Diffraction Spikes from Telescope Secondary Mirror Spiders

Stars. They are gazed at and wished upon. They have biblical, cultural, and scientific meaning. Stars retain a level of mystique regardless of wisdom or creed despite knowing they are simply balls of gas. Their allure across the ages has resulted in them being imaged using telescopes for quite some time. Over time this curiosity evolved into an entire scientific field of study. Along the way a number of telescoping imaging techniques were developed and perfected. With all these advancements one problem still remains in optical telescopes. Namely, diffraction spikes can cause images of stars to be less than fully representative of the star itself.

Imaging Improvement Techniques

Before diving into diffraction spikes, it must be recognized that imaging stars/planets/objects with telescopes at such distances and through layers of atmosphere can be tricky. One of the measures taken to obtain better image quality is to house the telescope at a high altitude to avoid much of the local weather. Other measures taken to obtain brighter and theoretically better resolution images include making a larger numerical aperture. In the case of reflecting telescopes, that means increasing the mirror size. However, creating such massive, perfect  mirrors is no small feat.

In practice, larger mirror telescopes (~4 m diameter) tend to have the same image sharpness as those with small mirrors (~20-40 cm) due to the atmospheric effects. Adaptive optics compensates for these atmospheric effects on the wavefront that make it difficult for reflective telescopes to reach a purely diffraction limited system. Among other things, namely focusing and directing the light, the secondary mirror assists with wavefront correction for better results when using adaptive optics.

The secondary mirrors of the Large Binocular Telescope (LBT) on Mt. Graham employ adaptive optics. Here, one of the primary mirrors is shown in the center and the secondary mirror is the dark object being supported in the top of the image, left of center. Courtesy of Kayla Filipek

About the same time adaptive optics was beginning to be practically used, so was active optics. Now, both are implemented to improve image quality. Active optics optimizes the primary (and/or secondary) mirror shape dependent upon environmental factors. The mirror(s) can be bent and cooled to compensate for whatever may be causing distortion, be it gravity, mechanical effects, temperature, wind, etc.

Diffraction Spikes

So, the mirrors are large, can be deformed, cooled, and the resulting image adjusted. But even then, diffraction persists. We know that stars are (roughly) spherical, yet they sometimes appear imaged with pointed geometries. The starburst effect when viewing with the eye is due to the atmospheric effects, but the spikes remain when imaged even though adaptive optics corrects for such atmospheric effects. These diffraction spikes are due to the arms/structs, or the spider, that supports the secondary mirror and can be referred to as diffraction spikes.

Diffraction spikes are the Fourier transform of the support arms. The resulting effect on the image depends on the number and curvature of the structs. A single struct creates two diffraction spikes, and two or more diffraction spikes appear as the same geometry of the support arms but rotated by 90^o. It has been determined that if the vanes are curved rather than straight, the diffraction effect is reduced. The diffraction spike gets spread out over a larger area, so the diffraction lines in the image are not as sharp. When the structs are curved into a half-circle, the diffraction spikes are essentially invisible to an observer. Instead of a spike, the light is now distributed over a less sharply defined area.

Examples of some spider configurations and the patterns of the resulting diffraction spikes. Courtesy of Medium.com

Diffraction also occurs along the edge of the aperture. This can create diffraction rings, like the Airy pattern. The Airy pattern can sometimes be faintly seen and cause an image to be somewhat blurry.  Strategies for diminishing the Airy pattern include stopping down both the focal and pupil plane.

Some telescopes have been constructed with no spider to eliminate diffraction from the mirror mount, or with just one supporting vane, but these can create a lack of stability, movement, and precision with the secondary mirror.

Predicting Diffraction Effects

One study found that imaging using curved spiders yielded no significant discrepancies in the point spread function (PSF). The central spike energy remained the same regardless of the number of arms. The curved supports had an insignificant effect on both the PSF and the modulated transfer function (MTF) values which is indicative of a comparably high resolution. Simulations have shown that thinner arms to the spider diffract less light but diffract more light from farther away, so the spikes appear longer. It was also determined that the light diffracted by the arms is proportional the front surface of the vanes as seen by the mirror.

Some commonly referred to image criteria, beyond the widely known MTF, include the Strehl Ratio and Fractional Encircled Energy. The Strehl Ratio is related to the MTF by being representative of the MTF averaged over all frequencies. It is the peak irradiance flux—what the non-optics world calls intensity. It is a measure of watts per meter squared as received by a surface/object. Strehl ratio is the ratio of peak irradiance of an aberrated PSF to the peak irradiance of the diffraction-limited PSF. Strehl ratio is a commonly used quantification of image quality. It can be modified for telescopes by dividing the diffraction-limited peak irradiance by the diffraction-limited peak irradiance without the spiders. A Strehl ratio of 0.8 is considered essentially diffraction-limited.

Fractional Encircled Energy is the radiant energy contained in a circle of a given radius centered on the PSF divided by the total radiant energy that reaches the focal plane. Researchers were able to predict this value for spiders of different widths using this criterion.

Off-axis Designs to Eliminate Diffraction Spikes

Though rarer than the average telescope, there are some telescope designs with off-axis mirrors. In this case, the pupil is unobstructed, and thus, the spider diffraction is eliminated since no structs are there to scatter the light. Since the telescope is decentered, this can increase the ease of alignment.

Conclusion

Whether or not one personally finds diffraction spikes attractive in an image or not, knowing what causes them, the predicted effects, and how to reduce or eliminate them is beneficial to the astronomer community.