Optics 3

This weblog post is the third of a series of nine about optics and optical equipment. This post is about deviations from normal sight, that can be corrected with eyeglasses, including sunglasses, or contact lenses.

Eye correction is important because many optical devices, such as telescopes, microscopes and cameras require manual adjustments to optimize results. This situation may not be too important if the device is being used directly to look at objects. However, if the device is being used indirectly to create images, uncorrected eyes may result in out of focus = blurred images, that may be anywhere from difficult to impossible to correct.

In the early 1970s, I spent a lot of time taking photographs with a friend who was losing his sight. He used photography to see his world before it dimmed forever. This situation has had a major impact on my attitudes toward vision, and photography.

In 2019, I wrote a weblog post about visual acuity, Optotypes. Acuity tests measure how sharp a person’s vision is at a distance. In many places it is tested using a Snellen eye chart, with rows of letters in decreasing sizes. It is read at a distance of 6m = 20′, although if mirror reflection is used, the distance can be reduced to 3m = 10 feet. I remember, at the age of 13, I asked the school nurse about my blurred vision. She gave me a Snellen test and said I should have my eyes tested. Shortly after this, I was wearing glasses. In many places, especially in Europe, the Landolt C test has replaced the Snellen test. This asks a patient to tell where the opening of a letter C is. The letter can be orientated in any of eight different positions, at 45 degrees from each other. Acuity tests, with the patient using her/ his ordinary prescription lenses, are used in many jurisdictions to prohibit people from driving. Unacceptable results in a darkened room, can be used to prohibit driving after dark.

In Optics 1, it was noted that Ibn al-Haytham in his Book of Optics (1021) along with Roger Bacon‘s written works on optics, described the function of corrective lenses for vision.

Reading stones, often used by monks when they illuminated manuscripts, were invented at some point between the 11th and 13th century. These were primitive plano-convex lenses (see illustration above) initially made by cutting a glass sphere in half. As the stones were experimented with, it was slowly understood that shallower lenses magnified more effectively. Around 1286, possibly in Pisa, Italy, the first pair of eyeglasses were made, although it is unclear who the inventor was.

There are several types of eye care/ health professions. The distinctions between them varies, depending on the jurisdiction regulating them. The text below is intended to give a flavour of the various professions, not rigorous legal definitions.

Ocularists make and fit ocular prostheses for people who have lost eyes due to trauma or illness.

Opticians make and fit ophthalmic lenses, spectacles = eyeglasses, contact lenses, low vision aids and ocular prosthetics.

The most problematic term is optometrist. In some jurisdictions it is a person with medical education, with an authorization to perform eye surgery. In others, the scope is more limited. Thus, some are trained and licensed to manage any eye disease, including infections, glaucoma and macular degeneration. Many can prescribe topical medications = eye drops, fewer can prescribe controlled ingested substances. Some may order imaging tests (CT/MRI), remove ocular foreign bodies and perform some laser procedures. Some are also qualified to perform some surgical procedures.

Orthoptists diagnose and manage eye movement and coordination problems, such as misalignment of the visual axis, binocular vision problems, convergence and accommodation problems, and pre/post surgical care of patients with: amblyopia (see below) and strabismus = a vision disorder in which the eyes do not properly align with each other when looking at an object. They treat patients using optical aids and eye exercises, but not with medications or surgery.

An ophthalmist is a physician who specializes in serious eye conditions, but is not a surgeon.

Ophthalmology is a surgical subspecialization that handles the diagnosis and treatment of eye disorders. Ophthalmologists are physicians that undergo subspecialty training in medical and surgical eye care.

Eyewear prescriptions

Corrective lenses are typically prescribed by an ophthalmologist or an optometrist. The prescription consists of all the specifications necessary to make the lenses, typically two! Typically the following information is included: the strength of each lens in quarter-diopter steps (0.25 D). Most people cannot generally distinguish between smaller increments. The use of improper corrective lenses may not be helpful and can even exacerbate binocular vision disorders. The goal is to provide the clearest, most comfortable, and most efficient vision, avoiding double vision and maximizing binocularity.

Eyewear is fragile. Many people have a service card they carry with them when travelling that specifies their eyeglass prescription. Hopefully, this will allow new glasses to be made anywhere in the world.

An eyewear prescription is a written order by an eyewear prescriber, that specifies the value of all parameters the prescriber has deemed necessary to construct appropriate corrective lenses for a patient. In Norway, and many other jurisdictions, most often the person performing the eye examination is also the same person selling you the glasses.

The parameters specified on eyewear prescriptions vary, but typically include the patient’s name, power of the lenses, any prism to be included, the pupillary distance, expiration date, and the prescriber’s signature. The prescription is typically determined during a refraction, using a phoropter and asking the patient which of two lenses is better, or by an automated refractor, or through the technique of retinoscopy. A dispensing optician will take a prescription written by an optometrist and order and/or assemble the frames and lenses to then be dispensed to the patient.

Sphere component

Because its shape minimizes some aberrations, convex-concave lenses (see the diagram at the beginning of this post) are most commonly used in corrective lenses. These can be defined as transmissive optical devices worn in front of the eye to improve visual perception.

Eyeglasses = spectacles are worn on the face a short distance in front of the eye. Contact lenses are worn directly on the surface of the eye. Intraocular lenses are surgically implanted, most commonly after cataract removal.

Every corrective lens prescription includes a spherical correction in diopters. Convergent powers are positive (e.g., +4.00 D) and condense light to correct for farsightedness/long-sightedness (hyperopia) or allow the patient to read more comfortably (see presbyopia and binocular vision disorders). Divergent powers are negative (e.g., −3.75 D) and spread out light to correct for nearsightedness/short-sightedness (myopia). If neither convergence nor divergence is required in the prescription, “plano” is used to denote a refractive power of zero.

The term sphere comes from the geometry of lenses. Lenses derive their power from curved surfaces. A spherical lens has the same curvature in every direction perpendicular to the optical axis. Spherical lenses are adequate correction when a person has no astigmatism. To correct for astigmatism, the “cylinder” and “axis” components specify how a particular lens is different from a lens composed of purely spherical surfaces.

Cylinder component

Patients with astigmatism need a cylindrical lens, or more generally a toric lens to see clearly. The geometry of a toric lens focuses light differently in different meridians. A meridian, in this case, is a plane that is incident with the optical axis. For example, a toric lens, when rotated correctly, could focus an object to the image of a horizontal line at one focal distance while focusing a vertical line to a separate focal distance.

The power of a toric lens can be specified by describing how the cylinder (the meridian that is most different from the spherical power) differs from the spherical power. Power evenly transitions between the two powers as you move from the meridian with the most convergence to the meridian with the least convergence. For regular toric lenses, these powers are perpendicular to each other and their location relative to vertical and horizontal are specified by the axis component. By convention, a horizontal axis is recorded as 180° meridians. The 90° meridian defines the vertical axis.

There are two different conventions for indicating the amount of cylinder: “plus cylinder notation” and “minus cylinder notation”. In the former, the cylinder power is a number of diopters more convergent than the sphere power. That means the spherical power describes the most divergent meridian and the cylindrical component describes the most convergent. In the minus cylinder notation, the cylinder power is a number of diopters more divergent than the sphere component. In this convention, the sphere power describes the most convergent meridian and the cylinder component describes the most divergent. Europe typically follows the plus cylinder convention while in the United States the minus cylinder notation is used by optometrists and the plus cylinder notation is used by ophthalmologists. Minus cylinder notation is also more common in Asia, although either style may be encountered there. There is no difference in these forms of notation and it is easy to convert between them:[1]

  • Add the sphere and cylinder numbers together to produce the converted sphere
  • Invert the sign of cylinder value
  • Add 90° to axis value, and if the new axis value exceeds 180°, subtract 180° from the result

For example, a lens with a vertical power of −3.75 and a horizontal power of −2.25 could be specified as either −2.25 −1.50 × 180 or −3.75 +1.50 × 090.

Axis component

The axis defines the location of the sphere and cylinder powers. The name axis comes from the concept of generating a cylinder by rotating a line around an axis. The curve of that cylinder is 90° from that axis of rotation.

The most common use is to treat refractive errors: myopia = near-sightedness = short-sightedness = a condition where incoming light focuses in front of, instead of on, the retina; hypermetropia = hyperopia = far-sightedness = long-sightedness = a condition where incoming light focuses behind, instead of on, the retina; condition of the eye where distant objects are seen clearly but near objects appear blurred ; astigmatism = rotational asymmetry resulting in distorted or blurred vision. If it occurs in early life and is left untreated, it may result in amblyopia = lazy eye = a disorder where the brain fails to fully process input from one eye and favors the other eye, over time resulting in decreased vision in an eye that typically appears normal in other aspects; and presbyopia = age-related farsightedness = physiological accommodation insufficiency associated with aging (typically people aged over 40) resulting in a progressively worsening ability to focus clearly on close objects.

Contact lenses

There are five types of contact lenses, based on type of lens material: 1) Polymethyl methacrylate (PMMA) lenses have excellent optics, but they do not transmit oxygen to the eye and can be difficult to adapt to. They are considered old fashioned. 2) Rigid gas permeable lenses (RGP) look and feel like PMMA lenses but are porous and allow oxygen to pass through them. They can be fit closer to the eye than PMMA lenses, making them more comfortable. They were introduced in 1978. 3) Hydrogel lenses are thin and pliable = soft, and conform to the front surface of the eye. These were introduced in the early 1970s. They made contact lens wear much more popular because they typically are immediately comfortable. 4) Silicone hydrogel lenses are an advanced type of soft contact lenses that are more porous than regular hydrogel lenses and allow even more oxygen to reach the cornea. These were introduced in 2002, and are now the most popular lenses prescribed in economically advanced countries. 5) Hybrid contact lenses provide wearing comfort similar to soft or silicone hydrogel lenses, but combine this with the clear optics of gas permeable lenses, due to a skirt of hydrogel or silicone hydrogel material. These lenses are difficult to fit and are more expensive to replace than other types. Only a small percentage of people wear hybrid contact lenses.

Once again there is a distinction made between spherical and toric lenses. Spherical contact lenses have the same lens power throughout the entire optical part of the lens. This means they can be used to correct myopia (nearsightedness) or hyperopia (farsightedness). Toric lenses allow contact lenses to correct for astigmatism.

At one time, contact lenses had to be changed every day. They were then cleaned, then stored in an appropriate container, with solution, over night. Then the maximum duration extended, soon becoming once a week, for certain types. Now 30 days is considered the legal maximum.

In our nuclear family, the use of contact lenses is extremely limited. Non-existent is incorrect, because one person decided that it would be best to use these at her wedding, so that her glasses would not date the event.


Recently, I was asked why I write weblog posts that remind people of Wikipedia articles. They suggested I should spend my time writing autobiographical materials about my life. Part of the reason has to do with my career as a teacher. My main task was to explain how the world operates. In addition, I am perpetually creating user manuals, usually for an audience of one. However, publishing them as blogs, allows more people to access the content.

Because the content is originally produced just for my own consumption, sources are seldom specified.

On 2024-04-27, this post, also called Optics 3, was started. By the end of the day, it had been divided into three, with this section being about eye prescriptions. The next post was renamed Optics 4, about eyeglasses. It is to be published on 2024-06-22. Optics 5 is about various types of safety glasses. This post is to be published on 2024-06-29.