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# Design, manufacture and metrology of additively manufactured, metal and
ceramic lightweight circular mirror prototypes

Greg Lister  UK Astronomy Technology Centre, Royal Observatory Edinburgh, EH9
3HJ, Edinburgh, UK  Rhys Tuck  UK Astronomy Technology Centre, Royal
Observatory Edinburgh, EH9 3HJ, Edinburgh, UK  Younes Chahid  UK Astronomy
Technology Centre, Royal Observatory Edinburgh, EH9 3HJ, Edinburgh, UK
Katherine Morris  UK Astronomy Technology Centre, Royal Observatory Edinburgh,
EH9 3HJ, Edinburgh, UK  Richard Kotlewski  UK Astronomy Technology Centre,
Royal Observatory Edinburgh, EH9 3HJ, Edinburgh, UK  Scott McPhee  UK
Astronomy Technology Centre, Royal Observatory Edinburgh, EH9 3HJ, Edinburgh,
UK  Cyril Bourgenot  Durham University, NETPark Research Institute,
Sedgefield, S1 3JD, UK  Ken Parkin  Durham University, NETPark Research
Institute, Sedgefield, S1 3JD, UK  Mat Beardsley  RAL Space, Harwell Science
and Innovation Campus, OX11 0QX, UK  Marta Civitani  INAF Astronomical
Observatory of Brera, Via E. Bianchi 46, 23807, Merate(LC), Italy  Gabriele
Vecchi  INAF Astronomical Observatory of Brera, Via E. Bianchi 46, 23807,
Merate(LC), Italy  Carolyn Atkins  UK Astronomy Technology Centre, Royal
Observatory Edinburgh, EH9 3HJ, Edinburgh, UK

###### Abstract

Spaced-based mirrors are a developing use-case for Additive Manufacturing
(AM), the process that builds a part layer-by-layer. The increased geometric
freedom results in novel and advantageous designs previously unachievable.
Conventionally, mirror fabrication uses subtractive (milling & turning),
formative (casting) and fabricative (bonding) manufacturing methods; however,
an additive method can simplify an assembly by consolidating individual
components into one, and incorporating lattice structures and function
optimised geometries to reduce the mass of components, which are beneficial to
space-based instrumentation as mass and volume are constrained. Attention must
be given to the printability of the design - build orientation and
powder/resin removal from lattices and internal cavities are challenges when
designing for AM.

This paper will describe the design, manufacture and metrology of mirror
prototypes from the Active Deployable Optical Telescope (ADOT) 6U CubeSat
project. The AM mirror is 52mm in diameter, 10mm deep, with a convex 100mm
radius of curvature reflective surface and deploys telescopically on three
booms. The objectives of the designs were to combine the boom mounting
features into the mirror and to lightweight both prototypes by 50% and 70%
using internal, thin-walled lattices. Four final lattice designs were
downselected through simulation and prototype validation. Prototypes were
printed in the aluminium alloy AlSi10Mg using powder bed fusion and fused
silica using stereolithography. Aluminium mirrors were single point diamond
turned and had surface roughness measurements taken. Fused silica designs were
adapted from the aluminium designs and have completed printing.

###### keywords:

Additive Manufacturing, Mirror Fabrication, Lattice Structures, Aluminium,
Fused Silica, Powder Bed Fusion, Stereolithography, Lightweighting, Surface
Roughness, Form Error, Porosity, X-ray Computed Tomography

##  1 INTRODUCTION

The uptake of Additive Manufacturing (AM) across the engineering environment
has been rapidly increasing over recent years. At its core, AM, often called
3D printing, is a process where parts are built in layers, it exists in its
own category of manufacturing process due to the distinct differences over
subtractive (milling, turning), formative (casting, injection moulding) and
fabricative (bonding) processes which are more commonly used in industry. AM
opens up the available design space and allows for unique and challenging
designs to solve engineering problems. Features such as complex internal
geometries, large overhangs, lattice structures and optimised free-form shapes
are traditionally difficult or impractical to manufacture in a cost and time
effective manner. With AM, these features can be more easily incorporated into
designs without conventional manufacturing constraints. The primary advantage
of including these AM-enabled features is reducing the mass of components
while maintaining structural integrity under specified loads, which is
frequently sought after in engineering, but designs can also benefit from
rapid prototyping, minimal waste material, and part consolidation.

Typically, AM is associated with desktop fused deposition modelling (FDM)
printers that extrude melted polymer filament, due to increasing popularity
among hobbyists as cost and barriers to entry drop; however, the term AM is
much broader and encompasses several technologies depending on the type of
material that is being printed, but all printers function on the same layer-
by-layer build principle. For engineering applications, where higher strength
materials are needed, it is common to use powder bed fusion (PBF) or
stereolithography (SLA) to process metals, polymers and ceramics. Across all
of the AM technologies, the range and type of metal, polymer and ceramic
materials that can be printed commercially through bureaux or independently
with stand-alone systems is also increasing, further promoting the use of AM
as a viable and cost-effective alternative manufacturing method.

There are a growing number of uses of AM in the aerospace, automotive and
medical sector, where the increasing complexity of designs can surpass the
capabilities of conventional manufacturing methods. End-use examples such as
porous titanium orthopedic implants [1] or topology optimised pistons for high
performance cars [2] show the clear benefits of AM. They are important to
demonstrate the viability and increase confidence in this relatively new
manufacturing method. Within astronomy however, the adoption of AM is not as
mature, but it is emerging as a potentially more cost effective solution to
hardware manufacture by producing lighter, optimised, one-off components.

Launch vehicles have limited payload capacity, which ultimately constrains the
mass and volume of hardware, this drives the demand for designers to reduce
the mass of components destined for space to minimise launch costs, or to
increase the mass budget for other components. Mass reduction will also reduce
the structural demands on supporting systems. Telescope mirrors are one such
component where lightweighting has been effectively used. Lightweighting of
mirrors can be achieved by adopting a contoured back, open back or sandwich
design, as shown in Figure 1. The three lightweight mirror variants each have
their own advantages and disadvantages with respect to cost, stiffness and
manufacturing complexity when using convention manufacturing techniques. Open
back and sandwich mirrors use a honeycomb, or 2.5D lattice structure which can
be manufactured by milling or waterjet cutting, these subtractive techniques
limit the type of honeycomb structures that can be used.

Figure 1: Examples of contoured back, open back and sandwich mirror designs.
Image credit: Atkins et al.(2022)[3]

AM can improve on both conventional open back mirrors by using more complex,
thin-walled ($<$1\text{\,}\mathrm{m}\mathrm{m}$$) lattice structures to reduce
print-through effects[4] and increase stiffness, and sandwich mirrors by
printing all parts of the mirror at once in addition to using stiffer
lattices. All while potentially reducing the cost and time to manufacture.
Previous metal lightweight mirrors have been printed in the aluminium alloy
AlSi10Mg[4, 5], the quality of the reflective surface is variable, with
porosity and scratch marks degrading the otherwise good surface, separate
efforts to investigate scratches and reduce roughness aim to investigate
this[6, 7]. The lattice structures used in these studies were generated from
non-specialised computer aided design (CAD) packages, which do not have the
functionality to model intricate geometry and handle the large file sizes
associated with them, as such the lattices were not optimised for the mirror
geometry and anticipated loads.

To target short wavelength applications (visible - ultraviolet), mirrors with
low surface roughness values are desired
($RMS\leq$1\text{\,}\mathrm{n}\mathrm{m}$$). The achievable surface roughness
with aluminium is limited (4-5 nm RMS[7]) because it is a relatively soft
metal. 3D printed ceramics such as fused silica using stereolithography and
silicon carbide using binder jetting can be a suitable option for short
wavelength mirrors, as they are mechanically harder and have lower
coefficients of thermal expansion (CTE).

There are several challenges associated with lightweight AM mirrors, for
example:

  * •

Porosity \- For PBF (laser and electron beam), porosity (voids in the
material) is practically unavoidable, they can be caused by uneven powder
distribution, gas bubbles, lack of fusion, too much fusion etc. Porosity
reduces the mechanical properties[8] and fatigue life of a part[9], and for
mirror applications, they can degrade the reflective surface quality.

  * •

Surface Roughness \- The surface roughness of AM parts is generally much
larger than machined or cast parts, and it varies with the chosen printing
technology, layer height and overhang angle to the build plate. Mirror
surfaces will need additional diamond turning or polishing steps from any as-
manufactured part, but the high surface roughness will necessitate machining
mounting interfaces and features. Roughness can also impact fatigue life[10]
and outgassing properties[11].

  * •

Lack of Standardisation \- Previous AM mirror projects have used external
manufacturing bureaux, who will use different machines/powders/settings and
will have used different mixtures of virgin and recycled powder. The
variations in the reflective surface quality of mirrors from different
suppliers therefore, cannot necessarily be attributed solely to part geometry.
There are factors outside of the designer’s control and currently no widely
adopted methods of material traceability.

The goal of this study is to explore the design freedoms and material choices
that AM offers for mirror fabrication. The three primary objectives were to
utilise AM’s ability to mass reduce and part consolidate, as well as exploring
metal and ceramic materials. This will be realised through the redesign of a
mirror from a nanosat/CubeSat technology demonstrator. The AM mirror
prototypes will aim to have mass reduction targets of 50% and 70% from an
equivalent solid mirror, this will be achieved by using an internal lattice
structure. The attachment points for the mirror to the CubeSat will also be
consolidated into the part. Prototypes will be printed in both metal and
ceramic to assess their suitability for future mirror fabrication after
producing a reflective surface. AM designs will need to meet manufacturing
requirements, both from the printing process and subtractive machining.
Metrology will be performed on the reflective surface, however pursuing a
perfect reflective surface was not in scope for this project, instead it will
focus primarily on the design and manufacture of the prototypes.

The CubeSat application, along with the optical, mechanical and AM
requirements are outlined in Section 2. Section 3 will explain the process of
lattice design and downselection, in addition to the fixture point designs. To
compare surface deformations between lattice designs, Zernike analysis will be
performed on the final parts in Section 4. Section 5 will cover the
manufacturing, this includes printing, rough machining and single point
diamond turning, metrology results will be presented in Section 6. Sections
2-6 focus on the metal prototypes, progress on the fused silica prototypes
will be reported in Section 7. The paper concludes with a summary and future
works.

##  2 Mirror Specifications and AM Constraints

###  2.1 ADOT 6U CubeSat

The mechanical and optical requirements for the prototype mirror come from the
Active Deployable Optical Telescope (ADOT) 6U CubeSat project (1U=10 cm3),
currently being undertaken in house at the UK Astronomy Technology Centre
(UKATC)[12]. Since spatial resolution is proportional to aperture size;
deployable mirrors are used to achieve a higher spatial resolution than a
fixed aperture satellite with the same payload volume. The
$30\text{\,}\mathrm{c}\mathrm{m}$ primary mirror is segmented into four
petals, one of them is fixed within the CubeSat chassis, the remaining three
rotate outwards and the secondary mirror deploys telescopically on three
booms. Figure 2 shows how the primary petals fold out and the deployment of
the secondary mirror. The proposed low cost, high resolution Earth/Astronomy
observation satellite is intended to operate in the visible to near infrared
range.

Figure 2: ADOT configurations, left to right: Fully stowed. Only secondary
mirror deployed. All mirrors deployed.

###  2.2 Mirror Specifications

The secondary mirror (M2) design, used in this study, is an approximation to
the actual M2 mirror of ADOT (see Figure 3). This was done to explore a
circular geometry, more specifically, to explore how lattices, which usually
consist of repeating cubic structures, could fit into a non-cubic geometry.
The AM approximation to M2 is circular, convex,
$100\text{\,}\mathrm{m}\mathrm{m}$ spherical radius of curvature (ROC),
$52\text{\,}\mathrm{m}\mathrm{m}$ in diameter with a maximum height of
$10\text{\,}\mathrm{m}\mathrm{m}$. The thickness of the mirror substrate and
walls is $1\text{\,}\mathrm{m}\mathrm{m}$. Key specifications are summarised
in Table 1. The mirror mounts on the three telescopic booms using M3 bolts,
the bolt thread interfaces with the booms and are only a clearance fit with
the mounts themselves, this will help to alleviate some of the issue of screw
pressure distorting the mirror surface[13]. Dimensions for the mounting
locations can be found in Figure 4. Considerations for the optical baffle are
out of scope for this project. While there are no well defined volumetric
constraints on the mounting features, their mass should be kept to a minimum
while meeting structural requirements.

Figure 3: Circular AM approximation to M2. Black circle encompasses the reflection of the primary mirror (M1) at M2. Table 1: Summary table of key M2 specifications. Parameter | Specification
---|---
Material | Aluminium (AlSi10Mg), fused silica
Mass reduction | 50% and 70%
Mechanical aperture |  $52\text{\,}\mathrm{m}\mathrm{m}$ ⌀
Clear aperture |  $50\text{\,}\mathrm{mm}$ ⌀
Height |  $10\text{\,}\mathrm{m}\mathrm{m}$ (at peak)
Mirror wall thickness | $1\text{\,}\mathrm{m}\mathrm{m}$
Mounting solution | 3 x M3 bolts
Optical prescription | Spherical, convex
Spherical ROC | $100\text{\,}\mathrm{m}\mathrm{m}$
Extra material on machined surfaces | $1\text{\,}\mathrm{m}\mathrm{m}$
Edge chamfer |  $0.5\text{\,}\mathrm{m}\mathrm{m}$ x 45°
Extra feature | 6 x Fiducial markers on sides
Figure 4: Top-down view of the mirror arrangement, with M2 mounting feature
dimensions

###  2.3 AM Design Considerations

Design for AM introduces different constraints and freedoms compared to
conventional manufacturing techniques, the distinctly different design rules
that need to be adhered to and the overall change in design mindset can be a
barrier to designing parts that make use of the advantages that AM has to
offer.

Print orientation is a significant challenge and is likely to dictate much of
the geometry of a part. Most 3D printing processes cannot print large
overhanging features, due to the nature of the machine building a part in
layers, successive layers need to be placed on existing material, if the
machine attempts to create overhanging features, there is increased chance of
the material sagging down or in the case of PBF, warping up. Maximum overhang
angles and unsupported horizontal distances vary depending on the AM process,
material and machine settings, a general set of design parameters are
presented by Atkins et al. (2019)[3] in the Opticon A2IM Cookbook for several
AM processes. If overhangs cannot be avoided by redesign or alternative print
orientation, sacrificial support material can be used to ensure a successful
build, this is not ideal however, as it requires additional time and effort to
remove the supports, increases the print time and cost due to the extra
material being processed, and leaves small defects on the part where the
supports connected to the part.

Lattices are also affected by the constraints of print orientation, any
internal lattices need to be self supporting during the build, since removing
support material from within them will be impractical, if not impossible. The
choice of unit cells, which is the single repeating cuboid in the structure,
will determine if a lattice is self supporting, the printability of the
lattice in all build directions should also be considered in the design phase.
The appeal of using lattice structures is to reduce mass while maintaining
stiffness, but not all unit cells have the same mechanical properties.
Lightweight mirrors that use lattices under the substrate have previously
suffered from print through effects after machining[4], this is a result of
material deflecting more in between where lattice members support the
substrate, attempts should be made to even out a surface deflection by first
choosing appropriate unit cells, then modifying the thickness of the walls if
needed.

After printing, parts usually require some form of post-processing, this can
differ with the process used, for the prototype secondary mirrors, which will
be printed using PBF and SLA, the immediate step after printing is to remove
the excess powder or resin. For intricate internal geometries, there needs to
be some escape holes to let the excess material flow out, if there is still
trapped powder/resin, this could effectively increase the mass of the part,
and contaminate future machining operations, there are also health and safety
risks associated with fine powder.

Printed parts do not necessarily conform to the original digital design file,
powder based printing processes especially can see large geometric deviations.
Rough machining is needed to transform the coarse and uneven surface from the
printer to a uniform and flat one prior to SPDT. As such this will require
additional material to be added to any surfaces that need to be machined. This
stage will also require some work holding solution, given the geometric
freedoms of AM, it is possible to design complex parts that are difficult or
impossible to hold for machining. Additional features can be created on the
part itself to assist with this, or custom one-off fixtures can be printed to
stabilise and locate complex parts.

##  3 Mirror Design

###  3.1 Lattice Design

Though various lattices are seen across engineering, parallels can be drawn
between them and natural structures. Stochastic (randomly distributed)
lattices (Figure 6) for example, share similarities to the porous structure
found in bones (Figure 5). To mimic these natural designs (biomimicry) and
harness their increased specific stiffness to the fullest extent, a new
manufacturing technique, like AM, is needed. Section 1 highlighted the
difficulty of traditional CAD to create and manipulate lattices in the 3D
modelling environment, to overcome this challenge, an AM specific modelling
package will be used. The software uses implicit modelling[14], unlike
traditional CAD, which not only allows for easy and fast modelling of large or
intricate lattices, but also makes it possible to manipulate and optimise
lattices and bodies with tools such as field-drive design[15].

Figure 5: Cancellous bone structure. Image credit: Kunio et al.(2010)[16]

####  3.1.1 Downselection

There are 33 unit cells to choose from across several categories; honeycomb,
strut/graph, stochastic and triply periodic minimal surface (TPMS), examples
of each can be seen in Figure 6. Honeycomb unit cells have constant cross
sections along one direction and are typically composed of sheets or surfaces.
These are seen used in conventionally lightweighted mirror structures. Strut
unit cells are comprised of arrangements of uniform cylindrical beams, they
are the simplest type of 3D lattice and the least computationally demanding,
which makes them ideal for modelling in traditional CAD. Stochastic lattices
also consist of beams, but are arranged in a random order, they often have
uneven mechanical properties due to the variation in structure density and
introduce too much uncertainty into the design process, therefore they are not
suitable for a lightweight mirror design. TPMS unit cells are defined
parametrically by a surface stretched over a set of points with the smallest
surface area, they can more efficiently distribute material for a given volume
and reduce local stress concentrations present in strut lattices. Strut unit
cells have been previously shown to have worse mechanical properties compared
to TPMS unit cells[17, 18].

Figure 6: Left to right: Honeycomb unit cell (Hexagonal), strut-based unit
cell (Face centred cubic), TPMS unit cell (SplitP), stochastic unit cell
(Voronoi)

Conformal lattices were also investigated to assess their structural
performance and suitability for a circular mirror. Typically, lattices are
cubic structures, like those in Figure 6, that repeat uniformly in the three
axes of a Cartesian coordinate system. This is implemented in the AM software
by creating a ‘cell map’, which is a representation of the volumes that the
unit cells will populate. An issue rises when the volume of a part intended
for a lattice is not rectangular, in the case of circular or ellipsoidal
mirrors for example. The outer cells are frequently truncated, see Figure 8,
leaving behind unsupported or unconnected geometry, this is a particular issue
for strut lattices. A conformal lattice, however, does not use fixed shape
cells in a uniform arrangement, instead the cells deform and stretch to match
the boundary of the volume, leaving behind no incomplete cells, this increases
the potential solution space and should be investigated for potentially
superior designs.

Conformal lattices have been discussed in literature in terms of design
approach and methodology[19, 20] but printed examples are limited[21, 22]. For
the case of a circular conformal lattice, a cylindrical coordinate system is
used to map the unit cells into, resulting in a polar grid structure, which
can be seen in Figure 8. If the radius of the cells is a multiple of the
volume radius, the cell map will terminate at the edge of the volume, as in
Figure 8, if not, then the lattice will need to be trimmed down, but the
continuous nature of TPMS unit cells is not as affected as having truncated
cells. One apparent issue is the cells becoming more spaced out along the
radial axis, for supporting a mirror surface, this uneven distribution in
lattice density is undesirable as the edges will deflect more than the centre
under a polishing/turning load, increasing the surface form error.

Figure 7: Cubic cell map overlaid onto a cylindrical volume with Gyroid unit
cells

Figure 8: Cylindrical coordinate cell map overlaid onto a cylindrical volume
with Gyroid unit cells

Several stages of downselection were implemented to converge on a set of
prototype designs, this involved comparing different unit cells and lattice
arrangements (cubic vs conformal) based on several criteria. The first stage
eliminated unit cells based on general printability constraints set out in
Section 2.3. This removed a number of strut-based unit cells that cannot be
confidently printed in any orientation without support. Although some of these
unit cells have been shown to print without failure at a small scale[23], the
prototype with 70% mass removed will have a more widely spaced lattice, making
unsupported bridges pose a greater threat. Additionally, the TPMS cell
Lidinoid was removed as it has enclosed volumes that would trap powder/resin.

Numerical simulation was then used to compare remaining options based on
mechanical properties. Unit cell simulations have been performed in literature
[17] and there are online databases such as LatticeRobot that document the
structural responses of a range of common unit cells. This data can be very
useful in performing initial downselection, removing the need for time-
consuming and computationally demanding simulations. However, given the
inclusion of conformal lattices in the study and nature of a circular lattice
volume, custom simulations were performed. The main loading condition that
influenced downselection was a compressive turning or polishing pressure
acting evenly on the mirror surface, an approximate value for this pressure is
$3500\text{\,}\mathrm{P}\mathrm{a}$[24] since the exact boundary condition
load for this type of machining process is very difficult to replicate in a
finite element analysis (FEA) model. This load is the primary cause for print-
through, or quilting [4], the other loads that were considered are a torque
around the centre of the mirror, as well as two lateral shearing forces at
45°apart, Figure 9 demonstrates these loads.

Figure 9: Scaled FEA deformations from uniform pressure (left), torque
(middle), and lateral force (right)

The model was restrained by fixing the bottom flat surface in z only and
fixing two vertical edges in x or y to prevent rotation[24]. Due to the unit
cells each having a different volume fraction, i.e the ratio of solid lattice
volume to the volume of the unit cube, some lattice parameter will need to
change for each analysis to maintain the target mass reduction. The chosen
method was to vary the wall/strut thickness for each unit cell and keep the
cell size constant. The test model has the same lattice volume that the
prototype mirror will have, initial test results were skewed by edge effects
(very high displacements), this was solved by adding the
$1\text{\,}\mathrm{m}\mathrm{m}$ wall around the edge.

A $0.4\text{\,}\mathrm{m}\mathrm{m}$ edge length was chosen for the FEA mesh,
this value was a balance between capturing the intricate geometry accurately
enough and minimising the computing power and time required to simulate each
lattice. Generating meshes for additive manufacture or simulation is
challenging for complex lattice structures, a relatively coarse mesh will not
accurately model the lattice and is likely to incur errors, but the mesh size
can quickly become impractical if a relatively fine setting is used. It is
common practice to perform a mesh convergence study prior to FEA, however,
given the challenges faced, this was not performed and the chosen edge length
and mesh settings were kept constant across all simulations. Even with
relatively fine mesh, some unit cells failed to produce results.

There are other options for simulating lattices, such as meshing strut-based
lattices using single beam elements, or homogenising the lattice by using a
solid with the equivalent mechanical properties of the unit cell, though these
may be quicker, they neglect edge effects, stress concentrations, are not
applicable for all types of unit cell and lattice arrangement and are not as
accurate as solid elements.

For each load, the displacement map of the reflective surface was exported to
MatLab for data analysis. Average, root mean square (RMS) and peak to value
(PV) values were normalised and used for comparison. The results for the
uniform pressure with 50% and 70% weight removed (WR) lattices are presented
in Figures 10 and 11. From the analysis, TPMS unit cells perform better than
strut ones, which agrees with similar studies [17, 18], both Diamond (TPMS)
and SplitP share the lead for best performance, with BCC usually performing
the worst out of the remaining options. The difficulty with simulating
lattices is highlighted with SplitP at 70% WR, which failed to mesh, even with
fine mesh parameters, the required quality to get a successful mesh would
increase the time of the other simulations beyond reason.

Figure 10: Average, RMS and PV results from uniform
$3500\text{\,}\mathrm{P}\mathrm{a}$ pressure for cubic lattice (left) and
conformal lattice (right) at 50% WR

Figure 11: Average, RMS and PV results from uniform
$3500\text{\,}\mathrm{P}\mathrm{a}$ pressure for cubic lattice (left) and
conformal lattice (right) at 70% WR

Figure 12 highlights conformal lattices performing slightly worse than cubic
ones, despite being a better fit within the circular lattice volume, the
difference is larger for graph unit cells (BCC, Diamond, Fluorite), but TPMS
unit cells have similar performance. Results from the torque and lateral
forces also showed that Diamond (TPMS) and SplitP perform the best for all
lattice arrangements and mass removed percentages, graphs for these were
omitted as they are not the primary load to consider.

Figure 12: Conformal Vs cubic lattices under uniform pressure

It was concluded from simulations that for the 50% weight remaining prototype,
both conformal and cubic lattices would be suitable. For the cubic lattices,
Fluorite and Diamond were chosen as the graph and TPMS unit cells
respectively, Schwarz and Gyroid were eliminated based on inferior performance
to Diamond, SplitP was removed due to previously observed difficulties in
powder removal via tests[13]. For the conformal lattices, graph unit cells
were shown not to be suitable due to how struts that support the reflective
surface would be distributed in the polar grid arrangement, there would be
large gaps between supporting members which could compromise printability,
TPMS unit cells have more continuous support that lends them better to such a
conformal lattice. For the 70% WR prototype, conformal lattices did not
perform as well as the cubic option, the decision was made to pursue the
conformal lattice only for the 50% WR prototype to allow for more flexibility
in the design.

####  3.1.2 Conformal Lattice Design

After deciding to take the conformal lattices forward, modifications were
needed to optimise the lattice for a mirror. As shown in Figures 8 and 14, the
unmodified lattice becomes denser towards the centre and vice versa, to the
point where there is a solid cylinder of material at the centre, this results
in a very uneven displacement response, which is clearly shown in the
displacement map of the surface (Figure 14).

Figure 13: Sectioned CAD model of a conformal lattice using Diamond TPMS unit
cell

Figure 14: Surface displacement plot of conformal Diamond TPMS in MatLab

One solution to reduce this effect was to vary the wall thickness of the
lattice radially, from thinner in the centre to thicker towards the edges. The
displacement data from the unmodified lattice was used as the scale for the
varying thickness, where higher displacements were observed in the original
lattice, the thickness value of the new lattice will be higher and vice versa,
the minimum and maximum values to vary the thickness over were chosen to meet
the desired mass reduction target. It was found that after simulating the new
lattice, the issue of the over supported centre was still present, though to a
much lesser extent and the outer annulus of the surface had much more even
support.

Even with a very low minimum thickness value, the over supported column of
material could not be avoided, the printability and powder removal from this
central section becomes an increasing concern the smaller the minimum value
goes. To overcome this, the decision was made to remove a portion of the
centre and replace it with a cubic lattice, which has more even support.
Figure 15(a) shows how this was implemented, with a solid
$0.8\text{\,}\mathrm{m}\mathrm{m}$ cylindrical wall separating the two
lattices. After simulating the same uniform pressure in Section 3.1.1, it was
found that the solid wall caused an over supported ring around the cubic
lattice. The purpose of replacing the centre of the conformal lattice was to
even out the support across the mirror surface, but the solid wall was
presenting a similar problem, just in a different location. To fix this,
several iterations of a lightweighted separating wall were tried, ultimately,
both the cubic and conformal lattices were extended into the
$0.8\text{\,}\mathrm{m}\mathrm{m}$ gap, then a Boolean union operation joined
all of the lattices together, the result of this can be seen in Figure 15(b).
Some of the resulting small features and gaps in the separating wall were
below the minimum recommended sizes for most L-PDF printers, but it was not
deemed a issue if they did not print successfully.

(a) Centre of the conformal lattice replaced with a cubic lattice

(b) Separating solid wall changed for a latticed wall

Figure 15: Conformal lattice design

####  3.1.3 Open back Vs Closed back

To increase bending stiffness, mirrors can use a sandwich design, this is
ideal for AM since the internal structure can be printed with no additional
bonding steps like conventional sandwich mirrors. Initially, a sandwich
structure was used, but this limited the flexibility of the design since the
lattice volume is quite small. This meant that in order to reduce the mass of
the equivalent solid mirror by 70%, the lattice density needed to be extremely
sparse, the surface deflection with such a lattice was arguably worse than
with no lattice at all, additionally, this became very challenging to print
with respect to orientation. The decision was made to adopt an open back
design for both mass reduction prototypes, this greatly increased flexibility
in the lattice design and made powder removal much less challenging.

####  3.1.4 Powder Removal Test

When iterating towards a final lattice design, there are several factors to
consider when deciding on cell size and wall/strut thickness. Investigations
into the effect of lattice density on structural performance found that in
general, a denser lattice of the same mass performs better, this means
decreasing both the wall thickness and cell size. However, there is a limit to
how small both of these can go. The aluminium prototypes will be printed using
a commercial bureau, who will have minimum recommended wall thicknesses, these
typically range from $0.8\text{\,}\mathrm{m}\mathrm{m}$ down to
$0.5\text{\,}\mathrm{m}\mathrm{m}$, beyond which the thermal distortions are
likely to affect the geometry significantly. If a lattice is made too dense in
the design stage, there is a possibility that the excess powder cannot be
easily removed. This is difficult to generalise since the ease that powder
flows will depend on the part geometry and unit cell choice.

There are general rules about minimum hole and feature sizes that can print
successfully[3] available in literature, but these don’t necessarily provide
enough information to determine if a lattice is printable. Westsik et al.
(2023)[13] printed a replica model of a lightweight mirror in a transparent
polymer using SLA, then assessed the powder removal capabilities of several
unit cells using red sand to simulate the metal powder. Given the relatively
dense nature of the lattices for the M2 mirror, in addition to the novelty of
a conformal lattice, a similar test was performed. Tests were not printed for
the 70% WR prototype since we were confident that trapped powder would not be
a problem.

The polymer model was designed in such a way to assess powder removal through
both an open back and side wall holes, as the print orientation was not yet
decided. There were four lattice designs to test, two cubic: Diamond (TPMS)
and Fluorite (Graph) and two conformal: Diamond (TPMS) and Gyroid (TPMS).
These made up the ‘core’ of the test model, which had a removable top and
bottom plate. Holes were placed in the side walls to assess the powder removal
capability if the mirror is printed convex surface up, for the conformal
lattices, side holes were strategically placed where the radial ‘channels’
meet the side walls. The holes were covered up when they were not used during
the tests.

Figure 16: Exploded CAD view of the SLA test model, one of four lattice
designs can be interchanged, cubic Fluorite is shown here

Figure 17: All four lattice tests printed in clear resin, red sand residue is
clearly visible in the Fluorite lattice. Image credit: Jason Cowan

The models were printed in Accura ClearVue resin, they were then lacquered and
polished to produce a transparent surface. In hindsight, the lacquer should
have been omitted, there is a chance that a relatively thick layer was
deposited at sharp corners of the lattice, but the bigger issue was the
‘stickiness’ of the lacquer, which likely didn’t cure fully inside the
lattice. This made the red sand adhere to the surface, it was then difficult
to tell if the powder was stuck in the pockets of the lattice, or if it was
just stuck to the surface. This problem primarily affected the cubic Fluorite
lattice. Tests of each lattice showed that both cubic and conformal Diamond
lattices were the easiest to remove powder from, the unit cell Diamond (TPMS)
has excellent flow channels for powder in orthogonal directions. The Fluorite
lattice was difficult to draw any conclusions from, other than it would
probably be too dense for L-PBF. The Gyroid conformal lattice did not let
powder flow out as easily as Diamond. Gyroid unit cells separate their unit
cube into two independent channels of flow that never come into contact with
one another, this could limit powder flow for 3D printing applications. Both
Diamond lattices were taken forward for aluminium printing. Figure 18 shows a
down selection flow chart with all the starting lattice options and which ones
were taken forward.

The cell sizes and wall thicknesses used in the powder removal tests are
summarised below:

  * •

Diamond cubic used 7 x 7 x 7 mm cells with $1.1\text{\,}\mathrm{m}\mathrm{m}$
wall thickness.

  * •

Fluorite cubic used 6 x 6 x 6 mm cells with $1.3\text{\,}\mathrm{m}\mathrm{m}$
strut thickness

  * •

Diamond conformal has two types of lattice. The inner cubic lattice used 7 x 7
x 7 mm cells with $0.9\text{\,}\mathrm{m}\mathrm{m}$ wall thickness. The outer
conformal lattice is defined by a cell radius, height and arc count (number of
segments in the circle) which were 6, 6 and 14 respectively.

  * •

Gyroid conformal also has two types of lattice. The inner cubic lattice used 5
x 5 x 5 mm cells with $0.9\text{\,}\mathrm{m}\mathrm{m}$ wall thickness. The
outer conformal lattice had a cell radius of $5\text{\,}\mathrm{m}\mathrm{m}$,
cell height of $5\text{\,}\mathrm{m}\mathrm{m}$ and an arc count of 16.

Figure 18: Downselection flow chart

###  3.2 Mounting Feature Design

Figure 4 showed the fixing point dimensions for M2. The fixture points that
mount M2 to the telescopic booms were consolidated into the mirror. They
needed to accommodate M3 bolts for mounting to the CubeSat, but they were also
used for the single point diamond turning setup. The design approach for the
mounts utilised topology optimisation (TO), which optimises geometry for a
given objective and set of constraints. The mounts were optimised to minimise
any distortion transfer to the reflective surface during single point diamond
turning. Considerations for launch loads such as shock loading and vibrations
and operational thermal loads were out of scope for this study,

The steps that were taken to perform the TO in this case are as follows:

  1. 1.

Define a study space, this will constrain the volume within which the TO can
add or remove material. Several study spaces were defined in CAD to explore
the design freedom of TO.

  2. 2.

Produce a solid volume mesh of the space. A finer mesh will result in a more
refined solution, at the cost of higher computational power. If minimum
feature size constraints are used, the quality of the mesh will need to be
increased to suit this.

  3. 3.

Define boundary conditions of the loading case and objectives of the study. TO
iterates until the objective function, which could be structural compliance,
displacement or stress for example, is minimised within some stopping
threshold. Since thermal and vibrational loads are out of scope of this study,
the main loads that were used for optimisation are from the SPDT set-up.

  4. 4.

Define constraints for the optimisation. The resulting geometry will be
controlled by the chosen constraints. The most influential constraint is the
volume fraction, which limits how much material can be removed from the
original study space. Further constraints might include planar symmetry and
minimum feature size.

  5. 5.

Convert the result into a solid volume mesh and perform FEA. Different
combinations of study spaces, objectives and constraints were used, so the
results needed to be compared and down selected.

To reduce the computation time, the mounts were optimised individually. The
mirror is symmetrical around one plane, so one of the optimised results could
be mirrored in this plane, this further simplified the design process. A
‘passive’ region around the bolt hole was set in the design space, which
ensures no material is removed from this area. A displacement restraint was
set in the bolt hole and on the bottom face of the screw pad - the solid
cylinder that the bolt hole was drilled in, and a moment was applied to the
concave curved face that would be touching the side wall of the mirror, Figure
19 shows these boundary conditions implemented in the study space. For a
structural compliance objective, the optimised geometry is independent of the
value used for the turning moment, so an arbitrary number was chosen, this was
beneficial since the moment induced by SPDT is difficult to approximate.

Figure 19: Point moment and displacement restraints applied to a TO study
space

Figure 20 shows TO results from three different design spaces, pictured at the
top, each with different constraints, these results were structurally
simulated to down select design spaces, and to see if there was any trend in
performance with certain constraints. The initial study looked at different
combinations of minimum feature and extrusion constraints at different volume
fractions. An extrusion constraint forces the geometry to maintain a constant
cross section along a specified direction. The minimum feature size constraint
was used to ensure that optimised geometry was not less than what could be
confidently printed, the mounts needed to be supported during printing, so
breaking off these support structures could damage mounts that are too thin.
It was found after simulating the results from the initial study, that
extrusion constraints negatively affected the stiffness and that for the same
mass, the smaller study space generally produced stiffer mounts.

Figure 20: Initial TO study. Four combinations of constraints applied to three
study spaces with varying volume fractions

The final mounts were optimised to minimise structural compliance with a
volume reduction of 60% from the original design space. There was a
$3\text{\,}\mathrm{m}\mathrm{m}$ minimum feature size constraint to limit the
TO process from making features smaller than this and a planar symmetry
constraint. A symmetry constraint was necessary to ensure that the mounts
would be stiff regardless of which direction the SPDT lathe spins. It can be
seen from Figure 4 that the three holes are not equally spaced, nor are they
on the same radius. The two holes separated by 90°are
$1\text{\,}\mathrm{m}\mathrm{m}$ further away from the centre of the mirror,
this caused the centre of gravity (CG) to be off-centre from the central axis
of the mirror. As a result of this, the set-up will not be balanced on the
lathe, this can affect the quality of the cut. To spare the effort of manually
balancing the work piece, the volume fraction constraint was reduced for the
one mount until the CG aligned with the centre of the mirror.

###  3.3 Design for Manufacture

The decision was made to print the mirror prototypes with the lattice face up
and the convex surface touching the build plate, this was to ensure easy
powder removal, but also to fully support the optical surface during the
print. In its current design state, the mirror prototype is not well suited to
printing; the convex surface forms a large, steep overhang with the build
plate, which will need to be supported along with the mounts and screw pads
(as shown in Figure 21). Since the convex surface will need to be rough
machined prior to SPDT, adding sacrificial material there to extend it to the
build plate will not add a further machining step, this will also help anchor
the part to the build plate. Through consultation with the AM bureau, they
requested that both the convex surface and the screw pads be made flat to the
build plate. They also suggested that the M3 bolt holes should be printed
solid and machined out to the correct size and position at a later stage.
Extra material will need to be added to any surfaces that are going to be
machined since printed parts exhibit relatively high surface roughness and
would not be suitable for use as flat datums, this is also shown in Figure 21.

The changes to the original design to meet manufacturing requirements
highlights the shift in design mindset needed for additive manufacture. The
layer-by-layer build process enforces rules on part geometry as demonstrated,
but it also allows for the inclusion of features to assist manufacturing and
post processing. All of the changes to the original design are summarised
below:

  * •

The convex surface was made flat to anchor it to the build plate and extended
by $1\text{\,}\mathrm{m}\mathrm{m}$ to allow for machining.

  * •

The screw pads were extended to the build plate as well to secure them during
the build and minimise any warping.

  * •

$1\text{\,}\mathrm{m}\mathrm{m}$ was added to the top faces, excluding the
lattice to allow for machining of a flat datum.

  * •

The bolt clearance holes were printed solid to precisely machine them in
after.

  * •

Additional material was added to raise the part
$3\text{\,}\mathrm{m}\mathrm{m}$ from the build plate to allow for WEDM.

Figure 21: M2 mirror prototype with no modifications (top) and after changes
(bottom)

###  3.4 Final designs

As mentioned in Section 3.1.4, it is difficult during the design phase to know
if a given lattice design is printable; this was especially true for the two
50% WR prototypes. In an attempt to decrease the uncertainty around
printability for any future works, all of the lattice parameters of the
printed designs are documented. CAD models of the final designs and lattices
are shown in Figure 22(a)-22(d). Six equally spaced fiducial markers
($0.5\text{\,}\mathrm{m}\mathrm{m}$ spherical indents) were placed in the wall
of the mirror.

  * •

Diamond cubic 50% WR used 8 x 8 x 8 mm cells, the wall thickness of the
lattice varies from $0.6\text{\,}\mathrm{m}\mathrm{m}$ to
$0.9\text{\,}\mathrm{m}\mathrm{m}$ based on the surface distortion of the
constant wall thickness lattice.

  * •

Diamond cubic 70% WR used 16 x 16 x 16 mm cells, the wall thickness of the
lattice is $0.8\text{\,}\mathrm{m}\mathrm{m}$, the field driven wall thickness
did not have as much of an effect with the 70% weight removed lattices.

  * •

Diamond conformal 50% WR has two different types of lattices. The inner cubic
lattice used 7 x 7 x 7 mm cells with a $0.7\text{\,}\mathrm{m}\mathrm{m}$ wall
thickness. The outer conformal lattice is defined by the cell radius, height
and arc count (number of segments in the circle), in this case they are 6, 6
and 14 respectively and the wall thickness varies from
$0.5\text{\,}\mathrm{m}\mathrm{m}$ to $0.8\text{\,}\mathrm{m}\mathrm{m}$.

  * •

Fluorite cubic 70% WR used 7 x 7 x 7 mm cells with
$1\text{\,}\mathrm{m}\mathrm{m}$ struts. The thickness does not vary because
of the sparse nature of the 70% mass reduced lattice.

(a) Diamond Cubic 50% WR

(b) Diamond Conformal 50% WR

(c) Diamond 70% WR

(d) Fluorite 70% WR

Figure 22: Final Designs

##  4 Zernike Analysis

Using the final designs, numerical simulations of the turning process were
performed to assess the mirror surface deformation and stress concentrations
in the mounts for each lattice. A fixture plate was needed to interface the
mirror to the lathe, Figure 23(a) shows how the plate has a large cut out on
one of the faces. The entire model, including lattice and mounts was meshed,
alongside the fixture plate, see Figure 23(b). The finite element model on
average contained five million elements. The three screw holes were
constrained in all directions and the bottom face of the mirror was set as a
contact point on the fixture plate, which was also fixed. These simulations
were performed for all of the lattices using the uniform
$3500\text{\,}\mathrm{P}\mathrm{a}$ pressure. The displacement map is shown in
Figure 23(c).

The maximum Von Mises stress for each design averages roughly
$0.1\text{\,}\mathrm{M}\mathrm{P}\mathrm{a}$ and is located in the contact
point between the mirror and fixture plate meshes. This highlights the how the
constraints on the model are not representative of reality. The connection of
the two meshes is fixed in all degrees of freedom, whereas in reality, the
mirror would be free to move in x and z, using the coordinate system of Figure
23. This could potentially cause incorrect surface distortions as a result of
the overconstrained model. The simulation tool in the AM design software did
not have the functionality for this and other software packages could not be
tested in the given time frame.

(a) Section view of the CAD model

(b) Finite element mesh

(c) Displacement map

Figure 23: Simulation model

As with the FEA data from the lattice downselection stage, the nodal
displacements were filtered to just the reflective surface, these were
exported to a Zernike fitting Matlab script. The numerical values from the FEA
were not considered as they are almost certainly not representative of the
true loads imparted on the mirror. For one, only an approximation for the SPDT
load was considered, no effects from any of the rough machining operations
were investigated. The objective of the Zernike analysis was not to see the
absolute displacement after Zernike fitting, rather the relative deformation
between the different lattices.

The first 36 Zernike terms were fit to the input FEA data via a least squares
fit method and the Zernike fit was subtracted from the input data to highlight
the lattice print through. The subtracted data is presented in Figures
24(a)-24(d) for each lattice, the print through pattern is clear.
Additionally, plots for the subtraction of the first three Zernike terms are
shown in Figures 25(a)-25(d).

Figure 26 shows the contribution of Zernike terms 0-35 for each lattice, all
display large amounts of defocus, other terms with noticeable contribution are
Astigmatism in x, Power and Trefoil (Z9). Defocus can be explained by the
solid wall around the lattice deflecting much less under pressure than the
lattice. The trefoil is expected since the mirror is supported by three mounts
at close to even separation and these regions will have slightly different
properties due to the increased stiffness from the mounts. Since the higher
order Zernike terms are relatively small compared to the lower order ones,
they are omitted in Figure 27 to more clearly see the difference between each
lattice. The Fluorite lattice can be seen to perform the worst, especially in
Defocus, which is expected since strut unit cells are less stiff and material
efficient[18, 17].

(a) Diamond Cubic 50% WR

(b) Diamond Conformal 50% WR

(c) Diamond Cubic 70% WR

(d) Fluorite Cubic 70% WR

Figure 24: Subtraction of Z35 fit

(a) Diamond Cubic 50% WR

(b) Diamond Conformal 50% WR

(c) Diamond Cubic 70% WR

(d) Fluorite Cubic 70% WR

Figure 25: Subtraction of Z3 fit Figure 26: Contribution of Zernike terms for
each lattice Figure 27: Contribution of just Z0-Z9 terms

##  5 Manufacture

###  5.1 Printing

In total, nine prototypes were printed in the aluminium alloy AlSi10Mg, a
duplicate set of the final four designs for redundancy, destructive testing,
X-Ray computed tomography (XCT) and hot isostatic pressing (HIP) and one high
resolution print for comparison. The high resolution part was printed on a
Concept Laser MLabs, which has a build volume of 90 x 90 x 90 mm and a quoted
layer height of 15-25$\mu$m. The other eight parts were built using an EOS
M290, with a build volume of 250 x 250 x 305 mm and quoted layer height of
30-60$\mu$m. The parts were removed from the build plate using wire electrical
discharge machining (WEDM), support material was manually removed and the
areas where they contacted the part were filed smooth. Due to the high
residual stresses introduced during the build process, parts are stress
relieved. They were also tumble finished to smoothen the outer surfaces.

Figure 28: Eight normal resolution parts still on the build plate, support
structures can be seen on the mounts. Image credit: Alan Magowan, LPE

Figure 28 shows the eight normal resolution parts still attached to the build
plate, the support structures on the mounts are clearly visible. All lattices
printed successfully, even the resolution of the separating wall in the
conformal lattices, discussed in Section 3.1.2, was very good. The two 70% WR
lattices, which are much less dense, also printed well with no signs of
sagging or crumbling across the larger overhangs. Figure 29 pictures the nine
prototypes, with the high resolution part in the middle. The high resolution
process has a smaller layer height and can print finer features, it was
decided that the conformal lattice would benefit most from this increased
resolution of all the lattice choices because it has the most intricate
geometry. This comes at the cost of a more expensive print with a smaller
build volume, one mirror only just fits in the printer’s area.

Figure 29: All aluminium mirror prototypes. Image credit: Jason Cowan

###  5.2 Post processing

####  5.2.1 Machining

Machining was needed to prepare the printed part for SPDT. Several operations
were needed to remove the additional features added in Section 3.3, Figure 30
shows the order of machining operations and which parts of the printed model
were removed at each stage. Figure 31(a)-31(d) shows how the part was held and
machined in house at the UKATC. In Figure 31(b), the mirror is located using
pins in the holes drilled in Operation 1. The convex surface was machined to a
spherical radius of $100.1\text{\,}\mathrm{m}\mathrm{m}$ to allow for
$100\text{\,}\mathrm{\SIUnitSymbolMicro m}$ of extra material to be removed
during SPDT to reach the target ROC.

Figure 30: Machining steps

(a) Operation 1: Skim top and drill holes

(b) Operation 2: Part located with pins

(c) Operation 2: Remove excess material on screw pads

(d) Operation 3: Milling convex radius of curvature

Figure 31: Subtractive Machining. Image credits: Richard Kotlewski

A suspected risk during the print was that the mounts would warp, extending
the screw pads to the build plate was done to mitigate this risk by more
securely attaching them. However, it is clear after machining that there was
still a small amount of warping as the faces of the three screw pads did not
lie in the same plane. Process simulation could have been used to assess the
deformation due to thermal stresses, but given the time frame, this was not
possible.

####  5.2.2 Single Point Diamond Turning

SPDT was performed at the Centre for Advanced Instrumentation, Durham
University on a Moore Nanotech 250 UPL. Three prototypes were cut, the high
and normal resolution conformal lattices, and a 70% WR Diamond cubic part. Two
more were intended to have hot isostatic pressing (HIP) done before SPDT, to
assess the difference in surface roughness. However, due to circumstances
outside of our control, the HIP process was delayed and these parts could not
be included. The parts had several rough cuts made at
$10\text{\,}\mathrm{\SIUnitSymbolMicro m}$ depth of cut to clean the surface,
then a single $2\text{\,}\mathrm{\SIUnitSymbolMicro m}$ deep finishing cut.
Figure 32 shows the mirror during turning.

Figure 32: Mirror on diamond turning lathe. Image credit: Ken Parkin

##  6 Metrology

###  6.1 Mass

The mirrors were weighed after machining and compared to the predicted values
from the CAD models. Table 2 presents the masses and errors, the actual masses
don’t deviate significantly from the predicted values. There can be several
sources of mass error across the workflow, STL meshes may not accurately
capture all geometry, density values in datasheets are approximate, tumble
finishing, which smoothens the surfaces will remove material and more.

Table 2: Mass measurements

Design |  Measured (g) |  Predicted (g) |  Error (%)
---|---|---|---
Diamond cubic 50% WR |  27.7 |  27.9 |  -0.7
Diamond cubic 70% WR |  20.6 |  21.1 |  -2.3
Fluorite cubic 70% WR |  20.3 |  20.5 |  -1.0
Diamond conformal 50% WR |  29.9 |  29.6 |  1.0
Diamond conformal 50% WR* |  27.5 |  29.6 |  -7.1

  * a

*High resolution

###  6.2 Surface Roughness

Figure 33 shows the three reflective surfaces after SPDT, all exhibit
concentric scratches and porosity. Qualitatively, the high resolution print
has more diffuse reflection, this is likely due to different machine settings.

(a) Normal resolution Diamond 70% WR

(b) Normal resolution Diamond conformal 50% WR

(c) High resolution Diamond conformal 50% WR

Figure 33: Pictures of mirror surfaces

Surface roughness measurements were taken at the Centre for Advanced
Instrumentation, Durham University using a Zygo Zegage Plus, X20
magnification, with 8th order polynomial removed from the data. Measurements
were made in four locations on the mirror surface: at the centre, off centre,
midway along the radius and towards the outer edge. Table 3 presents the
average (Sa), RMS (Sq) and PV (Sz) values in each location for the three
designs. Part 1 off centre is missing its dataset and Part 2 centre sampled a
defect, so was excluded. The parts are numbered as follows:

  1. 1.

Diamond Conformal 50% WR High resolution

  2. 2.

Diamond Conformal 50% WR Normal resolution

  3. 3.

Diamond Cubic 70% WR Normal resolution

Table 3: Surface Roughness Results

| Measurement / nm
---|---
| Centre | Off Centre | Midway | Outer
Part No. |  Sa |  Sq |  Sz |  Sa |  Sq |  Sz |  Sa |  Sq |  Sz |  Sa |  Sq |  Sz
1 |  8.30 |  13.2 |  726 |  N/A |  N/A |  N/A |  11.8 |  34.2 |  3150 |  34.3 |  315 |  25500
2 |  |  |  |  4.60 |  5.90 |  126 |  5.70 |  8.40 |  9.40 |  4.90 |  15.2 |  38.5
3 |  8.00 |  11.5 |  407 |  4.50 |  5.80 |  219 |  5.70 |  9.40 |  988 |  8.80 |  38.5 |  9160

Figures 34 and 35 show both microscopic and topographic images respectively
for each measurement location and design. Each square represents a roughly
$420\text{\,}\mathrm{\SIUnitSymbolMicro m}$ x
$420\text{\,}\mathrm{\SIUnitSymbolMicro m}$ area of the reflective surface.
Pores are visible in every measurement. Upon a first look from a limited set
of samples, it seems as though the high resolution print has fewer, but larger
pores compared to the normal resolution part. However, most of the defects
seen in the normal resolution microscope images are probably not porosity,
there are a number of long, thin black marks which are not characteristic of
pores. When comparing the topographic images to the microscope images, only
very few of these needle-like structures can be identified, but they do not
present as holes in the surface, rather protrusions, it is theorised these are
silicon particles. The relatively larger, irregular pores in the high
resolution part are indicative of lack of fusion in the layer. The difference
between the porosity between the two resolution parts likely comes down to the
machine setting. Orientation is not a factor as all parts were printed in the
same direction, and the chemical composition of the two powders is the same. A
roughly $200\text{\,}\mathrm{\SIUnitSymbolMicro m}$ defect is present in the
reflective surface at the centre of the Diamond conformal normal resolution
part which results in a roughness RMS of over
$1000\text{\,}\mathrm{n}\mathrm{m}$, it was suggested that this could be
caused by hard material being dragged into the centre during the cut. A
roughness RMS of $5.8\text{\,}\mathrm{n}\mathrm{m}$ was achieved off centre of
the normal resolution Diamond cubic part.

Eliminating the defects in the reflective surface is crucial before AM mirrors
can be taken further for use in final products, however, this was not the goal
for the prototypes. On-going work into optimising print parameters[6] and
investigating the effect that HIP has on surface roughness aims to resolve the
key challenges with AM mirrors[7].

Figure 34: Microscope images of each prototype Figure 35: Topographic images
of each prototype

##  7 Fused Silica Prototypes

Part of this study was to investigate M2 prototypes in a 3D printed ceramic
material, with the motivation to target shorter wavelength applications.
Ceramics are typically much more mechanical hard materials than metals,
therefore the achievable surface roughness is lower. The ceramic material
chosen for the prototypes was fused silica, Kotz et al.(2017)[25] presented a
novel, high-resolution method for 3D printing fused silica using resin
printing, or stereolithography (SLA), resulting in transparent parts suitable
for optical components. A fine silica (silicon dioxide) powder is held in a
polymer binder, which makes up the resin. Following the conventional SLA
process, thin layers (tens of microns) of resin are cured using an ultraviolet
light source ($\lambda$=$385\text{\,}\mathrm{n}\mathrm{m}$ for the specific
printer) to build a part. Green parts (newly printed parts), undergo thermal
debinding to remove the polymer binder, then sintering to fuse the remaining
silica into a fully dense part, this workflow is shown in Figure 36.

Figure 36: Fused silica printing and post processing. Image credit: Kotz et
al.(2017)[25]

###  7.1 Fused silica prototype design

As 3D printed fused silica mirrors are less mature than metal mirrors, the
scope of the ceramic investigation was reduced to focus on printability of a
lightweight mirror; material defects will be investigated at later stages.
Parallel investigations into 3D printed ceramics present polishing results of
solid $50\text{\,}\mathrm{m}\mathrm{m}$ diameter by
$5\text{\,}\mathrm{m}\mathrm{m}$ deep, flat fused silica disks[26], the
potential for short wavelength applications was demonstrated, a few defects
were observed, but not yet fully identified. Pursuing a curved surface mirror
will be valuable for future mirror projects to understand which print
orientations are suitable.

The design of the fused silica prototype was adapted from the aluminium
prototype. While the aluminium topology optimised mounts did not consider
launch conditions (shock loading and vibrations), they were included to
demonstrate the ability of AM to consolidate parts and were a convenient
workholding solution for machining/SPDT. The polishing setup will be different
to the SPDT one, for the ease of holding the mirrors, the mounts were omitted
from the design. Fused silica prototypes will aim for only 50% mass reduction
with one lattice design, to minimise uncertainty around lattice printability.

Diamond (TPMS) cubic was chosen as the lattice. Unlike the aluminium
prototype, the fused silica part will not have any post machining performed
(aside from polishing), this meant that the mirror could not be printed with
the curved surface on the build plate, instead, it was printed with the curved
surface pointing up, as shown in Figure 37. In this orientation, the optical
surface did not have full support from the lattice underneath, as mentioned in
Section 2.3, it is not acceptable to have support structures in the lattice.
To overcome this challenge, a blend radius was implemented to adequately
support the surface during the print, this can be seen in Figure 37.
Additional modifications included extending the optical surface by
$0.5\text{\,}\mathrm{m}\mathrm{m}$ and increasing the size of the chamfer.

Figure 37: Section view of a fused silica design

It was also decided to print a prototype with a flat surface to compare to
commercially available fused silica blanks, both mirrors use the same lattice
parameters, which were $1\text{\,}\mathrm{m}\mathrm{m}$ wall thickness and 10
x 10 x 10 mm cells. Table 4 presents the mechanical and optical specifications
of each mirror.

Table 4: Specifications of fused silica mirrors | Fused Silica Mirrors
---|---
Parameter | Curved Surface | Flat Surface
Mechanical aperture |  $52\text{\,}\mathrm{m}\mathrm{m}$⌀
Clear aperture |  $50\text{\,}\mathrm{m}\mathrm{m}$⌀
Height (at peak) | $10.5\text{\,}\mathrm{m}\mathrm{m}$ | $9\text{\,}\mathrm{m}\mathrm{m}$
Optical prescription | Convex, spherical | Flat
ROC | $100.5\text{\,}\mathrm{m}\mathrm{m}$ | -
Surface thickness | $1.5\text{\,}\mathrm{m}\mathrm{m}$
Edge chamfer |  $1\text{\,}\mathrm{m}\mathrm{m}$ x 45°
Extra feature | 6 x fiducial markers

###  7.2 Printing

In total, eight parts were printed, three curved surface parts, three flat
surface parts and two of the solid polishing test sample disks from Atkins et
al.(2024)[7]. They were printed on an Asiga Pro at a layer height of
$50\text{\,}\mathrm{\SIUnitSymbolMicro m}$. Figure 38 shows one of the curved
surface parts in production, the orange part is just after printing and it
becomes white after thermal debinding, it will eventually become transparent
after sintering.

(a) Curved surface part directly after printing

(b) Curved surface part after 600°C debinding

Figure 38: Fused silica parts in production. Image credits: Patrick Risch

##  8 Conclusion and Future Work

To conclude, this study has presented additively manufactured aluminium and
fused silica mirror prototypes that approximate the secondary mirror from the
6U ADOT CubeSat project. The aluminium mirrors were mass reduced by roughly
50% and 70% compared to a solid mirror using different lattices, the mounts
for the mirror in the ADOT assembly were topology optimised for stiffness and
consolidated into the part, they were also used for work holding during
machining and SPDT operations. Final lattice designs were downselected using
FEA, then prototype validation. Eight normal resolution parts were printed in
AlSi10Mg through an external bureau, a mixture of strut (Fluorite) and TPMS
(Diamond) unit cells were implemented into cubic (Diamond cubic 50% WR,
Diamond cubic 70% WR and Fluorite cubic 70% WR) and conformal (Diamond
conformal 50% WR) lattices. A high resolution Diamond conformal design was
also printed to investigate any differences in porosity and roughness between
normal and high resolution printers. Relative surface distortions and print
through effects from SPDT were shown using Zernike analysis. Machining was
conducted at the UKATC to prepare the parts for SPDT which was carried out at
the Centre for Advanced Instrumentation, along with the metrology. Fused
silica prototypes were adapted from the aluminium designs and modified to suit
a different print orientation. In addition to printing parts with a convex
surface, flat mirrors were also printed to compare to commercial fused silica
blanks.

Future work for the aluminium prototypes include diamond turning two parts
that have undergone HIP, then comparing surface roughness data to the dataset
presented in Section 6.2. Two more parts, that are yet to be turned, could
undergo bead blasting to assess the effect on porosity and roughness. X-Ray
Computer Tomography (XCT) will be used to analyse the effectiveness of HIP
with regards to porosity reduction, in addition to quantifying and verifying
the presence, location and shape of porosity. Fused silica mirrors will
undergo surface profilometry of the as-printed parts, to observe any print-
through and stair stepping effects. Polishing will be carried out at INAF
Astronomical Observatory of Brera.

## Acknowledgements

The authors acknowledge the UKRI Future Leaders Fellowship ‘Printing the
future of space telescopes’ under grant # MR/T042230/1, in addition to Patrick
Risch of Glassomer, and Alan Magowan of Laser Prototypes Europe for their
support and advice during design and manufacture of prototypes.

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