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Diffraction spike

A diffraction spike is an imaging artifact characterized by bright, linear rays extending radially from point-like sources of light, such as stars, in astronomical photographs and telescopic images, resulting from the diffraction of light waves around straight-edged obstructions in the optical system.^[1]^[2] These spikes arise due to the wave nature of light, which bends or diffracts when passing near the edges of opaque structures, such as the spider vanes that support the secondary mirror in reflecting telescopes.^[1] In Newtonian reflectors, for instance, a typical four-vane spider at 90-degree intervals produces four prominent spikes forming a cross pattern, while a three-vane configuration at 120-degree spacing generates six spikes.^[2]^[3] The length and intensity of the spikes increase with the brightness of the source and the thinness of the obstructing edges, as narrower features enhance diffraction effects.^[1] In addition to telescope supports, diffraction spikes can originate from the polygonal blades of a camera's iris diaphragm, where an odd-numbered aperture (e.g., seven blades) doubles the spike count to even numbers like 14.^[2] Refracting telescopes, lacking secondary mirrors and vanes, generally do not produce these spikes from internal structures, though external obstructions like camera mounts can introduce them.^[4] Notable examples include the four-spiked crosses in Hubble Space Telescope images from its four-strut secondary support and the distinctive eight-spiked patterns in James Webb Space Telescope observations, shaped by its 18 hexagonal primary mirror segments and three main struts.^[5]^[2] While primarily a visual artifact, diffraction spikes have been studied since the mid-20th century for their implications in optical design and image processing.^[3]

Physical Basis

Definition and Characteristics

A diffraction spike is an optical artifact consisting of bright streaks or rays that emanate radially from point-like light sources, such as stars, in images formed by optical systems. These spikes manifest as linear extensions from the central image of the source, often creating a starburst or sunstar effect in photographs and telescopic views.^[4]^[5] In typical configurations, such as those with linear obstacles like cross-shaped support structures, diffraction spikes appear as four prominent rays oriented at 90-degree intervals around the light source. The number of spikes can vary—for instance, three struts may produce six spikes—while their length and brightness depend on factors like the geometry and dimensions of the obstructions relative to the system's aperture. In reflecting telescopes, a four-vane spider typically produces four spikes, while a three-vane spider produces six, due to the diffraction pattern from each vane.^[2] Brighter sources tend to produce more pronounced and longer spikes, and in astronomical imaging, they are commonly seen as star-like bursts extending from bright celestial objects in night sky exposures.^[6] The length of these spikes generally scales inversely with the width of the obstructing elements relative to the aperture diameter and directly with the wavelength of the light, resulting in longer spikes for longer wavelengths or narrower relative obstructions. These characteristics arise from the interference of light waves, a fundamental diffraction phenomenon.^[7]

Underlying Diffraction Principles

Diffraction arises from the inherent wave nature of light, which causes waves to bend around obstacles or spread through apertures comparable in size to the wavelength, producing interference patterns that alter the expected geometric shadow or image. Unlike ray optics, which predicts sharp boundaries, wave optics reveals that light wavefronts superpose constructively and destructively, leading to bright and dark fringes beyond the obstacle. This fundamental behavior is essential for understanding phenomena like diffraction spikes, where point sources produce extended streaks due to such interference. The Huygens-Fresnel principle provides the theoretical foundation for these effects, positing that every point on an incoming wavefront serves as a source of secondary spherical wavelets propagating forward at the speed of light, with the resultant wavefront formed by the coherent superposition of these wavelets weighted by an obliquity factor. In the formation of diffraction spikes, obstructing edges in the optical path—such as narrow supports—disrupt the wavefront, generating secondary sources along those edges; constructive interference occurs preferentially in directions perpendicular to the edges, manifesting as elongated bright lines radiating from the source. This interference pattern emerges because the phase differences between wavelets align to reinforce intensity along the spike axis while canceling elsewhere. The angular width of a diffraction spike, θ, is approximately given by θ ≈ λ / d, where λ is the light's wavelength and d is the width of the obstructing edge; this relation derives from the analogy to single-slit diffraction, where the position of the first intensity minimum is at sin θ ≈ λ / d, or θ ≈ λ / d for small angles. To arrive at this, consider the path length difference from points across the edge: for a plane wave incident on an edge of width d, the diffraction integral yields the sinc-squared intensity envelope I(θ) = I_0 [sin(π d sin θ / λ) / (π d sin θ / λ)]², with the central maximum spanning from -λ/d to +λ/d in angle, but the characteristic scale set by the first zero at θ = λ / d. Thus, narrower obstructions (smaller d) produce wider spikes, scaling inversely with d. The intensity along the spike varies according to this diffraction envelope, with the primary maximum brightest near the source and tapering outward, while higher-order maxima create fainter parallel streaks; spikes appear particularly bright in directions aligned with the edges due to enhanced contributions from these secondary maxima in the interference pattern. For non-polarized light, typical in astronomical observations, spike visibility is modulated by polarization effects at the diffracting edges, where the pattern intensity differs for components parallel versus perpendicular to the edge—for instance, perpendicular polarization often yields stronger diffraction into the shadow region for conducting edges like metal supports.

Causes in Optical Systems

Secondary Support Structures

In reflecting telescopes, particularly Newtonian designs, secondary support structures known as spider vanes or struts hold the secondary mirror in position above the primary mirror, acting as linear obstacles that interrupt the incoming wavefront and generate diffraction spikes.^[7]^[2] These vanes, typically made of thin metal or composite materials, extend radially from the tube wall to the mirror holder, creating straight edges from which light diffracts.^[8] The pattern of spikes depends on the number and arrangement of vanes. A common cross-shaped configuration with four vanes spaced at 90 degrees produces four prominent spikes extending radially from bright point sources, as the diffraction from opposing edges superimposes to form visible pairs.^[8]^[2] In contrast, a three-vane setup, often arranged at 120 degrees for balanced support, yields six spikes separated by 60 degrees, doubling the number due to the asymmetric positioning of edges.^[7]^[2] Design variations in vane geometry significantly influence spike characteristics, especially in Newtonian reflectors where minimizing optical interference is key. Thinner or narrower vanes (e.g., widths around 1% of the aperture diameter) result in longer but fainter spikes, as the closely spaced edges concentrate less energy into broader diffraction patterns.^[9]^[7] Thicker or wider vanes, conversely, shorten the spikes while increasing their intensity, spreading more light and potentially degrading contrast around bright objects, though they provide greater structural rigidity for larger mirrors.^[9]^[7] To mitigate spike visibility, curved or asymmetric vanes have been employed, dispersing the diffracted light into less concentrated patterns rather than distinct linear spikes.^[7]^[8] This approach, which requires arching the vanes over approximately 180 degrees divided by the vane count (e.g., 45 degrees for four vanes), reduces symmetry and perceptual prominence without eliminating diffraction entirely.^[7] Such designs trace their evolution to 18th-century advancements in Newtonian reflectors, when larger instruments by makers like John Hadley and William Herschel necessitated robust yet low-obstruction supports for secondary mirrors.^[10]^[7]

Aperture Obstructions

Aperture obstructions in optical systems, particularly non-circular or partially blocked apertures in camera lenses, generate diffraction spikes through the bending of light waves at straight edges. These edges, formed by the overlapping blades of an iris diaphragm, act as barriers that diffract incoming light, creating linear patterns radiating from bright point sources such as stars or distant lights. In lenses with a polygonal iris, such as the common hexagonal design with six blades, the diffraction from each edge produces spikes that overlap in pairs for even-sided apertures, resulting in six prominent spikes overall.^[11]^[12] This shape-specific effect is particularly evident in astrophotography, where lenses featuring hexagonal apertures—often found in wide-angle optics like those used for night sky imaging—produce the characteristic six-spike pattern around bright stars, enhancing the starburst effect in long-exposure shots. Partial obstructions, such as a misaligned lens hood that vignettes the aperture unevenly, can introduce asymmetric diffraction patterns, leading to irregular or additional spikes that deviate from the symmetric polygonal form.^[13]^[14] The prominence of these spikes is highly dependent on aperture size, as smaller diameters increase the diffraction angle according to the relation θ ≈ λ / D, where λ is the wavelength of light and D is the aperture diameter; thus, stopping down to higher f-numbers (e.g., f/16 or f/22) widens the spikes and makes them more visible relative to the central Airy disk. This interference arises from diffraction at the aperture edges, as detailed in the underlying diffraction principles.^[11]^[15] Historically, mid-19th-century camera designs, which employed rudimentary fixed apertures or early iris mechanisms like those patented in 1858, often inadvertently produced such spikes due to imperfectly circular openings, though they were not recognized as diffraction effects until later optical theory developed. In modern photography, these spikes are sometimes intentionally accentuated by selecting lenses with specific blade counts for artistic sunstar effects in landscapes or celestial images.^[16]

Segmented Mirrors

Segmented primary mirrors in large astronomical telescopes, such as the 10-meter Keck Observatory telescopes with 36 hexagonal segments each and the James Webb Space Telescope (JWST) with 18 hexagonal beryllium segments forming a 6.5-meter aperture, introduce gaps between segments that function as a diffraction grating.^[17]^[18]^[19] These gaps, typically on the order of millimeters, diffract incoming light from point sources like stars, producing characteristic spike patterns distinct from those caused by other optical obstructions.^[17] The diffraction spikes arising from segmented mirrors exhibit complex patterns due to interference from the edges of multiple segments, resulting in multiple rays emanating from the central image. In the JWST, the 18 segments and three struts generate intricate, eight-pointed spikes (six prominent from the struts and two fainter from the segments) around bright stars, with the hexagonal geometry contributing to a symmetrical, starburst-like appearance visible in aligned images.^[5] Similarly, the Keck telescopes produce multifaceted diffraction patterns from their 36 segments, where the grating-like gaps create additional low-intensity rays that extend far from the core.^[17] Alignment of these segments presents significant challenges, as even small misalignments in piston, tip, or tilt can amplify spike complexity and intensity, degrading overall image quality. Active optics systems in the Keck telescopes use sensors and actuators to adjust segments in real-time, reducing piston errors to approximately 30 nanometers and minimizing diffraction effects for diffraction-limited performance.^[17] For the JWST, post-launch alignment in early 2022 involved over 130 actuators per segment to fine-tune positioning over several months, culminating in a unified image by March where spike intensity was notably reduced through optimized co-phasing.^[19]^[20] While these spikes can reveal the degree of mirror co-phasing—symmetric patterns in aligned test images confirming precise segment integration—they also degrade point source resolution by distributing light into extended structures, complicating observations of faint companions near bright objects.^[17] This trade-off highlights the need for ongoing active corrections to balance segmentation benefits with optical fidelity.^[17]

Optical Surface Defects

Optical surface defects, including dust particles, scratches, and fingerprints on lenses or mirrors, induce localized diffraction and scattering of incoming light, resulting in irregular spike-like patterns emanating from bright sources in astronomical images. These effects arise from the interaction of light waves with microscopic irregularities, redistributing energy into the extended wings of the point spread function (PSF) rather than the central Airy disk. Unlike diffraction from smooth structural edges, such scattering is stochastic and depends on the defect's geometry and position relative to the optical axis. The resulting spikes are characteristically irregular and faint, lacking the geometric symmetry of those produced by secondary support structures, with their intensity scaling with the defect's size, depth, and contrast against the surrounding surface. Small defects like dust grains produce broad, diffuse extensions in the PSF, sometimes reaching thousands of Airy rings, while scratches may create more linear but asymmetric features. This scattering is more pronounced at shorter wavelengths due to the increased sensitivity of diffraction to surface microroughness. In amateur telescopes, such spikes often appear from accumulated dew, which traps dust and forms water films that scatter light nonuniformly, or from environmental contaminants like pollen adhering to exposed optics during observations. Professional observatories counteract these issues through rigorous maintenance, employing carbon dioxide (CO2) snow cleaning systems that blast frozen CO2 particles to dislodge contaminants without abrasives or residues, thereby minimizing scattering. For instance, the European Southern Observatory's Very Large Telescope uses this method to preserve mirror surface quality.^[21]^[22] Defect-induced spikes differ from other diffraction phenomena in their wavelength dependence, where the scattering efficiency varies across the spectrum, often yielding polychromatic appearances if the defect scatters broadly without strong color selectivity. This contrasts with the achromatic, symmetric patterns from aperture obstructions, as surface irregularities introduce random phase perturbations that broaden and color the diffracted light.

Manifestations in Imaging and Vision

In Astronomical and Photographic Imaging

In astronomical and photographic imaging, diffraction spikes manifest as prominent radial lines extending from bright point sources, such as stars, against the dark backdrop of space, creating a starburst effect that can enhance the dramatic aesthetics of deep-sky photographs. These artifacts are particularly evident in images captured by reflecting telescopes, where they radiate from overexposed stars, adding a sense of depth and highlighting the instrument's optical design. For instance, in Hubble Space Telescope images of open clusters like NGC 2660, spikes surround bright foreground stars, emphasizing their prominence while the extended structures of galaxies remain unaffected.^[23] The visibility of diffraction spikes depends on several observational factors, including the brightness of the source, exposure time, and the telescope's focal ratio. Brighter objects produce longer and more intense spikes due to greater light diffraction, while longer exposures amplify their contrast in low-light conditions. A lower f-ratio (faster optics) results in shorter spikes on the image plane, as the linear length of the spikes scales approximately with the focal ratio F according to the relation ~2λF/ς, where λ is the wavelength and ς is the vane width-to-length ratio, making them less obtrusive in wide-field astrophotography. In practice, spikes appear around Venus or Jupiter in terrestrial wide-field shots taken with camera lenses featuring multi-bladed apertures, producing even-numbered rays (e.g., 14 from a 7-blade iris) that mimic celestial fireworks.^[7]^[2] Although diffraction spikes can resemble the natural twinkling (scintillation) of stars caused by atmospheric turbulence, they are purely instrumental artifacts arising from obstructions like secondary mirror supports, distinguishable by their fixed orientation and symmetry relative to the optical axis. In professional astrophotography, these spikes are often retained for artistic appeal, as seen in iconic Hubble composites, but can detract from scientific analysis by complicating photometry of point sources. Post-processing techniques mitigate this; traditional software like Adobe Photoshop allows manual cloning or masking to remove spikes, while 2020s advancements in AI-driven tools, such as StarNet2 (updated 2022) and StarXTerminator (debut 2021), enable automated star removal—including associated spikes—using neural networks trained on diverse astronomical datasets, streamlining workflows in platforms like PixInsight.^[24]^[25]

In Human Visual Perception

The human eye functions as an optical system where the pupil serves as the limiting aperture, and its edges can diffract incoming light from bright point sources, producing faint radiating spikes similar to those in artificial imaging devices. This diffraction occurs as light waves bend around the irregular boundaries of the iris, particularly noticeable around intense lights such as car headlights during nighttime driving. Lens imperfections, including subtle aberrations in the cornea and crystalline lens, further contribute to these patterns by scattering light unevenly across the visual field.^[12]^[26]^[27] Physiologically, these diffraction spikes manifest as interference patterns on the retina, where diffracted light waves constructively and destructively interfere to form star-like rays emanating from the source. The effect is more pronounced in low-light conditions when the pupil dilates to a larger diameter—often exceeding 7 mm—allowing more light entry but amplifying diffraction due to the increased aperture size and exposure of lens suture lines that act as secondary diffracting edges. In dark environments, this dilation enhances the visibility of spikes from distant point sources, as the eye's reduced ambient light adaptation heightens contrast sensitivity to these artifacts. Retinal processing of these patterns occurs via the photoreceptors, but the spikes are primarily optical in origin rather than neural.^[26]^[12]^[27]^[28] Common examples include observing spikes radiating from streetlights or vehicle headlights at night, where the effect can impair visual clarity and contribute to discomfort during tasks like driving. Under dark skies, the naked eye may perceive similar spikes around bright stars, appearing as subtle rays due to the eye's diffraction-limited resolution in low illumination. Conditions such as cataracts exacerbate these spikes by clouding the lens and increasing light scattering, leading to more intense starburst patterns that intensify with pupil dilation.^[12]^[27]^[29]^[30] Unlike fixed imaging systems, diffraction spikes in human vision are transient and highly subjective, varying with individual factors like age-related lens changes or corneal irregularities such as astigmatism, which can elongate or distort the rays. Corrective measures, including glasses or contact lenses that address astigmatism, often reduce the prominence of these spikes by minimizing optical aberrations, though they do not alter pupil dynamics directly. This biological variability contrasts with the consistent, mechanically induced spikes in cameras or telescopes, emphasizing the eye's adaptive yet imperfect optics.^[27]^[31]^[32]^[26]

Practical Applications

Focusing and Alignment Tools

The Bahtinov mask is a diffractive focusing aid placed over the front aperture of a telescope, designed to produce an asymmetric pattern of three diffraction spikes from a point source such as a bright star, enabling precise alignment and focus. Invented in 2005 by Russian amateur astronomer Pavel Bahtinov, this tool revolutionized manual focusing for amateur astronomers by leveraging diffraction principles to create a visual indicator of optical alignment.^[33]^[34] When a star is viewed through the Bahtinov mask, the mask's slotted pattern generates two angled outer spikes that remain relatively fixed, while the central spike shifts position depending on the degree and direction of defocus. At perfect focus, the central spike aligns precisely between the outer two, allowing adjustments to achieve sub-arcsecond precision without physical contact with the optics. This method is particularly valuable in astrophotography for capturing sharp images of planets, stars, and other point-like celestial objects, as it facilitates remote or automated focusing in setups where direct visual confirmation is challenging.^[35] Beyond the Bahtinov mask, simpler spike-inducing tools, such as the Hartmann mask, employ multiple apertures or slits to generate overlapping diffraction patterns that converge when in focus, providing an alternative for quick alignment in smaller telescopes. In large observatories, software simulations of diffraction spike patterns are used to model point spread functions (PSFs) and verify telescope alignment by comparing observed spikes against predicted ones, aiding in the correction of optical aberrations during observations.^[36] The primary advantages of these diffraction-based tools include their non-invasive nature, which avoids mechanical wear on focusers, and their effectiveness for remote operations in dark skies, where faint stars produce clear spike patterns. However, they have limitations in bright skies or high light pollution, where scattered light can obscure the spikes and reduce focusing accuracy.^[35]^[37]

Artistic and Special Effects

Astrophotographers often deliberately include or amplify diffraction spikes in composite images to heighten visual appeal, transforming point-like stars into more dynamic, starburst-like features that convey cosmic grandeur. For refractor telescopes, which typically lack natural spikes due to the absence of secondary supports, enthusiasts apply custom masks—such as taut strings or wires stretched across the objective lens—to induce diffraction patterns mimicking those from reflectors.^[38] These additions, sometimes via 3D-printed filters for devices like the Seestar S50, allow for controlled spike generation without post-processing fakery, appealing to those who view the effect as an artistic enhancement rather than a flaw.^[39]^[40] In digital visual effects, CGI tools simulate diffraction spikes to replicate authentic optical artifacts in sci-fi scenes, evolving from practical lens-based methods in 1970s films to sophisticated software rendering in the 2020s. For instance, Blender's compositor employs the Glare node configured for "streaks" or "simple star" modes to add radial spikes around light sources, enabling precise control over length, color, and intensity for holographic displays or stellar explosions.^[41] This shift mirrors broader VFX trends, where early practical effects in films like Star Wars (1977) relied on physical models and optics for star fields, while contemporary productions use algorithmic simulations to integrate spikes seamlessly with CGI environments, reducing costs and expanding creative possibilities.^[42]^[43] Diffraction spikes, or analogous starburst motifs, carry cultural significance in graphic design, symbolizing "star power" and celestial allure in movie posters and album artwork to evoke fame and energy. These radial patterns draw from astronomical imagery, positioning central figures—such as celebrities or bands—as radiant focal points, a convention seen in promotional materials since the mid-20th century to capture attention and imply stellar prominence.^[44]

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