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Collimated beam

A collimated beam is a beam of electromagnetic radiation, such as light, in which all rays are parallel to one another, resulting in minimal divergence and a nearly constant beam diameter over propagation distances.^[1] This property contrasts with diverging or converging beams, where rays spread out or converge, and is fundamentally limited by diffraction effects in real optical systems.^[2] Collimated beams are typically produced using optical elements like lenses or mirrors to transform a point source or diverging beam into parallel rays; for instance, placing a light source at the focal point of a positive lens generates a collimated output, though the exact degree of collimation depends on the source size, focal length, and aperture diffraction.^[1] In laser systems, many outputs are inherently collimated due to the coherent nature of the emission, but additional collimators—such as aspheric lenses for fiber-coupled lasers—are often employed to achieve low divergence and a stable beam radius, characterized by a long Rayleigh length for Gaussian beams.^[3] The beam quality factor M^2 influences the effectiveness, with values near 1 indicating near-ideal collimation limited only by diffraction.^[3] These beams are essential in various optical and physics applications, including metrology for precise measurements, optical processing for image manipulation, and free-space communication for efficient signal propagation without significant loss.^[2] In laboratory setups, collimated beams maintain consistent intensity profiles across components, facilitating experiments in spectroscopy and interferometry.^[3] They also enable laser-based instrumentation, such as in medical imaging where X-ray collimation reduces tissue exposure, and in beam delivery systems for industrial cutting or alignment tools.^[3]

Fundamentals

Definition

A collimated beam is a beam of rays—such as those of light, particles, or other waves—that are parallel to each other and exhibit negligible divergence or convergence during propagation over significant distances.^[3]^[4] This parallelism ensures that the beam maintains its directional integrity, making it distinct from other types of beams in optical and particle physics applications.^[5] Key attributes of a collimated beam include strong directionality along a defined collimation axis, beam divergence approaching zero (typically on the order of milliradians or less), and a uniform intensity profile across the beam's cross-section.^[3]^[6] These properties arise from the beam's approximate plane wavefront, which prevents spreading due to diffraction or geometric factors in ideal conditions, though perfect collimation is theoretically unattainable due to fundamental wave limits.^[5] In contrast to converging (focused) beams that narrow to a point or diverging beams that spread outward, collimated beams preserve their width and parallelism.^[6] For instance, sunlight incident on Earth approximates a collimated beam because of the sun's immense distance, resulting in nearly parallel rays, whereas a typical flashlight produces a diverging beam that expands rapidly over meters.^[7]^[8] The conceptual foundation for collimated beams in optics traces to 17th-century wave theory, as articulated by Christiaan Huygens, who modeled light propagation as secondary wavelets from wavefront points, implying parallel ray behavior for plane waves.^[9]

Etymology

The term "collimated" derives from the Latin verb collimāre, meaning "to aim" or "to direct," which itself arose as a scribal error or corruption of collineāre, signifying "to direct in a straight line" or "to align."^[10] This linguistic evolution reflects the concept of precise alignment, akin to sighting along a straight path, and entered English through scientific contexts in the early 17th century, with the first attested use in 1623 in optical or astronomical writings.^[11] A folk etymology sometimes links collimāre to col- (together or with) and lima (a file or straightedge), evoking the idea of straightening or polishing a beam like filing a surface smooth, though the primary origin remains the misreading of collineāre.^[10] In the scientific lexicon, particularly optics and astronomy, "collimated" gained prominence in the 19th century as a descriptor for parallel rays of light or alignment in instruments. This usage aligned with emerging needs in observational astronomy to describe beams or sights rendered parallel to minimize divergence. The related term "collimator," denoting a device that produces or maintains parallel rays, emerged in the 1800s, with early descriptions in optical instruments around 1839–1840 by figures such as Jacques Babinet and William Simms, who described auxiliary telescopes functioning as collimators in spectroscopes.^[12] By the mid-19th century, "collimator" had become standard in physics and engineering, directly tied to the adjectival "collimated" to specify beams of light exhibiting minimal spread, as in alignment contexts for spectroscopic and telescopic calibration.

Physical Properties

Geometric Characteristics

In geometric optics, a collimated beam is characterized by a bundle of parallel rays that propagate without convergence or divergence, maintaining a consistent direction over propagation distances. This parallelism implies that all rays within the beam travel in the same direction, ensuring minimal spreading and preserving the beam's spatial integrity for applications requiring precise alignment.^[3] The beam cross-section typically exhibits a Gaussian intensity profile across its transverse plane, where the intensity peaks at the center and tapers symmetrically, with no significant expansion over short to moderate distances; for instance, laser beams often follow this distribution.^[13] This profile arises from the aligned ray paths, which keep the beam's diameter approximately constant, facilitating focused delivery of energy or information without distortion.^[14] The collimation axis represents the central reference line along which the parallel rays align, defining the beam's overall orientation and serving as the symmetry axis for the ray bundle in a homogeneous medium. This axis guides the beam's propagation path and is critical for directing the light toward a target with high fidelity.^[3] In theory, an ideal collimated beam achieves perfect parallelism with zero divergence, representing an abstraction in ray optics where rays remain infinitely parallel. However, real-world beams exhibit slight divergence due to inherent diffraction limits imposed by the finite aperture size and wavelength, resulting in gradual beam expansion beyond the Rayleigh length. This practical limitation balances beam quality with achievable collimation, often quantified by the beam parameter product in high-precision systems.^[3]^[15]

Mathematical Description

The mathematical description of a collimated beam relies on the paraxial approximation to the Helmholtz equation, which governs wave propagation in free space. The Helmholtz equation, \nabla^2 E + k^2 E = 0, where E is the electric field and k = 2\pi / \lambda is the wavenumber, is simplified under the paraxial assumption that the beam propagates primarily along the z-direction with small transverse variations and angles \theta \ll 1. This leads to the paraxial wave equation, \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} + 2ik \frac{\partial u}{\partial z} = 0, where u(x, y, z) is the slowly varying envelope of the field E = u e^{ikz}.^[16] In this framework, the collimation condition for rays is that the ray angle \theta remains constant along the propagation direction, satisfying \frac{d\theta}{dz} = 0. This condition arises directly from the paraxial limit, where transverse wavevectors are small compared to the longitudinal one, ensuring minimal spreading and parallel ray trajectories in the ideal case.^[17] For beams approximating Gaussian profiles, which are fundamental solutions to the paraxial wave equation, the divergence angle \theta is quantified as \theta \approx \frac{\lambda}{\pi w_0}, where \lambda is the wavelength and w_0 is the beam waist radius at the narrowest point. This half-angle divergence describes the far-field spreading of the beam intensity to $1/e^2 of its peak value. The beam radius along the propagation distance z is then given by w(z) = w_0 \sqrt{1 + \left(\frac{z}{z_R}\right)^2}, where the Rayleigh range z_R = \frac{\pi w_0^2}{\lambda}. For a well-collimated beam with large w_0 (such that z \ll z_R), w(z) \approx w_0, maintaining a nearly constant radius over significant distances.^[18]^[16] Beyond Gaussian approximations, the fundamental diffraction limit sets the minimum achievable divergence for any beam passing through a circular aperture of diameter D. This limit is \theta_{\min} = 1.22 \frac{\lambda}{D}, corresponding to the angular radius of the first minimum in the Airy diffraction pattern, which defines the smallest resolvable angle in the far field.^[19]

Sources

Laser-Based Sources

Laser-based sources inherently generate collimated beams through the process of stimulated emission, where population inversion in the gain medium produces coherent light that is amplified within an optical cavity. The cavity's feedback mechanism—typically involving high-reflectivity mirrors—selects and reinforces low-divergence modes, ensuring the output beam propagates with minimal spreading. This results in high spatial coherence, which is quantified by the beam quality factor M², approaching 1 for ideal Gaussian beams in many lasers, indicating near-perfect collimation compared to an ideal diffraction-limited source.^[20]^[21] Various types of lasers exhibit this collimation, tailored by their active media and design. Gas lasers, such as the helium-neon (He-Ne) laser operating at 632.8 nm, produce beams with a full-angle divergence of approximately 1.3 mrad, enabling stable propagation over moderate distances without additional optics. Solid-state lasers like the neodymium-doped yttrium aluminum garnet (Nd:YAG) at 1064 nm achieve M² values close to 1 in high-quality configurations, supporting tight focusing and low divergence for industrial applications. Semiconductor diode lasers, however, emit from a small active region, leading to initial high divergence (often tens of degrees in the fast axis); this is typically corrected using aspheric collimating lenses to achieve effective collimation with M² factors near 1 after processing.^[6]^[18]^[22] The primary advantage of laser collimation stems from their high spatial coherence, allowing beams to maintain low divergence over extended distances—potentially kilometers in free space—without requiring external optics, which is essential for applications like long-range sensing and communication. This property arises from the phase-locked emission across the beam aperture, contrasting with incoherent sources that diverge rapidly.^[23] Despite these strengths, limitations exist, particularly in high-power operation where thermal lensing can degrade beam quality. Heat generated in the gain medium creates refractive index gradients, acting as a dynamic lens that introduces wavefront distortions and slight decollimation, increasing the effective M² and divergence in systems exceeding kilowatt levels.^[24]

Synchrotron and Radiation Sources

Synchrotron radiation is generated when relativistic electrons, accelerated to energies typically in the GeV range, are forced to follow curved trajectories in storage rings by strong magnetic fields. These electrons, with Lorentz factors γ often exceeding 10^4, emit electromagnetic radiation as they undergo centripetal acceleration. Due to relativistic effects, the radiation is inherently collimated into a narrow forward cone with an opening angle approximately $1/\gamma, typically on the order of milliradians, resulting in a highly directional beam without additional optical elements.^[25]^[26] The emitted synchrotron radiation exhibits a broadband spectrum spanning from ultraviolet to X-ray wavelengths, providing continuously tunable photon energies across a wide range. This radiation is characterized by exceptionally high intensity, often exceeding 10^12 photons per second per millielectronvolt bandwidth, and low emittance values around 1 nm·rad, which contribute to superior beam quality and brightness compared to conventional sources.^[27]^[28]^[29] Facilities such as the European Synchrotron Radiation Facility (ESRF) in Grenoble and the Advanced Photon Source (APS) at Argonne National Laboratory utilize insertion devices like undulators to further enhance the natural collimation of synchrotron radiation. In undulators, the periodic magnetic field causes electrons to oscillate, producing interference that narrows the beam divergence to microradians, often below 20 μrad, enabling precise focusing for advanced experiments.^[25]^[30] Synchrotron radiation was first observed in the late 1940s during experiments with early electron accelerators, including cyclotrons and synchrotrons at General Electric laboratories. Its practical application as a research tool began in the 1970s with the development of dedicated beamlines at facilities like Daresbury Laboratory, marking the transition to purpose-built synchrotron light sources.^[31]^[32]

Distant Natural Sources

Distant natural sources, such as celestial objects, generate effectively collimated beams at Earth due to their immense distances, which render the angular size subtended by the source negligible and cause incoming rays to propagate nearly parallel. This principle arises because the beam divergence angle θ is approximately the ratio of the source's physical size to its distance from the observer, resulting in a very small θ for sources billions of kilometers away. For instance, the Sun, despite its diameter of 1.39 million kilometers, subtends an angular size of about 0.53° from Earth at an average distance of 150 million kilometers, making its rays appear parallel over typical terrestrial scales.^[33]^[34]^[35] Examples of such collimated beams include sunlight and starlight. Starlight from distant stars arrives at Earth as precisely parallel rays, treated as plane waves in astronomical optics because the stars' distances—often thousands of light-years—make their angular sizes effectively zero. The Sun's beam divergence of θ ≈ 0.53° is small enough that, for short paths like those in laboratory or observational setups, sunlight behaves as effectively collimated.^[36] The Earth's atmosphere introduces some effects, but Rayleigh scattering has minimal impact on the collimation of the direct visible light beam from these sources. Rayleigh scattering preferentially removes shorter wavelengths from the direct path, contributing to the blue sky, yet approximately 80-90% of the incident sunlight passes through unscattered when the Sun is overhead, preserving the parallelism of the unscattered photons.^[37] In observational contexts, such as solar telescopes, incoming light from distant sources like the Sun is approximated as plane waves to facilitate optical design and wavefront analysis, aligning with the geometric parallelism inherent to collimated beams. This treatment simplifies imaging and spectroscopy by assuming uniform phase fronts across the aperture.^[36]

Engineered Optical Sources

Engineered optical sources produce collimated beams by employing mirrors and lenses to redirect light from divergent, incoherent emitters such as lamps or light-emitting diodes (LEDs), enabling applications in illumination, spectroscopy, and interferometry where laser coherence is unnecessary.^[38] These systems transform spherical wavefronts from point-like sources into planar wavefronts, approximating parallelism over finite distances, though perfect collimation remains theoretically unattainable due to diffraction effects.^[2] Parabolic mirrors serve as key devices for collimation by placing the emitter at the focal point, where the reflective surface directs rays to converge at infinity, producing a beam free from spherical aberration.^[39] Off-axis variants avoid central obscuration, making them suitable for compact setups in spectrometers and imaging systems.^[40] Pinhole collimators, often integrated into spectrometer entrances, restrict the source's spatial extent to a small aperture, minimizing divergence before further optical processing and enhancing spectral resolution.^[41] Practical examples include aspheric lenses collimating white light from LEDs, which position the emitter at the lens focal length to yield uniform beams for microscopy or machine vision, achieving efficiencies up to 80% in high-NA designs.^[42] Similarly, tungsten-halogen lamps are collimated using condenser optics for broadband illumination in calibration standards. In interferometers, beam expanders—typically Galilean telescopes—enlarge collimated beams from such sources while preserving parallelism, facilitating precise fringe patterns in white-light interferometry.^[43] Historically, 19th-century lighthouses employed Fresnel lenses to collimate lamp light into directed beams visible over 20 miles, revolutionizing maritime safety since their 1822 introduction at Cordouan Lighthouse.^[44] Performance of these sources is constrained by the diffraction limit, where beam divergence approximates λ/D (with λ as wavelength and D as aperture diameter), setting the fundamental bound on collimation quality for a given setup.^[18] Larger apertures reduce this angle, but practical systems often achieve divergences of milliradians from extended sources. Trade-offs include spherical aberrations from non-ideal surfaces, which blur peripheral rays, and chromatic aberrations in refractive elements, dispersing polychromatic light and necessitating achromatic designs for broadband operation.^[45] These limitations can degrade beam uniformity by 10-20% in uncorrected optics, though aspheric or reflective configurations mitigate them effectively.^[46]

Collimation Processes

Methods of Collimation

Collimation of optical beams is achieved through a variety of practical techniques that manipulate the beam's divergence and wavefront to produce parallel rays over a desired propagation distance. These methods rely on optical elements to filter spatial noise, refocus divergent rays, and correct aberrations, ensuring minimal angular spread as described by beam divergence metrics such as θ ≈ λ / (π w_0), where λ is the wavelength and w_0 is the beam waist radius.^[47] A basic method for collimation involves placing a point source or the waist of a diverging beam at the focal point of a positive lens, which transforms the light into parallel rays. The degree of collimation is limited by the source size and diffraction from the aperture.^[3] Optical methods for collimation often begin with spatial filtering using pinholes, which act as low-pass filters to remove high-spatial-frequency components from the beam profile. In this approach, a focusing lens directs the incoming beam onto a pinhole aperture sized near the diffraction limit (typically 5–50 μm for visible wavelengths), allowing only the central, low-divergence portion of the light to pass while blocking peripheral irregularities. The diffracted output from the pinhole is then recollimated by a second lens, producing a smoother, more uniform beam with reduced wavefront perturbations and improved coherence. This technique is particularly effective for cleaning noisy laser outputs.^[48] Another fundamental optical method employs lens doublets in afocal configurations to maintain parallelism between input and output beams without introducing focal points. An afocal system consists of two lenses—a divergent front element and a convergent rear element—separated by their combined focal lengths, such that a collimated input beam emerges collimated but potentially expanded or compressed in diameter. Achromatic doublets, often air-spaced to minimize chromatic aberration, are preferred for broadband applications. This setup is ideal for beam expansion in interferometry or laser delivery systems.^[49]^[50] Precise alignment of collimating optics is essential to achieve sub-arcsecond beam pointing accuracy, typically using autocollimators or interferometers. Autocollimators project a reticle pattern onto the optical surface and measure the reflected beam's angular deviation via position-sensitive detectors, enabling adjustments to within 0.1 arcseconds by iteratively aligning retroreflected spots. Interferometric methods, such as those employing Fizeau or Twyman-Green configurations, quantify tilt and piston errors across the aperture using phase-shifting algorithms, correcting misalignments that could introduce divergence exceeding 1 arcsecond. These tools ensure the beam axis remains parallel to the optical bench reference, with resolutions down to 0.01 arcseconds in high-precision setups.^[51]^[52] Advanced techniques enhance collimation in dynamic or aberrated environments. Adaptive optics systems correct wavefront errors in real time using deformable mirrors or spatial light modulators, driven by Shack-Hartmann sensors that measure local tilts and apply conjugate phase corrections to flatten the beam front. This restores collimation in turbulent media or after propagation through distorting elements.^[53] A standard procedure for implementing collimation involves several verifiable steps to optimize performance. First, measure the initial beam divergence using a beam profiler at multiple propagation distances, fitting the beam waist evolution to quantify θ and w_0. Next, select appropriate apertures or optics based on the source size and wavelength, ensuring the pinhole diameter or lens focal length matches the diffraction-limited spot (e.g., f = D / θ for collimating a divergent source of diameter D). Finally, verify the collimated output with a second profiler or shear-plate interferometer, adjusting for parallelism until the far-field beam diameter stabilizes within 1% over 1–10 m. This iterative process confirms effective collimation, with typical residual divergences below 0.1 mrad.^[2]

Effects of Decollimation

Decollimation of a collimated beam refers to the loss of parallelism in its rays, resulting in divergence and spreading over propagation distance. This phenomenon arises from several physical causes, with diffraction being the fundamental and inevitable mechanism due to the wave nature of light. In Gaussian beams, diffraction causes the beam waist to expand beyond the Rayleigh range, governed by the propagation equation w(z) = w_0 \sqrt{1 + \left( \frac{z}{z_R} \right)^2 }, where w(z) is the beam radius at distance z from the waist, w_0 is the minimum beam radius, and z_R = \frac{\pi w_0^2}{\lambda} is the Rayleigh range depending on wavelength \lambda.^[54] This spreading leads to a quadratic decrease in on-axis intensity, I(z) \propto \frac{1}{1 + \left( \frac{z}{z_R} \right)^2 }, reducing the beam's energy density and effectiveness for long-distance applications.^[54] Scattering, particularly Mie scattering from atmospheric aerosols and particles comparable in size to the wavelength, further contributes to decollimation by redirecting portions of the beam energy into non-parallel directions. In foggy conditions, water droplets cause significant forward scattering with angular deviations, effectively broadening the beam profile and attenuating the direct path.^[55] Optical aberrations, such as spherical aberration in lens systems, introduce wavefront distortions that convert a nominally collimated beam into one with varying ray angles across its aperture, exacerbating divergence.^[56] The degradation of beam quality due to these effects is quantified by the beam quality factor M^2, which measures deviation from an ideal diffraction-limited Gaussian beam where M^2 = 1; values greater than 1 indicate increased divergence and poorer focusability. For instance, in high-power laser propagation through fog, thermal blooming—a nonlinear effect from absorption-induced refractive index gradients—combines with Mie scattering to cause rapid beam blooming, where the on-axis intensity can drop by orders of magnitude over kilometers.^[57] While collimation methods can extend the effective Rayleigh range, fundamental limits imposed by diffraction and environmental interactions set unavoidable bounds on beam parallelism.^[3]

Applications

In Optics and Imaging

In interferometry, collimated beams play a critical role in maintaining fringe stability within Michelson interferometer setups by ensuring uniform wavefront phase across the beam path, which minimizes phase distortions and enhances interference pattern precision. This is particularly vital in high-sensitivity applications like gravitational wave detection, where the Laser Interferometer Gravitational-Wave Observatory (LIGO) employs well-collimated laser beams to propagate along precisely defined optical paths in its dual-recycled Fabry-Pérot Michelson interferometer, enabling detection of minute displacements on the order of 10^{-19} meters.^[58] Such collimation reduces beam divergence and supports stable fringe visibility, as demonstrated in prototype Michelson systems with Fabry-Pérot cavities that use nearly collimated input beams for mode matching and isolation.^[59] In microscopy, collimated illumination is integral to confocal systems, where it delivers uniform light distribution across the sample plane, thereby achieving consistent optical sectioning and field depth for high-resolution imaging. By filling the objective's back aperture with a large-diameter, well-collimated beam, confocal microscopes ensure even excitation and detection, reducing variations in depth of field that could otherwise degrade 3D reconstructions of biological specimens.^[60] This approach enhances axial resolution, typically to sub-micrometer levels, as seen in laser scanning confocal microscopy where collimated laser input supports precise pinhole filtering for out-of-focus light rejection.^[61] Collimated beams are equally essential in projection systems, including optical projectors and holography, where they promote sharp, distortion-free images by propagating parallel rays that limit spherical aberration and maintain focus uniformity over the projection field. In holography, for instance, collimated reference and object beams enable distortion-free multiplexing in photorefractive media, allowing high-fidelity reconstruction of complex 3D scenes without geometric warping.^[62] Similarly, in projector optics, collimation of the illumination beam ensures even coverage of spatial light modulators, yielding projected images with minimal edge blurring and preserved aspect ratios. Advancements since the early 2000s have integrated collimated LED sources into digital holography, offering compact, low-coherence alternatives to traditional lasers for versatile imaging in biomedical and industrial contexts. These LED collimators provide broadband illumination with reduced speckle noise, facilitating off-axis digital holographic setups for rapid 3D visualization of dynamic samples like zebrafish vasculature, where they achieve sub-micron resolution without the complexity of laser stabilization.^[63] This shift has enabled portable, cost-effective systems while preserving the geometric uniformity inherent to collimated beams for accurate phase retrieval.

In Particle Physics and Instrumentation

In particle accelerators, collimated beams of protons and electrons are essential for achieving high luminosity and precise collisions. Quadrupole magnets play a critical role in focusing these beams, reducing their divergence to maintain collimation throughout the accelerator lattice. For instance, in the Large Hadron Collider (LHC) Run 3, superconducting quadrupole magnets in the inner triplet configuration focus proton bunches to transverse sizes of approximately 10–16 μm at the interaction point with β* values as low as 0.3 m and normalized emittances around 2 μm, corresponding to beam divergences below 30 μrad. This tight collimation is vital for maximizing interaction rates while minimizing losses that could damage accelerator components.^[64]^[65] In particle detectors, collimators are deployed to define the interaction regions and suppress extraneous particles, thereby reducing background noise that could obscure signal events. At hadron colliders like the LHC, the multi-stage collimation system—comprising primary, secondary, and tertiary collimators—absorbs beam halo particles far from the experiments, preventing them from reaching the detectors and generating unwanted radiation. This setup significantly lowers the background in calorimeters, such as those in ATLAS and CMS, where collimators help isolate proton-proton collision products by limiting the acceptance to the primary vertex region. By optimizing collimator jaw positions, backgrounds from beam-gas interactions and residual halo can be reduced by factors of 10 or more, enhancing the sensitivity to rare physics processes.^[66]^[67] A prominent example of collimated beams in instrumentation is found in neutron scattering experiments, where precise collimation ensures high-resolution structural analysis of materials. Radial collimators with gauge sizes as small as 0.5 mm are used to produce neutron beams with minimal angular spread, achieving spatial precision on the order of millimeters at the sample position. These devices, often employing Soller slit or microchannel plate geometries, suppress parasitic scattering and improve signal-to-noise ratios in techniques like small-angle neutron scattering (SANS). Such collimation allows probing length scales from nanometers to micrometers, as demonstrated in facilities like the Spallation Neutron Source.^[68]^[69] Advancements in collimation for particle colliders accelerated in the 1990s with the adoption of superconducting quadrupole magnets, enabling stronger focusing fields and thus tighter beam confinement. Projects like the Superconducting Super Collider (SSC) developed quadrupoles with gradients up to 18 T/m using NbTi superconductors, which supported emittance preservation below 10 μm and reduced beam halo excursions. These innovations, building on earlier ISR insertions, paved the way for modern colliders by allowing operation at higher intensities without excessive losses, as later refined in the LHC's 8.3 T dipole and quadrupole systems.^[70]^[71]

In Astronomy and Remote Sensing

In astronomical telescopes such as the Ritchey-Chrétien design, incoming starlight from distant celestial objects is treated as a collimated beam of parallel rays due to the effectively infinite distance of the sources, allowing the hyperbolic primary and secondary mirrors to focus the light to a point without introducing spherical aberration or coma across a wide field of view.^[72] This collimation assumption is fundamental to the telescope's aplanatic performance, enabling high-resolution imaging of point-like stars and extended objects like galaxies.^[73] Atmospheric turbulence, however, introduces wavefront distortions that effectively decollimates the incoming beam, blurring images through the phenomenon known as "seeing," with typical angular resolutions limited to about 1 arcsecond under good conditions.^[74] Adaptive optics systems mitigate this by using deformable mirrors to real-time correct the distorted wavefronts, restoring near-diffraction-limited performance; laser guide stars, created by projecting collimated sodium laser beams into the upper atmosphere to simulate a reference star, extend this correction to nearly any sky position where natural guide stars are faint or absent. In remote sensing applications, collimated pulsed laser beams are central to LIDAR systems for atmospheric profiling, where the narrow, parallel output minimizes beam divergence over long paths to enable precise range-resolved measurements of aerosols, clouds, and trace gases. For instance, NASA's Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) mission, operational from 2006 to 2023, employed a collimated dual-wavelength (532 nm and 1064 nm) LIDAR beam from a Nd:YAG laser to vertically profile global atmospheric constituents, providing depolarization data for particle characterization via backscatter returns collected by a 1-meter telescope.^[75] A successor mission, EarthCARE, launched in 2024 by ESA and JAXA, employs a similar collimated LIDAR system at 355 nm for advanced cloud-aerosol profiling.^[76] High-resolution spectroscopy in astronomy also relies on collimated input beams to echelle gratings, which operate in high diffraction orders to achieve resolving powers exceeding 100,000 over broad spectral ranges, ensuring uniform illumination and minimal aberrations for accurate radial velocity and abundance measurements of stars and exoplanets.^[77] The collimation step, typically via off-axis parabolic mirrors or fiber-coupled optics, aligns the beam perpendicular to the grating to optimize blaze efficiency and reduce crosstalk between orders.^[78]

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### Summary of Considerations in Collimation
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Collimated beams are laser beams with weak divergence within some region of interest. This implies that they have a relatively large beam radius.
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Below is a merged summary of the "Collimator" history and etymology in astronomy, consolidating all information from the provided segments into a single, detailed response. To maximize clarity and density, I will use a table in CSV format to organize key details (e.g., definition, etymology, history, and mentions of John Herschel/1833), followed by a narrative summary that integrates additional context and useful URLs.
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The paraxial approximation is a frequently used approximation, essentially assuming small angular deviations of the propagation directions from some beam ...Missing: collimated dθ/ dz = Helmholtz
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1. Synchrotron Radiation Sources - NASA ADS
Synchrotron radiation is a very bright, broadband, polarized, and a pulsed source of light extending from the infrared to the x-ray region. It is an ...<|separator|>
[28]
Low-emittance beam injection for a synchrotron radiation source ...
The obtained emittance of ∼ 1 nm rad at the injection point is small enough for the future SPring-8-II, whose requirement is of the order of ∼ 10 nm rad .
[29]
[PDF] Synchrotron Radiation Sources for the Future - CLASSE (Cornell)
Low emittance storage rings permit use of undulators, which produce very highly collimated x-ray beams, with divergences on the order of 20 µrad. There is now ...Missing: microradians | Show results with:microradians
[30]
Synchrotron radiation: A continuing revolution in X-ray science ...
The development of synchrotron radiation sources is discussed as new, so called diffraction limited storage rings (DLSR), are coming online.
[31]
History of Synchrotron Radiation Sources
THE FIRST GENERATION: STORAGE RINGS ... With Tantalus I, the superiority of the electron storage ring as a source of synchrotron radiation became evident.
[32]
Our Sun: Facts - NASA Science
The Sun is a 4.5 billion-year-old yellow dwarf star, 93 million miles from Earth, 100 times wider than Earth, and 865,000 miles in diameter. Its core is 27 ...Size and Distance · Orbit and Rotation · Formation · Structure
[33]
sun_moon_angular.html - UNLV Physics
Sun angular diameter: mean 0.5332°, range 0.5242°--0.5422°. Moon angular diameter: mean 0.5286°, range 0.4889°--0.5683°.
[34]
How Big Is the Solar System? - NASA Science
Feb 1, 2020 · One AU, about 93 million miles (150 million kilometers), represents the average distance from the Sun to the Earth. It would take an airliner ...
[35]
Solar Imaging with a Synthesis Telescope - NASA ADS
Recall that the far-field approximation allows us to treat the incoming radiation as a plane wave—when this assumption is violated, the error in the phase is ...
[36]
Ask Us -- Cosmic Rays - NASA's Cosmicopia
Jun 18, 2012 · At this energy, cosmic rays will spiral with a radius of curvature of roughly ~1016 m (which is much less than the distance to the Crab nebula, ...
[37]
Blue Sky and Rayleigh Scattering - HyperPhysics
This scattering, called Rayleigh scattering, is more effective at short wavelengths (the blue end of the visible spectrum). Therefore the light scattered down ...
[38]
What percentage of sunlight isn't scattered by air molecules?
Aug 3, 2017 · 90% of light at the top of the atmosphere (of a star or indeed the Sun) makes makes it straight through the atmosphere if the star/Sun was directly overhead.
[39]
Parabolic Mirrors – laser mirrors, off-axis reflectors, applications
Parabolic mirrors are non-spherical mirrors particularly suited for tightly focusing or collimating laser light.What is a Parabolic Mirror? · Off-axis Reflectors · Calculating the Performance of...
[40]
https://wp.optics.arizona.edu/optomech/wp-content/uploads/sites/53/2016/10/521_Tutorial_Newman_Kevin.pdf
[41]
[PDF] An introduction to off-axis parabolic mirrors
Oct 21, 2013 · A parabolic mirror takes light from a point source located at the focus and creates a collimated beam. In other words, a source with spherical ...<|control11|><|separator|>
[42]
How to build a spectrometer - theory - Ansys Optics
The polychromatic light enters the spectrometer through the entrance pinhole resulting in a divergent beam. The collimator lens is then used to generate ...
[43]
Collimated LED Light Sources for Microscopy - Thorlabs
Each collimated LED consists of a mounted LED and a lamphouse-port-compatible housing that contains an AR-coated aspheric collimation optic (see the Specs tab ...
[44]
Interferometry Of Large Diameter Beam Expanders
Hence, careful optical interferometry was performed on a laser beam expander and its associated relay optics, before it was used for propagation experiments.
[45]
Fresnel Lenses: 1800 - Present - FindLight
Sep 28, 2022 · Fresnel lenses work very well for collimating a bright central light source, they can also be used to focus incoming collimated light.
[46]
https://www.rp-photonics.com/spherical_aberrations.html
[47]
Spherical Aberrations - RP Photonics
Spherical aberrations result from the fact that spherical optical surface shapes are generally not ideal. Similar problems can occur even for flat plates.
[48]
None
### Summary of Spatial Filtering with Pinholes for Collimation
[49]
[PDF] SPATIAL FILTERING - UCSB Physics
The collimator is a small pinhole and when the laser passes through it, the light diffracts outwards. Remove the collimator. Place a lens-holder on the optical ...
[50]
(PDF) AFOCAL SYSTEMS - Academia.edu
10, providing a pupil in a collimated beam in which to insert a scanner. ... Kaselitz, Afocal Lens System Attachment for Photographic Objectives, U.S. ...
[51]
Aberration-Based Quality Metrics in Holographic Lenses - PMC
Apr 24, 2020 · The HL and L2, separated by a distance f ′ H L + f ′ L formed an afocal lens system [55,56], from which the collimated emerging beam ends up ...
[52]
Autocollimation | Precision Optical Inc.
Our interferometers are capable of measurement accuracy exceeding 0.1 seconds of arc. Precision Optical also employs our CMM (Coordinate-Measuring Machine) ...
[53]
A Review: High-Precision Angle Measurement Technologies - PMC
This article introduces the technology of angle measurement from the perspectives of single-axis and multi-axis measurement schemes.<|separator|>
[54]
High precision wavefront correction using an influence function ...
Adaptive optics (AO) is widely used to test and correct wavefront aberration ... Through the collimation of L2 and L3, the beam passes through the MLA ...
[55]
Collimation method using a double grating system - ResearchGate
Aug 6, 2025 · We present a collimation technique based on a double grating system to locate with high accuracy an emitter in the focal plane of a lens.<|separator|>
[56]
Optical beam collimation procedures and collimation testing
Apr 30, 2020 · This paper attempts to describe these techniques. 2 What is Collimation? If a point source is placed at the front focal point of a positive lens ...
[57]
https://apps.dtic.mil/sti/tr/pdf/ADA096797.pdf
[58]
[PDF] Atmospheric Propagation Effects Relevant to Optical Communications
The attenuation or extinction loss of light energy from the laser beam for this category is generally due to Rayleigh and. Mie scattering. The direct beam ...
[59]
Beam collimation in the presence of aberrations - ScienceDirect.com
This paper describes the application of multiple beam shearing interferometry to beam collimation in the presence of lens aberrations.
[60]
[PDF] Atmospheric Sensitivities of High Energy Lasers - DTIC
Absorption of MEL radiation also leads to thermal blooming, i.e., a heating of the air that spreads, distorts, and bends the beam which is discussed in tne ...
[61]
[PDF] Interferometer Techniques for Gravitational-Wave Detection
Nov 18, 2015 · The laser beams are well collimated ... EOM is used to phase modulate the laser beam before entering the Michelson interferometer.
[62]
Prototype Michelson interferometer with Fabry-Perot cavities
assembly is a nearly collimated beam. It is mode matched to the Fabry-Perot (FP) cavities with a single positive lens and isolated by two Faraday isolators ...<|control11|><|separator|>
[63]
Non-Coherent Light Sources for Confocal Microscopy
Since spinning disk confocal microscopes require a large-diameter, well-collimated ... uniform illumination in the specimen plane. Non-Coherent Light ...
[64]
The Use of Laser Scanning Confocal Microscopy (LSCM) in ...
Jun 26, 2020 · [2-6] Laser scanning confocal microscopes (LSCMs) use collimated ... With laser scanning confocal imaging, however, the depth of field ...
[65]
Distortion-free multiplexed holography in striated photorefractive ...
An Ar-ion laser beam (514 nm) is spatially filtered, collimated, and split by beam splitter BS1 into a reference and an object beam. The latter is then ...
[66]
Heterogeneities of zebrafish vasculature development studied by a ...
Sep 14, 2022 · Digital Holography and Three-Dimensional Imaging · Imaging Systems ... LED collimator, f = 30 mm. L3, Thorlabs, AC254-50-A, illumination lens ...<|control11|><|separator|>
[67]
[PDF] CHAPTER 2 BEAM PARAMETERS AND DEFINITIONS - Indico Global
The nominal normalized transverse emittance for the LHC is n = 3.75 µm. (2.12). Page 12. 2.6 LHC SYSTEM PREFIXES. Table 2.5: LHC system prefixes. LHC Systems ...
[68]
Accelerator Report: Beams are circulating in the LHC - CERN
Mar 14, 2024 · The inner triplet is a set of quadrupole magnets that focus the beam to very small dimensions at the centre of the experiments. Some of the ...Missing: collimated | Show results with:collimated
[69]
https://www-pub.iaea.org/MTCD/Publications/PDF/te_1486_web.pdf
[70]
The collimation system: defence against beam loss - CERN Courier
Aug 19, 2013 · Collimators are also used to minimize background in the experiments. The LHC collimation system provides multi-stage cleaning where primary ...
[71]
Development of 0.5 mm gauge size radial collimators for high ...
The 0.50 mm GS radial collimator stands as the smallest GS ever fabricated for neutron scattering experiments, indicating its potential for enabling ...Missing: collimation | Show results with:collimation
[72]
[PDF] Small angle neutron scattering
In order to cover such small angles, a beam of high intensity, small cross-section (~1 mm2) and a sample-to-detector distance of around 1 meter are needed.
[73]
Sections of Magnets for Superconducting Super Collider
A sequence of electromagnets produces the necessary magnetic fields to both guide and focus the proton beams. Dipole magnets produce the field configurations ...
[74]
[PDF] Superconducting Magnets for Particle Accelerators
Jul 2, 2013 · This article is a review of the main superconducting accelerator magnet projects; it highlights the main characteristics and main achievements, ...
[75]
Reflecting Telescopes - Las Cumbres Observatory
Curved mirrors can bend light and make parallel light rays converge to a focus. This focus is directly in the path of the incoming light, so there are several ...
[76]
Ritchey Chrétien Telescope Overview - Avantier Inc.
The RC telescope employs two hyperbolic mirrors: – Primary Mirror: A concave hyperboloid that collects incoming light and focuses it toward the secondary mirror ...Missing: parallel | Show results with:parallel
[77]
Adaptive optics using multiple laser guide stars - SPIE
Apr 2, 2009 · Astronomers refer to this effect as 'seeing,' and—depending on weather conditions—it can reduce image resolution from 0.5 to 1 arcsecond at ...
[78]
Projects | CALIPSO - ASDC
The CALIPSO satellite comprises three instruments, the Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP Lidar), the Imaging Infrared Radiometer (IIR) ...
[79]
Fast high resolution echelle spectroscopy of a laboratory plasma
Jun 21, 2006 · The most important modification to this spectrometer is the installation of an echelle plane grating. ... collimated beam on the grating.
[80]
Echelle gratings acting as one - Optica Publishing Group
Light from the input fiber is collimated and conducted through a folding mirror to the first grating of the EED. The Bk7 prism used satisfies Eq. ( 13 ) ...