Magnification Characteristic of a +90-Diopter Double-Aspheric Fundus Examination Lens

Abstract

purpose. To investigate the magnification characteristic of the +90-D double-aspheric fundus examination lens for biomicroscopic measurement of the optic disc.

methods. A calibrated Gullstrand-type model eye adjusted for axial ametropia between −12.5 and +12.6 D was used to measure the change in magnification of the system with refractive error and variation in fundus lens position. A correction factor p (in degrees per millimeter) at different axial ametropias was also calculated.

results. The total change in magnification of the system from myopia to hyperopia was −15.1% to +13.7%. When the fundus lens position was altered with respect to the model eye by ±2 mm under myopic conditions, the change in magnification of the system was −4.8% to +8.1%. In the hyperopic condition the change was −4.8% to +6.0%. The fundus lens exhibited a linear relationship between p and the degree of ametropia of the model eye and a constant relationship between p and ametropia of −5 to +5 D.

conclusions. Axial ametropia has a significant effect on biomicroscopic measurement of the optic disc with the +90-D lens. Therefore, a correction factor (p) was calculated that can be used in calculations for determining true optic disc size. These findings may be important for improving clinical disc biometry.

Determining the actual size of the optic disc is possible by histopathologic study, magnification-corrected photogrammetry, scanning laser ophthalmoscopy, or use of the interference fringe scale. ^{1 2 3 4} However, the aforementioned methods are not applicable in a routine clinical setting. Measurement of the optic nerve head is usually performed at the slit lamp biomicroscope using an auxiliary lens to overcome the high focal convergence of the examined eye. 

In this study, we investigated the magnification characteristic of a +90-D fundus examination lens over a wide range of ametropia in the center of the image field. 

Materials and Methods

A commercially available +90-D double-aspheric fundus lens (Volk Opticals, Mentor, OH) and a calibrated slit lamp biomicroscope with adjustable beam length (model 900; Haag-Streit, Bern-Koeniz, Switzerland) were used for this study. 

It is well known that the calculation of the true size of an object in the ocular fundus depends on the knowledge of the refraction, corneal curvature, and axial length of the eye (correction factor q, in millimeters per degree) ^{1 5 6} ; the magnification of the instrumentation used to obtain the image (correction factor p, in degrees per millimeter) ⁷ ; and the position of the instrumentation with respect to the eye. Thus, for calculating the true size of the optic disc, the total magnification of the system must be known. 

To measure the change in magnification of the system with refractive error and variation in condensing lens position, a curved scale in the form of concentric half circles was fitted with the help of an excimer laser in the center of the artificial fundus surface of a calibrated Gullstrand-type model eye. This scale has to be curved, because the optics of the slit lamp biomicroscope and fundus lens are designed for use with a curved field, so that a flat scale is only approximate to the retina in practice. An image of the scale has recently been published. ⁸  

Distilled water, which has a refractive index similar to that of the media in the eye (1.336) was introduced in the anterior and vitreous chambers. In this situation, the equivalent power of the model eye is +59.4 D. By means of a screw ruled in micrometers, the vitreous chamber depth can be precisely varied to produce axial ametropia. 

The fundus object was viewed with the fundus lens as in a routine examination of the optic nerve head. The instruments were aligned perpendicularly to the model eye’s cornea, and the fundus object was brought into focus by moving the biomicroscope away from the condensing lens until a sharp image of the fundus object was provided in the center of view. Figure 1 shows the optical diagram of the experimental setup. 

A narrow slit beam, with width maintained at 0.2 mm, was progressively reduced in size from 8 mm until it coincided with the diameter of the smallest half circle, which has a true size of 4 mm. The beam length was then recorded, by the second observer, from the millimeter scale at the top of the instrument. Because the slit lamp beam length is calibrated in 0.1 mm, the reading was judged to the nearest 0.05 mm. After each reading, the millimeter scale was reset to 8 mm. 

Measurements were taken with the vitreous depth of the model eye set at a range of ocular refractions from −12.5 to +12.6 D. The pupil diameter was 8.0 mm. At each ametropia setting, three measurements were obtained. 

By dividing the measured length by four, we obtained the actual magnification of the fundus image at the different axial ametropia settings, and by the formula p = (k/17.453)(t/s), where k is the ametropia of the eye + equivalent power of the eye, t is the fundus object size (4 mm), and s is its measured size on the slit lamp biomicroscope, we calculated the fundus lens correction factor p. ⁷  

Measurements were repeated at a separate session, and the 95% confidence interval for repeatability was calculated. ⁹  

To investigate the change in magnification of the system and the correction factor p with variation in condensing lens position, measurements of the fundus object size were obtained as described when the fundus lens position was altered by ±2 mm relative to the model eye’s cornea under myopic and hyperopic conditions. 

Results

Figure 2 shows the total change in magnification of the system. The minimum magnification was −0.62× and the maximum −0.83×. The minus sign indicates an inverted image. The change in magnification therefore was −15.1% for myopia and +13.7% for hyperopia. 

Figure 3 shows the change in magnification of the system when the lens position was altered ±2 mm relative to the model eye’s cornea. The magnification of the system was −0.59× when the condensing lens was too close and −0.67× when the lens was too far away from the eye under myopic conditions. The change in magnification was −0.88× when too close and −0.79× when too far away under hyperopic conditions. In practice, this degree of error should not arise if the operator is careful when positioning the condensing lens, but it serves to demonstrate the possible error caused by incorrect lens positioning when large refractive errors are present. 

Figure 4 shows the determined values of correction factor p. The value of p is constant from −5 to +5 D. In the presence of a high refractive error, the fundus lens shows a linear relationship between correction factor p and ametropia, which can be determined from linear regression analysis. The corresponding mean value of p and the equation of the regression line to the results in Figure 4 are given in Table 1 . The regression line equation gives an estimate of the value of p for any degree of ametropia. 

Figure 5 shows the change in correction factor p (in degrees per millimeter) when the lens position was altered by ±2 mm to the model eye’s cornea. The factor p was 4.58 when the condensing lens was too close and 3.98 when the lens was too far away from the eye under myopic conditions. The change in factor p was 4.71 when too close and 5.24 when too far away under hyperopic conditions. 

The 95% confidence interval for repeated measurements is from +4.25% to −4.71%. This is expressed as a percentage of the image size and is within acceptable limits. 

Discussion

The results of our study indicate that the magnification of the fundus image obtained by the +90-D lens is markedly influenced by axial ametropia and by the position of the fundus lens in front of the examined eye (Figs. 2 3) . These variations in the magnification property of the system are so marked that the application of a single magnification correction factor may not be appropriate for accurate assessment of the size of structures of the posterior fundus. 

Thus, appropriate corrections for the parameters of the eye involved and the instruments used are essential in calculating the absolute dimensions of the optic nerve head from its image size. A standard technique for calculating the true optic disc size has been devised by Littmann. ^{1 5} Littmann expressed the relationship between the size t of an optic disc and the corresponding size s of its image by the formula t = pqs in which the ocular factor q is a variable specific to the examined eye. Several methods are available for determining q for a human eye within ±20° of the optical axis, based on ametropia and keratometry, ^{1 5} ametropia and axial length, ^{1 5} and axial length only. ⁶  

The factor p refers to the instrumentation used to obtain the image. Because the factor p remains unchanged for axial and refractive ametropias of the same degree, ¹⁰ the Gullstrand-type model eye used for our study had a fixed corneal curvature and power of the intraocular lens, providing a model for ametropia only by varying the axial length of the model eye. Furthermore, the axial length is the most important factor for the change of the magnification due to ametropia. ⁶ The change in magnification recorded in our setup is therefore most likely the maximum deviation to be expected in vivo, where a wide variation of the crystalline lens and the total axial length provide the refractive status of the patient’s eye. 

Ophthalmologists can determine p for the +90-D lens from Table 1 . In practice, it is important that the slit lamp and condensing lens be aligned correctly in front of the patient’s cornea and the optic disc be centered in the image field to maximize the repeatability of the experimental setup. 

The +90-D lens exhibited a linear relationship between p and degree of ametropia of the model eye and a constant relationship between p and ametropia of −5 to +5 D. As far as we are aware, this has not been reported previously for the +90-D lens. It means that the +90-D lens and the slit lamp biomicroscope build a pure telecentric device only for an ametropic range of −5 to +5 D. The reason for this lies in the difficulty of coinciding the focal plane of the condensing lens with the first principal plane of the eye in the presence of a high refractive error. It means that in a normal clinical setting at the slit lamp biomicroscope with the +90-D lens in the presence of a high refractive error, the image obtained may appear to be focused adequately to make a measurement with the slit beam, when in fact the focal plane of the condensing lens is not exactly at the first principal plane of the examined eye. 

The factor p of the 90-D lens may be useful in calculating the true optic disc size, without recourse to expensive technology. ^{1 2 3 4} Furthermore, it makes optic disc measurements obtained by the +90-D lens comparable with biomicroscopic measurements obtained by other high-power positive lenses. ¹¹ This would be of particular importance when comparing the morphometric characteristics of the optic nerve head between individuals with regard to diagnosis and therapy. 

 Submitted for publication October 26, 2001; revised January 24, 2002; accepted February 8, 2002.

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Figure 1.

 

Optical diagram of the experimental setup. The scale on the fundus is imaged between the condensing lens and the biomicroscope’s head and is real and inverted.

Figure 2.

 

The change in magnification plotted against ocular refraction for the 90-D lens.

Figure 3.

 

The change in magnification for the 90-D lens with variation of distance between condensing lens and model eye in the presence of a high refractive error. Solid symbols: myopic condition; open symbols: hyperopic condition.

Figure 4.

 

Value of correction factor p plotted against ocular refraction for the 90-D lens.

Table 1.

 

Values and Equation of Regression Line of Correction Factor p for the 90-D lens, by Slit Lamp Biomicroscopy

Range of Ocular Refraction Investigated (D)	Factor p (deg/mm)	Range of Factor p (deg/mm)
−5 to +5	4.64 ± 0.02 (mean± SD)	4.61–4.69
−12.5 to+12.6	0.025 A+ 4.66	4.30–5.00

 A, Ametropia of the examined eye; it can be calculated from F _s/(1−0.001vF _s), where v is the vertex distance (positive) from the back surface of the spectacle correction of power F _s to the cornea. 95% confidence interval for repeated measurements of the image size = +4.25% to −4.71%.

Figure 5.

 

The change in correction factor p for the 90-D lens with variation of distance between condensing lens and model eye in the presence of a high refractive error. Solid symbols: myopic condition; open symbols: hyperopic condition.

The authors thank Bernhard Rassow of the Medical Optics Laboratory, University of Hamburg, Germany, for providing the model eye.