Zernike polynomials

Laser light is monochromatic, meaning that the color of the beam has a single specific color. The color of the light is defined by the wavelength of the electromagnetic waves that it is composed of. The beam can be either visible, infrared or ultraviolet. For example, a normal incandescent light appears yellowish, but actually emits a mixture of green, yellow, red, blue and even infrared light. Its wavelength ranges between 400 and 800 nanometers.

Laser power is one of the most important parameters to consider when choosing a laser, as it plays a key role in determining the effectiveness of laser processes. In laser material processing, laser power directly impacts the speed of processes like laser welding, laser cleaning, laser texturing, laser cutting, and laser marking.

Pearl No. 4: Measurements of spherical aberrations of the anterior corneal surface have found the average value to be 0.27 μm with a large standard deviation of 0.10 μm. Due to this variation, the value should be measured for each individual patient.3

Pearl No. 7: Using aspheric IOLs improves driving safety due to improved contrast sensitivity. This is particularly evident on nighttime simulation testing, in which up to a 45-foot advantage in stopping distance at 55 mph (88.51 km/hr) can be achieved.5

Concave mirror

Pearl No. 1: The wavefront characteristics of light can be described in mathematical terms using different systems, including Zernike polynomials and Fourier analysis. Using Zernike polynomials, sphere (defocus) and cylinder (astigmatism) describe the two higher-order aberrations (HOAs) that we measure with phoropters. These aberrations account for approximately 83% of the magnitude of the wavefront of light. Spherical aberration and coma are the next most significant HOAs. Spherical aberration describes the amount of bending that occurs as light passes through a refracting surface, such as the cornea, and compares the relative position of the focal points for the peripheral and central light beams. Positive spherical aberration occurs when the peripheral rays are focused in front of the central rays; this value is expressed in microns.

The beam is also said to be coherent, meaning that all the light rays in the beam are synchronized. They have the same phase and the same polarity. This coherence also helps the beam reach its high powers.

Aberration theory

Pearl No. 12: Negative aspheric IOLs have a slightly higher power centrally. For a 20.00 D lens, this power can be 0.50 D greater and, thus, provides some pseudoaccommodative effect. This is one explanation for increased near vision in patients implanted with aspheric IOLs.

Pearl No. 5: The presence of spherical aberrations can cause glare and halo around lights. The greater the degree of spherical aberration, the greater amount of halo that is induced (Figure 2).

In fiber lasers, the gain medium is an optical fiber doped with a rare-earth element. Ytterbium-doped fiber lasers, for example, emit a wavelength that is ideal for laser processing metals.

Lasers are ideal for industrial automation. Not only do they have the potential to increase productivity and repeatability, but they also possess key characteristics that facilitate automation. Examples include remote capabilities, low maintenance, almost no consumables and waste products, and minimal dust.

Coma aberration

Pearl No. 6: In cataract surgery, targeting emmetropia has a greater effect on Snellen acuity outcome than manipulating spherical aberration. Thus, surgeons should first optimize their formulas for IOL power calculation before adjusting spherical aberration. Aspheric IOLs improve the quality of vision by providing greater contrast sensitivity, not by increasing Snellen acuity. An increase in spherical aberration away from 0.00 causes a decrease in contrast sensitivity.4

On the other hand, a standard industrial red laser (helium-neon, for example) has a wavelength that ranges between 632.800 to 632.802 nanometers. Common incandescent light is polychromatic and a helium-neon laser is monochromatic. Monochromaticity is what makes laser light unique and allows for some of its special applications.

Pearl No. 15: Leaving spherical aberration (positive or negative) in the optical system improves depth of focus, but at the cost of loss of contrast vision. Current strategies involve targeting up to -0.30 to -0.40 µm of spherical aberration in one eye, so as to increase depth of focus without significantly affecting Snellen acuity.

Pearl No. 8: The impact of spherical aberration is dependent on pupil size. For practical purposes, spherical aberration comes into play when pupils are greater than 4 mm; thus, it has the most impact under mesopic or scotopic conditions and in younger patients. Older individuals may have large pupils, so pupils should be measured for each patient if aspheric IOLs are to be used.

Industrial lasers are used to cut metals and fabrics, mark tracking codes for industrial traceability, weld metals with high precision, clean metal surfaces, change the surface roughness, and measure part dimensions. They are widely used in several industries such as the EV and primary metals industries.

So now, we have a cavity filled with a gain medium that, when excited by an energy source, emits light. Two mirrors enable the selection of a specific direction, provoke the accumulation of light and stimulate the emission of even more light. So how does the light come out of the cavity? Well, actually, one of the mirrors isn't perfectly reflective. It let some of the light through and that’s how the laser beam is created. That beam has special characteristics that can be used for laser marking, cleaning, cutting or even welding.

Chromatic aberration

The second problem, the rarity of spontaneous emissions, is solved by provoking stimulated emissions. When light waves pass near excited electrons, these electrons are stimulated and have a higher probability of going to their ground state thereby emitting light at the same wavelength, direction and polarization as the one that passed near it.

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Pearl No. 14: Tilt and decentration affect the performance of aspheric IOLs. Aspheric lenses must be decentered more than 0.8 mm and tilted more than 10° before all effect is lost.8

球 差

In CO2 lasers however, simple electrical discharges can cause the carbon dioxide gas to emit light. This happens because by exciting the molecules (using a discharge) the electrons in the gas reach a higher energy state. However, electrons prefer being in their lower energy state (the ground state). So, some electrons will spontaneously go back to that ground state by emitting light to spend their excess energy. In this case, light is randomly emitted in every direction though spontaneous emissions of light are rare. Both of these factors are problems for creating lasers. These problems can be solved by using the third component, the two mirrors.

You now know the basic principles behind creating lasers. Modern industrial lasers are optimized using more elaborate techniques to increase their power, precision, and robustness, but the principles remain the same. For the curious minds, this article in Photonics Media goes more deeply into how laser technology works.

For a lot of people, lasers are small boxes that shoot red dots, which drive cats crazy. But in fact, laser systems are used in many manufacturing processes.

The mirrors are put on both sides of the laser cavity with critical parallel alignment. The mirrors will bounce the light endlessly creating perfectly perpendicular light rays. The accumulation of light along the axis of the laser cavity eventually creates a high-power laser beam. This solves the first problem of creating a coherent laser beam out of randomly emitted light.

George H.H. Beiko, BM, BCh, FRCSC, is an Assistant Professor of Ophthalmology at McMaster University and a Lecturer at the University of Toronto, Canada. Dr. Beiko states that he is a consultant to Abbott Medical Optics Inc. He may be reached at e-mail: george.beiko@ sympatico.ca.

There are numerous industrial applications that could benefit from the use of a laser, which is found in many industries. But before you can decide if a laser machine would be useful for one of your applications, it might be helpful to have an understanding of the components of a laser and how they work.

Optical aberration

Pearl No. 10: Refractive error can compensate for residual spherical aberration. Positive spherical aberration causes a myopic shift, and negative spherical aberration causes a hyperopic shift in refraction. Although refractive error is independent of pupil size, spherical aberration is dependent on pupil size; for small pupils, it can be negligible, but for larger pupils it is significant in its effect. Thus, refractive error will compensate for spherical aberration at larger pupil sizes but will introduce defocus at smaller pupil sizes (Figure 4). This information can be used to customize results for individual patients based on the choice of aspheric IOL.7

Lasers come at different power levels, colors and beam sizes, but they all rely on the same principles. Here's what an industrial laser is and how it works.

Pearl No. 9: The clearest image is provided when the total spherical aberration value for the eye is 0.00. Most of the effect of targeting this value is seen in nighttime lighting conditions (Figure 3).6

Pearl No. 2: The wavefront of the human eye can be measured using wavefront analyzers such as Shack- Hartmann systems and Tracey aberrometers (iTRACE; Tracey Technologies, Corp.). Corneal topographers can measure the front surface of the cornea (Figure 1), and this data can be transformed to determine the HOAs of the cornea. By convention, corneal spherical aberration is measured at 6 mm.1

Field curvature

Pearl No. 3: In the human eye, HOAs come primarily from the anterior corneal surface and the lens; other sources are the posterior corneal surface and the retina. In an aphakic eye, the anterior corneal surface accounts for 98% of wavefront changes. Small-incision (less than 2.8 mm) cataract surgery causes minimal changes in the spherical aberration of the eye and, for practical terms, can be considered to have no effect.2

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Pearl No. 13: Corneal spherical aberration and Q value are not the same thing. Spherical aberration describes how a wavefront deviates from the ideal after passing through a refracting surface. In actuality, it is a measure of the effect a surface has on light and is measured in microns. The Q value describes the refracting surface and is a measure of the shape of a surface; it has no units. The shape of a surface does affect spherical aberration. An ideal spherical surface has a Q value of 0.00. A prolate surface has a negative Q value; a parabola is a prolate surface that eliminates all spherical aberration and has a Q value of -0.50. The human cornea has an average Q value of -0.26; it would require a value of -0.52 to eliminate all spherical aberration. The Q value of a young adult crystalline lens is -0.25; thus, the combined value for a young phakic eye results in elimination of spherical aberration. As the lens ages, the Q value changes, and after age 40 is 0.00. With a perfect single refracting surface such as an ellipse, keratometry and Q value could be used to calculate the spherical aberration of that surface. For a corneal Q value of -0.26 and average keratometry of 44.00 D, the calculated spherical aberration is 0.18 μm. The average measured spherical aberration of the cornea is 0.27 μm because the cornea has a complex surface that is steeper centrally. Common aspheric IOLs correct the average theoretical corneal spherical aberration, the average measured corneal spherical aberration, or do not influence it.

The laser beam has a single direction. Its direction is fixed and its beam diameter is small and almost constant over large distances. This concentration of light is what allows lasers to have very high power output. High-energy pulsed lasers, with power in the megawatts, are strong enough to cut through metal.

Laser ablation machines are increasingly used in the manufacturing and automotive industries. They are a popular option to meet short cycle times, automate processes, reduce operating costs, and add precision to ensure high-quality results.

The gain medium is the material you put in your laser cavity. It can be a solid (a ruby crystal), a liquid (a dye solution) or a gas (a helium-neon mixture). The important feature is that it emits light in the desired wavelength when excited.

The energy source is what causes the gain medium to emit light in the laser cavity. Very often, the energy source is a set of diode lasers which transform electricity into light.