Trajectories of changing refractive status.

Refractive status can be represented as a point plotted on a three-dimensional graph. As the refractive status changes a curve is traced out on the graph. Trajectories of changing refractive status are illustrated in a number of representative ideal cases. The three-dimensional graphs are shown by means of stereo-pairs. Trajectories are constructed from clinical data and interpreted with reference to the ideal examples. They show changing refractive status with age, after cataract extraction, and after radial keratotomy. The trajectories may prove to be a useful tool for both clinician and researcher. They show overall trends and allow prediction of future changes. Certain types of trajectories could prove to be characteristic of certain conditions and thus be useful for diagnosis. Trajectories allow monitoring of change after intervention.

Meridional profiles of variance-covariance of dioptric power. Part 2. Profiles representing variation in one or more of sphere, cylinder and axis.

Meridional profiles of variation of dioptric power are constructed. Using the basic theory developed in an accompanying paper, samples are selected in a systematic way to illustrate variation only in sphere, only in cylinder and only in axis, and in all possible combinations of sphere, cylinder and axis. For each of the seven samples, scatter plots are constructed together with ellipsoids that represent the estimated distribution of powers in the population from which the sample was taken. The surfaces of the ellipsoids are surfaces of constant probability density within which 95% of the population is calculated to lie. The scatter plots and distribution ellipsoids are plotted in a three-dimensional space called h-space. Meridional profiles of variation are constructed for each of the samples. Properties of the profiles are discussed. Meridional profiles are also presented for eyes before and after radial keratotomy. Among other things, the profiles show meridians of greatest and least variation and are intuitively satisfying. They are potentially useful for the researcher and clinician including the surgeon. They may help to improve surgical and therapeutic techniques. Certain patterns may prove to be characteristic of physiological or pathological conditions, in which case meridional profiles may have use as a diagnostic tool.

Analysis of refractive status of Hong Kong Chinese infants.

Recently developed methods of quantifying changing dioptric power are applied to the refractive status of Hong Kong Chinese infants from about 10 to about 40 weeks of age. The analysis confirms that hyperopia decreases during the period and that with-the-rule astigmatism predominates. Change, however, is not constant over the period. The rate of decrease of hyperopia slows down and the refractive status becomes more spherical. The mean refractive status is calculated at 10, 20, 30 and 40 weeks. The spread of refractive status is represented by variance-covariance matrices calculated for each group and 95% confidence ellipsoids on the mean are constructed. The variance-covariance exhibits little change over the period. The right and left eyes show similar behaviour.

Keratoreformation by contact lenses after radial keratotomy: a re-analysis.

A recent paper analysed change in refraction and corneal curvature associated with contact lens wear in patients who had had radial keratotomy at least a year beforehand. Conventional methods of analysis were used. This paper applies methods that have only recently become available. The results are clearer and less ambiguous. Formally, the analysis shows that there are significant mean changes in refraction (estimated to be +1.69/-0.50 x 105) and corneal power (-0.66/-0.25 x 155). In spite of the difference between these two mean changes, the analysis shows that the change in refraction may be associated with change in the corneal power alone. There is no reason to believe that any other change is occurring in the eye. Care needs to be executed in assigning a causative role to contact lenses in changing refraction and corneal curvature. Almost certainly the lenses do have such a role but the analysis does not formally allow an unequivocal conclusion concerning that role.

Ellipsoidal confidence regions for mean refractive status.

Confidence regions for mean dioptric power can be represented by ellipsoids in a three-dimensional space called h-space. A convenient graphical representation is provided by stereo-pair drawings that, at a glance, show the estimated accuracy with which the mean power is known. As an example, a sample of autorefractor measurements made on one eye were used to construct a 95% confidence ellipsoid for the mean objective refractive status of that eye. Key dimensions of the ellipsoid are compared with those of another eye. The analysis is of fundamental importance for scientific studies of variation and change of refractive status. Its potential clinical importance is also discussed.

The distribution of dioptric power: ellipsoids of constant probability density.

A sample from a population of dioptric powers may be used to estimate the distribution of dioptric powers in the population itself. This paper describes the method and shows further how one can obtain a graphical representation of the distribution. The graphical representation takes the form of ellipsoids of constant probability density. The centroid of each ellipsoid estimates the mean of the population while the size, shape and orientation show the extent and nature of the spread of the population. For illustrative purposes the theory is applied to measurements of refractive status before and after radial keratotomy. The ellipsoids are presented as stereo-pairs. They are useful for comparative and predictive purposes. Thus the ellipsoid that contains 95% of the population after surgery defines the set of refractive errors within which the refractive error of a particular eye can be expected to fall with a probability of 95%.