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Finally, n in the formula indicates not only that we are dealing with multiples of the wavelength but also the order of the minimum or maximum. When n = 1, the resulting angle of incidence is the angle of the first minimum or maximum, while n = 2 is the second one and so on until we obtain an impossible statement like sin θ must be greater than 1.

Figure 3: The input parameters in Figure 2 create a collimated output beam with a waist located a distance one focal length (50 mm) from the lens. Note that this figure's scale is larger than the scale in Figure 2. Close to the beam waist (<>zR'), the beam's divergence can be described by a full divergence angle (). A wavelength of 632.8 nm was assumed.

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The third case presents a complex pattern. Here, the wave front corresponding with the first crest (red line) is divided into three parts and features two minimums. The next wave front (blue line) has one minimum, and after that, we again see the difference between crests and troughs, even if they’re bent.

Collimated Lamp or LED LightAn ideal point source emits light uniformly in all directions, and a positive spherical lens placed one focal length (f ) away collimates the light it collects into a beam with zero divergence. This ideal model can be adapted for use with a broadband-wavelength source, like a lamp or LED. Physical sources like these resemble groupings of multiple point sources. An adapted model for these sources takes into account the diameter (d ) of the physical light source, as well as the distance (i.e. the focal length) between the light source and the lens. The ratio of these values provides an estimate of the full divergence angle (θ ),

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Unlike LEDs and lamps, laser sources do not emit light uniformly in all directions, although the laser light's divergence can be large. If the light comes from a single-wavelength laser, there's a good chance its intensity cross section resembles a Gaussian function. The collimated beam's behavior can then be described using Gaussian beam equations, and the equations describing beam divergence would need to include the wavelength.

There are similarities between point source model adaptations for lasers and broadband sources. For example, laser sources should also be placed one focal length away from the lens to minimize the divergence of the collimated beam. In addition, the smaller the laser source (input beam waist diameter), the lower the collimated beam's divergence.

Some applications specify a distance <

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If we increase the wavelength of the wave, the difference between maximums and minimums is no longer evident. What happens is that the waves interfere with each other destructively according to the width d of the slit and the wavelength λ. We use the following formula to determine where the destructive interference occurs:

We have a planar wave propagating towards an aperture. Right after the middle of that aperture, what do we expect to find?

in which () is the wavelength. When the input beam's waist and Rayleigh range are smaller, the collimated output beam has a lower divergence. (See Figures 2 and 3 for an example.) The divergence along the entire collimated beam can be reduced by shrinking the input source beam's waist diameter.

of the collimated beam. The better the physical source resembles a single ideal point source, the lower the divergence angle of the collimated beam (Figure 1). The resemblance is closer when the physical source is very small, far away from the lens, or both.

Collimation definition in radiography

In comparison to the wavelength, what should be the width of an obstacle in order for the wave to be disrupted but the wave front to remain unbroken?

In Figure 1, light emitted from each point on the source fills the lens' clear aperture. Rays traced from different points on the source show the output beam's diameter is smallest at the lens, and the beam appears to diverge from the clear aperture of the lens. If light from each point on the source filled only a fraction of the lens' clear aperture, the beam waist would be displaced from the lens.

The dimension of the aperture affects its interaction with the wave. In the centre of the aperture, when its length d is greater than the wavelength λ, part of the wave passes through unaltered, creating a maximum beyond it.

Figure 1: If a broadband-wavelength source, like a lamp or LED, is placed one focal length (f ) away from a lens, light from each point on the source is individually collimated. The full divergence angle (θ ~ d / f ) of the output beam depends on the focal length and source diameter (d ).

When a wave propagates across an object, there is an interaction between the two. An example is a calm breeze moving the water around a rock that cuts through the surface of a lake. In these conditions, parallel waves are formed where there is nothing to block them, while right behind the rock, the shape of the waves becomes irregular. The bigger the rock, the bigger the irregularity.

Ideally, collimated light would have a constant diameter from the lens out to infinity, but no physical collimated beam maintains exactly the same diameter as it propagates. The collimated beam's divergence, which is the rate at which the beam's diameter changes, depends on the properties of both the light source and the collimator. Due to this, the collimated beam from a broadband-wavelength source, such as a lamp or light emitting diode (LED), behaves differently than the collimated beam from a narrowband-wavelength source, like a laser.

Figure 4: The input laser light better resembles a point source when it has a smaller beam waist (Wo), and therefore a shorter input Rayleigh range (zR). The collimated output beam has a Rayleigh range (zR') that depends on Wo , focal length, and wavelength. Increasing the focal length, or decreasing the wavelength, increases zR' and decreases the overall output beam divergence. The values plotted above were calculated for a 632.8 nm wavelength and a focal length of 50 mm. For comparison, values for a wavelength of 1550 nm and a focal length of 25 mm have also been calculated.

Keeping the same example but exchanging the rock for an open gate, we experience the same behaviour. The wave forms parallel lines before the obstacle but irregular ones while passing through and beyond the gate’s opening. The irregularities are caused by the gate’s edges.

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Collimated Laser LightThe laser source's size helps determine the properties of the collimated beam. Size is typically referenced to the beam waist radius (Wo ) or diameter (2Wo ), often through its Rayleigh range (zR),

A Lamp or LED as a Good-Enough Point SourceA physical source adequately resembles an ideal point source when the divergence of the collimated output beam meets the application's requirements. If the divergence is too large, one option is to increase the focal length of the collimating lens, so the source can be moved farther away. However, this can have the negative effect of reducing the amount of light collected by the lens and output in the collimated beam.

Far from the output beam waist (>>zR'), the beam divergence is comparatively larger. The divergence in this region is reduced when the output beam waist diameter (and Rayleigh range) are increased. Here, the beam has an approximately constant full divergence angle,

We have a planar wave propagating towards an aperture. Right after the middle of that aperture, what do we expect to find?

Near the waist, the output beam best resembles an ideally collimated beam. In this region, the beam divergence is lowest, and the beam diameter stays close to the output beam waist diameter (2W'o ). But, since the beam diameter increases with distance from the waist, the extent over which the beam is considered collimated is limited. The application determines the limit, which is typically referenced to the output beam's Rayleigh range (zR'),

Our first example of diffraction was a rock in the water, i.e., an object in the way of the wave. This is the inverse of an aperture, but as there are borders that cause diffraction, let’s explore this, too. While in the case of an aperture, the wave can propagate, creating a maximum just after the aperture, an object ‘breaks’ the wave front, causing a minimum immediately after the obstacle.

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Here, n = 0, 1, 2 is used to indicate the integer multiples of the wavelength. We can read it as n times the wavelength, and this quantity is equal to the length of the aperture multiplied by the sine of the angle of incidence θ, in this case, π/2. We, therefore, have constructive interference, which produces a maximum (the brighter parts in the image) at those points that are multiples of half the wavelength. We express this with the following equation:

In comparison to the wavelength, what should be the width of an obstacle in order for the wave to be disrupted but the wave front to remain unbroken?

If the source waist is one focal length away from the lens, the collimated beam's waist is located one focal length away from the lens' opposite side. The beam's divergence increases with distance from the waist, and generalizations about the beam divergence can be made for regions close to and far from the waist.

We have a planar wave propagating towards an aperture. Right after the middle of that aperture, what do we expect to find?

Collimatedlaser meaning

The wave is disrupted by the smallest obstacle but not enough to break the wave front. This is because the width of the obstacle is small compared to the wavelength.

A bigger obstacle, whose width is similar to the wavelength, causes a single minimum right after it (red circle, 2nd image from the left), which indicates that the wave front has been broken.

It is evident that the obstacle causes a misalignment of the wave front. Above the yellow line, there are two little crests that are unexpected and caused by the bending of the wave. This misalignment is observed in the sudden maximums after the obstacle has a phase shift.

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In comparison to the wavelength, what should be the width of an obstacle in order for the wave to be disrupted but the wave front to remain unbroken?

Laser Point SourcesThe point source model can also be adapted for laser light, but in this case the source is defined as the input beam waist. The source size is the waist diameter (2Wo ). Typical sources include a focal spot, an optical fiber's end face, and the facet of a single-mode laser diode.

In comparison to the wavelength, what should be the width of an obstacle in order for the wave to be disrupted but the wave front to remain unbroken?

Figure 2: A 632.8 nm laser source, which has a 5 µm diameter waist (Wo) and a 31 µm Rayleigh range (zR), is collimated by a 50 mm focal length (f ) lens.

Diffraction is a phenomenon that affects waves when they encounter an object or an opening along their path of propagation. The way their propagation is affected by the object or the opening depends on the dimensions of the obstacle.