Ground and space telescopes

Discontinuous telescope pupils, that is telescope apertures that have some portion of the aperture blocked are responsible for diffraction “noise” at the image plane. Breckinridge, Kuper and Shack (1982)⁵ were the first to discuss the role of secondary support diffraction spikes in finding exoplanets. Figure 2 below shows the diffraction pattern from the HST caused by the secondary support structure. Near the star we also see the “diffuse-light” effects of narrow angle scattered light. The sources of narrow angle scattered light in telescope/coronagraph systems were discussed by Harvey, et. al.⁶

Figure 2

HST image of a star showing the diffraction spikes that mask exoplanets at 4 position angles. The halo around the star is produced in the telescope/instrument system by narrow angle scattered light. The Airy diffraction pattern for HST is about 100 milliarc seconds which is too large to observe terrestrial exoplanets.

Figure 3 shows the pupil, left and the irradiance at the image plane for an on-axis star at 1-micron wavelength for the 30-meter diameter CELT (now called the Thirty Meter Telescope, TMT)⁷. The PSF is plotted on a log₁₀ intensity scale and the grey scale across the top of the PSF image on the right shows intensity order of magnitude from 10⁰ to 10^-10. The field of view is 1 x 1 arc-second. We see light scattered beyond 1 arc-second at intensities greater than 10^-4 to obscure accurate exoplanet radiometric and spectral measurements. This scattered light is caused by the periodic structure across the telescope primary mirror produced by the close-packet hexagonal segments. Clearly if we can devise a pupil architecture or topology to mitigate this prominent diffraction pattern science data quality and exoplanet yield will increase.

Figure 3.

a.) Illustration of the proposed 30 m diameter pupil of the CELT (now called the Thirty-meter telescope), complete with segmentation geometry, central obscuration and associated secondary mirror struts; b.) Monochromatic logarithmic PSF (wavelength=1 micron) for this Image. The field of view is 1 x 1 arcsecond. Diffraction effects of the triangular central obscuration and the secondary mirror struts are readily apparent, as are the characteristic hexagonal symmetry of the mirror perimeter and the inter-segment gaps.

Segmented space telescope diffraction

Space telescopes that are segmented use close-packed regular hexagon-sided mirrors to pack into a nearly circular telescope pupil. Figure 4 below shows, on the left, one of the concept apertures for the Large Ultra-Violet Infrared (LUVOIR) mission study. On the right we see the individual segments of the primary. This telescope primary exhibits three diffraction gratings which diffract light from the much brighter star across the image plane and create background noise for imaging and spectroscopy of exoplanets. The direction of the “rulings” of the gratings are shown using red, blue and yellow arrows.

Figure 4

LUVOIR pupil left and its partitioning into three linear diffraction gratings. The 3 “ruling” directions are clocked 60-degrees in relation to each other. The directions of the grating rulings are shown by the arrows in the three colors: red, blue and yellow.

The rulings are discontinuous across the LUVOIR pupil, but that does not make a difference to the diffractive properties of the straight lines. Figure 5 shows 2 of the 3 sets of diffraction grating rulings across the hexagonally segmented LUVOIR pupil. The third set of rulings, the horizontal set are not show to avoid confusion in the drawing.

Figure 5

Two of the three diffraction gratings across the close-packed hexagon-segmented primary mirror are shown. The spacing of the “ruling” is d.

Figure 5 shows the close-packed hexagon-segmented primary mirror with lines drawn to show the grating “rulings” and the direction of the rulings. Note that to keep confusion down we have not drawn in the set of horizontal “rulings”. The “groove-spacing” is seen to be d, where d is one-half the face-to-face distance across the individual regular hexagons. The diffraction causes a structured background across the image plane that may obscure important exoplanets and may introduce unwanted polarization aberrations into the coronagraph to affect image quality.

The PSF for a monochromatic star

Gratings diffract light into orders which map a single on-axis point (a monochromatic star, for example) into multiple images of that monochromatic star. If the source is polychromatic then the grating maps the polychromatic single on-axis point into multiple spectral images stretched out radially.

The angular separation between diffraction orders is θ as given in Eq. 1 above.

In figure 6 we see that a Lyot coronagraph occulting mask would only block light from the zero-diffraction order, which contains light from the bright central star. But light from the higher diffraction orders n>1 will scatter around the occulting mask to flood the detector plane. The occulting mask could be designed such that each order has its own mask, but that would block portions of the FOV where exoplanets might be found.

Figure 6

shows, left, a pupil map and right a representation of the monochromatic PSF associated with the close-packed hexagon-segmented primary mirror shown on the left. The points on the right-hand side show the location of the diffraction orders. The center is the image of the star and the first ring of points corresponds to the 1^st order of the three diffraction gratings. The second ring of points corresponds to the 2nd order of the three diffraction gratings.

To determine if the diffraction images of the parent star will obscure exoplanets, we calculate the angular separation between zero order and the first order, n=1, for polychromatic light. Table 2 below shows the angular separation of the 450, 500, 550 nm wavelength monochromatic diffraction orders as a function of the face-to-face segment size.

Table 2

Angular separation of the diffraction orders for face-to-face segment sizes: 1,2,3,4 meters. This applies to the diffraction orders shown in Fig. 6, above.

We compare the entries in Table 2 with the entries in Table 1 and see that the unwanted diffraction images of the parent star fall within the same FOV region as the exoplanets. Clearly there would be a significant advantage to the development of a straightforward, low absorption way to eliminate these diffraction orders. The pinwheel pupil provides that opportunity.

The PSF for a polychromatic star

Exoplanets are very faint thermal sources. If they are to be observed in monochromatic or narrow band light integration times become impossibly long. The HabEx coronagraph is planned to observe in 100 nm bandwidths. One of these bandwidths in 450 to 550 nm and we have used those values to compute the diffraction angles shown in Table 2. The star image at n=1 for the 1-meter face-to-face segments is a colored radial streak or small spectrum with 450 nm light at 93 masec and 550 nm light at 113 masec. The 2-meter face-to-face segments is a colored radial streak or small spectrum with 450 nm light at 47 masec and 550 nm light at 57 masec. This continues to the 4-meter face-to-face segments which give a colored radial streak or small spectrum with 450 nm light at 23 masec and 550 nm light at 28 masec.

Isoplanatic point spread function for image processing

The polychromatic PSF shown in figure 6 (right) not linear shift invariant and is therefore the optical system is not isoplanatic. Also, looking at Fig 6, right, we see that the PSF is not rotationally symmetric either. These two facts complicate digital image processing. In this paper, we have devised a pupil segmentation or topology architecture that will produce images from an emulated filled aperture telescope pupil even though the pupil is mechanically segmented. This promises to reduce significantly the effects of an anisoplanatic PSF and will make digital image processing more reliable and less uncertain.

Compensating for hexagonal segments

Technologies to compensate for the diffraction patterns produced by straight line gaps and straight-line support structures across primary mirrors of large telescopes has been an area of active study recently ⁸,⁹,¹⁰,¹¹,¹².¹³.

None of these methods may be completely satisfactory, however, since light is absorbed in the process.

Background

Breckinridge (2018)¹⁴ suggested partitioning the primary into curved sided segments and curving the secondary support structures to reduce diffraction noise at its source to control diffraction noise at the image plane of exoplanet coronagraphs. We have shown above that the hexagonal segment architecture or pupil topology leads to unwanted diffraction noise in the system. It is good engineering practice to seek ways to eliminate or reduce “noise” at its source, rather than devise complicated and signal absorbing methods to compensate. Methods to mitigate diffraction noise were developed over the years by amateur astronomers, and later optical scientists. However, the professional space and ground astronomical optical telescope and instrument community seems not aware of these techniques.

C. H. Werenskiold (1941)¹⁵ reported on the work of A. Couder published in the French journal: Astronomy, Jan 1934 and translated into English and republished in Amateur Telescope Making Advanced (scientific American Publishing), pp 620-622. Couder proposed controlling diffraction in Newtonian and Cassegrain type telescopes by placing lune shaped curved masks over the straight edge support structure of the secondary. These masks blocked significantly, the light-gathering ability of the telescope, negatively affecting the telescope transmittance. Werenskiold proposed curving the secondary support structures themselves as shown below in Fig 7 to reduce masking of the primary mirror and control the diffraction spikes.

Figure 7

The four secondary support structures built by Werenskiold¹⁴ and used for visual observation of planets. View looking from the open end of a reflecting telescope back toward the primary mirror. He reports that #4 gives the lowest quality image and that curving the support structure appears to remove the diffraction spikes from visual images to give higher contrast for visual planetary observations.

Werenskiold writes: “It is generally conceded that a reflector, in regard to definition obtained, is apt to be somewhat inferior to a refractor of comparable size. However, the use of a curved spider in a reflector appears to be a promising step towards reducing this difference in comparative performance of the two telescope types.”

Pupil architecture of topology

Richter¹⁶ selected 6 diffraction masks and photographed the diffraction pattern from each to show that curved arcs on the pupil left no discernible diffraction pattern at the image plane. Harvey¹⁷ (in this volume) used FRED¹⁸ and applied the design methodology outlined in Richter¹⁵ and developed further by Harvey and Ftaclas¹⁹ along with the computer analysis program FRED to show that the image plane diffraction patterns from curved secondary support structure is less than 10^-6 where-as the image plane diffraction patterns from straight line secondary support structure are ~10^-2.

Based on our intuitive understanding of diffraction from curved segments we designed a pupil topology for a “first look” at the diffraction effects. The design we chose is shown in Figure 8 below. We selected a 10-meter Cassegrain primary with an obscuration ratio of 0.16 and six curved secondary mirror support struts, each with a 30° arc of a circle and 20 mm wide gaps. There are three rings or zones of segments curved on all sides. Each zone contains 12 curved sided segments to create a telescope entrance pupil that has 36 segments.

Figure 8

Cassegrain primary with an obscuration ratio of 0.16 and six curved secondary mirror support struts (shown in Red), each with a 30° arc of a circle and and 20 mm wide. There are three rings or zones of segments curved on all sides. Each zone contains 12 curved sided segments to create a telescope entrance pupil that has 36 segments.

Figure 9 shows a plot of monochromatic intensity, on a linear scale, as a function of azimuth angle at field 0.75 arc sec. for three 10-m diameter pupil architectures: unobstructed, spider and pinwheel. The computation was performed using MatLab. Computational capacity limited the size of the sample interval across the pupil and we believe that may have resulted in an incorrect representation of the image plane diffracted light. However, several features in Fig 9 are worth noting. The profile for the 4-spider mask, shown in red, is much higher than that for the pinwheel which indicates that the pinwheel pupil is making a contribution to smoothing out the diffraction pattern. The prominent dip in energy at the feet of the spider diffraction pattern is probably the result of the very narrow bandwidth of this monochromatic computation. The noise on the pinwheel is probably caused by having an insufficient number of samples across the pupil, which was dictated by the array sizes and the computational time limits of Matlab. Consequently, we decided to drop MatLab as our computational tool and turn to Photon Engineering. LLC and the FRED software. Computations using FRED were successful and are shown in the paper: SPIE Proc 10698-60¹⁷.

Figure 9

Image plane linear-scale monochromatic intensity distribution from three 10-m diameter pupil topologies: unobstructed, spider and pinwheel are shown at field radius 0.75 arc-second for azimuth angles -180 to + 180 degrees.