Diffraction spikes

Diffraction spikes are the straight lines of light that radiate from stars and other bright point sources in images made with reflecting telescopes, and from street lights and the sun in photographs taken with a stopped-down lens. They are part of the system's point spread function: any straight edge in the aperture diffracts light into a narrow streak perpendicular to that edge, on both sides of the image. A thin support vane across a telescope pupil has two long parallel edges and so produces one spike pair oriented at 90° to the vane. The four-vane spider of a Newtonian or of the Hubble Space Telescope gives the four-point cross; the James Webb Space Telescope gives six large spikes plus two smaller horizontal ones.

Counting spikes

Each straight edge contributes a spike pair perpendicular to it, and parallel edges contribute to the same pair. This gives a simple counting rule for $n$ edges or vanes spaced evenly around the aperture:

• $n$ even: opposite edges are parallel, so the pattern has $n$ spikes. Four vanes give 4 spikes; a hexagon gives 6.
• $n$ odd: no two edges are parallel, so each makes its own pair and the pattern has $2n$ spikes. Three vanes at 120° give 6 spikes; a heptagon gives 14.

JWST combines both effects. Its primary mirror is a mosaic of 18 hexagonal segments whose edges run in three directions, giving six spikes; the struts holding the secondary mirror add their own. Two of the struts lie parallel to segment edges and reinforce existing spikes, while the vertical strut adds a new horizontal pair, for a total of 6 plus 2.

Size and brightness

The spike shape follows from Fourier optics: in the far field, the diffracted amplitude of an obstruction is the Fourier transform of its shape. A vane of width $w$ and length $L$ produces light spread over an angle of order

$$\theta_\parallel \sim \frac{\lambda}{w}$$

along the spike and only about $\lambda/L$ across it. The spike is therefore long and thin, and thinner vanes give longer spikes.

Worked example: a 200 mm Newtonian with a 60 mm secondary held by four 1 mm vanes, each 70 mm long. At 550 nm, the spike envelope extends to about $\lambda/w = 5.5\times10^{-4}$ rad, or 113 arcseconds, with a sinc² falloff and faint tails beyond. Across the spike, $\lambda/L$ is 1.6 arcseconds, a little more than twice the Airy disk radius of 0.69 arcseconds for this aperture. The vanes cover 280 mm² of an unobstructed annulus of 28,600 mm², or 1.0 %; by Babinet's principle the light they scatter is of the same order, so roughly 1 % of the starlight goes into the spikes. That fraction is small, but the spikes of a bright star can cross the image of a much fainter neighbour.

The spike length also depends on wavelength: the envelope width scales with $\lambda$, so in colour images the spikes are dispersed, with red farther out than blue, much like the orders of a diffraction grating.

Sunstars in camera lenses

A camera iris made of $n$ straight or slightly curved blades forms a polygonal aperture, and each blade edge acts like a vane edge. The same counting rule applies: a lens with 8 blades gives an 8-point sunstar and one with 7 or 9 blades gives 14 or 18 points. Sunstars are strongest when the lens is stopped down to a high f-number such as f/16, where the blade edges are straightest and dominate the small aperture. Lenses with many rounded blades are designed to keep the aperture nearly circular for smooth background blur, and produce weaker, less defined sunstars. Cross-screen or star filters create a similar effect deliberately with a fine ruled grid on the filter.

Suppressing spikes

In astronomy, spikes can hide faint companions near bright stars. Options include curved vanes, which spread the same diffracted light into a diffuse halo instead of concentrated lines; off-axis designs with an unobstructed pupil; and, for high-contrast imaging, pupil masks and coronagraphs that block the spike directions. Rotating the telescope or the camera between exposures moves the spikes relative to the sky, so they can be identified and removed in processing. Spikes are sometimes mistaken for optical defects; a quick check is whether they rotate with the spider.

Common questions

Why do stars in JWST images have eight points?

The hexagonal primary mirror segments give six spikes, and the vertical secondary-mirror strut adds two horizontal ones. The other two struts are aligned with segment edges, so they strengthen existing spikes.

Do real stars have spikes?

No. A star is a point source whose image would be an Airy pattern with circular rings in an unobstructed telescope with a round pupil. The spikes are imposed by the instrument's aperture. The eye can add its own irregular rays, from structure in the lens and from eyelashes.

Why do some telescopes show no diffraction spikes?

Refractors and unobstructed off-axis reflectors have no vanes in the light path, and their round apertures have no straight edges, so their point spread function is close to the ideal circular pattern.

References: E. Hecht, Optics, 5th ed. (Pearson, 2017), Ch. 10 and 11; J. W. Goodman, Introduction to Fourier Optics, 4th ed. (W. H. Freeman, 2017); M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, 1999), Ch. 8.