## The Optical Principles of Plus-Lens Magnifiers

The plus lens used as a magnifying aid is creating an increased retinal image size by allowing an object to be held close to the eye without requiring the accommodative effort that would usually be expected from viewing at this distance. (The individual with active accommodation can be thought of as having this magnifier inside their eye.) Optimum positioning is achieved by placing the object at the anterior focal point of the positive convex lens, so that parallel light leaves the lens, the virtual image is at infinity, and the patient’s accommodation can be relaxed ( Fig. 7.1A ). It can be seen that the ray of light from the top of the object will pass through the optical centre of the positive lens, making an angle *θ* ′ with the optical axis. As all the rays of light leaving the lens are parallel to each other, they all make this same angle with the optical axis, including the ray which passes through the nodal point of the eye. Although the magnifier-to-object distance must be held constant and equal to the (short) focal length of the plus-lens, the magnifier-to-eye distance can be increased without affecting *θ’* and so the magnification remains the same ( Fig. 7.1B ).

In this way it is possible to use a plus-lens magnifier close to the eye, or remote from it: it can be spectacle-mounted, hand-held or on a stand, depending on the visual task requirements of the patient. Spectacle-mounted plus-lenses are occasionally called ‘microscopic’ lenses from the obsolete term ‘simple microscope’ applied to such systems. The confusing term ‘loupe’ may also be applied to magnifying plus lenses. This is variously defined as a hand-held plus lens held remote from the eye ( ), a low-power spectacle-mounted binocular correction, and, in British Standard (BS) 3521, as either a magnifier of power 5× or higher, or a low-powered binocular magnifier ( ). Both these terms should be abandoned to avoid misinterpretation.

## A Problem in Defining Magnification

The plus lens creates magnification by allowing the patient to adopt a closer viewing distance, and so

where the ‘new object distance’ will be the focal length of the plus lens. The ‘original object distance’—the distance at which objects were habitually held—will be individual for each patient, but in order to allow the convenient labelling of magnifiers, some standard value must be adopted. Traditionally this is taken to be 25 cm, and if this viewing distance were to be used by the patient, they would require 4.00 DS of accommodation or a +4.00 DS reading addition, or some combination of the two.

Thus the formula is restated as

This formula causes some controversy, because the assumed ‘standard’ viewing distance of 25 cm may bear no relation to the actual reading distance that the patient has been using, and the reading addition in their prescription may not be +4.00 DS. This has led to suggestions that all plus-lens magnifiers should simply be labelled with the measured power, and then the prescriber could calculate the magnification provided in each individual case. It would be possible to devise a formula unique to the particular patient concerned: if a presbyopic patient habitually read at 40 cm with a +2.50 addition (i.e. with the object at the focal point of the lens), then their own magnification formula would be

To take another example, if a young child usually accommodated to read at a distance of 33 cm, this would require 3 DS of accommodation and his magnification formula would be *M* = *F* /3. These formulae would then describe, for these individual cases, exactly how much larger the retinal image would be when using the magnifier as compared to the habitual reading situation.

## Specifying Magnifier Power

A further difficulty exists, however, even in specifying the refractive power of these positive convex lenses: should the value of *F* in the magnification formula be front vertex power, back vertex power, or equivalent power? For a thin lens, these are all equal, but for a thick lens ( Fig. 7.2 ):

Back vertex power

Front vertex power

where *F* _{1} is the front surface power, *F* _{2} is the back surface power, *F* _{eq }is the equivalent power, *t* is the lens centre thickness, and *n* ′ is the refractive index of the lens material. Both these power values can be determined using a focimeter, by placing the respective surface (vertex) of the lens against the lens rest of the instrument. It can be seen by comparing Figs. 7.2A and B , however, that it is equivalent power which is the relevant measure. As noted earlier, the retinal image size is determined by the angle subtended at the nodal point of the eye by the parallel beam of rays leaving the magnifier lens. This angle is that made by the ray entering the lens from the top of the object, which passes undeviated through the lens, and which makes an angle *θ* ′ at the optical centre of the thin lens or at the nodal point (principal point) of the thick lens. Thus, for a thick lens, the angle *θ′* is inversely proportional to the equivalent focal length, and thus depends on the equivalent power.

For a plus-lens therefore the magnification formula is more accurately stated as:

Labelling of plus-lens magnifiers by the manufacturer with this value of *F* _{eq }would allow the clinician to devise a measure of magnification that was more appropriate to the individual patient circumstances. Despite this, it is often not available, and if a power value is given it may well be that of back vertex power. It can be seen from Fig. 7.2B that the vertex focal lengths are often shorter than the equivalent focal length, so the corresponding power is higher: this may suggest a better patient performance with the magnifier than will be borne out in practice.

Equivalent power

and this cannot be measured using a focimeter, although if the magnifier lens is plano-convex with *F* _{2} = 0, the first principal plane coincides with the front surface of the lens, *f* _{eq }= *f* _{v }, and so the equivalent power ( *F* _{eq }) is equal to the front vertex power ( *F* _{v }). For other lens forms, there are two methods by which equivalent power can be measured relatively easily in practice.

## Measuring Equivalent Power

## Method 1—Suitable for Large-Diameter Single-Lens Systems

The formula below is used to determine equivalent power

with direct measurement of the unknown parameters.

A lens measure placed centrally on the surface is used to determine *F* _{1} and *F* _{2} , but the lens measure will be calibrated for crown glass ( *n′* = 1.523) so the readings must be compensated for this by multiplying the measured surface powers by the factor ( *n′* − 1)/(1.523 − 1) where *n′* is the refractive index of the magnifier lens. Thickness callipers can be used to measure *t* (which must be converted into metres for the calculation), and *n′* is available from reference sources.

This method, although straightforward, is only suitable for certain magnifiers. The magnifying system must be a single-lens system with only two surfaces (so that the overall power derives only from the combination of these), and it must be possible to place a lens measure across each surface: in some cases the lens diameter is smaller than the separation of the pointed feet on the lens measure, or a large plastic rim/housing around the lens prevents the lens measure from touching the lens surface. If the lens is aspheric, the surface power will be decreasing from centre to edge. If the lens diameter is large compared to the distance between the legs of the lens measure, this will not lead to much inaccuracy: however, for lower diameter lenses with surfaces above 10 DS, the power will be underestimated.

## Method 2—Applicable to Any Plus-Lens System

This method can be used to measure a single- or multi-lens system, and can be performed on lenses of any diameter ( ).

Fig. 7.3A shows the thick lens magnifier with parallel light from an infinitely distant object now being brought to a focus at the anterior focal point. The reciprocal of *f* _{eq }*′* would give equivalent power, but this cannot be measured accurately because the principal plane cannot be located. The image height *h′* can be measured, however, and power determined indirectly. To do this, the object must be moved closer than infinity ( Fig. 7.3B ). The angle subtended by the object at the first principal point is the same as the angle subtended by the image at the second principal point, and so in the image space

and in the object space

where *h* is the object size, *l* the object distance, and *l′* the image distance.

Equating these gives

So

If the object distance *l* is assumed to be close to infinity, then the image distance *l′* approximates to the equivalent focal length *f* _{eq }*′* and

so

If all the measurements are taken in metres, *F* _{eq }is in dioptres. An illuminated Snellen letter chart makes a suitable object, with the height of the illuminated panel (or an individual letter on it) being measured to determine the object size *h* . The object distance ( *l* ) should be as large as possible so that the inaccuracy in locating the principal plane of the magnifier is insignificant: either 3 or 4 m should be possible in the average consulting room. The observer should be about 20 cm from the securely held plus-lens, viewing the (blurred) object through the plus-lens with a small measuring magnifier held up to the eye ( Fig. 7.4 ).

The observer then approaches the plus lens until the (inverted) image is clearly in focus and superimposed on the millimetre scale of the magnifier. The image size ( *h′* ) should then be measured as accurately as possible, and all the values obtained (in metres) substituted into Eq. (7.1) to determine the equivalent power. To minimize percentage error, the object should be chosen so that the image size is approximately 5 mm.

## Practical Considerations

## Working Space and Working Distance

All plus-lens magnifiers placed in the spectacle plane produce magnification by allowing the patient to bring the object closer to the eye than the patient’s available accommodation will allow. As long as parallel light leaves the magnifying system, however, the system-to-eye distance can be varied without affecting the magnification, and the *working distance* from eye to object can be large. Under these circumstances, it is the magnifier-to-object distance—the *working space* —that must be restricted, and which determines the magnification achieved. Hand-held and stand-mounted magnifiers are obviously designed to take advantage of the variable magnifier-to-eye distance, but it is also exploited by some spectacle-mounted devices where the back vertex distance is extreme ( Fig. 7.5 )

Despite this increase in the working distance, however, the working space remains limited—at its largest, this cannot be greater than the anterior focal length of the system. Herein lies one of the major limitations of all plus-lens magnifiers: they range in power up to +80.00 DS, when the working space drops as low as 12.5 mm. There are some tasks where this is feasible (e.g. reading for short periods), although psychologically difficult because it is so conspicuous and unusual. It may also be very tiring to maintain the working space and difficult to illuminate the task area where the magnifier or patient overshadows it: the use of auxiliary reading stands and built-in illumination may need to be considered. For other tasks, such a restricted working space is impossibly small (e.g. writing, knitting or playing music) and in such cases alternative methods of magnification may need to be sought.

## Depth-of-Field

Positioning of the object of interest at the anterior focal point of the magnifier (or in fact at any designated position) is critical, and movement of the object away from this plane will cause the vergence of light, leaving the magnifier to alter. Assuming that the eye’s accommodative state remains unchanged, this will cause the previous retinal point focus to become a blur circle. The range of magnifier-to-object separations over which the object (or the magnifier) can be moved without the patient noticing any change in image clarity is termed the depth-of-field. This depth-of-field will differ for different patients using the same magnifier, as the size of the retinal blur circle depends on the pupil size, and patients will differ in their ability to detect blur. Nonetheless, it has long been recognised that depth-of-field is very small in plus-lens magnifiers, and this is in fact one of the justifications for using a stand-mounted magnifier. Short ‘distance posts’ could be fitted to the temporal front of a spectacle frame containing high-plus lenses to allow the maintenance of the correct working space, or a length of string of the correct working distance could be attached to the frame as a reminder of where to hold the task.

Fig. 7.6 illustrates the situation of an object placed a distance *l* _{1} from a plus-lens magnifier (in this case, the object is at the focal point and *l* _{1} is equal to the focal length of the magnifier). The object can move to a distance of *l* _{2} from the lens before the patient notices that the image is blurred, so the linear depth-of-field is Δ *l* for movement of an object towards the lens (and of course, the object could also move an equivalent distance away from the lens).

By simple geometry,

Considering the refraction of light by the magnifier,

And

Therefore:

To take an example, consider a magnifier of power *F* _{M }= +4.00 DS, with the object at the focal point ( *L* _{1 }′ = 0). Assume that a ±0.50 DS change in vergence is the minimum that could be detected by a patient, so *L* _{2 }′ (the depth-of-focus) is ±0.50 DS. If *L* _{2 }′ = −0.50 DS (for the case in which the object moves towards the lens), substituting into Eq. (7.2) gives

If *L* _{2 }′ = +0.50 DS (the object moves away from the lens),

This gives a total depth-of-field of 63 mm for a +4.00 DS ( *M* = 1×) magnifier. If we wish to investigate how the depth-of-field alters as the magnifier power changes, the previous method is rather lengthy, and a more direct method is preferable ( ). As shown in Fig. 7.6 , with the object distance equal to the focal length of the magnifier, the rays of light (shown as solid lines) which leave the magnifier are parallel ( *L′* = 0, image at infinity). As the object moves a small distance Δ *l* closer to the magnifier, the vergence of the rays of light (now shown by dashed lines) leaving the lens changes by a small amount Δ *L′* . When this change Δ *L′* reaches a certain detectable value (which will be different for each patient), the image seen by the patient becomes blurred.

In terms of vergences, the refraction by the lens can be expressed as:

So

And

To find the effect of a change in *l* by a small amount Δ *l* , the corresponding small change Δ *L′* in *L′* can be found by differentiating Eq. (7.3) :

The change in *L′* is occurring about the position where *L′* = 0, so the formula becomes:

or, in words,

maximum tolerable change in object position (in metres) is equal to

In the low-vision context, devices are more often labelled with the magnification rather than the power, and

So lens power = 4 × *M*

Therefore:

Now the change in object position here is in metres, although this is likely to be a very small number. Changing the formula so that Δ *l* is measured in millimetres gives:

This gives the tolerable change in object position moving towards the lens (Δ *l* positive, as Δ *L′* negative), but of course the object can also move away with a corresponding decrease in *L′* (Δ *L′* positive and Δ *l* negative). This means that the full tolerable range of possible object positions (the depth-of-field) is:

For the example already given earlier, where *M* = 1, it can be seen that:

which matches well to the value of 63 mm calculated by the alternative method given earlier. By comparison, if the magnifier power is now increased, for example, to +20.00 DS, and *M* = 5×,

Thus, whilst the depth-of-field is large for the low-powered magnifier, the entire permissible range of movement within which the object will be seen clearly through the +20.00 DS magnifier is only 2.5 mm, which illustrates one of the practical difficulties encountered in using such devices. Of course, the visually impaired patient may not be so sensitive to blurring of the image and may be able to tolerate more movement. Equally, a patient with active accommodation may be able to alter their accommodative effort to aid in focussing the image. It is also apparent that a change in object position can be useful to create a change in the vergence of light leaving the magnifier lens, which will compensate for uncorrected spherical ametropia.

## Field-of-View

The field-of-view of a magnifying lens is defined as the angle subtended by the lens periphery at the image of the eye’s entrance pupil.

Considering Fig. 7.7 , the entrance pupil is at *E* , a distance *a* behind the lens, with its image at *E′* with an image distance *a′* .

Refraction of light by the magnifier ( *F* _{M }) gives, in terms of vergences:

or

so

tan ϕ = D 2 a ′ and substituting from Eq. (7.4)

This gives the angular semi-field-of-view *ϕ* of the plus lens, but in purely practical terms, it is more useful to know the linear dimension *y* of the field-of-view, as this can be more easily related to a task (e.g. the width of a column of newsprint).

From Fig. 7.7 :

Equating Eqs. (7.5) and (7.6) :

So total linear extent of field-of-view:

sometimes written as

Eqs. (7.7) and (7.8) are general expressions applicable in any circumstances, but Eq. (7.7) can be considerably simplified by considering the situation where the magnifier is used with the object at the anterior focal point so that and

In fact, for all practical purposes, in low-vision work, these formulae are equally valid if the substitution *a* = *d* is made, so Eq. (7.9) becomes

where *D* is magnifier diameter, *F* _{M }is the equivalent power of the magnifier, and *d* is the distance of the magnifier from the corneal vertex. All of these formulae can be applied to spectacle, hand-held or stand-mounted plus-lens magnifiers.

Thus the field-of-view which the patient obtains with a magnifier depends on the following:

- 1.

The magnifier-to-eye distance. Halving this, for example, will double the field-of-view, and whenever possible, the patient should be encouraged to hold the magnifier close to the eye. This is illustrated in Fig. 7.9 which shows the dramatic increase in the field-of-view when the magnifier is spectacle-mounted. This parameter is the most powerful influence on the area which can be viewed through the lens.

- 2.

The lens diameter. When the patient is bothered by the limited field-of-view, complaining that only a few letters are visible through the magnifier, this is the parameter which the patient feels should be changed. It must be explained that there are practical limitations of weight, manufacturing capability and peripheral aberrations which limit lens diameter, although using the optimum lens form may allow increased diameter whilst maintaining image quality.

- 3.

The power of the lens. As lens power increases, the field-of-view decreases, in addition to the secondary effect that more powerful lenses are usually smaller in size. This is one of the reasons for the practice in low-vision work of giving the minimum magnification which allows the patient to perform the task. It can be seen from Fig. 7.8 , however, that lens power is of less significance than the magnifier-to-eye distance: for example, the field-of-view of an 8× magnifier at 10 cm from the eye is greater than that of a 4× magnifier with a 25 cm magnifier-to-eye distance.

To maximise field-of-view then, the patient must be encouraged to hold the magnifier as close to the eye as possible (i.e. as close as the particular task allows). As already pointed out, changes in this magnifier-to-eye distance do not alter the magnification, but in fact, the patient may often feel that magnification is actually greater with the longer magnifier-to-eye distance. The reason for this is illustrated in Fig. 7.9 .

On the right-hand side, the real situation shows the decreasing angular subtense of the magnifier lens, with the word seen within the aperture remaining the same size but gradually taking up more of the field-of-view: the field-of-view has decreased whilst magnification has stayed constant. It may be perceived by the patient, however, as the situation on the left-hand side of Fig. 7.9 : it appears as if the subtense of the magnifier itself (i.e. the field-of-view) remains constant, so as the word being seen fills more of the available field-of-view, it must be increasing in size.

## Lens Forms for Minimum Aberration

Whether lenses are to be used to correct ametropia or as magnifying aids, there is obviously a desire to minimise the aberrations which will affect the quality of the image created by the lens, and presumably the patient’s visual performance. There is little experimental evidence, however, to support the assumption that the lens form which gives the clearest image will give the best performance: it is certainly possible that the visual system of the visually impaired patient is not capable of detecting imperfections in the image, and would be less affected by them than a normally sighted subject would be. Nonetheless, magnifier lenses are designed to be optimal for the normal visual system.

The aberrations which can be identified for a lens can be divided into *chromatic* and *monochromatic* . The monochromatic aberrations are further subdivided into *spherical aberration, coma, oblique astigmatism, field curvature and distortion* . Whilst they are separated in this way for descriptive purposes, all the aberrations would actually be present simultaneously in the image to some extent. Fig. 7.10 shows a grid pattern which can be used to visualise each of these aberrations, and each is best seen using a large-diameter (~70 mm) plano-convex or meniscus lens of approximately +8.00 DS.

Chromatic aberration describes the greater power of the lens for blue light than red, due to its higher refractive index for these wavelengths. The greater the refractive index difference shown by the lens material between the extremes of the spectrum, the greater this power difference and the *dispersion* shown by the lens. It is desirable to minimise dispersion, and this quality is usually represented by a high value of the reciprocal of dispersion— *constringence* . Once the lens material is selected, there is little that can be done to reduce chromatic aberration with a single lens. It can be eliminated with an achromatic lens system: this would typically be a doublet combining a positive and a negative lens, each made of a different material. The refractive powers of the two lenses sum to give the required effect, whilst the chromatic dispersion of one is cancelled by the other. To visualise transverse chromatic aberration, place the grid target at about 30 cm from the eye, and the plus-lens flat on top of it with the geometrical centre of the lens over the centre point on the grid. Then bring the lens slowly off the page until the outer circle on the grid becomes slightly blurred, and at that point, its black outline will be edged with blue on the inner side and yellow on the outer edge. The effect is more noticeable on the circles seen through the edge of the lens, because the prismatic effect (deviation) is greater through these outer zones: transverse chromatic aberration is the difference in the prismatic effect of the lens for the extremes of the spectrum. The coloured fringes are only seen with high-contrast, black-white targets, due to the different image size created by rays of different wavelength. With low-contrast targets, this difference in image size simply creates a blurred edge to the image, reducing its sharpness and clarity: in normal viewing conditions, therefore, the effect of chromatic aberration is simply to blur images seen through the lens periphery rather than create coloured fringes.

Of the monochromatic aberrations, spherical aberration and coma are clinically insignificant for spectacle-mounted lenses until very high powers are reached (>+48.00 DS, 12× magnification). This is because these aberrations are apparent in the image when rays from the periphery of the lens are refracted to a different focus to those passing through a point closer to the optical centre. When the lens is worn close to the eye, the eye’s pupil acts as the aperture stop and the limited-diameter bundle of rays entering the eye has passed through a restricted area of the lens, within which the power should vary very little. In hand-held or stand-mounted magnifiers, by contrast, the longer eye-to-magnifier distance means that the eye pupil no longer forms the aperture stop of the system: rays of light entering the entire magnifier aperture can enter the eye simultaneously, and so spherical aberration and coma can adversely affect the image. The problem increases with the aperture of the lens, so one possible solution is simply to decrease magnifier diameter; the use of aspheric surfaces can also effectively reduce spherical aberration, as can the use of a doublet or triplet lens system.

The main aberrations to be considered in magnifier lenses, however, are oblique astigmatism, field curvature and distortion. Placing the plus-lens over the grid in Fig. 7.10 as before, it should be moved gradually off the page, and it will be seen that the outer rings of the grid pattern go blurred before the inner rings. This indicates that the image distance decreases progressively for correspondingly more peripheral rays, creating a curved image plane—the so-called field curvature. Examining the blurring ring at one point, however, it will be seen that the radiating spokes on the grid are still clear, whilst the concentric circle has blurred: the lens is showing oblique astigmatism for rays passing off-axis through the lens. Placing the plus-lens over the square grid in Fig. 7.11A , and drawing the lens slowly off the page produces an image as in Fig. 7.11B , where the shape of the image shows pincushion distortion.

These same aberrations are also problematic when plus lenses are used to correct a hypermetropic refractive error, and oblique astigmatism and field curvature are controlled (and a ‘best form’ lens produced) by careful combination of back and front surface powers. The lens wearer adapts to the distortion in the image because of their awareness of the true nature of their environment, and this does not usually need to be considered. In magnifier lenses, there is no such compensation for spatial distortion, and this becomes an important influence on image quality unless lens form is adjusted accordingly. A more significant difference, however, is the fact that ametropic corrections are optimised for viewing an object at distance (infinity) or at a ‘normal’ near working distance (about 33 cm), whereas the magnifier will be used with the object at the anterior focal point (or even closer). Unfortunately, even taking this into account, no single lens form can eliminate all of the aberrations simultaneously, and the lens designer must decide which aberration will most significantly affect image quality and arrive at the best compromise design. This was attempted in the ‘Stigmagna’ range of lenses which correct for oblique astigmatism and distortion ( ) and in the calculations of which attempt to minimise field curvature as well.

As lens power increases beyond +20.00 DS (5× magnification), careful choice of spherical surfaces is no longer sufficient to produce adequate image quality, and aspheric surfaces must be used. In contrast to a spherical surface where the radius of curvature remains constant across the entire diameter, aspheric surfaces flatten (the radius of curvature increases) towards the periphery. The degree of flattening increases as the surface chosen changes from elliptical to paraboloid and is greatest for a hyperboloid form. By careful manipulation of the spherical back surface power, and the particular aspheric form used for the front surface, oblique astigmatism and distortion can both be made negligible. The ‘Hyperocular’ lens form for magnifiers ( ) is one such design where in lower powers (4× to 5×), an ellipsoid front surface is used, but for higher powers (8× to 12×), the degree of flattening must be greater and a hyperboloid surface is needed ( ). In order to determine whether a particular plus-lens surface is spherical or aspheric in form, a lens measure can be placed perpendicular to, and centrally on, the surface. Keeping the lens measure perpendicular to the surface, it should now be moved towards the periphery of the lens, and the reading noted: a progressive decrease in the power will occur on the flattening aspheric surface, whereas the reading will remain constant on a spherical surface.

Table 7.1 illustrates the range of lens forms which can be used to minimise the aberrations of spectacle-mounted magnifiers. Whilst lower-powered plus lenses which use spherical surfaces are often meniscus in form with a concave back surface, those above approximately +17.00 DS and those which use aspheric surfaces are usually bi-convex. It is usual in a spectacle-mounted lens to have the most convex surface away from the eye (as it would be if used for correcting refractive error) but when the lens is used away from the eye in a hand-held or stand-mounted form, this position should be reversed and the most convex surface held towards the eye to minimise aberrations. In fact, the ‘change-over’ between these two positions occurs when the eye-to-magnifier distance is equal to the focal length of the lens.

Approximate Power Range (DS) | Lens Form |
---|---|

Up to +8.00/+10.00 DS (2× to 2.5×) | ‘Standard’ prescription best form, spherical surfaces, meniscus |

+8.00 to +16.00 (2× to 4×) | Lenticular (restricted aperture), spherical surfaces, meniscus |

+10.00 to +24.00 (2.5× to 6×) | Stigmagna or Lederer ‘special’ spectacle magnifier form, spherical surfaces, meniscus in low power, plano-convex and bi-convex in higher powers |

+16.00 to +48.00 (4× to 12×) | Hyperocular, aspheric front surface (ellipsoid lower powers, hyperboloid in higher powers), biconvex |

+40.00 to +80.00 (10× to 20×) | Achromatic doublet or triplet lens system |

The same adjustment of the lens forms with increasing lens power will be required in hand-held and stand magnifiers, although in this case, the aberrations are likely to become more severe at lower powers. This is because the pupil of the eye no longer forms the aperture stop of the system, with the consequence that rays of light passing through the whole lens aperture are present in the final image. This causes greater problems with spherical aberration, and aspheric surfaces are often employed in low-powered hand and stand magnifiers as the flattening of the lens surface and the consequent fall-off in power help to counteract this. Thus, a lens of a particular power can be made in larger diameter, whilst still retaining acceptable image quality, if aspheric surfaces are used. Even so, the increased eye-to-magnifier distance increases aberrations to such a degree that the use of compound systems may also become necessary at lower powers.

## Lens Forms for Minimum Thickness

The design of the Fresnel lens (and prism) is such that the refracting effect of the optical surfaces is retained (the appropriate curvature for the lens, or the correct angle for the prism), but the bulk of the material in between is removed. This is shown schematically in Fig. 7.12 .