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Ophthalmic lenses and dispensing Contents of CD-ROM Click on page How to navigate the CD-ROM Action of a prism The transverse test Action of a cylinder Use of the focimeter The correction of ametropia Effective power in DV Effective power in NV Vergence impressed in NV Centration of spectacle lenses Effects of centration errors Lens thickness and weight Lens design and performance Iso-V-Prism zones Exit Ophthalmic Lenses & Dispensing First time users click here How to navigate the CD-ROM Click to return to CD contents To reverse this step, right click and To advance through the show in the order intended, This button returns you select ‘previous’ from the pop-up menu. click anywhere on the screen. to the CONTENTS PAGE. You may like to try this now, Click now to continue. Click on it now to end the or just left click to continue. navigation instructions. In someEach topicsscreen you willhere see athree button like this > Click has tosmall start action buttons It enables you to return to the contents page for the topic. This button enables you to proceed to the next topic. This button enables you to When you click on it you skip go back to the previous screen. the rest of the current topic. Click anywhere to continue Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Click to return to CD contents Action of a prism Now the prism has been rotated clockwise through 90° WhenThis the Note prism is ahow crossline is the rotated horizontal chart. clockwise Onlimb thebefore of next themouse the crossline crossline clickchart you chart will the lines The base setting can be marked on the it has rotated to from its original position. Thelens basewhen lies on the been left and also appear placeappears ato prism rotate, to held be always with displaced its displaced base towards DOWN in the the indirection prism front of apex. of thethe chart… prism apex. this position where a continuous appearance of the vertical limb is only the vertical limb is displaced towards the prism apex. obtained. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Click to return to CD contents The transverse test - plus lens . been movedtoslowly downwards TheThe lenslens hashas nownow been returned its original positionbefore beforethe the chart, The and lens the hasthe horizontal now been limb moved appears slowly toto move the right upwards, chart, and the On limbs move back their original positions andagain appear next mouse will place abefore Notice that the limbs aretoinclick theiryou correct position thecontinuous chart, and AGAINST the vertical the movement limb appears the to lens. move to the with the limbs viewed outside the chart. plus sphere centrally inthrough frontof ofthe the chart... but they appear magnified lens... left, AGAINST the movement of the lens. MOVEMENT is obtained plusthe lenses in the transverse test. The AGAINST optical centre can be marked on thefrom lensall over intersection of the crosslines. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing The transverse test - minus lens Click to return to CD contents . The lens has now been returned to their its original The lens has slowly downwards Notice that the limbs are in correct position The lens hasnow nowbeen beenmoved moved slowly toposition the rightbefore beforethe On the next mouse click youappears will place chart,chart, and limbs move to also their original positions and appear and the horizontal limb appears to move downwards, but they appear minified through the lens... thethe chart, and the back vertical limb also toamove to minus sphere in front of chart... continuous with thecentrally limbs viewed outside chart. WITH the of lens. theagain right, WITH themovement movement ofthe thethe lens. The optical can be marked on the lens thelenses intersection of the crosslines. WITHcentre MOVEMENT is obtained from all over minus in the transverse test. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Click to return to CD contents Action of a plus cylinder Rotating the cylinder back again causes the limbs to SCISSOR backon to the theirlens original The cylinder axis can be marked whenposition. it has been rotated to On clockwise This Notice is a crossline rotation that Further the of chart. limbs the clockwise cylinder, appear On the rotation the to next be vertical mouse in of their the limb click original cylinder, rotates youpositions will anticlockwise place this position where a continuous appearance of the crosslines is obtained. and the ahorizontal but plus that cylinder just limb the produces held rotates vertical with clockwise further limb its axis is SCISSORS magnified VERTICAL towardsseen itinMOVEMENT. inthe inaduring front SCISSORS horizontal ofthe therotation chart… meridian. MOVEMENT. You can emulate the actual movement by reversing four times through this sequence (right click and select previous). Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Click to return to CD contents Action of a minus cylinder Rotating the cylinder back again causes the limbs to, The cylinder axis can be marked theoriginal lens when it has been rotated to SCISSOR back to on their position. On clockwise Notice On rotation that the next the Further of the limbs mouse cylinder, clockwise appear click the you to rotation be vertical will in place their of limb the original a also minus cylinder, rotates positions cylinder clockwise and this position where a continuous appearance of the crosslines isbut obtained. the horizontal that justlimb the held rotates vertical produces with its anticlockwise limb axis further appears VERTICAL SCISSORS towards minified in front itinMOVEMENT. inthe of a SCISSORS horizontal the chart…meridian. MOVEMENT. You can emulate the actual movement seen during the rotation test by reversing three times through this sequence (right click and select previous). Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Click to return to CD contents Use of the focimeter 120 120 100 100 90 90 80 80 60 60 140 140 40 40 160 160 20 20 180 180 + 180 180 0.75 0.75 0.75 0.50 0.50 0.50 0.25 0.25 0.25 0.00 0.00 0.00 0.25 0.25 0.25 0.50 0.50 0.50 0.75 0.75 0.75 This is the circular target which is brought into focus by rotation of the dioptre This is power the protractor knob. from which cylinder axis and base setting can be read. This is the central target area. The circular scales are calibrated in prism dioptres This aand typical view adjustment, of thewhich measuring scales If the instrument is correct when there no The target The vertical mayisbe ofinthe horizontal linear type crosslines must can be first rotated beisseen rotated tolens coincide sounder that the when you look a manually operated focimeter. test,coincide the the target should beinto seen in sharp focus the centre ofoblique the lines with cylinder with the axis principal direction, meridians or the ofbase an at astigmatic setting of an lens under test. andHere the power scale should readmeridians, zero, case here. Inprotractor the following prism. demonstration they now lie we along will assume the the as useis150 ofthe aand circular 60. target. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Click to return to CD contents Use of the focimeter 100 120 90 80 60 140 40 160 20 180 + 180 0.75 17.75 17.75 0.75 0.50 18.00 18.00 0.50 0.25 18.25 18.25 0.25 0.00 18.50 18.50 0.00 0.25 18.75 18.75 0.25 0.50 19.00 19.00 0.50 0.75 19.25 19.25 0.75 Then rotate the eyepiece slowly back inwards until the scales just come into sharp focus. Stop as soon as they come into focus. In order to do this, begin by turning the power adjusting Now rotate the adjustable eyepiece ring of the telescope to rack Before use end a manually operated focimeter knob rightyou to one of its reading range. It doesyou not out Youthe should eyepiece now to find itsthat fullest theextent. dioptricThe scale protractor reads exactly scale on zero. the mustwhether adjust its focusing your ownrange. use. matter it is the pluseyepiece or minusfor end of the graticule will become blurred is no longer in focus. If it does not now read zero,until the itinstrument needs servicing! You will notice that the green target is so much out of focus that it can no longer be seen. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Click to return to CD contents Use of the focimeter 120 120 100 100 90 90 80 80 60 60 140 140 40 160 160 20 20 180 180 The lens under test must be a plano-prism since the dioptre scale is reading zero. + 180 180 0.75 0.75 0.50 0.50 0.25 0.25 0.00 0.00 0.25 0.25 0.50 0.50 0.75 0.75 The base if thesetting target of lies anin oblique the position prism shown will here be here found and easier a left toeye read If theFinally, green target lies infocimeter the position indicated itcan signifies that theisoptical Now that the is ready for use we consider will notice that theis target is exactly centred over thethat middle The target is displaced upwards and its under if the you test, rotate the the reading crosslines 3 which base UP lie @ along 150 the which 90 &could meridians equally bethe that IfYou green target lies ingreen the position indicated here it180 signifies element under test incorporates 4 base IN at the measuring point, assuming We will begin by considering how the focimeter measures prism power. how it is used to read the powers of prisms and lenses. of the crosslines. Nois displacement of the target signifies that there is centre seen to lie over second ring. until one limb passes as 1.5 through base UP the and centre 2.6 ofbase the target. IN.measuring optical element incorporates 2 base UP at the the lens under testexpressed isunder for thetest right eye. It would be 4 base OUT if it were a point. left eye. no prismatic effect at the point on the lens which is being measured. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Click to return to CD contents Use of the focimeter 120 120 120 140 140 140 90 90 90 100 100 100 80 80 80 60 60 60 40 40 40 160 160 160 20 20 20 180 180 180 180 180 180 + 4.75 6.75 4.75 0.75 0.75 4.50 6.50 4.50 0.50 0.50 4.25 6.25 4.25 0.25 0.25 4.00 6.00 4.00 0.00 0.00 3.75 5.75 3.75 0.25 0.25 3.50 5.50 3.50 0.50 0.50 3.25 5.25 3.25 0.75 0.75 Adjusttothe position of the the target lens toappears centre the target.focus Continue refocus until in sharp willthe now consider focimeter islens usedrest In order Here, toWe read a the spherical back lens vertex hasishow been power placed of aalens onadjusting the you must ensure and that Refocus target by rotation of the power knob. (If the lens under test to frame, it read again. The power of the lensglazed under test can noworbe totarget determine the of spherical lenses. the At lens the is green placed withhas concave disappeared. surface Itelement, isblurred intoo contact blurred with to the be seen. lens rest. some point the target willpower reappear, and off-centre. incorporates aitsstrong it may from the power scaleprismatic and is seen to be -6.00. not be possible to centre the target.) Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Click to return to CD contents Use of the focimeter 120 120 120 120 140 140 140 140 90 90 90 90 100 100 100 100 80 80 80 80 60 60 60 60 40 40 40 40 160 160 160 160 20 20 20 20 180 180 180 180 -++ 180 180 180 180 1.25 0.25 1.25 0.25 0.25 0.75 0.75 1.50 0.50 1.50 0.50 0.50 0.50 1.75 0.75 1.75 0.75 0.75 0.25 0.25 2.00 1.00 2.00 1.00 1.00 0.00 0.00 2.25 1.25 2.25 1.25 1.25 0.25 0.25 2.50 1.50 2.50 1.50 1.50 0.50 0.50 2.75 1.75 2.75 1.75 1.75 0.75 0.75 Note that in whichever thethe prescription the first reading is the We canform record power of is therecorded, lens, either When aFurther spherical lens isof under test the consists of acylinder circle When Here The an Here the readings astigmatic We best the rotation will focus best are now lens +1.00 focus is consider the is obtained under power is when obtained how test, the with adjusting vertical the each the with focimeter horizontal dot the knob lines is vertical drawn brings are is lines in lines out the of into of ofadots. line sphere, the second reading the of the sphere the power ...or, / -1.00 xtarget 90. asreadings +1.00 / as +1.00 xsum 180... From these two we+2.00 can deduce the powerand of the lens under(the test. the focus which focal target the used and lines target iswhen parallel +2.00 to inwhen read thewhen with other reading the theone the power reading principal horizontal on of the of on an meridian principal power the astigmatic lines power scale are meridians into scale in lens. is sharp +2.00. focus. is focus. +1.00. the lens. of thefocus cylinder is whatever must be added to the first reading toof obtain the second) and the axis direction is the same as the lines in the second reading. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Use of the focimeter Click to return to CD contents 120 100 90 80 140 60 40 160 20 180 180 5.00 4.25 4.75 4.00 4.50 3.75 4.25 3.50 4.00 3.25 3.75 3.00 3.50 2.75 In the The case of an oblique cylinder should rotate the other power principal of the the meridian lens under the you lines test is, come therefore, into focus Notice that power scale reads -4.25 vertical and horizontal until are parallel when the -4.25 power /the +0.75 adjustment xcrosslines 150 (or knob -3.50 is turned / they -0.75 tox -3.50. 60). when lines lie along the 60 meridian. with the principal meridians of the lens under test. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Use of the focimeter Click to return to CD contents 120 100 90 80 140 60 40 160 20 180 180 2.25 2.25 0.50 2.00 2.00 0.75 1.75 1.75 1.00 1.50 1.50 1.25 1.25 1.25 1.50 1.00 1.00 1.75 0.75 0.75 2.00 The power of the lens under test is -1.50 / +2.75 x 15 Try this one by yourself ! ( or +1.25 / -2.75 x 105) Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Click to return to CD contents Use of the focimeter 120 100 90 80 140 60 40 160 20 180 180 4.00 1.50 1.00 1.50 2.00 1.25 4.25 2.00 2.25 1.50 4.50 2.25 2.50 1.75 4.75 2.50 2.75 2.00 5.00 2.75 3.00 2.25 5.25 3.00 3.25 2.50 5.50 3.25 Eitheris+2.50 / -0.75 x 45 Add +2.25! Here another one to try yourself This This This is the reading is one second reading is taken reading at at the at the the major near major What is the power of the lens? or This time a progressive power lens is under test. reference reference point point inin the themouse distance near portion. portion. Answer given on next click +1.75 / +0.75 x 135 Add +2.25 Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing The correction of ametropia Click to return to CD contents Vertex distance Correction of hypermetropia Correction of myopia Effective power in distance vision Effective power in near vision Vergence impressed in near vision Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing The correction of ametropia Click to return to CD contents Vertex distance vertex distance BS 2738: Part 3: 1991 Method of presentation of prescription orders for spectacle lenses BS 3.1 3521:On Part 1991 Glossary of terms relating to the ophthalmic and spectacle all 1: prescriptions and prescription orders, power oflenses the sphere (sphericalframes power) shall be stated for each eye or lens. vertexdistance distance should be from indicated by stating 01 205 vertex Distance the visual pointthe of anumber lens to of themillimetres corneal apex following the prescription, for example: NOTE. If the prescribed power is sufficiently high such that the vertex distance becomes significant, e.g. if the power exceeds 5.00 D, then the distance at which the power was +6.00/-0.50 90 at 12 measured should additionally be recorded inx the prescription. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing The correction of ametropia Click to return to CD contents Correction of Hypermetropia far point distance k M´ MR In hypermetropia, light from a distant object is is focused behind themacula. retina. This may There is a point, behind the eye, which conjugate withofthe If the can make surfaces sufficient effort too of accommodation, it may increase be due to eye the refracting weak refractive error), the axial Light converging towards thisbeing point would be(purely focused by the eye’s power to produce a sharp(axial image of a distant on thecase, macula, M´. lengthitsof the eye beingattoo error), or, point as isobject usually a combination optical system theshort macula. This virtual is calledthe the Far Point, MR. of these two factors (correlation ametropia). Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing The correction of ametropia Click to return to CD contents Correction of Hypermetropia vertex distance far point distance k d M´ F´ MR f ´V its second principal focus. Light from a distant object is focused by the lens at Since this is conjugate with thelens macula, the eye’s ownits optical system can In order for a spectacle to correct an eye, second produce focus, a sharpF´,focus the distant at the principal mustofcoincide withobject the eye’s farmacula, point MM´. R. TheThe backspectacle vertex focal length is made the sum lens, therefore, liesup at from its own ofback the vertex d, and pointfar distance, vertex focal fromthe thefareye’s point. k. V distance, V V length F´ f = ‘´ K==/ (1 kk +++dddK) ...but it is much easier to think of it terms of focal length! This can be expressed in dioptres... Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing The correction of ametropia Click to return to CD contents Correction of Myopia k M´ F´ MR The far point, MRlight , of the eyeobject lies Light inisfront of the placed atby the Myopia In myopia, is corrected from bymyopic minus a distant focused from ad distant ineye. frontAn object of object the retina. is focused f ´Vlenses. the lens farThis point be principal intosharp focus at the macula in the at may itswould second be due the refracting focus, which surfaces lies inbeing front too ofunaccommodated the strong lens.(refractive Since theeye. second principal myopia), focusthe coincides axial length with of thethe eye’s eye far being point, toowhich great is (axial conjugate myopia), with the macula, orthe a combination eye can produce of these a sharp two factors focus of(correlation the distantametropia). object at the macula, M´. f ´V = k + d Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Effective power in distance vision Click to return to CD contents Hypermetropia x F´ f´Vf´V new f ´lens f ´V +anx eye is that the second The condition for a spectacle correct V =toold principal focus of the lens must coincide with the eye’s far point. We will now consider what happens when changes are distance made to the vertex distance. To correct the eye at a greater vertex a plus must be made weaker. Thus if a plus lenslens is moved away from the eye, its focal length must be increased by the change in vertex distance. Plus lenses moved away from the eye get stronger. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Effective power in distance vision Click to return to CD contents Myopia x F´ MR f ´V new f ´V = old f ´V + x myopia, the pointaway lies infrom frontthe of eye, the eye. If aInminus lens is far moved its focal length To must be decreased the change in vertex distance. correct the eye atby a greater vertex distance a minus lens must be made stronger. Minus lenses moved away from the eye get weaker. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Effective power in near vision Click to return to CD contents stationary object -3.00 0 B -33.3 cm +3.00 We arriving will now at consider happens vertexand distance of a thin The vergence the frontwhat surface of thewhen lens the is -3.00D assuming a lens is leaving altered the when thesurface the lenswill is being used near vision. the light. lens, the vergence back be zero, thefor lens collimates Here, a +3.00D lens is being used for near vision at 33.3 cm in front of the lens. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Effective power in near vision Click to return to CD contents stationary object x -0.25 -3.25 B l < 33.3cm +3.00 Clearly, The light the leaving new the is lens distance is moved nowwill divergent decrease and by the the eye movement will need oftothe make lens an Suppose that the object lens now away from the eye, (i.e., down the nose) effort andofthe accommodation vergence arriving (about at the 0.25D) lens inwill order increase, to view theoriginal to near -3.25D. point clearly. towards object, which, in this case, has remained inhere its position. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Effective power in near vision Click to return to CD contents stationary object x B -3.25 -0.25 l < 33.3cm +3.00 It can be shown that, for small movements, x, the change in effective power is given by -xF(2L1 + F ) where L1 is the original object distance and F is the power of the lens. x is considered to be negative if the lens moves to the left, away from the eye. A graph of this expression showing how effective power varies with lenses of different powers is given later. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Effective power in near vision Click to return to CD contents object moves with lens x x B -3.00-3.000 B 0 -33.3 cm cm -33.3 +3.00 +3.00 Under these circumstances it can be shown that the change in effective power is 2a We will by now consider second situation where, when thethrough lens is case moved, thethe object given -xF( Lthe + F)lens . The shown above iseye, the unique when termalso Here, hassituation moved away from the a distance, moves through distance asmoved the theby object distance is, therefore, constant. in the bracket, Lthe + same F,object is equal zero, so lens, theaway change in effective power must be x, andthe hastoalso the same distance, x. also equal to zero. This result is indicated on the graph of effective power which follows. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Effective power in near vision Click to return to CD contents Change in effective power when lenses are used for near vision at 33.3cm and subsequently moved 5 mm away from the eye. +1.00 +0.80 +0.60 +0.40 Q = -x(L1+ F)2 +0.20 0.00 -0.20 Q = -xF(2L1+ F) -0.40 -10.0 -8.0 -6.0 -4.0 -2.0 0.0 +2.0 +4.0 +6.0 +8.0 +10.0 Lens power 2 when This is is aa plot plot of ofNote the expression, thatthat Q =Q0 =for Q -xsingle (LF1 =+1 + case F)F) whenxx(2L (L ==1-0.005m ++FF)) ==0.and 0. L11 = -3.00D. This the expression, Q == -xF(2L -0.005m and -3.00D. Note 0 the when 0, or when when 1 Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Vergence impressed in near vision Click to return to CD contents L1 = 0 = BVP BVP L´L´22 = F´ The form thevertex lens ispower immaterial. Provided that the are the The of back of a lens represents theBVPs vergence leaving the back surface when the incident vergence is zero. same, in distance vision, lenses of different forms are interchangeable . Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Click to return to CD contents Vergence impressed in near vision Note that you must first find the front curve before you can determine L´2. F1 = +12.06 B L1 = -3 L´2=2=+6.58 = +6.69 +6.87 L’L’ 2 B´ B’B’ +10.00 if the form changed equiconvex, its details remaining In Finally near the vision, the vergence impressed by a lens depends not only on its BVP, Now lenslens form hasischanged totoplano-convex, its other other details remaining same, for near object position, the vergence leaving the butthe also upon itsthe form andsame thickness. Here, a +10.00D made with a lens -3.00 the same, and, forsame the near object position, thelens vergence leaving the Clearly, in near vision, lenses of the same back vertex is now to beto+6.87. Again youaxial must find powers lens base curve, glass, nbe = 1.5 and an of 9mm, iscurve usedofforthe near lens willfound beinfound +6.69. Again youthickness must findsurface the front power but made in different forms are the not interchangeable. before tracing from the near object point. In this case, = Flens = is +4.92. vision attracing -33.3cm. The leaving the surface of +6.58D. before from thevergence near object point. Inback this case, F1 F is1 the found be +9.43. 2 to Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Vergence impressed in near vision Click to return to CD contents Near vision effectivity error The difference between the actual vergence leaving the lens, L´2, and the anticipated vergence on lens L1 the = -3basis of thin L’ +6.58 has been called the 2 = theory, error due to near vision effectivity (or near vision effectivity error, NVEE). Foranticipated example, in the case(found of the from +10.00 lens a -3.00 base The vergence L´ = L +made F ) forasthe +10.00 lens For this form the error due to near vision effectivity is -0.42 D. meniscus vergence leaving the lensiswas found to be =+6.58D. forms whichthe have just been considered -3.00 + 10.00 +7.00D. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Vergence impressed in near vision Click to return to CD contents Near vision effectivity error IfErrors the trial lens was of thelens usual plano-convex form, Suppose due that toseen near thethat trial vision used to the are determine a problem the We have the effectivity NVEE of final lens with the curved surface designed to face the eye, near with vision medium prescription to high-power was equiconvex plus lenses. in form. form which is likely to be dispensed is -0.42D. the “error” would be even worse, almost 0.50D! final lens Its NVEE is seen to be only -0.12D. Changing from this form to the final lens form without adjusting the power of the lens would mean that there is a loss in power of about 0.3 D. trial lens of symmetrical common form trial lens L´ 2 = +6.58 L´ L´ 2 =2 +7.02 = +6.87 NVEE = -0.42 NVEE NVEE= =+0.02 -0.12 Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Vergence impressed in near vision Click to return Lenses of different forms are not interchangeable In near vision. to CD contents In practice, tables of correction factors are available giving compensation for NVEE. Correction Factors The lens is then said to be compensated for errors due to near vision effectivity. Typically, compensation is required for both single vision lenses and for the near addition of bifocal lenses. Note that in the case of bifocal additions, the compensation is also required for the near addition when the DP precription is minus. This correction factor is valid when the seg is on the back surface of the lens. 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25 3.50 When lenses are prescribed for near vision, the form of the final lens is usually different from that of the trial lens. In such cases the back vertex power of the final lens must be increased by the amount shown in the Table opposite so that the effect of the final lens is the same as that of the trial lens. Near addition (D) Lens Power -10.0 -8.0 -6.0 -4.0 -2.0 0.0 +2.0 +4.0 +5.0 +6.0 +7.0 +8.0 +10.0 +12.0 +14.0 37 -0.25 0.0 +0.25 +0.50 +0.75 38 Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Centration of spectacle lenses Click to return to CD contents Horizontal centration of lenses Near centration distance Obtaining the measurements Geometrical insetting of bifocal segments Specification of segment top position Prismatic aspheric lenses Vertical centration - the centre of rotation condition The centre of rotation condition for near vision Centration errors - dispersion - off-axis blur Ghost images due to prism in a lens Graphical construction to find prismatic effect Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Horizontal centration of lenses Click to return to CD contents The type of centration errors we could make if we just specified a Furthermore, if progressive lenses were without The horizontal centration power specifications whichdispensed are actually required binocular PDdistance is illustrated here.the It is assumed that the horizontal centre This isasymmetry called interpupillary distance orthe PD. specifying monocular centration distances, their corridors clear vision are the measured fromof centre The becomes very distance of the frame exactly matches the PD, so that no horizontal You will see that, really, the PD isshown only useful as aRcheck wouldofbe offset. DoLook you very notice carefully how asymmetric at this face. it M is? the bridge of the frame. They are here as and ML. obvious if we bisect the face! decentration needs to be specified. for our measurement of the horizontal centration distance. MR PD ML OC These distances are equal. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Horizontal centration Click to return to CD contents Centration distance Under circumstances lie where visual First,these note that we assumethe thatcentration the visualpoints axes would pass through thethe centres axes intersect the spectacle plane. Into the of rotation prescribed prism, the We This distance, already of noted course, that is we the need know as absence the the horizontal distance distance from each between centration What we are trying to same achieve is demonstrated here. ofhave the eyes’ pupils and through the eyes’ centres and that these optical lensbridge would be positioned at the centration point. point the tomid-point the mid-point of of the ofdistance bridge the ofvision theofframe the frame andshown the which eye’s thecentre subject of is rotation. to wear. axes are centre parallel inthe and are directed towards infinity. Optimum position for optical centre spectacle plane monocular CD . R mid-point of frame bridge Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Horizontal centration Near centration distance Click to return to CD contents In near vision, we are interested in the Notice Thethat near this centration distance distance is not the issame seen l If monocular we know the reading distance, l, and the near centration distances as the to NCD be distance a function between of thethe distance pupil centres. CD. = CD. centre of rotation then the NCD measured in thedistance, spectacles, plane. l + can be expressed in terms of thesCD. l Remember, that it is the monocular NCDs which should be recorded. Optimum position for near optical centre NCD spectacle plane centres of converging pupils s CD Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Horizontal centration Click to return to CD contents Obtaining the measurements The following routine will be found to provide accurate and consistent results. • Fit the frame . . • Attach tape - if empty frame • Mark centre of bridge • Dot pupil centres Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Horizontal centration Click to return to CD contents Obtaining the measurements The monocular centration distances can now be measured and recorded. . Left eye value . Right eye value Monoc CDs are recorded as follows: 32 / 35. The right eye value is always written first. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Horizontal centration Click to return to CD contents Bifocal inset Suppose in the diagram below thatthe thenear bifocal segments seen only by Ldo eye Bifocal segments areeye usually inset to bring fields into coincidence. The fields ofonly view through the right and left would have seen byobtained R Ifapertures the near fields notthe coincide areas simply apertures here in otherwise, opaque, occluders. same shape the apertures, supposed to be D-shape, flat-top segments. there will be areas which fall only within the field of one eye. To make the fields coincident they should binocular overlap exactly field in the near point plane. segment aperture Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Bifocal segment insetting Click to return to CD contents The following method ensures that the segment insetting brings the near fields into coincidence. B This shows the distance InNow, order todiagram obtain the field of view. we will place amaximum bifocal lens portion a plus bifocal lens the centre ofofthe bifocal segment should be whose distance prescription is which Now, a plus lens which is correctly centred has been correctly centred for placed at the point where the visual invision front of the other eye. inaxis fornegative distance has been placed front It goes without saying, that distance in front of we the want eye. intersects the vision spectacle plane. of the andofitthe is seen that,aperture owing toto the the eye centre segment Noteout that the minus lens the exerts base prism exerted lens, the eye lie on when the visual axis by in order for the Clearly, the distance prescription is prism base in more at thetonear visual must converge view the near object. eye tothe obtain the maximum field of view. positive segment must of be inset more point, relieving the effort than we would decentre convergence,so minus single bifocalvision lenses forlenses near vision. should be inset less If there were no spectacle lens in front of the eye, it would rotate into this direction in order to view the near object point, B, on the midline. and inset so placed its centre lies It ... has now been in position Othe converging visual axis. inon the spectacle plane... D D than single vision lenses. spectacle plane This is the bifocal segment mid-line Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Geometrical insetting to bring the near fields into coincidence Click to return to CD contents monoc CD =p R s OS distance OC It can be shown thatfor theL geometrical Substituting -3.00D and +37.00Dinset, for Sg, for distance lens of power,isF,27mm) mounted (D) (soathe lens-eye separation weSobtain The following tablecentre of geometrical insetting inthe front of the eye’s rotation and L (D) useful average rule forofgeometrical inset: has been prepared from is this expression from the near point given by: g= g p.L = 3.p / (L / (40 + F-- F) S) g l Visual axis +8.00 +4.00 0.00 -4.00 -8.00 Table of geometrical insetting monocular centration distances 28 29 30 31 32 33 34 35 36 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 2.3 2.4 2.5 2.6 2.7 2.8 2.8 2.9 3.0 2.1 2.2 2.3 2.3 2.4 2.5 2.6 2.6 2.7 1.9 2.0 2.0 2.1 2.2 2.3 2.3 2.4 2.5 1.8 1.8 1.9 1.9 2.0 2.1 2.1 2.2 2.3 Tables such as this may be provided in practice in order to assist bifocal fitting. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing 37 3.5 3.1 2.8 2.5 2.3 Specification of segment top position Click to return to CD contents segment top position 44 HCL 23 22 If theAlthough final frame issegment the height can measured with a23simple For example, iffitted, the heights are measured as mm, ruler. Note, Bifocals however, thefor general thatsegment segment heights purpose height could usebe are is be defined specified usually as fitted as the measured, so distance that it is Remember thehorizontal other eye also. from the better the segment segment to give topthe top istosegment tangential tomeasure the lower top with position, the lower which tangent edge is of the tothe the vertical iris. lens and vertical dimension the frame isfor 44 mm, distance periphery With most ofthe the and subjects, segment shouldbox this be top, measured coincides above orof with asbelow illustrated the the linehorizontal of the the lower right centre lid. eye.line. then the segment top position = 1 above HCL. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Horizontal centration Click to return to CD contents Prismatic aspheric lenses An aspherical surface such as the ellipsoid shown here has a pole. s there is a further consideration. When dispensing aspheric lenses which incorporate prism, A1 x P The amount of decentration can be found as follows. A1 = pole of aspherical surface s = centre of rotation distance P = prismatic To effect ofWhen lens obtain the best frominthe prismperformance is incorporated theaspheric lens, thedesign, visual the In order coincide with the the visual thevisual pole of the pole of axis thetoaspherical surface should lieaxis, on axis. is deviated towards the apex of the the prism. aspherical surface must be decentred towards the prism The apex, pole theis, aspherical surfacedirection noxlonger on = the0.3 visual inofthe opposite to lies the prism base. Theofthat amount decentration = P.s / 100 P axis. So when the prism power is 3, the necessary decentration is about 1mm. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Vertical centration of spectacle lenses Click to return to CD contents The centre of rotation condition pantoscopic angle visual axis Typically the pantoscopic angle is 100. optical axis optimum position optimum for optical position centre for optical centre However, spectacle for frames are normallytilt toshown, compensate the pantoscopic ItInisorder easily from the geometry of the fitted socentre that the front is parallel with the The optical axis of the lens then continues If the spectacle frame is fitted like this, the the optical of the lens must be lowered 0 figure, that for each 1 pantoscopic angle, the line joining thebefore supra -orbital ridge and the to pass through the eye’s centre of rotation. optimum position for the optical centre would from its position the pupil centre. The optical centre should be lowered by 0.5 mm i.e.,the front tilted before thepupil. eyes. bechin, directly in front ofisthe centre of the amount depends upon the pantoscopic angle. The degree of tilt is called the pantoscopic angle. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Vertical centration of spectacle lenses Click to return to CD contents Required position of optical centre. HCL .. . Taking notecentre of thegive angle, the vertical required height the optical The ofpantoscopic rotation condition for centration is easily or, better still, the required heights of the OC from of the HCL. centresatisfied can be obtained pupil centre heightoffrom by fitting by themeasuring frame andthe marking the position the the lower horizontal tangent thehead lensisperiphery and simplyposition. subtracting pupil centres whentothe held in the primary 0.5mm from this measured value for each 1º of pantoscopic tilt. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Vertical centration of spectacle lenses Click to return to CD contents The centre of rotation condition for near vision D = distance visual point Primary visual axis for DV R = eye’s centre of rotation O = optical centre of lens D R O This figure indicates that the centre of rotation condition has been satisfied for distance vision. We see that in satisfying the centre of rotation condition for distance vision, the requirement for near vision is satisfied at the same time! Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Centration errors Click to return to CD contents . For Theexample most obvious if plus problem lenses are which not decentred arises from inwards incorrectly for near centred vision In addition to problems with binocular vision, the prism which is introduced by poorly lenses there is will thatbe unprescribed base out prism prismatic centred lenses may produce other noticeable effects which are a source of complaint. effect exerted is introduced at the nearbefore visual the points. eyes. . Errors in the vertical meridian of the lenses may give rise to intolerable vertical differential prismatic effects. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Centration errors Click to return to CD contents dispersion by a prism incident white light is dispersed by a prism into its monochromatic constituents. The angle between the emergent red and blue ends of the spectrum represents the angular dispersion or chromatic aberration of the prism. The chromatic aberration exhibited by a plano prism of power, P, made in a material whose V-value or Abbe Number is denoted by vd , is given by: P Click to return to previous screen chromatic aberration = Ophthalmic Lenses & Dispensing vd Click to skip to next topic Centration errors dispersion by a lens Click to return to CD contents incident white light is dispersed by a lens into its monochromatic constituents c OC lens power = F transverse chromatic aberration c.F the dispersion being due The same effect occurs with lenses, In theSo, case lens, the isTCA known aslens transverse TCA. Patorepresents the effect prismatic exerted bychromatic the the in of the case of a effect lens, where, c.F is theataberration, prismatic effect. =effect the prismatic of the at the point oflens incidence. point of incidence and is given vby Prentice’s rule, P = c.F. d P TCA = v d just as in the case of a plano-prism. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Centration errors Click to return to CD contents effects of dispersion When the prism is turned through 90º, Now consider the low-contrast When viewed through a through prism whose When viewed through a prism whose When the prism is turned 90º, Consider first a high contrast target The effectbase-setting of transverse chromatism upon the wearer depends upon the object being viewed. however, coloured fringes may be seen target the right. coincides with the base setting coincides the lines, however, theillustrated edges of on the bars oflines, the such as the one shownwith on the left. on edges bars the target. no effect can be seen on the acuity. target. no the effect can of bethe seen onof the target. target appear blurred, reducing high-contrast target low-contrast target This effect is sometimes described as off-axis blur and is due to the dispersion caused by the prism along its base-setting. It is minimized, by using lens materials with the highest possible V-value, or Abbé Number. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Centration errors Click to return to CD contents effects of poorly centred lenses This experiment demonstrates another effect of poorly centred lenses. Notice that the spot appears Rotate prism and notice On the the next mouse click youhow displaced towards the prism the ghost image alsoabove rotates. will introduce asitting low-power apex and that the It always appears displaced prism (say ½ see ) base DOWN spot you can a ghost image towards the prism apex. in frontisofinthe spotlight... which focus, like the spot. A A H H E E D DX XR RC C spot spot Click here to turn on >> the muscle spotlight. Now click here to >> room room turn off the room light. EGSKBY EGSKBY TQPKLNVDXA TQPKLNVDXA Once you have located this ghost in a darkened consulting room, switch the room light on again and see that the ghost is still visible, although somewhat more difficult to discern. The optics of this ghost image are considered in the next slide. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Centration errors Click to return to CD contents effect of poorly centred lenses Ghost image Dioptric image requirements areprism all met by prisms of the low intensity power! If theThese refractive index of the material is 1.5 In order for The a ghost image to be troublesome, three conditions dioptric image produced byofthe prism isimage, seen inmust this be direction. This shows the formation the ghost which is satisfied. of this ghost image is only 0.15%. Despite its dimness, you will 1) The ghost should be bright enough to bereflection noticeable. produced by total internal at the lens surfaces. This ghost image is experiment often complained of quite by wearers of low-power prisms, have seen in the that it is noticeable, even when 2) The vergence of the ghost should beofsimilar to thatdof= the The deviation this image, (n -lens. 1)a by subjects who are are switched wearing multifocals have been prism-thinned the lights back on in which the consulting room. The vergence of The this ghost canof bethis shown to beimage (3n-1).F (n-1). n = 1.5, this deviation catoptric is /(3n - 1)When a and those who are wearing low-power, poorly centred lenses. turns out to be 7F. For a plano-prism its vergence is zero and it is in sharp focus. 3) The ghost must lie close to the fixation line (but not superimposed). A multi-layer anti-reflection coating reduces the intensity of the image, almost to zero. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Graphical construction Click to return to CD contents to find prismatic effect on an astigmatic lens Example: find the vertical and horizontal prismatic effects at a point which lies 10mm down and 4mm inwards from the optical centre of the lens R +4.00 / +2.00 x 30. Begin by finding the prism due to the sphere. Notice theThis cross-sectional ofof the lens iseffect the optical the The prismatic due shape tocentre the sphere region of meridian, R. In the vertical spherical +4.00 component. isthe found from Prentice’s law, P meridian = cF. Ininthe horizontal the cross-sectional the lens shape resembles a prism base UP. shape resembles a prism with its base OUT. Thismeridian, is point atcwhich In the vertical = 1cmwe are findingmeridian the prismatic effect. In the horizontal c = 0.4cm. Hence: . OC . R PV = 1 x 4 = 4 base UP PH = 0.4 x 4 = 1.6 base OUT Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Graphical construction Click to return to CD contents to find prismatic effect on an astigmatic lens Example: find the vertical and horizontal prismatic effects at a point which lies 10mm down and 4mm inwards from the optical centre of the lens R +4.00 / +2.00 x 30. There is no power along the axis meridian of a plano-cylinder, hence the cylinder can exert no prismatic effect along +2.00 its axisxmeridian. Now we must consider the prism due to the cylinder 30 +2.00 x 30 All the power of a cylinder lies at right angles to its axis, i.e., along its power meridian, so a cylinder exerts prismatic effect only along its power meridian. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Graphical construction Click to return to CD contents to find prismatic effect on an astigmatic lens Example: find the vertical and horizontal prismatic effects at a point which lies 10mm down and 4mm inwards from the optical centre of the lens R +4.00 / +2.00 x 30. P The cylinder can only produce a prismatic We will first consider how to find the baseeffect direction the prismtothe due to thei.e., cylinder. at right angles its prismatic axis, along In order toofdetermine effect themust 120 meridian of the lens.and at R, we resolve the vertical R horizontal decentration alongpart the Now notice This find iswhere the point the at thickest which we ofpower the We must the perpendicular distance, meridian of theprismatic are finding cylinder lies with respect toeffect. point, R. axis. It is PR, of the point Rcylinder. from the cylinder up and out along 120 with respect to R. +2.00 x 30 . Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Graphical construction Click to return to CD contents to find prismatic effect on an astigmatic lens Example: find the vertical and horizontal prismatic effects at a point which lies 10mm down and 4mm inwards from the optical centre of the lens R +4.00 / +2.00 x 30. Evidently, P lies above R and on its Then mark the position of the point, First, construct and Next, determine theorigin base direction of R, Next draw indetails the an cylinder axis along The simplest method is to use a 30º graphical construction, of which follow. temporal side. When thehere cylinder is to scale on the diagram, 10mm mark the nasal side of the lens the prismatic effect at R. Ask yourself, If the cylinder had been negative in sign, P its prescribed axis direction, here, 30º. Now drop a perpendicular from R Does P lie above R or below it? P N positive sign ,inas in this down andin4mm from theexample, origin. “where does Paxis lie with respect wouldDoes represent thethe position of theof prism apex. to thePcylinder meeting at lie on side RtoP. orR?” does P represents the nasal position of itthe prism The base would been side DOWN & IN it lieso onhere, thehave temporal R? base, the base is say, UPof&10:1. OUT. Choose a large scale, . R Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Graphical construction Click to return to CD contents to find prismatic effect on an astigmatic lens Example: find the vertical and horizontal prismatic effects at a point which lies 10mm down and 4mm inwards from the optical centre of the lens R +4.00 / +2.00 x 30. P Q N . R The vertical prismatic effect at R due to the cylinder is given by: PQPR, (cm) xvertical Fcyl. and Since we the PQ QR isdistance, the the require effective effective decentration decentration of of the the Theis represents the horizontal prismatic can plano-cylinder in theeffects vertical horizontal meridian. meridian. effective decentration of thewe planonow resolve PRitsinto vertical and cylinder along power meridian. horizontal components, andatQR. The horizontal prismaticPQ effect R due to the cylinder is given by: QR (cm) x Fcyl. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Graphical construction Click to return to CD contents to find prismatic effect on an astigmatic lens Example: find the vertical and horizontal prismatic effects at a point which lies 10mm down and 4mm inwards from the optical centre of the lens R +4.00 / +2.00 x 30. In this example: by measurement: PQ = 9.2mm QR = 5.3mm P N Hence the prism due to the cylinder is: Q . R PV = 0.92 x 2.00 = 1.84 base UP PH = 0.53 x 2.00 = 1.06 base OUT Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Graphical construction Click to return to CD contents to find prismatic effect on an astigmatic lens Example: find the vertical and horizontal prismatic effects at a point which lies 10mm down and 4mm inwards from the optical centre of the lens R +4.00 / +2.00 x 30. Prism due to sphere OC . .R So we have found: Prism due to sphere = 4 base UP & 1.6 base OUT Prism due to cylinder = 1.84 base UP & 1.06 base OUT Prism due to cylinder P Q N Total prismatic effect = 5.84 base UP & 2.66 base OUT .R Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Lens thickness and weight Click to return to CD contents Edge thickness of a minus lens Thickness of plus lens Variation in thickness of aspheric lens Astigmatic prismatic lenses Graphical construction for thinnest point on edge Lens weight Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Lens thickness Click to return to CD contents Edge thickness of minus lens t This is a cross-sectional view of a plano-concave lens e s y Sag 10.00 at 60, n = 1.56 e is the edge thickness We have: y = 30, r = 56 r t is the centre thickness First, find the radius of surface r sag = 1000(n - 1) / Curve Suppose wethe wanted to from: find the of a 10.00D curve at 60 2 2 The the semi-diameter of the is 60 / 2 = 30mm diameter, of lens the lens being 1.56. y refractive index 30material s is the sagsof=the concave surface = = 8.71mm. Centre of surface = 1000(1.56 - 1)2 /of10curvature 2 r + r2 - y2 56 + 56 - 30 From the geometry of the figure = 56mm e = t+s The quantity, s, is calculated from the sag formula, s = y2 r + r2 - y2 Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Lens thickness Click to return to CD contents Edge thickness of minus lens t s1 This is a cross-sectional view of a curved minus lens s2 e e is the edge thickness t is the centre thickness s1 is the sag of the convex surface s2 is the sag of the concave surface From the geometry of the figure: so t + s2 = e + s1 e = t + s 2 - s1 Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Lens thickness Click to return to CD contents Edge thickness of minus lens Consider a -6.00 lens, made in glass, n = 1.523, with +4.00 base and centre thickness of 1.0mm. 7.0mm 5.0mm 3.5mm At diameter diameter is 60mm: If the reduced to 40mm: 50mm: s1 = 3.5 s1 = 1.5 2.4 s2 = 9.5 s2 = 4.0 6.4 e = te+s s12 - s1 = 2t -+s = 7.0mm = 3.5mm 5.0mm -6.00 at 40 edge subs = 3.5 mm -6.00atat60 50 edge edgesubs subs==7.0mm 5.0mm -6.00 The cross-sectional shape of a minus lens reminds us that the smaller the lens diameter, the thinner will become the lens. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Lens thickness Click to return to CD contents Edge thickness of minus lens Consider a -6.00 lens, made in glass, n = 1.523, with +4.00 base and centre thickness of 1.0mm. Note: If the overall diameter of the lens is 50mm but it has been decentred 4mm inwards, the edge thickness would change as follows: This Thisisisthe theoptical geometric centre centre of the of the lens lens .. 25 29 50 25 21 The edge thickness on the temporal side of the lens, eT, is that of a 58 diameter lens. The edge thickness on the nasal side of the lens, eN, is that of a 42 diameter lens. eN = 3.7mm eT = 6.2mm Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Lens thickness Click to return to CD contents Thickness of plus lens This is a cross-sectional view of a plano-convex lens s e t e is the edge thickness t is the centre thickness s is the sag of the convex surface From the geometry of the figure t = s+e Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Lens thickness Click to return to CD contents Thickness of plus lens This is a cross-sectional view of a curved plus lens t s1 s2 e s1 is the sag of the convex surface s2 is the sag of the concave surface e is the edge thickness t is the centre thickness From the geometry of the figure: so t + s2 = e + s1 t = e + s1 - s2 Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Lens thickness Click to return to CD contents Thickness of plus lens If edged down to the smaller diameter 40mm with the edge increases even more. Consider a +6.00 uncut, CR 39, n of = 1.498, -4.00thickness base andthickness edge thickness of 0.5mm. When this uncut ismade edgedindown to a diameter of 50mm the edge increases. At diameter 50mm: 65mm: F1 = +9.52 t = 7.5mm 7.5mm s1 = 4.0 11.3 6.4 s2 = 2.5 1.6 4.3 e = t - (s1 - s2) = 5.1mm 0.5mm 3.6mm +6.00 at 40 65 50 edge subs = 5.1mm 0.5mm 3.6mm In order Thisto edge obtain thickness a reasonable is unacceptable edge thickness, and it is plus quite lenses clearshould that plus be lenses surfaced downover to aabout suitable +2.00D diameter should fornot thebe shape edged when down all to themuch prescription smaller details sizes. are known. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Lens thickness Click to return to CD contents Thickness of plus lens The problems are even greater with plus astigmatic lenses Consider the specification +3.00 / +2.00 x 180 which is to be edged to a 48 x 40 oval shape. 1.5 e thin mm 1.5 mm e thick 1.6mm 1.6 mm The thickest points on the edge of the lens lie at each end of the horizontal meridian. The centre thickness will then be 3.5 mm. +3.00 48 The Thehorizontal horizontaldiameter power of of the the lens lens is is 48mm +3.00 40 +5.00 The The vertical vertical diameter power It will The be realised that the edge substance ofto this lens thinnest points on the edge the lens lie varies We will custom-design theoflens of of the the lens lens is is 40mm +5.00 from at only to at 1.6mm round edge the1.5mm extremities of the vertical meridian. give 1.5mm this point onthe the edge.of the lens. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Lens thickness Click to return to CD contents Thickness of plus lens The problems are even greater with plus astigmatic lenses Now consider the specification +3.00 / +2.00 x 90 which is to be edged to the same oval shape. The thickest points on the edge of the lens now lie at each end of the vertical meridian. e thick 3.3 mm 3.3mm The centre thickness will then be 4.5 mm. +5.00 48 e thin 1.5mm The Thehorizontal horizontaldiameter power of of the the lens lens is is 48mm +5.00 40 +3.00 The The vertical vertical diameter power Not only is Itthe lens 1.0mm thicker inon the centre, thethe edge from 1.5mm The thinnest points the edge of lensnow nowvaries willcustom-design be realised that edge substance We will again thethe lens to give 1.5mmof atthis thislens pointnow on the edge. of of the lens lens is 40mm +3.00 at the thinvaries edge, at the thick edge simply because the axis lies at 90. lieto at3.3mm the1.5mm extremities of is the horizontal meridian. from to 3.3mm round the edge of the lens. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Lens thickness Click to return to CD contents Variation in thickness of aspheric lens Aspheric lenses have the advantage that they are flatter and thinner than spherical lenses so that when edged down the edge thickness is not so great. 65mm: At diameter 50mm: Spherical lens F1 = +9.52 t = 7.5mm 7.5 6.4 Aspheric lens F1 = +6.80 t = 6.4mm 65 +6.00 uncuts at 50 edge thickness = Spherical Aspheric 0.5 3.6 0.5 2.8 Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Lens thickness Click to return to CD contents Astigmatic prismatic lenses In the generalWe case, will now a plus consider lens may thehave thickness spherical, of circular cylindrical plus and lenses prismatic power. which incorporate both cylindrical and prismatic power. This is the spherical component of the lens. It This This is is athe plano-cylindrical prismatic component component with its with its axis may be considered to incorporate the bending of the baseatDOWN 90. Note (at 270). that Note this component that this component has zero edge lens. Note that if the element is centred, its edge hasthickness zero edge at thickness the extremities at its apex of the(at 180 90). meridian. thickness will be the same all round the periphery. cylindrical spherical prismaticelement element Variation in edge thickness of circular lenses Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Lens thickness Click to return to CD contents Astigmatic prismatic lenses The thickness of a plus sphero-cylindrical lens which incorporates prism (or decentration) is seen to be made up from the thickness of each of these three individual components. spherical element cylindrical element prismatic element Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Lens thickness Click to return to CD contents Astigmatic prismatic lenses Consider the prescription R +2.00 / +4.00 x 90 with 4 base OUT which is to be produced with an uncut diameter of 60mm and zero edge thickness. The spherical element is +2.00 The cylindrical element is +4.00 x 90 The prismatic element is 4 base OUT The centre thickness of this component is 1.9mm The centre thickness of this component is 3.6mm The centre thickness of this component is 2.4mm Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Lens thickness Click to return to CD contents Astigmatic prismatic lenses Consider the prescription R +2.00 / +4.00 x 90 with 4 base OUT which is to be produced with an uncut diameter of 60mm and zero edge thickness. The thickness of the specification is made up as follows: The spherical element The prismatic element 4 base OUT, tC = 2.4 +2.00, tC = 1.9 Note that the edge thickness of this lens is zero at the nasal edge. The total centre thickness of the lens is seen to be 7.9mm. The cylindrical element +4.00 x 90, tC = 3.6 Click to return to previous screen Ophthalmic Lenses & Dispensing Click to skip to next topic Lens thickness Click to return to CD contents Astigmatic prismatic lenses Now consider the prescription R +2.00 / +4.00 x 90 with 4 base DOWN also to be produced with an uncut diameter of 60mm and zero edge thickness. The spherical element is +2.00 The cylindrical element is +4.00 x 90 The prismatic element is 4 base DOWN The centre thickness of this component is 1.9mm The centre thickness of this component is 3.6mm The centre thickness of this component is 2.4mm Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Lens thickness Click to return to CD contents Astigmatic prismatic lenses R +2.00 / +4.00 x 90 with 4 base DOWN 60mm and ethin = 0. The thickness of the specification is made up as follows: Note that the minimum edge thickness of the lens is no longer zero. Both prism and cylinder contribute some thickness to the thinnest point on the edge. The prismatic element 4 base DOWN, tC = 2.4 The spherical element +2.00, tC = 1.9 If this lens is to have zero edge thickness it is seen that the centre thickness must be reduced. The cylindrical element +4.00 x 90, tC = 3.6 Click to return to previous screen Ophthalmic Lenses & Dispensing Click to skip to next topic Lens thickness Click to return to CD contents Astigmatic prismatic lenses R +2.00 / +4.00 x 90 with 4 base DOWN 60mm and ethin = 0. To obtain zero edge thickness, the centre thickness can be reduced by 2.0mm. The spherical element Nowthickness The the edge here thickness can beofreduced the lensby is 2.0mm zero. The prismatic element 4 base DOWN, tC = 0.4 +2.00, tC = 1.9 To obtain zero edge thickness the centre thickness of the lens need be only 5.9mm. The cylindrical element +4.00 x 90, tC = 3.6 Click to return to previous screen Ophthalmic Lenses & Dispensing Click to skip to next topic Lens thickness Click to return to CD contents Astigmatic prismatic lenses R +2.00 / +4.00 x 90 with 4 base DOWN 60mm and ethin = 0. position onpoints the edge of the lens where the edge thickness zero. InNote fact,the there are two on the edge where the edge thickness is is a minimum. emin emin 160 20 160 20 180 meridian Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Lens thickness Click to return to CD contents Astigmatic prismatic lenses The position on the edge of an astigmatic, prismatic lens where the thickness is a minimum can be determined by means of a graphical construction. Note first, that the thinnest point on the edge of the cylinder lies at When these two components are the extremities of the minus cyl axis. combined, the thinnest point on the edge of the combination must lie somewhere between thethinnest prism Also note that the apex point and the cylinder axis. on minus the edge of a plano prism lies at the prism apex. prism apex emin minus cyl axis The The prismatic cylindricalelement element Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Lens thickness Click to return to CD contents Astigmatic prismatic lenses The position on the edge of an astigmatic, prismatic lens where the thickness is a minimum can be determined as follows. The angle Next, between the edge the angle, ruler (line EFD) andthe thebase basesetting line AB, FEB in calculate the of acute , between of (angle the place a ruler on the construction and adjust itsdraw position until the the Finally figure) givesand the angle, , between the minus cylinder axis adirection and the lies point prism the minus cylinder axis direction and line from B,zero 200P Next, draw aof horizontal Then, line, AB, construct 10 units perpendicular, to represent BC, the from minus B from cylinder axis direction. First, calculate thethe quantity: z =a long onthe line AB, the edge passes through point Dwhere and BD the distance to the on edge of astigmatic, prismatic the thickness isbelow). a zero minimum. length, z, inclined at angle, , dF tolens AB, (line in the figure BC, ismeasured exactly 10inunits. (EF =angle 10 units in thethe diagram Noteperpendicular, the angle is always the acute between minusbelow.) cylinder axis direction and the prism base setting, in the direction towards the prism apex. where and C P is the prism power d is the lens diameter F is the power of the cylinder D z A F B E Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Lens thickness Click to return to CD contents Astigmatic prismatic lenses By way of example, take the prescription R +2.00 / +4.00 x 90 with 4 base DOWN which is to be produced with an uncut diameter of 60mm and zero edge thickness. Next, acute angle, , between setting of B the prism, which lies Next, drawcalculate aplace horizontal line, Then, AB, construct 10 units along perpendicular, to the represent the from minus cylinder axis direction. Finally athe ruler onBy the construction and adjust itsBC, position until the zero lies measurement angle base = 20º. where P is the prism power, 4. in aton90, and axis direction, is atdistance 180. The angle , , isthe 90º line AB,the theminus edgecylinder through Dwhich and the from zero toeach Remember that when passes = 90 there are point two minima on the dedge of the lens, 200P is the lens diameter, this example, we must draw 10 a line B,=of10 length, 3.33 units, inclined at 90º 60 to AB First, calculatesothe quantity: zunits. = from perpendicular, BC, is exactly (EF units in the diagram below.) symmetrical with the minus cylinderdF axis on and the side of the prism apex. (line BD in the figure below). F is the power of the cylinder, 4 z = 200x4 60x4 = 3.33 C D F z = 3.33 = 90 A B E Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Lens weight Click to return to CD contents Density One of the physical properties which is published by lens material manufacturers is the density of the material. Glasses Plastics Material nd Density White 15 White 16 White 17 White 18 White 19 1.523 1.600 1.701 1.802 1.885 2.54 2.63 3.21 3.65 3.99 1.500 1.557 1.586 1.595 1.670 1.710 1.32 1.23 1.20 1.36 1.32 1.40 CR 39 mid-index Polycarbonate high index high index high index The density is expressed in grams per cubic cm (g/cm3) Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Lens weight Click to return to CD contents Density 10mm Water CR 39has material a density has aofdensity exactlyof1.0 1.32. 10mm 3 of water This means so 1cmthat 1cm3 of weighs CR 391gram. weighs 1.32g. 10mm Density expresses the weight in grams of one cubic centimetre of the material. 1cm33 of crown glass weighs 2.54g so 1cm of CR 39 weighs 1.32 grams so this glass is 2.54x heavier than water CR 39 is 1.32x heavier than water. and about twice as heavy as CR 39! Note that the weight is found by multiplying the volume by the density of the material. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Lens weight Click to return to CD contents Density But, in reality Naturally, we cannot we want justspectacle comparelenses the densities to be asoflight the materials as possible. since higher The density of plastics materials is about half that of glass so refractive index materials will have less volume, owing to the fact that the same that plastics lenses areofabout half on theamust weight glass lenses. curve Thiswill means produce thatathe higher density surface the power material higher beofrefractive as low as index possible. material. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Lens weight Click to return to CD contents Weight of plus lens y Consider,The first, the cylindrical plate weight of a circular spectacle lens is founde by multiplying the volume of the lens by the density of the lens material. The volume of this plate is .y2.e spherical cap… …combined withup a cylindrical plate. components. A plano-convex lensacan be considered to be made from two separate Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Lens weight Click to return to CD contents Weight of plus lens y s Now consider the spherical cap y r The volume of the cap is .s2(3r - s) / 3 Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Lens weight Click to return to CD contents Weight of plus lens The volume of a plano-convex lens is the sum the of the The of volume The volume of the cap 2.e can- be that if the lens is of the 2usual curved form necessary 2(3r theplus cylindrical spherical cap plate 2 itisis.y 2 isSo .sItthe s) /seen 3volumes volume of a plusofmeniscus lens isplate .(s1and (3rthe 1 - s1) / 3 - s2 (3r2 - s2) / 3 + y .e) to subtract the spherical cap which forms the concave surface from the sum 2the of the convex cap and the plate thickness. . which (s2 and (3r represents - ss) and / 3 +r yrelate .e). edge where s1 and r1 relate toi.e., thevolume convex = surface to the concave surface. 2 2 spherical cap cylindrical The volume of a plano-convex lens isplate the sum of the Note that thevolumes density ofofthe material is normally in gramscap. per cubic centimeter thelens cylindrical plate and quoted the spherical so the volume of the lens must be calculated in cubic centimeters, by substituting s, r and y in cm into the above formula. Also, the formula relates only to the volume of a round lens. The weight of the lens is found by multiplying its volume by the density of the lens material. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Lens weight Click to return to CD contents Weight of minus lens e So A plano-concave the volume of alens plano-concave can be considered lens is the to consist volumeofofathe thick plate cylindrical which represents plate of thickness, the edge e, thickness from which minus a spherical the volume capofhas thebeen spherical removed. cap. The volume of the plate is .y2.e and the volume of the cap is .s2(3r - s) / 3 hence, the volume of the lens is .(y2.e - s2(3r - s) / 3) Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Lens weight Click to return to CD contents Weight of minus lens 2 (3rvolume the case a curved form minus of -the … so the In volume of aof minus meniscus lens islens, .(s1the s22convex (3r2 - s2) / 3 + y2.e) 1 - s1) / 3 spherical cap which represents the front surface must be added... where s1 and r1 relate to the convex surface and s2 and r2 relate to the concave surface. This is exactly the same result as that obtained for plus meniscus lenses. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Lens weight Click to return to CD contents Weight of minus lens .s12 (3r1 - s1) / 3 + .y2.e - .s22 (3r2 - s2) / 3 The total …the volume volume of…minus a curved of a flat the lens cylindrical volume is made ofplate the up from concave which therepresents volume spherical of the cap. the edge convex thickness... spherical cap... This statement is true for both plus and minus lenses. The volume of meniscus lenses is .(s12 (3r1 - s1) / 3 - s22 (3r2 - s2) / 3 + y2.e) Remember that the volume must be calculated in cubic centimetres by substituting s, r and y in cm into the above formula. Also, the formula relates only to the volume of a round lens. Once again, the weight of the lens is found by multiplying its volume by the density of the material. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Lens weight Click to return to CD contents Weight of minus lens As an example, consider a -6.00D lens made in spectacle crown glass, n = 1.523, D = 2.54, with a +4.00D base curve, a centre thickness of 1.0mm and edged to a 60mm diameter. r1 = 13.075cm s1 = 0.349cm The convex spherical cap has a radius of 130.75mm and a sag at ø60 of 3.49mm. edge thickness of the lens is 6.97mm TheThe concave spherical cap has a radius of 52.3mm and a sag at ø60 of 9.46mm. r2 = 5.23cm s2 = 0.946cm e = 0. 697cm y = 3.0cm The volume of the lens is .(s12 (3r1 - s1) / 3 - s22 (3r2 - s2) / 3 + y2.e) = .(0.3492 (3x13.075 - 0.349) / 3 - 0.9462 (3x5.23 - 0.946) / 3 + 32x0.697) = 10.85cm3 Weight = volume x density = 10.85 x 2.54 = 27.56g. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Lens design and performance Click to return to CD contents Off-axis performance of spectacle lenses Field diagrams Best form lenses - point focal lenses Best form lenses - Percival lenses Best-form lenses - Minimum T-Error lenses Aspheric spectacle lenses Tscherning’s Ellipses Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Lens design and performance Click to return to CD contents Off-axis performance of spectacle lenses The back of a lens is the vergence leavingoff-axis the The eyevertex is notpower stationary but rotates to view through back surface is zero,these the light portions of thewhen lens. the Theincident effect ofvergence the lens under conditions Whenvaries the eye rotates 40ºobject. the effect of the is effect +4.00/+1.25. emanating from athe distant It expresses the the with ocular rotation and thelens form of the of lens. lens the eye20º looks optical When thewhen eye rotates the along effect the of the lensaxis. is +4.00/+0.25. The refracted pencil is afflicted with aberrational astigmatism. +4.00 / +1.25 +4.00 / +0. 25 +4.00 40º 20º +4.00 The form of this lens is quite shallow, the back surface power is only -1.50D. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Lens design and performance Click to return to CD contents Field diagrams In practice, the off-axis powers are measured from the vertex sphere, an imaginary spherical surface concentric with the eye’s centre of rotation. +4.00 / +1.25 +4.00 / +0. 25 +4.00 40º 20º vertex sphere +4.00 For a 40º rotation of the eye, the sagittal oblique vertex sphere power is +4.00 and the tangential oblique vertex sphere power is +5.25 Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Lens design and performance Click to return to CD contents Field diagrams ocular rotation The off-axis performance is usually shown in the form of a field diagram where oblique vertex sphere powers are plotted against ocular rotation. +4.00 / +1.25 400 .S .T .. For 40º rotation the For 0º rotation the effect is +4.00/+1.25. effect is +4.00. For 20º rotation the effect is +4.00/+0.25. 300 200 +4.00 / +0. 25 +4.00 40º 20º 100 . 00 +3.0 +4.0 oblique vertex sphere powers +5.0 FIELD DIAGRAM vertex sphere +4.00 S = plot of sagittal powers FIELD DIAGRAMS FOR SPECTACLE LENSES Tangential & sagittal oblique vertex sphere powers 6.00 4.00 2.00 0 5 10 15 20 25 30 35 0.00 40 oblique vertex sphere powers T = plot of tangential powers ocular rotation in degrees Click to return to previous screen In practice, field diagrams are plotted by the computer. Ophthalmic Lenses & Dispensing Click to skip to next topic Lens design and performance Click to return to CD contents Best form lenses T&S FIELD DIAGRAMS FOR SPECTACLE LENSES Tangential & sagittal oblique vertex sphere powers 2.00 0 5 10 15 20 25 30 0.00 40 oblique vertex sphere powers 6.00 4.00 35 400 ocular rotation in degrees 0 The first 30 best-form lenses were quite steeply curved and were designed to be free from oblique astigmatism. -6.00 +4.00 Point focal lens 200 The fieldcurve diagram for a point focal A +4.00D lens would need an inside of -6.00D. 0 10 lens would look like this. 00 +3.0 +4.0 +5.0 FIELD DIAGRAM Point focal lenses are free from oblique astigmatism but suffer from mean oblique error; the mean oblique power of the lens decreases as the eye rotates away from the axis. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Lens design and performance Click to return to CD contents Best form lenses MOP = BVP S T A second 400type of best-form lens was introduced which was flatter in form and designed to be free from mean oblique error. 300 A small amount of oblique astigmatism was tolerated providing that the disk of least confusion of the astigmatic pencil fell on the 0 retina. This20followed a suggestion made by the ophthalmologist, Thesubsequently field diagramnamed for a Percival Dr A. Percival and the design was after him. 0 10 form lens would look like this. A +4.00 Percival form lens would need an inside curve of -4.00D. 6.00 4.00 2.00 0 5 10 15 20 25 30 35 0.00 40 oblique vertex sphere powers FIELD DIAGRAMS FOR SPECTACLE LENSES Tangential & sagittal oblique vertex sphere powers ocular rotation in degrees -4.00 +4.00 Percival lens 00 +3.0 +4.0 +5.0 FIELD DIAGRAM The mean oblique power, (MOP) is seen to be the same as the back vertex power of the lens, the mean oblique error is zero. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Lens design and performance Click to return to CD contents Best form lenses FIELD DIAGRAMS FOR SPECTACLE LENSES Tangential & sagittal oblique vertex sphere powers oblique vertex sphere powers 400 S T 6.00 4.00 2.00 0.00 0 5 10 15 20 25 30 35 40 Modern best-form lenses are designed with a compromise 0 bending30so that the tangential power is the same as the back vertex power. They are free from tangential error and known as 0 Minimum20T-Error forms. They exhibit a small amount of oblique The field diagram for a Minimum astigmatism, but only about half that of a Percival design. 0 10 T-Error form would look like this. ocular rotation in degrees -5.00 A +4.00D lens would need an inside curve of -5.00D. 0 0 +4.00 Minimum T-Error lens +3.0 +4.0 +5.0 FIELD DIAGRAM Minimum T-Error forms have the advantage that they perform well over a wide range of vertex distances. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Lens design and performance Click to return to CD contents 400 Best form lenses S T 6.00 4.00 2.00 0 5 10 15 20 25 30 0.00 35 oblique vertex sphere powers FIELD DIAGRAMS FOR SPECTACLE LENSES Tangential & sagittal oblique vertex sphere powers 40 Effects of changes in vertex distance with Minimum T-Error forms ocular rotation in degrees T&S S 400 400 300 300 300 200 200 200 100 100 100 00 +3.0 +4.0 +5.0 Minimum T-error at design vertex distance 00 +3.0 +4.0 +5.0 Point focal at long vertex distance 00 +3.0 +4.0 T +5.0 Percival at short vertex distance Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Lens design and performance Click to return to CD contents Aspheric spectacle lenses 1.0mm -5.25 70 6.6mm The flatter a spectacle lens is made, the thinner it may become. Best-form lenses made with spherical surfaces are usually quite steeply curved and therefore thicker than if made in flatter forms. For example, a point focal +4.00Dlens made in CR 39 material, would have back curve of -5.25, and if the uncut diameter is 70mm and the edge thickness is assumed to be 1.0mm, then the centre thickness of the lens would be 6.6mm and the weight of the uncut lens would be 20.3 grams. +4.00 Point focal lens made in CR 39. Weight = 20.3g Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Lens design and performance Click to return to CD contents Aspheric spectacle lenses T&S 1.0mm 400 300 200 6.00 4.00 2.00 0 5 10 15 20 25 0.00 40 oblique vertex sphere powers FIELD DIAGRAMS FOR SPECTACLE LENSES Tangential & sagittal oblique vertex sphere powers 30 70 6.6mm 35 -5.25 ocular rotation in degrees 100 +4.00 Point focal lens 00 +3.0 +4.0 +5.0 FIELD DIAGRAM Weight = 20.3g The field diagram for this point-focal +4.00 design would look like this. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Lens design and performance Click to return to CD contents Aspheric spectacle lenses 1.0mm 400 T 300 6.00 4.00 2.00 0 5 10 15 20 25 0.00 30 oblique vertex sphere powers FIELD DIAGRAMS FOR SPECTACLE LENSES Tangential & sagittal oblique vertex sphere powers 40 70 If the +4.00D lens is now flattened so that its back curve is only -1.50D, the centre thickness will reduce to 6.0mm 200 and the weight of the lens will reduce by some 2 grams. 35 -1.50 6.0mm S ocular rotation in degrees 100 +4.00 -1.50 base curve 00 +3.0 +4.0 +5.0 FIELD DIAGRAM Weight = 18.1g The field diagram for this flatter form +4.00Dlens would look like this. The off-axis performance of this flatter curved form is unacceptable! Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Lens design and performance Click to return to CD contents Aspheric spectacle lenses T&S 1.0mm 400 6.00 4.00 2.00 0 5 10 15 20 0.00 25 oblique vertex sphere powers FIELD DIAGRAMS FOR SPECTACLE LENSES Tangential & sagittal oblique vertex sphere powers 40 70 30 5.4mm 35 -1.50 If the front, spherical curve of this flatter form lens is now replaced a suitable aspherical surface, the negative 0 30by surface astigmatism which is inherent in the aspherical surface20 can neutralise the astigmatism of oblique incidence. 0 Furthermore, since the sag of the aspherical surface is less 0 than the10sag of a spherical surface of the same power, the centre thickness of the lens will reduce even further to 5.4mm. The weight 00 of the aspheric lens will reduce to just 16 grams. ocular rotation in degrees +4.00 -1.50 base curve Weight = 16.0g +3.0 +4.0 +5.0 FIELD DIAGRAM for aspheric form with convex hyperboloidal surface, p = -1.8. The field diagram for this aspheric +4.00D lens would look like this. The off-axis performance is the same as the steeper curved lens with spherical surfaces! Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Lens design and performance Tscherning’s Ellipses - point focal lenses Click to return to CD contents Back (F ) 2 curve According to third-order theory, lenses of power F made in a material of refractive -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0 +5 +10 Lens power (F) index 1.5 and mounted 26.67mm front Before the advent of theincomputer, accurate trigonometric ray-tracing had to be performed by of the eye’s centre of rotation, will be freelogarithm tables. The procedure was-5lengthy and to save time, hand, using six or seven-figure from astigmatism for equations distance vision approximate were when employed to provide a starting point for the design. These so-called, -10B Airy (1825), and later by the insidethird-order curve, F2 equations is given by: for spectacle lenses were first investigated by G -12.25 F Ostwalt and M Tscherning towards the end the 19th century. The latter published comprehensive 2)} / 28 of the forms in 1904. The equations are quadratic in type and-15 plot as ellipses. These were F2 = {14Fdetails -375±(22500-2100F-140F plotted and described by A Whitwell earlier this century who called them the Tscherning’s Ellipses. -20 -10.00D lenses +2.25 - 12.25 +14. 50 - 24. 50 -24.50 -25 Ostwalt point-focal form Wollaston point-focal form -30 It can be seen from the graph that there -35 is a certain range of powers which can be made free from oblique astigmatism and that within this range there are two forms for each power. The shallower form, which -40 is the one used in practice, is named after Ostwalt and the steeper form after W H Wollaston who had proposed such forms early in the 19th C. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Lens design and performance Click to return to CD contents Tscherning’s Ellipses - point focal lenses Back (F ) 2 curve For example, lenses made in a material -45 -40 0 +5 +10 of refractive index 1.5 and-50 mounted 26.67-35 -30 -25 -20 -15 -10 -5 Lens power (F) mm in front of the eye’s centre of rotation, -5 will be free from astigmatism for near ellipses caninside be constructed specified working distance, visionSimilar at 25cm when the curve , F2for point-focal, near vision lenses at a-9.10 -10 andby: also for Percival lens forms or minimum tangential error forms again, for either distance or near is given vision. Naturally, the ellipses differ in size and position in each of these different circumstances. -15 F2 = {14F -335±(36100-2660F-140F2)} / 28 -20 -25 -30 -35 It is seen from the graph that Ostwalt near vision forms are somewhat shallower than the forms required for distance vision.The Wollaston NV forms are virtually the same. The Ostwalt near vision design for a -40 -10.00D lens required for near vision at -25cm would be biconcave in form. In practice, the eye does not demand optimum acuity in near vision and best form lenses are invariably designed for distance vision. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Lens design and performance Click to return to CD contents Tscherning’s Ellipses - point focal lenses Back (F ) 2 curve If we assumesothat lenses are mounted 26.67mm frontinofathe eye’s centre of The ellipses illustrated far the have assumed that the lenses are in made material of refractive index 1.5. rotation, we obtain thematerial following ranges ofthe powers for lenses which can When the refractive index of the increases, canbe bemade made free from -22.22 range of lenses which +7.23 +7.66 -31.36 free from oblique astigmatism, according to when in refractive index, oblique astigmatism also curiously, in -15 the minus range. -50increases, -45 -40 but -35 -30 -25only -20third-order -10 theory, -5 0Whatever +5made +10 the Lens power (F) of different refractive indices: plus lensesmaterials over about +7.75 cannot be made free from astigmatism when restricted to spherical surfaces. -5 n Fellipses, Fminlenses made in a material of refractive index, n, It can be shown that the limits of Tscherning’s for max 1.5 +7.23 and mounted L´2 dioptres in front of the eye’s centre -22.22 of rotation are given by: -10 1.6 +7.50 -26.77 1.50 -31.36 3 -15 2L´21.7 (n - 1) +7.66 n 1.8 +7.74 Fmax = (n -1) --35.97 1.70 2-3n -20 n+2 1.9 +7.77 -40.60 -25 Although based upon approximate equations, these limits do give a good indication 2L´ 3 2 (n - 1) n of the ranges lenses which can (n be -1) made F minof = + free from astigmatism -30for different media. 2-3n n+2 -35 -40 Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Lens design and performance Click to return Tscherning’s to CD contents Ellipses - minimum tangential error forms Back (F ) 2 curve Similar equations to those given for point-focal lenses can be derived for -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0 +5 +10 Lens power (F) third-order, Minimum Tangential Error forms. Assuming the same details as those used for the point-focal designs, namely, n = 1.5 and the lenses -5 that lenses will mounted 26.67mm in front of the centres of rotation, we find exhibit minimum tangential error when their inside curves are given by: -10 -11.88 F2 = {49F -1125 ± (275625-17850F-1295F2)}-15 / 88. This equation also plots as an ellipse with limits +9.24 -20and -23.02. -10.00D lenses +1.18 - 11.88 -24.83 -25 Ostwalt Min T-error -30 -35 +14. 83 - 24. 83 Wollaston Min T-error -40 Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Iso -V-prism theory Click to return to CD contents Spherical lenses Plano-cylindrical lenses Sphero-cylindrical lenses Iso-V-differential prism zones Graphical construction for iso-V-prism zones Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Iso-V-prism zone theory Spherical lenses Click to return to CD contents Consider the prescription R -2.00 L -2.00/-2.00 x 180 iso-V-prism zone is acan zone on 1cm a lens where prismatic effect does 2 In theeye, case spherical lenses the iso-V-prism zones are simply InAnthe right theofeye roam from the vertical optical centre before it meets exceedeffect a stipulated amount. effect islaw ignored. horizontal bands, their cwidth behorizontal calculatedprismatic from Prentice’s P = c.F. ofnot prismatic (from = P /can F).All In the left eye, the vertical power of the lens is -4.00, so the eye can roam 0.5cm Hence the 2 iso-V-prism horizontal bands. from the optical centre before it meets zones 2 of are prismatic effect. R 20 mm wide L 10 mm wide Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Iso-V-prism zone theory Plano-cylindrical lenses Click to return to CD contents Inthe the1 case plano-cylindrical lenses zones are power of iso-V-prism aofcylinder lies atisright athe band angles 20mm toiso-V-prism its wide axis along meridian the 60º and meridian. If Hence theThe vertical prismatic effectzone is denoted by iso-V-prism PVthe then the oblique prism, PitR,iswhich For example, suppose it is required to find 1 zone for the cylinder +2.00 x 60. From the decentration relationship, the eye can roam, 2 / 2cm, or 10mm, still rise bands but they parallel to the the axis meridian of theisthe cylinder. necessary determine how far along power meridian eye from: can gives totoP the power meridian of the cylinder, found V, along Thelie power meridian lies along 150. along the 150 meridian before it meets 2 base 150 or 1 of vertical prism. roam before itprism encounters Thealong result150 the could vertical bedetermined depicted prismatic as effect follows: which is is: stipulated. Their dimensions can be as follows. The which gives rise to 1 vertically 1 base UP is produced by 2 base 150 JPR = PAV / sin (90 + ) PR = PV / sin (90 + ) 1 / sin 150 = 2 base 150. K = direction Where is the axis of theconstruction cylinder. This could have been determined by a graphical as follows. 2 1 iso-V-prism zone for +2.00 x 60 Power meridian 1 is a band, 20mm wide, lying along 60. J´ A´ K´ 20mm Note that along JJ´ the prism base is DOWN whereas along KK´ the prism base is UP. Along the axis meridian, AA´, the prismatic effect is zero. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Iso-V-prism zone theory Click to return to CD contents Sphero-cylindrical lenses From These In Since the Choosing In two decentration case all the points other boundary ofto asphero-cylindrical suitable cases are plotted, of the the scale, band zone one will the lenses on is anot each eye J, straight can be the can principal parallel iso-V-prism be roam line, plotted it2 meridian with is /2 on necessary cm the zone the will 10mm 30 thetolens, UP ItConsider is essential check the base direction along each principal meridian We the must 1 iso-V-prism now determine zone how forlens. far the lens eye -2.00 can /+3.50 roam xorof 30. Consider first the 30 relationship, meridian ofpoint, the The prism along 30 which along be be meridian parallel the able cylinder the 30 to meridian to same of locate the axis method axis lens two before but only 10mm points will which when lie in up was order the along just cylinder some to base 30be described other 30, axis the (or to meridian. lies for construct optical 1 atplano-cylinders. of 90 centre or the 180. prism). O. tousing ensure that the vertical prism are both base UP orline. both along the 30 meridian it2 meets 2 base UP at 30. will give rise tothe 1 base UP ,itbefore ismeets 1along /components sin 30 = from 2able base UP atvertical 30. base DOWN Failure to is do this willThe result in30 the band 90º off! The principal The powers power. of along the lens 30 are -2.00. -2.00D along prism along and +1.50D 30being is 2. along 120. . J 1 base UP 10 -2.00 2 base UP at 30 O +1.50 Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Iso-V-prism zone theory Click to return to CD contents Sphero-cylindrical lenses Choosing a suitable scale, point, J´,far can beeye plotted on the 120 WeNote must nowthe determine how the can roam that eye must rotate DOWN along Note that the vertical prismatic effect at roam any point on this line is which base DOWN UP. From the Consider decentration now the relationship, 120 meridian theof eye can lens. The 1.15 prism / .1.5 along 120 = O. 7.7mm meridian of the lens, 7.7mm down from the optical centre, along the 120 itthe meets 1.15 base UPcm at 120. 120 inmeridian order tobefore encounter prism base UP We can now construct the 1 base UP iso-V-prism line through the points JJ´. alongwill the give 120 rise meridian toalong 1 base before meets is 1 / sin 1.15 120prism base = 1.15 120, base (or of at vertical 120. prism). The power 120UP isit,+1.50. The along 30 1 isUP 1.15. 1 base UP 1 -2.00 J base UP . 1.15 base UP at 120 O 7.7 . J´ +1.50 Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Iso-V-prism zone theory Sphero-cylindrical lenses Click to return to CD contents It we willmeasure be realised that when the eye views through anybe point Finally, Assuming a right eye, the bandwidth, thethe base direction which isofthe thiseffect perpendicular prismatwill distance IN at any Note that vertical prismatic We can on also construct 1 base iso-V-prism line through the points KK´. We can now draw aorientation line,DOWN HH´, through O parallel todirection JJ´. this line itthe will encounter onlyKK´ horizontal prismatic effect. between point JJ´on the and line KK segment, ´,any and the OH of at the any point on i.e.,the the segment of HH OH´. ´. point onand the OUT line is band, base DOWN . line Note that OK = OJ, and OK´ = OJ´, so that JJ ´ and KK´ are equidistant from HH´. The result could be depicted as follows. H 1 base UP K J K´ If the-2.00 eye remains within the band J it will not encounter more than 1 of vertical prismatic effect. . 67.6º 67.6º O K´ K J´ 1 base DOWN . J´ 1 iso-V-prism zone for -2.00 / +3.50 x 30. By measurement, the band is 12.2mm wide and lies along the meridian, 67.6º. 12.2mm H´ +1.50 Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Iso-V-prism zone theory Iso-V-differential-prism zones Click to return to CD contents The zone for a -2.00D horizontal band 10mm wide. The zone If 1 theiso-V-prism issubject not very had wide. beenIn dispensed the verticalalens meridian pairisofsimply bifocal the a eyes lenses, can the only segment roam 5mm zone from which the optical incorporates centres before the is reading they meet prescription of vertical may not differential evenlens lie within prismatic effect! The differential prescription simply, how1 much stronger one is thanthe theband! other. For example, consider the prescription R -2.00 L-2.00 / -2.00 x 180. In thisThese case, where the powers of theapplication lenses known in the vertical Perhaps the most important of iso-V-prism zone is The iso-V-differential-prism zonesare are simply the iso-V-prism iso-V-differential-prism zones represent the areas on theory ameridians pair of (we are only interested vertical prismatic effects), power of10mm the left lens in the to enable us to in locate thefor areas a pair ofthe spectacles within which spectacles within which comfortable binocular vision is most likely to occur. zones plotted the on differential prescription. vertical meridian is -4.00, so the left eyedoes is stronger than the right eyeamount. by -2.00D. the vertical differential prism not exceed a stipulated The eye must remain within this zone so as not to encounter more than 1 of vertical differential prism. Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Iso-V-prism zone theory Iso-V-differential-prism zones Click to return to CD contents In these circumstances, the differential prescription can be obtained by It was stated example, earlier thatRthe differential prescription is simply, much In the previous -2.00 L-2.00 / -2.00 x 180, changing signstronger of the sphere changing the signs of the sphere and the cylinder in onehow eyethe (usually, iseye than theadding other. the In the general with astigmatic lenses whose inone thelens right and result toadding thecase, leftthe eye prescription results in -2.00axes x 180, choosing the weaker lens) and two prescriptions together, may is not bedifferential parallel,using the difference indecomposition power between eyes may not2.00D be obvious. which prescription. differential power, is therefore, along 90. ifthe necessary, astigmaticThe orthe Stoke’s construction. -2.00 Differential prescription 0.00 -2.00 x 180 Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Iso-V-prism zone theory Iso-V-differential-prism zones Click to return to CD contents Consider the prescription: R +1.50 /+2.00 x 135 L +3.50 / +2.00 x 105 The differential is found, before, by/ changing the sign We find: -1.50 / -2.00 + +3.50 +2.00 Soprescription the differential Rxx 135 = as +1.00 / +2.00 x 75 x 105 of the power in one eye and then adding the two prescriptions together. the general case, thedescribed direction the iso-V-differential prism zones Using the In graphical construction, earlier, for locating iso-V-prism = +2.00 x 45 + of +2.00 x 105 band may not with either cylinder we find in this instance thatcoincide the 2 zones are bands 32axis mmdirection. wide lying along 24º. = +1.00 / +2.00 x 75 24º 32mm Click to skip to next topic Click to return to previous screen Ophthalmic Lenses & Dispensing Click to return to CD contents Ophthalmic lenses and dispensing This presentation was created by Professor Mo Jalie © Reed Educational and Professional Publishing Ltd 1999 © Original articles, Optician Click to exit show Ophthalmic Lenses & Dispensing