The focused beam waist can be minimized by reducing the focal length of the lens and |s|-f. The terms next to w0 in Equation 17 are defined as another form of the magnification constant α in order to compare the values of the input beam to the output beam after going through the lens (Figure 8).3

The Rayleigh range of a Gaussian beam is defined as the value of z where the cross-sectional area of the beam is doubled. This occurs when w(z) has increased to √2 w0. Using Equation 4, the Rayleigh range (zR) can be expressed as:

A typical magnification for use in dentistry is 2.5×, but dental loupes can be anywhere in the range from 2× to 8×.[15] Optimal magnification is a function of the type of work the doctor does - namely, how much detail he or she needs to see, taking into consideration that when magnification increases, the field of view decreases. As a tool that sits on the face and is used for hours at a time, weight is also a significant factor in considering the type of loupes to use.

Beam widthgymnastics

Where w0 is beam waist before the lens and w0’ is the beam waist after the lens. The thin lens equation for Gaussian beams can then be rewritten to include the Rayleigh range of the beam after the lens (zR'):

The lengthy derivation is not covered in this text, but the beam radius at the target can be described by the following expression4:

Together with proper access to the oral cavity, light is an important part of performing precision dentistry. Because a dentist's head often eclipses the overhead dental lamp, loupes may be fitted with a light source. Loupe-mounted lights used to be fed by fiber optic cables that connected to either a wall-mounted or table-top light source. Newer models feature a more convenient LED lamp within the loupe-mounted light and an electric cord coming from either the conventional wall-mounted or table-top light source or a belt clip rechargeable battery pack. Options for loupe-mounted cameras and video recorders are also available.[16]

Conservators often use hand held loupes or head-mounted binocular magnifiers such as the Optivisor to examine artifacts and documents requiring cleaning or repair.

As |s| approaches either zero or infinity, d⁄df [wL (f )] = 0 when f = L. In both of these cases, the input beam is approximately collimated, and it thereby follows that the smallest beam radius would occur at the focal point of the lens.

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Laserbeamdiameter formula

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). Often, a 10× loupe is used to examine critical sharpness. Photographers using large format cameras may use a loupe to view the ground glass image to aid in focusing. Users of digital single-lens reflex cameras use loupes to help to identify dust and other particles on the sensor, in preparation for sensor cleaning.[citation needed]

Loupes are used in many professions where magnification enables precision work to be done with greater efficiency and ease. Examples include surgery, dentistry, ophthalmology, the jewelry trade, gemology, questioned document examination and watchmaking.[3] Loupes are also sometimes used in photography and printing.

Dental caries, also known as cavities, are most accurately identified by visual and tactile examination of a clean, dry tooth.[9] Magnification enables dentists to improve their ability to differentiate between a stain and a cavity. Cavities are rated and scored based on their visual presentation.[10] If magnification is too high diagnosis becomes difficult due to the small field of view. Ideal magnification for diagnostic purposes is up to 2×.[11][12] Treatment of dental caries, periodontal disease, and pulpal disease are all aided by magnification.

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Ergonomics have long been a pain point for doctors who need to physically strain, bending over and looking down, to treat their patients. Over time this posture results in discomfort, pain, and even neuromuscular disease.[14] Some modern loupes address this by incorporating refractive prisms which alter the course of the light through the telescopes, so that the dentist can maintain a neutral, upright position with eyes relaxed and looking straight ahead.

The dental specialty of endodontics has performed the vast majority of research regarding magnification in dentistry. Because the identification of accessory canals in addition to the primary pulp canals is essential to complete nonsurgical root canal therapy, magnification provides dentists enhanced visualization to locate and treat more obscured canals.

1/e^2beamdiameter

Counterintuitively, the intensity of a focused beam in a target at a fixed distance (L) away from the lens is not maximized when the waist is located at the target. The intensity on the target is actually maximized when the waist occurs at a location before the target (Figure 10). This phenomenon is known as Gaussian focal shift.

3Dbeamelement stiffness matrix

Loupes are an essential tool in both numismatics, the study of currency, and the related practice of coin collection. Coin collectors frequently employ loupes for better evaluation of the quality of their coins, since identifying surface wear is vital when attempting to classify the grade of a coin. Uncirculated coins (coins without wear) can command a substantial premium over coins with slight wear. This wear cannot always be seen with the naked eye. Numismatists can also employ loupes to identify some counterfeit coins that would pass a naked-eye visual inspection.[citation needed] Loupes are similarly used for evaluating other collectable objects, such as trading cards and antiques.

Treatment of periodontal disease is achieved by removing calculus deposits, plaque and therefore bacteria which causes inflammation and subsequently bone destruction. In severe cases, surgery to reduce pocket depth is indicated. Periodontists and hygienists must visualize plaque and calculus to remove it. Magnification can assist dentists and hygienists with identification and removal of plaque and calculus in addition to improving visualization for periodontal surgery.[13]

The wavefront of the laser is planar at the beam waist and approaches that shape again as the distance from the beam waist region increases. This occurs because the radius of curvature of the wavefront begins to approach infinity. The radius of curvature of the wavefront decreases from infinity at the beam waist to a minimum value at the Rayleigh range, and then returns to infinity when it is far away from the laser (Figure 3); this is true for both sides of the beam waist.3

1/e2beamdiameter calculator

In lower price ranges you'll be looking at infrared cameras/monoculars and mostly be limited to the range of the infrared lights they come with.

However, this irradiance profile does not stay constant as the beam propagates through space, hence the dependence of w(z) on z. Due to diffraction, a Gaussian beam will converge and diverge from an area called the beam waist (w0), which is where the beam diameter reaches a minimum value. The beam converges and diverges equally on both sides of the beam waist by the divergence angle θ (Figure 2). The beam waist and divergence angle are both measured from the axis and their relationship can be seen in Equation 2 and Equation 32:

The other limiting situation where the lens is far outside of the Rayleigh range and s >> zR, simplifying Equation 18 to:

Beam widthformula

In the above equations, λ is the wavelength of the laser and θ is a far field approximation. Therefore, θ does not accurately represent the divergence of the beam near the beam waist, but it becomes more accurate as the distance away from the beam waist increases. As seen in Equation 3, a small beam waist results in a larger divergence angle, while a large beam waist results in a smaller divergence angle (or a more collimated beam). This explains why laser beam expanders can reduce beam divergence by increasing beam diameter.

The total distance from the laser to the focused spot is calculated by adding the absolute value of s to s’. Equation 9 can also be written in a dimensionless form by multiplying both sides by f:

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In Equation 7, s’ is the distance from the lens to the image, s is the distance from the lens to the object, and f is the focal length of the lens. If the object and image are at opposite sides of the lens, s is a negative value and s’ is a positive value. This equation ignores the thickness of a real lens and is therefore only a simple approximation of real behavior (Figure 4). The thin lens equation can also be written in a dimensionless form by multiplying both sides of the equation by f:

Loupes are employed to assist watchmakers in assembling mechanical watches. Many aspects require the use of the loupe, in particular the assembly of the watch mechanism itself, the assembly and details of the watch dial, as well as the formation of the watch strap and installation of precious stones onto the watch face.

Laserbeam width

A plot of the normalized image distance (s’/f) versus the normalized object distance (s/f) shows the possible output waist locations at a given normalized Rayleigh range (zR/f) (Figure 6). This plot shows that Gaussian beams focused through a lens have a few key differences when compared to conventional thin lens imaging. Gaussian beam imaging has both minimum and maximum possible image distances, while conventional thin lens imaging does not. The maximum image distance of a refocused Gaussian beam occurs at an object distance of -(f + zR), as opposed to –f. The point on the plot where s/f is equal to -1 and s’/f is equal to 1 indicates that the output waist will be at the back focal point of the lens if the input is at the front focal point of a positive lens.

After multiplying both sides by the denominator from the left side of the equation and then multiplying both sides by (w0')2, Equation 14 becomes:

In order to understand the beam waist and Rayleigh range after the beam travels through the lens, it is necessary to know the magnification of the system (α), given by:

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Beamdiameter calculator

There are two limiting cases which further simplify the calculations of the output beam waist size and location: when s is much less than zR or much greater than zR.3 When the lens is well within the laser’s Rayleigh range, then s << zR and (|s| − f)2 < zR2. Equation 18 simplifies to:

In many laser optics applications, the laser beam is assumed to be Gaussian with an irradiance profile that follows an ideal Gaussian distribution. All actual laser beams will have some deviation from ideal Gaussian behavior. The M2 factor, also known as the beam quality factor, compares the performance of a real laser beam with that of a diffraction-limited Gaussian beam.1 Gaussian irradiance profiles are symmetric around the center of the beam and decrease as the distance from the center of the beam perpendicular to the direction of propagation increases (Figure 1). This distribution is described by Equation 12:

Similarly to when s << zR, the calculations for the output beam waist, divergence, Rayleigh range, and beam waist location are also simplified:

In many applications, such as laser materials processing or surgery, it is highly important to focus a laser beam down to the smallest spot possible to maximize intensity and minimize the heated area. In cases such as these, the goal is to minimize w0' (Figure 7). A modified version of Equation 13 may be used to identify how to minimize the output beam waist3:

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Many laser optics systems require manipulation of a laser beam as opposed to simply using the “raw” beam. This may be done using optical components such as lenses, mirrors, prisms, etc. Below is a guide to some of the most common manipulations of Gaussian beams.

The above equation will break down if the lens is at the beam waist (s=0). The inverse of the squared magnification constant can be used to relate the beam waist sizes and locations3:

This equation approaches the standard thin lens equation as zR/f approaches 0, allowing the standard thin lens equation to be used for lenses with a long focal length. Equations 9 and 10 can be used to find the location of the beam waist after being imaged through the lens (Figure 5).

Surgeons in many specialties commonly use loupes when doing surgery on delicate structures. The loupes used by surgeons are mounted in the lenses of glasses and are custom made for the individual surgeon, taking into account their corrected vision, interpupillary distance and desired focal distance. Multiple magnification powers are available. They are most commonly used in otolaryngology, neurosurgery, ophthalmology, plastic surgery, cardiac surgery, orthopedic surgery, and vascular surgery.

Differentiating Equation 34 with respect to the focal length of the focusing lens (f) and solving for f when d⁄df [wL (f )] = 0 reveals the lens focal length resulting in the minimum beam radius, and therefore highest intensity, at the target.

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A loupe (/ˈluːp/ LOOP) is a simple, small magnification device used to see small details more closely.[1] They generally have higher magnification than a magnifying glass, and are designed to be held or worn close to the eye. A loupe does not have an attached handle, and its focusing lens(es) are contained in an opaque cylinder or cone. On some loupes this cylinder folds into an enclosing housing that protects the lenses when not in use.

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Achieving a truly collimated beam where the divergence is 0 is not possible, but achieving an approximately collimated beam by either minimizing the divergence or maximizing the distance between the point of observation and the nearest beam waist is possible. Since the output divergence is inversely proportional to the magnification constant α, the output divergence reaches a minimum value when |s| = f (Figure 11).

In addition to describing imaging applications, the thin lens equation is applicable to the focusing of a Gaussian beam by treating the waist of the input beam as the object and the waist of the output beam as the image. Gaussian beams remain Gaussian after passing through an ideal lens with no aberrations. In 1983, Sidney Self developed a version of the thin lens equation that took Gaussian propagation into account4:

Dentists, hygienists, and dental therapists typically use binocular loupe glasses since they need both hands free when performing dental procedures. The magnification helps with accurate diagnoses of oral conditions and enhances surgical precision when completing treatment. Additionally, loupes can improve dentists' posture which can decrease occupational strain.[8] Some dental loupes are flip-type, which take the form of two small cylinders, one in front of each lens of the glasses. Other types are inset within the lens of the glasses.

Both of these results intuitively make sense because the beam’s wavefront is approximately planar both at and very far away from the beam waist. At these locations, the beam is almost perfectly collimated (Figure 9). According to the standard thin lens equation, a collimated input would have an image distance equal to the focal length of the lens.

Jewellers typically use a monocular, handheld loupe to magnify gemstones and other jewelry that they wish to inspect.[4] A 10× magnification is good to use for inspecting jewelry and hallmarks[4] 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 and field of view become too small to be instructive.[5] The accepted standard for grading diamonds is therefore that inclusions and blemishes visible at 10× impact the clarity grade.[6] The inclusions in VVS diamonds are hard to find even at 10×.[7]

In Equation 1, I0 is the peak irradiance at the center of the beam, r is the radial distance away from the axis, w(z) is the radius of the laser beam where the irradiance is 1/e2 (13.5%) of I0, z is the distance propagated from the plane where the wavefront is flat, and P is the total power of the beam.