Autorefractors measure the eye's sphere, cylinder and axis objectively and automatically. They find the eye's far point, as retinoscopy does (see Retinoscopy)
Wavefront aberrometers measure all of the eye's optical errors, including the higher-order aberrations that spectacles cannot correct

## Autorefractors

They use infrared light (about 800–950 nm): invisible, so the pupil stays large and the patient is not dazzled. The result is corrected for the eye's lower power in infrared (chromatic aberration)
The patient views a fogged target (a distant picture) to relax accommodation
Several meridians are measured to find the principal meridians, giving sphere, cylinder and axis in a few seconds

Scheiner principle: two pinholes in front of the pupil. If the retina is conjugate with the target, a single image is seen; otherwise the two beams form two separate images

In myopia the beams cross before the retina; in hypermetropia they have not yet met. So the arrangement of the two images shows the sign of the error as well as its size
The instrument moves its optics until the two images merge; this is the eye's refraction

Optometer principle: a positive lens with the eye at its second focal point. The target's distance from the lens's first focal point is then proportional to the eye's refractive error, giving a linear scale (the same idea as the Badal focimeter; see Focimeter)

Target movement x = refractive error × f²
Worked example: a +10D optometer lens (f = 10 cm). Each dioptre of ametropia moves the target 1 × 0.1² = 0.01 m = 1 cm. A −3.00D myope needs the target 3 cm nearer the lens than for an emmetrope

Other principles: scanning retinoscopy (measuring the speed of the reflex electronically) and image-quality analysis (moving the target until the retinal image is sharpest)

Instrument (proximal) myopia: knowing the target is close inside the machine makes the patient accommodate, so autorefractors tend to read too minus, especially in children and young adults
In children, use cycloplegia (see Retinoscopy)
Results are unreliable with small pupils, media opacities, irregular corneas (keratoconus, scars), poor fixation and nystagmus
An autorefraction is a starting point for subjective refraction, not a prescription (see Subjective Refraction)

Photoscreeners (eccentric photorefraction) photograph the red reflex of both eyes from about 1 m. The pattern of the crescent estimates refractive error, anisometropia and strabismus. They are used for screening young children

## Wavefront aberrometry

A wavefront joins points of light that are in phase. A perfect eye turns light from a point on the retina into a flat (plane) wavefront as it leaves the eye
The wavefront error is the difference between the real and the ideal wavefront, in microns

Hartmann–Shack (the commonest): a small spot of light is focused on the retina. The light leaving the eye passes through an array of tiny lenses (lenslets) onto a camera sensor

A flat wavefront gives a regular grid of spots
An aberrated wavefront gives displaced spots. Each displacement is proportional to the local slope of the wavefront, from which the whole wavefront is reconstructed

Other methods: Tscherning (a grid projected onto the retina and photographed), ray tracing (sequential spots), and dynamic skiascopy

## Zernike polynomials

The wavefront is described as a sum of standard shapes, the Zernike polynomials, arranged in orders. The size of each is its coefficient in microns; overall error is expressed as the root mean square (RMS)
Values depend strongly on pupil size, so the pupil diameter (e.g. 6 mm) must always be stated

Order	Aberrations	Correction
0 and 1	Piston; tilt (prism)	Not optical errors of focus
2 (lower order)	Defocus (sphere) and astigmatism (cylinder)	Spectacles, contact lenses: about 90% of the eye's aberration
3 (higher order)	Coma and trefoil	Rigid contact lenses, wavefront-guided surgery
4 (higher order)	Spherical aberration, secondary astigmatism, quadrafoil	Aspheric IOLs, wavefront-optimised ablation

Image quality can also be shown as the point spread function (the image of a point), the modulation transfer function (contrast transfer at each spatial frequency) and the Strehl ratio (peak of the actual point image ÷ the peak for a perfect eye)

Keratoconus: large vertical coma, from the inferiorly displaced cone
The normal cornea has positive spherical aberration (about +0.27 µm for a 6 mm pupil). Aspheric IOLs with negative spherical aberration offset it and improve contrast
Myopic laser refractive surgery increases positive spherical aberration, causing night glare and haloes with large pupils. Wavefront-guided and wavefront-optimised ablations aim to reduce this
Aberrations in the eye are described further in Aberrations