THE PRISMATIC EFFECT

Of DECENTRATION

– PART FOUR

Dr Prof Mo Jalie

DSc, SMSA, FBDO (Hons), SLD, Hon FCGI Hon FCOptom, MCMI, is a Visiting Professor of Optometry at the University of Ulster in Coleraine, and at the post-graduate facility at Varilux University. He served for nine years as Head of Department of Applied Optics at City & Islington College, where he taught optics, ophthalmic lenses and dispensing. He is a recognised international authority on spectacle lens design and has written several books including Principles of Ophthalmic Lenses. His most recent book, Ophthalmic Lenses & Dispensing was translated into Russian. He has authored over 200 papers on ophthalmic, contact and intra- ocular lenses, and on dispensing; and is a consultant editor to The Optician (UK) and technical editor to The Indian Optician journal. He holds patents for aspheric spectacle and intra-ocular lenses. Jalie is a past-chairman of the Academic Committee of the Association of British Dispensing Opticians, and was 

the first Chairman of the Faculty of Dispensing Opticians. He is the ABDO representative on the BSI committees on ophthalmic lenses and spectacle frames and a past member of the Education Committee of the General Optical Council. In 1998 Jalie was thrice honoured: he was made Honorary Fellow of the British College of Optometrists, a Life Fellow of the Association of British Dispensing Opticians, and in December of that year he was granted the Max Wiseman Memorial Research Medal.

A sphero-cylindrical prescription may be looked upon in either of two ways. One could look upon a sph-cyl. as a spherical lens to which has been added a plano- cylinder, or, we may consider it to be made up from two separate plano-cylinders placed together with their axes at right angles to one another. It should be apparent that we are only interested in the principal powers of the lens and not in its form, so the remarks here apply equally to toric lenses.

PRISMATIC EFFECT OF SPHERO-CYLINDERS

EXAMPLE (I)

Find the prismatic effects at a point 8mm above and 3mm inwards from the optical centre of the lens R -6.00 DS/+2.00 DC x 40.

 

The graphical construction is shown in Figure 1. The powers of the lens are -6.00 D along 40 and -4.00 D along 130 and these have been marked upon the principal meridians.

 

By measurement:

 

RP = c40 = 0.75cm and RQ = c130 = 0.42cm.

 

So, P40 = c40 x F40 = 0.75 x 6 = 4.5Δ base up @ 40,

 

(Since the power along 40, F40, is negative, point P represents the position of the prism apex).

 

P130 = c130 x F130 = 0.42 x 4 = 1.68 base up @ 130.

 

These two prisms are now to be constructed to scale on the graph (P40 = OX and P130 = OY) in order to compound them into the single resultant prism, PR, represented by the length OZ.

 

By measurement, PR = 4.8Δ base up @ 60½.

 

Finally, resolving PR into vertical and horizontal components, PV (= OV) and PH (= OH),

 

we find:
             PV = 4.2Δ base up and PH = 2.4Δ base in.

EXAMPLE (II):

Find the prismatic effects introduced by decentring the lens L -2.00 / +4.00 x 45, 1cm inwards.

 

The graphical construction is shown in Figure 2. The powers of the lens are -2.00 D along 45 and +2.00 D along 135 and these have been marked upon the principal meridians.

 

By measurement:

FIGURE 1 – PRISMATIC EFFECT AT A POINT 8MM ABOVE AND 3MM INWARDS FROM OC OF LENS, R -6.00 / +2.00 X 40

FIGURE 2 – PRISMATIC EFFECT PRODUCED BY DECENTERING THE LENS, L -2.00 / +4.00 X 45, 10MM INWARDS

RP = c45 = 0.71cm

 

and RQ = c135 = 0.71cm.

 

So, P45 = c45 x F45 = 0.71 x 2 = 1.42Δ base up @ 45,

 

P135 = c135 x F135 = 0.71 x 2 = 1.42 base up @ 135.

 

These two prisms can now be constructed on the graph to scale (P45 = OX and P135 = OY)

 

in order to compound them into the single resultant prism, PR, represented by the length OZ.

 

By measurement, PR = 2.0Δ base up which represents the total prismatic effect at R.

 

Note that in this example the lens has been decentred inwards, resulting in a vertical prism!

DECENTRATION TO PRODUCE PRISM – THE GENERAL CASE (GRAPHICAL METHODS)

        The graphical construction described above can be reversed to find the decentration necessary to produce a prescribed prismatic effect. The rules for this construction are as follows.

 

(1)     Construct vertical and horizontal meridians and the principal meridians and mark the nasal side of the lens (N).

 

(2)    Draw the prisms to scale with their bases in the correct directions and construct the resultant point, Z.

 

(3)    Resolve the prisms along the principal meridians of the lens (ZX and ZY) by dropping perpendiculars from Z to the principal meridians. Note that the prisms are represented by the lengths, OX and OY and that the positions of X and Y with respect to O, represent their base directions.

 

(4)    Measure OX and OY and calculate the magnitude and the directions of the decentrations necessary to produce them, (OP and OQ).

 

(5)    Compound the decentrations OP and OQ into a single resultant decentration, OR, and resolve OR into vertical and horizontal components, RV and RH. OV represents the required vertical decentration, cV, and OH the required horizontal decentration, cH.

THE PRINCIPAL POWERS OF THE LENS LIE ALONG THE 70 AND 160 MERIDIANS BUT THE PRISMATIC EFFECT WHICH HAS TO BE PRODUCED IS GIVEN AS VERTICAL AND HORIZONTAL COMPONENTS, SO THE FIRST STAGE OF THE SOLUTION IS TO COMPOUND THE GIVEN PRISMS INTO A SINGLE PRISMATIC EFFECT...

EXAMPLE (III):

Find the vertical and horizontal decentrations required to produce 4Δ base up and 2Δ base out with the lens R +4.50 DS / +2.50 DC x 70.

 

 The principal powers of the lens lie along the 70 and 160 meridians but the prismatic effect which has to be produced is given as vertical and horizontal components, so the first stage of the solution is to compound the given prisms into a single prismatic effect and then to resolve this along the 70 and 160 meridians of the lens.

This construction is shown in Figure 3. Note that the prisms are compounded following the rules given above. At this stage, we are not interested in the actual powers of the lens.

 

In Figure 3(a), the prisms 4Δ base up and 2Δ base out have been compounded, graphically into the single resultant prism, OZ, which is 4.47Δ base up @ 116.6°.

 

Find the vertical and horizontal decentrations required to produce 4Δ base up and 2Δ base out with the lens R +4.50 DS / +2.50 DC x 70.

 

The principal powers of the lens lie along the 70 and 160 meridians but the prismatic effect which has to be produced is given as vertical and horizontal components, so the first stage of the solution is to compound the given prisms into a single prismatic effect and then to resolve this along the 70 and 160 meridians of the lens.

FIGURE 3 – RESOLVING THE PRISMS 4Δ BASE UP & 2Δ BASE OUT ALONG THE 70 AND 160 MERIDIANS

This construction is shown in Figure 3. Note that the prisms are compounded following the rules given above. At this stage, we are not interested in the actual powers of the lens.

 

In Figure 3(a), the prisms 4Δ base up and 2Δ base out have been compounded, graphically into the single resultant prism, OZ, which is 4.47Δ base up @ 116.6°.

 

In Figure 3(b), this single prism, OZ, has been resolved along the 70 and 160 meridians by dropping perpendiculars, ZY and ZX, respectively, onto the principal meridians of the lens.

 

By measurement:

 

OX = P70 = 3.1Δ up @ 70,

and OY = P160 = 3.3Δ up @ 160

 

Note in which direction the base of the two prisms, P70 and P160, lie. The origin, O represents the apex of each prism.

When the prism powers are known along the two principal meridians of the lens, the decentrations required to produce these prisms can be found. Now the powers which lie along the principal meridians, F70 (+4.50) and F160 (+7.00), can be considered.

From the decentration relationship,

 

c70 = P70 / F70 = 3.1 / 4.50 = 0.69cm = 6.9mm up
@ 70 (since F70 is positive).

 

c160 = P160 / F160 = 3.3/7.00 = 0.47cm = 4.7mm up
@ 160 (since F160 is positive).

 

The decentrations c70 (OP) and c160 (OQ) must now be resolved into vertical and horizontal components

 

In Figure 4(a), the decentration, c70, has been drawn to scale, up along 70 (OP), and c160 drawn to scale, up along 160 (OQ). Completing the rectangle OPRQ, produces the single resultant decentration (OR), which would need to be obtained if the minimum size uncut needed to be determined. By measurement, OR = 8.3mm up @ 104½°.

 

In Figure 4(b), the single resultant decentration, OR, has been resolved into vertical and horizontal components, OV and OH, by dropping perpendiculars, RV and RH onto the vertical and horizontal meridians respectively.

 

By measurement, cV (OV), = 8mm up and cH (OH) = 2mm out.

 

In practice, each step of this solution can be constructed on a single diagram and this single construction where all the separate steps have been combined is shown in Figure 5. The full solution is repeated here.

 

The powers of the lens are +4.50 D along 70 and +7.00 D along 160 and these have been marked on the construction, together with an indication of the nasal side of the lens.

 

By measurement:

 

OX = P70 = 3.1Δ up @ 70,

and OY = P160 = 3.3Δ up @ 160

 

c70 = P70 / F70 = 3.1/4.50 = 0.69cm = 6.9mm up

@ 70 (since F70 is positive).

 

c160 = P160 / F160 = 3.3/7.00 = 0.47cm = 4.7mm up

@ 160 (since F160 is positive).

             

The decentrations c70 (OP) and c160 (OQ) can now be constructed to scale on the graph. Note that the scale used to compound the decentrations need not be the same as that used to construct the prisms. The most convenient scale should be chosen.

               

Completing the rectangle OPRQ, by measurement, OR= 8.3mm up @ 104½ and resolving OR into vertical and horizontal components, cV (OV), and cH (OH), we find cV = 8mm up and cH = 2mm out.

WHEN THE PRISM POWERS ARE KNOWN ALONG THE TWO PRINCIPAL MERIDIANS OF THE LENS, THE DECENTRATIONS REQUIRED TO PRODUCE THESE PRISMS CAN BE FOUND

FIGURE 4 – RESOLVING THE DECENTRATIONS INTO VERTICAL AND HORIZONTAL COMPONENTS

NOTE THAT THE SCALE USED TO COMPOUND THE DECENTRATIONS NEED NOT BE THE SAME AS THAT USED TO CONSTRUCT THE PRISMS. THE MOST CONVENIENT SCALE SHOULD BE CHOSEN

FIGURE 5 – COMPLETE, COMBINED CONSTRUCTION FOR EXAMPLE (III), R +4.50/+2.50 X 70 WITH 4Δ BASE UP AND 2Δ BASE OUT

… to be continued

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B. When you send gift cards or subscriptions, we may collect the information you provide about the gift recipients, including name and email address. We will use such information to fulfil your requests, provide the relevant service, or for anti-fraud purposes.

C. The Personal Information we collect allows us to respond to your requests, improve our products and services, customize the advertising and content you see, and communicate with you about new products.

 

D. If you do not want to receive emails from us, you may opt out of Company’s marketing and promotional messaging by changing the ‘Email Preferences’ under ‘My Account’ after logging in to your tionet account. However, while you maintain an account with Company, you will not be able to opt out of emails that send important notices, such as communications about purchases and changes to our terms, conditions, and policies.

 

E. We also collect data in a form that does not, on its own, permit direct association with any specific individual. We may collect, use, transfer, and disclose non-personally identifying information for any purpose.

 

F. We receive and store certain types of information whenever you interact with the Service. Company automatically collects information on our server logs from your browser including your Internet Protocol (IP) address, the name and identity of your computer, mobile device and other devices, your operating system, browser type and version, CPU speed, connection speed, and locale information based on IP address. To the extent that IP addresses or similar identifiers are considered personal information by local law, we also treat these identifiers as personal information. The Site collects usage information, such as the numbers and frequency of user visits to our website and its components, We use this information to give a personalized experience to our users and also improve our services.

 

G. We also collect information about your purchases and activities on the Service, which we may use to present you with offers that we believe may be of interest to you. As part of this use of information, we may provide non-personally identifying, aggregate information to our Participating Publishers and other third parties about how our users, collectively, use the Service.

1. Articles you’ve read– To understand your interests and showcase more relevant articles

2. Time spent on reading each magazine and article– To analyze the quality of content and provide appropriate feedback to publishers

3. Web and app pages you’ve visited– To track features used by you and recommend features that you’ve not used

H. We send push notifications to our apps after getting consent from our users. These push notifications inform users about the latest offers, new issues going live, personalized magazines and articles. The users can disable push notifications anytime.

 

COOKIE POLICY 

Cookies are alphanumeric identifiers that we transfer to your computer or device to enable our systems to recognize your browser and tell us how and when pages in our website are visited and by how many people.

 

Most browsers have an option for turning off the cookie feature, which will prevent or limit your browser from accepting new cookies, as well as (depending on the sophistication of your browser software) allowing you to decide on acceptance of each new cookie in a variety of ways. You may wish to leave the cookies activated because cookies enable you to take advantage of some of the Site’s most essential features.

 

SHARING OF YOUR PERSONAL INFORMATION

Personal Information will only be shared by Company to provide or improve our products, services, to contact you about our services; and with our advertisers to contact you about their new products etc; it will not be shared with third parties for their marketing purposes.

 

Others: We may access, read, preserve, disclose, or release Personal Information when we believe in good faith that release is necessary to comply with law and enforce or apply our Terms of Use; or protect the rights, property, or safety of Company, our employees, our users, or others.

 

SECURITY OF YOUR PERSONAL INFORMATION

We allow you to limit access to your account via a password for your privacy and security. If you access your account via a third party site or service, you may have additional or different sign-on protections via that third party site or service. You are responsible for ensuring against unauthorized access to your account and Personal Information by selecting and protecting your password and/or other sign-on mechanism appropriately and limiting access to your computer and browser by signing off after you have finished accessing your account.

 

We use industry-standard Secure Socket Layer (SSL) software to encrypt your Personal Information during transmission. However, because no data transmission over the Internet is completely secure, and no system of physical or electronic security is impenetrable, Company cannot guarantee the security of Personal Information in its possession or the security of its servers or databases. Unauthorized entry or use, hardware or software failure, and other factors, may compromise the security of user information at any time.

 

In the unlikely event that Company believes that the security of your Personal Information in its possession or control may have been compromised, Company may seek to notify you. If notification is appropriate, Company may notify you by email, messaging to your device, or other means within 72 hours of data compromise.

 

PERSONAL INFORMATION YOU CAN ACCESS

Company allows you to access the following information about you for the purpose of viewing, and in certain situations, updating that information: email address, name, location and marketing preferences. This list may change as the Service changes. The information you can view, update, and delete may change as the Website changes. If you have any questions about viewing or updating information, we have on file about you, please contact us at privacy@tionet.in or at The Indian Optician., A-99 Defence colony, New Delhi – 110024

 

You can add or update certain personal information on your account, such as name and email address. When you update information, however, we often maintain a copy of the unrevised information in our records.

 

Upon your written request to privacy@ tionet.in we will remove your Personal Information from our active user database provided that (a) you are current with all payment obligations, (b) we do not believe it reasonably necessary to keep such information for any pending legal action, and (c) we are under no obligation to retain such information. Please be aware that any unfulfilled subscriptions may be cancelled without refund and you will have to re-register in order to use the Service. It is your responsibility to request a refund from us.

 

TRADEMARKS

All names, images, logos identifying The Indian Optician are proprietary marks of The Indian Optician. All third-party brand, product, service and company names contained on this Website are the trademarks, service marks and trade names of their respective holders. TIO do not give permission for their use by any person other than the holders. Any such use may constitute an infringement of the holders’ rights.

 

EXTERNAL LINKS

The Indian Optician do not represent, warrant, endorse or hold responsibility over any external sites that may be linked to and from this Website. Any external site that you visit by clicking through a link on this Website is outside the control of TIO and you visit entirely at your own risk.

 

These Terms and Conditions and the other rules, guidelines, licenses and disclaimers posted on the Service (on the tionet website or tionet Apps constitute the entire agreement between tionet and you with respect to your use of the Service and supersede all previous written or oral agreements between us with respect to the subject matter hereof.

 

From time to time, tionet may revise these Terms and Conditions to keep them up to date with tionet products and services. Please refer to the tionet website and tionet Apps periodically for any changes. The update date first written above is used to alert you to recent modifications. Your access or use of the Service subsequent to such an update will signify your assent to be bound by such changes.

 

If you have any questions regarding our terms and conditions, please email us at infotiodel@gmail.com

 

JURISDICTION

These Terms & Conditions shall be governed by and construed in accordance with the laws of India. Disputes arising here from shall be exclusively subject to the jurisdiction of the courts of New Delhi to the exclusion of any other. If any of these Terms should be determined to be illegal, invalid or otherwise unenforceable by reason of the laws; it shall be severed and deleted from this clause. All other Terms of Use and Terms & Conditions shall remain in full force and continue to be binding and enforceable. The Indian Optician reserves the right to change any of its terms and conditions at any time by posting changes online.

 

LEGAL DISCLAIMERS

By registering on tionet.com and agreeing to its Terms of Use and Privacy Policy, you also agree and acknowledge the following Legal Disclaimer notice:

 

a. You agree that the use of tionet.in, the application and its services, are at solely at your own risk. Neither tionet.in nor its associates nor employees nor third party content providers guarantee that the service will be completely uninterrupted or error-free or fool proof against miscreant activities. Nor do they warranty that you will get the exact results as expected or promised by the website or product.

 

b. The website and the application are provided on an “AS IS” basis with no warranties expressly stated or promised regarding the results that would be obtained from the use of it.

 

c. In no event will TIONET.IN or any person or entity or third party involved in the creation, production and distribution of the content on the website and the application be liable in contract or legally for any damages, including and not limited to, direct, indirect, incidental, special, and consequential incurred to you while or on using tionet.com. By registering on the website or downloading the application, you agree that the provisions mentioned in this section shall apply to all use of and content on the website and the application.

d. The above disclaimer of liability applies to any damages or injury caused by any failure of performance, error, omission, inaccuracy, interruption, deletion, delay, defect in operation or transmission, computer virus attack, communication line failure, theft or destruction or unauthorised access to, alteration of or use of this website, on account of breach of contract or negligence or under any other cause of action.

e. You specifically acknowledge that tionet.com is not liable for any kind of defamatory or offensive or illegal conduct of other users or third parties or their content and that the risk of injury from the foregoing rests entirely with you.