26 Dispensing Optics APRIL 2016

An adaptive spectacle lens is a

lens whose power can be

made to change by applying

some sort of effort to the

lens. Unlike the usual power

variation lens (i.e. a progressive or

degressive power lens), the power of an

adaptive lens can be changed, either

across the whole lens aperture, or over

just a selected area of the lens, for

example, just the near portion.

Adaptive optics are employed in manyoptical instruments, for example, to createchanges in some areas of the primaryobjective lens of a telescope in order tocontrol aberrations, which have beencaused by changes in the surface geometry,or by disturbances in the object space.Needless to say, an aberration can belooked upon as an alteration in power fromthe desired value. In the case of thespectacle lens, an adaptive lens can beadjusted to produce just the correct powernecessary to correct a given degree ofametropia or presbyopia.

Currently, variable power can beproduced by four different methods:

1) Systems which depend upon a variable axial separation of its components.

2) Systems which depend upon adjustable sliding contact between the components.

3) Lenses whose surfaces can be deformed by alterations in the volume of the lens.

4) Lenses whose refractive index can be

altered by applying a small electric current to the lens.

In each of the first three cases, thechange can be altered and reversed by thewearer as many times as required. In thefourth case, it is an on-off change, dependingupon whether the current is being appliedor has been switched off. The followingsections describe the theory of thesemethods in detail1.

VARIABLE POWER FROM SYSTEMS WITHA VARIABLE SEPARATION OF THE LENSESConsider the two optical components,+20.00D and -20.00D illustrated in Figure1(a). When placed in close contact as shownin the Figure, they neutralise one another andthe result is a parallel sided afocal block.

Now suppose that the lenses areseparated by 2.4mm as shown in Figure1(b), the power of the system measured atthe concave surface of the -20.00Dcomponent is given by:

F1 + F2 = 20

- 20.00 = +1.00 D 1-dF1 1-0.0024x20

Shifting the +20.00 Dlens forwards by afurther 2.15mm produces +2.00D and ashift of 10mm from the zero positionproduces a power of +5.00D. Clearly, such acombination of lenses can be used toobtain a variable power system.

The change in effective power measuredat the concave surface is:

F1 - F1 =dF1

2

1-dF1 1-dF1

Since d is small when expressed inmetres, the denominator is not verydifferent from unity, and we can express thechange in power, A, as:

A =dF1

2

1000

where d is expressed in millimetres. Notethat since the numerator of this expressionis always positive, it does not matter whetherthe front moveable lens is the plus componentor the minus component.

To produce an adaptive optical systemwhich could provide variable power from,

CET

C-51040

This article has been approved for 1 CET point by the GOC. It is open to all FBDO members, and associatemember optometrists. The multiple-choice questions (MCQs) for this month’s CET are available online only,to comply with the GOC’s Good Practice Guidance for this type of CET. Insert your answers to the six MCQsonline at www.abdo.org.uk. After log-in, go to ‘CET Online’. Questions will be presented in random order.Please ensure that your email address and GOC number are up-to-date. The pass mark is 60 per cent. Theanswers will appear in the August 2016 issue of Dispensing Optics. The closing date is 12 July 2016.

COMPETENCIES COVEREDDispensing opticians: Standards of practice, Optical appliances, Refractive managementOptometrists: Standards of practice, Optical appliances

a)

b)

d

F1

Figure 1: Variable power by varying theseparation of the lens components

+20.00 -25.00 resultant effect = 0.00

10

Figure 2: Variable power system designedto produce range +5.00D to -5.00D

Adaptive spectacle lenses:part one by Professor Mo Jalie SMSA, FBDO(Hons), Hon FCGI, Hon FCOptom, MCMI

27Dispensing Optics APRIL 2016

say, +5.00D to -5.00D, we could choose a -25.00D rear component and a +20.00D front,moveable component as shown in Figure 2.When the lenses are in contact the powerof the combination is -5.00D. If the frontlens is then moved forward by 2.4mm, thepower of the combination becomes -4.00D.

The components have been reversedfrom those shown in Figure 1 in order toprovide a better optical performance over awider field with fewer off-axis aberrations,so the front surface of the plus lens mustbe compensated for the lens thicknesses.

In order to produce a variable power,ready-to-wear spectacle lens designed forreading purposes only, whose power coveredthe full permissible range suggested in BSEN ISO 14139 – Ophthalmic Optics –Specifications for ready-to-wear spectacles,of +1.00D to +3.50D, a back element of -19.00D could be combined with a frontmoveable lens of power +20.00D. Then,when the lenses are in contact they willprovide a power of +1.00D and themovement required to obtain a lens ofpower +3.50D would be just 5.55mm.

Requiring such a small movement of thecomponents, a device of this nature wouldbe very simple to construct with the frontlens mounted in, say, a screw threaded capwhich would not have an unusualappearance or be too cumbersome. Bennetthas recorded that adaptive spectacles ofthis nature were patented by H. Dixon2 ofLondon as long ago as 1785.

VARIABLE POWER FROM SLIDING COMPONENTSAdaptive prism systems are well known, therotary prism. Such a device employing two15Δ components can produce any resultantprism power from zero to 30Δ by rotatingthe two prisms in relation to one another.The rotary prism not only forms a usefultrial case accessory, but is also used as aprism compensator in the focimeter, eitherto extend the measuring range of theinstrument or to neutralize prism in a lensbefore power readings are taken.

THE STOKES’ LENSAnother accessory which may be found inthe trial case is the Stokes’ lens, which is anadaptive cylinder that can produce anycylinder power from zero up to twice thevalue of either component. However, theStokes’ lens also has a residual sphericalpower which is always half the value of theresultant cylinder power.

Consider the pair of ±6.00D plano-cylinders illustrated in Figure 3. Whenplaced together as shown in Figure 3(a)

they neutralise one another and theresultant effect is zero. This effect isconfirmed by the optical crossrepresentations of the principal powersshown in the Figure, and the fact that theyneutralise along every meridian is obvioussince the absence of material from theconvex cylinder is replaced by the presenceof material from the concave cylinder.

If the -6.00DC component is nowrotated through 90° as shown in Figure3(b), the combination becomes -6.00DC x180/+6.00DC x 90, which is equivalent to -6.00DS/+12.00DC x 90.

Suppose now that the -6.00DC x 90shown in Figure 3(a) was rotated through30° from the zero position. The resultant,found by summing the obliquely crossedcylinders, -6.00DC x 60/+6.00DC x 90, isfound to be -3.00DS/+6.00DC x 120.

This result can be found as follows. Ifwe have two equal but opposite poweredcylinders, F1 DC / -F1 DC with an angle αbetween their axes, we find from the theoryunderpinning Stokes’ construction that theaxis of the resultant cylinder lies at α/2from either axis, i.e. midway between their

two plus axis meridians, and that the powerof the resultant cylinder is given by

C = √(F12 + F2

2 + 2F1F2 cos 2α)

= √(2F12 - 2F1

2 cos 2α)

= √(4F12 sin2 α)

= 2 F1 sin αand S = (F1 + F - C) / 2

= -C / 2

= -F1 sin α.

For the example shown in Figure 4,-6.00DC x 60/+6.00DC x 90, α = 30°

C = 2 F1 sin α = 12 sin 30 = +6.00DC

S = -F1 sin α = -6 sin 30 = -3.00DS

So the resultant is -3.00/+6.00 x 120.If the minus cylinder is rotated through

60° from the zero position, the twocomponents now being +6.00DC x 90/-6.00DC x 30 the angle between the axismeridians, α, = 60°.

C = 2 F1 sin α = 12 sin 60 = +10.40 DC

S = -F1 sin α = -6 sin 60 = -5.20 DS

(i.e. half the value of the resultant cylinder)and the combination is equivalent to -5.20/+10.40 x 105.

If it is required to produce variablecylinder power but to maintain a fixed axisdirection, then the components must bearranged to rotate through equal angles,one clockwise and the other, anti-clockwisefrom the zero position, and this must lie at45° to the required axis direction. Forexample, if it is required to maintain an axisdirection of 45° then the cylinders shown inFigure 3(a) would be orientated so that theircommon axis meridian for the zero positionlay along 180˚ and, using the samemechanism as that found in the rotary prism,when one cylinder is rotated anti-clockwise,through 15°, so that its axis lay along 15°,the other cylinder would rotate clockwisethrough 15°, so that its axis lay along 165°.

The Stokes’ lens is used in someautomatic refractometers when it is usuallycombined with an adaptive spherical lens toneutralise the spherical component, whichresults from the variable cylinder.

ALVAREZ-LOHMANN LENSESAn adaptive lens which can provide bothvariable spherical and cylindrical power wasdescribed by Luis W. Alvarez3 in 1967. Threeyears later, an adaptive lens of similarconstruction was described by A. Lohmann4

and lenses of this type are often referred toas Alvarez-Lohmann lenses. Here, for brevitythey will be called simply, Alvarez lenses.

Consider the parallel-sided block ofoptical material, say a block of CR39,illustrated in Figure 5(a). Clearly, therewould be no movement of objects viewedthrough the block depicted in Figure 5(a),under the transverse test. On careful

+6.00 DC x 90 -6.00 DC x 90

+6.00 DC x 90 + -6.00 DC x 90 = 0.00

+ =

0.0

+6.0 -6.0

0.0 0.0

0.0

a)

0.0

+6.0 0.0 +

-6.0

=

-6.0

+6.0

+6.00 DCx90 + -6.00 DCx180 = -6.00/+12.00x90

b)

+6.00 DC x 90 -6.00 DC x 180

Figure 3: Stokes’ lens made with ±6.00Dcyls in minimum and maximum configurations

0.0

+6.0-6.0

+

0.0 -3.0+3.0

+6.00 DCx90 + -6.00 DCx60 = -3.00/+6.00x120

+6.00 DC x 90 -6.00 DC x 60

=

Figure 4: Stokes’ lens with acute angle of30° between the axes; +6.00DC x 90/-6.00DC x 60

28 Dispensing Optics APRIL 2016

Continuing Education and Training

inspection of the block, it is seen that theblock is actually made from two separatecomponents, which have been put togetheras shown in Figure 5(b).

A cross-sectional view of the twoseparated components is shown in Figure5(c). Like the plano-convex and plano-concave cylinders, which make up theStokes’ lens, the absence of material fromone component is entirely replaced by thepresence of material from the secondcomponent

Figure 6(a) shows that provided thatthe two components are sufficiently thin,despite its peculiar shape, the Alvarez lenswould still be afocal if its two componentswere placed together, with their planesurfaces in contact. Once again, theabsence of material from one component isprecisely compensated for by the presenceof material from the second.

Now consider the cross-sectionalshapes of the resulting element when thetwo components are separated by slidingthe two components along their planesurfaces, as shown in Figure 6(b). In Figure6(b) the components have been separatedby sliding the second componentdownwards in relation to the first, the planesurfaces remaining in contact. It can beseen that an optical element is formed,which has two convex surfaces and it willbe seen that the thickness of this elementvaries in every meridian in exactly the sameway as the thickness of a bi-convexspherical lens.

Furthermore, as can be deduced fromFigure 7, the greater the separation of thecomponents, the greater becomes thethickness difference across the componentsso the greater becomes the power of theresulting spherical lens. In Figure 8, the twocomponents of the Alvarez lens have beenslid in the opposite direction, when theresulting optical element is seen to possesstwo concave surfaces forming a negativelens. Once again, the further the movementof one component in relation to the other,the greater the increase in the minus powerof the lens.

Now consider how the thickness of theAlvarez lens changes when, starting fromthe afocal position of the elements, thecomponents are slid horizontally in relationto one another (Figure 9). It can be seenthat along the vertical meridian of thecombination the thickness does not change,the Alvarez lens remains afocal in thevertical meridian. Along the horizontalmeridian, however, as the separationincreases from the zero position shown inFigure 9(a), the thickness of thecombination starts to increase. It will beseen that this movement produces a plano-cylinder with its axis at 45°. The Alvarezlens now behaves like a plano-cylinderwhose cylindrical effect increases as theseparation of the components is increasedalong the horizontal meridian.

It follows that if the two componentsare separated in both the vertical and

horizontal meridians the resulting Alvarezlens will possess both spherical andcylindrical power, i.e. it has become avariable power sphero-cylindrical lens. Asstated above, the axis of the cylinder will liealong the 45° meridian of the elementsshown in Figures 6 to 9.

The contact surface between the twoelements does not need to be a planesurface as can be seen in Figure 10, whichshows a cross-sectional view of a curvedform of Alvarez lens. However, in designinga curved interface, sufficient space must beallowed between the two slidingcomponents to enable them to slidewithout making contact with one another.

VARIABLE POWER FROM FLUID-FILLEDLENSESIf a hollow, parallel-sided, plate of glasswith very thin, flexible walls is attached toa reservoir containing some transparentliquid, when the space between the walls isjust filled with the liquid the filled plate willact like a parallel-sided plate of glass withno power, as illustrated in Figure 11(a).

If a further volume of liquid is nowforced into the plate, the flexible walls willbulge outwards under the pressure of theliquid to form a bi-convex lens. Assumingthe walls of the deformable plate to be thinand remain parallel-sided, they play no part

a) b) c

Figure 5: Components of the Alvarez lensa) block of optical material, e.g. CR39b) block sliced into two as indicated c) cross-section of the two components

Figure 6: Alvarez lens arranged to form apositive lensa) components in afocal position b) components slid apart to form a plus lens

a) b)

Figure 8: Alvarez lens arranged to form anegative lensa) components in afocal position b) components slid apart to form a minus lens

a) b) Figure 10: Alvarez lens with a curved contactsurfacea) elements in afocal positionb) arrangement for plus lensc) arrangement for minus lens

a) b) c)

Figure 7: Increasing the separation of theelements increases the power of an Alvarez lens

side view

plan view

a) b)

Figure 9: Alvarez lens arranged to form aplano-cylindera) components in afocal position b) components slid apart to form a plano-cylinder

29Dispensing Optics APRIL 2016

in the power of the resulting lens which isdue entirely to the shape of the liquid lensof refractive index, n. On the other hand, iffluid is withdrawn from the sealed chamberit will suck the thin walls towards oneanother to produce a bi-concave lens asillustrated in Figure 12.

The power of the resulting lens willdepend upon the change in volume of theliquid. Since there is greater pressure exertedat the centre of the bi-convex lens wherethe thickness of fluid is greatest, the formof the convex surfaces will be paraboloidal.In the case of the withdrawal of fluid toproduce a minus lens, once more, the changein thickness of the fluid will produce a pairof concave paraboloidal surfaces.

Consider the paraboloidal capillustrated in Figure 13, whose radius at thevertex is r0, and whose sag at the diameter, 2y,is z. The volume, V, of the paraboloidal capis given by π z2 r0 and since for a paraboloid,

z =Y2

=d2

2r0 8r0

where, d = 2y, on substituting 100(n - 1)/Ffor r0 the volume of the cap is given by π d4F

cm3, d in cm.6400(n - 1)

The relationship between the power, F,and the volume of the lens, V, is therefore,

F =6400(n - 1)

V, V being expressed in cm3. π d4

Suppose that the fluid contained betweenthe walls is an oil of refractive index 1.586,and that the fluid lens is circular of diameter42mm, i.e. 4.2cm. When the cavity containedby the hollow parallel-sided walls, tE, is3mm thick, as shown in Figure 12(a), thevolume of the cylindrical plate formed bythe oil is simply

V0 =π d2 tE cm3 = π x 4.22 x 0.3 / 4 = 4.156 cm3.

4

In order to induce a change in power of+1.00D, the volume of the plate must beincreased by, V,

=π d4

cm3 = π x 4.24

= 0.261 cm3

6400(n - 1) 6400(0.586)

when its total volume becomes V + V0

= 4.156 + 0.261 = 4.417 cm3

The power of the lens, F, can then beexpressed as

F =6400(n - 1)

(V - V0). d4

It can be seen from this expression thatthe power increases linearly with thevolume of the lens.

The graph in Figure 14 shows a plot ofthe necessary change in volume against thepower of the lens. In real terms, the amountof fluid which has to be injected to increasethe power of the lens by +1.00D, or toremove from the lens to obtain a change of-1.00D, is just a little over 0.25 cm3.

Bennett records that the first knowndeformable lens produced by inducing achange in the power of a lens by changing

its volume, was thought to have been usedas an objective for a long-focus telescope,made in 1747 by a Dresden instrumentmaker named Grummert. A patent wasgranted to the French ophthalmologist DrCusco5 for the use of such a lens in abinocular optometer, used to studyaccommodation. The detail of one of hislenses is shown in Figure 15 where it canbe seen that one surface of the lens is rigid,only the right-hand surface being deformedwhen liquid is pumped into the system. Thepower of the variable focus lenses could becontrolled to 0.01D by an elaboratehydraulic system. The chief problem indesigning a deformable lens is that ofensuring that the hydraulic system forms aliquid-tight cavity.

A suggestion made by Dr B.M. Wrightwas to employ a triple-layer constructionthe three components being laminatedtogether to form the lens. The frontcomponent is a glass (or plastics lens) madeto the distance prescription, with anyastigmatic correction on the convex surfaceof this component. The central layer is a

pressure forces fluid into the lens chamber

reservoir

a) b)

Figure 11: Fluid-filled adaptive lensa) chamber filled with fluid b) pressure forces fluid into the chamber toproduce a bi-convex lens

z 0

z 0

volume of a paraboloidal cap = π z2 r0

z

00z

0

area of complete strip = π y2

volume of strip = π y2 δz

volume of cap = ∫ π y2 δz

= π∫2r0z δz

δz

y

z

Figure 13: Volume of a paraboloidal cap

a) b)

reservoir

pressure removed withdraws fluid from

the lens chamber

+10.00

+8.00

+6.00 +4.00

+2.00

0.00

change in volume in cm3 (V - V0)

power

1 2 3 4 5 Figure 12: Fluid-filled minus adaptive lensa) chamber filled with fluidb) pressure removed draws fluid out ofchamber to produce a bi-concave lens

Figure 14: Graph to show the relationshipbetween the power and the volume of a lens

Figure 16: Dr Wright’s deformable lens

liquid

liquid

Figure 15: Dr Cusco’s deformable lens

30 Dispensing Optics APRIL 2016

circular sheet of polyvinyl butyral, 0.37mmthick, with a central circular hole some 25mmin diameter to serve as the liquid chamber.The rear component is a cover slip of glass,0.15mm thick, capable of flexing to theextent required under pressure (Figure 16).

A duct 0.75mm in diameter was drilleddownwards through the upper edge of thelens, opening into the liquid chamber via ashort horizontally drilled hole. The fluidsupply is kept in a reservoir in one of thesides and supplied to each lens cavity via aduct in each frame rim, linked via the bridgeof the frame. Sliding a plunger on thereservoir side of the frame forces more fluidto enter the cavities, causing the cover slipto flex into a convex cross-section. Slidingthe plunger on the side of the frame in theopposite direction withdraws fluid from thelenses the cover slip resuming its unstressedform and the lens power to reduce.

The search for a method of providing afluid-tight seal which could withstand thepressure from the liquid passing throughsuch narrow ducts was unsuccessful and thedesign was eventually abandoned.

The second part of this article, to bepublished later in the year, will deal withrecent versions of fluid-filled lenses whichhave solved the problems of providing fluid-tight sealed units and electro-active lenses.

REFERENCES1. More historical information is given in

Bennett AG (1972) Variable and progressive power lenses. ManufacturingOptics International, IPC Science & Technology Press, Guildford.

2. Brit. Patent 1515. Dixon H (1785) Telescopes, microscopes spectacles etc.

3. US Patent 3305294. Alvarez LW (1967) Two-element variable-power

spherical lens.4. Lohmann A (1970) A new class of varifocal

lenses. Applied Optics 9: 1669–71.5. Fr. Patent 129293. Dr Cusco (1879)

Système de lentille à foyer variable sansdéplacement.

PROFESSOR MO JALIE is Visiting Professorin Optometry at the Ulster University andto the educational facility in Paris, EssilorAcademy Europe. He also works as aconsultant to the ophthalmic industry. Hewas the Head of Department of AppliedOptics at City & Islington College from1986 to 1995 where he taught optics,ophthalmic lenses and dispensing from1964. He has written several books andeducational CDs, holds four patents andruns a web-based course in Spectacle LensDesign, which is reviewed each year,leading to FBDO(Hons) SLD.