Institute of Medical Sciences, Ansari Nagar, New Delhi, India
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  • Vandana Choudhary,

    1. Cornea and Refractive Surgery Services, Rajendra Prasad Centre for Ophthalmic Sciences, All India Institute of Medical Sciences, Ansari Nagar, New Delhi, India
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  • Vimla Menon,

    1. Strabismus, Amblyopia and Neuro-ophthalmology Services, Rajendra Prasad Centre for Ophthalmic Sciences, All India Institute of Medical Sciences, Ansari Nagar, New Delhi, India
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  • Jeewan S. Titiyal

    1. Cornea and Refractive Surgery Services, Rajendra Prasad Centre for Ophthalmic Sciences, All India Institute of Medical Sciences, Ansari Nagar, New Delhi, India
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Gaurav Prakash, MD
Cornea and refractive surgery services
Rajendra Prasad Centre for Ophthalmic Sciences
All India Institute of Medical Sciences
Ansari Nagar
New Delhi 110029
Tel: (91 11) 26589817
Fax: (91 11) 26588919


Aim:  To evaluate the higher order aberrations and resultant bilateral wavefront patterns in paediatric patients with idiopathic amblyopia.

Material and Methods:  In this cross sectional observational trial, seventeen consecutive patients of previously diagnosed idiopathic amblyopia underwent wavefront analysis on Zyoptix platform (Bausch and Lomb, Rochester, NY, USA).

Results:  The mean age was 9 ± 3 years. There was no significant difference in comparison with means for the Zernike coefficients between normal and amblyopic eye. However, interrelation between Zernike coefficients, which is responsible for their interaction leading to difference in visual function, was different between amblyopic and fellow eyes. This was noticed using stepwise regression analysis. Predicting variables and R2 (r squared) values for each Zernike polynomial were calculated. The sets of significantly predicting coefficients were different in mostpatients, with only seven common pairs and 42 dissimilar dependent-predictor sets. Maximum difference in the R-squared values between amblyopic and normal (fellow) eyes was seen with coma-like and trefoil-like aberrations (third order and fifth order terms).

Conclusion:  It seems a strong possibility that a subset of ‘idiopathic’ amblyopia may be associated with loss of symmetry in wavefront patterns of the two eyes.


Amblyopia has been classically related to unequal foveal stimulation in the early age due to form vision deprivation, strabismus or refractive error (Wu & Hunter 2006; von Noorden & Campos 2007). However, there is a small subset of patients with amblyopia who do not have any of the earlier mentioned causative factors. These patients have been grouped as the so called ‘idiopathic amblyopes’. Previous studies in literature highlight the presence of this entity (von Noorden 1985; von Noorden & Campos 2007).

The component of refractive error that cannot be compensated by conventional sphero-cylindrical correction is called higher order aberrations (HOA), expressed most commonly in form of Zernike polynomials. Wavefront analysis of HOA has resulted in evolution of knowledge on vision-related entities like best-corrected visual acuity, visual performance, post-lasik symptoms and contrast sensitivity (Williams et al. 2004; Chalita et al. 2004; Oshika et al. 2006a,b).

It could be possible that in some of the patients with idiopathic amblyopia, the amblyopiogenic factor could be a difference in the HOA and the resultant point spread functions on the fovea. We reported a patient with idiopathic amblyopia in which the only interocular difference was in the higher order wavefront patterns between the amblyopic and normal eye (Prakash et al. 2007).The present study evaluates further more cases of children with idiopathic amblyopia, and analyses the HOA, resultant wavefront patterns and their interocular difference in these patients.


The study was conducted at a tertiary care ophthalmic centre. In this study, children with a diagnosis of idiopathic amblyopia/minimally anisometropic amblyopia [<1.0 D difference of both spherical (defocus) error and spherical equivalent (SEQ)] were evaluated. These patients were recalled from our amblyopia registry of strength of 760 amblyopic patients. All these patients were in follow-up for more than 6 months at our centre. The study was approved by the local ethics committee, and all the tenets of the Declaration of Helsinki were followed. Each of the participating patients and his/her parents were explained the study protocol, investigations and the observational nature of the study. All the parents gave explained written consent for participation in the study.

There were three steps in the analysis process:

Step 1: First step consisted of ruling out known causes of amblyopia and vision disparity. All patients underwent dilated cycloplegic retinoscopy and subsequent refraction to evaluate the refractive error and anisometropia. All the patients were screened for microtropia, tropia, cataract, ptosis, any macular or optic disc anomaly, optic nerve conduction deficit, visual field defects, previous history of any ocular or adnexal surgery and a documented history of higher magnitude of anisometropia in the past. Poor compliance with amblyopia treatment protocols was also an exclusion factor. Seventeen patients were thus found to have idiopathic amblyopia.

Step 2: In the second step, aberrometry was performed on 17 selected patients. The Zywave workstation (Bausch & Lomb, Rochester, NY, USA), a device based on the Hartmann–Shack principle, was used for all patients. It measures monochromatic aberrations of the entire eye and displays them up to the 5th order. One experienced examiner performed the aberrometry using a strict protocol described by the manufacturer. All measurements were performed in between 2 p.m. and 4 p.m. to compensate for diurnal variation. Built-in centration devices along with accommodation relaxation target were used to confirm alignment and minimize the effect of accommodation. Joystick movements were used to bring the pupil and iris edge to sharp focus. Patient was asked to blink once just before the scan and focus at the fixation target. Scans were then performed, with the adequacy of the scan being confirmed by the symmetrical and complete appearance of the focus status curve. The result table of the Zywave shows five measurements, and automatically chooses best three with the lowest reliability criteria (lower the reliability criteria, the better the repeatability). Additionally, quality of the centroid grid and the iris image were assessed to ensure good quality scans.

Step 3: Zernike polynomials assessment and rearrangement was the third step. The numerical values of Zernike polynomials were taken from ‘.ate’ files and band plots. These were then converted to the standard nomenclature of the Optical Society of America and entered into a MS Excel Sheet (Microsoft Inc., Redmond, WA, USA). Necessary corrections in the signed values were made according to avoid errors because of enantiomeric midline symmetry (Smolek et al. 2002). The data was then rearranged into patients (amblyopic eye) and controls (normal fellow eye with a vision of ≥20/20). The names of the Zernike coefficients are given henceforth in both the common name terms (e.g., coma, trefoil) and the dual index scheme, Zernike coefficient = Z(m,n) where, n is the angular frequency, m is the radial order.

Statistical analysis

The data was analysed using spss 13.0 for Windows (SPSS Inc., Chicago, IL, USA). The difference in mean values of spherocylinder and Zernike polynomials was analysed using Rank Sum test. Zernike polynomials tend to interact with each other and aberration mode may interact with more than one, which may in addition be effected by others, therefore making normal correlation analysis less effective because of the confounding effect. Therefore, we used stepwise regression analysis to find out the HOA significantly affecting other aberrations and their effects in isolation and as a total on a specific aberration.

A regression model was created for each higher order aberration value, in which the fit of all the other aberrations was seen. Those with a statistically significant fit in a stepwise regression analysis model were noted. The combined value of R squared gave an estimate of the amount of variability in one Zernike polynomial that can be explained by the set of these significantly predicting variables. Two sets of regression models were constructed for all the HOA, one for amblyopic eyes and one for normal eyes. The difference in significant predictability of each variable by other Zernike terms for normal and amblyopic eyes was estimated by finding the difference in the R-squared values for both the sets.


Demographic characteristics

Seventeen patients were analysed in the study.

There were 10 men and seven women. The mean age was 9 ± 3 years. Right eye was amblyopic in six patients and left eye in 11 patients. All these children were taken from a larger pool of amblyopic patients following up at our amblyopia services for at least 6 months. The maximum follow-up was of 1.5 years.

All these patients had been using best-corrected refraction and had been given trials of occlusion therapy. Patching was voluntarily stopped in only those patients who achieved the same level of visual acuity. All these patients were weaned off the occlusion therapy over 6–9 months. In patients without sustained improvement, patching had been restarted. Only patients without sustained improvement (n = 9)/less than expected improvement (n = 2)/no improvement (n = 6) were included in the current study. Most patients (n = 15) were still on patching treatment on their last follow-ups. Two patients of age 12 and 11 years were off patching after mild improvement that had been sustained over last 1 year. All patients had been compliant to occlusion therapy and spectacle/contact lens correction. The best corrected visual acuity (BCVA) ranged from 20/63 to 20/32 in the amblyopic eye and was ≥20/20 in all the normal fellow eyes.

Refractive error

The mean refractive error was +1.6 ± 2.6 dioptre sphere (DS) (SEQ of 1.0 ± 2.5D) in the fellow eyes and +1.6 ± 2.6 DS (SEQ of 1.0 ± 2.5 D) in amblyopic eye (p > 0.05, Rank Sum test). The difference in spherical error (fellow – amblyopic) ranged from −0.6 to + 0.6 D and in SEQ ranged from −0.5 to + 0.7 D. The summated HOA mean difference was −0.05 ± 0.2.

Corneal topographic analysis was performed by Orbscan (Bausch and Lomb, Rochester, NY). There was no difference in the Simulated Ks maximum, minimum and astigmatism values between the normal and amblyopic eyes as measured on (p > 0.05, Rank Sum test for all comparisons).

Comparison of means of Zernike coefficients

The mean values of the Zernike coefficients from 3rd to 5th order were computed (Table 1). The individual Zernike means were similar for both sets of eyes (Rank Sum test, p > 0.05 for all corresponding Zernike coefficients), as expected because normal unoperated eyes have follow Gaussian distribution of mean around zero for most Zernike polynomials.

Table 1.   Difference in mean values of higher order aberrations in normal and amblyopic eye.
Zernike coefficientNormal eyeAmblyopic eye
MeanStandard deviationStandard error of meanMeanStandard deviationStandard error of mean
Z(4, 0)−−

However, there were differences noticed in the wavefront outcome maps constructed by a customized wavefront plotting software on Matlab (Mathworks, Natick, MA, USA) platform. Figure 1 demonstrates the three dimensional plot (1A) , two dimensional plot (1B) , point spread function (1C) and modulation transfer function (1D) of the normal and amblyopic eyes and their difference. Therefore, regression fits were assessed between Zernike’s data to look at the relationships beyond measures of central tendency.

Figure 1.

 A customized Matlab (Matlab Inc., Natick, MA, USA) code was used to create the averaged three-dimensional (Fig. 1A) and two-dimensional plots (Fig. 1B) of the higher order aberrations of the fellow eyes and the amblyopic eyes. The difference plots were also plotted suggesting difference in the wavefront profiles. The point spread function (PSF) denotes how the optical system in question changes a point source of light. The modulation transfer function (MTF) demonstrates the effectiveness of the eye in transferring modulation (or contrast) from the subject to the image. The PSF and MTF of the normal and the amblyopic eye and their differences have been plotted (Fig. 1C,D).

Regression analysis

Stepwise regression analysis was performed to find out the Zernike coefficients significantly predicted (determined) by other Zernike coefficients. R2 (r-squared) values and unstandardized coefficients for each predicting Zernike polynomial were calculated. The sets of significantly predicting coefficients were different in most patients, with only 7 common pairs (14 values) and 42 dissimilar dependent predictor sets. For example, for normal eyes, Vertical trefoil, Z (3, −3) had an R squared of 0.787 for a regression model consisting of fourth order term Quadrafoil [positive, Z (4,4) ] and third order term Vertical Coma [ Z (3, −1)] This suggests that almost 78% of its variability of the vertical trefoil can be significantly predicted by Quadrafoil and Vertical Coma. However, for amblyopic eyes the same Vertical Trefoil Z (3, −3) had an R squared of 0.37, suggesting a significantly predictable variability of 37%, all of which is governed by fourth order term Quadrafoil [negative, Z (4,−4)].

On the same lines, differences in significantly predictable variability (R-squared values) were evaluated for corresponding Zernike terms for both normal (fellow) and amblyopic eyes. Highest amount of differences were seen in the values for third and fifth order aberrations; Third order : horizontal coma (R2 = 0.3 for normal versus 0.0 amblyopic), vertical trefoil (R2 = 0.8 for normal versus 0.4 for amblyopic), horizontal trefoil (R2 = 0.3 for normal versus 0.8 for amblyopic); Fifth order : secondary vertical coma (R2 = 0.9 for normal versus 0.8 for amblyopic), secondary horizontal coma (R2 = 0.4 for normal versus 0.5 for amblyopic), and secondary vertical trefoil (R2 = 0.4 for normal versus 0.7 for amblyopic), secondary horizontal trefoil (R2 = 0.6 for normal versus 0.9 for amblyopic), (Fig. 2). Other than this, one component each of quadrafoil (R2 = 0.9 for normal versus 0.6 for amblyopic) and pentafoil (R2 = 0.8 for normal versus 0.4 for amblyopic) showed high difference in R-squared. The amount of difference seen in fourth order terms was lower than that in including spherical aberration (R2 = 0.3 for normal versus 0.3 for amblyopic).

Figure 2.

 Bar diagram to demonstrate the difference between the R-squared values of predictor sets for Zernike polynomials in normal and amblyopic eyes. The difference is denoted as normal minus amblyopic. The computations are performed from third to fifth order. For example, the difference between predictability of normal – amblyopic eye higher order aberrations for vertical trefoil is 0.41. Maximum differences were seen in third and fifth order predictability between the normal and amblyopic eyes (V → Vertical, H → Horizontal, S → secondary).


Idiopathic amblyopia is a rare entity, evidenced by only a few sporadic patient reports and series. In these patients, known causes like strabismus, anisometropia, form vision deprivation or organic causes (fundus or optic nerve abnormality) are not found (von Noorden 1985)

Resolved anisometropia with residual amblyopia has been suggested as a possible explanation for this entity. The rationale is as follows: anisometropia in infancy often results into dense amblyopia. This difference in refractive error might reduce as the child grows, because of tendency towards emmetropization (Norton & Siegwart 1995; Brown et al. 1999). If this patient presents at a later age (say adulthood or late teenage), amblyopia would still be present without apparent cause at that cross sectional evaluation (if the previous history was unknown). However, our study’s design weakens the possibility of resolved anisometropia as the possible cause. This is because we evaluated only paediatric patient population, which has a potential for improvement of vision in conventional amblyopia after patching. The age range of children in our study has shown benefit in many patients after occlusion therapy [as demonstrated in the same age group (6–12 years) in the Paediatric Eye Disease Investigator Group trial] (Scheiman et al. 2005; Hertle et al. 2007). Even if these children had a residual amblyopia with resolving anisometropia, the stimulus that caused the amblyopia (i.e., anisometropia) was not present anymore, and they might have shown a response to patching protocols. This suggests that there could possibly be another abnormality in the binocular interaction of these eyes that is preventing an improvement in BCVA. This is in agreement with the initial hypotheses and findings of von Noorden in regard to idiopathic amblyopia (von Noorden 1985).To consider an analogy, let us assume for some time that we are only aware of spherical power (defocus) as a refractive error and there was no knowledge about astigmatism as a possible cause of poor vision. In this hypothetical scenario, some patients with meridonal anisometropy (because of high difference in astigmatism) would have still suffered from amblyopia. These patients would have been labelled as ‘idiopathic amblyopes’ as there would have been ‘no known cause’ for development of amblyopia.

Interestingly, they would also have been resistant/poorly responding to amblyopia treatment by patching the normal eye and spherical power correction for the amblyopic eye by glasses. This would have been because the amblyopiogenic factor would have been still uncorrected. Therefore, the common factor in these patients would have been the yet undiscovered refractive entity, i.e., astigmatism.

A similar case is possible in a subset of patients with minimally anisometropic or idiopathic amblyopia. Analysis of HOA is a step forward in determining the refractive error spectrum and it leaves open new possibilities.

Marked difference in wavefront profiles of one such patient gave us the insight into evaluation of wavefront patterns in evaluation of unexplained amblyopia (Prakash et al. 2007). We hypothesized that if the difference in higher order aberration patterns between the two eyes in case of idiopathic amblyopia could have present since early childhood, it could have led to a bifoveal pattern disruption resulting into HOA associated amblyopia. As lower order aberrations constitute a major component of the average wavefront errors, a high proportion of the retinal image in normal eye is governed by them (Chalita & Krueger 2004).

The effect of increasing HOA on the visual acuity has been studied in experimental settings, showing that even an artificially created difference of 0.25 microns for certain Zernike coefficients can be detrimental to visual function (Applegate et al. 2003).It is known that in test conditions, addition of two Zernike coefficients, especially those with the same sign and two radial orders apart may result in a better visual acuity because of formation of a lesser-distorted point spread on the retina(Applegate et al. 2002, 2003).There is a wide variation in the values of Zernike coefficients seen in normal population, even within ethnic groups (Porter et al. 2001; Wang & Koch 2003; Salmon & van de Pol 2006; Prakash et al. 2008).

It has been shown that there is high mirror symmetry between HOA of the corresponding eyes in normal people (Smolek et al. 2002; Thibos et al. 2002a,b). The Zernike coefficients tend to be randomly distributed about a mean value of zero (except for spherical aberration (Thibos et al. 2002a,b).This further rules out against comparing individual Zernike modes in a case–control-based ‘difference of mean’ method. For the same reason, we also avoided using a normal population-based control group and used the fellow eye as controls.

However, HOA interact with one another to form a combined effect on the visual function. Therefore, it will be useful to assess this multiple interaction by regression analysis and find out the amount of predictability of each higher order Zernike polynomial depending upon other Zernike polynomials.

Stepwise regression analysis showed differences in the multivariate interactions between these Zernike coefficients in the normal and amblyopic eyes. The highest amount of differences were seen in the R2 values for all the aberrations were seen in third and fifth order aberrations; coma, trefoil, secondary coma and secondary trefoil. Therefore, the role of coma-like and trefoil-like aberrations (which are asymmetrical) seems to be higher compared to the other set of predominant aberration in normal population, i.e., spherical aberration (which is a symmetrical aberration).

It is known that in a growing child, reduction of amount of anisometropia and emmetropization for the spherocylinder might occur (Brown et al. 1999). It might be possible that a similar process is used by the visual system to form a more symmetrical higher order point spread function between two eyes. The basis of this hypothesis is the finding of Brunette et al. (2003), which suggest an emmetropization like tendency with HOA. Their data showed a progressive decrease in HOA from childhood and adolescence, similar to low-order aberrations. The results of the study made the authors suggest that the definition of emmetropization should be broadened to include the reduction of HOA. The asymmetrical interactions between Zernike coefficients in our patients suggest that this process similar to emmetropization for HOA might be disturbed in these eyes suffering from ‘HOA associated amblyopia’, resulting into difference in HOA patterns between normal and amblyopic eye.

We do not suggest that all patients of idiopathic amblyopia suffer from difference in HOA patterns. Rather, we document the difference in HOA patterns in these patients and provide evidence towards a difference in wavefront regression patterns, especially of third order aberrations, in some patients of amblyopia previously labeled as ‘idiopathic’. Disturbances in foveal function of the apparently normal eye have also been suggested in past (Agervi et al. 2009). This warrants for careful assessment of HOA of the fellow eye too.

The role of wavefront-guided refractive surgery in children is evolving. It has been shown that wavefront-guided refractive surgery may reduce high HOAs in adults (Schallhorn et al. 2008). Similar long-term studies in children are required. Future evolution and understanding of stability of wavefront aberrations after lasik may be especially helpful in these patients with low lower-order anisometropia. It seems likely that better understanding of corneal biomechanics in children and better laser platforms can be useful in treatment of HOA in these patients. An international reporting registry can be developed to document these sporadic and rarely seen patients and their wavefront profile and use the data from defining limits and confidence intervals for these entities.


None for any coauthors.