Transposition of a cylinder, examples of optics. Features of using contact lenses to correct astigmatism. Principles of spectacle correction of astigmatism in children

After an examination and the necessary diagnostic tests, the doctor may prescribe you to wear glasses. The recipe entry will look something like this:
OD Sph −3.0D, Cyl −1.0D ax 180
OS Sph −3.0D, Cyl −2.0D ax 175
Dp 68 (33.5/34.5)
Let's try to figure out what these strange letters and numbers mean.

OD (oculus dexter) is the designation of the right eye, OS (oculus sinister) is the name of the left eye. In some cases, it may be indicated - OU (oculus uterque), which means “both eyes”. In ophthalmology, to avoid confusion, it is customary to always indicate the right eye first, then the left.

Sph (sphere) - denotes a spherical lens. These lenses are used to correct nearsightedness (myopia) and farsightedness (hypermetropia).


The number (in our example 3.0) indicates the optical power of the lens, expressed in dioptres - D (dioptria). In the case of collective lenses (for hyperopia), a “+” sign is placed in front of its value, in the case of diverging lenses (for myopia) - “-”; In our example, the “-” sign is used, which indicates the need to correct myopia.

Cyl (cylinder) - designation of a cylindrical lens. These lenses are used to correct astigmatism. By analogy with a spherical lens, it is not difficult to guess that 1.0, as in our example, is the optical power.

The cylinder value can be minus to correct myopic (nearsighted) astigmatism and positive to correct hypermetropic (farsighted) astigmatism.

A mandatory parameter of a cylindrical lens is such an indicator as Ax (axis) - the axis of the cylinder. It is measured in degrees from 0 to 180. This is due to the characteristics of the refraction of light passing through a cylindrical lens. Rays going perpendicular to the axis of the cylinder are refracted. And axes running parallel do not change their direction. Such properties allow us to “correct” the refraction of light in the specific meridian we need.

Dp (distantio pupillorum) - the distance between the centers of the pupils in millimeters (can be indicated in brackets for each eye separately).

So, let's summarize this information and read the recipe given. Myopia correction is required for the right eye using a lens with a power of 3.0 diopters. Correction of astigmatism is also necessary using a cylindrical lens with a power of 1.0 diopter and a cylinder axis of 180 degrees. For the left eye, the correction of myopia is the same as for the right, but to correct astigmatism, a cylindrical lens with a power of 2.0 diopters and an axis of 175 degrees is required. The interpupillary distance is 68 millimeters.

There are differences in issuing prescriptions for glasses abroad. There the number of characters is minimized and the recipe looks like this: −2.00 +1.50×80

Cylinder transposition

There are often cases when patients are faced with a phenomenon that is incomprehensible to them. When ordering glasses from a workshop, the customer can change the lens parameters. For example, an optician wrote the following prescription:
ОD sph - cyl +0.5 ax 180
OS sph - cyl +0.5 ax 0
DP=52mm
In the workshop, the following entry may appear on the order form:
OD sph +0.5 cyl −0.5 ax 90
OS sph +0.5 cyl −0.5 ax 90
DP=52mm

Don't worry - this is a normal phenomenon, a purely technical issue without any deception. An astigmatic lens always corresponds to two equivalent entries: one with a plus cylinder, and the other with a minus cylinder. The transition from one record to another is called cylinder transposition. Its principle is as follows:
1. Add the force of the sphere and the cylinder, taking into account the sign, to obtain a new value for the force of the sphere:
In this case, 0+0.5 gives a value of sph +0.5
2. Change the sign of the cylinder force to obtain a new value of the cylinder force:
+0.5 replace + with - and get cyl −0.5
3. Change the position of the axis by 90 degrees:
180 degrees turns into 90, just like 0 turns into 90.

This is how two outwardly different entries can appear, but essentially meaning the same parameters of lenses for glasses.

7018 0

As stated earlier, spectacle lenses can be single or multifocal.

Each of these types of lenses may include the following optical elements: spherical, astigmatic, prismatic, eikonic*. In addition, spectacle lenses can be light-protective with different transmittance coefficients.

The following are the rules for prescribing single vision lenses. Spherical (stigmatic) lenses are written as follows: after the designation sph (or in Russian - “sphere”), indicate the “+” sign for converging lenses and the “-” sign for diverging lenses and then the lens power in diopters (D). The power of the lens is indicated as a decimal fraction; for a whole number of diopters, 0 is placed after the decimal point.

For example:

sph -6.0 D; sph +1.25 D; sph -0.5 D.

When prescribing astigmatic lenses, after the number indicating the power of the spherical element, put a comma, then the symbol cyl (or in Russian - “cylinder”) and indicate the sign and power of the cylindrical element in diopters, as well as the position of its axis (non-active section) on the international scale TABO.

For example:

sph -0.5 D, sul -1.0 D x 10°.


Instead of a comma, sometimes a combination sign (o) is used, which resembles an equals sign, but with convex stripes. For example:

sph -0.5 D o cyl -1.0 D ax 10°.

Lately, the D symbol has often been omitted.

For example:

sph -0.5 o cyl -1.0 x 10°.

Abroad, the designation of spherocylindrical combinations is usually simplified: first they put the sign and power of a spherical lens with two digits after the decimal point, then the sign and power of a cylindrical lens, instead of the word axis (ax) - multiplication sign - x.

The above script looks like this:

-0.50-1.00 x 10°

If there is no cylindrical lens, only the first number is given; if there is no spherical lens, 0.00 is given instead of the first number.

In our recipes, if there is no spherical element, its designation can be omitted. For example, instead of sph 0.0 cyl +1.0 D akh 10°, you can write cyl +1.0 D akh 10°.

The position of the axis of the corrective cylindrical lens should be indicated on the TABO diagram with an arrow.

For complex astigmatism, a sphere and a cylinder of the same sign should be drawn; for mixed astigmatism, the opposite sign should be drawn. It is not allowed to write a combination of two cylindrical elements in one lens.

If the selection of glasses was carried out with a cylinder of one sign, and you need to write out a cylinder of another sign (for example, if for complex hypermetropic astigmatism, a trial selection is carried out with negative cylinders), then a transposition should be performed. In this case, a cylinder of one sign is replaced by a combination of a sphere of the same sign with a cylinder of the opposite sign with an axis located at an angle of 90° relative to the original axis of the cylinder.

The rules of transposition are as follows: the sign of the cylinder is changed to the opposite, the direction of the axis is changed to perpendicular (i.e., 90° should be subtracted or added), the sign of the sphere is changed to the opposite, and its strength is equal to the algebraic sum of the sphere and cylinder in the original notation.

Examples.

1. sph -1.0 D, cyl +1.0 D ax 100e = cyl -1.0 D ax 10e;
2. sph +6.0 D, cyl -2.0 D ax 80° = sph +6.0 D +(eph -2.0 D, cyl +2.0 D ax 170°) = sph +4.0 D, cyl +2.0 D ax 170°;
3. sph -1.5 D, cyl +2.5 D ax 105° = sph -1.5 D + (sph +2.5 D, cyl -2.5 D ax 15°) = sph +1.0 D, cyl -2.0 D ax 15°.


GOST 23265-78 “Eyeglass lenses” for optical production and medical supply services provides for a different system for designating the refraction of astigmatic lenses. It is not recommended for eyeglass prescriptions, but eye doctors and optometrists should know it to ensure that glasses are made correctly.

According to this system, to characterize an astigmatic lens, its three parameters are indicated in the following order:
1) the posterior apical refraction is less than the refractive cross section (for positive lenses - smaller in absolute value, for negative lenses - correspondingly larger);
2) the posterior apical refraction is greater than the refractive section;
3) the direction of the main section with the lowest refraction on the TABO scale in degrees.

Examples of converting the sphere-cylinder system to the GOST 23265-78 system are given in Table. 9.

As stated in Chap. 3, in Russia lenses with an astigmatic difference of up to 4.0 diopters and a posterior apical refraction from -30 to +20 diopters are mass-produced. With an astigmatic difference of up to 2.0 diopters, the intervals between the values ​​of the cylindrical element are 0.25 diopters, over 2.0 diopters - 0.5 diopters.

When prescribing glasses with prismatic action (after characterizing the spherical and cylindrical elements), the strength of the prismatic element in prismatic diopters (A) and the direction of the top-base line on the TABO scale are indicated. In this case, the TAY scale continues up to 360°.

Table 9. Examples of astigmatic refraction designations


Just like spherical and cylindrical lenses, prisms can be written in Latin and Russian transcription: prism - рр, base - bas.

For example:

sph +3.0 D, рг 2A bas 0°, sph -1.0 D, cyl -2.0 D ax 90°, рг 3 bas 180°.

When the top-base line is in a horizontal position, it is allowed to indicate its direction with the words: “base to the nose” and “base to the temple” - “bas nas” and “bas temp”.

In other positions of this line, its direction should be indicated on the TABO circular scale with the obligatory designation of an arrow according to the diagram.

When prescribing glasses with a prismatic action, the power of the corrective prism should be “distributed” approximately equally between the two eyes, that is, the prismatic element should be approximately the same in each eye, and the top-base line should have the opposite direction.

For example, if it is necessary to correct exophoria 6.0 prism, prisms should be prescribed:

OD рг З bas 0° (nas),
OS pr 3 bas 180° (nas).

When correcting combined heterophoria, corrected with an 8.0 prism with a base of 30° in front of the right eye, the following should be prescribed:

OD pr 4 bas 30°, OS pr 4 bas 210°.

According to existing standards, it is allowed to write out prismatic elements with a force from 0.5 to 10 prdptr.

Vertex correction – vertex distance

Vertex correction, vertex distance - everyone who wears glasses has probably heard such expressions. What is vertex distance and vertex correction? Why do you need to know and take into account the vertex distance and how to correctly calculate the vertex correction? Is there a difference between the diopters of glasses and lenses, and what should be the difference in diopters between contact lenses and glasses? In this article we will try to answer these questions.

Vertex distance is the distance from the back surface of the spectacle lens to the top of the cornea of ​​the eye. Normally, the vertex distance should be 12-15 mm. You can measure the vertex distance using a special or regular ruler. It is this vertex distance that guarantees that the image passing through the surface of the spectacle lens will fall on the retina and, accordingly, the person will see the objects in question well and clearly in the glasses.

What happens if the vertex distance shifts?

If the vertex distance does not correspond to the norm, the corrective power of the spectacle lenses changes.

Dispersive minus lenses

Spectacle lenses with minus diopters are divergent; they are designed to compensate for the strong refractive refraction in myopic people, in whom, without correction, the image is located in front of the retina. Properly selected minus lenses, taking into account the vertex distance of 12-15 mm, move the image onto the retina and ensure clarity of vision. Increasing the vertex distance with minus lenses (moving away from the eyes) leads to the fact that the image will again move and be in front of the retina, which means the clarity of vision will deteriorate.

If the vertex distance is reduced (closer to the eyes) with minus lenses, then you can get an excessively strong correction.

Converging plus lenses

Plus lenses are converging and are used to correct weak refraction in hyperopia and presbyopia.

With hypermetropia, the image falls behind the retina, and correction with converging plus lenses moves it onto the retina and makes the image clear.

When the vertex distance from the eyes shifts, that is, when it increases, the refractive power of the plus lens will increase, that is, excessive correction, since the image will move in front of the retina. When the plus lens approaches the eyes, the image will move behind the retina and visual acuity will decrease again.

Thus, changing the vertex distance when correcting with plus and minus lenses will lead to opposite results. Therefore, even if adequate spectacle correction is selected, but the vertex distance is not observed, visual acuity in glasses may differ from the selected correction.

This is why it is important to consider the vertex distance when selecting glasses and ensure that the frames fit correctly before the glasses are even made.

Vertex distance and contact lenses

Vertex distance is an indicator characteristic only for spectacle correction. When corrected with contact lenses, there is no vertex distance, since the contact lens is located directly on the surface of the cornea of ​​the eye. However, the selection of contact lenses is carried out using a trial frame and spectacle lenses from a diagnostic kit, where, of course, there is a vertex distance.

Vertex correction

The difference between the diopters of glasses and contact lenses

Should this vertex distance be taken into account when selecting contact lenses? Is there a difference between the diopters of glasses and contact lenses? What should the diopter ratio be?

In order for the diopters of contact lenses to correspond to the diopters of spectacle lenses, the concept of vertex correction was introduced.

Vertex correction is a mathematical value.

To determine the vertex correction for contact lenses, that is, how much the diopters of contact lenses should differ from the diopters in glasses, there is a special table for converting diopters corrected for vertex distance. Every contact correction room should have such a table. With its help, the optometrist determines how much the diopters of contact lenses need to be changed so that they correspond to the selected spectacle correction, taking into account the vertex distance.

Vertex correction is calculated differently for minus and plus lenses.

As we have already said, minus lenses will become stronger as the vertex distance decreases, that is, as you get closer to the eyes. Therefore, the diopters of minus contact lenses must be smaller to match the selected spectacle correction.

Conversely, lenses with positive values ​​become stronger as the vertex distance decreases (closer to the eyes). Therefore, plus contact lenses must be larger than the corresponding spectacle correction.

Diopter difference value

Another important point that affects the calculation of the vertex correction is the diopter value. How much less or more diopters should be, and what is the permissible difference in diopters, depends on the size of the diopters.

The higher the diopters, the greater the value of the vertex correction, and the more the diopters of glasses and contact lenses do not match and differ. Up to diopter values ​​-/+ 3.75D, the vertex correction value is not taken into account and the diopters in contact lenses correspond to the diopters in glasses.

Allowable diopter difference

Vertex correction is calculated for diopter values ​​above -/+4.0D:

  • From -/+4.0D to -/+5.75D, the difference between the diopter values ​​of contact and spectacle lenses is 0.25D.
  • From -/+6.0D to -/+7.5D, the vertex correction value is 0.5D.
  • From -/+8.0D to -/+10.0D, the difference between the diopters of contact and spectacle lenses is 1.0D.
  • From +/- 10.5D to +/-11.5D, the vertex correction is 1.5D.
  • From +/-12.0D the vertex correction will be equal to 2.0D.

Thus, negative contact lenses will be smaller than spectacle lenses by a vertex correction value above -4.0D, and up to -3.75D they will be the same as glasses. Plus contact lenses up to +3.75 will have the same diopters as the corresponding spectacle lenses, and above +4.0D they will be larger than the spectacle lens by the amount of vertex correction.

You might be interested:

Natalia Gusakova 07.07.18

Elena, hello! Since there is no vertex distance in contact lenses, theoretically, any difference is acceptable when correcting anisometropia with contact lenses. Among the limitations, I would probably name the primary correction of anisometropia at a fairly mature age, when any change in the already habitual correction can be difficult to tolerate. Therefore, at an earlier age, adequate correction is prescribed anisometropia, the easier it is tolerable.

Elena 07/04/18

Hello! I'm interested in the difference in SCL. Anisometropia. Any can be transferred. Or are there still some restrictions.

In order to solve current vision problems, you need to visit an ophthalmologist. Based on the research, the doctor will determine the cause of the decrease in vision power, and, if there are no other methods, will write a prescription for glasses. The prescription contains information for the optician who will select frames and lenses for you. In principle, you do not need to be able to read a recipe, but it is still advisable to understand what the notes mean.

Recording can be done in different ways:
OD sph -2.00 cyl -0.75 ax 40 at 14 add +1.00
OS sph +1.50 cyl -0.75 ax 75 on 14 add +1.00
Dp/p = 62 mm

Or so
OD -2.00/-0.75x40 at 14 add +1.00
OS +1.50/-0.75x75 on 14 add +1.00
Dp/p = 62 mm

O.D.- right eye;
OS- left eye;
Sph– spherical component, with a + sign means myopia, with a – sign means farsightedness.
Cyl– cylindrical component, indicated only for astigmatism;
Axis– axial value of the cylinder, also only with astigmatism.
At 14– vertex distance (CVD). The distance between the cornea and the lens of the glasses in millimeters; the number of diopters of the lens depends on it. Not related to contact lenses.
Add +1.00– addition. Difference between distance and near vision power, for presbyopia only.
P.D.– the distance in millimeters between the pupils of the eyes. It always differs with myopia (that is, myopia) and poor vision of objects in the distance (farsightedness), because The positioning of the pupils when looking at different distances is different. There is always a note about the type of glasses, as well as an indication of your disease (they write “glasses for myopia, for example”). Also indicated in the lens prescription.

Transposition. The rule for recalculating glasses lenses for astigmatism, when there is no difference between the positive and negative recording values.

Prescription for glasses or contact lenses Transposed recipe
Sph, D Cyl, D Ax, hail Sph, D Cyl, D Ax, hail
OD - right eye Select -20.00 -19.50 -19.00 -18.50 -18.00 -17.50 -17.00 -16.50 -16.00 -15.50 -15.00 -14.50 -14.00 -13.50 -13.00 -12.50 -12.00 -11.50 -11.00 -10.50 - 10.00 -9.50 -9.00 -8.50 - 8.00 -7.50 -7.00 -6.50 -6.00 -5.75 -5.50 -5.25 -5.00 -4.75 -4.50 -4.25 -4.00 -3.75 -3.50 -3.25 -3.00 -2.75 -2.50 -2.25 -2.00 -1.75 -1.50 -1.25 -1.0 0 - 0.75 -0.50 -0.25 0.00 +0.50 +1.00 +1.50 +2.00 +2.50 +3.00 +3.50 +4.00 +4.50 +5.00 +5.50 +6.00 +6.50 +7.00 +7.50 +8.00 +8.50 +9.00 +9.50 +10.00 +10 .50 +11.00 +11.50 +12.00 +12.50 +13.00 +13.50 +14.00 +14.50 +15.00 +15.50 +16.00 +16.50 +17.00 +17.50 +18.00 +18.50 +19.00 +19.50 +20.00 Select -6.00 -5.75 -5.50 -5.25 -5.00 -4.75 -4.50 -4.25 -4.00 -3.75 -3.50 -3.25 -3.00 -2.75 -2.50 -2.25 -2.00 -1.75 -1.50 -1.25 -1.00 -0.75 -0.50 -0.25 0.00 +0.25 +0.50 +0.75 +1.00 +1.25 +1.50 +1.75 +2.00 +2.25 +2.50 +2.75 +3.00 +3.25 +3.50 +3.75 +4.00 +4.25 +4.50 +4.75 +5.00 +5.25 +5.50 +5.75 +6.00 Select 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 173 174 175 176 177 178 179 180 180
OS - left eye Select -20.00 -19.50 -19.00 -18.50 -18.00 -17.50 -17.00 -16.50 -16.00 -15.50 -15.00 -14.50 -14.00 -13.50 -13.00 -12.50 -12.00 -11.50 -11.00 -10.50 - 10.00 -9.50 -9.00 -8.50 - 8.00 -7.50 -7.00 -6.50 -6.00 -5.75 -5.50 -5.25 -5.00 -4.75 -4.50 -4.25 -4.00 -3.75 -3.50 -3.25 -3.00 -2.75 -2.50 -2.25 -2.00 -1.75 -1.50 -1.25 -1.0 0 - 0.75 -0.50 -0.25 0.00 +0.50 +1.00 +1.50 +2.00 +2.50 +3.00 +3.50 +4.00 +4.50 +5.00 +5.50 +6.00 +6.50 +7.00 +7.50 +8.00 +8.50 +9.00 +9.50 +10.00 +10 .50 +11.00 +11.50 +12.
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