Transformable Reflective Telescope for optical testing and education
Woojin Park, Soojong Pak, Geon Hee Kim, Sunwoo Lee, Seunghyuk Chang, Sanghyuk Kim, Byeongjoon Jeong, Trenton James Brendel, Dae Wook Kim
TTransformable Reflective Telescope for optical testingand education
Woojin Park , Soojong Pak , ∗ , Geon Hee Kim , Sunwoo Lee ,Seunghyuk Chang , Sanghyuk Kim , Byeongjoon Jeong ,Trenton James Brendel , and Dae Wook Kim School of Space Research and Institute of Natural Science, Kyung Hee University,Yongin 17104, Republic of Korea Korea Basic Science Institute, 169-148, Daejeon 34133, Republic of Korea Center for Integrated Smart Sensors, Korea Advanced Institute of Science andTechnology (KAIST), Daejeon 34141, Republic of Korea Korea Astronomy and Space Science Institute, Daejeon 34055, Republic of Korea James C. Wyant College of Optical Sciences, University of Arizona, Tucson,Arizona 85721, USAE-mail: [email protected] , [email protected], ∗ Corresponding author
July 2020
Abstract.
We propose and experimentally demonstrate the Transformable ReflectiveTelescope (TRT) Kit for educational purposes and for performing various opticaltests with a single kit. The TRT Kit is a portable optical bench setup suitable forinterferometry, spectroscopy, measuring stray light, and developing adaptive optics,among other uses. Supplementary modules may be integrated easily thanks to themodular design of the TRT Kit. The Kit consists of five units; a primary mirrormodule, a secondary mirror module, a mounting base module, a baffle module, andan alignment module. Precise alignment and focusing are achieved using a precisionoptical rail on the alignment module. The TRT Kit transforms into three telescopeconfigurations: Newtonian, Cassegrain, and Gregorian. Students change telescopeconfigurations by exchanging the secondary mirror. The portable design and thealuminum primary mirror of the TRT Kit enable students to perform experimentsin various environments. The minimized baffle design utilizes commercial telescopetubes, allowing users to look directly into the optical system while suppressing straylight down to ∼ − point source transmittance (PST). The TRT Kit was tested usinga point source and field images. Point source measurement of the Newtonian telescope a r X i v : . [ phy s i c s . e d - ph ] J u l ransformable Reflective Telescope for optical testing and education configuration resulted in an 80% encircled energy diameter (EED) of 23.8 µ m. Keywords : Astronomical instrumentation (799), Optical telescopes (1174), Reflectingtelescopes (1380) ransformable Reflective Telescope for optical testing and education
1. Introduction
Reflective telescopes are primarily based on Newtonian, Cassegrain, and Gregoriandesigns. The Newtonian optical design is the simplest of the three and is generally well-adapted for commercial telescopes. Optical antennas and reflective objective mirrorsuse modified Cassegrain or Gregorian optical systems (Jiang et al., 2015; Gaˇivoronskiˇi& Zverev, 2012). Recently, Gregorian designs have become more important in large-aperture telescopes, as the Gregorian secondary mirror can be optically conjugated tothe upper layer of the Earth’s atmosphere enabling the use of adaptive optics (AO)techniques for diffraction-limited observation (Goncharov et al., 2003). For example,the aplanatic Gregorian optical design of the Giant Magellan Telescope (GMT) utilizesseven segmented primary mirrors, each 8.4 meters in diameter, and adaptive secondarymirrors (Johns et al., 2014).Newtonian, Cassegrain, and Gregorian optical systems rely chiefly upon a primarymirror and a secondary mirror. The parabolic primary mirror is used to correctfor spherical aberration is common across all three telescope designs. The principaldifferentiating factors among these three optical designs are the location and surfaceshape of the secondary mirror. The Transformable Reflective Telescope (TRT) may bereconfigured to each of the optical designs by simply changing the secondary mirror.A few transformable kits were introduced which are exchangeable for Newtonianor Cassegrain design. One setup uses a 45° - folding mirror within a Cassegrain designto change the setup into a Newtonian telescope (Maeda Akio and Sekiguchi Takamasa,1998). In this kit, the Newtonian setup requires a folding mirror which is larger in sizethan the secondary mirror found in the Cassegrain design. The other kit places thesecondary mirror along the optical axis of the primary mirror. By sliding the convexhyperbolic secondary mirror along the optical axis to the primary mirror, the Cassegrain ransformable Reflective Telescope for optical testing and education
2. TRT system design and analysis
The TRT Kit transforms into three traditional two-mirror optical systems, theNewtonian, Cassegrain, and Gregorian telescopes. Figure 1 illustrates the telescopeconfigurations. In each case, incident rays are reflected from the paraboloidal primarymirror and the secondary mirror sequentially, so that rays converge to a single focalpoint as depicted in the figure. The Newtonian, Cassegrain, and Gregorian systems useflat, convex hyperboloidal, and concave ellipsoidal secondary mirrors, respectively. The ransformable Reflective Telescope for optical testing and education
Figure 1.
Optical layout of (a) Newtonian, (b) Cassegrain, and (c) Gregoriantelescope. (PM: primary mirror, SM: secondary mirror, F: focal point).
Table 1.
Optical design parameters of the TRT Kit.Newtonian Cassegrain GregorianPrimary mirror Aperture (mm) 150Focal ratio F/4Surface type ParaboloidSecondary mirror Aperture (mm) 50 50 50Surface type Flat Hyperboloid EllipsoidConic constant - -2.778 -0.458Effective focal length (mm) 600 2400 3115FOV a (with the 22.2 × (cid:48) ) 127.2 × × × a Fields of view
All secondary mirrors have a 50 mm clear-aperture. The radius of curvature of theCassegrain and Gregorian secondary mirrors are -400 mm and +300 mm, respectively.The axial distance between the primary and secondary mirrors, which is also calleddespace, are 450 mm for Newtonian and Cassegrain, and 778.9 mm for Gregorian. Theback focal length of Newtonian, Cassegrain, and Gregorian are 178.5 mm, 600 mm, and928.9 mm, respectively. The conic constants for the TRT Kit Cassegrain and Gregorianconfigurations are -2.778 and -0.458, respectively. It is worth to note that optimal ransformable Reflective Telescope for optical testing and education
Optical performance changes from assembly and alignment errors are expected based ontolerance analysis. We used CODE V and ZEMAX for sensitivity analysis and Monte-Carlo simulation, respectively. Figure 2 shows the coordinate system for toleranceanalysis.
Figure 2.
The coordinate system for tolerance analysis (same abbreviations withFigure 1).
Sensitivity analysis is completed to gauge optical performance degradation byoptical alignment errors and mechanical deformations. Surface α -, β -, and γ - tilts,x- and y- decentration of each mirror, and despace are examined for sensitivity in theNewtonian, Cassegrain, and Gregorian telescope configurations. The criterion of theanalysis is 80% encircled energy diameter (EED) for the 550 nm wavelength, and thefocus is set as the compensator. Figure 3 shows sensitivity analysis results for the image ransformable Reflective Telescope for optical testing and education Figure 3.
Sensitivity analysis of Newtonian (top), Cassegrain (middle), and Gregorian(bottom) systems: (a, d, f, i, k, n) α - (circle), β - (square), and γ - (cross) tilts, (b, e,g, j, l, o) x- (circle) and y- (square) decenters, and (c, h, m) despace. The Newtonian secondary mirror is a simple flat used to fold the optical path anddoes not affect optical performance. It is shown as constant 80% EED curves acrossdecenters of the primary and secondary mirrors, tilts of the secondary mirror, anddespace in Figure 3. Despace is not critical to optical performance for all three systems.Decenters of the primary and secondary mirrors have the same trends because theyare directly coupled to each other. α - and β - tilts of the primary mirror are the mostsensitive parameters for all three systems.We performed Monte-Carlo simulations as a statistical tolerance analysis to examinethe effects of all errors simultaneously (Park et al., 2020). Monte-Carlo simulation isperformed for α - and β - tilts, x- and y- decenters, despace, and surface irregularity. The ransformable Reflective Telescope for optical testing and education µ mfor 80% EED which is based on the Nyquist sampling requirement for a sensor withwith 6 µ m pixels.Tabel 2 lists the final tolerance ranges of three TRT configurations from the Monte-Carlo simulation. The Gregorian is the most sensitive of the three systems analyzed.Overall tolerance ranges are acceptable and are within general fabrication and alignmenterrors. Alignment accuracy of the TRT Kit will be discussed in Section 3. Table 2.
Tolerance limits of Newtonian, Cassegrain, and Gregorian from the Monte-Carlo simulations.Parameter Newtonian Cassegrain Gregorian α -, β - Tilt PM ± (cid:48) ± (cid:48) ± (cid:48) SM ± (cid:48) ± (cid:48) ± (cid:48) x-, y- Decenter ± ± ± ± ± ± ± λ ± λ ± λ Focus a ±
20 mm a The focus is set as the compensator.
The TRT Kit is a modularized and portable system, enabling easy assembly of eachtype of telescope and adaptable optical test setup. The total dimensions are 610 mm(L) ×
158 mm (W) ×
188 mm (H), and the total weight is around 2 kg. The lengthextends to 970 mm in the Gregorian configuration. Illustrations for the Newtonian andGregorian configurations are displayed in Figure 4. The mounting base module containsthe array of holes and taps like an optical table so the TRT Kit becomes transformable,and the equally spacing holes can be used for measuring some distance such as the focallength and despace. A precision linear stage is used for fine focusing in the accuracy of>10 µ m, and 2-inch camera adapters are found near the two focal points. Red parts ransformable Reflective Telescope for optical testing and education Figure 4.
3D optomechanical modeling of the TRT Kit. Newtonian (top) andGregorian (bottom) systems are shown.
Static analysis of the TRT Kit was accomplished with SolidWorks (DassaultSystems) mechanical design software. Optomechanical structures are made of aluminumalloy (Al6061-T6). The boundary condition used in the simulation fixes the bottom ofthe dovetail (green arrows in Figure 5) in place, allowing other parts to move relativeto this static mount.The maximum mechanical deformation of optomechanical structures due to itsweight is 0.11 mm and 0.7 mm for the compact (Newtonian, Cassegrain) and extended(Gregorian) configurations (Figure 5). Based on tolerance analysis results, themechanical deformations are not critical to optical performance. ransformable Reflective Telescope for optical testing and education Figure 5.
Static analysis results of the compact mode (top) and the extendedmode (bottom). The red arrows represent gravity, and fixed (reference) positionsare indicated with green arrows.
3. TRT manufacturing, assembly, and alignment
The primary mirror is made of aluminum alloy (Al6061-T6) with protected aluminumcoated on the mirror surface. The aluminum mirrors have advantages over othersubstrates in handling and thermal stability, characteristics required for the portabilityof the system (Hadjimichael et al., 2002). The TRT primary mirrors are easy to replacewith mirrors of different aperture size, surface type, and material. Fabrication processesof aluminum mirrors are as follows: pre-fabrication, stress relieving and aging, single-point diamond turning (SPDT), and protective coating. The entrance pupil diameterof the primary mirror is 150 mm and it has an F-number of 4 (see, Table 1).The SPDT (Freeform 700A; Precitech) process produces a high-quality surface ransformable Reflective Telescope for optical testing and education
Figure 6.
Surface measurement results of the primary mirror. The overall surfaceshape is measured with the UA3P (left). The surface micro-roughness is measuredwith NT2000 (right).
Figure 6 represents surface measurement results of the fabricated aluminum primarymirror. The surface figure error of the mirror is 0.067 µ m RMS (Root Mean Square)and 1.84 µ m PV (Peak to Valley). The average surface roughness (Ra) is 4.8 nm asmeasured with the WYKO NT2000 vertical scanning and phase-shifting interferencemicroscope.The primary and secondary mirrors are aluminum coated with >95% reflectivity,so the total throughput of the two mirror telescopes are about 90.3% for all threeconfigurations. The TRT Kit has three main modules, a primary mirror module, a secondary mirrormodule, and a mounting base module. The modules are designed for interchangeability. ransformable Reflective Telescope for optical testing and education Figure 7.
The TRT assembly, including (a) the mounting base module, (b) theprimary mirror module, (c) the secondary mirror module, and (d) all three modulesassembled in the final TRT Kit configuration. Colored arrows indicate the screw andpin attachment points in the assembly process.
The total number of optical and optomechanical components is 13. Screws and pinsmaintain the optical alignment. Because the modules are completely independent ofone another, students may assemble each module separately and then cooperate toconstruct the final version of the TRT Kit.Figure 7 illustrates the assembly method of each module. (a) The mounting basemodule consists of four mechanical parts, labeled B1 to B4, which support the primaryand secondary mirror modules. The TRT Kit mounts onto commercial telescope mounts,thanks to a universal dovetail adapter (B4) attached to the base. (b) The primary mirroris mounted to P1 by threading P3 to P2, and a rubber ring is inserted between P3 andthe primary mirror to protect the reflective mirror surface. (c) The tip and tilt of thesecondary mirror is adjusted with screws attached to the mirror through S3 and spaced120° apart for three-point alignment. The linear stage for precise mirror transition is ransformable Reflective Telescope for optical testing and education ± (cid:48) tolerance, which is measured by usingCoordinate Measurement Machines (CMM), thanks to the pins between P1 and B1.The secondary mirror is replaced to other types using screws for S3 and the secondarymirror. The mounting base module needs to be reassembled for the Gregorian system(see, the bottom panel in Figure 4). Shack-Hartmann wave-front sensors and CMM are commonly used for optical alignment(Wu et al., 2016). Three-Point Laser Alignment (TPLA) is another common practiceused to align optics. TPLA uses three mounted lasers aligned parallel to the opticalaxis of the primary mirror.
Figure 8.
Layouts of TPLA for the Newtonian telescope. This method can be adaptedto the other types of telescopes (same abbreviations with Figure 1).
The laser mount contains a screen with holes at points optically conjugate to the ransformable Reflective Telescope for optical testing and education (cid:48) , 0.18 (cid:48) , and 0.14 (cid:48) tilterrors of the secondary mirror in Newtonian, Cassegrain, and Gregorian, respectively.These alignment accuracy are acceptable by comparing to tolerances of the telescopes(Table 2).
Figure 9.
The TRT Kit alignment with TPLA method. (Center) The laser mountattached to the TRT Kit. (Sub-pictures) (a) The lasers come from the source, (b) andare reflected by the primary mirror, (c) the secondary mirror, (d) and the flat mirror.After traveling back through the system, (a) the beams reach the screen. ransformable Reflective Telescope for optical testing and education
4. TRT baffle and stray light control
Stray light analysis and effective baffle design are necessary to suppress unwanted lightthat degrades the image. Stray light is extraneous, unwanted light which is detected bythe sensor reflection from mechanical structures or scattering from optical components.Stray light presents itself as noise in the image, reducing the signal to noise ratio (SNR).The baffle design of on-axis reflective optical systems, such as Cassegrain, andRitchey-Chretien telescopes is a well-defined process described by mathematical models.An iterative method is needed to design proper baffle systems (Ho & Chang, 2009;Kumar et al., 2013; Song et al., 2002).For this portable optical device, stray light suppression is critical and even moreimportant than it is for instruments operated indoors, as there are more potential sourcesof stray light when imaging outdoors. Baffle structures are easy to assemble with screwsand T-mounts. Figure 10 demonstrates baffle structures suitable for all three opticalconfigurations, though only the Newtonian configuration is shown. The plate bafflesbehind the primary and secondary mirrors are designed to effectively suppress criticalstray light paths that directly illuminate the detector. These critical ray paths are ofparticular importance for the folded Newtonian system, which is susceptible to morepotential sources of stray light as a result of the folded design.Stray light analysis was completed with LightTools software (Synopsys Inc.).In the simulation, a 6500 K black body source was used to illuminate the opticalsystem, approximating the spectral distribution of daylight. Assuming ideal diffusivesurfaces, baffles and optomechanical structures scatter light with 1 % and 5 % Lambertianreflectance, respectively. Incidence angles of simulated stray light paths span 0° - 180°for all systems. The amount of stray light suppression can be defined with the Point ransformable Reflective Telescope for optical testing and education Figure 10.
The TRT Kit with baffle structures. Yellow colors represent the baffles ofthe telescope.
Source Transmittance (PST):
P ST ( θ, λ ) = L D ( θ, λ ) L A ( θ, λ ) (1)where L D( θ , λ
0) is spectral radiance on the detector, and L A( θ , λ
0) is spectral radianceon the entrance aperture. The PST represents how much stray light can be suppressedby the baffle structure as a function of incidence angle. Figure 11 presents results fromstray light analysis for the TRT Kit. Blue dots represent the PST with baffles, and reddots indicate the PST without baffles. The incident angles of 0°, 90°, and 180° indicatethe incident light along +z, -y, and -z direction (see, Figure 10 for the coordinate system).Baffles suppress 75% - 95% of stray light from all incidence angle (0° to 180°). ThePST reaches a minimum of around 10 − with baffles. Note that some of sharp dropsin PST near the 20° to 90° incidence angles for the Gregorian system are a result ofunder-sampling.Compared to the other systems, the detector is most exposed to stray light withoutthe baffle in the Newtonian system. Incoming stray light from specific angle (95° - ransformable Reflective Telescope for optical testing and education Figure 11.
Stray light analysis results of (a) Newtonian, (b) Cassegrain, and (c)Gregorian systems. Blue dots represent the PST with baffles, and red dots indicatethe PST without baffles.
5. TRT system performance and application
The optical performance of the TRT Kit was evaluated with three optical tests:observations of field images, point source tests, and night sky observations. Figure 12includes pictures that are taken with (a) the Newtonian, (b) Cassegrain, and (c)Gregorian telescopes. These three pictures clearly indicate the difference in FOV of thethree configurations (see, Table 1). The picture captured with the Gregorian telescope ransformable Reflective Telescope for optical testing and education
Figure 12.
The TRT Kit field test pictures. The pictures were captured with the (a)Newtonian, (b) Cassegrain, and (c) Gregorian telescopes, respectively. Each telescopehas a different FOV, and the picture with the Gregorian telescope is reversed.
Point source tests were also performed using the Newtonian configuration at theon-axis. Figure 13 shows the point source image with 23.8 µ m 80 % EED, correspondingto ∼ Figure 13.
The point source image (left) and EED (right).
Figure 14 depicts the Messier 27 (M27) nebula captured using the Newtonian TRTKit configuration. The observation demonstrates great optical performance capable ofimaging detailed structures of the extended source and the fine circular shapes of starsacross the field. ransformable Reflective Telescope for optical testing and education Figure 14.
The M27 nebula with stars that were observed using the Newtoniantelescope.
Since the TRT Kit is modularized, it transforms to the spectrometer by installing thespectrometer module, which consists of a grating, a slit, and a light source. Figure 15includes the main TRT Kit, the baffles, and the spectrometer module to configure theEbert-Fastie spectrometer.
Figure 15.
The spectrometer module with the TRT Kit.
A grating with 300 (grooves/mm) groove density and 4.3° blaze angle, and a neonlamp were installed for the spectrum that is illustrated in Figure 16. At the position ransformable Reflective Telescope for optical testing and education
Figure 16.
Neon spectrum images from the TRT Kit and the spectrometer module.
6. Discussion and summary
We developed the TRT Kit to transform into the Newtonian, Cassegrain, and Gregoriantelescopes, as well as the Ebert-Fastie spectrometer. The modular structure of the TRTKit maximizes versatility for various optical tests. Students only need to replace thesecondary mirror to switch to other types of telescope or optical system.The maximum optomechanical deformations by self-weight are 0.11 mm forNewtonian and Cassegrain configurations, and 0.7 mm for the Gregorian design.Even though these deformations may degrade the optical performance, the errors areacceptable by comparing to Monte-Carlo simulation results.Optimized baffle structures are designed for stray light suppression. It suppressed ransformable Reflective Telescope for optical testing and education − to 10 − PST across all angles of incidence.The aluminum parabolic primary mirror was fabricated with SPDT. Surface errorson the primary mirror are ≤ λ /8 RMS and the average surface roughness is 4.8 nm. Themirrors are made of aluminum to prevent imaging quality degradation by nonuniformthermal expansion or contraction.The TRT Kit has a simple optical alignment procedure which requires onlysecondary mirrors to be aligned. The TPLA module makes optical alignment nearlyeffortless.Point source measurement resulted in a 23.8 µ m 80 % EED. When observing thenight sky, we were able to distinguish the fine structures of the M27 nebular. The TRTKit is useful not only for optical experiments but also as an astronomical telescope.The TRT Kit is a versatile, portable telescope and optical test system. It canbe utilized for many optical experiments involving spectroscopy, Gaussian theory,Fourier optics, and for developing an adaptive optics system by using the differenttypes of telescope configurations such as Gregorian and Cassegrain, which createunique conjugate planes requiring different deformable mirror and wavefront sensorconfigurations. The compact size and portable design of the TRT Kit enable its usein many different environments.The TRT Kit transformable design concept has obtained a domestic patent fromthe Korean Intellectual Property Office (application number KR10-2015-0153977) butthe commercialization has not yet been processed. Estimated fabrication cost ofoptomechanical parts is about 600 - 1000 US dollars which probably affordable forhigh school or university. The TRT Kit is suitable for both educational purposes andscientific research. We would like to widely distribute the transformable telescope kitto students, researchers, and others who are interested in using the Kit.
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