Table of Contents
Preface: The Journey
In January 2019, I attended a Night Life event at the Academy of Sciences in San Francisco. That evening, I ran into Jim Mirl - a recent hire on the engineering team on which I worked. Jim is a specialist in high-precision diamond machining. During our conversation, Jim casually offered to cut a custom mirror for me, if I ever wanted to make a telescope. Unbeknownst to either of us at the time, his offer set me on a mission that would last over two years.
When Jim made his generous offer, I did not know how a telescope worked - I merely knew that I was excited to build one. The extent of my optics education was a several-week section during a college physics course ten years prior. Thus, I began by revisiting optics. Next, I studied how telescopes are built, and how they are used by hobbyist astronomers. After three months, I felt ready to start my design. The CAD took about six weeks to complete, and the subsequent build took another six weeks. At some point, I was distracted by some other projects (a new bicycle frame, and some chef knives), but by August 2019, I had completed my first telescope.
My first telescope: a 13” diameter Ritchey-Chretien.
Unfortunately, my first telescope did not work. The optics did not yield clear images. Measuring the shape of the mirrors showed that the profile was wildly out of spec: on the order of tens of microns. In order for the system to work as desired, the form tolerance should have been within λ/15 (42 nm.) The error was a result of two independent factors:
The mirror was far too thin, and sagged significantly under its own weight.
The mirror cell was poorly designed, and strained the optical surface as the mirror was fastened / as the mirror cell orientation was adjusted.
I was disheartened - my hundreds of hours of effort had resulted in a dud. After sulking for a week, I decided to try again. By that time, I had befriended another recent hire on my engineering team: an optics specialist named Mike Borden. Mike generously spent many evenings teaching me the STOp analysis method described above, and he gave me some excellent books on telescope design. It took several months to work through the material that Mike supplied.
I started work on my second telescope in January 2020. The design phase lasted for three months. I was able to reuse many structural concepts from my first telescope (such as the secondary mirror spider and the truss joints.) As such, the design and STOp analysis of the mirror cells dominated more than half of this period.
By March 2020, I was ready to start fabrication. However, the COVID-19 global pandemic threw a wrench into my plans: the shop at which I worked shut down. I subsequently started my own shop space, but ramping up took several months. A subsequent hip surgery kept me out of the shop for another month. Finally, by September 2020, I was able to start fabrication.
On December 2, 2020, the telescope saw its first light. It was a very exciting moment - the culmination of nearly two years of effort. I had finished the calibration process at 10 PM - too late to set up the tracking mount, so I wheeled it outside on the assembly stand and found the moon through a 50 mm eyepiece (25 x magnification.) As I observed the craters and veins on the moon’s surface in crisp detail, I was overcome with a feeling of pride. I also felt an immense relief: following the failure of my previous telescope, I had been dreading discovering that I had just spent another year on a failed project.
December 2, 2020: first light.
Since then, I have spent many nights under the stars, observing and photographing the sky. While astronomy is an extremely rewarding pursuit in itself, the satisfaction derived from using an instrument that I personally built is even greater. What started as an engineering project has evolved into a passion for astronomy - one that will last a lifetime.
The following report describes the factors considered in designing a telescope. It assumes an understanding of concepts ubiquitous to mechanical engineering. Furthermore, it contains terms that are consistent with the jargon used by professionals in the optics industry. Put simply: while this document will serve as a riveting text to optics specialists, it may appear as utter Gobbledegook to the uninitiated.
In an attempt to increase accessibility, I’ve released a supplemental lecture that introduces readers to many terms and concepts used below. Specifically, the following topics are addressed:
An Introduction to Imaging Systems
Telescopes: A Specific Type of Imaging System
Focal Length and Aperture
Telescopes and the Human Eye
Mirrors and Lenses
Additionally, underlined keywords in this document will link to credible sources for the interested reader. Further questions should be submitted via the Ronen Sarig Designs contact page, and I will attempt to answer them in a timely manner.
An amateur-grade imaging system consists of a combination of the following components:
Optical tube assembly (OTA)
Tripod or pier
Field flatteners, coma correctors, etc.
The term “telescope” is used ambiguously. In some cases it refers to an entire imaging system (e.g., “the James Webb Space Telescope”), whereas other times it refers merely to the OTA. This report details the design and construction of a custom OTA. Commercially-available components comprise the remainder of the Imaging system.
The OTA is highlighted from among a full imaging system, consisting of an OTA, guide scope, and finder scope, mounted on an equatorial Go-To mount.
Kapege.de / CC BY-SA, source
Overview of Terms / General Specifications
Specific verbiage will be used to refer to sections of the telescope:
Terms used to refer to sections of the telescope.
OTA general specifications:
Focal length: 1250 mm
Aperture: 250 mm
Weight: 30.7 lbs (13.9 kg)
Eyepiece diameter: 2”
Frame length: 42” (1068 mm)
Back focus: 96 mm
Astrophotography vs Visual Observation
The telescope is intended for both visual observation and astrophotography. Requirements for the latter use are more stringent, and therefore drove most of the design specifications.
Systems used for astrophotography require higher optical resolution than do those used for visual observation. While the resolving power of the human eye is limited to about 1.2 arcminutes, the resolving power of a digital sensor can be much higher. For example, a 1250 mm F/5 telescope coupled with a Canon 5D Mark III camera yields a resolving power of 1.02 arcseconds - about 71x greater than that of the eye. In order to fully utilize a high resolution sensor, optical aberrations must be minimized.
Additionally, astrophotography often involves long-exposure imaging. During the exposure, a tracking mount is used to continuously rotate the telescope to compensate for the rotation of the earth. Various techniques are utilized to increase the accuracy of the tracking mount, such as using high-accuracy electronic encoders, or a secondary tracking scope that provides position feedback to the computer driving the mount. In most cases, a lighter payload yields tighter tracking. Manufacturers of tracking mounts recommend overrating the capacity of a mount by 50%, or even doubling it, when the mount is to be used for astrophotography. This telescope was designed to be used with an iOptron CEM60 tracking mount (max payload: 60 lbs), so the OTA target weight was set to 30 lbs (the final design weighed 30.7 lbs.) Including all peripheral components (camera, filter wheel, tracking scope, guide scope, counterweights), the payload weighs 43 lbs.
The camera equipment used in astrophotography generally takes up more space along the optical path than does an eyepiece used in visual observation. Therefore, the distance between the end of the focuser and the focal plane must correspondingly be longer. This dimension is referred to as the back focus. For example, a Canon DSLR camera used with a filter wheel requires 75mm of back focus, whereas many eyepieces require 0 back focus, or even a negative distance (where the objective element of the eyepiece is positioned forward from the end of the focuser.) With the focuser fully retracted, the back focus of this telescope is 96 mm.
While a long back focus is advantageous for astrophotography, it introduces optical ramifications. A longer back focus corresponds to a wider beam cross-section as the rays pass through the focuser drawtube, which may increase vignetting. In addition, a reflecting telescope would require a larger secondary mirror in order to capture the wide reflected beam, which would thereby block a greater portion of incoming light.
A Newtonian with a short back focus. Off-axis rays reach the sensor.
A Newtonian with long back focus. Off-axis rays are partially blocked by the focuser, which causes vignetting. In addition, a larger secondary mirror is required in order to capture the full reflected beam path.
Correspondingly, since eyepieces require a shorter back focus, a method of reducing back focus is required when the telescope is used for visual observation. For this dual-use system, the GSO 2” linear bearing Crayford focuser was chosen. GSO supplies spacers which can be placed between the OTA and the focuser to absorb the back focus of the system. The spacers are stiff, and they boast a generous inner diameter of 78 mm.
A 25 mm spacer is added between the OTA and focuser in order to properly focus an eyepiece.
For my previous telescope project - a Ritchey-Chretien reflector - custom mirrors were designed, and Jim Mirl diamond turned the mirrors from QC-10 aluminum alloy. This process yields excellent form accuracy and surface finish (better than λ/20 RMS). However, the coefficient of thermal expansion of aluminum is high, and this property makes it a poor material for use in telescopes - instruments which can undergo significant changes in temperature during a night of use. Instead, Low-CTE glass or glass ceramic is generally used for consumer-grade telescope optics. Unfortunately, our machine was incapable of grinding those materials, so we resorted to using aluminum.
A single-point diamond machine cutting the secondary mirror of my first telescope.
A diamond-tipped tool used for SPDM.
The 13” diameter primary mirror of my first telescope, as cut by SPDM. Nice Rolex, Jim.
Machining the secondary mirror of my first telescope using SPDM.
For this telescope, glass mirrors were used. The cost of custom-machined glass optics would have exceeded the project budget, so off-the-shelf mirrors were purchased. This is the main reason that the Newtonian architecture was chosen over a more advanced aberration-free architecture. The mirror set was purchased for $375 - an incredible price considering that the mirrors are made of Schott BK-7 glass, include an Al / SiO2 coating with reflectance over 88% across the visible spectrum, and boast a form tolerance of λ/16 RMS. A comparably-sized off-the-shelf Ritchey-Chrétien mirror set would cost approximately ten times as much, and custom glass optics could easily bump the price to five figures.
250 mm parabolic primary mirror.
74 mm (minor diameter) flat secondary mirror.
Compatibility with Standardized Systems
Since the OTA comprises merely one component in the full imaging system, it was designed to be compatible with commercially available peripherals. The telescope industry has developed standards to ensure modularity, and the OTA conforms to those standards. For instance, a Losmandy-style dovetail plate is used to affix the OTA to the tracking mount, and Vixen-style dovetail mounts are used to attach peripheral scopes and counterweights.
A large aperture is beneficial for both astrophotography and visual observation. For astrophotography, a larger aperture corresponds to shorter exposure times for the same amount of light collected, thereby reducing blur caused by tracking error and mechanical vibration. Meanwhile, for visual observation: a larger aperture increases the brightness of the image - an important factor when operating at high magnification. (At higher magnification, perceived brightness is reduced - a phenomenon which can be explained by The Law of Conservation of Energy.) However, a larger aperture corresponds to an increase in mass. Ultimately, the aperture size was limited by the mass specification. Several low-detail designs were created to estimate the mass of systems of varying aperture, and a primary mirror diameter of 250 mm was chosen.
250 mm parabolic primary mirror.
This drives the field of the view of the system. The chosen aperture diameter narrowed the commercially available options to an F/4 or an F/5 mirror (a 1000 mm or 1250 mm focal length, respectively.) Similarly, most peripheral optical components such as field flatteners and coma correctors are optimized for that F-number range. The F/5 mirror was chosen to allow for the greatest angular resolution possible. If wider fields of view are desired for astrophotography, mosaic images can be compiled, whereas long focal length eyepieces can be utilized for wide views during visual observation. If even higher magnification is desired, narrower fields of view can be achieved by using a barlow lens inline with the sensor.
The Newtonian telescope architecture was chosen due to the availability of off-the-shelf glass mirrors. This architecture consists of a parabolic primary mirror and a flat secondary pickoff mirror. Since it uses a single powered element, alignment of the mirrors is not critical, and calibration is simple. An angular or lateral displacement of either mirror merely impacts the location of the final image, not the quality. Conversely, misalignment of the elements in a system with multiple powered elements leads to aberrations. In addition, since the Newtonian is a reflector, it is free of chromatic aberration often present in refractor telescopes.
The Newtonian architecture consists of a parabolic primary mirror, and a 45° secondary pickoff mirror. Axial rays (green) are focused to a point in the center of the sensor, while off-axis rays (red) are focused toward the edge.
However, the Newtonian architecture presents several inherent disadvantages as well. In order to prevent the pickoff mirror from blocking significant incoming light, it must be placed relatively far from the primary mirror. This necessitates a long OTA, which drives both high mass and rotational inertia - two factors that decrease the performance of a tracking mount.
The Newtonian frame (left) must be almost as long as the focal length of the telescope, whereas the frame of a Cassegrain (right) is less than half the focal length.
In addition, the single powered optic generates significant coma. A commercially-available coma-corrector for Newtonians was purchased. However, the manufacturer did not respond when asked for a model, so the efficacy of the module will be determined empirically.
A commercially-available coma-corrector made by Baader Planetarium.
Optical systems are generally designed using ray-tracing software. In simulation, a beam of light is broken down into individual rays, and optical surfaces are described in equation form. By tracing the path of each ray as it reflects or refracts through the system, the behavior of the beam can be calculated. For this project, Zemax Opticstudio was used.
The Zemax OpticStudio workspace. In the image above, an axial beam of light is depicted in blue, and an off-axis beam is depicted in green. Vignetting at various angles is plotted in the lower-left of the screen.
Early in the design, Zemax was used to check the optical implications of mechanical design choices, and a back-and-forth between Zemax and SolidWorks ensued. For example, the placement of the focuser relative to the secondary mirror affects the back-focus of the system, and as well as vignetting.
The mirrors, sensor, and focuser aperture were modeled in SolidWorks (left.) An analogous model was constructed in Zemax (right) in order to optimize the placement of these components.
By comparing vignetting and FOV analyses provided by Zemax, a secondary mirror diameter and location was chosen to maximize light collection across the field of view.
Vignetting effects for various sizes of secondary mirror. The 74 mm mirror was chosen for its light throughput at the center of the field-of-view.
Simulation and STOp Analysis
STOp stands for Structural Thermal Optical. The method is used to determine the implications of structural deformation and thermal effects on an optical system.
Earlier in the design, ray-trace software was used to optimize placement of optical elements. Surfaces were represented as idealized mathematical formulas in Zemax. However, in order to accurately predict the performance of the system, real-world effects must be considered into the ray-trace model. These include lateral or angular shifts of the elements, deformation of the surfaces themselves, and optical effects that result from real world conditions such as gravity, acceleration, and temperature change.
These effects are first calculated using FEA software, in this case Ansys Mechanical. Once the stressing factors are modeled, the software outputs a two-dimensional set of nodes that describe the modified optical surfaces.
The primary mirror. Mechanical stresses are modeled in finite-element-analysis software. The resultant deformed optical surface is approximated by a set of nodes.
This nodal “surface” must then be translated into equation form in order to be used in the ray-tracing software. A third piece of software is used to calculate a series of Zernike Polynomials that provide a best-fit for the nodal FEA output. This translation was done using SigFit. However, those on a budget have been known to write their own Zernike Transform scripts using MATLAB.
The SigFit user interface (2020).
A portion of the fit file output by SigFit. Lateral displacements and tilt are calculated, and removed from the calculation (these values are specified at the top of the file.) Next, a Zernike decomposition is conducted on the resultant surface, and the polynomial coefficients are reported. These coefficients can then be input to a ray-tracing software.
The first 21 zernike polynomials.
By Zom-B at en.wikipedia, CC BY 3.0, source
In Zemax, the zernike polynomials are applied to the optical surfaces in order to characterize the performance.
The STOp analysis workflow.
Primary Mirror Cell Requirements
After the primary mirror, secondary mirror, and focuser were placed, the next task was to design the mirror cells. The design of the primary mirror cell was the most complex portion of the project, and therefore a full STOp analysis was conducted for this assembly. The maximum wavefront error caused by deformation of the primary mirror was specified at λ/20, or about 30 nm. (For an explanation of the wavefront error budget, consult the Wavefront Error section of my Introduction to Telescopes lecture.)
Four effects were considered in the STOp analysis:
Deformation of the mirror due to its own weight (mirror sag)
Mechanical stresses imposed on the mirror from fastening and adjustment of the cell
Mechanical stresses imposed on the mirror by the cell due to thermal expansion
Mechanical stresses imposed on the mirror as the telescope is reoriented relative to gravity
The factors that affect mirror sag due to gravity are:
Mirror thickness (drives stiffness)
Mirror material (drives stiffness and weight)
Interface between the mirror and cell
Since a commercially-available mirror was used, the first two factors were fixed. Adhesive mounting pads were chosen as the fastening method between mirror and cell, as is conventional for telescopes of this size. Combinations of 3 and 6 mounting pads (arranged in a ring) were simulated at various radii. Ultimately, 3 points of contact were chosen, because mirror cell real estate was required for other mechanisms. The location for the mounting points proved optimal at 65% of mirror radius, which resulted in a deflection due to mirror sag of 0.038 λ (P-V).
Left: deformation of the mirror when mounted on six pads is modeled in Ansys.
Right: mirror deformation is plotted for various diameters of six support pads arranged in a ring.
Left: three support pads on the underside of the primary mirror at 65% mirror diameter.
Right: the wavefront error caused by deformation under gravity is plotted in Zemax.
Stresses from Fastening and Adjustment of the Mirror Cell
During calibration, the primary mirror is aligned to the optical axis of the telescope by tilting the mirror on two axes. In order to allow repeatable angular adjustment of the mirror, a kinematic mount was implemented. The mirror cell baseplate rests on three ball-end screws, and is secured in position by six springs. This strategy effectively decouples the baseplate from any mechanical deformation of the telescope frame. The only mechanical forces imposed on the baseplate by the rest of the assembly are spring tension, and the opposing forces of the ball-end screws. These forces were simulated in the STOp analysis to analyze the resulting deflection of the baseplate and mirror.
The mirror cell baseplate (purple) is attached to the frame (green) at three locations.
Detail of the kinematic-mount mechanism: a ball-end screw pushes against two dowel pins embedded in the mirror baseplate. Springs on either side of the screw pull the baseplate against the ball with calculated force. Each of these mechanisms constrains two axes of linear motion, but allows translation in the axis parallel to the dowel pins, as well as the three rotation axes.
Worst-case spring forces were calculated to accurately characterize deformation of the mirror cell baseplate.
The spring forces were used as an input to Ansys, where deflection of the mirror cell baseplate was modeled.
Stresses due to Thermal Expansion
The mirror is made from thermally-stable BK-7 glass, while the baseplate had to be made from a more machinable material (a metal, or composite.) The dissimilar materials would have mismatched coefficients of thermal expansion. Therefore, the expansion / contraction of the baseplate had to be decoupled from that of the mirror, to avoid stressing the mirror.
Stresses from Reorientation of Gravity
Most ground telescopes are able to reorient in order to point at different areas of the sky. A well-designed cell minimizes mirror deformation as the telescope is moved through its angular range (ideally from -90° to 90°.) In addition, the cell must prevent angular and lateral mirror shift - a formidable challenge, since the primary mirror constitutes 25% of the mass of the entire OTA.
Primary Mirror Cell Solutions
Initially, bipodal flexures were considered as a method to attach the mirror to the baseplate. This is a common strategy for mounting mid-size telescope mirrors. Not only do the flexures decouple the mirror from mechanical strain of the baseplate, they also compensate for dissimilar thermal expansion of the mirror and baseplate. Various geometries and material combinations were tried for the baseplate, flexures, and adhesive pads, and over fifty simulations were run for different gravity vectors, temperature differentials, and kinematic spring tensions.
The mirror is attached to the cell baseplate with three pairs of bipodal flexures.
The bipodal flexures decouple strain of the cell baseplate from deformation of the optical surface.
The following materials were simulated for use:
Ferritic Stainless Steel
Austenitic Stainless Steel
It was determined that the optimal baseplate and flexure material combination for this design was Titanium baseplate / Titanium flexures.
Simulating bipodal flexures.
51 simulations were run to characterize the performance of different mirror cell designs. RMS wavefront error was compared.
Once the design had been “finalized”, a realization was made: there is a simpler way to accomplish the same results. A stiff baseplate could be bonded directly to the back side of the mirror if a flexible adhesive was used to fasten the mirror to the plate. The soft adhesive would act as a buffer, allowing the baseplate to deform independently of the mirror. A low-durometer silicone adhesive was chosen for this application, and the mirror was still adhered at three pads. Performance of this design was further improved by using a high-modulus carbon composite baseplate (for stiffness), and thermal stability was increased by using a quasi-isotropic (0/45°/90°) weave. The kinematic mount was designed such that the springs were as close to the opposing contact points as possible, thereby reducing the bending moment on the baseplate. In simulation, the soft adhesive proved to be equally effective as the machined flexures in the previous design. The worst-case wavefront error caused by compounding the factors was simulated to be 0.04 λ RMS.
A carbon fiber baseplate, bonded to the backside of the mirror with flexible adhesive proved effective at preventing mirror deformation.
The baseplate deforms under the stresses of gravity and spring force, but the mirror remains true to form. The color gradient across the mirror in the simulation above represents tilt of the entire body, not deformation of the optical surface.
The wavefront error plots of two mirror cell designs are compared. On the left: the optimal bipodal mirror cell, featuring grade II Titanium baseplate and flexures, Invar adhesive pads, and a rigid, low-CTE adhesive. On the right: the carbon fiber baseplate with soft adhesive pads. Both mirror cells were subjected to the following conditions: -15 K thermal change, gravity oriented at 90°, and an extreme baseplate-spring tension. The bipod-based design exhibited a RMS wavefront error of 0.050 λ, whereas the flexible-adhesive-based solution came in at 0.0419 λ.
A few notes about using soft adhesives to fasten the mirror:
While low-durometer adhesive bonds were shown to be as effective as flexures at preventing mirror deformation, an important distinction between the two solutions should be noted. The bipods were designed to flex in specific orientations, whereas the low-durometer adhesive bonds create an isotropic buffer. The bipods compensate for deformation of the baseplate and unequal thermal expansion, but they provide a rigid structure that would prevent the mirror from shifting laterally if the telescope was reorientated with respect to gravity (E.G. to point at an object near the horizon.) This would not be the case with the adhesive solution; The low-durometer silicone bonds will allow a slight amount of lateral mirror shift in such an occasion (about 23 um.) However, lateral displacement does not significantly affect performance of a Newtonian architecture. This dynamic is discussed further below.
For accurate simulation results, it is important that the actual adhesive bond thickness matches that which was modeled. In order to form a 0.25mm thick bond, a small piece of magnet wire was placed on each adhesive pad. When the mirror was pressed against the pad during bonding, the thickness of the wire controlled the thickness of the bond. This trick was courtesy of Danny Sing.
A segment of magnet-wire is placed on the adhesive pad in order to control bond thickness.
Secondary Mirror Mount
Due to its small size and low weight (232 g / 8 oz), the secondary mirror mount proved much simpler than the primary mirror cell. The same low-durometer adhesive was used to adhere the secondary mirror to a single bond pad. Once again, the bond thickness was controlled via the magnet wire method. CTE mismatch between the mirror and mount was inconsequential over such a short distance, and therefore the mount could be machined out of aluminum. When modeled, the worst-case deformation of the mirror due to compounding factors was simulated at 0.04 λ.
The secondary mirror is fastened to the kinematic mount via a single adhesive pad (red.)
Optical Implications of Frame Deformation
Earlier it was stated that for a Newtonian architecture, the form accuracy of the respective optical surfaces is more important than the alignment of the elements relative to each other. Still, maintaining alignment of the respective elements will yield the best performance.
There are two factors that contribute to deformation of the frame (and thus potential misalignment of the elements) after calibration:
Temperature changes cause expansion and contraction of components
Reorientation of the telescope relative to gravity, in order to point at different points in the sky
The first factor can be mitigated by symmetry of the structure: if opposing members expand and contract equally, the optical elements will remain aligned. Only the length of the optical path will vary, and this can be compensated by refocusing the telescope as temperature changes. Servoed autofocus units can be purchased, with programmable temperature compensation.
The ZWO EAF autofocuser features a temperature sensor. The unit can be programmed to compensate for thermal expansion and contraction of the OTA.
The second factor can lead to significant misalignment of the optical elements, and therefore affect a shift in image location as the telescope is reorientated. The Serrurier Truss architecture (described below) mitigates this effect. Furthermore, the use case of this telescope renders this dynamic insubstantial. A shift of the image is only consequential if it occurs during a single exposure; If it occurs across multiple exposures, the exposures can be realigned by a photo-stacking program later on.
Consider how far an image might shift during a single exposure: for this telescope, a 10-minute exposure is as long as can be expected. During that time, the earth rotates 2.5°. It was deemed that any misalignment that might occur from that rotation is insignificant, and therefore a STOp analysis of the overall structure was not conducted.
The driving factor for this lack of simulation was a scarcity of computation resources. A simulation of the overall structural deformation would have exceeded the computation budget that could be allocated to this project, therefore priority was given to simulating the mirror cells. Under different circumstances (additional resources) a full analysis would be conducted in order to validate the above assumption.
Ambient temperature changes over a night of imaging cause the telescope to expand / contract, and a change in optical path length results in defocusing the image. For this reason, it is ideal to use a low-CTE material for parts that comprise the length of the optical path. Carbon fiber composite is an ideal material - its CTE is very small at 2 um/m. When selecting a weave, it is important that some carbon fibers are oriented in the direction along which low thermal expansion is critical.
The struts that comprise a majority of the optical path length are made from low-CTE carbon fiber composite
This effect drives not only the material selection, but also part geometry. For example, the struts were designed to attach to the midframe in such a manner as to minimize the run of aluminum in the optical path.
The carbon fiber struts make up the majority of the optical path length. The distance from the secondary mirror to the focuser (indicated in red) is created by aluminum parts, and is therefore sensitive to temperature changes. However, this portion of the path length is short, and therefore does not contribute much to thermal expansion and contraction.
This time, the struts are attached in a manner such that a larger portion of the optical path length is created by aluminum parts. This configuration is more sensitive to temperature changes than the design in the previous diagram.
It is possible to design high-CTE parts that expand in the opposite direction with respect to optical path - thereby offsetting the expansion of other elements:
A short run of high-CTE aluminum expands when temperature increases. However, because the struts attach behind each mirror, expansion of the aluminum section decreases the overall path length - offsetting the expansion of the carbon fiber struts. In this manner, a net thermal expansion of zero is achievable.
However, this strategy has trade-offs:
It requires more material overall, increasing mass in a weight-limited system
Furthermore, it increases the overall length of the telescope - and places the additional mass at the endpoints. The rotational inertia of the system is increased, which impacts performance of the tracking telescope mount.
In order to qualify a telescope design, a specification for allowable thermal expansion was required. First, the effect of defocusing the sensor was tested in Zemax. The results were plotted:
It was determined that a defocus of +/- 50 um could be tolerated without significantly affecting image quality. Note that spot size for the 0° field doesn’t exceed a single pixel until a defocus of 75 um is reached, when using a 6 um pixel sensor - a size found in many DSLRs.
Next, the expected temperature change over a night of imaging was calculated. Historical temperature data was analyzed for the area in which the telescope would be used. During most nights, temperature changed 6-7 °C, with rare swings as wide as 10 °C. However, refocusing the telescope once during a particularly thermally unstable session is acceptable, so the specification for temperature change was chosen to be 5 °C.
Historical temperature data drove thermal performance requirements.
The overall thermal performance for various geometries and combinations of materials was compared using a thermal bill of components - where CTE x (temperature change) x (path length) x (direction of expansion) of every component that comprised optical path length was added, to calculate total thermal expansion of the optical path. In this manner different designs could be compared against the 50 um expansion goal.
Thermal bill of components.
In the end, a design that used carbon fiber struts to comprise the majority of the optical path length proved sufficient. Designs that included high-CTE parts that expanded in the opposite direction were scrapped, due to the aforementioned disadvantages.
The carbon fiber struts comprised 72% of the optical path length. The top and bottom plates of the secondary subframe comprise 13% of the optical path length. Ideally, these parts would have consisted of a low CTE material such as carbon fiber as well. However, cutting large rings out of plate is an inefficient use of material, and carbon fiber plate is expensive. Since the portion of the total path length is small, aluminum was used as a low-cost alternative.
The secondary frame and focuser are made of aluminum alloy.
Finally, the focuser stack comprises the final 15% of the total optical path length. An off-the-shelf focuser was used, and the sole material choice was aluminum.
Because telescopes are large instruments that require precise alignment, they are generally designed to be constructed from relatively low-precision components, and precision is attained with calibration. Therefore, many components could be designed for low-precision fabrication methods (such as waterjet cutting), with minimal post-machining. Most parts were fastened using solely screw clearance holes for alignment. The adjustable-length trusses allow for large-scale adjustment, and final collimation of the optics was achieved by tilting the mirror cells.
The telescope was designed to utilize the following tools and assembly methods:
CO2 LASER cutter
(SPDT lathe for previous telescope’s optics)
Positive retention mechanisms involving springs and pins (see the kinematic mount design)
Welding was avoided, due to the risk of distortion.
Overall, the full assembly consisted of 992 parts. This included:
44 parts that were cut on the waterjet, then post-machined.
32 parts that were cut on the CNC lathe
7 parts that were cut on the CNC mill, including one out of carbon fiber
8 parts cut on the CO2 LASER cutter
16 parts cut manually (mill, lathe, saws, etc.)
The remaining part count consists of fasteners, springs, pins, ball-joint linkages, and other off-the-shelf components.
The following attributes were considered while selecting the material for each part:
Coefficient of Thermal Expansion (CTE)
Stiffness (Young’s Modulus)
Materials comparison table.
Strength was not a significant factor in material selection. The strain required to yield any part would far exceed the maximum allowable strain required in order to maintain optical alignment.
6061-T6 aluminum was chosen for the majority of the components, because of its machinability, low cost, and low density.
Many components were machined of aluminum alloy.
The secondary mirror spider arms are made from 0.035” thick stainless steel sheet. The arms were cut using a waterjet, then set screws were attached by brazing.
The secondary mirror spider.
Brazing the spider arms.
The trusses were made of carbon fiber composite tubes. Carbon fiber composite has an extremely high stiffness to density ratio - about 2.7x as high as that of aluminum, steel, and carbon fiber, all of which are roughly equal. Since the truss structure comprises a majority of the length of the telescope, a stiff / low-density material is an ideal choice for the truss tubes.
Carbon fiber composite struts have a high stiffness to density ratio.
The primary mirror cell baseplate was machined from a carbon fiber composite sheet. A quasi-isotropic weave was used, to prevent thermal expansion along the plane of the plate. In addition, high-modulus fibers were selected for stiffness. The kinematic mount springs pull on the plate, and reducing deformation of the plate is essential to preventing the strain from propagating to the surface of the mirror.
Carbon fiber was chosen for the mirror cell baseplate, due to its stiffness.
The stiff carbon fiber baseplate resists deformation from the spring force.
All aluminum parts were bead blasted and anodized black, in order to reduce reflection of stray light.
Fasteners were chosen to be black-oxide coated stainless steel. The material provides corrosion resistance, and the oxide prevents reflection of stray light.
Carbon fiber components were coated with West System 105 epoxy for UV protection.
The purchased mirror set included a PVD aluminum coating, with a SiO2 overcoat. The reflectance was measured using a spectrophotometer:
The primary and secondary mirror reflectance was measured using a spectrophotometer.
Serrurier Truss Design
Long telescopes can suffer from deformation of the frame: as gravity pulls the ends downward, the mirrors may become misaligned. The Serrurier truss architecture mitigates this effect: by supporting the telescope at the center of mass, the distance to each end is inversely proportional to the mass at that end. It follows that the two ends will sag equally, maintaining alignment. In addition, the parallelogram-nature of the truss structure ensures that angular alignment is also maintained.
In a Serrurier Truss design the mirrors maintain alignment even as the telescope frame deforms under gravity.
By Cmglee - Own work, CC BY-SA 3.0, Centers of Mass
Centers of Mass
While the Serrurier truss architecture compensates for lateral misalignment, additional consideration was taken to mitigate angular misalignment. The centers of mass of the primary and secondary subframes were designed to align with the endpoints of the trusses. This minimizes gravity-induced torsion on each subframe, and thereby preventing angular misalignment of the mirrors.
The attachment points of the struts are aligned with the centers of mass of the primary and secondary subframes. This prevents torquing of the subframes.
The telescope was designed such that its overall center of mass could be positioned along the declination axis of the mount. This allows the tracking mount to point the telescope across the sky without fighting gravity; It merely needs to overcome inertia. Positioning the COM along the declination axis requires adjustability on two axes:
The telescope can be positioned along its optical axis by shifting the dovetail mounting plate in the mount clamp
For a Newtonian telescope, the mass of the focuser / camera / eyepiece assembly is not along the optical / declination axes plane. Counterweights can be adjusted to bring the overall COM of the telescope in plane.
Counterweights (green) can be used to position the center of mass of the telescope (orange) over the dovetail mount (yellow.)
Once the trusses are adjusted for rough placement of the primary and secondary mirrors (within 5 mm), precise alignment of the optical axis can be achieved by tilting the mirrors. A 3-sided kinematic mount was designed for both the primary and secondary mirrors.
The mechanism relies on three Thorlabs ¼”-80 screws with precision ball bearings embedded in the tips. The screws are threaded through brass bushings that are pressed into the back plate of the telescope frame. The ball-end screws push against two dowel pins that are corner-crowded into pockets on the mirror mounting plate. The travel of the screws is limited by an external travel limiter (shown in pink), and therefore the spring force pulling on the mirror mounting plate is constrained.
The ball-ended screw contacts a pair of dowel pins embedded in the mirror cell backplate.
Two tension springs pull the backplate against the ball-ended screw with a known force.
This layout allows mirror angle to be adjusted without shifting the mirror laterally while doing so. In addition, since the secondary mirror is held at a 45°, two short screws and one long one were used such that the plane created by the three ball bearings was adjacent to the mirror. This minimizes lateral mirror shift compared to a design where three identical screws are used, and a tower is used to affix the mirror at 45°. In such a scheme, adjusting the tilt of the tower will result in shifting its endpoint (where it attaches to the secondary mirror), resulting in lateral shift.
Two short screws and one long screw are used to position the secondary mirror. This prevents lateral shift of the mirror as angle is adjusted.
The rigidity of the design relies on the tight fit between the screws and the brass bushings. For this design, a relatively short (0.438”) bushing was used. In hindsight, I realized that relying on tight thread fit for lateral rigidity is a poor strategy. If I were to use a similar concept in the future, I would select a longer bushing in order to maximize contact distance between the screw and the bushing, or I would choose a different style of kinematic mount altogether.
The following attributes were considered while selecting an adhesive for fastening the mirrors to their respective cells:
The stiffness (durometer) of the adhesive must be regarded as a tradeoff: while a stiff adhesive prevents the mirror from shifting when the telescope is reoriented, it doesn’t act as a mechanical buffer between the mirror and adjacent part. If these two parts have a mismatched CTE, this can lead to a “bimetallic strip effect” which can warp the mirror when temperature changes. In addition, any mechanical distortion of the adjacent part will couple into the mirror. Instead, a low-durometer adhesive can be used to provide a mechanical buffer between the mirror and adjacent part - but displacement of the mirror as the telescope reorients may become significant.
Most adhesives have high CTE, when compared with metals or glass:
BK7 optical glass has a CTE of 0.6 um/m°C
6061 aluminum alloy has a CTE of 23.6 um/m°C
Epoxies tend to have CTEs in the 40-80 um/m°C
Silicones tend to have CTEs in the 200-300 um/m°C
A stiff adhesive with mismatched CTE will apply stress to the bonded parts, and this can lead to aberration of optical elements. This effect is less significant for low-durometer adhesives, such as silicones.
Many adhesives shrink as they cure (and some grow.) As with CTE, an adhesive that shrinks as it cures can apply stress to the bonded parts. Once again, low-durometer adhesives do not apply as much stress as stiff adhesives.
Some adhesives require elevated temperatures in order to cure. This is common for two-part epoxies. Care should be taken when using such an adhesive, because the cure cycle can cause substantial deformation on its own. Since the cure is occurring at an elevated temperature (E.G. 120 °C), the parts and the adhesive will be in an expanded state as the bond forms. As the assembly cools, the parts and adhesive will shrink. A mismatched CTE between the parts and/or adhesive will cause the bimetallic strip effect, potentially warping the optics. This dynamic exacerbates the issues that arise from mismatched CTE, because the temperature delta between cure and usage is even greater. As before, this effect is mitigated by using a low-durometer adhesive.
An adhesive with adequate bond strength must be chosen to prevent the bond from failing completely.
To make assembly easy, viscosity was targeted for 5,000 - 70,000 cps.
1-part vs 2-part
Considering the above criteria, most viable adhesives will consist of a two part mixture. Humidity-cure silicone is an exception: this single-part adhesive creates low-durometer bonds, and is therefore a valid candidate. However, the geometry of the bond itself must be considered: if the bond is very thin compared to the dimensions of the bond pad, moisture may not penetrate deep enough to fully cure at the center of the bond. The mirror cell bond pads are 25 mm wide and 0.25 mm thick. Therefore, a two-part Pt-based catalyst silicone was chosen to bond the mirrors. In addition, two-part silicones have much lower shrinkage than one-part silicones do, so stress due to shrinkage was reduced as well.
For more information on two-part RTV silicones, see page 26 of the Wacker guide.
Finally, cost was considered. Masterbond EP42HT-2LTE seemed to be a very attractive candidate due to its incredibly low CTE (9 um/m°C) - until the minimum order quantity of 1 oz was quoted at $650.
The effects of stiffness, CTE, shrinkage ratio, and cure temperature have direct implications on the optics, and were therefore modeled during the STOp analysis. Ultimately, the results of the analysis drove a major architecture change, which was described in the above section on mirror cells.
The properties of several viable adhesives were compared:
ChemSet 412 was chosen to adhere both the primary and secondary mirrors for its low-durometer, low-shrinkage, low-cost, viscosity, and reasonable tensile strength.
ChemSet 412 Properties:
Durometer: Shore A 40
Cost: $16.32 / 50 ml cartridge
Viscosity: 5,200 cps
Tensile strength: 650 psi
ChemSet 412 was used to bond the mirrors.
A LASER-cut alignment jig and weights are used to adhere the secondary mirror.
Apertures, Light Baffles, and Shrouds
The primary mirror cell features a black plastic ring that blocks the outermost 2mm of the mirror. This ring acts as an aperture to block the mirror edge, where form tolerance is poor. In addition, the ring serves as a mirror-catch, in the event that the adhesive fastening the mirror should fail. The studs that support this ring do not contact the rim of the mirror, and they are covered with rubber heat-shrink tubing such that in the event of adhesive failure, the mirror would not contact metal directly.
A plastic ring acts as an aperture stop, as well as a mirror-catch.
A curved plastic sheet acts as a light baffle encapsulating the secondary mirror subframe, and another baffle covers the mid-frame. The front and rear truss sections are covered with fabric shrouds. These components serve to prevent stray light from entering the OTA, and to reduce dewing by containing outgoing radiation.
Light baffles and a fabric shroud block stray light and reduce dewing.
The back plate of the telescope frame features three 50 mm fans. When the telescope is initially exposed to cold air (taken outside), the mirror cools nonuniformly. This is primarily due to the mirror’s variable thickness. The temperature gradient will strain the mirror, introducing aberration. Over time, the mirror will reach uniform temperature, but this process can be expedited by running the fans. Once the telescope is in use, the fans are turned off, to reduce mechanical vibration and air currents that could impact imaging. The fans run off 5V, which is supplied by the head of the mount.
Three fans are used to cool the primary mirror.
Calibration of the telescope consisted of the two processes:
Alignment of the structure by adjusting the trusses
Collimation of the mirrors by tilting the mirrors
The telescope was designed to use low-tolerance mechanical parts that could be adjusted to achieve accuracy during calibration. The three sections of the frame are roughly aligned by adjusting the length of the sixteen truss members. For this process, a collimated LASER was used. Prior to mounting the secondary mirror, the LASER was attached to the front of the secondary spider. A hole in the spider allows the beam to pass through the spider, and continue through the body of the telescope.
A LASER, attached to the secondary SPIDER, is used to align the frame.
A center-marked plate was attached to the midframe, and the secondary/midframe trusses were adjusted such that the beam struck the center.
A center-marked plastic plate is used to align the midframe to the optical axis.
Next, the primary-frame/midframe struts were adjusted such that the primary mirror was centered.
Using a LASER to center the primary mirror on the optical axis. The geometric center of the primary mirror is marked with a white ring.
Once the secondary frame and midframe are centered relative to the primary mirror, the secondary mirror is installed in the telescope.
The next step involved using a dedicated collimation tool: the Baader Planetarium LASER Collimator. The collimator features a translucent plate with a hole, through which the outgoing LASER beam passes. In a perfectly collimated system, the return beam should align with the outgoing beam, and thus the return beam will be directed back through the hole. However, for an un-collimated system the beam will diverge from the outgoing beam, and strike the translucent plate.
The collimator is installed in the focuser drawtube. Since all sensors and eyepieces use the focuser, this LASER position provides a suitable axis for the final calibration. The LASER passes through the focuser, strikes the 45° secondary mirror, and is reflected toward the center of the primary mirror. The beam is then reflected off the primary, bounces off the secondary, and is returned to the collimator.
During this final calibration phase, the angle of the primary and secondary mirrors are adjusted until the return beam passes through the hole in the collimator plate. At this point, the telescope is ready for use.
The primary mirror is tilted such that the reflected beam exits the center-hole in the LASER collimator.
Usage and Results
In the months following its completion, the telescope has been used in combination with the tracking mount in order to take long-exposure images of deep-sky objects. In a comically backward order, I built my telescope prior to mastering astrophotography techniques. I must now improve my astrophotography skills to match the quality of my equipment. This report is meant to focus on the design and creation of the telescope, and therefore it will not describe astrophotography techniques in detail. However, following is a list of the techniques currently being used to achieve high-quality long-exposure shots:
Polar alignment of the mount using a polar scope
Camera control through APT software
Closed-loop guiding using PHD2
Live PEC correction of the mount
As of 3/5/2021, the majority of my effort has been dedicated to learning the techniques used in astrophotography. This often entails imaging during nights with suboptimal conditions (such as poor seeing, or high humidity) - merely to practice the techniques. The intention is to be practiced and prepared for nights with good conditions. However, practice has yielded decent preliminary images. My current favorite is below:
The Orion nebula. A single frame captured using a Canon 5D Mark III on iOptron CEM-60 mount at ISO 100, exposure 180 s, 1.25 m focal length (cropped), without guiding or PEC correction.
The Next Telescope
It is inevitable that even before a project is complete, an engineer thinks of the changes he will make “next time.” As this was my second attempt at building a telescope, I was granted an opportunity to incorporate many such changes. Now, at the culmination of my second attempt, I once again have a list of changes that I would make.
The choice of Newtonian architecture was driven by the availability of affordable off-the-shelf mirrors. However, the long, heavy structure is encumbering. The weight and rotational inertia of the OTA reduces the performance of the tracking mount, thereby making long-exposure imaging difficult. For my next attempt, I want to pursue a more compact architecture, such as a Cassegrain or a Ritchey-Chretein. The mirror set will likely cost an order of magnitude more, but the success of my most recent design reduces the risk that I will fail completely, as I did in my first attempt. Given the technical growth and enjoyment that I achieved from this project - I see the cost as well worth it.
Earlier it was stated that STOp analysis was conducted solely on the mirror cells. While mirror form is the most critical factor for imaging performance, consistent alignment will lead to improved results. In addition, preventing the mirror from shifting as the telescope reorients becomes increasingly important for longer exposures. In subsequent designs, I will endeavor to conduct a STOp analysis on the telescope structure itself. In addition, I will conduct a modal analysis in order to design a structure that reduces vibration.
Using a low-durometer mirror adhesive proved to be a “silver bullet” for the Newtonian architecture, where lateral mirror shift does not substantially reduce image quality. However, if an architecture with multiple powered optics is chosen (E.G. a Ritchey-Chretien), using a soft adhesive will no longer be a viable option. Such an architecture will likely require a flexure-based mirror cell and rigid mirror adhesive, as was explored early in the mirror-cell design phase.
At the time of writing this report, I theorize that an alternative to flexure-based mirror cells may exist: if soft adhesive is used for both mirrors and the bonds are sized such that both mirrors shift laterally by the same amount as the telescope tilts: image quality might be preserved, while only the image location will change during reorientation. However, this concept needs validation by simulation.
If I have seen further it is by standing on the shoulders of Giants. - Isaac Newton
I must thank several people who helped this project come to fruition:
Jim Mirl: for teaching me techniques for design and fabrication of SPDM optics, and for cutting the mirror set for my first telescope.
Martin Millischer: for teaching me to use optical metrology tools, and for helping me debug the issues with my first telescope.
Gaetan Pennecot: for teaching me to use Zemax ray-tracing software.
Mike Borden: for teaching me the STOp analysis method, and for instruction in mirror cell design.
Nick Heys, Austin Roche, and Peter Verdone: for continual mentoring in machining.
I also want to thank the whole of the amateur astronomy community. The amount of information available for free on the internet is astounding. Not only is the knowledge base vast, but the level of detail and technicality rivals that of any institution. In particular, the free and open-source software available (such as PHD2, ASTAP, Stellarium, and APT) has made an extremely complex practice accessible to hobbyists. My hope that this report (and antecedent lecture on telescope basics) will benefit others, in the way that I benefited from those that preceded me.
Thank you for reading,