How to pronounceaberration

The expression for these coefficients in terms of the constants of the optical system, i.e. the radii, thicknesses, refractive indices and distances between the lenses, was solved by L. Seidel;[17] in 1840, J. Petzval constructed his portrait objective, from similar calculations which have never been published.[18] The theory was elaborated by S. Finterswalder,[19] who also published a posthumous paper of Seidel containing a short view of his work;[20] a simpler form was given by A. Kerber.[21] A. Konig and M. von Rohr[22]: 317–323  have represented Kerber's method, and have deduced the Seidel formulae from geometrical considerations based on the Abbe method, and have interpreted the analytical results geometrically.[22]: 212–316 [8]

Alexandra Arriaga: Yeah. Wow. Amazing. California. Can you tell us a little bit about your background and your intellectual trajectory? More specifically, what drew you from one interest area to the next?

The nature of the reproduction consists in the rays proceeding from a point O being united in another point O'; in general, this will not be the case, for ξ', η' vary if ξ, η be constant, but x, y variable. It may be assumed that the planes I' and II' are drawn where the images of the planes I and II are formed by rays near the axis by the ordinary Gaussian rules; and by an extension of these rules, not, however, corresponding to reality, the Gauss image point O'0, with coordinates ξ'0, η'0, of the point O at some distance from the axis could be constructed. Writing Dξ'=ξ'-ξ'0 and Dη'=η'-η'0, then Dξ' and Dη' are the aberrations belonging to ξ, η and x, y, and are functions of these magnitudes which, when expanded in series, contain only odd powers, for the same reasons as given above. On account of the aberrations of all rays which pass through O, a patch of light, depending in size on the lowest powers of ξ, η, x, y which the aberrations contain, will be formed in the plane I'. These degrees, named by J. Petzval[16] the numerical orders of the image, are consequently only odd powers; the condition for the formation of an image of the mth order is that in the series for Dξ' and Dη' the coefficients of the powers of the 3rd, 5th...(m-2)th degrees must vanish. The images of the Gauss theory being of the third order, the next problem is to obtain an image of 5th order, or to make the coefficients of the powers of 3rd degree zero. This necessitates the satisfying of five equations; in other words, there are five alterations of the 3rd order, the vanishing of which produces an image of the 5th order.[8]

Sir Isaac Newton was probably the discoverer of astigmation; the position of the astigmatic image lines was determined by Thomas Young;[10] and the theory was developed by Allvar Gullstrand.[11][12][8] A bibliography by P. Culmann is given in Moritz von Rohr's Die Bilderzeugung in optischen Instrumenten.[13][8]

A ray proceeding from an object point O (fig. 5) can be defined by the coordinates (ξ, η). Of this point O in an object plane I, at right angles to the axis, and two other coordinates (x, y), the point in which the ray intersects the entrance pupil, i.e. the plane II. Similarly the corresponding image ray may be defined by the points (ξ', η'), and (x', y'), in the planes I' and II'. The origins of these four plane coordinate systems may be collinear with the axis of the optical system; and the corresponding axes may be parallel. Each of the four coordinates ξ', η', x', y' are functions of ξ, η, x, y; and if it be assumed that the field of view and the aperture be infinitely small, then ξ, η, x, y are of the same order of infinitesimals; consequently by expanding ξ', η', x', y' in ascending powers of ξ, η, x, y, series are obtained in which it is only necessary to consider the lowest powers. It is readily seen that if the optical system be symmetrical, the origins of the coordinate systems collinear with the optical axis and the corresponding axes parallel, then by changing the signs of ξ, η, x, y, the values ξ', η', x', y' must likewise change their sign, but retain their arithmetical values; this means that the series are restricted to odd powers of the unmarked variables.[8]

If the above errors be eliminated, the two astigmatic surfaces united, and a sharp image obtained with a wide aperture—there remains the necessity to correct the curvature of the image surface, especially when the image is to be received upon a plane surface, e.g. in photography. In most cases the surface is concave towards the system.[8]

The circle polynomials were introduced by Frits Zernike to evaluate the point image of an aberrated optical system taking into account the effects of diffraction. The perfect point image in the presence of diffraction had already been described by Airy, as early as 1835. It took almost hundred years to arrive at a comprehensive theory and modeling of the point image of aberrated systems (Zernike and Nijboer). The analysis by Nijboer and Zernike describes the intensity distribution close to the optimum focal plane. An extended theory that allows the calculation of the point image amplitude and intensity over a much larger volume in the focal region was recently developed (Extended Nijboer-Zernike theory). This Extended Nijboer-Zernike theory of point image or 'point-spread function' formation has found applications in general research on image formation, especially for systems with a high numerical aperture, and in characterizing optical systems with respect to their aberrations.[15]

Sphericalaberration

Dr. Burhenne: Oh, that's a great question. I like it when that's asked because there is just so much new stuff coming out, exciting stuff. If you're going into the health sciences, I would definitely recommend dentistry. Medicine of course as well, but I would always look towards the functional approach, kind of this integrative idea of preventing diseases and diving deep into everything about the patient. In other words, why are we here? Why do you have bleeding gums? Don't just look at the conventional models of Western medicine of just treating the symptoms and signs. So in dentistry, there's a revolution coming and I think the most exciting thing... In the short answer for dentistry, I would say go into orthodontics and become an orthodontist that is concerned about facial development and you can even reverse now through computer modeling and CAT scans and 3-D cone beam type of x-rays. You can now control and verify the reversal of improper facial development, which is essentially why I think why sleep apnea is on the rise and poor breathing issues and depression. For example, a lot of young women now because of the spatial development issue, are being prescribed psychotropics, the depression medication and it's really probably a function at least in half of the cases of not being able to breathe properly. That's a condition called UARS, upper airway resistance syndrome. Push back a little bit, look at the bigger picture. This can happen in any healthcare area. I would also advise not to necessarily just think that medicine is the big one. In other words, you can do this now. You can do functional healthcare as an acupuncturist, as a chiropractor. These are things and thoughts and methods that you can use and even pharmacologists now are doing some treating and especially in the area of diabetes. But always look towards the functional approach. I don't know if that answers your question, but-

Dr. Burhenne: ... it's an exciting area. We have these silent epidemics like sleep and inflammatory diseases, metabolic syndrome, increase in BMI, obesity in children, all these things that... We've got chemicals in the environment, we've got the glyphosate, fluoride, that's another big issue, controversial issue. But there's a lot of space there for... It's almost like global warming. We've ruined our environment, but in doing so, we've also ruined our biomes. Our microbiomes are our ability to fight off all the things that we did so well as ancestors. We're seeing a lot of an increase in death rates and we're dying earlier. We're not doing so well in our older years. So why is this? Well, there's a lot of room for improvement and again, it's going to be more of a functional approach.

Alexandra Arriaga: Hello everyone and welcome to another episode of "I AM GPH." My name is Alexandra Arriaga and today, we are going to talk to Dr. Mark Burhenne. Dr. Mark is Quip's dental advisor and you may be familiar with the name, "Quip." They have ads all over the city of really sleek toothbrushes that aim to improve people's oral health. Dr. Mark attended the University of the Pacific Dugoni School of Dentistry in San Francisco. In his bio, he writes, "In my 30 years of practice as a dentist, I've seen a lot of misinformation and people who have fallen through the cracks due to our healthcare system's failure to understand the oral-body connection," which is where his focus on whole body care really started. He's passionate about getting people the right information they need to be healthy. He founded askthedentist.com in 2010 as an avenue to advance that passion. Ask the Dentist promotes oral health for total wellness and empowers people to understand how the mouth is a window into the health of the rest of the body. If you would like to learn more about how to have a healthier mouth and therefore, a healthier you, please stay tuned. Hello, Dr. Mark. How are you doing today?

If a constant of reproduction, for instance the focal length, be made equal for two colors, then it is not the same for other colors, if two different glasses are employed. For example, the condition for achromatism (4) for two thin lenses in contact is fulfilled in only one part of the spectrum, since d n 2 / d n 1 {\displaystyle dn_{2}/dn_{1}} varies within the spectrum. This fact was first ascertained by J. Fraunhofer, who defined the colors by means of the dark lines in the solar spectrum; and showed that the ratio of the dispersion of two glasses varied about 20% from the red to the violet (the variation for glass and water is about 50%). If, therefore, for two colors, a and b, f a = f b = f {\displaystyle f_{a}=f_{b}=f} , then for a third color, c, the focal length is different; that is, if c lies between a and b, then f c < f {\displaystyle f_{c}

Dr. Burhenne: Both. Exactly. There's that connection now between a bug in the mouth and Alzheimer's. There's been for the last two, three decades connection between heart disease and bugs in the mouth. The one I mentioned earlier about colon cancer and there's more to be found. We're just beginning to discover what the actual mechanisms are. A lot of researchers are looking at histological slides and they're looking, "Oh my God, there's an oral bug in there. How did it get there?" Well, it's that leaky mouth, it's that oral microbiome, it's that dysbiosis that allowed that to happen. What better practitioner than a dentist to start identifying when that occurs and preventing it from occurring?

What is aberrationchromaticaberration

Alexandra Arriaga: Yeah. No, that's fascinating and so many different areas that you've tapped into. That's quite impressive. I want to ask you about Quip and I know that a lot of people are probably listening right now and they're thinking, "Wait, that sounds kind of familiar. I feel like I've seen advertisements for that around the city." What is Quip and how did you first hear about them?

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Dr. Burhenne: Well, it depends. I think it depends on the quality of the nylon bristle. I think there's some toothbrushes out there that you want to throw away after a few weeks of use. A high quality toothbrush, I would say two to three months is ideal, but it depends on how often you brush and do you soak your toothbrush in white vinegar? That can damage the bristle perhaps. How do people clean their toothbrushes? Do they brush after drinking lemon juice? That's acidic. That has an effect on the nylon bristles. So there are a lot of factors. But to be safe, I would say every two to three months.

Even if the image is sharp, it may be distorted compared to ideal pinhole projection. In pinhole projection, the magnification of an object is inversely proportional to its distance to the camera along the optical axis so that a camera pointing directly at a flat surface reproduces that flat surface. Distortion can be thought of as stretching the image non-uniformly, or, equivalently, as a variation in magnification across the field. While "distortion" can include arbitrary deformation of an image, the most pronounced modes of distortion produced by conventional imaging optics is "barrel distortion", in which the center of the image is magnified more than the perimeter (figure 3a). The reverse, in which the perimeter is magnified more than the center, is known as "pincushion distortion" (figure 3b). This effect is called lens distortion or image distortion, and there are algorithms to correct it.

Aberrationexamples

For two thin lenses separated by a distance D {\displaystyle D} the condition for achromatism is D = v 1 f 1 + v 2 f 2 {\displaystyle D=v_{1}f_{1}+v_{2}f_{2}} ; if v 1 = v 2 {\displaystyle v_{1}=v_{2}} (e.g. if the lenses be made of the same glass), this reduces to D = ( f 1 + f 2 ) / 2 {\displaystyle D=(f_{1}+f_{2})/2} , known as the condition for oculars.[8]

The constancy of a'/a necessary for this relation to hold was pointed out by R. H. Bow (Brit. Journ. Photog., 1861), and Thomas Sutton (Photographic Notes, 1862); it has been treated by O. Lummer and by M. von Rohr (Zeit. f. Instrumentenk., 1897, 17, and 1898, 18, p. 4). It requires the middle of the aperture stop to be reproduced in the centers of the entrance and exit pupils without spherical aberration. M. von Rohr showed that for systems fulfilling neither the Airy nor the Bow-Sutton condition, the ratio a' cos w'/a tan w will be constant for one distance of the object. This combined condition is exactly fulfilled by holosymmetrical objectives reproducing with the scale 1, and by hemisymmetrical, if the scale of reproduction be equal to the ratio of the sizes of the two components.[8]

Circular wavefront profiles associated with aberrations may be mathematically modeled using Zernike polynomials. Developed by Frits Zernike in the 1930s, Zernike's polynomials are orthogonal over a circle of unit radius. A complex, aberrated wavefront profile may be curve-fitted with Zernike polynomials to yield a set of fitting coefficients that individually represent different types of aberrations. These Zernike coefficients are linearly independent, thus individual aberration contributions to an overall wavefront may be isolated and quantified separately.

Dr. Burhenne: Well, I'm in the Napa Valley in St. Helena, but I've been practicing in the Silicon Valley for over 30 years, but the Bay Area essentially.

Aberrationin a sentence

Newton failed to perceive the existence of media of different dispersive powers required by achromatism; consequently he constructed large reflectors instead of refractors. James Gregory and Leonhard Euler arrived at the correct view from a false conception of the achromatism of the eye; this was determined by Chester More Hall in 1728, Klingenstierna in 1754 and by Dollond in 1757, who constructed the celebrated achromatic telescopes. (See telescope.)[8]

Alexandra Arriaga: If you could invite public health practitioners to join you in this quest for increasing the awareness for the oral microbiome and using oral health as a means to improve overall population health, what would you tell them?

Chromatic aberration occurs when different wavelengths are not focussed to the same point. Types of chromatic aberration are:

Practical methods solve this problem with an accuracy which mostly suffices for the special purpose of each species of instrument. The problem of finding a system which reproduces a given object upon a given plane with given magnification (insofar as aberrations must be taken into account) could be dealt with by means of the approximation theory; in most cases, however, the analytical difficulties were too great for older calculation methods but may be ameliorated by application of modern computer systems. Solutions, however, have been obtained in special cases.[24] At the present time constructors almost always employ the inverse method: they compose a system from certain, often quite personal experiences, and test, by the trigonometrical calculation of the paths of several rays, whether the system gives the desired reproduction (examples are given in A. Gleichen, Lehrbuch der geometrischen Optik, Leipzig and Berlin, 1902). The radii, thicknesses and distances are continually altered until the errors of the image become sufficiently small. By this method only certain errors of reproduction are investigated, especially individual members, or all, of those named above. The analytical approximation theory is often employed provisionally, since its accuracy does not generally suffice.[8]

In order to render spherical aberration and the deviation from the sine condition small throughout the whole aperture, there is given to a ray with a finite angle of aperture u* (width infinitely distant objects: with a finite height of incidence h*) the same distance of intersection, and the same sine ratio as to one neighboring the axis (u* or h* may not be much smaller than the largest aperture U or H to be used in the system). The rays with an angle of aperture smaller than u* would not have the same distance of intersection and the same sine ratio; these deviations are called zones, and the constructor endeavors to reduce these to a minimum. The same holds for the errors depending upon the angle of the field of view, w: astigmatism, curvature of field and distortion are eliminated for a definite value, w*, zones of astigmatism, curvature of field and distortion, attend smaller values of w. The practical optician names such systems: corrected for the angle of aperture u* (the height of incidence h*) or the angle of field of view w*. Spherical aberration and changes of the sine ratios are often represented graphically as functions of the aperture, in the same way as the deviations of two astigmatic image surfaces of the image plane of the axis point are represented as functions of the angles of the field of view.[8]

Although defocus is technically the lowest-order of the optical aberrations, it is usually not considered as a lens aberration, since it can be corrected by moving the lens (or the image plane) to bring the image plane to the optical focus of the lens.

In practice it is more advantageous (after Abbe) to determine the chromatic aberration (for instance, that of the distance of intersection) for a fixed position of the object, and express it by a sum in which each component conlins the amount due to each refracting surface.[26][27][8] In a plane containing the image point of one color, another colour produces a disk of confusion; this is similar to the confusion caused by two zones in spherical aberration. For infinitely distant objects the radius Of the chromatic disk of confusion is proportional to the linear aperture, and independent of the focal length (vide supra, Monochromatic Aberration of the Axis Point); and since this disk becomes the less harmful with an increasing image of a given object, or with increasing focal length, it follows that the deterioration of the image is proportional to the ratio of the aperture to the focal length, i.e. the relative aperture. (This explains the gigantic focal lengths in vogue before the discovery of achromatism.)[8]

In fig. 6, taken from M. von Rohr's Theorie und Geschichte des photographischen Objectivs, the abscissae are focal lengths, and the ordinates wavelengths. The Fraunhofer lines used are shown in adjacent table.[8]

The classical imaging problem is to reproduce perfectly a finite plane (the object) onto another plane (the image) through a finite aperture. It is impossible to do so perfectly for more than one such pair of planes (this was proven with increasing generality by Maxwell in 1858, by Bruns in 1895, and by Carathéodory in 1926, see summary in Walther, A., J. Opt. Soc. Am. A 6, 415–422 (1989)). For a single pair of planes (e.g. for a single focus setting of an objective), however, the problem can in principle be solved perfectly. Examples of such a theoretically perfect system include the Luneburg lens and the Maxwell fish-eye.

Alexandra Arriaga: Okay. Well, Dr. Mark, thank you so much for joining us. It's been a pleasure talking to you and we will hopefully stay in touch.

Glass with weaker dispersive power (greater v {\displaystyle v} ) is named crown glass; that with greater dispersive power, flint glass. For the construction of an achromatic collective lens ( f {\displaystyle f} positive) it follows, by means of equation (4), that a collective lens I. of crown glass and a dispersive lens II. of flint glass must be chosen; the latter, although the weaker, corrects the other chromatically by its greater dispersive power. For an achromatic dispersive lens the converse must be adopted. This is, at the present day, the ordinary type, e.g., of telescope objective; the values of the four radii must satisfy the equations (2) and (4). Two other conditions may also be postulated: one is always the elimination of the aberration on the axis; the second either the Herschel or Fraunhofer Condition, the latter being the best vide supra, Monochromatic Aberration). In practice, however, it is often more useful to avoid the second condition by making the lenses have contact, i.e. equal radii. According to P. Rudolph (Eder's Jahrb. f. Photog., 1891, 5, p. 225; 1893, 7, p. 221), cemented objectives of thin lenses permit the elimination of spherical aberration on the axis, if, as above, the collective lens has a smaller refractive index; on the other hand, they permit the elimination of astigmatism and curvature of the field, if the collective lens has a greater refractive index (this follows from the Petzval equation; see L. Seidel, Astr. Nachr., 1856, p. 289). Should the cemented system be positive, then the more powerful lens must be positive; and, according to (4), to the greater power belongs the weaker dispersive power (greater v {\displaystyle v} ), that is to say, crown glass; consequently the crown glass must have the greater refractive index for astigmatic and plane images. In all earlier kinds of glass, however, the dispersive power increased with the refractive index; that is, v {\displaystyle v} decreased as n {\displaystyle n} increased; but some of the Jena glasses by E. Abbe and O. Schott were crown glasses of high refractive index, and achromatic systems from such crown glasses, with flint glasses of lower refractive index, are called the new achromats, and were employed by P. Rudolph in the first anastigmats (photographic objectives).[8]

Aberrationmeaning in Hindi

Should there be in two lenses in contact the same focal lengths for three colours a, b, and c, i.e. f a = f b = f c = f {\displaystyle f_{a}=f_{b}=f_{c}=f} , then the relative partial dispersion ( n c − n b ) ( n a − n b ) {\displaystyle (n_{c}-n_{b})(n_{a}-n_{b})} must be equal for the two kinds of glass employed. This follows by considering equation (4) for the two pairs of colors ac and bc. Until recently no glasses were known with a proportional degree of absorption; but R. Blair (Trans. Edin. Soc., 1791, 3, p. 3), P. Barlow, and F. S. Archer overcame the difficulty by constructing fluid lenses between glass walls. Fraunhofer prepared glasses which reduced the secondary spectrum; but permanent success was only assured on the introduction of the Jena glasses by E. Abbe and O. Schott. In using glasses not having proportional dispersion, the deviation of a third colour can be eliminated by two lenses, if an interval be allowed between them; or by three lenses in contact, which may not all consist of the old glasses. In uniting three colors an achromatism of a higher order is derived; there is yet a residual tertiary spectrum, but it can always be neglected.[8]

Alexandra Arriaga: So it seems to me that obviously understanding the oral microbiome is going to be very important when we think about how to stay healthy and how to keep healthy teeth. Now I'm wondering what type of ingredients should we look for in our toothpaste, for example?

In optics, aberration is a property of optical systems, such as lenses, that causes light to be spread out over some region of space rather than focused to a point.[1] Aberrations cause the image formed by a lens to be blurred or distorted, with the nature of the distortion depending on the type of aberration. Aberration can be defined as a departure of the performance of an optical system from the predictions of paraxial optics.[2] In an imaging system, it occurs when light from one point of an object does not converge into (or does not diverge from) a single point after transmission through the system. Aberrations occur because the simple paraxial theory is not a completely accurate model of the effect of an optical system on light, rather than due to flaws in the optical elements.[3]

where m and n are nonnegative integers with n ≥ m {\displaystyle n\geq m} , Φ is the azimuthal angle in radians, and ρ is the normalized radial distance. The radial polynomials R n m {\displaystyle R_{n}^{m}} have no azimuthal dependence, and are defined as

Dr. Burhenne: That's a good question. You can over brush. I've mentioned that before, but it's also when to brush is also important. Let me start with how many times. Twice a day is fine, but brushing after a very acidic meal or beverage can be very dangerous. For example, when you drink like a diet soda, a sports drink, what are they called? The Red Bulls and all that; those are also very acidic. Wine, coffee, teas; if you brush right after that or even a lemonade, you could literally be scrubbing off some enamel and some denton Because the pH is so low that the phosphates and the calcium structure of the tooth lifts a little bit. It pulls a little bit and it dissolves a little bit and they can recalcify if you can up the pH again and that would mean drinking some Pellegrino water. In fact, the Europeans do this all the time. When they drink wine or something very acidic, like a coffee, they're always sipping on a mineral water and then they don't rush afterwards to brush their teeth. Americans are always concerned about staining their teeth. So they had their coffee quickly and then they brush their teeth and they're literally brushing tooth structure away. So I would say twice a day is fine, two minutes done properly with the right technique with a soft nylon bristle, something that's not worn, the right technique and then not after acidic foods or drinks.

The condition for the reproduction of a surface element in the place of a sharply reproduced point — the constant of the sine relationship must also be fulfilled with large apertures for several colors. E. Abbe succeeded in computing microscope objectives free from error of the axis point and satisfying the sine condition for several colors, which therefore, according to his definition, were aplanatic for several colors; such systems he termed apochromatic. While, however, the magnification of the individual zones is the same, it is not the same for red as for blue; and there is a chromatic difference of magnification. This is produced in the same amount, but in the opposite sense, by the oculars, which Abbe used with these objectives (compensating oculars), so that it is eliminated in the image of the whole microscope. The best telescope objectives, and photographic objectives intended for three-color work, are also apochromatic, even if they do not possess quite the same quality of correction as microscope objectives do. The chromatic differences of other errors of reproduction seldom have practical importance.[8]

Alexandra Arriaga: What do you think is the best combination of habits that one can have to have the healthiest mouth possible?

What is aberrationin optics

In optical systems composed of lenses, the position, magnitude and errors of the image depend upon the refractive indices of the glass employed (see Lens (optics) and Monochromatic aberration, above). Since the index of refraction varies with the color or wavelength of the light (see dispersion), it follows that a system of lenses (uncorrected) projects images of different colors in somewhat different places and sizes and with different aberrations; i.e. there are chromatic differences of the distances of intersection, of magnifications, and of monochromatic aberrations. If mixed light be employed (e.g. white light) all these images are formed and they cause a confusion, named chromatic aberration; for instance, instead of a white margin on a dark background, there is perceived a colored margin, or narrow spectrum. The absence of this error is termed achromatism, and an optical system so corrected is termed achromatic. A system is said to be chromatically under-corrected when it shows the same kind of chromatic error as a thin positive lens, otherwise it is said to be overcorrected.[8]

In addition to these aberrations, piston and tilt are effects which shift the position of the focal point. Piston and tilt are not true optical aberrations, since when an otherwise perfect wavefront is altered by piston and tilt, it will still form a perfect, aberration-free image, only shifted to a different position.

With an ideal lens, light from any given point on an object would pass through the lens and come together at a single point in the image plane (or, more generally, the image surface). Real lenses do not focus light exactly to a single point, however, even when they are perfectly made. These deviations from the idealized lens performance are called aberrations of the lens.

Alexandra Arriaga: Okay. What would you say are some of the biggest myths about oral health that people still subscribe to?

What is aberrationin physics

Dr. Burhenne: Right. Anything that is used to manufacture toothpaste in large quantities, like surfactants, emulsifiers, when you make, when you mix a big vat of something, you want to make sure it mixes properly. So you add all these chemicals or substances that help it to mix and stay mix so it doesn't separate. Those things actually will have an effect on your mucosa, your oral mucosa, which by the way is one of the subsets of the oral microbiome. There's a biome on the side of your cheek, there's a biome on your tongue, there's a biome in your saliva. You're disrupting those microbiomes because you have a surfactant, you've got a chemical that's not there for you, for your health; it's there to make a bigger batch of toothpaste and that can disrupt and dry out the mouth, for example. Also alcohol; toothpaste manufacturers have been using that for a long time. We even have some pesticides in our toothpaste and very low levels like triclosan, bacterial sidles, we've got detergents, we've got soaps in all these oral products and these are things that are not good. I take blame for this because dentistry was behind all of this for a long, long time. I think that thinking is changing. We need to instead of disinfecting and knocking down a healthy oral environment, we need to be nourishing it. We need to be feeding it so that it can continue and maintain itself and do what it's supposed to do and that is to protect from immune attacks in the mouth. The mouth is very susceptible to infection. It's the only area of the body that has a hard tissue like bone, which is like a tooth similar to a tooth, teeth sticking out of this barrier. The body's always trying to protect itself by the skin, the gut, mucosa. These are all designed to let some things through, but if they get leaky they can cause infections, bacteremias and the mouth is doing that every day and it needs biofilm; that's the plaque layer that we've been told to brush and remove and polish away. We need a proper biofilm. We need a good mucosa. We need good nasal tissue mucosa in the nose to produce bugs that help produce substances and chemicals that help prevent infections in the mouth. Imagine having teeth in your gut. The gut’s leaky enough as it is right? And the teeth in the mouth, they stick out of this barrier. How do you keep those areas clean? How do you prevent bacteria from outside of the body, which is in the mouth from getting to the inside of the body and causing superinfection or just infections, and bacteremias, and damage via endotoxins, and allowing some bacteria that can cause for example, that can further your chance of getting colon cancer or Alzheimer's? There's a pathway now that was just discovered through cytotoxin release in a gingipain, a substance called gingipain that crosses the blood-brain barrier that essentially makes the brain lay down the amyloid protein, the plaque protein to protect itself. Well, that comes from the mouth. That comes from gum disease and that happens right around the area, we call it the violation of the biological width, it's where the tooth is sticking out through the bone, through the tissue, there's that little pocket, that little sulcus or moat, whatever you want to call it, and that's where all the activity happens. If the microbiome isn't doing its job, you'll get an infection in the folds of these gum pockets and then you get gum disease. Gum disease of course, can raise your overall inflammatory levels, can raise your CRP levels, it can cause all sorts of problems. It can complicate diabetes. It's a tough area of the mouth. It's to control and that's why we need to respect this oral microbiome.

The Gaussian theory is only an approximation; monochromatic or spherical aberrations still occur, which will be different for different colors; and should they be compensated for one color, the image of another color would prove disturbing. The most important is the chromatic difference of aberration of the axis point, which is still present to disturb the image, after par-axial rays of different colors are united by an appropriate combination of glasses. If a collective system be corrected for the axis point for a definite wavelength, then, on account of the greater dispersion in the negative components — the flint glasses, — overcorrection will arise for the shorter wavelengths (this being the error of the negative components), and under-correction for the longer wavelengths (the error of crown glass lenses preponderating in the red). This error was treated by Jean le Rond d'Alembert, and, in special detail, by C. F. Gauss. It increases rapidly with the aperture, and is more important with medium apertures than the secondary spectrum of par-axial rays; consequently, spherical aberration must be eliminated for two colors, and if this be impossible, then it must be eliminated for those particular wavelengths which are most effectual for the instrument in question (a graphical representation of this error is given in M. von Rohr, Theorie und Geschichte des photographischen Objectivs).[8]

Alexandra Arriaga: It seems like beyond just the aspect of, "Oh, keeping a healthy mouth and not developing cavities," there seems like there's more and more science backing up the fact that our mouths can actually either prevent a lot of disease or produce it if we're not careful. Right?

where ρ {\displaystyle \rho } is the normalized pupil radius with 0 ≤ ρ ≤ 1 {\displaystyle 0\leq \rho \leq 1} , ϕ {\displaystyle \phi } is the azimuthal angle around the pupil with 0 ≤ ϕ ≤ 2 π {\displaystyle 0\leq \phi \leq 2\pi } , and the fitting coefficients a 0 , … , a 8 {\displaystyle a_{0},\ldots ,a_{8}} are the wavefront errors in wavelengths.

The final form of a practical system consequently rests on compromise; enlargement of the aperture results in a diminution of the available field of view, and vice versa. But the larger aperture will give the larger resolution. The following may be regarded as typical:[8]

Alexandra Arriaga: A lot of students and alumni who are getting their MPH here at NYU are looking for the way to make an impact on the world and improve health and wellness for people. For those that are interested in pursuing a career in this area, what do those jobs look like? Or how or where can someone get started?

By opening the stop wider, similar deviations arise for lateral points as have been already discussed for axial points; but in this case they are much more complicated. The course of the rays in the meridional section is no longer symmetrical to the principal ray of the pencil; and on an intercepting plane there appears, instead of a luminous point, a patch of light, not symmetrical about a point, and often exhibiting a resemblance to a comet having its tail directed towards or away from the axis. From this appearance it takes its name. The unsymmetrical form of the meridional pencil—formerly the only one considered—is coma in the narrower sense only; other errors of coma have been treated by Arthur König and Moritz von Rohr,[13] and later by Allvar Gullstrand.[12][8]

If, in the first place, monochromatic aberrations be neglected — in other words, the Gaussian theory be accepted — then every reproduction is determined by the positions of the focal planes, and the magnitude of the focal lengths, or if the focal lengths, as ordinarily happens, be equal, by three constants of reproduction. These constants are determined by the data of the system (radii, thicknesses, distances, indices, etc., of the lenses); therefore their dependence on the refractive index, and consequently on the color,[8] are calculable.[25] The refractive indices for different wavelengths must be known for each kind of glass made use of. In this manner the conditions are maintained that any one constant of reproduction is equal for two different colors, i.e. this constant is achromatized. For example, it is possible, with one thick lens in air, to achromatize the position of a focal plane of the magnitude of the focal length. If all three constants of reproduction be achromatized, then the Gaussian image for all distances of objects is the same for the two colors, and the system is said to be in stable achromatism.[8]

Dr. Burhenne: Boy, I think the big one is flossing and brushing; that it is everything in dentistry in terms of preventing decay. I don't rank flossing and brushing as the number one prevention for example, gum disease, decay, cavities. The way I rank it, it's dry mouth, then diet, then biofilm management, which is brushing and flossing and then genetics and perhaps epigenetics. I think that's a myth. I think you can eat... People think they can eat whatever they want as long as they're brushing and flossing. That is definitely a very widely held myth. So really, that probably is the biggest myth that people have. They can eat whatever they want as long as they brush and floss, and there's so many other factors at play. They don't realize that for example, if they had a dry mouth because they can't breathe through their nose, they have a cold, that this creates a dysbiosis of the oral microbiome. It's not just that one bug causes a cavity and if you have that bug in the mouth, it causes a cavity. Then some dentists will tell you that you feed that bug, you feed that bug a lot of sugar, then more acids are created and that causes a cavity. It's way more complicated than that. A dry mouth will lower the pH in the mouth. That causes a dysbiosis of this biome. So it's not just brushing and flossing. My point is, is that you have to know a lot more than brushing and flossing and you can over brush. I don't think you can over floss, but you can over brush. That's possible.

Dr. Burhenne: Well, there's a study out of a Columbia College, I think it was late 1998, maybe the year 2000 and it essentially looked at what a reduction of inflammatory oral health diseases, a 30% or 40% reduction would mean in terms of total healthcare dollars spent in the US. It was a $247 billion reduction. Oral health and systemic health are intimately connected. You cannot treat the mouth or look at the mouth in a vacuum and that's what we've been doing. Medicine's been doing its thing. It looks at the mouth as a black box. That's what they're referred to as. Dentists have been just looking at the mouth, we haven't been looking at the systemic implications and the big picture of how oral health affects systemic health. So there has to be a lot of collaboration. I've actually created a letter, a two page form called the CRP physician letter and that allows a physician who is looking at the patient's CRP, for example, a cardiologist who's trying to lower the patient's CRP, that's a measure of the overall inflammation in that person's systems and body. That's a letter that should be sent to the dentist. The dentist should fill it out because gum disease or even gingivitis contributes to the CRP. Why would a physician... Or it could work both ways. Why treat a patient for CRP if you're not addressing all the issues that contribute to CRP. So this kind of collaboration, this letter is used by the IFM; that's the functional group of medical doctors. It's being used in other big medical systems here on the West Coast. I think the Cleveland Clinic is using it now. This is a letter that can be very helpful and it can help physicians or any other healthcare practitioner to realize that you need to address what goes on in the mouth when you're addressing the whole body. Of course, it works both ways; dentists need to look at the bigger picture, of course. If we don't take care of the mouth, that's going to lead to a patient who's going to contract Alzheimer's 10, 15 years earlier than they would have if they hadn't dealt with that gum disease.

Alexandra Arriaga: Absolutely. So knowing all this information, how delicate the balance of this microbiome can be; what would you say is the best standard of care for our mouths? Should we still brush our teeth three times a day?

Dr. Burhenne: Quip, it's an interesting name. To be honest with you, even though I was affiliated with the company in its earlier stages, I'm still not quite sure how they came up with that name. But of course, how do you come up with the name, "Twitter," and things like that. So it's a wonderful company. It's a startup based in New York. I think Simon, the CEO reached out to me and he had read my website and he realized that we both had the same idea and we were aligned in terms of how we thought about biofilm management, which is a fancy word for flossing and brushing. So he was fascinated by what I was saying. It was not necessarily what the profession of dentistry was saying to the letter. So we hit it off and we visited each other and then he hired me and we helped get the company off the ground. He reached out to me and I was flattered and excited to be part of it because he really had a unique way of reinventing the toothbrush, which I think he essentially did. Toothbrushes have been out for decades. Right? He came along and really... He's an industrial designer. Again, I've always been fascinated by industrial design, and how things look and feel, and how they function, and how they interact with humans in our lives. He basically took the notion that industrial design combined with behavioral reinforcement of good habits basically leads to better therapeutic results. The toothbrush hasn't changed in a long time. It needed a refresh and that's essentially what he did. So I was very, very happy with the design. He's done that now recently with the flosser, the flossing device. I would definitely check it out. It's a novel way of being able to keep floss nearby and clean and handy. So that's kind of how we got connected. It was through the website and he was on his journey of...He's English. One of the myths of dentistry is that the English have bad teeth. I didn't rib them about that, but he asked me, he said, "Listen, the Americans are obsessed with teeth, so this is where I'm going to start my toothbrush company. Why start it in England?" That's how we kind of got together. We both kind of had the same idea of what a toothbrush needed to be and if you've looked, I'm sure you've shopped for a toothbrush lately, it is overwhelming. Oh my goodness, the selection.

Dr. Burhenne: Boy, best advice in a few sentences. I would say just to make it simple, mouth tape. I'll give you a short explanation of that. I'm big on dry mouth. Dry mouth is an issue. Dry mouth leads to so many different things. Then if you can tape your mouth shut at night and keep your mouth closed while you sleep, you're going to do so much. I would Google it. Google mouth taping and you'll see a host information on there. A lot of it from our website, but a lot of it from other sources as well, like production of nitric oxide; being happier; breathing better; sleeping better; feeling better in the morning; fewer cavities; less bad breath. I can go on and on and on, but that would just be probably one of the biggest things we talk about at askthedentist.com is mouth taping. Keep your mouth shut at night and you'll feel great the next morning in so many ways.

Instead of making d f {\displaystyle df} vanish, a certain value can be assigned to it which will produce, by the addition of the two lenses, any desired chromatic deviation, e.g. sufficient to eliminate one present in other parts of the system. If the lenses I. and II. be cemented and have the same refractive index for one color, then its effect for that one color is that of a lens of one piece; by such decomposition of a lens it can be made chromatic or achromatic at will, without altering its spherical effect. If its chromatic effect ( d f / f {\displaystyle df/f} ) be greater than that of the same lens, this being made of the more dispersive of the two glasses employed, it is termed hyper-chromatic.[8]

The preceding review of the several errors of reproduction belongs to the Abbe theory of aberrations, in which definite aberrations are discussed separately; it is well suited to practical needs, for in the construction of an optical instrument certain errors are sought to be eliminated, the selection of which is justified by experience. In the mathematical sense, however, this selection is arbitrary; the reproduction of a finite object with a finite aperture entails, in all probability, an infinite number of aberrations. This number is only finite if the object and aperture are assumed to be infinitely small of a certain order; and with each order of infinite smallness, i.e. with each degree of approximation to reality (to finite objects and apertures), a certain number of aberrations is associated. This connection is only supplied by theories which treat aberrations generally and analytically by means of indefinite series.[8]

Let S (fig. 1) be any optical system, rays proceeding from an axis point O under an angle u1 will unite in the axis point O'1; and those under an angle u2 in the axis point O'2. If there is refraction at a collective spherical surface, or through a thin positive lens, O'2 will lie in front of O'1 so long as the angle u2 is greater than u1 (under correction); and conversely with a dispersive surface or lenses (over correction). The caustic, in the first case, resembles the sign > (greater than); in the second < (less than). If the angle u1 is very small, O'1 is the Gaussian image; and O'1 O'2 is termed the longitudinal aberration, and O'1R the lateral aberration of the pencils with aperture u2. If the pencil with the angle u2 is that of the maximum aberration of all the pencils transmitted, then in a plane perpendicular to the axis at O'1 there is a circular disk of confusion of radius O'1R, and in a parallel plane at O'2 another one of radius O'2R2; between these two is situated the disk of least confusion.[8]

Dr. Burhenne: It's the respect for what's going on in the mouth and truly understanding or attempting to understand how complex it is and how important it is to nourish and maintain it. So definitely respect for the oral microbiome is key. Keeping your mouth shut, I mean I say that just to get attention, but mouth breathing is a big issue. A dry mouth is a big issue, which lowers the pH. Saliva's a great buffer. Saliva is one of the microbiomes in the mouth. It has substances and components in it that help remineralize teeth and help fight off infections. Anything that dries out your mouth, that would be medications. If you're exercising lots, stay well hydrated. You could be dehydrated. That causes a dry mouth. Sleeping with your mouth open at night can cause lots of disruption or dysbiosis of the oral microbiome. Also, I think it's important. I tell patients on the website that they need to seek out a functional dentist. Because of the oral microbiome because we can't see a lot of the symptoms early on of a dysbiosis like gum disease or cavities, we wait to take an x-ray and then we see the cavity and we treat it. In dental school, we were told that dentists were the most preventative minded health practitioners out there. Now I would disagree with that. We need to go one step back, further back. We need to treat diseases in their pro domo periods. That is essentially respecting the oral microbiome. I would tell patients to find a functional dentist, someone who is looking for root cause treatments, not just treating your symptoms. Dentists, they see a hole in the mouth, in the tooth and they fix it. They see deep pockets; they go in there and they scrape them clean and they hope for the best. That is not the kind of practitioner I want to be today because of what I know about the oral microbiome. Yes, brush and floss. I'm not going to say not to do that, but all these things that affect the oral microbiome; dry mouth, diet, biofilm management, genetics and epigenetics, for example, something epigenetic would be facial development. As we are evolving, the younger people that we're seeing now don't look like our ancestors. They have narrower faces, tapering jaws. The width of our jaw is not developing correctly because we have a lot of allergies, because we're being born via cesarean instead of being pushed through the birth canal. We're not picking up mom's microbiome, vaginal microbiome, and we're not being shaped and pushed through the canal. We're not breastfeeding as much. All of these things have an effect on how our faces develop and hence, how we breathe and we are not good nose breathers anymore; then of course causes a dry mouth. It lowers the pH. That's why I tell people to keep their mouth shut, unless they're talking to me and then I won't say that. Anyway, when I came out of dental school, I was learning how to create just beautiful restorations and reversing symptoms and signs of diseases in the mouth. Now it's more about aggressively counseling the patient and looking for and measuring, we have tests now, we have DNA tests that we can use. Prevention occurs even earlier. It can occur with prenatal advice, making sure they take the right form of a B vitamin that prevents midline defects, which would cause a tongue tie. If you have a tongue tie, then you can't breastfeed properly, then you won't be able to breathe later as an adult properly. There's a lot that dentistry can do to further the role of any healthcare practitioner, physician, dentists in terms of providing functional advice, functional care, and preventing diseases like diabetes, even Alzheimer's. I see myself as on the front line of the fight against Alzheimer's as a dentist and I think dentists now need to, and I counsel them to be practitioners of the oral microbiome. I think that's what a general dentist, any dentist, how they should be thinking.

The largest opening of the pencils, which take part in the reproduction of O, i.e., the angle u, is generally determined by the margin of one of the lenses or by a hole in a thin plate placed between, before, or behind the lenses of the system. This hole is termed the stop or diaphragm; Abbe used the term aperture stop for both the hole and the limiting margin of the lens. The component S1 of the system, situated between the aperture stop and the object O, projects an image of the diaphragm, termed by Abbe the entrance pupil; the exit pupil is the image formed by the component S2, which is placed behind the aperture stop. All rays which issue from O and pass through the aperture stop also pass through the entrance and exit pupils, since these are images of the aperture stop. Since the maximum aperture of the pencils issuing from O is the angle u subtended by the entrance pupil at this point, the magnitude of the aberration will be determined by the position and diameter of the entrance pupil. If the system be entirely behind the aperture stop, then this is itself the entrance pupil (front stop); if entirely in front, it is the exit pupil (back stop).[8]

If rays issuing from O (fig. 1) are concurrent, it does not follow that points in a portion of a plane perpendicular at O to the axis will be also concurrent, even if the part of the plane be very small. As the diameter of the lens increases (i.e., with increasing aperture), the neighboring point N will be reproduced, but attended by aberrations comparable in magnitude to ON. These aberrations are avoided if, according to Abbe, the sine condition, sin u'1/sin u1=sin u'2/sin u2, holds for all rays reproducing the point O. If the object point O is infinitely distant, u1 and u2 are to be replaced by h1 and h2, the perpendicular heights of incidence; the sine condition then becomes sin u'1/h1=sin u'2/h2. A system fulfilling this condition and free from spherical aberration is called aplanatic (Greek a-, privative, plann, a wandering). This word was first used by Robert Blair to characterize a superior achromatism, and, subsequently, by many writers to denote freedom from spherical aberration as well.[8]

Dr. Burhenne: But also, a lot of people don't realize that. I would say the majority of people just think a nylon bristle's a nylon bristle and it's not. There are high quality and low quality versions. There's a process called end rounding. If you think about it, the way the toothbrush is made, it's a nylon stick or handle. While it's soft, a machine comes in and drops in hundreds or thousands of bristles and that's important too, the count, the count of bristles and then to level that off to make it all nice and straight and flat, there's a machine that comes and cuts them. A freshly cut nylon fiber is quite sharp if you think about it. It's like the sharp ends of a cylinder. So then there's a machine that has to end round and polish and make those little nylon tips, hemispherical and smooth. That way, it doesn't abrade denton. The hardness of a nylon bristle is almost the same hardness of denton. You can literally wear your teeth away if you're using a cheap toothbrush or if you're using a worn toothbrush. That's another nice aspect of Quip. They automatically... Simon got it right away. You've got to replace your toothbrush. How do I get people to do that? People forget, they don't know how long it's been. So he has this reminder system where if you sign up for it, it's a subscription service of course. I subscribe to it, I just don't even think about it anymore. It's wonderful. I just get this little foil package in the mail. It's got my new toothbrush head in it and I just pop off the old one, throw it away and pop on the new one.

Dr. Burhenne: Well, I started off being a dentist and I still am, but that description will ensue in the discussion here, but that's changed on how I look at dentistry. Essentially, my father was a very well known physician and he wanted me to be a physician. He was a pioneer in radiology and I kept pushing back and realizing I could never fill his shoes. I was in college taking History of Art classes and enjoying myself immensely. Then halfway through college realized that may not be the best way to make a living or maybe I was missing out on something. So I started taking some science classes and microbiology. Invertebrate zoology actually fascinated me. There's a lot of artistic beauty in that alone, in evolution. I started broadening my horizons in college. Then I took, and again, this is 35, almost 40 years ago, at the college I was at, there was this very archaic CPU machine down in the basement with big seven and a half inch floppy drives. It was a personality test linked to a career tool. I was shocked as I filled it out. I was very honest and answering the questions. When the number one hit came up, which was dentistry, I was shocked. It just never occurred to me that that would be something that I would be good at based on my personality and what I like to do and what I find interesting. From there, I just immersed myself into pre dental courses, became a dentist, was educated on the West Coast at the University of Pacific Dental School and then did a lot of continuing education and clinical CE groups and just never looked back. It kept getting broader and wider and then I got into sleep, and dentistry and sleep are related, connected in so many different ways. Then of course the oral microbiome came along. Unfortunately, it came a little later than the gut microbiome, which is still pretty new stuff. Dentistry is a fascinating field and it's still about to expand even more in terms of facial development and all these epigenetic factors on what's constricting our facial development and changing how we look and how we can breathe. So it's been a roller coaster ride. I wrote a book. I've just kind of dived into so many different areas and I have a website on oral health that I cofounded with my daughter. My daughter, when she came of age, a skilled millennial in social media and having worked at Google and Facebook and Twitter, she said, "Dad, all this information you keep telling me at the dinner table, we gotta get out to the masses." So we created askthedentist.com. We get 12 to 15 million unique hits a year on that. So it's been fun. A long time ago my dad told me that the role of a doctor was nothing else but to teach and that's without even knowing it at first, that's what I've been doing for such a long time with my patients, with readers and people on the website, readers of the book, and podcasts, and just getting the information out. So it's been very exciting, a lot of fun.

Dr. Burhenne: The key is, is to respect this oral microbiome. We essentially are a super organism. In other words, we're not just humans, and this is the whole concept of this oral microbiome. This is one of the big changes in dentistry I was referring to earlier, which is so exciting I think. Everyone knows what the gut microbiome. It's been around for what? 12, 13 years. The word microbiota is a relatively new word. I think it's only been in use for 15 years, but the oral microbiome, which is another biome, there are biomes everywhere in the body. There's a biome in your armpit. There's a vaginal biome. There's maybe a biome in the brain. These are microbiota. These are bugs. These are bacteria, viruses, fungi, even for example, it could be a simple yeast cell. These are all living inside of us for a purpose, for a reason. They are essentially a community. They're ecological communities of bugs inside of us. So I look at these bugs and again, I refer to super organism. We're not just human. We are more than that, I look at this as a partner. This is a partner that partners with us that helps us have better health. It prevents disease. It determines so much in terms of longevity, even cognitive behavior, how we act, happiness. These bugs are very important. They're commensal, they're symbiotic, they're pathogenic; those are the bad ones of course. If they're not treated well, if you don't respect the oral microbiome, in other words, if you're using a mouthwash with a lot of alcohol in it, you are putting down some bugs. You are essentially carpet bombing the mouth and for 10, 15, 20 minutes, all these bugs die off. I mean, not completely. You cannot sterilize the mouth. This is a disinfection and then they all grow back. Well, they may not grow back the way it was supposed to be in terms of this communal ratio of all these bugs to each other because they're all doing things. Even the bad bugs are there for a reason. We don't quite understand how and why, but we know that if we kill off a certain bug and we're very selective in killing bugs, that that's not always a good thing. So I would say anything that helps this organism in your mouth, which by the way is related to the gut microbiome as well, remember when you have bugs in your mouth, you're swallowing probably over a liter of saliva a day. In that liter, liter and a half of saliva; there are trillions of bugs that you are seeding the gut microbiome with. So you better have good bugs in your mouth. This could affect the gut microbiome and we all know how important the gut microbiome is in terms of overall health and preventing disease and the immune system and the gut brain access and all that. So the oral microbiome; respect of it, not abusing it, not over brushing, not killing all the bugs with all the ingredients of toothpaste and mouthwash that are pretty much in every single mouthwash and toothpaste out there. Now, the mainstream mouthwashes and toothpastes are quite bad for you. They disrupt this oral microbiome, and in doing so, they predispose you to gum disease and to cavities.

The investigations of James Clerk Maxwell[9] and Ernst Abbe[note 1] showed that the properties of these reproductions, i.e., the relative position and magnitude of the images, are not special properties of optical systems, but necessary consequences of the supposition (per Abbe) of the reproduction of all points of a space in image points, and are independent of the manner in which the reproduction is effected. These authors showed, however, that no optical system can justify these suppositions, since they are contradictory to the fundamental laws of reflection and refraction. Consequently, the Gaussian theory only supplies a convenient method of approximating reality; realistic optical systems fall short of this unattainable ideal. Currently, all that can be accomplished is the projection of a single plane onto another plane; but even in this, aberrations always occurs and it may be unlikely that these will ever be entirely corrected.[8]

If the object point be infinitely distant, all rays received by the first member of the system are parallel, and their intersections, after traversing the system, vary according to their perpendicular height of incidence, i.e. their distance from the axis. This distance replaces the angle u in the preceding considerations; and the aperture, i.e., the radius of the entrance pupil, is its maximum value.[8]

An image-forming optical system with aberration will produce an image which is not sharp. Makers of optical instruments need to correct optical systems to compensate for aberration. Aberrations are particularly impactful in telescopes, where they can significantly degrade the quality of observed celestial objects. Understanding and correcting these optical imperfections are crucial for astronomers to achieve clear and accurate observations.[4]

Chromatic aberrations are caused by dispersion, the variation of a lens's refractive index with wavelength. Because of dispersion, different wavelengths of light come to focus at different points. Chromatic aberration does not appear when monochromatic light is used.

A point O (fig. 2) at a finite distance from the axis (or with an infinitely distant object, a point which subtends a finite angle at the system) is, in general, even then not sharply reproduced if the pencil of rays issuing from it and traversing the system is made infinitely narrow by reducing the aperture stop; such a pencil consists of the rays which can pass from the object point through the now infinitely small entrance pupil. It is seen (ignoring exceptional cases) that the pencil does not meet the refracting or reflecting surface at right angles; therefore it is astigmatic (Gr. a-, privative, stigmia, a point). Naming the central ray passing through the entrance pupil the axis of the pencil or principal ray, it can be said: the rays of the pencil intersect, not in one point, but in two focal lines, which can be assumed to be at right angles to the principal ray; of these, one lies in the plane containing the principal ray and the axis of the system, i.e. in the first principal section or meridional section, and the other at right angles to it, i.e. in the second principal section or sagittal section. We receive, therefore, in no single intercepting plane behind the system, as, for example, a focusing screen, an image of the object point; on the other hand, in each of two planes lines O' and O" are separately formed (in neighboring planes ellipses are formed), and in a plane between O' and O" a circle of least confusion. The interval O'O", termed the astigmatic difference, increases, in general, with the angle W made by the principal ray OP with the axis of the system, i.e. with the field of view. Two astigmatic image surfaces correspond to one object plane; and these are in contact at the axis point; on the one lie the focal lines of the first kind, on the other those of the second. Systems in which the two astigmatic surfaces coincide are termed anastigmatic or stigmatic.[8]

The aberrations of the third order are: (1) aberration of the axis point; (2) aberration of points whose distance from the axis is very small, less than of the third order — the deviation from the sine condition and coma here fall together in one class; (3) astigmatism; (4) curvature of the field; (5) distortion.[8]

Alexandra Arriaga: Okay. Sounds good. Now speaking more about you as a dentist, how has the way that you've treated your patients changed as you learn more about the impact of the oral microbiome?

In a perfect optical system in the classical theory of optics,[5][6] rays of light proceeding from any object point unite in an image point; and therefore the object space is reproduced in an image space. The introduction of simple auxiliary terms, due to Gauss,[7][8] named the focal lengths and focal planes, permits the determination of the image of any object for any system. The Gaussian theory, however, is only true so long as the angles made by all rays with the optical axis (the symmetrical axis of the system) are infinitely small, i.e., with infinitesimal objects, images and lenses; in practice these conditions may not be realized, and the images projected by uncorrected systems are, in general, ill-defined and often blurred if the aperture or field of view exceeds certain limits.[8]

Dr. Burhenne: That's what I keep telling people. You have to have respect for the mouth. It's really, really important. Otherwise, you're going to have issues. Of course, diet is part of it. Prebiotics are important. If you keep eating a lot of sugar, that's going to change the pH in the mouth. If you take a lot of pharmaceutical drugs or if you take a lot of antibiotics, these are all things that would... All the things that take down the gut microbiome can also affect the oral microbiome. If the oral microbiome is not functioning properly, then you're going to have issues. You're going to have bad breath, you're going to have higher rate of getting cavities, for example.

Aberration can be analyzed with the techniques of geometrical optics. The articles on reflection, refraction and caustics discuss the general features of reflected and refracted rays.

Aberrations fall into two classes: monochromatic and chromatic. Monochromatic aberrations are caused by the geometry of the lens or mirror and occur both when light is reflected and when it is refracted. They appear even when using monochromatic light, hence the name.

The focal lengths are made equal for the lines C and F. In the neighborhood of 550 nm the tangent to the curve is parallel to the axis of wavelengths; and the focal length varies least over a fairly large range of color, therefore in this neighborhood the color union is at its best. Moreover, this region of the spectrum is that which appears brightest to the human eye, and consequently this curve of the secondary on spectrum, obtained by making f C = f F {\displaystyle f_{C}=f_{F}} , is, according to the experiments of Sir G. G. Stokes (Proc. Roy. Soc., 1878), the most suitable for visual instruments (optical achromatism,). In a similar manner, for systems used in photography, the vertex of the color curve must be placed in the position of the maximum sensibility of the plates; this is generally supposed to be at G'; and to accomplish this the F and violet mercury lines are united. This artifice is specially adopted in objectives for astronomical photography (pure actinic achromatism). For ordinary photography, however, there is this disadvantage: the image on the focusing-screen and the correct adjustment of the photographic sensitive plate are not in register; in astronomical photography this difference is constant, but in other kinds it depends on the distance of the objects. On this account the lines D and G' are united for ordinary photographic objectives; the optical as well as the actinic image is chromatically inferior, but both lie in the same place; and consequently the best correction lies in F (this is known as the actinic correction or freedom from chemical focus).[8]

As in Fourier synthesis using sines and cosines, a wavefront may be perfectly represented by a sufficiently large number of higher-order Zernike polynomials. However, wavefronts with very steep gradients or very high spatial frequency structure, such as produced by propagation through atmospheric turbulence or aerodynamic flowfields, are not well modeled by Zernike polynomials, which tend to low-pass filter fine spatial definition in the wavefront. In this case, other fitting methods such as fractals or singular value decomposition may yield improved fitting results.

Alexandra Arriaga: Wow. So there is a lot of room for collaboration. That's great to know. Last, but not least in a few words, what would you say is your best advice for everyone listening to keep excellent oral health?

The aberrations can also be expressed by means of the characteristic function of the system and its differential coefficients, instead of by the radii, &c., of the lenses; these formulae are not immediately applicable, but give, however, the relation between the number of aberrations and the order. Sir William Rowan Hamilton (British Assoc. Report, 1833, p. 360) thus derived the aberrations of the third order; and in later times the method was pursued by Clerk Maxwell (Proc. London Math. Soc., 1874–1875; (see also the treatises of R. S. Heath and L. A. Herman), M. Thiesen (Berlin. Akad. Sitzber., 1890, 35, p. 804), H. Bruns (Leipzig. Math. Phys. Ber., 1895, 21, p. 410), and particularly successfully by K. Schwarzschild (Göttingen. Akad. Abhandl., 1905, 4, No. 1), who thus discovered the aberrations of the 5th order (of which there are nine), and possibly the shortest proof of the practical (Seidel) formulae. A. Gullstrand (vide supra, and Ann. d. Phys., 1905, 18, p. 941) founded his theory of aberrations on the differential geometry of surfaces.[8]

Since the aberration increases with the distance of the ray from the center of the lens, the aberration increases as the lens diameter increases (or, correspondingly, with the diameter of the aperture), and hence can be minimized by reducing the aperture, at the cost of also reducing the amount of light reaching the image plane.

This aberration is quite distinct from that of the sharpness of reproduction; in unsharp, reproduction, the question of distortion arises if only parts of the object can be recognized in the figure. If, in an unsharp image, a patch of light corresponds to an object point, the center of gravity of the patch may be regarded as the image point, this being the point where the plane receiving the image, e.g., a focusing screen, intersects the ray passing through the middle of the stop. This assumption is justified if a poor image on the focusing screen remains stationary when the aperture is diminished; in practice, this generally occurs. This ray, named by Abbe a principal ray (not to be confused with the principal rays of the Gaussian theory), passes through the center of the entrance pupil before the first refraction, and the center of the exit pupil after the last refraction. From this it follows that correctness of drawing depends solely upon the principal rays; and is independent of the sharpness or curvature of the image field. Referring to fig. 4, we have O'Q'/OQ = a' tan w'/a tan w = 1/N, where N is the scale or magnification of the image. For N to be constant for all values of w, a' tan w'/a tan w must also be constant. If the ratio a'/a be sufficiently constant, as is often the case, the above relation reduces to the condition of Airy, i.e. tan w'/ tan w= a constant. This simple relation (see Camb. Phil. Trans., 1830, 3, p. 1) is fulfilled in all systems which are symmetrical with respect to their diaphragm (briefly named symmetrical or holosymmetrical objectives), or which consist of two like, but different-sized, components, placed from the diaphragm in the ratio of their size, and presenting the same curvature to it (hemisymmetrical objectives); in these systems tan w' / tan w = 1.[8]

Alexandra Arriaga: It is so overwhelming. It wasn't until recently that I figured out that the bristles had different types of softness or harshness. I don't know if this is everyone. Maybe it's just me, but I had actually never noticed. Then I started noticing that some were soft, medium and I was like, "Wow. Okay." Then a friend of mine who actually is a dentist told me that the soft ones are the best ones.