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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 phenomenon in which electromagnetic waves, such as light waves, vibrate in a preferred plane or planes; or the process of confining the vibrations to ...

The quest to overcome chromatic aberration led to the development of Achromatic Lenses in the early 18th century. Famed mathematician and physicist Sir Isaac Newton was among the first to observe and attempt to correct this issue. However, it was not until the late 18th century that notable opticians such as John Dollond made significant progress in designing Achromatic Lenses.

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.

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Aspheric lenses contain at least one surface that is neither cylindrical or spherical and are used to correct spherical aberration while chromatic lenses are used to correct color/chromatic aberrations.

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In the realm of precision optics, achromatic lenses have become indispensable tools, allowing scientists, engineers, and photographers to achieve high-quality imaging and focus correction. These lenses are designed to minimize chromatic aberration, a common optical phenomenon that causes color fringing and reduces image sharpness. Achromatic lenses are widely used in various applications, from astronomical telescopes to high-resolution microscopes, ensuring that light dispersion is effectively corrected. In this article, we will delve into the principles, design, and applications of achromatic lenses, highlighting their vital role in advancing modern optics.

Photography: Achromatic Lenses are employed in high-quality camera lenses to produce sharp and well-defined images, free from chromatic aberrations.

Microscopes: In microscopy, Achromatic Lenses improve the resolution and minimize color distortion, enabling researchers to study minute biological structures with precision.

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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.

A cylindrical lens is a lens with at least one optical surface has the shape of a section of a cylinder. While spherical lenses surfaces are defined from a fix ...

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2013429 — Understanding Microscope Objectives · Achromatic objectives–This objective brings red and blue light to a common focus, and is corrected for ...

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.

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Laser Systems: These lenses are used in laser systems to focus and direct laser beams without compromising their coherence and color purity.

Optical lenses are components that focus or disperse a light beam toward or away from specific targets. Lenses are made from materials that are transparent across specific wavelength ranges depending on the application. Optical lenses can be crafted with various properties such as Plano-Convex or Bi-Convex, which focuses light on a point while Plano-Concave and Double-Concave diverges the light beams.

Achromatic Lenses have revolutionized the field of optics by mitigating the adverse effects of chromatic aberration, making them invaluable tools for achieving precise imaging and focus correction. Their impact can be seen across various domains, from space exploration to medical research. As technology continues to advance, Achromatic Lenses will undoubtedly play an essential role in shaping the future of precision optics and imaging applications.

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.

There are two main types of achromatic lenses: the achromatic doublet and the achromatic triplet. The achromatic doublet consists of two lens elements, while the achromatic triplet utilizes three. The triplet design offers better correction of chromatic aberration and spherical aberration, but it is more challenging to manufacture and align accurately.

Achromatic doublet lenses are focusing components used in laboratory and medical devices to reduce chromatic aberrations from broadband light sources. A doublet is typically composed of two individual lenses with varying levels of dispersion, fused together and shaped so that the chromatic aberration of one is counteracted by another. Firebird accomplishes this by fusing one concave and one convex lens together into a compound assembly.

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

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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.

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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.

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A basic achromatic objective is a refractive objective that consists of just an achromatic lens and a meniscus lens, mounted within appropriate housing. The ...

While Achromatic Lenses significantly reduce chromatic aberration, they are not perfect. In some cases, residual chromatic aberration may remain, especially in lenses designed for broader spectral ranges. Additionally, Achromatic Lenses are sensitive to off-axis aberrations, which can impact image quality in wide-angle applications.

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.

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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Chromatic aberration occurs due to the different wavelengths of light refracting at varying angles when passing through an optical lens. This dispersion leads to color fringing and reduces the sharpness and clarity of the resulting image. Blue light, with its shorter wavelength, is refracted more than red light, which has a longer wavelength. The result is a visible spectrum of colors at the edges of objects, making them appear blurred and distorted.

Telescopes: Achromatic Lenses play a crucial role in astronomical telescopes, allowing astronomers to observe celestial objects with enhanced clarity and color fidelity.

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.

Achromatic lenses are constructed using a combination of two or more lens elements made from different types of glass. Typically, a positive lens made from a crown glass and a negative lens made from a flint glass are combined to form an achromatic lens pair. The crown glass element has a lower refractive index, while the flint glass element has a higher dispersion rate. By carefully selecting the curvature and thickness of these elements, the lens designer can precisely cancel out the chromatic aberration at a specific wavelength or over a broad spectrum, depending on the application.

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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.