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I.INTRODUCTIONThe AsteroidFinder is a scientific mission to detect asteroids in the solar system using a space born optical telescope mounted on the DLR compact satellite bus SSB flying in a Low Earth Orbit (LEO). The instrument requirements that drive the design of the instrument are the limiting magnitude of 18.5mag (V-Band), the astrometric accuracy and the field of view (FOV) of the telescope. Near-Earth objects (NEO) like asteroids and comets pose a hazard to life on Earth. Among them Apollo- and Aten-type asteroids which cross the Earth’s orbit are potentially dangerous for the earth. Ground-based surveys to detect such objects essentially cover regions in dark-sky directions more than 90° from the Sun. However, there is high theoretical evidence that there is a population of asteroids on orbits that lie entirely within the Earth’s orbit, the so-called inner-Earth objects (IEO) or Apohele asteroids, remaining virtually undetectable from the Earth’s day side for ground telescopes. A space based telescope like the AsteroidFinder is able to scan sky areas much closer to the sun. The telescope will observe the sky between 30° and 60° in solar elongation. The detection of objects is limited by the light-gathering power of the telescope, the achievable detector sensitivity and, as the lowest limit, by the sky background, which is due to the zodiacal light with its minimum V-band surface brightness of 23.3mag/arcsec2 around 140° solar elongation, increasing gradually toward the sun and toward the ecliptic plane. II.MISSION AND OPTICAL PAYLOAD REQUIREMENTSA.Mission Statements and RequirementsThe AsteroidFinder shall scan the sky between 30° and 60° in solar elongation. This guarantees that the normal vector of the solar panels is always within 30° of the solar direction of the Sun (Fig. 1). With an exposure time of 1min from observation data the NEO provisional orbital parameters shall be identified for follow-up observations. The telescope will be fixed body-mounted to the DLR standard satellite bus (SSB) platform. Pointing shall be achieved through rotation of the spacecraft by means of a 3-axis stabilized platform with pointing accuracy of 5arcmin and a stability of 7arcsec/s. A pointing stability like that should be sufficient for an electron multiplying CCD (EM-CCD) sensor with its high read out rate and short integration time of ~100ms. The telescope temperature shall be kept at -30°C and the focal plane shall be cooled to -80°C by passive means, only. The temperature gradient tolerance range for the telescope is expected to be 15°C. There shall be no re-focusing mechanism. The satellite shall be launched into a sun-synchronous terminator orbit with an inclination of 98°, equatorial crossing time 6:00 local time of descending node (LTDN) and an altitude range from 650 km to 850 km optimized for a maximum observation time by avoiding eclipses by the Earth and minimum cosmic ray impact. The satellite envelope shall not exceed 650×550×880 mm3 in a stowed configuration, the mass (bus and main payload) shall not exceed 130kg and the satellite lifetime shall be 1 year minimum. B.Optical Payload RequirementsTab. 1 shows the main requirements for the AsteroidFinder telescope. Design drivers are in particular the requirements for the point spread function (PSF), the large field of view (FOV) and the distortion requirement. Tab. 1.Optical payload requirements.
C.Limiting SensitivityThe limiting sensitivity of the AsteroidFinder telescope is defined by the zodiacal light background. Within the 30° to 60° angular range with respect to the sun the brightness of the zodiacal light, IZL lies in the range of 120S10 < IZL < 1000S10, while at the ecliptic pole it is IZL = 60S10. In the V band 1S10 corresponds to 27.7mag/arcsec2. A pixel size of 13µm×13µm, equal to 12.4arcsec2, leads to a limiting sensitivity of 19.8mag for IZL = 120S10 and 20.5mag for IZL = 60S10. Fig. 2 shows the effective flux/pixel, calculated for different celestial stray light sources as a function of their respective V band magnitude. The effective flux/pixel is calculated within a band pass of 400nm to 1000nm, assuming a mean quantum efficiency of QE = 0.5, a mean transmission of T = 0.83 (4 reflections with a reflectivity of 0.95) and an ensquared energy per pixel of EE = 0.8. The typical ranges for those stray light sources which can be regarded as in field or off-axis are indicated. These sources have to be compared with the limiting detection sensitivity of 18.5mag for an asteroid and the 23.3mag/arcsec2 (at 140° solar elongation) for the zodiacal light. For a limiting magnitude of 18.5mag, the required off-axis stray light rejection, defined as the limiting flux at the detector divided by the input flux from the source on axis is 1·10-18 for the sun and 3.5·10-18 for the light originating from the Earth. III.ORBITAL STRAY LIGHT ANALYSISA.Geometrical ConsiderationsThe prevention of direct straylight intrusion from sun or earth into the telescope entrance aperture is one of the main objectives in the design of the space craft (S/C). Direct sun light is blocked by a large earth/sun shield. In addition, precautions against intrusion of straylight originating from the Earth out of a 150° solid angle cone need to be taken. Fig. 3 shows the situation for a worst-case orbital height of 650km. B.ESARAD® Radiative AnalysisThe ESARAD® thermal-radiative analysis produced quantitative results for the illumination conditions under the various observational, orbital and seasonal situations. The orbital views with its solar illumination are shown in Fig. 3. In no situation a direct illumination of the aperture through earth or sun light could be detected, but only light scattered in first or higher order from structures in the vicinity of the telescope entrance aperture. During most of the orbital time and for most observation angles the mean stray light level at the telescope aperture is between 10-6W and 10-7W. Within the earth eclipse (solar declination of -23.5°, around the North Pole) the stray light level falls below 10-12W. The worst case appears above the South Pole at a solar declination of -23.5° in winter time, where the straylight level reaches a maximum of 2·10-3W for an observation angle of 60°. For that worst-case scenario Fig. 4 shows the straylight flux through the telescope aperture within a spectral range of 0.2µm < λ < 2.8µm. IV.TELESCOPE OPTICAL DESIGN AND ANALYSISA.Optical DesignAn analysis of a Ritchey-Chretien type telescope showed that it does not seem to be feasible to meet the mission requirements regarding envelope, mass and lifetime and the optical requirements with respect to the limiting sensitivity, i.e. straylight mitigation, with an on-axis or refractive design, an off-axis all-reflective three mirror anastigmat (TMA) has been assumed as baseline, analogous to [1]. More precisely, the telescope is a Cook type F/3.4 system with 2.8 deg radial FOV (Fig. 5) and a focal length of 760mm. The image quality criterion of a PSF with a FWHM of 0.5 pixel requires a not quite diffraction limited system. The image quality has been optimized for a quadratic field with 26.6 mm side length, corresponding to a quadratic FOV of 2°×2°. The wave length range from 450 nm to 850 nm has been weighted according to the quantum efficiency of the e2v CCD201-20 sensor. The Cook TMA provides for an accessible intermediate image and a real exit pupil, which enables effective baffling the telescope. Unlike the similar Korsch TMA, the tertiary mirror is smaller than the primary mirror [2]. The Cook TMA features an optical axis so the mirror surfaces are rotationally symmetric with an off-axis field (2°) and an off-axis entrance pupil. With the standard Cook TMA design and purely conical surfaces the optical performance had not been satisfactory, so additional aspherical coefficients for the mirrors and an additional Schmidt-type corrector plate (SCP) with a reflection angle of 90° have been applied. Nevertheless the optical design features an optical axis and all surfaces are rotationally symmetric with respect to that. The corrector plate is rotationally symmetric after accounting for the 90° reflection. The axial symmetry of the optical elements simplifies manufacturing and testing and usually makes the system less sensitive to misalignments. Fig. 6 shows the PSF within the area of one pixel (13µm × 13µm). While the image quality is close to the diffraction limit at the field center only, the PSF 0.5 pixel FWHM requirement is met over the full FOV, though. To utilize the limited available volume in an optimal way, square or rectangular mirrors have been chosen. The size of the entrance aperture is 230mm × 228mm. A Lyot stop is located between tertiary mirror and corrector plate. The effective aperture equals 474cm2 at the field center and at one field edge and decreases to 430cm2 at the other field edge due to different viewing factors for different field points and due to pupil aberrations. The maximum distortion is 1.4% and the optical system is almost telecentric at image side. B.Straylight AnalysisA field stop at the position of the intermediate image and a Lyot stop at the exit pupil provide an effective means to mitigate stray light induced by in-field as well as out-of-field light sources. To show the potential of stray light mitigation of the Cook TMA system a simplified baffling has been implemented in ZEMAX®. The baffle geometry is shown in Fig. 5. The amount of stray light impinging onto the FPA has been evaluated using the ZEMAX® non-sequential straylight simulation feature. In addition to the field- and Lyot stop several surfaces have been placed to effectively block straylight paths. All non-mirror surfaces are assumed to be Lambertian reflectors with a reflectivity of 5%. There hasn’t been made use of additional vanes to block stray light paths in the proximity of a surface. Aside from light directly reflected at the detector surface, there is no 1st order stray light getting through. (The order of stray light refers to the number of non-specular reflections from stray light entering the entrance pupil to hitting the detector surface.) Within a FOV of ~4° light is scattered in the proximity of the FPA which induces 2nd order stray light. As there are no bright objects (sun, earth, moon, illuminated baffles) to be expected in this region, this near in-field stray light isn’t considered to be critical. The internal baffling scheme mitigates stray light by factor of ~1·10-4 overall. Irrespective the in-field stray light the mitigation ratio is ~3·10-8. Most part of the out-of-field stray light is induced by 3rd order scattering. The reference for the stray light levels is the amount of light that is reflected specularly at the mirrors without scattering at any other surface. Depending on season and observation angle light originating from the earth scatters at the external sun/earth shield and enters the entrance aperture of the telescope. While the fraction of light scattered at the internal baffling of the telescope may be neglected, light scattering caused by mirror contamination – esp. the primary mirror – can reach significant values. Fig. 5 shows the path of rays scattered at the external baffle and at the contaminations of the primary mirror. The scattering at the external baffle is assumed to be Lambertian with a reflection coefficient of 5% and the primary mirror contamination corresponds to cleanliness level L300. The light originating from earth hits the external baffle under an angle of ~15° and for simplicity is assumed to be parallel. For a power of 3W of light from earth ~5mW of scattered light from the sun/earth shielding external baffle enter the telescope’s entrance aperture. A fraction of 2·10-10 of light entering the entrance aperture reaches the FPA. This leads to a background of 2·10-19W/pixel total or 3·10-20W/pixel in the V band which is well below the limiting sensitivity of 1·10-18W/pixel defined by the Zodiacal light background. V.MIRROR AND STRUCTURE MATERIAL TRADE OFFA.Thermal Design and AnalysisFor a purely passive thermal design as is the case for the AsteroidFinder telescope, the main objectives for the thermal design are a minimum temperature gradient within the telescope housing and a temperature level below -30°C. To achieve these requirements the thermal design exhibits following key features: Insulation of the telescope from external environment by multi-layer insulation (MLI), minimization of the radiative heat exchange between the telescope and the MLI by providing low emittance surfaces on the external sides of the telescope housing and entrance baffle as well as on the internal MLI layer and minimization of heat leaks by thermal decoupling over the following interfaces: telescope housing – S/C bus, telescope housing – entrance baffle and telescope housing – detector. Analogous to the orbital stray light analysis a preliminary ESARAD®/ESATAN® radiative-thermal analysis has been implemented for an all-aluminum and an all-HB-Cesic® telescope. The analysis for the two configurations led to the conclusion, that the temperature level of the telescope housing is in the target range of -30°C for any orbital/seasonal configuration and that the temperature gradient within the telescope housing is about 2.5K. With a safety margin factor of 2 a temperature gradient of 5K might be assumed. It is ~20% lower in case of HB-Cesic® due to the increased wall thickness, which needs to be larger than for aluminum, since the allowable stress level for HB-Cesic® is lower. The temperature gradient is smaller than the given tolerance range for the telescope of 15°C. The gradient however is still in a range, where it will have an impact to the optical performance and consequently will drive the selection of mirror bulk and structural material as discussed below. B.Choice of Materials for Mirror Segments and StructureFor different material combinations the telescope temperature and the maximum temperature gradients have been analyzed. The impact of the thermal effects on the optical performance has been analyzed with a ZEMAX® optical model, which included a simplified thermal model as outlined in Fig. 7. Three material configurations have been considered:
The encircled energy (EE) at the field center is shown in Fig. 6 for the three material configurations as a function of the temperature gradient. With an EE criterion of 80% the maximum tolerable temperature gradients are found to be:
An all aluminum design without active temperature control is not able to fulfill the optical requirement for a temperature variation of 15K. While on first sight the material combination CFRP/Zerodur® seems to be favourable moisture absorption of CFRP during fabrication and storage leads to a not well controllable dimensional change on the order of the thermal effects of the all-aluminum design. As there shall be no focusing mechanism, only the HB-Cesic® design is compliant with the mission and optical payload requirements. VI.CONCLUSIONThe optical and radiative-thermal analyses show the feasibility of the space-borne AsteroidFinder telescope in compliance with the mission and optical payload requirements utilizing an all-HB-Cesic® design approach. The non-obscurated off-axis TMA telescope optical design is able to cope with the challenging straylight environment of in a LEO and to achieve the critical requirement of a limiting magnitude of 18.5mag for asteroid detection and orbital parameter determination. ACKNOWLEDGEMENTFunding for the development of the AsteroidFinder telescope is provided by German Aerospace Center DLR. REFERENCESD. C. Harrison and J. C. Chow,
“The Space-Based Visible Sensor,”
John Hopkins APL Technical Digest, 17 226
–236
(1996). Google Scholar
Lloyd Jones,
“Reflective and Catadioptric Objectives,”
Handbook of Optics, 2 2McGraw-Hill,1995). Google Scholar
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