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The development of different materials suitable for manufacturing spectacle lenses has presented the dispensing optician with a problem: how can materials be identified? Whereas glass and plastics materials are easily distinguishable, any further classification is difficult without more detailed examination.
Knowledge of the refractive index of a spectacle lens is desirable:
- Where spectacles are to be replicated
- Following a change in prescription, where the same refractive index is to be dispensed and no record is available of the original
- Where only one lens is to be replaced
- As part of the general verification process.
It is possible to estimate the refractive index of a spectacle lens by using equipment readily available in any optical practice. This article looks at the accuracy of two methods.
Methods
It was decided to compare two methods, both of which would only require basic equipment, and for students to carry out the tests. Those selected were distance learning students currently employed full time in an optical practice.
Method 1
Six glass ophthalmic lenses were selected for testing and were randomly lettered A to F. All were negative lenses of spherical power. A telescope focimeter was used to find the back vertex power, recorded as FF on the results sheet. All focimeters were of the same design and the eyepieces adjusted by each student as required. A lens measure was then carefully placed on each surface to determine the surface powers and these were recorded as F1 and F2. The addition of the two surface powers was recorded as FL.
The lens measures used were of the same pattern and zero checked using a plane mirror. They were all calibrated for use on material of refractive index 1.523. The curve variation factor (CVF) was calculated by dividing FL by FF. The refractive index (nlens ) was then found by working through the expression:
nlens = 0.523 + CVF
CVF
derived from the well known formula:
nlens = 1+ (0.523 x Fv')
(F1 + F2 )
Method 2
It is not uncommon in practice to use the approximate sag formula
s = y2F
2000(n - 1)
to determine the finished edge thickness of a lens. The greatest distance from the position of the optical centre of the lens to the inside rim of the frame, or the edge of the lens, gives the value for y. With a known refractive index and lens power the sag can be determined. In the case of a minus lens the sag value is added to the known centre substance to give the maximum edge thickness. By re-arranging the equation to make n the subject and measuring the edge and centre substance, the value of the refractive index may be determined.
A telescope focimeter was used to find the back vertex power in the same way as for method 1 (FF) and the optical centre of the lens located by an inked dot. Lens thickness calipers were then used to find the thickness of the lens at the optical centre. Referring to Figures 1 and 2, this value was recorded as t. All the calipers were of the same design and the distance between the points tested for accuracy. A point either at or towards the periphery of the lens was then located and the distance measured from the point to the optical centre (y). The calipers were then used to find the thickness of the lens at the chosen point (e). The value s was found by deducting t from e. This represents the sag of a surface. Ignoring the form in which the lens was made, it was now possible to calculate the refractive index of the lens using the following expression derived from the approximate sag formula:
nlens = 1 + y2F
2000s
Twenty students were issued with instructions on the use of the equipment provided. Each student then applied methods 1 and 2 on each of the six lenses following the sequence outlined on each instruction sheet.
Instruction sheet for refractive index estimation
Method 1: using focimeter and lens measure.
- Use the focimeter to find the back vertex power of the lens [FF]
- Carefully place the lens measure perpendicular to each surface in turn to find the surface powers. [F1 and F2]
- Apply F1 + F2 = F to find the addition of the surface powers [FL]
- Divide FL by FF to find the curve variation factor [CVF]
- Calculate the refractive index of the lens [nlens] by working through the expression:
nlens = 0.523 + CVF
CVF
Instruction sheet for refractive index estimation
Method 2: using focimeter and thickness calipers.
- Use the focimeter to find the back vertex power of the lens [FF]
- Dot the optical centre of the lens
- Use thickness calipers to find the thickness of the lens at the optical centre [t]
- Locate any point at the lens periphery
- Measure the distance from the optical centre to the point at the periphery [y]
- Use thickness calipers to carefully measure the edge thickness at the point at the periphery [e]
- Deduct t from e [s]
- Calculate the refractive index of the lens [nlens] by working through the expression:
nlens = 1 + y2F
2000s
Abbreviations used in instruction sheets
FF Power found by focimetry (BVP)
F1 Front surface power found by lens measure
F2 Back surface power found by lens measure
FL The addition of F1 and F2
CVF Curve variation factor, FL/FF
n Refractive index
t Centre thickness of spectacle lens
y Distance from optical centre to where edge thickness measured
e Edge thickness, or thickness at the value y
s Sag assuming a plano-concave form.
Results
The measurements were recorded by each student using both methods. From the measurements, calculations were carried out to determine the refractive index of each lens.
The average value of refractive index from the 20 results obtained for each lens was also determined.
The results are illustrated in Figure 3. The vertical scale represents the refractive index found and the horizontal scale the test number for both methods
The correct value for each lens is quoted in Table 1 below for the helium d-line for a wavelength of 587.56nm.
Discussion
Limitations of equipment
Accurate readings of surface powers using a lens measure can only be obtained if the instrument is held perpendicular to the lens surface. If this method were to be used in practice on plastics lenses, great care would be needed to avoid scratching or damage to an anti-reflection coating. This would be especially important where the surface under test was toroidal and the points of contact of the instrument have to be aligned along a principal meridian.
When using calipers it is critical that the thickness of the lens is accurately recorded for any specific value of y. Positioning the caliper jaws at the periphery of the lens is therefore preferable, although care must be taken if a glazing bevel extends to the edge of the lens, or a safety chamfer has been used.
Limitations of form
In method 1, as negative lenses were used, it was assumed that the algebraic sum of the surface powers was equal to the total power as found by the lens measure and that there was no surface power compensation for thickness.
In method 2, the approximate sag formula was used to calculate the value of n. The radius of curvature would be required to use the accurate formula and a spherometer to measure the surface. This instrument cannot be used on toroidal surfaces so is not used in dispensing. Although a more accurate sag measurement would be obtained if the accurate formula s = r - v(r2 - y2) was employed, it should be apparent from r = (n-1) / F that without a spherometer, r may only be determined if the refractive index is already known.
By using the approximate formula the form of the lens can be ignored so a plano-concave lens was assumed for calculation purposes.
It is not appropriate to estimate the refractive index of positive lenses by either method. Thin lens theory, where the surface power F1 is combined with that of F2, cannot be applied when the lens thickness requires surface power compensation to achieve the required lens power.
With aspheric surfaces the sag is not constant across the whole surface so it is not practicable to use thickness calipers or a lens measure to help determine the refractive index in practice. With the increasing use of aspherical surfaces even on lower powered lenses, neither method is therefore reliable.
How accurate should the estimation be?
In practice, it is necessary to know whether a lens is 1.498 (standard CR39), 1.53 (Trivex), 1.537 (Spectralite), 1.560, 1.586 (polycarbonate), 1.60, 1.67, 1.70 or 1.74 for plastics materials and 1.523, 1.60, 1.701, 1.802 or 1.885 for glass. The average difference between these indices is 0.03 for plastics and 0.09 for glass, so any method used to estimate the value should be accurate by this amount.
Table 2 looks at the number of significant errors where an incorrect refractive index would have been assumed, due to the calculated value being outside the 0.09 tolerance value.
The lens measure method produced 23 (19 per cent) false results, ie the wrong material was identified. For the caliper method, nine (7.5 per cent) were false.
Although the tests were carried out on glass lenses, it is informative to apply the tolerance for plastics materials (0.03) to the results. False results are 54 per cent for the lens measure and 36 per cent for calipers.
Factors affecting accuracy of refractive index results
We have seen above that any method of determining the refractive index of a lens material must give results to an accuracy of 0.03 for plastics and 0.09 for glass. It was important therefore to look at how any error in the measurements for either method would affect this accuracy.
The lens measure dial is calibrated so that surface powers may only be recorded to the nearest 0.25D. It is therefore apparent that a combination of three measurements per surface within these tolerances is possible.
Taking an example of a -8.00DS lens of refractive index 1.701, accurate F1 and F2 lens measure readings of +2.00DS and -8.00DS respectively would be expected. Compounding 0.25D F1 and F2 differences from the expected readings would give an error in the refractive index value of 0.06: twice that of the acceptable tolerance for plastic.
A further issue with this method can be illustrated whereby a correct value of refractive index may be obtained despite both F1 and F2 readings being 0.25D greater or lesser than the correct powers eg +2.25DS and -8.25DS or +1.75DS and -7.75DS.
With the caliper method measurements were recorded to the nearest millimetre.
For a given power, any error in the measurement of the semi aperture of the lens (y) will produce an error in the value of the refractive index. Errors when using smaller y values would give correspondingly greater errors in refractive index results. Again using a -8.00DS lens of known refractive index 1.701 a 1mm error on a y value of 25mm is 0.07. Increasing the y value to 35mm with the same 1mm error reduces the refractive index error to 0.04.
The centre thickness of the lenses was determined also with the use of calipers. The sag value, which is found by deducting the centre thickness from the thickness at the distance y from the optical centre, has only to change by 0.5mm for the refractive index error to be significant. With the above lens and using a y value of 32mm, an accurate refractive index measurement is obtained with a sag of 5.85mm. Table 3 shows that a deviation in this sag measurement of just 0.55mm can produce a refractive index error of over 0.07.
Conclusion
Plastics lenses currently account for more than 90 per cent of single-vision lens usage in the UK. Using the lens measure method is likely to produce an error in just over half the lenses tested and using calipers, in just over one third.
From the results of the tests carried out, the investigation into tolerances and possible errors and problems in collecting data, it seems unlikely therefore that either method could be used safely and with sufficient accuracy in practice.
A possible solution
Why not have engravings on single-vision lenses? Manufacturers of progressive power lenses provide trade marks and other data by means of permanent engravings so that lenses can be readily identified. If the same system was employed for all lens materials and types, there would be no need to estimate or calculate the refractive index. ?
Acknowledgements
Norville Optical Group for supplying the test lenses.
Additional reading
Essentials of Dispensing, Tunnacliffe AH. ABDO 2nd ed 1998.
Principles of Ophthalmic Lenses, Jalie M. ABDO 5th ed 1988.
Materials for Spectacle Lenses, Jalie M. Optometry Today, Jan 28, 2005.
? Andrew Cripps and Paul McCarthy are senior lecturers in the Department of Optometry and Ophthalmic Dispensing, Science and Technology, Anglia Ruskin University and Vision and Eye Research Unit, Postgraduate Medical Institute, Anglia Ruskin University
