Corneal Module

This module is relevant for corneal refractive surgery. For IOL power selection only (including adaption after corneal refractive surgery) it is not necessarily required. The corneal module is called either from the main menue or from the Retinal Image by clicking to Cornea.

2-Dimensional Optical Errors

Choose the DEMO topography by clicking to Cornea Files, then select (ok) and load (ok once again) it. Then click to 2-Dim. Opt. Error. Refraction errors are calculated in two dimensions: meridional, i.e. in the direction of the meridians, and azimuthal, i.e. perpendicular to the first. The vector sum of both components is the total refraction error which is calculated e.g. for the blurring of the Landolt’s rings. The azimuthal component mainly describes the deviation from the rotational symmetry. Other than the meridional component, the azimuthal one is not influenced if spherical power is changed. In addition, optical path length differences to the center (so-called "wavefrontdifferences") are calculated by clicking to Wavefront Diff. These three optical errors (meridional, azimuthal or wavefront differences) can be displayed either exactly, i.e. the results of the ray-tracing, or these data can be approximated by a Zernike polynomial series. To do so, first the corresponding option has to be highlighted. Than the maximum radial order [3-12] of the series has to be entered. If 0 or nothing is entered, the exact error map is displayed. If a Zernike series has been calculated, the coefficients can be stored in ASCII-format on a file for which the name has to be entered additionally. No such file is generated if no name is entered. In adition, the Zernike coefficients are displayed in a window and can be manually changed. We start with meridional. In the following branch for the pseudocolor mode it is proposed first to click to automatic. This means that pseudocolors are adapted in such a way that "in mean" a useful dynamic range is covered. This, however, is normally not exactly the range the user is willing to see. The procedure should be repeated therefore, this time clicking to user-defined for the pseudocolors. For the upper threshold +1.5 may be entered, for the lower one -3.0. Below the map RMS (r <3.0mm):1.00910 is displayed. The root mean square refraction error of the meridional component is ≈ 1.0 diopter inside a circle of 3.0mm around the center. Of course, the pseudocolor maps as well as the RMS-values strongly depend on the IOL. The circle, for which the RMS-values are calculated, has the radius of the optical zone of the IOL. This is also taken as the "unit circle" for the calculation of the Zernike series. Clicking to azimuthal generates the pseudocolor map of the azimuthal refraction component. Their dynamical range is normally much smaller compared to the meridional one. Therefore, the pseudocolor range is always calculated automatically. The azimuthal RMS-value is 0.61324 diopters in our example. For Wavefront-Diff., the RMS-value of 0.00247mm means that there is an RMS-difference of 2.47μm in the optical path lengths relative to the central value. If after Wavefront-Diff. 4 is entered as the maximum radial order of the Zernike approximation, the RMS-value is marginally changed to 0.00240mm. In addition, the image has a diameter of only 6mm in maximum (diameter of the IOL optics).

Corneal Model

In many applications, particularly in corneal refractive surgery, the use of an approximation of the corneal shape by only a few parameters is more advantageous than using the whole set of topographic raw data. This is what we call a corneal model. Such a model can be calculated from the topography by extracting these parameters. Alternatively, the parameters may simply be entered into OKULIX. Choose the DEMO topography by clicking to Cornea Files, then select (ok) and load (ok once again) it. Then click to Corneal Model. For all following calculations R1,R2,alpha,e should be preferred, not Zernike-Approx.. The number of independent parameters is much smaller (four), the first three of them are commonly used in ophthalmology, and at least the central 4mm-zone is approximated with higher accuracy than by Zernike polynomial approximation ⁶. If the radio button "reconstruct full zone" is activated by clicking on it, the missing data points of the topography are reconstructed. Clicking to R1,R2,alpha,e opens a window in which corneal radii, angles and numerical eccentricity are preset with the same values as displayed in the topography. If other values are entered here, an arbitrary cornea can be generated in the computer. If clicking to ok, the values are applied. After the calculation of the model approximation the values shown for radii and numerical eccentricity are slightly different from the starting values. R=7.971 (previous: R=7.972) and e=0.452 (previous: e=0.450). The new parameters are extracted again from the two-dimensional data set. The said differences therefore demonstrate the accuracy of the approximation. Also the deviation of the model approximation from the raw data can be quantified exactly. To demonstrate this, first the DEMO topography has to be loaded again. Choose the DEMO topography by clicking to Cornea Files, then select (ok) and load (ok once again) it. Then click to Diff. to Model. Now choose R1,R2,alpha,e. The result of the comparison is the difference between the original data and the model, displayed in pseudocolors. The difference can be alternatively given in height (mm) or refraction (dpt) units. If Height is selected, the maximum difference at the margin is ±0.011mm or 11μm. The additional information "RMS (r < 3.0mm):0.00165" shows that the root mean square difference is 1.65μm inside a central circle of 3mm radius.

Lasik / PRK

Choose the DEMO topography by clicking to Cornea Files, then select (ok) and load (ok once again) it. Then click to Lasik/PRK. The paraxial ("old") refraction is 0.942dpt, provided, the data of the standard IOL have not been changed. We start with a myopic correction and therefore we enter -3.0 for the old refraction. All other parameters should remain unchanged for simplicity reasons, therefore: ok. The program now askes whether spherical aberration is to be minimised. This is the default procedure. The corneal asphericity is adapted to the IOL data resulting in a total spherical aberration close to zero. Select this default (ok). After that, the slightly oval ablation profile is displayed in pseudocolors. A little window opens in the upper left corner in which the name of the "shot-file" can be entered. If such a name is entered, a new window opens to select the laser type. In our example, nothing should be entered, i.e.: ok. After that we are asked if the ablation profile has to be ablated from the cornea (in the computer) or not. Click to ablate. The procedure can be performed exactly or with errors in order to demonstrate their influence on the result. We choose exactly. Now the topographic map is replaced by the corresponding map after laser ablation. Also corneal thickness is replaced by the modified two-dimensional profile (but not indicated). The quality of the result can be checked in two different ways. First click to 2-Dim. Opt. Error, then meridional refr. and user-defined for the pseudocolors. Enter 0.2 for the upper and -0.2 for the lower threshold. The pseudocolor map shows that the major part of the optical zone is very close to 0.0. If you exit from the corneal module by STOP and click to Retinal Image, you can generate a Landolt’s ring which is recognizable also for a pupil width of 4.0 and a size corresponding to a visual acuity of 2.0 (20/10), provided the spherical prescription glass has been set to the target refraction (eagle’s eye). To do so, click to Image param. and then enter the said values. In the same sense an hyperopic correction can be simulated by entering e.g. +3.0 as the old refraction, starting from the same values as for the myopic correction. Even if the results seem to be ideal, the ablation profile should not be calculated in the described manner. The laser ablation can never be exe- 34 cuted with the same precision as the calculation. Therefore, high-frequency errors would not be corrected at their location in the topography, but always slightly shifted. This in fact amplifies the high-frequency errors at the current state of the laser technology. However, the problem can be solved if the measured topography is replaced by the "corneal model" (see previous section). This does not contain any high-frequency errors. Therefore, they are smoothed out. To quantify the influence of decentration errors in corneal refractive surgery it is suggested to start from a very simple case. First click to Ray Diagram, then to Default Values and STOP in order to reset all parameters. Alternatively, OKULIX has to be closed (STOP) and started again. Then click to Cornea and Model Cornea and R1, R2, alpha, e. Enter 7.2 for R1 and R2 to create a spherical cornea and a myopic eye, then click to Lasik/PRK. The "old" refraction now is -3.276dpt. The target refraction should be zero, therefore click to ok to accept all parameters. Minimize spherical aberration: ok. Also for the shot file only click to ok, after that to ablate, this time with errors. Enter 0.3 for the decentration in x- and the same value for the y-direction. The resulting topography therefore is shifted to the upper right direction. The refraction error is interesting: 2-Dim. Opt. Error, then meridional refr. and user-defined. Enter +2.0 for the upper and -2.0 for the lower threshold. The area in which emmetropia is achieved is much more decentrated to the upper right than by the length of the decentration vector. The whole lower left area is hyperopic. If the visual impression is simulated by STOP and Retinal image, a large halo appears at the upper right, corresponding to a so-called coma error due to the decentration. The visual impression can be only marginally improved by prescription glasses. Hyperopic spherocylindrical glasses with the minus cylinder axis in the decentration direction give the best correction, e.g. (+0.5/-0.5/45°) or (+1.0/-1.0/45°). The same example should be calculated for a pure spherical laser ablation. The default setting "Minimize spher. Aberration" has to be disabled by clicking to the corresponding radio button, and the numerical eccentricity in the next window has to be zero. The result is much better, as can be seen again with the refraction map and the simulated Landolt’s ring.