According to one textbook, "The first part of our problem, namely, the establishment of a system of first-order equations satisfying the spacetime symmetry condition, can be solved in a very simple way, with the help of the analogy between mechanics and optics, which was the starting point for the development of wave mechanics and which can still be used—with reservations—as a source of inspiration."[22]

... a single principle, that of Maupertuis, and later in another form as Hamilton's Principle of least action ... Fermat's ... principle ..., which nowadays is usually called the principle of least action. ... Huygens propounded an undulatory theory of light, while Newton, calling on an analogy with the material point dynamics that he created, developed a corpuscular theory, the so-called "emission theory", which enabled him even to explain, albeit with a contrived hypothesis, effects nowadays considered wave effects, (i.e., Newton's rings).

While Hamilton discovered the analogy in 1831, it was not applied practically until Hans Busch used it to explain electron beam focusing in 1925.[7] According to Cornelius Lanczos, the analogy has been important in the development of ideas in quantum physics.[3] Erwin Schrödinger cites the analogy in the very first sentence of his paper introducing his wave mechanics.[8] Later in the body of his paper he says:

Albert Messiah considers a classical limit of the Schrödinger equation. He finds there an optical analogy. The trajectories of his particles are orthogonal to the surfaces of equal phase. He writes "In the language of optics, the latter are the wave fronts, and the trajectories of the particles are the rays. Hence the classical approximation is equivalent to the geometric optics approximation: we find once again, as a consequence of the Schrödinger equation, the basic postulate of the theory of matter waves."[13]

Unfortunately this powerful and momentous conception of Hamilton is deprived, in most modern reproductions, of its beautiful raiment as a superfluous accessory, in favour of a more colourless representation of the analytical correspondence.[9]

The first textbook in English on wave mechanics[20] devotes the second of its two chapters to "Wave mechanics in relation to ordinary mechanics". It opines "... de Broglie and Schrödinger have turned this false analogy into a true one by using the natural Unit or Measure of Action, h, .... ... We must now go into Hamilton's theory in more detail, for when once its true meaning is grasped the step to wave mechanics is but a short one—indeed now, after the event, almost seems to suggest itself."[21]

The most common complication or side effect following LASIK is dry eyes. Complications involving the LASIK flap include free, incomplete, or buttonholed flaps, striae/folds or slipped/displaced flaps. If the flap created during the LASIK procedure is irregular, incomplete, or buttonholed, laser treatment cannot safely be performed in the same session. However, after a healing period, a secondary LASIK or PRK procedure may be performed in some cases. Flap related complications are extremely rare when the flap is prepared using a femtosecond laser.

The wavefronts and rays or the equal-action surfaces and trajectories are dual objects linked by orthogonality.[10] On one hand, a ray can be regarded as the orbit of a particle of light. It successively punctures the wave surfaces. The successive punctures can be regarded as defining the trajectory of the particle. On the other hand, a wave-front can be regarded as a level surface of displacement of some quantity, such as electric field intensity, hydrostatic pressure, particle number density, oscillatory phase, or probability amplitude. Then the physical meaning of the rays is less evident.[12]

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Quantitative and formal analysis based on the analogy use the Hamilton–Jacobi equation; conversely the analogy provides an alternative and more accessible path for introducing the Hamilton–Jacobi equation approach to mechanics. The orthogonality of mechanical trajectories characteristic of geometrical optics to the optical wavefronts characteristic of a full wave equation, resulting from the variational principle, leads to the corresponding differential equations.[10]

MECANIK MO2

Complications occur in LASIK as in any other surgical procedure. Serious adverse complications leading to significant permanent visual loss occur rarely. Less serious side effects such as dry eyes, night time starbursts, and/or reduced contrast sensitivity occur relatively frequently.

The orthogonality of the wavefronts to rays (or equal-action surfaces to trajectories) means we can compute one set from the other set.[10] This explains how Kirchhoff's diffraction formula predicts a wave phenomenon – diffraction – using only geometrical ray tracing.[7]: 745  Rays traced from the source to an aperture give a wavefront that becomes sources for rays reaching the diffraction pattern where they are summed using complex phases from the orthogonal wavefronts.

LASIK is indicated for the correction of low, moderate, and high myopia with and without astigmatism. The specific dioptric limits depends on the specific laser system and the regulatory agency of each country. In the U.S.A. the approved indications can be found on the Food and Drug Administration (FDA) labeling. The correction of high myopia may present a greater risk of post-LASIK ectasia and decreased quality of vision in some patients. The surgeon and patient should decide whether LASIK is indicated based on a full preoperative evaluation and consideration of goals and alternatives, including spectacles, contact lens, and phakic intraocular lens implantation.

The propagation of light can be considered in terms of rays and wavefronts in ordinary physical three-dimensional space. The wavefronts are two-dimensional curved surfaces; the rays are one-dimensional curved lines.[11] Hamilton's analogy amounts to two interpretations of a figure like the one shown here. In the optical interpretation, the green wavefronts are lines of constant phase and the orthogonal red lines are the rays of geometrical optics. In the mechanical interpretation, the green lines denote constant values of action derived by applying Hamilton's principle to mechanical motion and the red lines are the orthogonal object trajectories.[11]

Going beyond ordinary three-dimensional physical space, one can imagine a higher dimensional abstract configuration "space", with a dimension a multiple of 3. In this space, one can imagine again rays as one-dimensional curved lines. Now the wavefronts are hypersurfaces of dimension one less than the dimension of the space.[6] Such a multi-dimensional space can serve as a configuration space for a multi-particle system.

5. Alain Saad, Damien Gatinel. Topographic and Tomographic Properties of Forme Fruste Keratoconus Corneas. Investigative Ophthalmology & Visual Science November 2010, Vol.51, 5546-5555.

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Wavefront-guided LASIK, also called custom LASIK, is a variation of LASIK where the excimer laser ablates a sophisticated pattern based on measurements from a wavefront aberrometer (Figure 4). The goal of WFG LASIK is to achieve a more optically perfect ablation based on all of the optical aberrations measured using a wavefront aberrometer, not just spherical and cylindrical refractive errors. The data from published studies indicates that WFG LASIK is both safe and effective. However, in comparison to conventional LASIK, WFG surgery did not result in improved outcomes.

2. Schallhorn SC, Farjo AA, Huang D, Boxer Wachler BS, Trattler WB, Tanzer DJ, Majmudar PA, Sugar A. Wavefront-Guided LASIK for the Correction of Primary Myopia and Astigmatism. A Report by the American Academy of Ophthalmology. Ophthalmology 2008;115:1249 –1261

3. Stonecipher K, Ignacio TS, and Stonecipher M. Advances in refractive surgery: microkeratome and femtosecond laser flap creation in relation to safety, efficacy, predictability, and biomechanical stability Curr Opin Ophthalmol 2006; 17:368–372.

LASIK is an excellent procedure for most patients with myopia and astigmatism. Proper pre-operative screening is essential. While surgical complications are rare, good postoperative care is important.

Diameter of the field of view (mm) = F / M, where F is the number of field of view (FOV) of the eyepiece, and M is the magnification (mag.) of the objective.

MECANIK MO1

An eyelid speculum is placed in the operative eye, which has been anesthetized with drops, and the fellow eye is covered. The cornea is marked to aid in postoperative flap alignment. A suction ring is placed on the eye to achieve fixation. The microkeratome (or femtosecond laser) is used to create a hinged corneal flap. After the flap has been created, it is reflected away from the cut surface. Excimer laser ablation is performed, centered on the pupil or on the corneal vertex. Eye-tracker and iris registration technology are increasingly used to ensure a well-centered laser treatment. Following the excimer laser, the flap is replaced.

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For the correction of low to moderate myopia of less than -6D and low to moderate astigmatism of less than 2D, results from studies in the literature have shown that LASIK is effective and predictable in terms of obtaining very good to excellent uncorrected visual acuity and that it is safe in terms of minimal loss of visual acuity. In a study evaluating the outcome of LASIK in high myopia, Reinstein et al showed that postoperative spheriqual equivalent was ±0.50 D in 55% and ±1.00 D in 83% of eyes after primary treatment. After re-treatment, 69% of eyes were within ±0.50 D and 95% were within ±1.00 D.

The Hamilton optico-mechanical analogy is closely related to Fermat's principle and thus to the Huygens–Fresnel principle.[10] Fermat's principle states that the rays between wavefronts will take the path least time; the concept of successive wavefronts derives from Huygens principle.

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Hamilton's optico-mechanical analogy played a critical part[14][11] in the thinking of Schrödinger, one of the originators of quantum mechanics. Section 1 of his paper published in December 1926 is titled "The Hamiltonian analogy between mechanics and optics".[15] Section 1 of the first of his four lectures on wave mechanics delivered in 1928 is titled "Derivation of the fundamental idea of wave mechanics from Hamilton's analogy between ordinary mechanics and geometrical optics".[16]

Fuchs corneal endothelial dystrophy, keratoconus, pellucid marginal degeneration, epithelial basement membrane dystrophy (EBMD), peripheral retinal tears (especially in highly myopic eyes), systemic autoimmune disease, pregnancy, lactation, severe dry eyes, and significant blepharitis are contraindications.

Patients may have mild postoperative discomfort for 4 to 6 hours following LASIK treatment, during which time they should keep their eyes closed and rest or take a nap. Patients should not rub their eyes after surgery. Steroid and antibiotic drops are used for 4 to 10 days after surgery. Preservative-free tears may be used for weeks to months depending on dry eye symptoms and corneal punctate staining. Refractive stabilization for myopes take up to 3 months depending on the amount of treatment performed. Residual refractive error can be corrected after stabilization, typically by relifting the flap and ablating the stromal bed in a retreatment procedure (also called an enhancement). To ensure preservation of at least 250 μm of residual bed thickness after laser retreatment, preoperative OCT or intraoperative ultrasound pachymetry could be performed.

4. Dan Z. Reinstein, MD, MA(Cantab), FRCOphth; Glenn I. Carp, MBBCh, FC Ophth(SA); Timothy J. Archer, MA(Oxon), DipCompSci(Cantab); Tariq A. Lewis, MSci, ARCS, OMT; Marine Gobbe, MSTOptom, PhD; Johnny Moore, FRCOphth, PhD, MD; Tara Moore, BSc, PhD Long-term Visual and Refractive Outcomes After LASIK for High Myopia and Astigmatism From −8.00 to −14.25 D Journal of Refractive Surgery. 2016;32(5):290-297

In the opinion of Léon Rosenfeld, a close colleague of Niels Bohr, "... Schrödinger [was] inspired by Hamilton's beautiful comparison of classical mechanics and geometrical optics ..."[19]

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Hamilton's optico-mechanical analogy is a conceptual parallel between trajectories in classical mechanics and wavefronts in optics, introduced by William Rowan Hamilton around 1831.[1] It may be viewed as linking Huygens' principle of optics with Maupertuis' principle of mechanics.[2][3][4][5][6]

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In other words, the polarization vector of the electric field, the polarization vector of the mag- netic field, and the direction k that the plane wave is ...

LASIK flaps are cut with either mechanical microkeratomes or femtosecond lasers. Mechanical microkeratomes are typically labeled for nominal cut depths of between 120 and 180 µm. There is a trend to cut thinner flaps with the newer microkeratome models, which are more precise. Thinner flaps preserve greater stromal bed thickness and reduce the risk of ectasia. Femtosecond lasers tend to create more precise and uniform flap thickness, and settings of 100-120 µm are typically used. A residual posterior stromal thickness of at least 250 μm is recommended to reduce the risk of post-LASIK ectasia. Some surgeons also believe that the stromal bed should be at least half of the original corneal thickness. To help ensure an acceptable final postoperative residual stromal thickness, flap thickness can be measured by intraoperative ultrasound pachymetry. Anterior segment optical coherence tomography (OCT) can be used to measure flap and stromal bed thicknesses (Figure 3). Flap thicknesses can deviate significantly from the nominal setting and routine measurement can help the surgeon evaluate the range of actual thickness obtained.

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All content on Eyewiki is protected by copyright law and the Terms of Service. This content may not be reproduced, copied, or put into any artificial intelligence program, including large language and generative AI models, without permission from the Academy.

LASIK (laser in situ keratomileusis) is a surgical procedure designed to correct refractive errors. LASIK involves creating a corneal flap using a microkeratome (Figure 1) or a femtosecond laser, reshaping the cornea using an excimer laser to remove tissue from the underlying stromal bed and then replacing the flap.

Complications that occur at the level of the interface between the flap and the stromal bed include diffuse lamellar keratitis, infection, and epithelial ingrowth. Post-LASIK ectasia may occur when the biomechanical stability of the cornea is altered. It is uncertain if there is any relationship between LASIK and an increased incidence of postoperative retinal detachment. Ischemic optic neuropathy is a rare complication that has been reported following LASIK.

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Preoperative evaluation should include a complete eye examination, a full medical and ophthalmologic history, and informed consent. Dry and cycloplegic refraction should be performed for all patients. Rigid contact lenses should be removed for several weeks and soft lenses for several days to weeks before examination. Refraction should be stable within 0.5 D for 1 year or more before LASIK surgery. Measurement of corneal topography is essential, and is used to screen for irregular astigmatism, keratoconus and forme fruste keratoconus which are associated with unpredictable refractive outcomes and progressive ectasia after LASIK. Measurement of corneal thickness is also critical in the preoperative assessment for LASIK because of its importance in the calculation of anticipated residual stromal bed thickness. Nowadays, corneal tomography and keratoconus detection softwares such as the BAD display on the Pentacam or the SCORE analyser on the Orbscan help to screen between normal corneas and ectasia susceptible corneas. A thin cornea may also be an indication of subtle keratoconus, and indicates a need for caution in tissue removal. Other tests which should be performed include measuring pupil size and eye movements and corneal aberrometry.

1. Sugar A, Rapuano C.J., Culbertson W. W., Huang D.,Varley G. A., Agapitos P.J, de Luise V.P., Koch D.D. Laser In Situ Keratomileusis for Myopia and Astigmatism: Safety and Efficacy. A Report by the American Academy of Ophthalmology. Ophthalmology 2002;109:175–187.

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Before surgery the excimer laser, suction ring, microkeratome and blade (or femtosecond laser settings), are checked by the technician and the surgeon. The surgeon also confirms that the correct treatment data are entered into the laser computer.

LASIK evolved from a variety of techniques in refractive surgery. Keratomileusis, with both freeze and non-freeze techniques was used in the USA in the 1970s. This procedure was followed by automated lamellar keratoplasty (ALK), in which a microkeratome was used to create either a free cap or a hinged corneal flap. Tissue from the corneal bed was removed to alter the refractive error and the flap was replaced. Keratomileusis and ALK were relatively imprecise mechanical techniques. After its development, the excimer (excited dimer) laser was used to reshape the cornea in a technique called photorefractive keratectomy (PRK). LASIK combines the technique of creating a hinged corneal flap from ALK with excimer laser ablation from PRK (Figure 2). Potential advantages of LASIK over PRK include earlier postoperative stabilization and faster improvement of visual acuity; less postoperative patient discomfort; shorter duration of postoperative medication use; and an easier enhancement procedure.

In a brief paper in 1923, de Broglie wrote : "Dynamics must undergo the same evolution that optics has undergone when undulations took the place of purely geometrical optics."[17] In his 1924 thesis, though Louis de Broglie did not name the optico-mechanical analogy, he wrote in his introduction,[18]

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The femtosecond laser creates a corneal incision by delivering laser pulses at a predetermined depth in the cornea. These pulses cause microphotodisruption, an expanding bubble of gas (CO2) and water that cleave the tissue and create a plane of separation (Figure 5). Compared to conventional mechanical microkeratomes, femtosecond lasers create LASIK flaps with more predictable and uniform thickness, and fewer complications. However, side effects unique to the femtosecond laser, such as transient light sensitivity syndrome, have been reported with first generations of femtosecond lasers. Femtosecond laser aided LASIK has been shown to provide better predictability of refractive outcomes and lower enhancement rates than LASIK performed using a microkeratome.

Figure 3. Optical coherence tomography (OCT) image of a LASIK flap showing measurement of the flap and stromal bed thickness. The upper numbers represent the transverse distance from the corneal vertex in millimetres. The lower numbers represent flap thickness and residual stromal bed thickness in microns, respectively.