Jul 14, 2008 — The ideas of depth of focus and depth of field both concern the ability of an image-forming device to make sharp images, but under different ...

Aluminium is the cheapest and most common coating, and yields a reflectivity of around 88%-92% over the visible spectrum. Aluminum mirror are also good for UV ...

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Straight Wavefront: Huygens’s principle applied to a straight wavefront. Each point on the wavefront emits a semicircular wavelet that moves a distance s=vt. The new wavefront is a line tangent to the wavelets.

Reflections in Diffraction Patterns: Each dot, called a reflection, in this diffraction pattern forms from the constructive interference of scattered X-rays passing through a crystal. The data can be used to determine the crystalline structure.

Huygens’s Refraction: Huygens’s principle applied to a straight wavefront traveling from one medium to another where its speed is less. The ray bends toward the perpendicular, since the wavelets have a lower speed in the second medium.

\[\mathrm { I } ( \theta ) = \mathrm { I } _ { 0 } \left( \dfrac { \sin ( \pi \mathrm { x } ) } { \pi \mathrm { x } } \right) ^ { 2 }\]

Collimatedflashlight

Let's take an example using numbers from my own laser. I will first pretend there are no collimating optics in the laser, which is not true but will serve as a good example as to why diode lasers without collimating optics are not good for free space setups. From the laser's spec sheet, I know that the \(M^2\) value in the bad direction is 25 and that its waist size, which is probably half the size of the diode in one principle direction, is 107 microns. Using the above equation, I get a value of 56 centimeters, which means that an ideal Gaussian beam with these specs will stay collimated over about half a meter.

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Through our globally recognized Novanta brands in advanced photonics, ARGES, Cambridge Technology, Laser Quantum and Synrad, we deliver tailored laser and beam ...

Single Slit Diffraction – Four Wavelengths: This figure shows single slit diffraction, but the slit is the length of 4 wavelengths.

How to make acollimatedbeam

Jan 6, 2023 — Applications · 1. Optical power meters · 2. LD monitors · 3. Radiation thermometers · 4. Flame monitors (flame detection) · 5. Moisture ...

Just like everything else in science, I have learned a very good lesson from this experience. The laser I decided to purchase is a 800 mW BrixX laser from Omicron. The cost is under $10,000, which I consider to be a pretty good deal for the amount of power it puts out. There is no fiber-coupled version, but all of our lasers are free space anyway so I did not consider this to be a big problem. The beam is astigmatic, which is to be expected from a high power laser diode.

Apr 22, 2021 — Grimaldi gave the name diffraction to this phenomenon. Diffraction refers to the deviation from rectilinear propagation that occurs when waves ...

This effect can be seen with light passing through small apertures or larger apertures. This same effect happens when light passes through our pupils, and this is why the human eye has limited acuity.

However, my real multimode beam will have a Rayleigh range that is smaller than this value by a factor of 25, which is only about 2 centimeters. For this reason, diode laser beams almost always have collimating optics; the beam from the diode itself is highly divergent.

The wave characteristics of light cause the light to pass through the slits and interfere with itself, producing the light and dark areas on the wall behind the slits. The light that appears on the wall behind the slits is scattered and absorbed by the wall, which is a characteristic of a particle.

Typically we define near infrared (NIR) from 780 nm to 1400 nm and shortwave infrared (SWIR) from 1400 nm to 3000 nm. But it is also common to refer to the ...

Diffraction grating has periodic structure that splits and diffracts light into several beams travelling in different directions.

Since each lens produces a magnification that multiplies the height of the image, it is apparent that the overall magnification m is the product of the ...

The Rayleigh range of a Gaussian laser beam should therefore be larger than the characteristic distance of my setup that I identified in the previous step. But what about multimode beams like the one from my laser diode? This is where the concept of an "embedded Gaussian" comes into play. (For more information about this idea, see this tutorial by Tony Siegman.) I can predict the collimated distance by computing the Rayleigh range of an ideal Gaussian beam, and then divide it by the \(M^2\) parameter for the beam.

Collimating lens

Constructive wave interference occurs when waves interfere with each other crest-to-crest (peak-to-peak) or trough-to-trough (valley-to-valley) and the waves are exactly in phase with each other. This amplifies the resultant wave. Destructive wave interference occurs when waves interfere with each other crest-to-trough (peak-to-valley) and are exactly out of phase with each other. This cancels out any wave and results in no light. These concepts are shown in. It should be noted that this example uses a single, monochromatic wavelength, which is not common in real life; a more practical example is shown in.

Christiaan Huygens was a Dutch scientist who developed a useful technique for determining how and where waves propagate. In 1678, he proposed that every point that a luminous disturbance touches becomes itself a source of a spherical wave. The sum of the secondary waves (waves that are a result of the disturbance) determines the form of the new wave. shows secondary waves traveling forward from their point of origin. He was able to come up with an explanation of the linear and spherical wave propagation, and derive the laws of reflection and refraction (covered in previous atoms ) using this principle. He could not, however, explain what is commonly known as diffraction effects. Diffraction effects are the deviations from rectilinear propagation that occurs when light encounters edges, screens and apertures. These effects were explained in 1816 by French physicist Augustin-Jean Fresnel.

So, how can I predict the distance over which my beam can stay collimated to better judge how well it will work for my setup? The first thing to realize is that no beam can stay collimated forever. Real laser beams experience diffraction, which causes them to spread as they propagate. This means that the first thing I should do is to consider the distances spanned by the beam paths. In a microscopy setup, this path will probably not be longer than a couple meters. In mine, it's roughly two meters since I am combining a number of laser beams together and need the extra space.

Young’s Double Slit Experiment: Light is sent through two vertical slits and is diffracted into a pattern of vertical lines spread out horizontally. Without diffraction and interference, the light would simply make two lines on the screen.

Ordinary pressed CD and DVD media are every-day examples of diffraction gratings and can be used to demonstrate the effect by reflecting sunlight off them onto a white wall. (see ). This is a side effect of their manufacture, as one surface of a CD has many small pits in the plastic, arranged in a spiral; that surface has a thin layer of metal applied to make the pits more visible. The structure of a DVD is optically similar, although it may have more than one pitted surface, and all pitted surfaces are inside the disc. In a standard pressed vinyl record when viewed from a low angle perpendicular to the grooves, one can see a similar, but less defined effect to that in a CD/DVD. This is due to viewing angle (less than the critical angle of reflection of the black vinyl) and the path of the light being reflected due to being changed by the grooves, leaving a rainbow relief pattern behind.

Collimate telescope

Why was Young’s experiment so much more credible than Huygens’? Because, while Huygens’ was correct, he could not demonstrate that light acted as a wave, while the double-slit experiment shows this very clearly. Since light has relatively short wavelengths, to show wave effects it must interact with something small — Young’s small, closely spaced slits worked.

The astigmatism is not necessarily a big problem for me, though. What is surprising to me is how difficult it is to keep the beam collimated over large distances, that is, to keep it roughly the same size as it propagates. My application requires a fairly small beam size since the exit pupil of the objective is only 6 millimeters in diameter. With M-squared values direct from the laser of 12 and 25, it is quite difficult to keep the beam collimated for a long enough distance to steer the beam through all the optics and to keep it small enough to prevent overfilling the objective's exit pupil and losing power.

Some bird feathers use natural diffraction grating which produce constructive interference, giving the feathers an iridescent effect. Iridescence is the effect where surfaces seem to change color when the angle of illumination is changed. An opal is another example of diffraction grating that reflects the light into different colors.

In single slit diffraction, the diffraction pattern is determined by the wavelength and by the length of the slit. Figure 1 shows a visualization of this pattern. This is the most simplistic way of using the Huygens-Fresnel Principle, which was covered in a previous atom, and applying it to slit diffraction. But what happens when the slit is NOT the exact (or close to exact) length of a single wave?

The double-slit experiment, also called Young’s experiment, shows that matter and energy can display both wave and particle characteristics. As we discussed in the atom about the Huygens principle, Christiaan Huygens proved in 1628 that light was a wave. But some people disagreed with him, most notably Isaac Newton. Newton felt that color, interference, and diffraction effects needed a better explanation. People did not accept the theory that light was a wave until 1801, when English physicist Thomas Young performed his double-slit experiment. In his experiment, he sent light through two closely spaced vertical slits and observed the resulting pattern on the wall behind them. The pattern that resulted can be seen in.

A slit that is wider than a single wave will produce interference -like effects downstream from the slit. It is easier to understand by thinking of the slit not as a long slit, but as a number of point sources spaced evenly across the width of the slit. This can be seen in Figure 2.

Along with the diffraction effects that we have discussed in previous atoms, diffraction also limits the detail that we can obtain in images. shows three different circumstances of resolution limits due to diffraction:

There is an inverse relationship between lens size and magnification that is due to physics, and there is no way to design around that fact. The larger the ...

The pattern that results from double-slit diffraction is not random, although it may seem that way. Each slit is a different distance from a given point on the wall behind it. For each different distance, a different number of wavelengths fit into that path. The waves all start out in phase (matching crest-to-crest), but depending on the distance of the point on the wall from the slit, they could be in phase at that point and interfere constructively, or they could end up out of phase and interfere with each other destructively.

The intensity (I) of waves at any angle can also be calculated as a relation to slit width, wavelength and intensity of the original waves before passing through the slit:

Reflection: Huygens’s principle applied to a straight wavefront striking a mirror. The wavelets shown were emitted as each point on the wavefront struck the mirror. The tangent to these wavelets shows that the new wavefront has been reflected at an angle equal to the incident angle. The direction of propagation is perpendicular to the wavefront, as shown by the downward-pointing arrows.

This principle is actually something you have seen or experienced often, but just don’t realize. Although this principle applies to all types of waves, it is easier to explain using sound waves, since sound waves have longer wavelengths. If someone is playing music in their room, with the door closed, you might not be able to hear it while walking past the room. However, if that person where to open their door while playing music, you could hear it not only when directly in front of the door opening, but also on a considerable distance down the hall to either side. is a direct effect of diffraction. When light passes through much smaller openings, called slits, Huygens’s principle shows that light bends similar to the way sound does, just on a much smaller scale. We will examine in later atoms single slit diffraction and double slit diffraction, but for now it is just important that we understand the basic concept of diffraction.

Single slit diffraction is the phenomenon that occurs when waves pass through a narrow gap and bend, forming an interference pattern.

Collimatedvs coherent

Collimatedbeam

What I have learned from this is that free-space diode lasers, and more generally multimode laser beams, require extra consideration to ensure that they will stay collimated in long setups.

As we explained in a previous atom, diffraction is defined as the bending of a wave around the edges of an opening or obstacle. Diffraction is a phenomenon all wave types can experience. It is explained by the Huygens-Fresnel Principle, and the principal of superposition of waves. The former states that every point on a wavefront is a source of wavelets. These wavelets spread out in the forward direction, at the same speed as the source wave. The new wavefront is a line tangent to all of the wavelets. The superposition principle states that at any point, the net result of multiple stimuli is the sum of all stimuli.

Rayleigh Criterion: (a) This is a graph of intensity of the diffraction pattern for a circular aperture. Note that, similar to a single slit, the central maximum is wider and brighter than those to the sides. (b) Two point objects produce overlapping diffraction patterns. Shown here is the Rayleigh criterion for being just resolvable. The central maximum of one pattern lies on the first minimum of the other.

The variation in wave intensity can be mathematically modeled. From the center of the slit, the diffracting waves propagate radially. The angle of the minimum intensity (θmin) can be related to wavelength (λ) and the slit’s width (d) such that:

To examine this effect better, lets consider a single monochromatic wavelength. This will produce a wavefront that is all in the same phase. Downstream from the slit, the light at any given point is made up of contributions from each of these point sources. The resulting phase differences are caused by the different in path lengths that the contributing portions of the rays traveled from the slit.

Figure 1 shows a simple example of the Huygens’s Principle of diffraction. The principle can be shown with the equation below:

Laser collimatedbeam

θ – angle the objects are separated by, in radian λ – wavelength of light D – aperture diameter. shows this concept visually. This equation also gives the angular spreading of a source of light having a diameter D.

Readable Surface of a CD: The readable surface of a Compact Disc includes a spiral track wound tightly enough to cause light to diffract into a full visible spectrum.

The fluorescence microscopy setup in my lab requires quite a bit of power. The minimum irradiance requirement is greater than 1 kW per square centimeter, and this must cover an area spanning a few tens of microns across after focusing through the objective. When I was designing the setup, the highest priority was placed on finding a cheap laser with as much power as possible at a wavelength of 647 nm; I considered all other qualities of the laser of secondary importance.

The Rayleigh criterion determines the separation angle between two light sources which are distinguishable from each other.

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Returning to my own setup, if I resize the beam using a telescope to have a waist radius of 2 millimeters so it almost entirely fits inside the objective's exit pupil, the Rayleigh range of the embedded Gaussian beam will be almost 20 meters, which is pretty long. The real beam, however, will have a Rayleigh range of about 780 millimeters meters due to the high \(M^2\) value. Practically, this means I have about one meter of collimated laser beam with which to work since I have double the Rayleigh range of collimated distance, but really I want the beam to travel less distance than this.

X-ray crystallography is a method of determining the atomic and molecular structure of a crystal, in which the crystalline atoms cause a beam of X-rays to diffract into many specific directions. By measuring the angles and intensities of these diffracted beams, a crystallographer can produce a three-dimensional picture of the density of electrons within the crystal. From this electron density, the mean positions of the atoms in the crystal can be determined, as well as their chemical bonds, their disorder and various other information.

Fortunately I can shrink the beam path enough that this should not be a problem, but it does serve as a very good lesson when looking for lasers for a microscopy application.

Practical Constructive and Destructive Wave Interference: Double slits produce two coherent sources of waves that interfere. (a) Light spreads out (diffracts) from each slit because the slits are narrow. These waves overlap and interfere constructively (bright lines) and destructively (dark regions). We can only see this if the light falls onto a screen and is scattered into our eyes. (b) Double-slit interference pattern for water waves are nearly identical to that for light. Wave action is greatest in regions of constructive interference and least in regions of destructive interference. (c) When light that has passed through double slits falls on a screen, we see a pattern such as this.

The double-slit experiment, also called Young’s experiment, shows that matter and energy can display both wave and particle characteristics.

The example in uses two coherent light sources of a single monochromatic wavelength for simplicity. (This means that the light sources were in the same phase. ) The two slits cause the two coherent light sources to interfere with each other either constructively or destructively.

The Huygens-Fresnel principle states that every point on a wavefront is a source of wavelets. These wavelets spread out in the forward direction, at the same speed as the source wave. The new wavefront is a line tangent to all of the wavelets.

As we explained in the previous paragraph, diffraction is defined as the bending of a wave around the edges of an opening or an obstacle.

Collimation radiology

In an X-ray diffraction measurement, a crystal is mounted on a goniometer and gradually rotated while being bombarded with X-rays, producing a diffraction pattern of regularly spaced spots known as reflections (see ). The two-dimensional images taken at different rotations are converted into a three-dimensional model of the density of electrons within the crystal using the mathematical method of Fourier transforms, combined with chemical data known for the sample.

Resolution Limits: (a) Monochromatic light passed through a small circular aperture produces this diffraction pattern. (b) Two point light sources that are close to one another produce overlapping images because of diffraction. (c) If they are closer together, they cannot be resolved or distinguished.

A diffraction grating is an optical component with a periodic structure that splits and diffracts light into several beams travelling in different directions. The directions of these beams depend on the spacing of the grating and the wavelength of the light so that the grating acts as the dispersive element. Because of this, gratings are often used in monochromators, spectrometers, wavelength division multiplexing devices, optical pulse compressing devices, and many other optical instruments.

Single Slit Diffraction – One Wavelength: Visualization of single slit diffraction when the slit is equal to one wavelength.

Once I identify the length scale over which the beam should stay collimated, I need to examine the beam parameter that is best associated with collimation. For a pure Gaussian beam, this parameter is the Rayleigh range. The Rayleigh range is the distance between the beam waist and the point where the cross-sectional area of the beam has doubled, or, equivalently, to the point where the radius of the beam has increased over the waist radius by a factor of the \(\sqrt{2}\). For a pure Gaussian beam with a waist radius of \(w_0\) and a wavelength of \(\lambda\), the Rayleigh range is given by the equation

In the 19th century, Lord Rayleigh invented a criteria for determining when two light sources were distinguishable from each other, or resolved. According to the criteria, two point sources are considered just resolved (just distinguishable enough from each other to recognize two sources) if the center of the diffraction pattern of one is directly overlapped by the first minimum of the diffraction pattern of the other. If the distance is greater between these points, the sources are well resolved (i.e., they are easy to distingiush from each other). If the distance is smaller, they are not resolved (i.e., they cannot be distinguished from each other). The equation to determine this is:

Each point on the wavefront emits a wave at speed, v. The emitted waves are semicircular, and occur at t, time later. The new wavefront is tangent to the wavelets. This principle works for all wave types, not just light waves. The principle is helpful in describing reflection, refraction and interference. shows visually how Huygens’s Principle can be used to explain reflection, and shows how it can be applied to refraction.

It is represented by the symbol \(z_R\) in the figure below from Wikipedia. The total distance over which the beam will stay collimated is represented by \(b\) and is just twice the Rayleigh range.

A photographic slide with a fine pattern of purple lines forms a complex grating. For practical applications, gratings generally have ridges or rulings on their surface rather than dark lines. Such gratings can be either transmissive or reflective. Gratings which modulate the phase rather than the amplitude of the incident light are also produced, frequently using holography.

Theoretical Constructive and Destructive Wave Interference: The amplitudes of waves add together. (a) Pure constructive interference is obtained when identical waves are in phase. (b) Pure destructive interference occurs when identical waves are exactly out of phase (shifted by half a wavelength).