Toric Contact Lens Fitting

Fitting Rigid Toric Lenses

Indications for the use of rigid toric lenses

Rigid toric lenses are indicated in preference to rigid spherical lenses under the following circumstances:

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to improve vision in cases where a lens employing spherical front and back optic zone radii is unable to provide adequate refractive correction
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to improve the physical fit where a lens with a spherical back optic zone radius (BOZR) and spherical back peripheral zone radii fails to provide an adequate physical fit.

These two situations are not always distinct, and a toric lens may be used for both physical and optical reasons. For example, when fitting an eye with both a high degree of residual astigmatism and a large amount of corneal toricity, a toric lens is required optically, to correct the residual astigmatism, and physically, to optimise the lens fit ( ).

Forms of Rigid Toric Lens

Rigid toric corneal lenses, most commonly with a toroidal back optic zone and peripheral zone, are generally used to obtain a good physical fit on a cornea that is too toroidal to allow a good fit with a completely spherical lens. There are several varieties of these lenses:

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Toroidal back surface with a spherical front optic surface.
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Bitoric construction – toroidal back surface with a toroidal front surface.
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Oblique bitoric construction – the principal meridians are not parallel.
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Toric periphery – a spherical back optic zone and a toroidal peripheral zone, used in an attempt to improve the physical fit of a lens on an astigmatic cornea, while avoiding the optical complications inherent in lenses with toroidal back optic zones (this form of lens can also be produced with a toroidal front surface).
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Occasionally, a lens is produced with a toroidal back optic zone and a spherical peripheral zone, with the intention of improving the circulation of tears beneath the lens. However, this can cause the lens to become less stable to resisting rotation. One limitation on the spherical peripheral radii is that they have to be greater than or equal to the flatter radius for the preceding toroidal curve (this form of lens can be made with or without a toroidal front surface).
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A spherical back optic zone and spherical peripheral zone combined with a toroidal front optic surface. This type of lens is required where there is significant residual (noncorneal) astigmatism but minimal corneal astigmatism. The residual astigmatism needs to be corrected with a toroidal front surface and a spherical back optic zone due to the negligible corneal astigmatism. Some form of orientation mechanism will, of course, be required such as prism ballast or truncation (see later). Note: These are rarely used, as a toric soft lens is usually the preferred option.

Criteria for Use of Rigid Toric Lenses

Corneal lenses with both spherical BOZR and peripheral radii are often successful on corneas with varying degrees of astigmatism. It is important, therefore, to decide what degree of corneal astigmatism should indicate the use of toroidal back optic zones. In general, these should be used only when a lens with a spherical BOZR cannot be made to fit successfully. It is rare to find that toroidal back optic zones are necessary unless the corneal astigmatism exceeds 2.0–2.50 D (i.e. the difference in the corneal radii, as measured with a keratometer, exceeds approximately 0.4–0.5 mm).

In cases of uncertainty (e.g. where the corneal astigmatism is between 1.50 and 2.50 D), a toroidal back optic zone would be used in preference to a spherical back surface curve when:

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A spherical lens exhibits poor centration or excessive movement.
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Excessive lens flexure is noted with a spherical lens.
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Fluorescein patterns with a spherical lens reveal excessive bearing along the flatter corneal meridian, regardless of what BOZR is fitted.
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Significant 3 and 9 o'clock staining occurs with a spherical lens.
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There is marked corneal distortion and spectacle blur on lens removal. This occurs as a result of poor alignment between the spherical lens and the toric cornea, with the spherical lens subsequently having a moulding effect on the toric cornea.
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There is significant residual astigmatism. In this case, a spherical back surface may provide an adequate fit, but a toric back surface will stabilise the lens, prevent rotation, and allow correction of the residual astigmatism.

Other factors can also affect the decision:

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Lid positions and tension
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  With a high degree of with-the-rule corneal astigmatism and a low, loose lower lid, a toroidal back optic zone may be needed to obtain a good physical fit and centration.
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  With a firm, high lower lid, a spherical lens may well be successful.
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With-the-rule corneal astigmatism (steeper axis vertical)
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  A spherical BOZR may exhibit heavy bearing along the flatter (horizontal) meridian of the cornea and poor centration ( Fig. 11.1 ), causing physical discomfort and/or poor vision.
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  A toroidal back optic and peripheral curves will improve the physical fit and centration ( Fig. 11.2 ).
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Against-the-rule corneal astigmatism (steeper axis horizontal) usually necessitates fitting a toroidal back optic zone earlier than with an equivalent amount of with-the-rule corneal astigmatism, as rigid spherical lenses tend to decentre laterally even with moderate amounts of against-the-rule astigmatism (1.50–2.00 D).

Design Considerations

Toroidal back optic zone lenses should be fitted on or near alignment.

Key Point

FACT: The fluorescein pattern will be similar to that seen with a well-fitted spherical lens on a spherical cornea (see Fig. 11.2).
A toric lens aligning too closely to the cornea can lead to poor tear interchange.
FACT: Consequently, it is advisable to use a toroidal back optic zone with the steeper radius fitted slightly flatter (longer radius) than the corresponding corneal radius so as to assist the interchange of tears. The flatter radius will generally be fitted ‘on K‘ or else a little steeper than its corresponding corneal radius.

Example 1 Toric lens

\begin{matrix} Keratometry reading : 7.90 mm (42.72 D) along 180 \\ 7.35 mm (45.91 D) along 90 \\ Prescribed lens : \\ C 3 Toric / \frac{7.85}{7.40} : 7.50 / \frac{8.45}{8.00} : 8.50 / \frac{9.25}{8.80} : 9.50 \end{matrix}

$\begin{matrix} Keratometry reading : 7.90 mm (42.72 D) along 180 \\ 7.35 mm (45.91 D) along 90 \\ Prescribed lens : \\ C 3 Toric / \frac{7.85}{7.40} : 7.50 / \frac{8.45}{8.00} : 8.50 / \frac{9.25}{8.80} : 9.50 \end{matrix}$

Many practitioners use spherical trial lenses when fitting rigid toric lenses. However, even a limited set of diagnostic fitting lenses with both toroidal back optic and peripheral curves can be extremely valuable. A suggestion for a minimum set is one covering the range 7.50 × 7.00 mm to 8.50 × 8.00 mm BOZR in 0.1 mm increments in both meridians.

The BOZR should be chosen with at least 0.3 mm (1.50 D) meridional difference in radii; otherwise the toroidal BOZR may not position properly on the toroidal cornea, leading to lens rotation and possible visual disturbance. ¹

1 BOZR indicates back optic zone radius for a spherical surface and back optic zone radii for a toroidal surface.

Each meridian is considered separately, and the peripheral fittings in the two principal meridians are selected to provide the same difference between back optic and peripheral radii most commonly used by the practitioner in fitting spherical corneas. The peripheral curves usually have the same degree of toricity as the BOZR.

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For example, if the back peripheral radius (BPR) is 0.9 mm flatter than the BOZR for a spherical lens, then for a lens with toroidal BOZR of 7.90/7.40, the BPR ordered would be 8.80/8.30. The same will apply to any subsequent radii.

For lenses with a spherical back optic zone and a toroidal peripheral zone, the width of the peripheral curve should be as large as possible to increase the likelihood of alignment with the toric cornea. The meridional difference in the peripheral curves should be at least 0.6 mm to help minimise lens rotation ( ), and the total diameter (TD) should be small to help minimise meridional sag differences. They are fitted steeper centrally than the flatter corneal meridian to achieve a compromise fit.

Example 2: Toric Periphery

\begin{matrix} Keratometry reading : 7.90 mm (42.72 D) along 180 \\ 7.30 mm (46.23 D) along 90 \\ BOZR chosen : 7.70 mm \\ BOZD chosen : 6.50 mm \\ TD chosen : 9.50 mm \\ Prescribed lens : \\ C 4 / 7.70 : 650 / \frac{8.50}{7.90} : 7.50 / \frac{9.20}{8.60} : 8.50 / \frac{10.00}{9.40} : 9.50 \end{matrix}

$\begin{matrix} Keratometry reading : 7.90 mm (42.72 D) along 180 \\ 7.30 mm (46.23 D) along 90 \\ BOZR chosen : 7.70 mm \\ BOZD chosen : 6.50 mm \\ TD chosen : 9.50 mm \\ Prescribed lens : \\ C 4 / 7.70 : 650 / \frac{8.50}{7.90} : 7.50 / \frac{9.20}{8.60} : 8.50 / \frac{10.00}{9.40} : 9.50 \end{matrix}$

This type of lens is likely to fit poorly on this amount of corneal astigmatism, and the toroidal peripheral zones are, at best, a compromise. They usually rotate more than lenses with all-toroidal back surfaces, and the steeper peripheral radii occasionally end up in close proximity to the flatter corneal meridian, causing problems.

It is possible to see if the lens is rotating by observing the peripheral fluorescein fit. It may be helpful to have the flatter or steeper peripheral meridian marked with two dots or lines, one at each edge of the lens. Two dots are more useful than one for this purpose.

Lenses with spherical back optic zones and toroidal peripheral zones can also be used in keratoconic eyes to enhance lens centration and eradicate inferior lens standoff, and will often stabilise reasonably well as the BPR1 is the main bearing surface (see Chapter 20 ).

Optical Considerations (see also Chapter 7 )

The complexity of calculations to determine the necessary radii and power of toric lenses is often exaggerated. However, the fundamentals of the optics of contact lenses must be understood to appreciate some of the complications ( ).

Corneal astigmatism and the effect of the tear lens

Front surface corneal astigmatism is only partly neutralised by the back surface astigmatism of the resultant tear lens when a rigid lens with spherical back surface is placed on the eye. The refractive index (RI) of tears is 1.336, whereas that of the cornea is 1.376. The amount neutralised is thus 336/376, almost 90%. It is assumed that the back surface of the cornea neutralises the remaining 10% of its front surface astigmatism, and the RI of calibration of most keratometers (1.3375) is chosen to take this effect into account. This gives the user a guide to the total refractive effect of the cornea. Hence, keratometers measure front surface corneal radii but give total corneal power on the assumption that the back surface has −10% of the power of the front surface.

Key Point

The RI of 1.3375 is very close to that of the tears (1.336). Thus the corneal astigmatism measured with the keratometer should be completely corrected by the tear lens between the cornea and contact lens, provided the back of the contact lens is spherical.

Refraction with toroidal back optic zones

Calculating the back vertex powers (BVPs) for a rigid lens with a toroidal back optic zone is more complex than determining the BVP for a spherical lens, yet the two processes involve the same basic principles. For spherical lenses:

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Contact lens power in air plus tear lens power in air should add up to the ocular refraction.
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With toric lenses, the same rule applies, but here the two separate meridians must each be considered.

Example 3: Calculating the BVP for a Rigid Lens With a Toroidal Back Optic Zone

Spectacle refraction (vertex distance ignored): +2.50/−3.00 × 180.

(Note: The effect of the vertex distance must be taken into account if this distance is great or if the refractive power in either meridian exceeds 4.00 D.)

\begin{matrix} Keratometry reading : 8.04 mm (42.00 D) along 180 \\ 7.50 mm (45.00 D) along 90 \end{matrix}

$\begin{matrix} Keratometry reading : 8.04 mm (42.00 D) along 180 \\ 7.50 mm (45.00 D) along 90 \end{matrix}$

A rigid spherical trial lens with BOZR 7.95 mm and BVP +1.00 D is placed on the cornea. Refraction with this lens in situ gives +1.00DS (no residual astigmatism) and 6/6 (0.0 logMAR) acuity. (Note: The over-refraction is best performed over a spherical trial lens aligned along the flattest meridian of the cornea, and only one over-refraction is required to calculate both BVPs.)

Based on the keratometry readings, BOZR of 8.00 and 7.55 mm are chosen to fit the horizontal and vertical meridians, respectively, and the BVP of the two meridians of the contact lens (BVP _CL ) are determined with a rigid spherical trial lens, except that two meridians need to be considered instead of one.

{BVP}_{CL} = {BVP}_{trial} + OR

${BVP}_{CL} = {BVP}_{trial} + OR$

where BVP _trial = BVP of the trial lens along each meridian and OR = over-refraction.

For a spherical lens, if the BOZR of the trial lens is different from the BOZR to be ordered, the change in resultant tear lens power must be considered.

Based on a tear lens RI of 1.336, this change in tear lens power is given by the formula:

(\frac{336}{{BOZR}_{final}} - \frac{336}{{BOZR}_{trial}})

$(\frac{336}{{BOZR}_{final}} - \frac{336}{{BOZR}_{trial}})$

where BOZR _final is the BOZR of the lens to be ordered and BOZR _trial is the BOZR of the trial lens. Thus the useful rule of thumb is:

Key Point

For every 0.05 mm that the BOZR is flattened, approximately +0.25 D must be added to the BVP of the contact lens.
Likewise, for every 0.05 mm that the BOZR is steepened, approximately −0.25 D must be added to the BVP of the contact lens.

This approximation holds for only relatively small differences in BOZR; if in doubt, it is safer to use the above formula.

The BVP that needs to be ordered (BVPCL) when calculated in full is then:

{BVP}_{CL} = {BVP}_{trial} + OR - (\frac{336}{{BOZR}_{final}} - \frac{336}{{BOZR}_{trial}})

${BVP}_{CL} = {BVP}_{trial} + OR - (\frac{336}{{BOZR}_{final}} - \frac{336}{{BOZR}_{trial}})$

There will also be a change to the trial lens BOZR in at least one meridian. In this example, the back optic zone radii to be ordered are both different from the trial lens BOZR, and so it will be necessary to allow for the change in tear lens power in both meridians. Note: Calculations are for power at each meridian; power is at 90° to the axis.

\begin{matrix} Along 180 : {BVP}_{CL} = + 1.00 + 1.00 - (\frac{336}{8.00} - \frac{336}{7.95}) \\ = + 2.25 D \\ Along 90 : {BVP}_{CL} = + 1.00 + 1.00 - (\frac{336}{7.55} - \frac{336}{7.95}) \\ = - 0.25 D \end{matrix}

$\begin{matrix} Along 180 : {BVP}_{CL} = + 1.00 + 1.00 - (\frac{336}{8.00} - \frac{336}{7.95}) \\ = + 2.25 D \\ Along 90 : {BVP}_{CL} = + 1.00 + 1.00 - (\frac{336}{7.55} - \frac{336}{7.95}) \\ = - 0.25 D \end{matrix}$

(When calculating BVP, round off values to the nearest 0.25 D.)

The final prescription (Rx) of lens is therefore:

BOZR 8.00 mm along 180: +2.25 D
BOZR 7.55 mm along 90: −0.25 D

Alternatively, the BVPs of the contact lens can be calculated empirically, firstly by using the required BOZR and the keratometry reading of the patient to calculate the tear lens power (BVP _tears ), and secondly by using the formula:

{BVP}_{CL} = ocular refraction - {BVP}_{tears}

${BVP}_{CL} = ocular refraction - {BVP}_{tears}$

to calculate the BVPs along both meridians.

The power of the tear lens is obtained from the following formula:

{BVP}_{tears} = (\frac{336}{BOZR} - \frac{336}{K})

${BVP}_{tears} = (\frac{336}{BOZR} - \frac{336}{K})$

where K is the corneal front surface radius of curvature (in millimetres) along that respective meridian.

Key Point

It can be approximated (for very small differences) that there is 0.25 D of tear lens power for every 0.05 mm difference between the BOZR and the corneal front surface radius of curvature.

\begin{matrix} Along 180 : {BVP}_{tears} = (\frac{336}{8.00} - \frac{336}{8.04}) ~ + 0.25 D \\ {BVP}_{CL} = + 2.50 - 0.25 = + 2.25 D \\ Along 90 : {BVP}_{tears} = (\frac{336}{7.55} - \frac{336}{7.50}) ~ - 0.25 D \\ {BVP}_{CL} = - 0.50 - (- 0.25) = - 0.25 D \end{matrix}

$\begin{matrix} Along 180 : {BVP}_{tears} = (\frac{336}{8.00} - \frac{336}{8.04}) ~ + 0.25 D \\ {BVP}_{CL} = + 2.50 - 0.25 = + 2.25 D \\ Along 90 : {BVP}_{tears} = (\frac{336}{7.55} - \frac{336}{7.50}) ~ - 0.25 D \\ {BVP}_{CL} = - 0.50 - (- 0.25) = - 0.25 D \end{matrix}$

Although the empirical method is probably simpler, more accurate results are obtained when the BVP is calculated from a refraction over a trial lens.

Residual astigmatism

Residual astigmatism is frequently confused with induced astigmatism or corneal astigmatism. Residual astigmatism has been variously defined ( ), including the simplistic definition which states that residual astigmatism is the component of the spectacle (ocular) astigmatism which is not due to the cornea.

In the context of rigid lens fitting:

Key Point

Definition: Residual astigmatism is the astigmatic component of a lens required to correct fully an eye wearing a spherical powered rigid contact lens with a spherical BOZR.

Example 4: Calculating the BVP for a Rigid Lens With a Toroidal Back Optic Zone When There Is Residual Astigmatism Present

\begin{matrix} Spectacle refraction \\ (vertex distance ignored) : + 2.50 / - 2.00 \times 180 \\ Keratometry reading : 8.04 mm (42.00 D) along 180 \\ 7.50 mm (45.00 D) along 90 \end{matrix}

$\begin{matrix} Spectacle refraction \\ (vertex distance ignored) : + 2.50 / - 2.00 \times 180 \\ Keratometry reading : 8.04 mm (42.00 D) along 180 \\ 7.50 mm (45.00 D) along 90 \end{matrix}$

A rigid spherical trial lens with BOZR 7.95 mm and BVP +1.00 D is placed on the cornea. Refraction with this lens in situ gives +2.00/−1.00 × 90 and 6/6 (0.0 logMAR) acuity.

Based on the keratometry readings, BOZR of 8.00 and 7.55 mm are chosen to fit the horizontal and vertical meridians, respectively.

In this case, the residual astigmatism is equal to −1.00DC × 90. If the patient is to be given the best possible vision, it is necessary to incorporate the correction for this residual cylinder into the BVP to be ordered.

The method for determining the BVPs is the same as used in the previous example:

\begin{matrix} Along 180 : {BVP}_{CL} = + 1.00 + 1.00 - (\frac{336}{8.00} - \frac{336}{7.95}) = + 2.25 D \\ Along 90 : {BVP}_{CL} = + 1.00 + 2.00 - (\frac{336}{7.55} - \frac{336}{7.95}) = + 0.75 D \end{matrix}

$\begin{matrix} Along 180 : {BVP}_{CL} = + 1.00 + 1.00 - (\frac{336}{8.00} - \frac{336}{7.95}) = + 2.25 D \\ Along 90 : {BVP}_{CL} = + 1.00 + 2.00 - (\frac{336}{7.55} - \frac{336}{7.95}) = + 0.75 D \end{matrix}$

( Note : The values for the over-refraction are in bold to emphasise the fact that there is residual astigmatism present in this case.)

Final Rx of the lens:

\begin{matrix} BOZR 8.00 mm along 180 : + 2.25 D \\ BOZR 7.55 mm along 90 : + 0.75 D \end{matrix}

$\begin{matrix} BOZR 8.00 mm along 180 : + 2.25 D \\ BOZR 7.55 mm along 90 : + 0.75 D \end{matrix}$

In Examples 3 and 4, the powers specified are the BVPs of the toric lens in the appropriate meridians. These are the powers read by the laboratory when checking the lens on a focimeter (vertometer).

It is useful, in considering bitoric lenses, to draw a representation of meridional powers to avoid confusing axes and meridians ( Fig. 11.3 ).

Fig. 11.3, Meridional powers required in Example 4. This shows the powers and directions as they will be measured by the contact lens laboratory.

The incorporation of the correction for residual astigmatism into the toric lens prescription is not difficult:

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If residual astigmatism, in negative cylinder form, has its axis parallel to the negative cylinder axis in the spectacle prescription, then the spectacle astigmatism is greater than corneal astigmatism by an amount equal to the residual astigmatism.
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Alternatively, if residual astigmatism, in negative cylinder form, has its axis perpendicular to the negative cylinder axis in the spectacle prescription, then the corneal astigmatism is greater than spectacle astigmatism by an amount equal to the residual astigmatism.

The axis of the residual astigmatism may not correspond exactly with one of the principal corneal meridians. If the difference between the axes of the spectacle refraction and the principal meridians of the cornea is less than 20°, one can assume that the axes of the spectacle refraction over the lens do correspond with the principal meridians of corneal curvature and that complex oblique cylinder calculations are obviated. The resulting error is usually not significant ( ). If the difference between the axes is more than 20°, an oblique bitoric lens (where the principal meridians of the toroidal front and back surfaces are not parallel) will be required.

The information provided so far on refraction with toroidal back optic zones is sufficient to be able to calculate the BVPs of rigid toric lenses, yet no mention has been made of terms such as ‘induced astigmatism’ and ‘bitoric lenses’. These elements are important, but power calculations for rigid toric lenses can be carried out without them and are relatively straightforward. Factors such as induced astigmatism arise from the specified back optic zone radii and calculated BVPs, such that they are incidental to the determination of the toric lens prescription.

Induced astigmatism

Key Point

Definition: Induced astigmatism is the astigmatic effect created in the contact lens/tear lens system by the toroidal back optic zone bounding two surfaces of different RI, namely the lens and the tears.

Example 5

Consider the lens designed in Example 3.

Back surface toric curves are 8.00 and 7.55 mm, and n = 1.47. The surface powers of these curves in air are −58.75 and −62.25, giving a back surface cylinder of −3.50DC × 180.

On the eye, where the back surface is against tears (n = 1.336), the powers of the back surface interface are −16.75 and −17.75, respectively, and the back surface cylinder in tear fluid is −1.00DC × 180. This 1.00 D back surface cylinder (‘induced astigmatism’) must be compensated by generating a +1.00DC × 180 on the front surface ( ).

The front surface cylinder correction for the induced astigmatism is automatically incorporated into the lens prescription when the practitioner calculates the BVPs for the rigid toric lens. Once again, consider the lens designed in Example 3, where BOZR = 8.00/7.55 mm and n = 1.47, ct = 0.25 mm, BVP is +2.25 and −0.25 as calculated. The front surface powers (calculated using thick lens formulae) would be +60.37/+61.35, respectively. Specification of the appropriate BOZR and BVP therefore results in the front surface incorporating the required compensating cylinder of +1.00DC × 180.

Consequently, once the practitioner has calculated the required BVP, it is not necessary to perform the additional calculations to determine what cylinder is needed on the front surface of the lens to correct for the induced astigmatism. This arises from the specified BOZR and calculated BVPs. In other words, the ascertained toric lens prescription determines the degree of induced astigmatism, not the other way around. This important point is demonstrated as follows:

Example 6

\begin{matrix} Spectacle refraction \\ (vertex distance ignored) : + 3.00 / - 6.00 \times 180 \\ Keratometry reading : 8.00 mm (42.19 D) along 180 \\ 7.00 mm (48.21 D) along 90 \end{matrix}

$\begin{matrix} Spectacle refraction \\ (vertex distance ignored) : + 3.00 / - 6.00 \times 180 \\ Keratometry reading : 8.00 mm (42.19 D) along 180 \\ 7.00 mm (48.21 D) along 90 \end{matrix}$

A rigid spherical trial lens with BOZR 8.00 mm and BVP +1.00 D is placed on the cornea. Refraction with this lens in situ gives +2.00DS (no residual astigmatism) and 6/6 acuity.

Based on the keratometry readings, BOZR of 8.00 and 7.00 mm are chosen to fit the horizontal and vertical meridians, respectively.

\begin{matrix} Along 180 : {BVP}_{CL} = + 1.00 + 2.00 - (\frac{336}{8.00} - \frac{336}{8.00}) \\ = + 3.00 D \\ Along 90 : {BVP}_{CL} = + 1.00 + 2.00 - (\frac{336}{7.00} - \frac{336}{8.00}) \\ = - 3.00 D \end{matrix}

$\begin{matrix} Along 180 : {BVP}_{CL} = + 1.00 + 2.00 - (\frac{336}{8.00} - \frac{336}{8.00}) \\ = + 3.00 D \\ Along 90 : {BVP}_{CL} = + 1.00 + 2.00 - (\frac{336}{7.00} - \frac{336}{8.00}) \\ = - 3.00 D \end{matrix}$

Specification of these BVPs (+3.00 D and −3.00 D) along with the respective BOZR (8.00 mm and 7.00 mm) will automatically bring about the incorporation of the front surface cylinder to correct for the induced astigmatism. This can be demonstrated by calculating the resultant front surface powers based on the BVPs and BOZR to be ordered.

Assume the RI for the rigid lens material is 1.47 and the lens centre thickness is 0.30 mm:

Along 180: Back surface power of the contact lens

\begin{matrix} = \frac{1000 (1 - 1.47)}{8.00} = - 58.75 D \\ BVP = + 3.00 D \end{matrix}

$\begin{matrix} = \frac{1000 (1 - 1.47)}{8.00} = - 58.75 D \\ BVP = + 3.00 D \end{matrix}$

Using thick lens formula for the front surface power (see ‘Shape Factor’ Chapter 7 ), F ₁ :

F_{1} = \frac{F_{ν^{'}} - F_{2}}{1 + (F_{ν^{'}} - F_{2}) \frac{t}{n}}

$F_{1} = \frac{F_{ν^{'}} - F_{2}}{1 + (F_{ν^{'}} - F_{2}) \frac{t}{n}}$

Front surface power of the contact lens = +60.98 D

Along 90: Back surface power of the contact lens

\begin{matrix} = \frac{1000 (1 - 1.47)}{7.00} = - 67.14 D \\ BVP = - 3.00 D \end{matrix}

$\begin{matrix} = \frac{1000 (1 - 1.47)}{7.00} = - 67.14 D \\ BVP = - 3.00 D \end{matrix}$

Again, using thick lens formula:

Front surface power of the contact lens = +63.31

Hence, the total power of the front surface is +60.98DS with +2.33DC × 180. This front surface cylinder represents the correction for the induced astigmatism.

The correction for the induced astigmatism is always a plus cylinder with the same axis as the flatter principal meridian of the cornea (in other words, the same axis as the corneal cylinder). The magnitude of the induced astigmatism is directly proportional to the degree of contact lens toricity and the RI of the lens material.

A quick way to calculate the induced astigmatism is to use the appropriate radii as they change from the rigid lens to tears. That is:

\begin{matrix} Power of the RGP lens / tear boundary \\ = \frac{1000 (1.336 - 1.47)}{r} \\ = \frac{- 134}{r} \end{matrix}

$\begin{matrix} Power of the RGP lens / tear boundary \\ = \frac{1000 (1.336 - 1.47)}{r} \\ = \frac{- 134}{r} \end{matrix}$

where r = radius (in millimetres) and assuming n = 1.47 for the rigid lens material.

By subtracting this value for one principal meridian from the other, the value for the induced astigmatism may be obtained directly. For rigid lens materials with a different RI, −134/r no longer applies; for example, an RI of 1.45 would yield a figure of 114/r for determining the surface power at the lens/tear boundary.

Spherical power equivalent or compensated bitoric lenses

These are lenses which, like spherical lenses, do not correct for any residual astigmatism ( ). They are bitoric because the front surface contains a cylinder solely for the correction of the induced astigmatism. The lenses designed in Examples 3 and 6 would be classed as compensated bitoric lenses.

Key Point

Definition: A compensated bitoric is a lens designed to correct all of the refractive cylinder created due to the corneal toricity ( ).

If the corneal toricity is equal to the spectacle astigmatism, when a compensated bitoric is placed on the cornea, the cylinder will be fully corrected. It can rotate on the eye without visual disturbance because the effect of the rotation is counteracted by an equal change in the cylinder power of the tear lens.

Regarding the front surface cylinder, the correction for induced astigmatism is necessary only because the toroidal back optic zone creates the induced astigmatism along its principal meridians. Consequently, it does not matter if the lens does rotate, as it carries its correction for induced astigmatism with it when it moves away from its intended position.

Cylindrical power equivalent toric lenses

All other types of rigid toric lenses come under this classification, and the unifying feature of these lenses is that they incorporate a correction for residual astigmatism. This category can be further subdivided as follows.

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Fitting Rigid Toric Lenses

Indications for the use of rigid toric lenses

Forms of Rigid Toric Lens

Criteria for Use of Rigid Toric Lenses

Design Considerations

Example 1 Toric lens

Example 2: Toric Periphery

Optical Considerations (see also Chapter 7 )

Corneal astigmatism and the effect of the tear lens

Refraction with toroidal back optic zones

Example 3: Calculating the BVP for a Rigid Lens With a Toroidal Back Optic Zone

Residual astigmatism

Example 4: Calculating the BVP for a Rigid Lens With a Toroidal Back Optic Zone When There Is Residual Astigmatism Present

Induced astigmatism

Example 5

Example 6

Spherical power equivalent or compensated bitoric lenses

Cylindrical power equivalent toric lenses

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