123 Sentences With "magnifications" | Random Sentence Generator

Not much more could be learned about the stars until higher magnifications were achieved.

Fractals are geometric patterns that repeat at different magnifications and stem from chaos theory.

The Macro Pro Lens Set ($27) lets you shoot macro photos at three different magnifications: 28x, 26x, and 21x.

"Even higher magnifications would allow us to learn details about Icarus and the population of luminous stars at high redshift," Kelly told me.

Hovering over with the S Pen offers up magnifications of portions of the screen and can also be used to translate pieces of text — even in images — into different languages.

You can use a magnifying glass to look at the individual pages, but to actually read the text you'll need to reach for a laboratory microscope capable of magnifications up to 150X.

When the first telescopes were developed in The Netherlands in the early 21883s, amateurs and experts alike were excited to try them, even though they only had weak magnifications of 21923X or 21940X.

Look at different chocolate samples under a scanning electron microscope (SEM), as Dailey's students did (at magnifications ranging from 400 to 5,000 times), and you'll see that each has a slightly different crystal structure.

Other telescope designs are used such as Schmidt and Maksutov optical assemblies. They may have a ruggedised design, a mounting for attaching to a tripod, and an ergonomically designed and located knob for focus control. Eyepieces are usually interchangeable to give different magnifications, or may consist of a single variable "zoom" eyepiece to give a range of magnifications. Magnifications of less than 20× are unusual, as are magnifications of more than 60× since it can lead to poorer image brightness, a narrow field of view, and show too much image shake, even on a tripod.

Higher magnifications for the same detector image a smaller area of the sample.

These spheres became the lenses of his microscopes, with the smallest spheres providing the highest magnifications.

Light microscopes are designed for placement of the specimen's polished surface on the specimen stage either upright or inverted. Each type has advantages and disadvantages. Most LOM work is done at magnifications between 50 and 1000X. However, with a good microscope, it is possible to perform examination at higher magnifications, e.g.

Archaeological research focused on residue adhering to artifacts start at lower magnifications, commonly using a stereoscope. Most data obtained at this stage is qualitative, an important first stage to fuller analysis. Magnifications of between x10 and x50 are sufficient to locate target residues, describe features and confirm internal structures of the identified residues.

Tasco imports telescopic sights for center-fire rifles, rimfire rifles, and handguns featuring magnifications of 1 to 40 power. They also import non-magnifying red dot sights.

A 10th magnitude star lies next to the galaxy, thus making it a challenging object at low magnifications. NGC 2974 is part of the Herschel 400 Catalogue.

This leads to the techniques of Gaussian optics and paraxial ray tracing, which are used to find basic properties of optical systems, such as approximate image and object positions and magnifications.

Alternatives to optical microscopy which do not use visible light include scanning electron microscopy and transmission electron microscopy and scanning probe microscopy and as a result, can achieve much greater magnifications.

Fujifilm's Hybrid Viewfinder allows photographers to choose between an optical finder (OVF) and a high-resolution electronic view (EVF), complete with previews of depth of field and white balance. It also allows different optical magnifications and frame sizes to allow accurate framing with any of the XF- mount lenses in the system. When an XF lens is mounted on the camera body, the most appropriate of the two available viewfinder magnifications is combined with the correct frame size.

Wide FOV eyepieces work best at low magnifications with large apertures, where the relative size of an object is viewed at higher comparative standards with minimal magnification giving an overall brighter image to begin with.

The projection lens magnification is fixed. Different views of measured pieces often require different magnifications. However, the usual projector factory configuration is with a single lens, so according to needs, additional lenses may be purchased and used.

Tasco offers several models of spotting scopes. These scopes are designed for rugged outdoor use and feature rubber armor protection as well as optional camouflage. Models have magnifications between 12 and 45 times, and feature panoramic view finding.

Magnifications range from 100× to 1,000,000× or higher for both microscope types. The scanning tunneling microscope uses quantum tunneling of electrons from a sharp metal tip into the studied material and can produce atomically resolved images of its surface.

Also, total magnification in both fixed and zoom systems can be varied by changing eyepieces. Intermediate between fixed magnification and zoom magnification systems is a system attributed to Galileo as the "Galilean optical system" ; here an arrangement of fixed-focus convex lenses is used to provide a fixed magnification, but with the crucial distinction that the same optical components in the same spacing will, if physically inverted, result in a different, though still fixed, magnification. This allows one set of lenses to provide two different magnifications ; two sets of lenses to provide four magnifications on one turret ; three sets of lenses provide six magnifications and will still fit into one turret. Practical experience shows that such Galilean optics systems are as useful as a considerably more expensive zoom system, with the advantage of knowing the magnification in use as a set value without having to read analogue scales.

The desirable amount of magnification depends upon the intended application, and in most binoculars is a permanent, non-adjustable feature of the device (zoom binoculars are the exception). Hand-held binoculars typically have magnifications ranging from 7x to 10x, so they will be less susceptible to the effects of shaking hands.Clifford E. Swartz, Back-of-the-envelope Physics, JHU Press - 2003, page 73 A larger magnification leads to a smaller field of view and may require a tripod for image stability. Some specialized binoculars for astronomy or military use have magnifications ranging from 15x to 25x.

The actual power or magnification of a compound optical microscope is the product of the powers of the ocular (eyepiece) and the objective lens. The maximum normal magnifications of the ocular and objective are 10× and 100× respectively, giving a final magnification of 1,000×.

The precise magnification is determined by the working distance between the camera and the object, and good supports are needed to control the image, especially at higher magnifications. The magnifying abilities of these instruments are often overstated; typically offering 200× magnification, this claim is based usually on 25× to 30× actual magnification which is then further magnified by the expansion of the image by display on the screen. High magnifications are available only if the camera has a high resolution, so the image from a 5-megapixel camera can be enlarged to a greater extent than that from a 2-megapixel camera, for example.

Byrne would structure his paintings according to the elements of the narrative he wished to tell. He would use distortions and magnifications to emphasise the importance of particular objects within a landscape or narrative. Sometimes he distorted buildings in a way which displays multiple sides from the same perspective.Moore, Ross, 1954-.

The lyrics are written and sung by singer Anohni, with the melody and music composed by J. Ralph who also produced the recording. The song was inspired by the mating call of the last individual survivor of the now extinct Kauaʻi ʻōʻō.Billboard The music video features magnifications of various marine microorganisms.

The structure of a fractal object is reiterated in its magnifications. Fractals can be magnified indefinitely without losing their structure and becoming "smooth"; they have infinite perimeters—some with infinite, and others with finite surface areas. One such fractal curve with an infinite perimeter and finite surface area is the Koch snowflake.

These and other considerations are major factors influencing the choice of magnification and objective lens diameter. Although very high numerical magnification sounds impressive on paper, in reality, for a pocket monocular it is rarely a good choice because of the very narrow field of view, poor image brightness and great difficulty in keeping the image still when hand holding. Most serious users will eventually come to realise why 8× or 10× are so popular, as they represent possibly the best compromise and are the magnifications most commonly adopted in the very highest quality field monoculars (and binoculars). Where a monocular ends and a telescope starts is debatable but a telescope is normally used for high magnifications (>20×) and with correspondingly larger objective lens diameter (e.g. 60–90mm).

Trichoscopy is a method of hair and scalp evaluation and is used for diagnosing hair and scalp diseases. The method is based on dermoscopy. In trichoscopy hair and scalp structures may be visualized at many-fold magnification. Currently magnifications ranging from 10-fold to 70-fold are most popular in research and clinical practice.

Optical aberrations are "corrected" by design of the reconstruction algorithm. A reconstruction algorithm that truly models the optical setup will not suffer from optical aberrations. Low cost In optical microscopy systems, optical aberrations are traditionally corrected by combining lenses into a complex and costly image forming microscope objective. Furthermore, the narrow focal depth at high magnifications requires precision mechanics.

Tasco imports binoculars with magnifications range between seven and ten power on a variety of models. They also offer Snapshot series binoculars, which include an ability to record video and capture still pictures as seen through the binoculars. Users can transfer images to a computer through a USB cable. Tasco provides software for viewing and printing.

GIA clarity grading is performed under 10x magnification with darkfield illumination. The GIA Laboratory uses as standard equipment binocular stereo microscopes which are able to zoom to higher magnifications. These microscopes are equipped with darkfield illumination, as well as an ultraviolet filtered overhead light. When grading is performed using a 10x handheld loupe, darkfield illumination is more difficult to achieve.

They may offer a choice of magnifications. They usually have motors to advance and rewind film. When coding blips are recorded on the film a reader is used that can read the blips to find any required image. Portable readers are plastic devices that fold for carrying; when open they project an image from microfiche on to a reflective screen.

This camera is attached to a fiberoptic light source and shows the image of the inside of the joint. Probes are used for examination of internal structures by palpating, pulling of moving tissue. They are essential for diagnostic investigation of the joint. All probes bear markings at 5 mm intervals to indicate the scale, since the cameras used in arthroscopy have different magnifications.

The Hirox Digital Microscope System supports magnifications of up to 7000×. A primary difference between an optical and a digital microscope is the magnification. With an optical microscope the magnification is the lens magnification multiplied by the eyepiece magnification. The magnification for a digital microscope is defined as the ratio of the size of image on the monitor to the subject size.

Geometric optics is often simplified by making the paraxial approximation, or "small angle approximation". The mathematical behaviour then becomes linear, allowing optical components and systems to be described by simple matrices. This leads to the techniques of Gaussian optics and paraxial ray tracing, which are used to find basic properties of optical systems, such as approximate image and object positions and magnifications.

A modern transmission electron microscopeDiagram of a transmission electron microscope Electron microscope constructed by Ernst Ruska in 1933 An electron microscope is a microscope that uses a beam of accelerated electrons as a source of illumination. As the wavelength of an electron can be up to 100,000 times shorter than that of visible light photons, electron microscopes have a higher resolving power than light microscopes and can reveal the structure of smaller objects. A scanning transmission electron microscope has achieved better than 50 pm resolution in annular dark-field imaging mode and magnifications of up to about 10,000,000× whereas most light microscopes are limited by diffraction to about 200 nm resolution and useful magnifications below 2000×. Electron microscopes use shaped magnetic fields to form electron optical lens systems that are analogous to the glass lenses of an optical light microscope.

Low-powered digital microscopes, USB microscopes, are also commercially available. These are essentially webcams with a high-powered macro lens and generally do not use transillumination. The camera attached directly to the USB port of a computer, so that the images are shown directly on the monitor. They offer modest magnifications (up to about 200×) without the need to use eyepieces, and at very low cost.

Replication, in metallography, is the use of thin plastic films to nondestructively duplicate the microstructure of a component. The film is then examined at high magnifications. Replication is a method of copying the topography of a surface by casting or impressing material onto the surface. It is the commonly used technique to duplicate surfaces that are inaccessible in metrology to other forms of nondestructive testing.

Using a telescope equipped with a properly aligned equatorial mount, the observer may also follow the equatorial coordinate system on a star map to "hop" or "slide" along the lines of right ascension or declination from a well known object to find a target. This can be assisted using setting circles. Once an instrument is centered on the target object, higher magnifications may be used for observation.

Analog (film) photographers use loupes to review, edit or analyze negatives and slides on a light table. Typical magnifications for viewing slides full-frame depend on image format; 35 mm frames (24×36 mm slides to 38×38 mm superslides) are best viewed at ca. 5×, while ca. 3× is optimal for viewing medium format slides (6×4.5 cm / 6×6 cm / 6×7 cm).

Photomicrographs of regions of substantia nigra in this Parkinson's patient show Lewy bodies and Lewy neurites in various magnifications. Top panels show a 60-times magnification of the alpha-synuclein intraneuronal inclusions aggregated to form Lewy bodies. The bottom panels are 20x magnification images that show strand-like Lewy neurites and rounded Lewy bodies of various sizes. Neuromelanin-laden cells of the substantia nigra are visible in the background.

Oil-immersion objective in use From the above it is understood that oil between the specimen and the objective lens improves the resolving power by a factor 1/n. Objectives specifically designed for this purpose are known as oil immersion objectives. Oil immersion objectives are used only at very large magnifications that require high resolving power. Objectives with high power magnification have short focal lengths, facilitating the use of oil.

The stage is a platform below the objective lens which supports the specimen being viewed. In the center of the stage is a hole through which light passes to illuminate the specimen. The stage usually has arms to hold slides (rectangular glass plates with typical dimensions of 25×75 mm, on which the specimen is mounted). At magnifications higher than 100× moving a slide by hand is not practical.

Correction fluid copolymer visualized under scanning electron microscopy (SEM). The micro-structural details of the copolymer resin are visible under high magnifications. Correction fluid was applied on a glass base (visible in the bottom-right corner of all SEM images). The exact composition of correction fluid varies between manufacturers, but most fluids are composed of an opacifying agent, a solvent (or thinner) and an adulterant 'fragrance' to discourage abuse.

The Leclerc tank features the HL 60 gunner's primary sight from SAGEM. The sight has two day channels; a direct one with ×3.3 and ×10 magnification (×14 in case of the UAE version) and a video channel with ×10 magnification. The thermal channel offers ×3 and ×10 magnifications. The Athos thermal imager has a detection range of 5000 m, can recognize targets at 2500 m and identify them at 2000 m.

Diagnosis of mesothelioma can be suspected with imaging but is confirmed with biopsy. It must be clinically and histologically differentiated from other pleural and pulmonary malignancies, including reactive pleural disease, primary lung carcinoma, pleural metastases of other cancers, and other primary pleural cancers. Primary pericardial mesothelioma is often diagnosed after it has metastasized to lymph nodes or the lungs.Micrographs showing conventionally- stained mesothelioma in a core biopsy (higher magnifications on right).

A 30× Hastings triplet magnifier Magnifying glasses typically have low magnifying power: 2×–6×, with the lower-power types being much more common. At higher magnifications, the image quality of a simple magnifying glass becomes poor due to optical aberrations, particularly spherical aberration. When more magnification or a better image is required, other types of hand magnifier are typically used. A Coddington magnifier provides higher magnification with improved image quality.

Even better images can be obtained with a multiple-lens magnifier, such as a Hastings triplet. High power magnifiers are sometimes mounted in a cylindrical or conical holder with no handle. This is called a loupe. Such magnifiers can reach up to about 30×, and at these magnifications the aperture of the magnifier becomes very small and it must be placed very close to both the object and the eye.

Like many of Harriot's other notes, depictions of the sunspots were not published. Similar to the early observation of the Moon, Galileo was also known to contribute his observations of sunspots and published his findings in 1613. The specifics as to how Harriot's telescope was set up remains largely unknown. However, it is known that Harriot used different magnifications of telescopes with 10X and 20X power being used most often.

They are subtabulately shouldered at the summit, marked by numerous fine lines of growth and equally abundant, loosely placed, wavy spiral striations. These lines of growth and spiral markings give the surface a finely reticulated appearance when viewed under high magnifications. The periphery and base of the body whorl are decidedly rounded and inflated, marked like the space between the sutures. The aperture is large, suboval, slightly effuse anteriorly.

The diffraction limit set in stone on a monument for Ernst Abbe. At very high magnifications with transmitted light, point objects are seen as fuzzy discs surrounded by diffraction rings. These are called Airy disks. The resolving power of a microscope is taken as the ability to distinguish between two closely spaced Airy disks (or, in other words the ability of the microscope to reveal adjacent structural detail as distinct and separate).

Microscope objectives are characterized by two parameters, namely, magnification and numerical aperture. The former typically ranges from 5× to 100× while the latter ranges from 0.14 to 0.7, corresponding to focal lengths of about 40 to 2 mm, respectively. Objective lenses with higher magnifications normally have a higher numerical aperture and a shorter depth of field in the resulting image. Some high performance objective lenses may require matched eyepieces to deliver the best optical performance.

The presence or absence of flaws or inclusions in a diamond is usually decided by examining the stone carefully with a lens having the standard magnifications of 10x. No other magnification should be taken as authoritative. Stones which show no apparent flaws or inclusions under this magnification are regarded as flawless. The term for a scarcely perceptible inclusion is "VVS" for "very very slight (or small)" – which is sometimes offered as flawless.

When viewed at low magnifications, the individual pixels appear as the primary image, while close examination reveals that the image is in fact made up of many hundreds or thousands of smaller images. Most of the time they are a computer-created type of montage. There are two kinds of mosaic, depending on how the matching is done. In the simpler kind, each part of the target image is averaged down to a single color.

Schematic (bottom) and electron micrographs (top) of the growth of a honeycomb polystyrene film by breath-figure self-assembly. A water filter membrane prepared by breath-figure self-assembly, viewed at different synthesis steps and magnifications. The membrane material is a mixture of poly(phenylene oxide) and silica nanoparticles. Breath-figure self-assembly is the self- assembly process of formation of honeycomb micro-scaled polymer patterns by the condensation of water droplets.

Numerical aperture for microscope lenses typically ranges from 0.10 to 1.25, corresponding to focal lengths of about 40 mm to 2 mm, respectively. A typical microscope has three or four objective lenses with different magnifications, screwed into a circular "nosepiece" which may be rotated to select the required lens. These lenses are often color coded for easier use. The least powerful lens is called the scanning objective lens, and is typically a 4× objective.

NGC 5979, a planetary nebula of apparent magnitude 12.3, has a blue-green hue at higher magnifications, while Henize 2-138 is a smaller planetary nebula of magnitude 11.0. NGC 5938 is a remote spiral galaxy around 300 million light-years (90 megaparsecs) away. It is located 5 degrees south of Epsilon Trianguli Australis. ESO 69-6 is a pair of merging galaxies located about 600 million light-years (185 megaparsecs) away.

With a Mirau objective, as shown in Figure 3, the reference beam is reflected back in the direction of the objective front lens by a beam splitter. On the front lens there is a miniaturized mirror the same size as the illuminated surface on the object. Therefore, for high magnifications, the mirror is so small that its shadowing effect can be ignored. Moving the interference objective modifies the length of the measurement arm.

The lens is the first that incorporated Sigma's FLD glass elements, designed to correct color aberrations like fluoride glass does. Chromatic aberrations are indeed superior to earlier Sigma wide-angle lenses. In fact, although they might be noticeable at 100% image magnification, they are not at the magnifications now common with prints relative to the number of megapixels that images are commonly captured at. According to Sigma's website, Super Multi-Layer Coating reduces flare and ghosting.

ScreenCorder is a desktop recording tool for Microsoft Windows Operating Systems, developed and distributed by MatchWare. The program allows the user to record everything that happens on their desktop as viewed on their monitor, edit the recording and then export it to a redistributable video format. Uses include the creation of training videos, product support videos, sales presentations, and demonstration videos. Recorded content can be enhanced with audio instructions, graphic speech bubbles, magnifications, animations, and multimedia content.

Studies have also suggested a possible antioxidant activity of alpha-synuclein in the membrane. Photomicrographs of regions of substantia nigra in a patient showing Lewy bodies and Lewy neurites in various magnifications Membrane interaction of alpha-synuclein modulates or affects its rate of aggregation. The membrane- mediated modulation of aggregation is very similar to that observed for other amyloid proteins such as IAPP and abeta. Aggregated states of alpha-synuclein permeate the membrane of lipid vesicles.

The team consisted of several PhD students including Ernst Ruska and Bodo von Borries. The research team worked on lens design and CRO column placement, to optimize parameters to construct better CROs, and make electron optical components to generate low magnification (nearly 1:1) images. In 1931, the group successfully generated magnified images of mesh grids placed over the anode aperture. The device used two magnetic lenses to achieve higher magnifications, arguably creating the first electron microscope.

Catalogue essay, John Himmelfarb: Inland Romance, Oakton College: William A. Koehnline Gallery, 2001. The Chicago Tribune’s Alan Artner and others also linked the series to Himmelfarb's calligraphic works, seeing a relationship between the lattice shapes and outlined magnifications of his hieroglyphs (as in Veneer Court, 1998) that suggested the monumental work of Franz Kline. In addition, a new lyricism and Abstract Expressionist painterliness came to the fore (e.g., Limestone Fox, 2000), along with his characteristically dynamic linework and dense, piled-on compositions.

The use of fluorite for prisms and lenses was studied and promoted by Victor Schumann near the end of the 19th century. Naturally occurring fluorite crystals without optical defects were only large enough to produce microscope objectives. With the advent of synthetically grown fluorite crystals in the 1950s - 60s, it could be used instead of glass in some high-performance optical telescope and camera lens elements. In telescopes, fluorite elements allow high-resolution images of astronomical objects at high magnifications.

Stereomicroscope with an illuminated butterfly specimen Small specimens necessarily require intense illumination, especially at high magnifications, and this is usually provided by a fibre-optic light source. Fiber optics utilize halogen lamps which provide high light output for a given power input. The lamps are small enough to be fitted easily near the microscope, although they often need cooling to ameliorate high temperatures from the bulb. The fibre-optic stalk gives the operator much freedom in choosing appropriate lighting conditions for the sample.

Some binoculars use image-stabilization technology to reduce shake at higher magnifications. This is done by having a gyroscope move part of the instrument, or by powered mechanisms driven by gyroscopic or inertial detectors, or via a mount designed to oppose and damp the effect of shaking movements. Stabilization may be enabled or disabled by the user as required. These techniques allow binoculars up to 20× to be hand-held, and much improve the image stability of lower-power instruments.

Many celestial objects of interest are too faint to be visible to the unaided eye. Telescopes or binoculars collect much more light, making faint objects visible, but have a smaller field of view, thus complicating orientation on the sky. The field of view of binoculars is rarely more than eight degrees, while that of typical amateur telescopes may be substantially less than one degree, depending on the magnification used. Many objects are best observed using higher magnifications, which inevitably go along with narrow fields of view.

BelOMO 10× achromatic triplet jewellers' loupe Jewelers typically use a monocular, handheld loupe in order to magnify gemstones and other jewelry that they wish to inspect."Jewelry - How to Use a Loupe - Using Jewelry Magnifiers". Jewelry.About.com A 10× magnification is good to use for inspecting jewelry and hallmarks and is the Gemological Institute of America's standard for grading diamond clarity. Stones will sometimes be inspected at higher magnifications than 10×, although the depth of field, which is the area in focus, becomes too small to be instructive.

Ultramicrotomy is a method for cutting specimens into extremely thin slices, called ultra-thin sections, that can be studied and documented at different magnifications in a transmission electron microscope (TEM). It is used mostly for biological specimens, but sections of plastics and soft metals can also be prepared. Sections must be very thin because the 50 to 125 kV electrons of the standard electron microscope cannot pass through biological material much thicker than 150 nm. For best resolutions, sections should be from 30 to 60 nm.

Since these systems can be made from any standard optical microscope, they may be a lower cost approach for people who already have microscopes. More important, though, is that microscope-based systems have less depth of field issues generally versus dynamic imaging systems. This is because the sample is placed on a microscope slide, and then usually covered with a cover slip, thus limiting the plane containing the particles relative to the optical axis. This means that more particles will be in acceptable focus at high magnifications.

200x200px 200x200px In mathematics, a fractal is a self-similar subset of Euclidean space whose fractal dimension strictly exceeds its topological dimension. Fractals appear the same at different levels, as illustrated in successive magnifications of the Mandelbrot set. Fractals exhibit similar patterns at increasingly small scales called self-similarity, also known as expanding symmetry or unfolding symmetry; if this replication is exactly the same at every scale, as in the Menger sponge, it is called affine self- similar. Fractal geometry lies within the mathematical branch of measure theory.

In short, the work-function anisotropy of the crystal planes is mapped onto the screen as intensity variations. The magnification is given by the ratio M = L/R, where R is the tip apex radius, and L is the tip–screen distance. Linear magnifications of about 105 to 106 are attained. The spatial resolution of this technique is of the order of 2 nm and is limited by the momentum of the emitted electrons parallel to the tip surface, which is of the order of the Fermi velocity of the electron in metal.

The third open cluster, Pismis 20, contains 12 stars in a diameter of 4.5 arcseconds but exhibits a magnitude similar to NGC 5823 (7.8). At 8270 light-years, it requires an amateur telescope with an aperture over 300 mm to be easily discerned. Hubble Space Telescope's view of NGC 5315, showing its intricate structure and central star The planetary nebula NGC 5315 has a magnitude of 9.8 around a central star of magnitude 14.2, located 5.2 degrees west-southwest of Alpha Circini. It is only visible as a disc at magnifications over 200-fold.

The magnification through a telescope makes an object appear larger while limiting the FOV. Magnification is often misleading as the optical power of the telescope, its characteristic is the most misunderstood term used to describe the observable world. At higher magnifications the image quality significantly reduces, usage of a Barlow lens increases the effective focal length of an optical system—multiplies image quality reduction. Similar minor effects may be present when using star diagonals, as light travels through a multitude of lenses that increase or decrease effective focal length.

They usually offer modest magnifications (about 1× to 200×) at very low cost without the need to use eyepieces, at least compared to conventional stereomicroscopes for example."Introduction to Stereomicroscopy" by Paul E. Nothnagle, William Chambers, and Michael W. Davidson, Nikon MicroscopyU. The quality of the final image depends on the camera capacity or megapixels available with the system, varying from 1.3 MP, 2 MP, 5 MP and upwards, as well as operator skill and illumination quality. Both still images and videos can be recorded on most systems.

The stage of an inverted microscope is usually fixed, and focus is adjusted by moving the objective lens along a vertical axis to bring it closer to or further from the specimen. The focus mechanism typically has a dual concentric knob for coarse and fine adjustment. Depending on the size of the microscope, four to six objective lenses of different magnifications may be fitted to a rotating turret known as a nosepiece. These microscopes may also be fitted with accessories for fitting still and video cameras, fluorescence illumination, confocal scanning and many other applications.

The grinding process usually reduces the stones to 50% of their original weight. The diamond blade is then mounted into a soft metal shaft (Wood's metal) and finally polished to a very sharp edge. The knife's edge is extremely sharp and free of imperfections, which helps produce ultrathin sections of very regular thickness to get views of specimens at high magnifications with the transmission electron microscope (TEM).Micro Star Technologies, diamond knives The shaft containing the final edge is then mounted in a metal trough, or "boat", and cemented, usually with an epoxy plastic.

Crescograph, Bose Institute, Kolkata A crescograph is a device for measuring the growth in plants. It was invented in the early 20th century by Sir Jagadish Chandra Bose. The Bose crescograph uses a series of clockwork gears and a smoked glass plate to record the movement of the tip of a plant (or its roots). It was able to record at magnifications of up to 10,000 times through the use of two different levers. One lever records at 100 times magnification while the other lever takes that image and records at another 100 times magnification.

When the pH of the environment is 3.5, acridine orange becomes excited by blue light (460 nm). When acridine orange is excited by blue light, the fluorescent dye can differentially stain human cells green and prokaryotic cells orange (600 nm), allowing for rapid detection with a fluorescent microscope. The differential staining capability of acridine orange provides quick scanning of specimen smears at lower magnifications of 400x compared to Gram stains that operate at 1000x magnification. The differentiation of cells is aided by a dark background that allows colored organisms to be easily detected.

It is a loosely scattered cluster in the Milky Way that measures 49 arcminutes across and features approximately twelve bright stars, although more than 60 stars of approximately 9th magnitude become visible at low magnifications in a telescope. It is considered to be one of the more inconspicuous open clusters. The other open cluster in Andromeda is NGC 7686, which has a similar magnitude of 5.6 and is also a part of the Milky Way. It contains approximately 20 stars in a diameter of 15 arcminutes, making it a tighter cluster than NGC 752.

Zeiss' first compound microscopes were offered in his 5th, 1858, price list. These are described as "Small body tube, consisting of a field lens and two oculars with an adaptor to attach the tube to the stand and doublet objectives of stands 1 through 5 to allow use of the doublets as objectives to obtain two stronger magnifications after the fashion of the compound microscope. The 120 power doublet of the simple microscope yields in this fashion 300 and 600 fold magnification." Despite Schleiden's approval, these improvised compound microscopes were not a long-term solution.

More recently, advances in aberration corrector design have been able to reduce spherical aberrations and to achieve resolution below 0.5 Ångströms (50 pm) at magnifications above 50 million times.Scale of Things Chart. Science.energy.gov Improved resolution allows for the imaging of lighter atoms that scatter electrons less efficiently, such as lithium atoms in lithium battery materials. The ability to determine the position of atoms within materials has made the HRTEM an indispensable tool for nanotechnology research and development in many fields, including heterogeneous catalysis and the development of semiconductor devices for electronics and photonics.

Jones-Smith and Mathur raised a valid concern applicable to all forms of fractal expressionism: are art works too small for the painted patterns to repeat over sufficient magnifications to assume the visual characteristics of fractals? In the case of Pollock paintings, the largest range used by Taylor et al. to determine each fractal parameter in a Pollock painting is less than two orders of magnitude in magnification. Nature's fractals repeat over limited magnification ranges (typically just over one order of magnitude), prompting scientists to debate what range is required to reliably establish fractal behavior.

In order to keep the particles in focus, the flow depth is restricted so that the particles remain in a plane of best focus perpendicular to the optical axis. This is similar in concept to the effect of the microscope slide plus cover slip in a static imaging system. Since depth of field decreases exponentially with increasing magnification, the depth of the flow cell must be narrowed significantly with higher magnifications. The major drawback to dynamic image acquisition is that the flow cell depth must be limited as described above.

Rangefinder viewfinders usually have a field of view a little greater than the lens in use. This allows the photographer to be able to see what is going on outside of the frame, and therefore better anticipate the action, at the expense of a smaller image. In addition, with viewfinders with magnifications larger than 0.8x (e.g. some Leica cameras, the Epson RD-1/s, Canon 7, Nikon S, and in particular the Voigtländer Bessa R3A and R3M with their 1:1 magnification), photographers can keep both eyes open and effectively see a floating viewfinder frame superimposed on their real world view.

All grades reflect the appearance to an experienced grader when viewed from above at 10x magnification, though higher magnifications and viewing from other angles are used during the grading process. The grader studies the diamond for internal characteristics and judges them on the basis of five clarity factors: size, number, position, nature, and color or relief. The clarity grade is assessed on the basis of the most noticeable inclusions, the so-called "grade setting inclusions". Less significant inclusions are ignored for the purposes of setting the grade; however, they may still be plotted onto a diamond plot chart.

NGC 6445 lies 2.1 degrees southwest from the open cluster Messier 23. NGC 6445 can be located by star hopping from Messier 23, by firstly locating an arc of 7th and 8th magnitude stars one degree southwest of M23, with the nebula lying 5 arcminutes west of an 8th magnitude star that lies 40 arcminutes west of the southernmost star of the arc. The globular cluster NGC 6440 lies 23 arcminutes to the south and both ojects can be seen in a wide field eyepiece. In low magnification the nebula appears like a fuzzy star and higher magnifications reveal its rectangular disk.

Under these conditions, tissues should be rapidly fresh frozen in liquid nitrogen and cut with a cryostat. The disadvantages of frozen sections include poor morphology, poor resolution at higher magnifications, difficulty in cutting over paraffin sections, and the need for frozen storage. Alternatively, vibratome sections do not require the tissue to be processed through organic solvents or high heat, which can destroy the antigenicity, or disrupted by freeze thawing. The disadvantage of vibratome sections is that the sectioning process is slow and difficult with soft and poorly fixed tissues, and that chatter marks or vibratome lines are often apparent in the sections.

Unlike the other known planets, Ceres and Pallas remained points of light even under the highest telescope magnifications instead of resolving into discs. Apart from their rapid movement, they appeared indistinguishable from stars. Accordingly, in 1802, William Herschel suggested they be placed into a separate category, named "asteroids", after the Greek asteroeides, meaning "star-like". Upon completing a series of observations of Ceres and Pallas, he concluded, > Neither the appellation of planets nor that of comets, can with any > propriety of language be given to these two stars ... They resemble small > stars so much as hardly to be distinguished from them.

It has two controls, one which moves the Abbe condenser closer to or further from the stage, and another, the iris diaphragm, which controls the diameter of the beam of light. The controls can be used to optimize brightness, evenness of illumination, and contrast. Abbe condensers are difficult to use for magnifications of above 400X, as the aplanatic cone is only representative of a numerical aperture (NA) of 0.6. This condenser is composed of two lenses, a plano-convex lens somewhat larger than a hemisphere and a large bi-convex lens serving as a collecting lens to the first.

Uyeda, N., Hang, P.T. and Brindley, G.W. (1973) The nature of garnierites – II Electron-optical study. Clays and Clay Minerals, 21, 41-50. The main difference between the serpentine-like and talc-like variants of garnierite is the spacing between layers in the structure, seen in x-ray powder diffraction studies. The serpentine-like variants have 7 Å basal spacings while the talc-like variants have a basal spacing of 10 Å. At 106X magnifications, the 7 and 10 Å layer spacings (d(001)) are obvious and measureable, with the 7 Å spacings being better defined than the 10 Å spacings.

Sheet film is, simply enough, big, and as such has a proportionately great ability to hold information. The image on an 8x10 inch piece of sheet film has approximately fifty six times the surface area of a standard 35mm image. As compared to megapixels, when taking the LP/mm resolution of 8x10 Velvia the resolution is up to a value of 5,285 megapixels. (Lines per mm x2)^2 x area=megapixels In theory, the "enlargability" of such an image is proportionately great although the very high image quality of small format lenses sometimes allows somewhat greater magnifications than some large format lenses.

Another ion source seen in commercially available instruments is a helium ion source, which is inherently less damaging to the sample than Ga ions although it will still sputter small amounts of material especially at high magnifications and long scan times. As helium ions can be focused into a small probe size and provide a much smaller sample interaction than high energy (>1 kV) electrons in the SEM, the He ion microscope can generate equal or higher resolution images with good material contrast and a higher depth of focus. Commercial instruments are capable of sub 1 nm resolution.

Telescopic sights are favored for obvious reasons – it is impossible to see the kill zone of the furthest targets clearly with the naked eye. Another advantage of high-magnification scopes is their ability to act as a simple range-finding tool. At very high magnifications, most scopes have a very shallow depth of field, and one can accurately focus on a series of targets at known distances and mark the scope for future reference. In competition you simply focus on the target and deduce the distance from the marks you made on the scope's focus control.

The clusters are both distinct from the surrounding star field and are clearly concentrated at their centers. The constituent stars, numbering over 100 in each cluster, range widely in brightness.Levy, 2005, p. 86 M34 is an open cluster that appears at magnitude 5.5, and is approximately 1,500 light-years from Earth. It contains about 100 stars scattered over a field of view larger than that of the full moon. M34 can be resolved with good eyesight but is best viewed using a telescope at low magnifications. IC 348 is a somewhat young open cluster that is still contained within the nebula from which its stars formed.

This allows for a much wider field of view and greater eye relief, but the image for the viewer is inverted. Considerably higher magnifications can be reached with this design, but to overcome aberrations the simple objective lens needs to have a very high f-ratio (Johannes Hevelius built one with a focal length, and even longer tubeless "aerial telescopes" were constructed). The design also allows for use of a micrometer at the focal plane (to determine the angular size and/or distance between objects observed). Huygens built an aerial telescope for Royal Society of London with a 19 cm (7.5″) single-element lens.

The shutter release is redesigned with two distinct levels of pressure: the first detent locks the exposure reading, the second fires the shutter. The M7 is also the first Leica M series to support film DX encoding and exposure compensation using the dial that has been on the back of Leica cameras since the M3. Originally used simply as a reminder of the sensitivity of the film, and then as film speed setting coupled to the light meter starting with the M6, the dial now controls exposure compensation on the M7. The M7 offers viewfinders with magnifications 0.58, 0.72 (28 mm) and 0.85 (35 mm).

A copyscope is type of refracting telescope that can be made by hand rather than bought in which the objective lens comes from an old photocopy machine, hence the origin of the name. The lenses usually come from defective or old photocopiers, allowing for the objective to be obtained for free or at a low cost. They are usually modest diameter lenses, ranging from 50mm to 60mm, of short focal length, good for use in a portable, wide-field telescope, but unsuitable for higher magnifications. Given the use of good components, however, a copyscope can become a rich-field instrument capable of reaching many extended objects and even star fields.

Etch Pits formed on the ends of dislocations in silicon, orientation (111) Field ion microscopy and atom probe techniques offer methods of producing much higher magnifications (typically 3 million times and above) and permit the observation of dislocations at an atomic level. Where surface relief can be resolved to the level of an atomic step, screw dislocations appear as distinctive spiral features – thus revealing an important mechanism of crystal growth: where there is a surface step, atoms can more easily add to the crystal, and the surface step associated with a screw dislocation is never destroyed no matter how many atoms are added to it.

Since the Lewises main interest was microscopic cell structures, their objective was to create optically clear media, which led to the creation of the Locke-Lewis solution. This medium is composed of salt solutions supplemented with bouillon and dextrose. The tissue grown in this medium was prepared in a method that become known as the “Lewis Culture” where the tissue bits were put into a hanging drop on the underside of a thin glass slip. In the Locke-Lewis solution, the more robust cells, such as fibroblasts and macrophages, had a tendency to migrate out of the explant and flatten, making them easy to observe under high magnifications.

Optical microscopy-based techniques involve potting sectioned samples of the laminate, polished using standard metallographic techniques, and obtaining digital cross-sectional photomicrographs using an optical microscope and magnifications between 100 and 2500.Michael T. Cann, Daniel O. Adams and Claudio L. Schneider, Characterization of Fiber Volume Fraction Gradients in Composite Laminates, Journal of Composite Materials, 2008 42: 447 Digital images may be recorded at a number of locations along the length and through-the-thickness of the laminate. Computer programs aid in the analysis of fiber ratio in the photomicrograph of the polished composite specimen. This method is preferred as a non-destructive approach to determining fiber volume fraction.

Practical tip to screen distances may range from several centimeters to several meters, with increased detector area required at larger to subtend the same field of view. Practically speaking, the usable magnification will be limited by several effects, such as lateral vibration of the atoms prior to evaporation. Whilst the magnification of both the field ion and atom probe microscopes is extremely high, the exact magnification is dependent upon conditions specific to the examined specimen, so unlike for conventional electron microscopes, there is often little direct control on magnification, and furthermore, obtained images may have strongly variable magnifications due to fluctuations in the shape of the electric field at the surface.

Steppers increased the possible resolution many times over that of the aligners, and were the first systems to allow features smaller than 1 micron. However, the relentless drive of Moore's law pushed the industry to the point where even the maximum magnifications possible in the projection system were not enough to continue shrinking the feature sizes. This led to the 1990 introduction of the step-and-scan systems, which combine a stepper system with a scanner that images only a portion of the mask at a time. Doing so allows much greater focussing over the tiny part of the mask, although it also makes the IC production process much slower.

An Amici prism is a type of roof prism which splits the image in two parts and thus allows an upright image without left-right mirroring. This means that what is seen in the eyepiece is the same as what is seen when looking at the sky, or a star chart or lunar map. The disadvantage of typical "correct image" Amici roof prism diagonals is that because the light path bounces around through a piece of glass, the total amount of light transmitted is less and the multiple reflections required can introduce optical aberrations. At higher magnifications (> 100x) brighter objects have a bright line through the object viewed.

Phenom electron microscope Phenom is a small, table-top sized scanning electron microscope (SEM) originally developed by Philips and FEI and further developed by Phenom-World. The microscope features a combination of optical and electron-optical images; the optical image enables a "Neverlost" function so operators may navigate to any point on the sample. Sample loading takes place in 4 seconds (to obtain the CMOS overview image) and only 30 seconds into the vacuum space via rapid transfer technology (no conventional load lock). The system user interface is controlled with a touch screen No SEM experience is required for users to achieve magnifications of up to 100,000 times with a resolution of down to 15 nm.

It can be reduced by stopping down, which increases depth of field so that though the different wavelengths focus at different distances, they are still in acceptable focus. Transverse CA does not occur in the center of the image and increases towards the edge. It is not affected by stopping down. In digital sensors, axial CA results in the red and blue planes being defocused (assuming that the green plane is in focus), which is relatively difficult to remedy in post-processing, while transverse CA results in the red, green, and blue planes being at different magnifications (magnification changing along radii, as in geometric distortion), and can be corrected by radially scaling the planes appropriately so they line up.

For the next five years Hope continued to travel widely across Europe, Asia and the Americas. These trips influenced his painting which became more ‘dramatic, vivid and colourful’, he began to paint on a larger scale ‘incorporating monuments, temples and even mythological creatures’Walter Granek (2002), The Art of Laurence Hope, University Of Queensland Art Museum from Cambodia and Mayan civilisations. During this time he continued to have a number of major exhibitions including a retrospective at the Holdsworth Galleries in Sydney and the Commonwealth Art Gallery in London. In 1977 his exhibition Opal the Rainbow Gem at the ICA in London featured Cibachrome prints, and acrylic paintings made from them, of the gemstone taken at magnifications of up to x5400 through a microscope.

They are used for various outdoor activities such as birdwatching and other naturalist activities, for hunting and target shooting to verify a marksman's shot placements, for tactical ranging and surveillance, and for any other application that requires more magnification than a pair of binoculars, typically on the order of 20× to 60×. The light-gathering power and resolution of a spotting scope is determined by the diameter of the objective lens, typically between . The larger the objective, the more massive and expensive the telescope. The optical assembly has a small refracting objective lens, an image erecting system that uses either image erecting relay lenses or prisms (Porro prisms or roof prisms), and an eyepiece that is usually removable and interchangeable to give different magnifications.

The method is destructive in nature removing ions from a sample surface in order to image and identify them, generating magnifications sufficient to observe individual atoms as they are removed from the sample surface. Through coupling of this magnification method with time of flight mass spectrometry, ions evaporated by application of electric pulses can have their mass-to-charge ratio computed. Through successive evaporation of material, layers of atoms are removed from a specimen, allowing for probing not only of the surface, but also through the material itself. Computer methods are used to rebuild a three-dimensional view of the sample, prior to it being evaporated, providing atomic scale information on the structure of a sample, as well as providing the type atomic species information.

Unlike the techniques presented in the last section in which probe size can be relatively large compared to island size, surface microscopies such scanning electron microscopy (SEM), transmission electron microscopy (TEM), scanning tunneling microscopy (STM), and Atomic force microscopy (AFM) offer the opportunity for direct viewing of deposit/substrate combination events. The extreme magnifications afforded by these techniques, often down to the nanometer length scale, make them particularly applicable for visualizing the strongly 3D islands. UHV-SEM and TEM are routinely used to image island formation during SK growth, enabling a wide range of information to be gathered, ranging from island densities to equilibrium shapes. AFM and STM have become increasingly utilized to correlate island geometry to the surface morphology of the surrounding substrate and wetting layer.

However the magnification achievable was lower than with light microscopy. Magnifications higher than those available with a light microscope were achieved in September 1933 with images of cotton fibers quickly acquired before being damaged by the electron beam. At this time, interest in the electron microscope had increased, with other groups, such as that of Paul Anderson and Kenneth Fitzsimmons of Washington State University and that of Albert Prebus and James Hillier at the University of Toronto, who constructed the first TEMs in North America in 1935 and 1938, respectively, continually advancing TEM design. Research continued on the electron microscope at Siemens in 1936, where the aim of the research was the development and improvement of TEM imaging properties, particularly with regard to biological specimens.

This technique, as described below, is derived using the paraxial approximation, which requires that all ray directions (directions normal to the wavefronts) are at small angles θ relative to the optical axis of the system, such that the approximation \sin \theta \approx \theta remains valid. A small θ further implies that the transverse extent of the ray bundles (x and y) is small compared to the length of the optical system (thus "paraxial"). Since a decent imaging system where this is not the case for all rays must still focus the paraxial rays correctly, this matrix method will properly describe the positions of focal planes and magnifications, however aberrations still need to be evaluated using full ray-tracing techniques.Extension of matrix methods to tracing (non-paraxial) meridional rays is included here.

A TEM stage is required to have the ability to hold a specimen and be manipulated to bring the region of interest into the path of the electron beam. As the TEM can operate over a wide range of magnifications, the stage must simultaneously be highly resistant to mechanical drift, with drift requirements as low as a few nm/minute while being able to move several μm/minute, with repositioning accuracy on the order of nanometers. Earlier designs of TEM accomplished this with a complex set of mechanical downgearing devices, allowing the operator to finely control the motion of the stage by several rotating rods. Modern devices may use electrical stage designs, using screw gearing in concert with stepper motors, providing the operator with a computer-based stage input, such as a joystick or trackball.

The spatial variation in this information (the "image") may be viewed by projecting the magnified electron image onto a fluorescent viewing screen coated with a phosphor or scintillator material such as zinc sulfide. Alternatively, the image can be photographically recorded by exposing a photographic film or plate directly to the electron beam, or a high-resolution phosphor may be coupled by means of a lens optical system or a fibre optic light-guide to the sensor of a digital camera. The image detected by the digital camera may be displayed on a monitor or computer. The resolution of TEMs is limited primarily by spherical aberration, but a new generation of hardware correctors can reduce spherical aberration to increase the resolution in high-resolution transmission electron microscopy (HRTEM) to below 0.5 angstrom (50 picometres), enabling magnifications above 50 million times.

Butterfly wing at different magnifications reveals microstructured chitin acting as a diffraction grating A number of fixed structures can create structural colours, by mechanisms including diffraction gratings, selective mirrors, photonic crystals, crystal fibres and deformed matrices. Structures can be far more elaborate than a single thin film: films can be stacked up to give strong iridescence, to combine two colours, or to balance out the inevitable change of colour with angle to give a more diffuse, less iridescent effect. Each mechanism offers a specific solution to the problem of creating a bright colour or combination of colours visible from different directions. Drawing of 'firtree' micro-structures in Morpho butterfly wing scale A diffraction grating constructed of layers of chitin and air gives rise to the iridescent colours of various butterfly wing scales as well as to the tail feathers of birds such as the peacock.

The M24 originally came tapped for the Leupold Ultra M3A 10×42mm fixed-power scope, which came with a circle- shaped mil-dot glass-etched reticle. This was later replaced in 1998 by the Leupold Mk 4 LR/T M1 10×40mm fixed-power scope with an elongated-shaped mil- dot wire reticle. The first number is the scope's magnification (10) and the second number in millimeters (40mm) is the diameter of the objective lens. A fixed power scope has only one magnification (e.g., 10×) and a variable power scope can be adjusted to focus between a range of magnifications (e.g., 3–9× is adjustable from a minimum power of 3× to a maximum power of 9×). The rifle itself comes with a detachable Harris 9–13" 1A2-LM or Harris 9–13" 1A2-L bipod unit. The M24 SWS was to be replaced with the M110 Semi-Automatic Sniper System, a contract awarded to Knight's Armament Company.

Naegamvala's work included observations of nebulae, solar flash spectrum, and the transit of Mercury on 9 May 1891. His independently organised, and conducted, expedition to Jeur, in western India, to observe the solar chromosphere and corona, during the 1898 eclipse, broke a psychological barrier to the entry of Indian scientists to the study of astronomy. His observations were published in several scientific journals; one paper in The Astrophysical Journal, 5 in Monthly Notices of the Royal Astronomical Society, and two in The Observatory. His spectroscopic observations of the Orion Nebula, using several spectroscopes and the 16½-inch Grubb telescope at several magnifications, showed that its green nebular line is sharp, symmetrical, and narrow, and not "fluted", thus refuting Norman Lockyer's "meteoric hypothesis" of the nebulae, according to which the spectrographic lines arise from the collisional heat of the meteoric particles, and require the nebular line to be fluted (extended or shaded like molecular bands–the likely molecular band at this wavelength being that of MgO).

A. nidulans laboratory strain; a similar strain with a mutation in the yA marker gene involved in green pigmentation; an A. oryzae strain used in soy fermentation; A. oryzae RIB40 A scan of Aspergillus taken at 235 magnifications under a scanning electron microscope A. nidulans (Emericella nidulans) has been used as a research organism for many years and was used by Guido Pontecorvo to demonstrate parasexuality in fungi. Recently, A. nidulans was one of the pioneering organisms to have its genome sequenced by researchers at the Broad Institute. As of 2008, a further seven Aspergillus species have had their genomes sequenced: the industrially useful A. niger (two strains), A. oryzae, and A. terreus, and the pathogens A. clavatus, A. fischerianus (Neosartorya fischeri), A. flavus, and A. fumigatus (two strains). A. fischerianus is hardly ever pathogenic, but is very closely related to the common pathogen A. fumigatus; it was sequenced in part to better understand A. fumigatus pathogenicity.

At the same time, he also found the popular European scopes on the market were missing the right features needed for his night hunting applications such as parallax adjustment and high magnifications, and the American products often had small objective size and very fine reticles and hence lacking in light- gathering power and reticle clarity. When going to the 1986 SHOT Show in New Orleans to try market his spotlights, Dennis found a manufacturer in Japan that can produce scopes designed to his suggested specifications, and ordered a batch of 500 units to be made and sold in the Australian market. The sale was a success, and Dennis decided to establish his own company named Lightforce to sell his products, with the intention to also venture into the US market. The American branch was initially established in Seattle with only two staff members, and primarily focused on marketing spotlighting products as Dennis considered the American optics market was already well-established with little room for a small new competitor like his company.

"A Mathematical Theory of Stochastic Microlensing I. Random Time Delay Functions and Lensing Maps," A. O. Petters, B. Rider, and A. M. Teguia, J. Math Phys., 50, 072503 (2009); astro-ph arXiv:0807.0232v2 "A Mathematical Theory of Stochastic Microlensing II. Random Images, Shear, and the Kac-Rice Formula," A. O. Petters, B. Rider, and A. M. Teguia (2008); astro-ph arXiv:0807.4984 The work forms a concrete framework from which extensions to more general random maps can be made. In two additional papers, he and Aazami found geometric universal magnification invariants of higher- order caustics occurring in lensing and caustics produced by generic general maps up to codimension five."A Universal Magnification Theorem for Higher- Order Caustic Singularities," A. B. Aazami and A. O. Petters, J. Math. Phys. 50, 032501 (2009); astro-ph arXiv:0811.3447v2 "A Universal Magnification Theorem II. Caustics up to Codimension Five," A. B. Aazami and A. O. Petters, 50, 082501 (2009); math-ph arXiv:0904.2236v4 National Science Foundation, Science360 News Server, April 16, 2009 The invariants hold with a probability of 1 for random lenses and thereby form important consistency checks for research on random image magnifications of sources near stable caustics.