Monochromatic Aberrations

Monochromatic Aberraations

“paraxial” formulae only apply for small angles. lenses do not behave as expected off-axis. each aberration will be considered in turn. in reality all happen simultaneously. and white light leads to chromatic aberration. changes in lens form may decrease one, but increase another. these are for rays parallel to optical axis, spherical aberration. for obliquely-incident rays, coma, distortion, oblique astigmatism, field curvature.

Spherical Aberration

Peripheral rays refracted to different focal point. Usually more powerful in peripheral zone. Proportional to (optical aperture)² . not important in spectacle lenses. eye’s pupil means that area of lens used is limited. lens form for minimum spherical aberration. biconvex. F₁/F₂ = 6. this may INCREASE other MORE SIGNIFICANT aberrations.

Coma

Image not a single point, but overlapping blur circles. Comet-shaped image WITH LARGE RAY BUNDLE. C is centre of curvature. size of comatic image increases in proportion to distance of object from axis. in spectacle lenses aperture of ray bundle restricted by eye’s pupil, therefore not a problem. minimum coma when minimum spherical aberration.

Distortion

More peripheral rays refracted proportionally more. OX’/OX not equal OZ’/OZ. Magnification greater in more peripheral zone of lens. Positive lens shows NEGATIVE PINCUSHION distortion. Minus lenses give POSITIVE, or BARREL distortion. For no distortion, need equal magnification no matter what object size (image same SHAPE as object). OX’/OX = OZ’/OZ. This is called TANGENT CONDITION. cannot be achieved in spectacle lenses. impractically steeply curved lens form required.

Effect of distortion on wearer

is significant in spectacle lenses, is noticed by patients, particularly in high-plus prescriptions. floor and table-top appear to bulge upwards. doorway appears narrowed in centre. object curved through edge of lens, but straight through centre of lens. therefore appears to move, object appears of different curvature to each eye. therefore appears in depth. But patient is in a familiar environment, therefore adapts within a few days (at the very most), although warn patient of initial symptoms.

Oblique Astigmatism

On axis, the lens is spherical. Both meridians have same power, and bring rays to focus at same point. Off axis, the spherical lens behaves like a sphcyl. The two meridians refract to a different extent, and the point focus becomes two perpendicular line foci. Circle of least confusion (image which is closest in shape to original point object) is between T’ and S’. As object moves below axis, image moves above. As the object moves further off the axis, the cylindrical effect increases. This can be extended to a three-dimensional plot. The sagittal and tangential foci are always perpendicular to each other.

Consequences of Oblique Astigmatism

poor acuity looking through edge of lens because (different) sph and cyl instead of intended sphere BUT changing lens form has a dramatic effect, the oblique astigmatism can be reduced to zero, this lens would be called POINT FOCAL. If we eliminate the cyl, does this leave the exact spherical power? This image plane is called the Petzval surface. Is this a flat image plane? Newton’s Relation - xx’ = ff’ or xx’ = -f’² for a thin lens when f = -f’’. So if object distance increases, the image distance decreases. So if lens is point focal, those foci are on the curved Petzval surface. “Field curvature”.

Far Point

Obviously, the lens is intended to correct refractive error. For the myope, the focal point of lens should coincide with the Far Point of the eye. For the hypermetrope, the correcting lens converges light towards the Far Point for the eye to create an image on the retina. The far point is not a single location. As the eye rotates to view through different parts of lens, the Far Point rotates as well. The different far point positions lie on the Far Point Sphere which has its centre of curvature at the centre of rotation of the eye. So, If the far point of the eye lies on a curved surface (Far Point Sphere), and the point focus of the lens lies on a curved surface (Petzval surface), can the two be made to coincide? NO! except for one single lens power (»-20.00DS). For all other lens powers, the two only coincide on the axis (if they did not, then the lens would not correct refractive error). The overall effect with a Point Focal lens - The “gap” is called the IMAGE SHELL ERROR.

Alternative

Percival lens form. Allow some oblique astigmatism such that. MEAN OBLIQUE POWER = DIOPTRIC DISTANCE OF FAR POINT. Perfect spectacle lens would be a point image on Far Point Sphere -regardless of obliquity of rays of light. This cannot be achieved! Remember Chromatic aberration depends on the material (V value), Spherical Aberration and Coma are not important, Distortion is important, but relies on patient to adapt. Curvature and Oblique Astigmatism are important.

Spectacle Lens Design

Very limited range of parameters, lens must fit as close to the eye as possible, optimise field of view. lens must be as thin as possible, weight and cosmetic appearance. number of materials (indices) is limited. THIS LEAVES LENS FORM as the most useful variable. a quadratic equation for F_2. two solutions - one lens more steeply curved, and therefore less practical. For the +5.00, the answers are -8.11 and -15.30. So the single point image is on the Petzval Surface but there it is some error relative to Far Point Sphere.

Percival Lenses

Again two forms for each back vertex power. Called Ostwalt and Wollaston forms. Ostwalt form is flatter and therefore more cosmetically appealing. The best way to illustrate is using TSCHERNING ELLIPSES. Wray’s Analysis - A straight line to the Ostwalt part of the Point Focal Distance Vision lenses. Simple formula for the straight line F₂ = (F/2) - 7. BEWARE - you still get a reasonable answer even for powers where it does not apply. The equations and ellipses are only valid over a limited range approx +7.00 to -22.00DS. The minus range can be extended by using high index lenses. Beyond this the aberrations can only be minimised. The forms are different for distance and near spectacles. For sphcyl prescriptions - there is not a form which makes cyl accurate in both meridians simultaneously. can equalise the error in each meridian. approximate form by taking +sph cyl form and using sphere power in formulae.

Best Form Lenses

Either Point Focal or Percival lenses could be called “best form”. There are even other possibilities. eg. Minimum Tangential Error form. The tangential focus coincides with Far Point Sphere. Resistant to changes in vertex distance. In US literature, called “corrected curve”. Flattest base curve, Cosmesis and thickness/weight. Compromise. Leave it to the prescription house, Unless your patient has a non-tolerance. Lens form tends to be considered when a patient reports non-tolerance. But check Lens positioning, Ordered and supplied correctly Within tolerances, Rx. Has form changed from previous prescription? this may have altered the, reflections, aberrations, magnification.

Current Best Form Lenses

Early lenses were flat forms. sph and cyl on opposite surfaces. +sph cyl; -sph cyl. “Curved” lenses replaced flat forms. Meniscus if spherical. Toric if spherocylindrical. Early manufacturers each marketed their own range. ordered by name. starting in 1908 with Carl Zeiss PUNKTAL. Punktal - chose point focal design paradigm, form of each lens power calculated individually, several thousand “base curves” held in stock. base curve: the finished surface on a semi-finished lens. very expensive process.

Surfacing

Current situation (traditional surfacing) - limited range of base curves available, leave it to the prescription house to choose appropriate form, choose nearest approximation (within 2DS of optimum power). This is sufficient because you can’t control all aberrations, can’t optimise for both distance and near tasks, manufacturer cannot take into account vertex distance. Freeform surfacing (digital or direct) - Every point on each surface of the lens is cut individually. Both surfaces can be shaped “on demand”. Cutting programmed by computer so lens can be individually designed. So you could make every lens to a unique base curve (to 0.01D accuracy!). But you could still only make it “perfect” for a particular set of circumstances - vd, viewing distance, etc.

When to not supply best form

Lens form to minimise thickness - Meniscus/toric lenses are the thickest/heaviest form, Get more so as front surface gets more convex. Thinnest are equi-convex/concave. Compromise by using plano-convex/concave, especially for high minus. Think very carefully before changing this high myope into “best form” lenses. “wrap-around”/sports frames. Wrap-around lenses need a high base curve - Need very high base curve simply to match shape of lens to curve of frame, But image quality can be better than expected because close to Wollaston form, and has been claimed to give better peripheral vision over a wider field.

Selecting Toroidal Surface

Don’t just have a base curve choice. Could also choose back surface or front surface torics. Identified by lens measure. no choice in traditionally surfaced multifocals/lenticulars, opposite surface to segment/aperture. What about in single vision? Zeiss - for low cylinder power the best image quality is, back surface torics -10.00 to -20.00, front surface torics plano to +10.00, no difference plano to -10.00. for high cylinder powers, back surface torics, for cosmetic appearance - so edge thickness variation is behind the bevel/rim. Hoya - for all cylinders suggest back surface torics because of spectacle magnification.

Spectacle Magnification

plus lenses make the image larger. minus lenses make the image smaller. applies to the patient’s view through the lenses, the observer’s view of the patient’s eyes. SM = shape factor x power factor

      =       1           x                   1       

          1 - (t/n)F₁                  1 - dF_v’

t = lens thickness              d = distance back vertex to entrance pupil

n = refractive index           F_v’ = back vertex power

F₁ = front surface power

SM for a sph-cyl lens - MUST be different for each meridian, since power factor differs, Although you can try to minimise vd. BUT shape factor will be same if F₁ the same in each meridian. THEREFORE make front surface spherical AND use back surface toric. SM needs to be minimised for all lenses. power factor - fit lens closer to eye. shape factor - flat front surface, thin lens, high index.