The behavior of the field of a Gaussian beam as it propagates is described by a few parameters such as the spot size, the radius of curvature, and the Gouy phase.

For a Gaussian beam propagating in free space, the spot size ( radius ) w ( z ) will be at a minimum value w < sub > 0 </ sub > at one place along the beam axis, known as the beam waist.

Because the divergence is inversely proportional to the spot size, a Gaussian beam that is focused to a small spot spreads out rapidly as it propagates away from that spot.

For a Gaussian beam, the BPP is the product of the beam's divergence and waist size.

Information about the spot size and radius of curvature of a Gaussian beam can be encoded in the complex beam parameter,:

The NA of a Gaussian laser beam is then related to its minimum spot size by

where ρ = 2r < sup > 2 </ sup >/ w < sup > 2 </ sup >, and L < sub > p </ sub >< sup > l </ sup > is the associated Laguerre polynomial of order p and index l. w is the spot size of the mode corresponding to the Gaussian beam radius.

The overall size of the mode is determined by the Gaussian beam radius w, and this may increase or decrease with the propagation of the beam, however the modes preserve their general shape during propagation.

where,,, and are the waist, spot size, radius of curvature, and Gouy phase shift as given for a Gaussian beam ; is a normalization constant ; and is the k < sup > th </ sup > physicist's Hermite polynomial.

The probability density function of having an error of a given size can be modelled by a Gaussian function ; the mean value will be the relative sent value, and its variance will be given by:

When we have generated enough of these relations ( it's generally sufficient that the number of relations be a few more than the size of P ), we can use the methods of linear algebra ( for example, Gaussian elimination ) to multiply together these various relations in such a way that the exponents of the primes on the right-hand side are all even:

Gaussian blurring is commonly used when reducing the size of an image.

Oversize solids in the fluid are retained, but the separation is not complete ; solids will be contaminated with some fluid and filtrate will contain fine particles ( depending on the pore size and filter thickness ).

* A parametric equaliser is an audio filter that allows the frequency of maximum cut or boost to be set by one control, and the size of the cut or boost by another.

* 120 nm — greatest particle size that can fit through a ULPA filter

* 300 nm — greatest particle size that can fit through a HEPA ( High Efficiency Particulate Air ) filter ( N100 removes up to 99. 97 % at 0. 3 micrometres, N95 removes up to 95 % at 0. 3 micrometres )

When the area of the sampling spot ( the size of the pixel sensor ) is not large enough to provide sufficient spatial anti-aliasing, a separate anti-aliasing filter ( optical low-pass filter ) is typically included in a camera system to further blur the optical image.

Despite its size, the whale shark feeds only on plankton, squid, and small fish by filter feeding.

Other factors impact a sensor's resolution, including sensor size, lens quality, and the organization of the pixels ( for example, a monochrome camera without a Bayer filter mosaic has a higher resolution than a typical color camera ).

Filter performance depends on the size of the particle or fiber, the filter packing density and depth and also the air flow rate.

In comparison, drip or filter coffee was estimated to have a median caffeine content of 110 mg, with a median concentration of 620 µl / ml for the same cup size.

The EDID includes manufacturer name and serial number, product type, phosphor or filter type, timings supported by the display, display size, luminance data and ( for digital displays only ) pixel mapping data.

For a filter to be compatible with a coffee maker, the filter needs to be a specific shape and size.

Other widgets may be unique for a particular tool, such as edge controls to change the cone of a spotlight, points and handles to define the position and tangent vector for a spline control point, circles of variable size to define a blur filter width or paintbrush size, IK targets for hands and feet, or color wheels and swatches for quickly choosing colors.

Commonly filter with pore size 0. 2 µm ( microfiltration ) will effectively remove microorganisms.

Of the species, James ' flamingo has the finest filter feeding apparatus and it well adapted to eating small particles compared to its body size.

The first versions of Final Cut Pro and Final Cut Express used a binary file which contained all montage information such as timecode information, clip's in / out-points, size / crop / position, composition nesting, filter settings, automation data, etc.

The cameras have equal numbers of photodiodes, and produce similar RAW data file sizes, but the Bayer filter camera produces a larger native file size via demosaicing.

The 14-MP Foveon chip produces 4. 7 MP native-size RGB files ; 14-MP Bayer filter cameras produce a 14 MP native file size by interpolation ( demosaicing ).

Other filter sizes within this range may be hard to find since the filter size may be non-standard or may be rarely used on camera lenses.

Cokin also makes a filter holder for 100 mm filters, which they call the “ Z ” size.

Where larger Northwest adzes are similar in size to their European counterparts, the smaller sizes are typically much lighter such that they can be used for the detailed smoothing, shaping and surface texturing required for figure carving.

Although the size of the smoothing length can be fixed in both space and time, this does not take advantage of the full power of SPH.

It is a formal theory for handling image structures at different scales, by representing an image as a one-parameter family of smoothed images, the scale-space representation, parametrized by the size of the smoothing kernel used for suppressing fine-scale structures.

Or put another way, the hardest missile site planned today could be destroyed by placing a one-kiloton warhead ( 1/20th the size of those used in Hiroshima and Nagasaki ) within 100 to 200 feet of the target!!

When tire size is measured in this manner a constant of 168 is used in the formula.

Close to a large city they might even specify the size of the nails used ; ;

The K factor, a term used to denote the rate of heat transmission through a material ( B.t.u./sq. ft. of material/hr./*0F./in. of thickness ) ranges from 0.24 to 0.28 for flexible urethane foams and from 0.12 to 0.16 for rigid urethane foams, depending upon the formulation, density, cell size, and nature of blowing agents used.

Thru development, the reactor and its steam turbines had been reduced greatly in size, and also in complexity, allowing a single propeller to be used, the navy said.

Its size is determined by its function as a glycogen and fat storage unit, and may change with the seasons as these reserves are built or used up.

The number of carbon atoms is used to define the size of the alkane ( e. g., C < sub > 2 </ sub >- alkane ).

" The small-angle formula can be used to convert such an angular measurement into a distance / size ratio.

The key size used for an AES cipher specifies the number of repetitions of transformation rounds that convert the input, called the plaintext, into the final output, called the ciphertext.

Agate is also still used today for decorative displays, cabochons, beads, carvings and Intarsia art as well as face-polished and tumble-polished specimens of varying size and origin.

It was of similar size, was carried on poles by priests, was not allowed to touch the ground, was revered as a voice of their God, and was used as a weapon of great power, sweeping enemies aside.

Because the original designer had left the company another employee completely redesigned most of the system, ( adding a display snow remover circuit, true 80 / 64 column text mode support, ( with different size letters for TRS-80 and CP / M mode, so that in TRS-80 mode the full screen was also used, not just a 64x16 portion of the 80x25 screen ) with an improved font set ( adding " gray scale " version of the TRS-80 mozaik graphics and many special PETSCII like characters ), and a more flexible and reliable floppy disk controller and keyboard interface plus many other small improvements ), also an enclosure was developed for the main computer system, ( in the form of a 19-inch rack for the Eurocards ) and for two floppy disk drives and the power supply.

However, sometimes they were used in larger units up to squadron size.

Commonly used for storing uncompressed ( PCM ), CD-quality sound files, which means that they can be large in size — around 10 MB per minute.

Applicators of different adhesives are designed according to the adhesive being used and the size of the area to which the adhesive will be applied.

* Autocorrelation is used to analyze Dynamic light scattering data, which notably enables to determine the particle size distributions of nanometer-sized particles or micelles suspended in a fluid.

Also known as the toggle-head spear, it was about the same size as the simple harpoon and used to hunt the same animals, however, this harpoon provided a more efficient and lethal weapon.

The term octet is used to unambiguously specify a size of eight bits, and is used extensively in protocol definitions, for example.

Replacement grips are thicker, and are often used to increase the size of the handle.

Blocks (" records " in IBM's terminology ) of 88, 96, 880 and 960 were often used because they related to the fixed block size of punch cards.

where is the numerical integration step size of the trapezoidal rule used in the bilinear transform derivation.

* Key size, i. e., the size of key used to encrypt a message.