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Optical Aberrations and Best Form Lenses Cheat Sheet (DRAFT) by

A cheat sheet for Optical Aberrations and Best Form Lenses, a subtopic for ophthalmic dispensing.

This is a draft cheat sheet. It is a work in progress and is not finished yet.

Optical Aberra­tions and Best Form Lenses

Lens Form - Types
Curved Lenses
Curved surface determines whether plus or minus
Meniscus lenses are convex­-co­ncave lenses they have one outward faced curved and one inward
Flat surfaces are plano and have 0 power
Outward curve shaper than inward curve? Lens has a positive focal length and acts as a magnifier. Forms either real or virtual image.
Lenses are determined by their surface curvat­ures, can be flat or curved
Toric lenses are curved surfaces. One surface spherical, the other toroidal. Used when cylinder in prescr­iption.
Curved surfaces are either meniscus or toric lenses
 
F1 + F2 = F Total is the nominal power of a lens

Aberra­tions

Lens aberra­tions can reduce image quality as the wearer gazes away or looks obliquely from the optical axis.
There are 6 different lens aberra­tions that impact quality of peripheral vision through a lens:
Oblique Astigm­atism, Power Error, Spherical Aberra­tions, Coma, Distor­tion. These are monoch­romatic and occur indepe­ndently of colour.
Chromatic Aberra­tions are the conseq­uence of the dispersive properties of the actual lens material.
As the eye rotates behind the lens, the far point moves with the eye at a fixed distance from the Centre of rotation. This movement is known as the far point sphere.
The far point sphere is a spherical surface that represents the ideal focal points for a lens as the eye rotates to look through it.
Lens aberra­tions arise when light refracted by a lens fail to focus on the far point sphere.

Distortion

Distortion is an optical aberration that deforms and bends straight lines and makes them appear curvy in images.
There are 3 types of optical distor­tion:

Oblique Astigm­atism

An abberation that occurs when lightrays from an object in the periphery strike the lens obliquely and are then refracted by the tangential and sagittal meridians differ­ently.
Oblique astigm­atism can also be induced by tilting the lens, as this places the line of sight at a signif­icant angle to the optical axis.
The Tangential meridian (T) refracts more incident lightrays than the Sagittal meridian (S). Conseq­uently, incident light from an off-axis object are brought to a focus at 2 different points.
OA due to lens tilt can be minimised by ensuring that the optical axis of the lens passes through the centre of rotation in the eye.
The image of the object point is no longer focused at a single point, but is separated at 2 different foci, the Tangential Focus and the Sagittal Focus.
This can be achieved by manipu­lating the relati­onship between the pantos­copic tilt.
Oblique astigm­atism occurs when the wearer looks at an angle (obliq­uely) through the lens or through the lens periphery.
The pantos­copic tilt is the lens tilt towards the cheeks and the height (H) of the wearer's pupil centre above the optical centre (OC)
 
1mm of Optical Centre Drop (H) for Every 2 Degrees of Pantos­copic Tilt
Oblique astigm­atism is an astigmatic focusing error, and has a similar effect to unwanted cyl power in a prescr­iption.
  

Curvature of Field - Aspherical Lens

Any surface that isn't spherical is aspheric
Conic sections are the sections when a plane intersects a cone
Toroidal surfaces are aspheric
If a plane intersects a cone at right angles exactly to a vertical line passing through the apex the cut face would be a circle
Aspheric surfaces are from concoids: a family of curves
Various curves that represent a section of the cone for aspheric lenses are: Cone, Ellipse, Parabola, Hyperbola
Eccent­ricity is the slight variation of angle that the plane has from the circular section, moving into the Ellipse section
If the plane of inters­ection is exactly parallel to one side of the cone, it is the parabola section
The eccent­ricity for the conic sections are:
e = 0 for Circle, 0 <e < 1 for Ellipse, e = 1 for Parabola, e > 1 for Hyperbola
Aspherical lenses are astigm­atic.
As you move away from the central vertex to the periphery of the lens, it results in negative surface astigm­atism.
The negative surface astigm­atism is used to neutralise the positive oblique astigm­atism.
Positive oblique astigm­atism arises off the axis gaze.

Power Error

When no OA is present, a lens brings light to a focus on the Petzval Surface - a curved image plane.
Power error is a result of the fact that the focal plane of the lens for off-axis object points departs from the FPS of the eye.
Curvature of Field is an aberration that arises from the difference in focus between a flat focal plane and the Petzval surface
PE occurs even when there is no OA
Curvature of Field is a concern for flat image planes, such as a camera. However the FPS (ideal plane of the eye) is also curved.
In PE, the Tangential and Sagittal meridians may refract incident light to a single point focus, however this is not on the FPS
The Petzval surface is flatter than the FPS.
The FPS is the desired point of focus
Power Error arises as the difference in focus between the Petzval surface and the FPS.
The dioptric difference between the actual focus and the desired focus results in a PE
Unlike oblique astigm­atism, power error is a spheri­cal­-like focusing error and is similar to unwanted spherical power in a prescr­iption

Coma

Off-axis points of light appear comet shaped
As lightrays from the edges pass through a lens they vary in magnif­ication and create a series of asymme­trical circular shapes
Reducing the lens down to a smaller aperture can reduce coma
Corneal conditions like Keraco­tonus, corneal injuries or abrasians can result in coma
 

Transverse Chromatic Aberra­tions

Off axis blur occurs under low contrast condit­ions. Wearer may notice colour fringes. Transverse Chromatic Aberra­tions reduce visual acuity.
Transverse Chromatism can be eliminated by an Achromatic Lens (a pair of lenses bonded together). Chromatism of one component neutra­lises the chromatism of the second.
Power is given by selecting a material with the highest V-value.
Wollaston Lens reduce chroma­tism. The lens is bent into a steep curve. However Woollaston lenses are expensive and very bulbous

Ideal Best Form Lens

Signif­icant aberra­tions are: Transverse Chromatic Aberra­tion, Distor­tion, Oblique Astigm­atism, Curvature of Field
In practice, best form lenses usually eliminate: Oblique Astigm­atism, Distor­tion, Curvature of Field
Spherical Aberration and Coma are both aberra­tions of wide aperture systems such as photog­raphy. A spectacle lens may be quite large but it is not a common issue.
Aspheric Lens are the most common Best Form Lens