Lens Design and Aberrations PDF

OPHD 2604 Lens Design and Aberrations Chapter 18 20 March 2024 Lens Aberrations: WHAT: A lens component that causes lenses to form less than a perfect image A correct power spectacles can fail to produce a perfect image = the cause of this is lens aberrations Optical aberration can be considered as...

OPHD 2604 Lens Design and Aberrations Chapter 18 20 March 2024 Lens Aberrations: WHAT: A lens component that causes lenses to form less than a perfect image A correct power spectacles can fail to produce a perfect image = the cause of this is lens aberrations Optical aberration can be considered as a flaw or distortion in the image generated by an optical system Lens Aberrations: Spherical lens produces point images of point objects The image produced should be the same colour as the object and any magnification should be uniform Details of the image should be proportional to those of the object These assumptions are however only valid if we are referring to monochromatic light and suppose it to be incident upon the lens close to the optical axis When a single refracting surface does not produce point images of point objects the image is said to suffer from aberrations, which affect the quality Lens Aberrations: WHY: Paraxial rays (central rays) are not refracted in the same way as the non-paraxial rays (peripheral rays) HOW: White light is composed of many wavelengths which has an effect on the deviating power since the refractive index of the lens varies with different wavelengths Greater wavelength = less refractive index Lens Aberrations: The eye experiences aberrations as well, but has mechanisms to overcome them Low degree aberrations: ― Normal ammetropia (myopia, hyperopia, astigmatism) Higher degree aberrations: ― Spherical, chromatic, coma, oblique astigmatism, distortion Important Terminology: 1. ABBE number Number used to identify the amount of chromatic aberrations for a lens material Inverse relationship to chromatic aberrations in a lens ― The lower the abbe value, the more the chromatic aberrations present 2. On and Off Axis On axis aberrations effect vision when looking straight ahead through the lens Off axis effects peripheral vision Important Terminology: Abbe Number Dispensing factors for lenses with LOW Abbe values: 1. Use monocular PD measurements 2. Measure major reference point heights 3. Use shorter vertex distance 4. Have a sufficient pantoscopic tilt, but not more than 10 degrees 5. Have equal edge thickness especially on high powered lenses 6. Have sufficient positive face form Classification of Aberrations: 1. Chromatic aberrations: Due to the material of the lens refracting different wavelengths differently and which will disappear when monochromatic light is used Lens that causes the image to have fringes Divided into: a. axial or longitudinal aberrations b. transverse or lateral aberrations Will disappear when monochromatic light is used: WHY? ― Aberrations that are colour related Classification of Aberrations: 2. Lens-form aberrations: Due to the form of the lens and vary as the form of the lens varies Occur even with monochromatic light Sometimes referred to as monochromatic aberrations Known as second order type of aberrations These are divided into: a. b. c. d. e. Spherical aberration Coma Oblique astigmatism Curvature of field Distortion Monochromatic aberrations deform (field curvature and distortion) or degrade (spherical aberration, coma and astigmatism) the imaging ability of lenses Chromatic Aberrations Chromatic Aberration: Arise because of the dispersive power of optical materials ― Dispersive power refers to the ability of a lens or prism to disperse white light into its constituent colours ― Will not occur with monochromatic light Material dependent Sees peripheral colour fringes Higher power = more chromatic aberrations Divided into two categories: 1. Axial/longitudinal chromatic abs. 2. Transverse/lateral chromatic abs. Chromatic Aberration: 1. Axial/longitudinal chromatic aberrations: Formed by a point light source that has several wavelength (white light) that forms a series of point images along the optical axis When white light passes through a thin lens system it will be dispersed into its monochromatic components Light with longer wavelength is refracted less than those with shorter wavelength ― Blue light will focus closer to the lens than red light The axial distance between the focal point for the two different wavelengths is referred to as axial or longitudinal chromatic aberration Each image is of different colour and slightly different focal length The light of different wavelengths will focus at different focal distances from the lens Chromatic Aberration: 1. Axial chromatic aberrations: Chromatic Aberration: Types 2. Transverse/lateral chromatic aberration: Images of different wavelengths are formed at varying points on the axis and are also of different sizes Variation in the linear magnification or size of the images is referred to as transverse or lateral chromatic aberration Chromatic Aberration: Types SUMMARY: Longitudinal – red fringe, same size Lateral – elongation Chromatic Aberration: Correction 1. Achromatic lenses: Comprise lenses of varying material combined so that the dispersion is neutralized while the overall refractive power is preserved ― Plus lens of one material combined with a minus lens of another material (different refractive indices) ― Combination of a convex lens of high refractive power and low dispersive power with a concave lens of low refractive power but higher dispersive power ― Aberration can be neutralized while preserving most of the convex lens refractive power Example: Crown glass low dispersion and flint glass high dispersion Chromatic Aberration: Correction 1. Achromatic lenses: Adjusted optical centre: NB to take note of the following when dispensing achromatic lenses Mono PD OC height Pantoscopic tilt Decrease vertex distance Smaller frame Reduced edge thickness Chromatic Aberration: Correction 2. Achromatic prisms: It is possible to place two prisms together with their bases in opposition and eliminate the chromatic aberration Such a combination of prisms is known as an achromatic prism Ocular Chromatic Aberrations Ocular Chromatic Aberration: Refraction by the human eye is also subject to chromatic aberration Total dispersion from the red to the blue image being approximately 1.50D - 2.00D The emmetropic eye focuses from the yellow-green portion of the spectrum ― This focused wavelength lies approximately in the middle of the range of retinal sensitivity Thus approximately 0.75 – 1.00D of chromatic aberration lie on either side of the maximally sharp focus Ocular Chromatic Aberration: Clinically: ― Chromatic aberration of the eye is made use of in the duochrome test ― In this test the patient simultaneously view letters by means of red and green light, and can easily tell which appear clearer ―The test is sensitive to an alteration in refraction of 0.25 D or less ―This test is useful in ensuring that myopes are not overcorrected Lens Form Aberrations Lens Form Aberrations 5 Types of Seidel Aberrations: 1. Spherical aberration 2. Coma 3. Oblique astigmatism 4. Curvature of field 5. Distortion Lens form aberrations: 1. SPHERICAL Paraxial rays are those rays that pass through the central areas of the lens Peripheral rays are those rays that enter the lens nearer to the edge than centre Spherical aberrations are present when peripheral rays focus at different points on the optic axis than paraxial rays do CENTRALLY: there are less aberrations vs EDGES: which have more aberrations Pupil limits peripheral rays: Spherical aberrations is not a problem in the eye Lens form aberrations: 1. SPHERICAL It was previously assumed that refraction by a lens will result in all rays being brought to a common focus ― This is not the case since the deviating power of the lens increases as the heights of incidence of the separate rays increase from the optical axis Therefore, spherical aberration is the name given to the effect where the focal length of a lens will vary depending on how far you are from the center of the lens What this means in reality is that a parallel ray of light entering the lens near the centre of the lens will be refracted less than a parallel ray entering near the edges of the lens Lens form aberrations: 1. SPHERICAL Lens form aberrations: 1. SPHERICAL How does the eye REDUCE spherical aberration: The anterior corneal surface is flatter peripherally than at its center, and therefore acts as an aplanatic surface The nucleus of the lens of the eye has a higher refractive index of the lens cortex ― Thus the axial zone of the lens has greater refractive power than the periphery The iris acts as a stop to reduce spherical aberration The impairment of visual acuity that occurs when the pupil is dilated is almost entirely due to spherical aberration Optimum pupil size is 2- 2.5mm Lens form aberrations: 1. SPHERICAL The retinal cones are more sensitive to light which enters the eye paraxially than to light which enters obliquely through the peripheral cornea (Stiles Crawford effect) ― This directional sensitivity of the cone photoreceptors limits the visual effects of the residual spherical aberration in the eye Stiles Crawford effect: light entering the eye near the edge of the pupil produces a lower photoreceptor response compared to light of equal intensity entering near the center of the pupil ― Means: light entering the eye near the center of the pupil appears brighter than light entering near the edge ― Property of the human eye that refers to the directional sensitivity of the cone photoreceptors Lens form aberrations: 2. COMA Coma is similar to spherical aberration, in that it is really spherical aberration applied to light rays entering the lens at an angle The focal point of the lens will vary the further away the ray hits the lens from the centre Rays passing through the periphery of the lens are deviated more than the central rays and come to focus nearer the principal axis ― Due to this you will get blurring of your image the further off-axis you go Comet shaped Different points of the lens will produce different magnification Image is elongated thus appears like a comet coma Degrades and deforms images Lens form aberrations: 2. COMA This occurs because of the magnifications produced by marginal and paraxial zones are not equal In a convex lens, the least magnification is associated with the marginal rays which consequently form the smallest image and the coma is said to be negative ― If the reverse is true, then the coma is said to be positive The object point is off axis of the lens An aberration that causes light from peripheral areas of the lens to be focused farther away from the true image point Difference in magnification for rays passing through different zones The focal areas (point) of the peripheral zones lie in different location than the more central rays No point images that is formed off axis There are unlimited ‘circles’ of blur that blend together The point of the cone points towards the axis Due to pupil size coma aberrations is less problematic in the eye Lens form aberrations: 2. COMA Lens form aberrations: 2. COMA Correction of COMA aberration: If the magnification effects of the marginal and paraxial zone can be made the same, coma will be eliminated It can be reduced by a suitable choice of radii of curvature Coma can be eliminated totally unlike spherical aberration but unfortunately the form of lens for zero coma is not quite the same as that for minimum spherical aberration The lens form which exhibits minimum spherical aberration cannot be free from coma However, as in the case of oblique astigmatism, this aberration can be avoided by limiting rays to the axial (centre) area of the lens and by using the principal axis of the lens rather than a subsidiary axis Lens form aberrations: 3. OBLIQUE ASTIGMATISM Occurs when rays of light traverse a spherical lens obliquely = Leads to a toric effect being introduced ― When light hits a spherical lens at an angle Astigmatism arises because if an object point is a distance from the optical axis then the cone of rays from that point will strike the lens asymmetrically Oblique astigmatism causes the light to focus as two line images ― Resembles an astigmatic lens ― Tangential images and sagittal images The object point is off axis of the lens Lens form aberrations: 3. OBLIQUE ASTIGMATISM The focal length of the lens will vary depending on where you hit the lens ― This will lead to rays which are less parallel to the optical axis being focussed differently from those which are parallel or almost parallel to the optical axis ― This means that for some points the object will always be blurred as while you can focus the light for some of the rays you cannot focus it for all of them Astigmatic difference → is the distance between the two line foci (images) When expressed in diopters, astigmatic difference is called oblique astigmatic error Oblique astigmatism is troublesome for the spectacles lens wearer and must be checked when designing spectacles Oblique astigmatism can be reduced by selecting optimum base curve for a given lens power Lens form aberrations: 3. OBLIQUE ASTIGMATISM Lens form aberrations: 3. OBLIQUE ASTIGMATISM Sturm’s Conoid: a representation of how light rays are refracted through two different powered meridians (eg. Spherocylindical lens) Instead of ONE focal point, they form TWO focal points Lens form aberrations: 3. OBLIQUE ASTIGMATISM Correction of OBLIQUE ASTIGMATISM: 3 ways The lens needs to be orientated such that incident light is parallel to the principal axis Aberration may be reduced by restricting the aperture of the lens Reduced with the use of meniscus lenses rather than flat form lenses Lens form aberrations: Ocular Astigmatism: The visual effect is minimal Factors that reduce ocular oblique astigmatism: 1. The aplanatic curvature of the cornea 2. The retina is not plane but spherical Thus, the circle of least confusion of the Sturm’s conoid formed by oblique astigmatism fall on the retina The astigmatic image falls on the peripheral retina which has relatively poor resolving power compared to the retina at the macula Visual appreciation of the astigmatic image is therefore limited Lens form aberrations: 4. CURVATURE OF FIELD A plane object gives rise to a curved image For rays entering the lens on or near the optical axis (paraxial rays) the focal length of the lens is constant ― This leads to the problem of field curvature As the distance from the centre of the lens to the focus point is constant then the image described by the lens is going to be a curved surface not a flat one The aberration causes spherical component of the lens to have the effect of being off power in the periphery when worn Light entering the peripheral areas of the lens does not focus where it should be; on the far point Image shell error = is the dioptric difference between place where the image actually focuses and where it should focus Usage of correct base curve will ensure that oblique astigmatism and power error are held at minimum Lens form aberrations: 4. CURVATURE OF FIELD If an object is perpendicular to the axis of a refracting system, it will give rise to an image that is also perpendicular to the axis only for refraction in the paraxial region With larger apertures however, the image of a planar object will be curved In the absence of astigmatism, the image will lie on a curved, paraboloid surface called the Petzval surface This defect of the image is known as Petzval Field Curvature, or sometimes as curvature of field Curvature of field occurs even when spherical aberration, oblique astigmatism and coma have been eliminated A less curved image is formed with lens materials of a higher refractive index Lens form aberrations: 4. CURVATURE OF FIELD Lens form aberrations: 4. CURVATURE OF FIELD Lens form aberrations: 5. DISTORTION Inability of a lens system to produce an image the same shape as the object Due to: Increased prismatic effect of the periphery of the lens producing variation in magnification (unequal) at different distances from the axis of a lens Occurs because of difference in magnification at different areas of the periphery of the lens in proportion to the distance of those areas from the optical centre of the lens Image is clear but shape is changed Lens form aberrations: 5. DISTORTION If the magnification increases with increasing distance from the axis, the outer parts of the image will appear larger than in the case of the ideal image This distortion is known a pincushion distortion (positive distortion) Occurs with plus lenses WHAT: 1. Rays at centre are less magnified 2. Periphery more magnified 3. Corners are larger Lens form aberrations: 5. DISTORTION If the magnification decreases with increasing distance from the axis, the outer parts of the image will appear smaller than in the case of the ideal image This distortion is known as barrel distortion (negative distortion) Occurs with negative lenses WHAT: 1. Rays in centre more magnified than off axis 2. Minification at the periphery 3. Thus corners are smaller Lens form aberrations: 5. DISTORTION Distortion is a significant defect in spectacle lenses and sometimes particularly with higher powered lenses, creates curvature of objects and false movement or spatial distortions Distortion can be reduced but not eliminated, in ophthalmic lenses by using steep base curves, so that the deviation of oblique rays entering the eye is approximately the same at each surface of the lens Correction: Aspheric lenses used to reduce distortions Lens Design Four variables of Lens Design: 1. 2. 3. 4. Vertex distance Lens thickness Refractive index Front and back lens surface powers Aspherics: WHAT: Aspheric = NOT spherical The degree of curvature of a spherical lens is continuously uniform with a consistent radius of curvature throughout its entire surface With aspherics, the surface changes shape Therefore = does NOT have the same radius of curvature across the entire surface Based on a surface curvature that comes from a conic section Aspherics: 4 basic types of conic sections: 1. CIRCLE: A shape formed by a horizontal plane (a slice through an upright cone) 2. ELLIPSE: A shape formed by an angled plane through a cone that does not intersect the base of the cone 3. PARABOLA: A curve that is formed by the intersection of a cone with a plane having one side parallel to the side of the cone 4. HYPERBOLA: A shape formed when a cone is intersected by a plane that makes a greater angle with the base of the cone than the side of the cone makes with its base Aspherics: Aspherics: WHY: There are 5 reasons (purposes) why aspherics would be used: 1. Optically correct lens aberrations 2. Allow the lens to be made flatter This reduces magnification and make it more attractive 3. Produce a thinner and thus, more lightweight lens 4. Ensure a good and tight fit in the frame 5. Make a lens with progressive optics Aspherics: Fitting Guidelines: 1. Monocular PD 2. Measure the MRP (major reference point) in the convention way Subtract 1mm for each 2 degrees of pantoscopic tilt NB: OC should not be more than 5mm below the pupil Aspherics: WHEN: 1. Plus Lens Wearers: Recommended when Rx goes above +3.00D Can be from +2.00 to +4.00 or even lower Take frame size into consideration: as the size increases, the amount of plus power needed before recommending aspheric lenses decreases ― The larger the lens = the lower the power will be when aspherics are recommended Aspherics: WHEN: 2. Minus Lens Wearers: Recommended for powers higher than -3.00D The ‘minimum’ lens power recommended for aspherics will differ depending on frame size and wearer concerns If high index aspherics is used to primarily thin the lenses – it is counterproductive to place such a lens in a frame with a small eye size and narrow vertical dimension if that frame is a nylon-cord frame ― WHY: nylon-cord frames need a minimum edge thickness to allow for grooving of the edges Aspherics: WHEN: 3. Anisometropia A difference of more than 2.00D between the right and left eye There will be differences between magnification Aspherics are of course flatter, thinner and closer to the eye, thus reducing magnification differences 4. Others: Children who are sensitive to how their lenses look Older patients to decrease the weight CL wearers – will hopefully wear glasses and not overwear CL Base Curve: Incorrect base curve selection will lead to the central (straight ahead vision) to be clear and comfortable, but the vision in the periphery will be downgraded ― Due to those lens aberrations A general guideline to choosing the correct BC: 1. Plano lenses have back surface curvatures of -6.00D 2. As the lens power becomes more MINUS: the back surface steepens, and the front surface flattens 3. As the lens power becomes more PLUS: the back surface progressively becomes flatter, while the front surface become more steeper From the front – minus lenses appear more flat than plus lenses Base Curve: Factors that modify the base curve choice: Most metal frame eyewires are curved to best accept a lens with a 6 base curve ― Most common base curve Plastic frame styles that have a poor lens retention may retain their lenses better if the lenses have a flatter base curve Lens thickness increase lens magnification (especially plus lenses) ― Much of this magnification comes from a steep base curve ―Therefore the magnification can be reduced by using a flatter base curve Rx with large amounts of prism end up being thicker ― Large prisms are easy to work with when produced on a lower (flatter) base curve High PLUS Lens Designs: 1. Regular spheric lenses Known as ‘full field’ lens Not the best optics 2. High-index aspherics Best choice Not as readily available in higher plus powers 3. Lenticulars 4. High plus multidrop lens High PLUS Lens Designs: LENTICULARS: A lens that has a central area with the prescribed lens power surrounded by an outside area with little or no power Central area = aperture Outer area = carrier Developed for the purpose of thinning the lens Available as either spherical or aspherical ― Aspheric is the better choice ― Aspheric: an aspherically designed plus lens that has been placed on a near-plano carrier High PLUS Lens Designs: LENTICULARS: Disadvantages: 1. Look of the lens (not aesthetical) ― Small frame: edge of the aperture is still visible ― Large frame: the lens looks like the yolk of an egg Advantages: 1. Weight reduction 2. Thickness reduction 3. Good optics (aspheric lenticulars) High PLUS Lens Designs: HIGH PLUS MULTIDROP LENSES: Designed to overcome the cosmetic negatives of lenticulars while maintaining a thin lens Back surface curve that was almost flat Front surface had a 24mm spherically based area Outside of that front surface area – the lens surface became aspheric and dropped in power (usually by 1.00D at a time, until 4.00D was reduced) Optics were less than optimal High MINUS Lens Designs: 1. Lenticular minus design Same idea as with plus lenticulars Contains a central area with the prescribed power The peripheral area (carrier) serves only to extend the physical size of the lens without increasing the thickenss Found in several forms: MYODISC is the most relevant type Self Review: Atoric Lenses Base Curve Calculations END!