# CATEcor: an Open Science, Shaded-Truss, Externally-Occulted Coronagraph

C.E.Craig DeForest0000-0002-7164-2786  D.B.Daniel B. Seaton0000-0002-0494-2025
A.Amir Caspi0000-0001-8702-8273  M.Matt Beasley  S.Sarah J.
Davis0009-0008-4901-0601  N.F.Nicholas F. Erickson0000-0001-6028-1703
S.A.Sarah A. Kovac0000-0003-1714-5970  R.Ritesh Patel0000-0001-8504-2725
A.Anna Tosolini0009-0000-3510-8116  M.J.Matthew J. West0000-0002-0631-2393
Southwest Research Institute, Boulder, Colorado, USA  Independent Researcher

###### Abstract

We present the design of a portable coronagraph, CATEcor, that incorporates a
novel “shaded truss” style of external occultation and serves as a proof-of-
concept for that family of coronagraphs. The shaded truss design style has the
potential for broad application in various scientific settings. We conceived
CATEcor itself as a simple instrument to observe the corona during the darker
skies available during a partial solar eclipse, or for students or interested
amateurs to detect the corona under ideal non-eclipsed conditions. CATEcor is
therefore optimized for simplicity and accessibility to the public. It is
implemented using an existing dioptric telescope and an adapter rig that
mounts in front of the objective lens, restricting the telescope aperture and
providing external occultation. The adapter rig, including occulter, is
fabricated using fusion deposition modeling (FDM; colloquially “3D printing”),
greatly reducing cost. The structure is designed to be integrated with
moderate care and may be replicated in a university or amateur setting. While
CATEcor is a simple demonstration unit, the design concept, process, and
trades are useful for other more sophisticated coronagraphs in the same
general family, which might operate under normal daytime skies outside the
annular-eclipse conditions used for CATEcor.

###### keywords:

Solar eclipse; Solar K corona; solar instrumentation

Sometimes, the truth is found not in seeking, but in hiding. – Khaled Hosseini

##  1 Introduction

Solar coronagraphs work by blocking out the Sun to produce an “artificial
eclipse” (Lyot, 1930), allowing imaging of the corona itself around the bright
Sun. Ground-based instruments must contend not only with instrumental
scattering but also with sky brightness (Figure 1). Such instruments are
optimized to image the innermost portion of the corona, which rises above the
local sky brightness; they include the Mauna Loa K-coronameter (Altschuler and
Perry, 1972; Fisher et al., 1981) and more modern instruments including CoMP
(Tomczyk and McIntosh, 2009) and K-Cor (de Wijn et al., 2012). Instruments
that image low coronal altitudes generally use internal occultation, in which
an initial focusing optic produces a real image of the Sun, and the light in
that image is rejected from the instrument by a physical object or a hole in a
reflecting optic. Internal occultation allows very precise selection of which
altitudes within the corona will be imaged, at the cost of requiring a very-
low-scatter initial optic and generating instrumental stray light in the far
field.

Spaceborne coronagraphs have practically no limitation from sky brightness,
and can image the corona much farther from the Sun, by using external
occultation to reject the bulk of the Sun’s rays even before the first optic.
This greatly reduces stray light in the far field, at the cost of vignetting
the field near the Sun itself. Examples of externally occulted coronagraphs
include LASCO/C3 (Brueckner et al., 1995) and STEREO/COR2 (Howard et al.,
2008). The most recent generation of spaceborne coronagraphs, including CCOR
(Thernisien et al., 2021) and PUNCH/NFI (Colaninno et al., 2019), eschew
internal or secondary occultation altogether and rely entirely on a highly
engineered external occulter to reduce stray light to levels compatible with
coronal imaging as far as 30 apparent solar radii ($R_{\odot}$) from the Sun.

The limitations of ground-based coronagraphs are greatly mitigated during
conditions that significantly improve (reduce) sky brightness. Figure 1 shows
typical sky brightness curves under various conditions. During an annular
solar eclipse, or at exceptionally high altitude in the atmosphere (e.g.,
above 80,000 ft. altitude), sky brightness can be reduced by an order of
magnitude or more compared to high desert conditions; in turn, that may enable
imaging of the middle corona (West et al., 2023) at or above 3 R⊙ from the Sun
without flying an instrument into space or requiring a total solar eclipse.
This insight led us to consider new instrument designs that might enable
ground-based imaging of the middle corona, farther from the Sun than is
possible from the ground under normal conditions.

Figure 1: Ground-based solar coronagraphs must contend with not only
instrumental scatter but the background sky brightness (dotted lines for
various conditions), which falls off slowly compared with the brightness of
the K-corona itself (grey line). This drives coronagraph solutions that are
optimized for the very low corona, requiring internal occultation. In very
high-altitude conditions or during an annular solar eclipse, the sky
brightness is reduced by an order of magnitude or more, enabling externally
occulted coronagraphs to image the corona to 3 or more solar radii. Figure
adapted with permission from Golub and Pasachoff (2009).

The imaging quality required to capture the middle corona is modest by the
standards of either spaceborne coronagraphs (which are optimized for very low
stray light and small instrument dimensions) or ground-based coronagraphs
(which are optimized to image very close to the Sun). Hence we did not
consider a complete new instrument, but a module that could extend an
existing, well-defined imaging system. We adopted the telescope and camera
from the Citizen Continental-America Telescopic Eclipse 2024 (CATE24) program
(Caspi et al., 2023; Patel et al., 2023), which in turn is a next-generation
version of the original Citizen CATE (Penn et al., 2020) project carried out
in 2017. The CATE24 observing equipment comprises a Long Perng doublet
refracting telescope with 80 mm aperture and 500 mm focal length (f/6.25) on a
German Equatorial Mount, and a FLIR Blackfly polarizing CMOS camera with an
integrated multiplex polarizer mask, allowing recovery of Stokes I, Q, and U
across the entire field of view (FOV) from each exposure. The imaging
resolution is 2.9′′ FWHM, limited by diffraction from the aperture, and is
matched to the 1.43′′/pixel plate scale of the overall system. (See Patel et
al., 2023, for further details.)

CATEcor modifies the CATE24 telescope with a clip-on assembly comprising an
aperture stop just in front of the telescope objective, and an external
occulter 75 cm in front of the stop. The occulter is supported by a truss that
remains fully shaded by the occulter itself; this reduces scatter from the
support structure, and reduces or eliminates the need for a dark “vestibule”
to support a pylon and the occulter, as in existing externally occulted
instruments (e.g., Howard et al., 2008). CATEcor thus embodies a new type of
instrument, a “shaded-truss externally-occulted coronagraph111The shaded-truss
design is the subject of a patent application by Southwest Research Institute.
First public disclosure was 2023 October 6. Contact the authors for more
information.”. Compared to conventional internally-occulted coronagraph
designs, the shaded-truss approach has lighter weight, lower instrumental
stray light in the far field, and the beneficial smooth inner-field
sensitivity rolloff that is characteristic of other externally-occulted
designs, at the cost of a more complex vignetting function (as the instrument
looks through a complex, structured truss).

The entire CATEcor assembly may be integrated from readily obtainable parts
and 3D printed elements, permitting individuals to reproduce CATEcor for
hobbyist or student applications; thus we refer to CATEcor as an “open
science” instrument.

In the following sections, we describe the trade space and requirements that
drive CATEcor, and present the actual design in sufficient detail to reproduce
the instrument. Section 2 gives requirements for CATEcor; Section 3 presents
the design concept, develops specifications for the optomechanical elements,
and presents the design elements. Section 4 describes fabrication and
integration steps for the instrument. Section 5 includes results from a full-
Sun test observation. Section 6 contains discussion of the novel design space
of CATEcor and its relevance to future instrumentation, and we draw
conclusions in Section 7. We also used CATEcor to image the corona at an
annular eclipse; that observation is detailed by Seaton et al. (2024).

##  2 Requirements for CATEcor

Two objectives drove us to build CATEcor: (1) to demonstrate coronal imaging
with at-hand materials including a low-cost commercial telescope available to
amateurs (the CATE24 telescope; Patel et al., 2023) and supplies and
manufacturing technology available to hobbyists; and (2) to validate a novel,
simplified coronagraph concept for coronal imaging. The primary design
requirements were:

Overall structure: CATEcor is intended as an easily manufacturable addition to
the existing CATE24 telescopes, which may be directly mounted on the telescope
and balanced with existing CATE24 project mounts, tripods, counterweights,
etc. Alignment and calibration must be accessible to amateurs or students with
the same skill level required of CATE24 operators in the main program.

Imaging resolution: The resolution requirement is driven by feature size in
the corona. Streamer tops are approximately 2–3′ across, levying an azimuthal-
direction resolution requirement of 2′ at apparent distances of 1.8 R⊙ or more
from disk center. This is modest or trivial for a small refractor such as the
80 mm aperture CATE24 telescopes, but significant for an externally occulted
coronagraph where the effective aperture may be very small, and drives
geometric aspects of the shaded-truss design. A 2′ diffraction limit requires
an effective aperture roughly 1 mm across or more. It also drives noise
performance of the instrument, as in DeForest et al. (2018).

Field of view: CATEcor must be in principle able to image full circle from 1.5
R⊙ to 2.5 R⊙ under the dark sky associated with a 90% annular eclipse, and
must capture sufficient altitude range of the corona to unambiguously
demonstrate imaging. The CATE24 telescopes have adequate FOV, extending to at
least $3$ R⊙ in all directions. For an externally occulted design, the inner
edge of the FOV is set by the occulter/aperture geometry. The outer limit of
the effective FOV is determined by background brightness and associated noise
characteristics. CATEcor is expected to capture from close to 1.5 R⊙ to
roughly 2 R⊙ with the possibility of a full solar radius from 1.5–2.5 R⊙,
based on typical K-corona brightness (Figure 1).

##  3 The CATEcor design

We conceived CATEcor as a front-end external occulter-and-aperture assembly
(Figure 2) to mount directly to the existing CATE24 telescopes, which are 80
mm diameter aperture tube-based dioptric telescopes with 100 mm diameter
retractable dust covers. In keeping with the CATE24 project philosophy of
reducing barriers to scientific measurement, we specifically designed CATEcor
to be easily assembled from readily available hardware and hobbyist Fusion
Deposition Modeling (FDM) equipment (“3D printing”). In principle, CATEcor
could be duplicated by anyone with acccess to an amateur telescope, a
computer, a 3D printer, and a hardware store.

The CATEcor assembly comprises fasteners and ancillary elements, linking four
3D printed parts: an external occulter (Figure 3), an aperture piece (Figures
4 and 5), a front plate (Figure 6), and a telescope tube extension (Figure 7).
The occulter is attached to the aperture piece by a 75 cm carbon-fiber hexapod
truss made from commercially available carbon-fiber rods, which are glued into
3D printed features in the occulter and aperture piece.

The telescope tube extension, front plate, and aperture piece were all
designed using the extremely simple web-based tool TinkerCAD (Backman and
Mononen, 2013). TinkerCAD was ideal because it is specifically designed to
lower barriers to CAD design by hobbyists and students, highlighting the
accessibility of appropriate mechanical design tools for everyone. The largest
drawback of TinkerCAD for this application is that it it uses a coarse
polyhedral tesselation for all curved surfaces. Typical outside dihedral
angles produced by TinkerCAD, when approximating round surfaces, are 6∘ or
more. This was acceptable for the mechanical interface structures such as the
telescope attachment, but unacceptable for the occulter itself. We therefore
used the open-source FreeCAD software (Riegel, Mayer, and contributors, 2002)
for the occulter itself.

All of the 3D printed parts’ designs are freely available in “.stl” and other
formats, and are available for download (DeForest, 2023).

In the following subsections, we describe and develop the fundamental design
concept of a shaded-truss externally occulted coronagraph (Section 3.1);
develop the occulter design (Section 3.2); and describe the designs for the
truss (Section 3.3), aperture (Section 3.4), front plate (Section 3.5), and
telescope extension tube (Section 3.6).

###  3.1 Shaded-truss externally occulted coronagraph concept design

The coronagraph design space is dominated by the observed strong radial
gradient in the K-coronal brightness (Figure 1). Coronagraphs generally
capture an annular FOV. The inner edge is limited by the geometry and
diffraction characteristics of the occulter. The outer edge is limited by
background sources of light: sky brightness for ground-based instruments or
instrumental stray light for spaceborne instruments. At large apparent
distances (elongations), the desired K-corona signal drops well below other
background sources including the F-corona; but digital post-processing enables
separation of the K signal even at very large elongation angles and contrast
ratios as low as a few $\times~{}10^{-4}$ (Jackson, 1985; DeForest, Howard,
and Tappin, 2011), enabling both wide-field coronagraphs (e.g., Brueckner et
al., 1995) and the relatively new field of heliospheric imaging (e.g., Eyles
et al., 2003; Howard et al., 2008; DeForest et al., 2022). Although Fresnel
diffraction is important to certain parts of coronagraph design (specifically
the occulter), ray optics are sufficient to design most of the instrument
geometry, with recourse to wave optics only for the detailed design of the
occulter itself.

Externally occulted coronagraphs trade simplicity (of a direct occulter
casting a shadow on the entrance to a camera or telescope) for fuzziness of
the boundary of occultation on the image plane. The fuzziness arises because
external occulters at finite distance in front of the optics are imaged out of
focus in the field of view. That is because the corona itself is at optically
infinite distance, and therefore focusing the optics to image the corona
necessarily defocuses the image of the much-closer occulter.

Figure 2: Geometry of a generic externally occulted coronagraph shows the
related geometrical quantities used to specify even the simple CATEcor
instrument. The occulter is sized to completely shadow the aperture and the
dark baffle area. The inner edge of the FOV, $\varepsilon_{i}$, is set by the
angle between the edge of the occulter and the near edge of the aperture. The
innermost unvignetted portion of the FOV, $\varepsilon_{u}$, is set by the
angle between the edge of the occulter and the farthest edge of the aperture.
The umbra and penumbra extend inward and outward, respectively, from the edge
of the occulter as shown. The spreading angle between the umbral and penumbral
boundaries is the apparent solar diameter 2 $R_{\odot}$, and is exaggerated by
a factor of 5 in this conceptual diagram.

Figure 2 illustrates the basic geometry of a generic dioptric externally
occulted coronagraph, exaggerating the apparent size of the Sun by a factor of
5 for clarity. An occulter casts a shadow down the length of the instrument.
Penumbral and umbral edges formed by the outer edge of the occulter are marked
in orange. The occulter is sized such that the edge of the umbra lands outside
a “dark aperture” that extends beyond the objective lens of the system. The
principal design quantities are: $d$, the distance between the aperture and
last effective plane of the occulter; $r_{a}$, the radius of the aperture;
$r_{d}$, the radius of the dark zone behind the occulter; and $r_{o}$, the
radius of the final disk of the occulter itself. While instrument dimensions
are lengths, the extent of the annular FOV is best described with solar
elongation angles (apparent radial distances) $\varepsilon$. The inner edge of
the FOV is set by the angle between the outermost edge of the occulter and the
nearest portion of the active aperture of the imaging optics, i.e.,

$\varepsilon_{i}=\left(r_{o}-r_{a}\right)/d\,,$ (1)

under the small-angle approximation that $\sin(\theta)=\theta$. Meanwhile, the
first non-vignetted elongation $\varepsilon_{u}$ is just

$\varepsilon_{u}=\left(2r_{o}+2r_{a}\right)/d\,.$ (2)

In turn, the occulter size $r_{o}$ is determined by the dark radius $r_{d}$,
the distance $d$, and the apparent size of the Sun $R_{\odot}$. For very long
instruments in which $r_{d}\ll r_{o}$, $r_{a}$ is negligible and
$\varepsilon_{u}\geq 2~{}R_{\odot}$; for short instruments such as CATEcor,
$r_{o}\approx r_{d}$ and $\varepsilon_{u}\geq 4~{}R_{\odot}$. CATEcor
observations are vignetted throughout the anticipated effective FOV.

Note that $R_{\odot}$ varies between the dates of perihelion and aphelion. At
the time of CATEcor’s initial deployment, 2023 October, $R_{\odot}$ is roughly
16′ and therefore,

$r_{o}\geq r_{d}+R_{\odot}d=r_{d}+4.654\times 10^{-3}d\,.$ (3)

The actual diameter of the occulter is generally slightly larger than the
equality of Equation 3, to allow for pointing error and/or a margin for
Fresnel diffraction; in general, one can hold pointing margin in $r_{d}$ and
use the equality rather than the inequality in Equation 3.

The inner edge of the FOV is the angle where the vignetting function reaches
0%, i.e., the angle at which a single ray can pass the occulter and enter the
near edge of the objective. It is thus determined by

$\varepsilon_{i}=R_{\odot}+\frac{\left(r_{d}-r_{a}\right)}{d}\,,$ (4)

where again $R_{\odot}$ is the apparent solar radius (an angle) rather than
the actual physical size of the Sun (a length). The narrower the occulted
umbral buffer $r_{d}-r_{a}$ can be, the narrower the FOV. Further, for a given
required umbral buffer $r_{d}-r_{a}$ around the aperture, larger/longer
instruments can image closer to the Sun than smaller/shorter instruments.

The design drivers for the external shaded-truss concept are the structure of
the occulter and the design of the support.

The occulter itself must combat Fresnel diffraction of sunlight around the
occulting edge. Existing externally occulted coronagraphs use carefully
aligned multi-disk designs with tight positional and angular tolerances. We
designed an occulter form (Section 3.2) that greatly increases alignment
tolerance while still reducing Fresnel diffraction (compared to a disk) and
maintaining light weight.

The shaded-truss design supports the occulter on a cantilever truss that must
be stiff enough to maintain occulter alignment, while remaining fully within
the umbral shadow of the occulter and also obscuring as little of the FOV as
practical. We designed a simple hexapod truss built from narrow carbon fiber
rods (Section 3.3).

The length of the truss is only loosely constrained by the design. In general,
longer trusses perform better: the Fresnel diffraction brightness varies as
$\sqrt{\lambda/L\theta}$, where $\lambda$ is wavelength, L is the length
between the occulter and objective lens, and $\theta$ is bend angle (inner FOV
edge). The mechanical stiffness and buckling resistance of the truss
constrains the length: occulter mass increases as $L^{3}$ and the first
normal-mode frequency of the spring pendulum formed by the truss and occulter
therefore decreases as $L^{-2}$. We chose 75cm to place the first normal mode
in the 10-20 Hz range with 2mm diameter carbon-fiber rods and an occulter
under 50 g, and found that it met the Fresnel diffraction requirements for
this particular instrument.

###  3.2 Occulter design

Occulters are limited in effectiveness by Fresnel diffraction, which allows
direct sunlight to diffract around the sharp (projected) edge of the occulter
and into the optics. The effect of diffraction is reduced by larger instrument
size or by larger inner-edge elongation angles, and by multiple bends. Fresnel
scattering effects are in general complicated and require careful numerical
analysis. However, in simple geometries and approximations, Fresnel
diffraction is tractable. The straight razor-edge approximation to Fresnel
diffraction can be performed in 1-D and requires a cornu-spiral calculation
(e.g., Hecht and Zajac, 1974, §10.3.9). In the case of a single plane-wave
(collimated beam), the full integral reduces to the Fresnel special functions
$S$ and $C$, and may be written:

$I_{scatter}=\frac{I_{B}}{F^{2}}\left[\left(C(\theta
F)-\sqrt{\frac{\pi}{8}}\right)^{2}+\left(S(\theta
F)-\sqrt{\frac{\pi}{8}}\right)^{2}\right]\,,$ (5)

where $I_{scatter}$ is the intensity of light scattered around the occulter
from the single collimated source to a detector, $\theta$ is the scattering
angle around a nearly-straight section of occulter, $F\equiv\left(\pi
d/\lambda\right)^{0.5}$, $d$ is the length of “throw” from the occulter to the
detector, and $\lambda$ is the wavelength of light being considered. For
polychromatic or white light, an integral over $\lambda$ is implied. The
special functions $S$ and $C$ are defined by:

$S(\alpha)=\int_{0}^{\alpha}\sin\left(u^{2}\right)du$ (6)

and

$C(\alpha)=\int_{0}^{\alpha}\cos\left(u^{2}\right)du\,.$ (7)

While Equation 5 strictly applies to linear cases, it is appropriate and
conservative for estimating the stray light diffracted around the occulter
provided that the ray-approximation impact parameter between a given ray at
the aperture and the occulter itself is small compared to the radius of the
occulter, i.e., for the observed “bright ring” of Fresnel-scattered light
observed near the occulter on the image plane (Howard et al., 2008).

For $d=75$ cm, $\lambda$ over the range 450–650 nm, and an apparent
occultation diameter of 1.4 R⊙, averaging Equation 5 across plane-wave
contributions from the extended solar disk and across wavelength yields a
total scattering coefficient of $7\times 10^{-4}$, most of which is contained
in the bright ring around the occulter. Taking the in-lens scattering
coefficient to be of order $10^{-2}$, which is conservative by roughly
$10\times$ compared to typical values, this brightness corresponds to a hazy
background brightness of roughly $10^{-5}$ B⊙ at 2 R⊙ in the FOV. During a 90%
annular solar eclipse, this brightness level is reduced by another order of
magnitude, to $10^{-6}$ B⊙, which is comparable to the expected sky brightness
at 2 R⊙ in Figure 1.

Conventional occulter designs have evolved from single disks to multi-disk
assemblies, so that multiple Fresnel scattering events are required for light
to enter the instrument aperture (e.g., Howard et al., 2008; Dudley et al.,
2023). These assemblies can be difficult to manufacture and to align. One way
to simplify alignment is to eliminate angular alignment altogether, by forming
the occulter from a section of a sphere as in the spaceborne ASPIICS
instrument (Zhukov, 2016) whose free-flying occulter is intended to operate
hundreds of meters away from the aperture; this solution works well when the
sphere’s radius is long enough to enforce multiple Fresnel scattering events
along the surface of the occulter, which is not the case for CATEcor.

We designed the CATEcor occulter to make use of a characteristic of FDM 3D
printing: printed objects are fabricated in layers, which produces micro-
ridges along the structure of the final object. A gently curved 3D printed
surface therefore approximates a more precisely machined set of edges similar
to the edges of a multi-disk occulter. We initially considered a spherical
envelope similar to that of ASPIICS because spherical surfaces are simple to
align. But a spherical FDM occulter with diameter of a few cm would be
sufficiently rounded that typically only one of the FDM ridges would interact
with the light, and a spherical occulter would therefore behave optically like
a single disk.

Multi-disk occulters in general have more gently curved envelopes than a
similarly sized sphere. The ideal envelope is close to an “ogive”: a figure of
revolution of a large circle, about a chord near the perimeter of the circle.
The ogive shape allows a constant angular offset between uniformly-spaced
disks. To improve the CATEcor occulter’s effectiveness, we used an approximate
ogive shape with sufficiently long major diameter to allow multiple FDM ridges
to interact with the light, thereby approximating the effect of a series of
very finely machined disks in a more conventional occulter.

We approximated an ogive form with a prolate circular ellipsoid. This choice
was because ellipsoids are simple to create in 3D CAD programs, by stretching
a spherical primitive shape. We selected an ellipsoid with minor diameter 37
mm and major diameter 117 mm, i.e. stretched in the prolate direction by a
factor of $\sqrt{10}$ compared to a 37 mm diameter sphere. The 37 mm minor
diameter arises from the inner FOV angle and the selected length of the truss
suspending the occulter (Figure 2). The stretching resulted in a local major
radius of curvature of 185 mm at the equator of the ellipsoid, exactly 10
times the minor radius of 18.5 mm. We retained only a small section of the
ellipsoid, near its equator; this yielded an approximate truncated-ogive bowed
cylinder shape as diagrammed in Figure 3. This provides for a significant
length of interaction between the corrugated surface and near-tangent incident
light from the solar disk, while also allowing some angular alignment
tolerance for the assembly. The truncation was slightly asymmetric about the
equator, as shown in Figure 3, to provide a small amount of additional
interaction surface to explore the interplay between stray light and aperture
size.

Figure 3: Conceptual cross-section of the CATEcor occulter shows the truncated
ellipsoid, which approximates a shape with constant major radius of curvature
(i.e. an ogive). The occulter is a figure of revolution about the centerline.
The active occultation band obscures 2.4 $R_{\odot}$ of sky to block both the
Sun’s disk and the 0.4 $R_{\odot}$ design margin. The additional thickness
provides rigidity, mount holes for the occulted hexapod truss, and wide
alignment tolerance of roughly $\pm 1$∘. Not shown: center through-hole for
alignment and six dark-side blind holes for the hexapod truss.

The major radius of curvature of the CATEcor occulter is 185 mm at the widest
point, and therefore the 0.4 $R_{\odot}$ angular separation between the solar
umbra and the start of the FOV imposes a separation of 340 $\mu$m between the
point of tangency of rays from the solar limb and the closest point of
tangency of rays that can enter the aperture of the instrument. To enter the
aperture, rays from the photosphere must thus traverse between 0.34 mm and
2.06 mm of the occulter’s outer envelope, to enter the aperture as part of the
observed bright ring around the occulter. The shorter distance represents the
smallest bending angle of solar rays; this is traversed by rays from the solar
limb point closest to the edge of the FOV, to enter the outermost portion of
the aperture. The longer distance represents the largest bending angle, which
is traversed by the ray from the solar limb point farthest from the edge of
the FOV, to enter the outermost portion of the aperture. Points not on the
ultimate perimeter of the aperture are, of course, better shielded and require
rays to curve around more of the occulter. The 0.34–2.06 mm buffer zone on the
curved envelope of the surface reduces overall Fresnel scattering by a factor
of 10–100 compared to a single razor-sharp edge. This establishes a zone from
0.86 mm above the widest point, to 1.81 mm below the widest point, as the
“zone of occultation” in ideal geometry. However, other uncertainties require
an occulter thicker than the approximately 3 mm this would imply.

Mounting and aligning the occulter is a significant challenge for an
instrument that is designed to be reproduced by students, and we therefore
designed it with wide angular tolerance; this translates to additional
thickness beyond that required for the active occultation zone. Canting the
occulter by 1∘ moves the point of tangency up by 3.2 mm on one side and down
by 3.2 mm on the other, while maintaining the overall occultation properties.
Further, the observed head positioning uncertainty of typical FDM 3D-printed
objects is 50–70 $\mu$m; that yields an uncertainty in the occultation zone
placement of an additional $\pm 4.0$ mm. Thus the minimum height of the
occulter is dominated by alignment uncertainties: a total of 7.2 mm are
required on either side of the band of active occultation, for combined
fabrication and alignment tolerances.

FDM printed objects are formed in layers, which form a corrugated surface with
small bulges at the center of each layer and small canyons between the layers.
The CATEcor occulters are printed at 50 $\mu$m layer thickness, ensuring at
least 50 layers across the zone of occultation, and a minimum of 6 layers for
any one photospheric ray to bend around. Compared to a fully smooth polished
ogive surface, the layering yields a modicum of resistance to particulate
contamination, by reducing the effect of invisibly small 50 $\mu$m-sized dust
particles in the non-clean-room environment of a remote observing site.

The CATEcor occulters are specifically designed for manipulation of the inner
FOV, to explore futher occultation if necessary. Therefore they are extended 3
mm farther in the direction of the instrument, providing meaningful additional
deeper occultation (with a wider occultation zone) out to 3.2 R⊙. The final
design is thus a “puck” some 20 mm tall: a truncated ellipsoid (approximating
a truncated ogive) with minor radius 18.5 mm and major radius 185 mm, with the
widest point (widest cross section, at 37 mm diameter) 1.5 mm above the
centerline between top and bottom, and 8.5 mm behind the front (Sun-facing)
surface. As implemented with FDM printing, the puck is micro-corrugated at the
50 $\mu$m scale.

A through-hole at the center of the occulter permits alignment during
assembly, and is blocked in use by black adhesive tape.

The CATEcor occulters also contain 2.5 mm diameter blind holes to mount 2.0 mm
o.d. truss rods during assembly. These holes occur in pairs on a radius of
14.5 mm from the centerline, and are tilted by 1.1∘, to form the hexapod. The
holes are slightly oversized to avoid overconstraining the rods during
assembly.

###  3.3 Shaded-truss design

Externally occulted coronagraphs generally use a large baffled “vestibule” to
control stray light, with an occulter supported by a rigid pylon (e.g.,
Brueckner et al., 1995). Instead, CATEcor supports its occulter with a carbon-
fiber truss that is directly shaded by the occulter, simplifying stray light
control by keeping the support structure out of direct sunlight. The design
eschews the vestibule entirely. The optical field of regard is limited by a
baffle mounted on the telescope tube, as diagrammed in Figure 2. At a cost of
increasing the complexity of the instrument’s vignetting function, this
support method provides simplicity, greatly eases alignment, and reduces total
instrument mass and complexity.

CATEcor uses the simplest possible fully-constrained truss: six rods mounted
between two equilateral triangles of mount points, one on the occulter and one
on the perimeter of the optical aperture. We chose carbon fiber for the rod
material, for its ready commercial availability, high strength-to-weight
ratio, and stiffness. The rod diameter is 2 mm, chosen to reduce vignetting
while supporting a light occulter at 75 cm distance from the mount. The Euler
buckling force limit for an unsupported 75 cm long, 2 mm diameter carbon-fiber
rod is 4 N, with $10\times$ safety factor; CATEcor uses glue to fix the rod
ends, providing angular support and increasing the safety factor by another
factor of 4. The occulter mass is approximately 10 g, which imposes a bending
force of 2–3 N on the truss when extended horizontally, well within the
capability of the six 75 cm rods composing the hexapod.

Figure 4: The CATEcor aperture, seen here from the point of view of the
occulter, is sized to fit well inside the umbra of the occulter while still
supporting imaging at 1.5 R⊙. A surrounding deck encloses a precise iris
aperture (not shown). With ideal pointing the umbra of the occulter forms a 30
mm diameter circle; the baffle is entirely inside the umbra. The aperture is
encroached upon by three small decks above the iris, supporting the six rods
of the hexapod truss. The decks partially vignette the innermost portion of
the FOV. The effective aperture is shown for three points on the sky, aligned
with one of the hexapod supports: 1.5, 2, and 2.5 R⊙ from Sun center.

###  3.4 Aperture design

To minimize the dark aperture region in Figure 2, the CATEcor aperture is not
a complete circle: it is encroached upon by three decks supporting shaded
hexapod feet, reducing the diameter of the required dark-shadow region. The
aperture and truss are guarded by a thin printed circular baffle (Figure 2)
whose leading edges are just inside the umbra of the occulter and just outside
the aperture-plane triangle formed by the truss rods. The top few mm of the
baffle are just 0.5 mm wide to separate the umbra from penumbra while
retaining as much open aperture as possible.

Figure 4 shows the effective unvignetted aperture for three individual points
on the sky: the points at 1.5 R⊙, 2.0 R⊙, and 2.5 R⊙, on the planned observing
date of 14-Oct-2023 (apparent solar radius = 16′). The top edge of each
colored unvignetted aperture region is defined by the occulter itself; the
diagonal “cutouts” at 2 R⊙ and 2.5 R⊙ are from the truss rods.

The instrument resolution is governed by Fraunhofer diffraction through the
effective aperture, and is anisotropic. The radial diffraction limit at 1.5 R⊙
is set by the 1.5 mm distance from top to bottom of the sliver of effective
aperture, and is roughly 1.5′–2′, comparable to human visual acuity. The
tangential/lateral diffraction limit is roughly 0.3′ at that distance from the
Sun. At 2 R⊙, the radial diffraction limit is roughly 0.5′, and the lateral is
under 0.1′. Above 2 R⊙, the effective resolution is likely to be limited by
noise effects rather than seeing or diffraction (DeForest et al., 2018).

CATEcor includes an optical-grade adjustable-iris aperture stop, located just
behind the three hexapod decks. The stop is adjustable to explore the trade
between inner FOV diameter and stray light with smaller optical apertures.

Figure 5: CATEcor aperture piece mounts to the CATEcor front plate, and is
secured by six M3 bolts around the perimeter. Lateral stability is ensured by
positive lock between the tabs on the front plate and matching recess holes on
the underside of the aperture piece. 1/4 of the perimeter has a slot to allow
adjustment of the adjustable-iris aperture stop in the interior. Small finger
tabs on the perimeter help to mate/demate the press-fit features with the
front plate. Two of the three hexapod mounting decks can be seen at the base
of the central aperture.

The 28 mm diameter primary aperture, hexapod supporting decks, and tube/rim
baffle are 3D printed as a single piece (Figure 5). The aperture piece
supports the hexapod and is supported by a front plate located behind it. Each
hexapod deck has two 10 mm deep blind holes, 2.5 mm in diameter, canted at
0.6∘, to support the ends of two of the 2 mm diameter hexapod rods. The holes
are slightly oversized compared to the rods, to provide alignment play and to
allow room for glue to bond the rods rigidly to the aperture piece.

The aperture piece is fixed precisely relative to a supporting front plate, by
six radially-aligned rectangular alignment holes in the bottom surface. These
mate with rectangular-extrusion alignment tabs in the front plate. The pieces
press-fit together, and small finger tabs are provided to mate/demate the
pieces. The aperture piece is secured by six M3 fasteners which extend, via
through-holes that penetrate the aperture piece and front plate, into captive
square nuts in a supporting telescope tube.

A slot in the aperture piece gives tool access to an adjustment lever on an
adjustable-iris aperture stop underneath. The slot is 10 mm wide, too narrow
for fingers but wide enough to reach in with a small screwdriver or Allen key.
The slot is interrupted by a plastic beam to maintain stiffness of the entire
part. The top surface is radially beveled to reduce glinting stray light after
surface treatment (painting). The slot for adjustable-iris control acts as a
light trap in use, and does not noticeably increase stray light or glint.

Figure 6: CATEcor front plate rests on top of the tube adapter. A circular
groove at the bottom mates with the circular ridge at the top of the tube
adapter. A central 55 mm diameter hole allows light to enter the telescope
objective lens. A square recess in the structure accepts an adjustable-iris
aperture stop (not shown). Radial ridges mate positively with radial recesses
on the underside of the aperture piece, to ensure dimensional stability.
Hexagonal recesses (not visible) on the underside mate with M6 through-bolts
to secure the adjustable-iris aperture stop. The top and bottom feature
“optical maze” mounting rings both for alignment and to prevent stray light
entering through joints in the assembly. Small finger tabs on the perimeter
help to mate/demate the press-fit alignment features with the aperture piece.

###  3.5 Front plate design

The aperture piece rests on a front plate interface that accepts and supports
an adjustable-iris aperture stop assembly, and in turn rests on a telescope
adapter tube. The aperture stop assembly is bolted in place with three M6
through-bolts that mate with captive hex nuts on the underside of the front
plate. The caps of the bolts recess into holes in the aperture piece. The bolt
holes are slightly oversized to allow adjustment of the aperture stop’s
lateral position during assembly, before the bolts are torqued down.
Positional alignment is maintained between the mounted aperture piece and the
bolted-on aperture stop, via six extruded alignment features that mate with
alignment holes on the underside of the aperture piece. A circular mounting
ring, together with a corresponding groove on the underside of the aperture
piece, forms a four-bounce “optical maze” to prevent stray light entering the
dark space behind the aperture.

###  3.6 Telescope tube extension design

Figure 7: CATEcor tube extension is designed to slip over the dust cover of a
CATE24 telescope. It is secured by six nylon M8 bolts with captive hex nuts on
the inside and nylon washers and hex nuts on the outside. A circular mount
ring aligns the tube and prevents external light from entering. The front
plate and aperture are secured by six M3 through-bolts into captive square
nuts.

The telescope tube extension is fabricated with 10 mm thick walls for
stiffness, and is secured to the CATE24 telescope tube by six nylon M8 bolts
forming a dual triangular friction mount. The nylon M8 bolts are retained by
hex nuts held captive by interior hexagonal holes. The front plate and
aperture piece are secured to the tube with six steel M3 bolts that engage
with six captive square nuts near the top of the piece.

##  4 Fabrication and Integration

All 3D printed parts of CATEcor were printed on a hobbyist 3D FDM printer
(PRUSA Mk 3) in black polyethylene terephthalate glycol (PETG) plastic. The
FDM settings depended on the part. The telescope tube and front plate were not
required to have particularly precise shape and we printed them at high speed
with 200 $\mu$m layer thickness and 15% infill. For the aperture piece we used
“precision” (lower speed) extrusion settings, with 150 $\mu$m layer thickness,
with 30% infill and doubled perimeter wall thickness and top/bottom surface
layer count, for rigidity. The occulter required highly precise form and was
iterated several times to optimize printer-specific parameters for the
cleanest print. We printed it with 50 $\mu$m layer thickness, with external
perimeters deposited first to provide the cleanest possible exterior shape,
and 30% infill.

Figure 8: A jig piece used to align the occulter assembly matches the shape of
the CATEcor front plate, with rigid support for a seventh alignment rod at the
center of the assembly. The central gusseted tube fits into the central hole
of the CATEcor aperture piece, to align the aperture piece and occulter while
the hexapod truss undergoes assembly and gluing.

The trickiest and longest integration step was assembling the front-end
assembly comprising the occulter, hexapod rod truss, and aperture piece. We
describe that process here, to illustrate its simplicity and the lack of any
special tools required.

To align the occulter we printed a separate jig piece (Figure 8) that accepted
a seventh 2.0 mm diameter rod. We placed the jig directly under an alignment
hole drilled into a “2$\times$2” wooden alignment beam that was rigidly
mounted 90 cm above the work surface. We aligned the jig piece using a plumb
bob, then marked the work surface at the location of the jig piece so that the
jig piece could be moved and replaced at the same location.

We secured the rods to the occulter and aperture piece with household 2-hour
cure epoxy. After mixing the epoxy, we placed the occulter, upside down, on a
clean work surface, and used a bit of rod scrap to pack the six hexapod mount
holes in the occulter approximately 25% full of epoxy. We wiped up excess
epoxy using a paper towel, wiping radially inward from the edge of the
occulter to avoid smearing any epoxy on the active surface.

We mounted an aperture piece on the jig, then threaded the occulter, sunlit
side up, onto an uncut (120 cm long) 2 mm rod, threaded the top of the rod
upward through the hole in the alignment beam, then threaded the bottom of the
rod downward through the aperture piece into the central tube of the jig.
Finally, we placed the jig inside the alignment marks on the work surface.
This provided lateral positional alignment of approximately $\pm$2 mm between
the occulter and aperture piece, equivalent to angular alignment of $\pm$10′.
The occulter central hole fit tightly on the central alignment rod, affording
approximately $\pm$20′ of angular tolerance for an overall $\pm$0.5∘ alignment
precision compared to the $\pm$1∘ design tolerance.

Once the jig, aperture piece, alignment rod, and occulter were placed under
the alignment beam, we assembled the hexapod. For each rod, we wiped the ends
with an isopropanol-wetted paper towel, waited a few seconds for the ends to
dry, then dipped one end approximately 1 cm deep in the epoxy, wiped it on the
mixing container to remove excess, carefully inserted the glue-covered end
into one of the mount holes in the aperture piece, and finally bowed the rod
to insert the clean end into the corresponding pre-packed mounting hole in the
occulter. During the insertion, we secured the occulter by grasping it between
thumb and forefinger, by the sunlit and shaded flat surface (not the active
surface). For each rod, we examined the hole ends for excess epoxy and wiped
any excess using the end of a 1.5 mm flat-blade screwdriver. We assembled the
rods in circular order around the hexagonal assembly. When all rods were
inserted at both ends, we visually inspected the occulter for placement, and –
holding the rods and not the occulter – we rotated the occulter roughly 45∘ to
either side of its ideal alignment, to further spread the epoxy in the holes,
before aligning the occulter rotation angle.

To set the rotation angle we sighted through the truss, standing along one of
the six mirror symmetry planes of the truss assembly. Pairs of rods form vee
shapes at the bottom of the truss, and complementary pairs form inverted-vee
shapes at the top of the truss. Standing so that one vee on the front side
bottom lines up with the central rod should also cause the complementary
inverted-vee on the rear side top to line up with the central rod. We twisted
the occulter into best visual alignment by sighting along one of the three
major symmetry planes and verified alignment by sighting along the other two.

We allowed the epoxy to cure for 8 hours, then removed the central rod from
the jig, and removed the aperture-truss-occulter assembly. We verified
rigidity by plucking the truss while holding the aperture piece firmly against
the work surface, to observe the low oscillation modes and verify the low-
amplitude fundamental to be at or above 10 Hz. Because the hexapod is the
minimum complete support system, even one loose glue joint has a large effect
on the fundamental mode frequency and is obvious.

Based on initial testing (Section 5), we treated the surface to reduce glint.
We applied a light coat of commercial Krylon ultra-flat camouflage black spray
paint to the entire occulter assembly, holding the spray can some 8 inches
from the occulter and lightly “spritzing” the paint. Similar treatment was
applied down the length of the truss and in the interior of the aperture
assembly, to prevent glint from the finished plastic. Particularly on the
occulter itself, and also on the truss, we did not attempt full coverage, just
a single very light coat. This was sufficient to intercept any glint coming
along the occulter at grazing incidence. We tested both coated and uncoated
assemblies and found the stray light from uncoated assemblies to be reduced by
3$\times$ or more in the coated assembly (Section 5).

Figure 9: CATEcor adapter assembly drawing shows how the various parts,
including occulter, fit together. All parts are 3D printed using fusion
deposition modeling at various layer widths, except for the truss rods – which
are 2 mm diameter pultruded carbon fiber, cut to 76 cm length.

Assembling the rest of CATEcor is more straightforward. We fitted M8 nylon
screws with a bolt and washer, then threaded them through the holes in the
telescope extension tube and secured them with captive nylon nuts in the
interior hexagonal holes. We fitted a commercial iris into the front plate and
bolted it in with M6 bolts and captive nuts. We placed the front plate on the
telescope interface tube alignment ring. We placed the aperture/occulter
assembly on the front plate, so that the ejection tabs on the perimeter
approximately lined up, then secured the entire assembly using six M3 bolts
through the six perimeter holes in the aperture assembly, into captive square
nuts in the telescope extension tube. This resulted in the full assembly shown
in Figure 9.

To observe, we integrated the CATEcor assembly to a CATE24 telescope, on-site
at an observing location. We developed a procedure to avoid direct solar
exposure through the unprotected telescope onto the detector. We first aligned
the telescope and aimed it at the Sun, tracking solar rotation, with a solar
filter on the objective lens. One person held a shadow mask above the
telescope, casting a shadow onto the objective, while another person removed
the solar filter and replaced it with a CATEcor assembly. We stopped down the
iris aperture, and iterated a process of briefly removing the shadow mask to
observe the shadow of the occulter, then adjusting the nylon set screws to
bring the shadow closer to being centered on the aperture and checking
alignment again. After 3–4 iterations the occulter shadow was centered over
the aperture and we removed the shadow mask entirely. During observation, we
observed the aperture periodically and used the telescope pointing controls to
re-center the solar image and shadow as needed.

##  5 Initial testing

We constructed an engineering unit of the CATEcor coronagraph front-end
assembly, and performed simple testing on it including deployment on a CATE24
telescope on a sunny day.

The aperture-truss-occulter assembly, fully assembled, has a mass well under 1
kg and is readily manipulated by hand. It is easy to sight through the
aperture and occulter itself directly with one’s eye or with a small camera.
Figure 10 is the result of a crude initial optical test: a photograph of the
Colorado Front Range above Boulder, Colorado taken through a cell phone camera
held at the aperture of the assembly; and an exposure of the Sun through light
clouds taken in the same circumstance.

The truss structure is more strongly visible in Figure 10 than in scientific
images through a CATE24 telescope, because the cell phone aperture is much
smaller than the available aperture at the rear of the occulter assembly. The
truss takes the appearance of three pairs of “parallel” rods extending to the
occulter. The “parallel” rods are actually diverging from the aperture side of
the hexapod to the occulter, and the widely spaced rods are converging toward
single mount points on the occulter.

Figure 10: Initial test images taken through the CATEcor engineering unit
reveal the geometry of the instrument front-end. Left: the Colorado front
range above Boulder, CO; Right: the Sun with light clouds. These images were
collected with a cell phone camera held at the aperture at the rear of the
assembly. The truss is more strongly visible and the occulter appears slightly
larger than in final images, because the cell phone effective aperture is much
smaller than the full available aperture at the rear of the assembly.

After full integration, we deployed CATEcor on a clear sunny day at an
altitude of 12,000 ft. at Loveland Pass, Colorado, on 6-Oct-2023, in an
interval surrounding noon (roughly 12pm–3pm MDT; noon occured at 12:54pm). The
deployed instrument is shown in Figure 11. Despite a low cloud layer to the
north and northeast of the observing site, the sky color at the pass was dark
cerulean to cobalt blue with minimal white (Mie-scattered) halo around the
Sun, reflecting good “coronal sky” conditions. At the pass we observed some
light specks in the air, which we speculated to be high-flying pollen from
aspens or high-altitude grasses. Wind levels varied from 5 to 15 knots through
the course of the observation, resulting in visible wind shake of the occulter
shadow when the occulter was aligned on the Sun. The wind did not visibly
shake the telescope itself (see Seaton et al., 2024, for additional
description of our initial field test).

Figure 11: Initial deployment of the CATEcor at Loveland Pass, Colorado, on
6-Oct-2023, helped establish alignment procedures, demonstrated dark
occultation, and revealed some glint around the uncoated occulter. The side
view shows the 75 cm distance between the rear of the occulter and the
interior of the aperture piece. The front view shows the apparent extreme
darkness of the instrument aperture, which is bathed in deep umbral shadow
from the occulter.

Initial images from 6-Oct-2023 were sufficiently dark that we proceeded to
manufacture and integrate several more occulter assemblies; but the images did
include features that we surmised to be glint. To half of the new occulters,
we applied a flat surface treatment as described in Section 4; on the other
half we left the occulter and truss surfaces un-coated. We performed either/or
tests in similar conditions by swapping out and re-aligning the occulter
assembly from a fully assembled CATEcor at each of two observing sites for the
14-Oct-2023 annular/partial eclipse, on 13-Oct-2023 (the day before the
eclipse itself). The two observing sites produced comparable results and
revealed that flat black paint reduces glint without appreciably affecting the
diffraction pattern around the occulter. Figure 12 shows typical stray light
images from the uncoated and coated occulter assemblies in full Sun.

Figure 12: Bare/painted either-or test images with two copies of the CATEcor
occulter show the importance of surface treatment to prevent specular
reflection and glint. Both images were collected with a single CATE24
telescope and two separate Sun-pointed CATEcor occulters: one bare, and one
painted. These images are from Loveland Pass, Colorado on 13-October-2023, and
have the same exposure time and scaling. Panel (A) shows the
diffraction/stray-light pattern with bare surfaces. Panel (B) shows the
diffraction/stray-light pattern with painted surfaces. Angular glint features
and overall background are greatly reduced with the painted occulter.

Figure 12, Panel B, shows a typical stray light pattern from a coated CATEcor
occulter assembly. The familiar diffraction “bright ring” is visible, and is
conjugate to an Arago spot (Arago, 1819) formed by the occulter at the
entrance aperture of the telescope. The ring is interrupted in three places by
vignetting due to the truss holding the occulter. The bright ring has an inner
radius of approximately 1.3 R⊙, and extends to 5 subsidiary peaks extending to
1.5 R⊙. The extent of the subsidiary peaks is a measure of precision in the
figure of the occulter. It is a sign both that the signal at this dynamic-
range setting is dominated by diffracted light as expected, and also that the
occulter and truss work as designed: while present in the FOV, the shaded
truss does not significantly contribute to the stray light pattern observed in
the final CATEcor coronagraph images.

We used painted CATEcor occulters on CATE24 telescopes at both Loveland Pass,
Colorado and Sandia Peak, New Mexico to observe the partial or annular
(respectively) eclipse of 14-Oct-2023. Results of that experiment, including
initial detection of the solar corona out to 2 R⊙ from Sun center, are
reported in Seaton et al. (2024).

##  6 Discussion

The CATEcor coronagraph, as built, is best described as a proof-of-concept
instrument. We have conceived, designed, produced, and tested a novel class of
instrument, a shaded-truss externally occulted coronagraph, that takes
advantage of the umbral shadow of the external occulter itself to reduce (and
effectively eliminate) stray light from the support structure.

###  6.1 Design advantages

The shaded-truss concept has several advantages in the coronagraph design
space. By separating the functions of stray light control and occulter
support, shaded-truss designs greatly reduce the bulk of the coronagraph
front-end. In the CATEcor design, only a very small baffle isolates the
aperture itself from the bright sunlight impinging on the instrument,
essentially reducing the front-end stray light control structure to a
minimalist support and a very lightweight occulting body. Further, because the
front-end support is very light, it is feasible to suspend an external
occulter at surprisingly large distances from the aperture, improving
performance compared to designs with a stray-light control structure (i.e.,
vestibule) surrounding the occulter and a conventional support pylon.

These advantages of the shaded-truss approach are sufficiently great that we
were able to conceive, design, manufacture, integrate, and test a coronagraph
front-end in under six weeks, using freeware CAD tools, hobbyist parts, and a
consumer-grade FDM 3D printer. Despite the preposterously simple design,
fabrication, and integration approach – which are accessible to any hobbyist
with access to a “makerspace” workshop and a good hardware store – the
resulting coronagraph is demonstrated to be cleanly diffraction limited and
readily deployable in combination with common amateur-astronomy equipment.
This, in turn, implies that shaded-truss coronagraphs have potential to be
important tools either for educational and amateur coronal viewing, or for
quantitative scientific work. We also demonstrated this particular design by
observing the Sun’s corona at the annular (partial) eclipse of 14-Oct-2023
(Seaton et al., 2024).

Compared to conventional externally occulted designs, shaded-truss
coronagraphs can bring the occulter farther from the aperture, reducing the
limitations of external occultation. The ideal external occulter is infinitely
far from the aperture and infinitely large, as exemplified by the Moon during
a total solar eclipse. Existing externally occulted designs use separation
distances well under a meter, largely because it is infeasible, in a
deployable or spaceborne instrument, to build a large combined structural and
stray-light-controlling structure in front of the optics. This limits the
sharpness of the partially-vignetted zone around the Sun, and therefore the
inner radius of the FOV of externally occulted coronagraphs. By permitting a
long cantilever distance between the aperture and occulter, shaded-truss
designs better approximate the ideal conditions of a total solar eclipse,
lessening the primary disadvantage of external occultation.

Conventional externally occulted coronagraphs have strictly limited fields of
view, which are determined by the diameter of the aperture in the leading
structure. By divorcing the functions of structure and stray-light control, a
shaded-truss coronagraph affords a much broader FOV. The CATEcor outer FOV was
limited by the CATE24 telescope itself at a few solar radii; but the occulting
assembly, which was not particularly optimized for FOV, could nevertheless
admit images beyond 40 R⊙ in all directions (Figure 10). This permits a
broader design space for future instruments that could in principle cover from
a few tenths of a solar radius to many degrees from the Sun in a single field
of view.

###  6.2 Lessons learned

Several immediate design improvements are apparent from this proof-of-concept
study.

The occulter itself uses the corrugation inherent to 3D printing to force
multiple diffractive scatters for light to enter the primary aperture. We
found, on deployment, that this fine corrugation was not sufficiently deep to
prevent dust and other forms of contamination from “spoiling” the cleanliness
of the occulter’s active surface. On deployment, we noticed that small bright
quasi-glints could be seen around the perimeter of the occulter. Close
inspection showed that these glints were dust particles, fibers, and other
contaminants that landed on the surface during observation and extended into
the bright sunlight around the occulter itself. Designing and printing a more
deeply, explicitly corrugated surface would greatly reduce the effect of this
type of contamination, while not affecting strongly the other properties of
the occulter. Likewise, blowing off dust and lint with filtered, clean air or
nitrogen just before acquiring data may improve future observations.

Aligning the occulter and telescope to the Sun was difficult. Understanding
the alignment post facto, during analysis, was similarly difficult, since the
Sun was (by design) not visible behind the occulter, and there were no other
celestial references visible in the FOV. We are developing a design adaptation
that would allow us to track the position of the Sun relative to the occulter,
to solve this problem in future iterations.

The final occulter assembly’s stiffness was limited by the stiffness of the
occulter rods. We used 2 mm diameter rods in CATEcor, and in conjunction with
the chosen 75cm length of the truss, this choice imposed a roughly 10–15 Hz
fundamental frequency for small perturbations; the frequency was determined by
the stiffness of the rods themselves rather than of the truss as a whole. At
this modest level of stiffness, wind shake was a significant issue even in
light breezes. Subsequent designs could use a combination of thicker rods
and/or a mid-rod stiffener bracket to raise the stiffness, ideally into at
least the 20–30 Hz range.

While FDM 3D printing is a convenient process for prototyping, it is not
required for implementing a coronagraph of this general type. Other
fabrication methods, including (additive) resin printing and (subtractive)
conventional machining, and other materials, including metals and stiffer
plastics than the PETG used, provide much more precision and performance, and
would improve both the diffractive/optical performance and stiffness of this
demonstration design.

The offset between the occulter and aperture is not strictly limited to 75 cm
as in the CATEcor design. Commercial circular-cross-section carbon fiber rods
afford excellent strength-to-mass ratio and stiffness, but improved truss
designs and scientific-grade materials afford yet greater strength.
Lengthening the aperture-occulter distance improves performance by reducing
the inner diameter of the FOV, while also reducing the Fresnel diffraction
around the occulter. The truss design imposes a necessary tradeoff between
complexity of vignetting function and rigidity of the occulting structure;
CATEcor is a first exploratory cut at this novel design space, and is far from
optimized.

##  7 Conclusions

CATEcor is a proof-of-concept of a new type of instrument: a shaded-truss
externally occulted coronagraph. We designed it specifically to match the
conditions of the 14-October-2023 annular eclipse, but the concept has
applications beyond our initial deployment. In particular, because CATEcor was
designed entirely with open-source CAD tools and implemented with materials
and procedures available to amateur astronomers and advanced students, it
demonstrates the feasibility of “from scratch” observations of the solar
corona for non-scientists, students, and amateur astronomers. Further, CATEcor
opens a new design space of shaded-truss coronagraphs, with the potential to
offer better performance and broader fields of view than conventional designs.

This work was supported by the Citizen CATE 2024 project, and by Southwest
Research Institute via internal funding. Funding for Citizen CATE 2024 is
provided by grants from the NSF (awards 2231658, 2308305, & 2308306) and NASA
(grants 80NSSC21K0798 & 80NSSC23K0946). The authors thank the FreeCAD project
and AutoDesk for making powerful and accessible CAD tools available to the
general public.

DeForest analyzed, designed, and constructed the coronagraph. Seaton conceived
the idea of a low-cost externally occulted coronagraph for CATE. Caspi leads
the Citizen CATE 2024 project and provided design input, feedback, and
direction. Beasley provided optical design input. Kovac and Tosolini
participated in integration and deployment of the CATEcor coronagraph. West,
Patel, Davis, and Tosolini aided field-test of the design. All co-authors
reviewed the work and provided editing input.

CATEcor development and deployment was funded in part by the National Science
Foundation under Grants 2231658 and 2308305, and in part by Southwest Research
Institute under internal funding. Funding for Citizen CATE 2024 was provided
by grants from the NSF (awards 2231658, 2308305, & 2308306) and NASA (grants
80NSSC21K0798 & 80NSSC23K0946).

The mechanical design is intended to be accessible to the public. Printable
.stl files are published on Thingiverse (DeForest, 2023).

The authors have no conflicts of interest.

## References

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