# Collection of the wave front

The collection of the wave front presides over the conduct of a review aberrometrique. The optical quality of the eye is very correlated with the existence of phase shifts (optical path differences) within the wave front. Applications of wave-front collection mainly the study of Visual symptoms, suspected the origin to be optical. In refractive surgery, preoperative study of optical aberrations will determine the value of a personalized treatment and program delivery by guiding the laser shots.

### Analysis of the Wavefront in OPD

The analysis of the optical aberrations of the eye is based on the works of Hartmann and Tscherning-19^{e} century, which gave rise to two main categories of wave front analyzers.

### Study of the reflected wave front: Hartmann-Shack systems

^{e}(century), that allows to reveal the parasite image of a point seen by an eye equipped with optical aberrations. The technique has evolved and has been perfected through successive works of Hartmann and Schack (3).

#### Principles of the code of the wave front

**Schematically, the main steps to the wave front analysis are:**

-issuance of a cross laser focused on the fovea,

-collection of the reflected signal at the exit of the eye by a micro-network of lenses,

-Focusing on a digital sensor of the wavefront by each of the beam lenses (the wave front is thus "fragmented" into several contiguous portions),

-Measurement of the deflection of the beam of each lens relative to the reference position (which would correspond to a portion of flat wave front). The deviation corresponds to the distance of the position occupied by the centroid (image formed by the Microlens on the CCD sensor) with the reference.

-Mathematical calculation by integration, in order to obtain a dimensional representation of the wavefront.

#### Example: compilation of a wave front 'ideal' with a Schack Hartman aberrometer

We reason in a simplified way, and in a purely "monofocal" context "For a look" ideal ", which is devoid of any monochromatic optical aberration (System only limited by diffraction to the sources points at infinity), the emerging wave front as measured by the aberrometric out of the entrance pupil is flat.

No deviation is detected by Microlensing network, each portion of this "wave front" ideal to exit the eye being parallel to the plan of the Microlensing. There is no difference of optical path for all points of the pupil.

### Study of the wave by retinal Imaging front

##### -Type Analyzer Tscherning

##### -Launch of retinal rays: Tracey (retinal ray tracing) system

##### -Adjustable incidental Refractometry (Ingoing adjustable refractometry)

### Study of the wave front by refractometry (OPD scan system) scanning

**Analysis of the wave front**

#### Representation of the wave front

The wave front is a theoretical construct that allows to represent the differences of perspective (or dephasing) path across the entrance pupil (in the case of the eye, the pupil of entry corresponds to the circumference of the IRIS Ward). To be intelligible, the wave front analysis requires that the aberrations that are there are characterized (qualified) and quantified (rate). The representation of the wave front can be performed by a decomposition into a sum of functions particularly interesting in this context: the Zernike polynomials. The coefficients which control have a value proportional to the optical aberration that corresponds to them. The first Zernike polynomials easily interpret, because they correspond to the phase shifts inflict optical aberrations 'classic' as the trefoil, the defocus, regular astigmatism, coma, etc.

The polynomials of Zernike database includes theoretically an infinite number of polynomials; However, the software that performs the decomposition of the wave front is working with a 'truncated base' (i.e. a limited number of polynomials). The number of chosen polynomials is low, more calculations will be fast, but approached (less accurate). In addition, the number of microlenses in the matrix of the aberrometric sensor sets the maximum number of sampling points involved in the calculation of decay of the wave front.

#### Principles of the decomposition in elementary signals

The transcript of a surface wave gathered in Zernike polynomials so akin to the decomposition of a note of music in harmonic signals. Depending on the type of instrument played, intensity (grade) of each harmonic will be different and an intensity value can be attributed to each harmonic signal. At the end of this process, it will be broken down the initial note in a sum of elementary signals assigned with a value of loudness (amplitude of the signal). Depending on the accuracy and the practical level of analysis, it is possible to reconstruct secondarily more or less faithfully the note played from the information provided by the initial work of decomposition. You can also extract the note one or more harmonics; a note can be "cleared" selectively unwanted harmonics (for a same note, the timbre of an instrument depends on the harmonic composition of the played note).

#### Interest of the Zernike polynomials for the description of the wave front

#### Decomposition of the front of waves in elementary polynomials

The mathematical decomposition of a wavefront in Zernike polynomials is a mathematical process that requires normalization of the radius of the pupil (the value of the radius of the pupil is assumed to be 1 for the calculation of the coefficients) . However, the distribution of polynomials and the value of each coefficient varies according to the pupillary diameter obtained during the collection of the wavefront. In other words, a variation in the pupillary diameter value of the same patient between two Tests induces a variation in the value of the coefficients attributed to the different aberrations present within the studied wavefront. In general, the larger the pupillary diameter, the higher the value of the coefficients assigned to the different polynomials

In addition, the values assigned to each of the RMS coefficients of the polynomials used for the wavefront analysis should be interpreted with caution. While the quality of the visual function depends in part on the aberration rate within the wavefront, it is not directly proportional to this rate and the value of the coefficients considered separately or in a group. There are indeed compensations between the optical aberrations of different degrees derived from the decomposition in Zernike polynomials.

### Interpretation of the wave after polynomials of Zernike decomposition front

#### (A) Optical Aberrations based on their degree (radial order of classification of the Zernike polynomials)

**Aberrations of degree 0**

**Aberrations of degree 1**

This is the tilt. They are the consequence of a failure of inclination of one or more elements constituting the optical system.

**Aberrations of degree 2**

This is the defocus, and astigmatism. These aberrations correspond to the Ametropias Sphéro-cylindrical axial (sphere and cylinder). The defocus corresponds to a parabolic deformation of the wavefront with rotational symmetry. Astigmatism also represents a parabolic deformation of the wavefront, but varies with the meridian in question and has axial symmetry. It corresponds to the combination of two saddle-shaped surfaces, the resultant of which is a surface of the same type but whose orientation provides the axis of astigmatism.

(see section astigmatism on the site)

**Aberrations of degree 3**

They correspond to the coma and trefoil-type aberrations ("Clover"). The polynomials expressing them do not show symmetry of rotation or axial symmetry. They reflect a lack of alignment (decentralization) of the elements constituting the optical system. Their rate increases significantly after LASIK or PKR, probably reflecting a relative imperfection in the centering of the treatment. They induce a predominantly asymmetrical phase shift on the "edges" of the wavefront (increasing with the distance in the centre of the pupil).

**Aberrations of degree 4**

These are the aberrations of sphericity. The polynomials expressing them all exhibit axial symmetry, and for some, rotational symmetry. They increase with the pupillary diameter and reflect a phase shift of the wavefront points located on the periphery of the pupil. They increase considerably after conventional LASIK and PKR, but also and in a lesser way after Aberrometry-guided surgery. They reflect the existence of suboptimal resurfacing at the periphery of the optical zone and/or an insufficient diameter of the latter relative to that of pupil.

**Aberrations of degree higher than 4**

Depending on the degree, they exhibit axial symmetry (even degrees) or not (odd degrees). They reflect the existence of unsystematized multiple optical imperfections that exert a particular effect on the edges of the wavefront.. They generally have a low impact on the visual function except when their rates are particularly high (such as during irregular corneal scarring, incisional surgery or Transfixiante keratoplasty).

#### (-B) Application to the interpretation of the wave front

-in case of important spherical ametropia, the wavefront will have a global parabolic shape! This parable can be approximated by a spherical couple in first approximation; It is centered on the punctum remotum of the Ametropia eye.

-In case of Ametropia myopia, the top of the parabola is directed backward (the center is retarded).

-In case of Ametropia Hypermétropique, the top is directed forward (the edges are retarded).

-the existence of an associated astigmatism mislead a slight axial asymmetry, particularly perceptible at the edges of the parable of revolution. In case of mixed astigmatism, the shape of the wavefront resembles that of a "Pringle" type of chips.

-The existence of a high spherical aberration rate induces elongation of the parabola, with depression or localized vaulted of its apex.

-Finally, the presence of coma-type aberrations induces an additional and asymmetric elongation of the parabola.

In the presence of a cylindrical sphéro ametropia, high-degree aberrations generally have a much lower rate than low-degree aberrations (tilt, defocus, astigmatism). The form of the phase-shift that they print is generally better analyzed when the low-degree aberrations of the wavefront representation are extracted.

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