Extreme Accuracy Star Tracker in Support of HYPER Precision Cold Atom Interferometry.

Transcription

1 AAS Extreme Accuracy Star Tracker in Support of HYPER Precision Cold Atom Interferometry. S. P. Airey, G. Bagnasco, M. Barilli, S. Becucci, G. Cherubini, A. Romoli HYPER stands for Hyper-precision cold atom interferometry in space. HYPER is a potential Future Flexi-mission of the European Space Agency, ESA, in the fundamental physics domain. Following a preliminary feasibility study (Ref 1) conducted in the Concurrent Design Facility of the European Space Technology Center, ESTEC, which was supported by Professor W. Ertmer of the Institut für Quantenoptik, Hanover and his team of scientists, ESA awarded Astrium Germany and its industrial team with a follow-on Feasibility Study Contract. As part of this team, Galileo Avionica was responsible for the design and performance requirements simulation of the optical bench and precision star tracker, two of the components at the heart of the HYPER payload. This paper provides first of all an essential but quick introduction to cold atom-wave interferometry which is at the core of the high-performance HYPER payload and provides the capability of measuring accelerations and rotations with extremely high accuracy. A summary of the scientific mission objectives, which entail the repeated measurement of extremely small rotations and accelerations over at least one-year period with respect to an inertial reference frame, is described. Thereafter, a short resume of the main mission requirements is given. Among these requirements are two critical requirements, which dominate the overall spacecraft design: 1) the superior thermo-mechanical stability between the HYPER instruments and a Precision Star Tracker, PST, which provides the inertial attitude reference in science mode (Spectral Density=.75x10-10 rad/hz -0.5, in the frequency range between 3.x10-5 Hz and 0.15 Hz); ) ) the PST Absolute Measurement Accuracy (Spectral Density=1.75x10-9 rad/hz -0.5, in the frequency range between 3.x10-5 Hz and 5 Hz). S.P.Airey and G.Bagnasco are affiliated to the European Space Agency (ESA) M.Barilli, S.Becucci, G.Cherubini and A.Romoli are affiliated to Galileo Avionica Page 1

2 Finally, this paper highlights the challenges the Industrial Team faced in meeting those requirements and describes the optical design of this extremely accurate Precision Star Tracker. The preliminary results of the performance requirements simulation are also presented. ATOM-WAVE INTERFEROMETRY In the last two decades matter-wave interferometry has been pursued mainly in order to demonstrate and test the wave character of matter, one of the most puzzling effects in physics, predicted by quantum mechanics. Only recently has the technique of matter-wave interferometry also been used to realise very high-performance instruments for the measurement of accelerations, rotations and frequency shifts (Ref ). The technological advances that make atom-wave interferometry useful as a high accuracy sensor are those related to developments in the following two main fields: 1- Laser-controlled high precision Raman spectroscopy for the manipulation and control of cold atoms - Cooling techniques applied to matter-wave atom clouds to increase their coherent interaction time. These two techniques are brought together in an Atomic Sagnac Interferometer (ASI), where the Raman laser spectroscopy allows, as in a classical optical interferometer, the coherent splitting, redirection, recombination and spectroscopic detection of atoms by modifying their internal electronic state. At the same time, it modifies their macroscopic state, by absorbing photon momentum, leading to the formation of a so-called Sagnac loop, as shown in Figure 1, conceptually identical to a standard optical Sagnac interferometer used in Fiber Optic Gyros. Figure 1: Split, redirection and recombination of atoms by lasers in the two interferometer arms, leading to the formation of a Sagnac Loop In an interferometer experiencing rotations and/or accelerations the symmetry between the two matter-wave beams, which travel in opposite directions along the interferometer arms, is broken. This symmetry breakdown causes a measurable interference pattern, formed when the arms re-join. It is this measurement that is used to sense the accelerations and rotations to which the loop has been subjected. In order to discriminate between accelerations and rotations two ASIs, propagating in opposite directions, are combined into a single instrument, called the Atom Sagnac Unit Page

3 (ASU). The effects of the rotations will affect these ASIs differently whereas the accelerations will cause the same effect. The signals from the two ASIs can therefore be combined to measure, independently, either the pure rotation or the pure acceleration without cross talk from the other effect. The conceptual configuration of an ASU is shown in figure detection detection cold atom ic beam 3 D M O M π/ π π/ Interferom eter cold atom ic beam 3 D M O M Figure : Conceptual configuration of an ASU. In each ASI, as in a classical optical Sagnac interferometer, a phase shift M is created. While M Sagnac-Optical = 4 B A opt S / c λ (1) It can be shows that the equivalent phase shift in a matter wave interferometer is M Sagnac-Atoms = 4 B m atom A atom S / h () This phase shift between the two waves, travelling along the two arms of the interferometer, is caused by the Doppler effect between the atomic waves and the manipulating lasers, which are essentially fixed. Comparison of equation (1) and () suggests a theoretical superiority in sensitivity of the matter-wave interferometer, as: M Sagnac-Atoms / M Sagnac-Optical = m atom c λ / h (3) For typical experimental parameters (λ = 633 nm, m atom = Caesium mass) the increase in sensitivity would result in a factor 10 10, if the areas A were equal. In reality A atom is << A optics It can be shown that A atom in equation () is equal to A atom = L A atom V T / V L (4) where L is the length of the interferometer, V T = hk/ B m atom is the transverse velocity due to the two-photon momentum transferred to the atomic beam during the Raman transition, V L = (k B T/ m atom ) 1/ is the drift velocity of the atomic beam in the interferometer. From equation () and (4) it can be seen that the highest potential for further improvements of the sensitivity in the detection of M Sagnac-Atoms in an atom-wave interferometer resides in the Page 3

4 lowering of the drift velocity V L of the atoms by means of cooling techniques. Since 1975 several techniques have been developed to cool a large amount of atoms ( ) hence slowing them down. Table 1 identifies some of these techniques together with the temperatures and drift velocities they can typically achieve. Laser cooling does not only reduce the mean drift velocity, V L, of the atoms but also increases their coherence. Indeed, if all the atoms could be controlled to exactly the same velocity they would then behave as a single coherent wave whose wavelength would be given by the de-broglie relation: λ d-b = h / m atom V L (5) Thermal Atomic beam 300 K m/s Magneto-optical trap mk m/s Sub-Doppler Molasses :K 1 10 cm/s Bose-Einstein Condensation nk 1 mm/s Table 1: Atom Cooling Techniques and Performances At present, ASU rotation measurement accuracy of the order of 5.0x10-1 rad/sec or better with respect to an inertial reference frame, at a sampling frequency of 0.3 Hz are considered feasible. MISSION OBJECTIVES The primary scientific objectives of the HYPER mission is are: - to map, for the first time, the latitudinal structure (magnitude and sign) of the Lense-Thirring effect (LTE) induced by the Earth s rotation and predicted by the General Relativity with a measurement accuracy of 10 % - to determine, independently from Quantum Electro-Dynamics theories, the fine structure constant, ( =Be / hc), with a measurement accuracy improvement of one order of magnitude with respect to the present experimental results - to investigate various distinct sources of matter-wave de-coherence effects, predicted by quantum gravity theories Furthermore, as a secondary objective the successful completion of this mission would demonstrate for the first time the superior performance of cold atom matter-wave interferometer instruments. HYPER might therefore lead the way to a novel generation of inertial sensors and gyroscopes that would be needed to enable other future missions. The scientific objectives given above are only feasible in space, where the potential of coldatom matter-wave interferometry sensors can be fully exploited thanks to the provision, via drag free satellite control, of an environment almost totally free of disturbing accelerations, such as those due to gravity on Earth. Page 4

5 The present Industrial Feasibility Study concentrated only on demonstrating the feasibility of the Lense-Thirring (Ref 3) effect measurement. This effect causes the Gravitational Field surrounding a rotating mass to differ from that surrounding a non-rotating mass. A simple analogy can be drawn from Electromagnetic Field theory: a rotating charged sphere will create both an electric and a magnetic field, while a non-rotating charged sphere will produce only an electric field. In general, slowly rotating bodies like the Earth create only a tiny modification to the gravitational field with the consequence that their effects on the motion of a body in its immediate surroundings are almost totally insignificant. However, these tiny modifications to the local gravitational field will cause a gyroscope, placed in an orbit around the Earth, to precess according to the following formula: Σ LT = G/r 3 [3 r / r (S e θ r ) - S e ] (6) (S e is the spin angular momentum of the Earth and r is the vector identifying the position of the gyroscope) Although sign and strength of the induced rotation, Σ LT, depends on its latitudinal position along the orbit, the average precessional rate of the gyroscope over 1 orbit (in a 1000 km polar orbit) would be of the order of only radians/sec. This implies that with the previously quoted ASU rotation measurement accuracy (5.0x10-1 rad/sec, at a sampling frequency of 0.3 Hz) HYPER will need to gather the order of 10 7 measurements for about one year, in order to measure such a tiny effect with a 10% accuracy. PAYLOAD REQUIREMENTS AND DESIGN SOLUTIONS The performance requirements on the HYPER payload are driven by the need to measure the Lense-Thirring effect. The payload must therefore be capable of measuring the two perpendicular Σ LT components and of distinguishing the rate measurements from other effects such as accelerations. One ASU, described before, allows the unambiguous measurement of rates around a single axis. Therefore, two independent and orthogonal ASUs are needed for HYPER. This baseline configuration is presented in figure 3. Figure 3: Conceptual Payload configuration showing two ASUs, each consisting of two counter propagating ASIs, mounted on a single optical bench together with the Precision StarTracker. Page 5

6 However, each ASU measures the relative rotation of the atomic waves with respect to the manipulating lasers. As the lasers and the s/c are contained within the same local inertial frame they too will experience the Lense-Thirring effect. It is therefore fundamental that the manipulating lasers are maintained fixed with respect to a non-local inertial frame. A guide star provides the reference for this non-local inertial frame, tracked by a Precision Star Tracker. The two main payload requirements can thus be summarised as follows, in terms of spectral density: 1- the ASU-PST alignment stability:.75x10-10 rad/hz -0.5, in the frequency range between 3.x10-5 Hz and 0.15 Hz - the PST Absolute Measurement Accuracy: 1.75x10-9 rad/hz -0.5, in the frequency range between 3.x10-5 Hz and 5 Hz). The design concept adopted for HYPER foresees the two ASUs (made up of ASIs each) and the PST to be integrated together in a single compact module, which acts as a common optical bench. This design concept allows minimising the misalignment error sources between the PST and the two ASUs co-ordinate frames. In order to meet the challenging relative stability requirement over one orbit (about 100 minutes) and respect at the same time the mass limitations imposed by the selected Rockot laucher (< 1000 kg) ULETM (glass ceramic Titanium-silicate) has been selected as the baseline material for the Optical bench. The overall arrangement is shown in figure 4. Figure 4: Payload Design configuration showing respectively the four ASIs (in red), the ULETM optical bench with the integrated Precision Star-Tracker (in blue). Three laser fibre injectors (in green) for each ASU determine the paths of the manipulating lasers, which in turn determine the sensitive directions of each ASU. The main ASU reference frame is therefore defined by the line through the centre of these reflectors and is nominally perpendicular with the Precision Star-Tracker boresight. The task of fitting the PST telescope into a 700 mm optical bench and of ensuring its manufacturability and testability was another major design driver. Two kinds of optical concepts were considered initially for the PST. One foresaw a focusing telescope, based on Page 6

7 a Cassegrain or Ritchey-Chretien configuration; while the other consisted of an a-focal Galileian telescope using a negative lens as collimating element after a Cassegrain telescope. The first concept has the advantage of simplicity and it is less critical for what concerns surface defects and cleanliness of the secondary mirror. This mirror is the effective optical surface, which is crossed by the smallest section of the beam. The smaller its area, the greater is the undesired effect of a surface defect on the final image. The second concept of the a-focal telescope, having one additional element, is more sensitive to misalignments and its residual surfaces defects and particle contamination could result be more critical than the first option, changing the shape of Point Spread Function, PSF, and the background illumination depending from the star position. Both phenomena can be considered highly undesirable for the very high precision required to the PST. Indeed the background can decrease the sensitivity of the PST, and the change of PSF shape can affect the centroid error introducing a systematic error, which could be calibrated but only on the ground, without taking into account in flight contamination. As a result of these configurations, the first concept was initially selected. The following trade-offs led to refinement of the design concept on the basis of the system error analysis, which led to consider an optical system whose characteristics are resumed in table. Effective Focal Length Useful diameter Central Obstruction diameter FOV mm 190 mm 90 mm ±5 sec Resulting F/number 190 Table Particularly important was the assumption of the effective focal length of 36 m. Such a large focal length could cause strong criticality when realised with a simple Ritchey- Chretien. Indeed, since the overall optical bench length is constrained to 700 mm, assuming that the CCD relief with respect to the primary mirror effective surface is (for instance) 40 mm, the first order optics layout can be set up as shown in figure 5. Figure 5: Ritchey-Chretien first order layout The layout of figure 6 can be considered as a collimated telescope made by two elements, one positive with EFL f1 and the other negative with focal f', followed by a positive element f. Page 7

8 The telescope has magnification M given by: f1 h1 M = = (7) f ' h the second element shall have an EFL given by: f1 f ' = (8) M and the distance d is given by: M 1 = f1 + f ' = f (9) M d 1 and the back focal length X will result: X' = f " (10) Therefore the focal length f is given by: f 1 f' f" f1 X' = = = (11) φ ' + φ " f ' + f " f F 1 Then by putting, for instance: you obtain: X' = f = mm (1) f = mm (13) which means a magnification M of about 50 x. This magnification is critical if we consider that, for instance, a tolerance of 1 micron on the distance d causes a defocus just inside the depth of focus. Then, in order to reduce this and some other criticality, it is necessary to reduce M. Page 8

9 Figure 6 First order layout with thin lenses The improved optical system, schematised in figure 6, can be considered as a Galileian of magnification M, followed by a lens whose focal length is F/M. The basic idea is to increase the focal length f and to fold it twice by mean of two flat folding mirrors. The sizes of the elements were computed as follows: By indicating with L = 700 mm the overall length of the PST telescope and with R=40 mm the relief of the sensitive area of the CCD detector with respect to the effective optical surface of the primary mirror, then d = L R = = 660 mm. A first flat folding mirror M3 is located in the centre of the hole of the primary mirror M1, and it is slightly tilted, in order to reflect the beam outside of the secondary mirror M. The distance of M3 from M is d1 = d = 660 mm. A second flat folding mirror M4 orthogonal to the optical axis is set very close to the secondary mirror M. Therefore the distance d of M4 from M3 is given by d d1 = d = 660 mm. M4 reflects the beam coming from M3 toward the CCD, which is mounted at distance R= 40 mm from the front surface of M1. The distance d3 from M4 up to the CCD is then given by d3 d + R = L = 700 mm. Therefore the Back Focal Length X of the system will be given by: X' = d + d + d 3 = = 00 mm This means that the magnification of the Galileian is given by: M = F/X' = 36000/00 = 17.8 x reducing the magnification ratio of a factor.8. Figure 7 shows a perspective view of the optical layout. Page 9

10 Figure 7: Perspective view of the PST optics with two flat folding mirror. The beam coming from left crosses a flat parallel plate of silica, and it is reflected by the primary parabolic converging mirror M1 toward the secondary diverging parabolic mirror M. The beam is folded a first time by M3, slightly tilted (0.6 ) with respect to the optical axis of the telescope and a second time by M4, which is obtained on the inner surface of the silica plate. The sensitivity of the system to the distance between M1 and M is now decreased in such a way that a change of 5 microns is not critical. This renders easier the assembly of the system. Figure 8 shows another view of the optical layout. The performances of such PST optics are well inside the diffraction limit and from the point of view of the geometrical aberrations, it can be considered perfect, showing a Strehl ratio very close to 100% Figure 8: Optical layout A sensitivity analysis was performed in order to understand the alignment stability criticality of each optical system element. Table 3 provides the alignment sensitivity analysis preliminary results: Page 10

11 M1 M M3 M4 Tilt = Shift mm Table 3 The linear shifts of M3 and M4 have no effects, since they are flat mirrors. Since the two flat mirrors are small and supported respectively by the primary mirror, M1, and secondary mirror, M, these two mirror groups have been considered, in first approximation, as rigid bodies. For this reason no movement of M1 and M3 with respect of the CCD, supported as well by the M1, is expected and at the same time M movements should be equal to those experienced by M4. These considerations lead to table 4 with new, simplified alignment sensitivity values. Tilt =3.6 1 M M4 group Shift mm 0.89 Table 4 The combination of a large photon collecting area (useful diameter= 190 mm), of this compact Ritchey-Chretien optical design, modified with two flat folding mirrors and of a complex centroiding and error correction algorithms, developed for the selected 104 x 104 pixel CCD detector, allows the PST to get the best performances related to the limited volume allocated. BAFFLING AND STRAY LIGHT ANALYSIS A very important aspect of the PST baffle is that of the internal baffle design. Indeed the external baffle can be considered as a continuation of the internal envelope of the telescope, which is short (about 30 cm) compared with the telescope itself. The preliminary internal baffle design, which was developed in a previous step taking into account symmetry around the optical axis, has been revised in order to accommodate the two folding mirror. The most part of the baffle is modelled in order to have rotational symmetry, as it results from fig.9. Page 11

12 Figure 9 Lateral view of the PST internal baffle On the left there are two obstructing stops, placed before and after the silica flat and parallel plate P. A first cone C1, on the left, based on the plate P, surrounds the secondary mirror M and the flat folding mirror M4. It acts a first baffle of the beams. After reflection on the secondary mirror M the beam passes through a cylinder C, which is based on obstructed part of the primary mirror M1 and it surrounds the flat folding mirror M3. The cylinder C is better visible in the perspective view of fig.10. The beam reflected by M3, which is tilted of 0.6, comes back towards the flat folding mirror M4, close to the secondary mirror M. Figure 10 Perspective view of the PST internal baffle, seen from object side After reflection on M4, the beam comes on the detector D, passing between the cylinder C and the cone C3, coaxial to C. A flat stop S1, visible in fig.10, with an hole allowing the beam reaches the focal plane, is located between C and C3. A last stop S, close to the effective surface of the primary mirror M1, with a small lateral hole allows the primary beam impinging the detector. Page 1

13 Figure 11 Perspective view of the PST internal baffle, seen from image side Fig.11 shows another view of the internal baffle, showing more in details the cone C1 and the beams inside. This configuration has a good efficiency, being based on simple geometrical concepts. A preliminary analysis of the efficiency was done with ASAP TM of Breault Research Organisation, by considering reflective properties of the mechanical walls of the baffle.the result is that no reflected path arrives on the detector. Further analyses have been done. Fig.1 shows the efficiency of the baffle when painted with Chemglaze Z30. Figure 1 Baffle efficiency with Chemglaze Z30 Fig.13 is shows the efficiency of the baffle coated as a Lambertian diffuser with 5% of reflectivity. In the first case the attenuation of stray light is better than 10-4 and in the second it is well under the value of Page 13

14 Figure 13 Lambertian diffusion (5% reflectivity) HYPER PRECISION STAR TRACKER The characteristics of the PST baseline have been obtained as result of a trade-off performed with the following parameters: - IFOV REDUCTION, in order to reduce the contribution of all errors that can be characterised in terms of fraction of pixels such as Centroid and Noise Equivalent Angle (NEA): such reduction can be obtained by a longer focal length - INCREASE OF INTEGRATION TIME in order to increase the star signal on the CCD - INCREASE OF CCD Full Well Capacity (Pixel size), in order to avoid CCD saturation - MAINTAIN THE OPTICS DIAMETER, in order to keep the PST assembly mass - TRACKING MATRIXES, in order to match larger PSF produced by high F # and reduce Centroid error in terms of fraction of pixel The limiting magnitude has been driven by the need to have a sufficient number of suitable guide stars always available as the orientation of the orbit changes over one year and the need to guarantee a good signal to noise ratio. In order to evaluate in detail all the optical configurations and centroid algorithms, the GA single star simulator has been used. The simulator is able to take into account the use of various methods of centroiding, including the required very large tracking matrixes and different ways to weigh pixel values. All the pointing errors have been considered, showing that the main error contributors from the PST are the Centroid error and NEA. These simulator runs have allowed the best compromise between noise and signal sensitivity, with full consideration of the centroiding algorithm method and CCD selection, to be found. Page 14

15 The best performance was seen to be obtained by a 13 mm pixel size CCD, an IFOV of arcsec and a centroid algorithm based on 17x17 pixel tracking matrix. Considering Hipparcos star catalogue data, a guide star list containing 48 stars was constructed. The selected stars have the following main characteristics: +.81 V (Visual Magnitude) B-V Colour index Additionally there are no variable, binary or double stars and the proper motion of each of the stars is known with an accuracy of better than 8*10-3 arcsec/year and their right ascension, declination and parallax errors are known with an accuracy better than 3*10-3 arcsec THERMO-MECHANICAL ASPECTS As can be deduced from table 3, showing the telescope sensitivity analysis, a shift of the M-M4 group of 1 nm (with reference to M1-M3 group) produces a tilt on the optical axis of the same order of magnitude of the required stability (.75x10-10 rad/hz -0.5, in the frequency range between 3.x10-5 Hz and 0.15 Hz). This consideration gives the feeling about the sensitivity of the system and on which level of detail this study has to reach to assess the foreseen compliance of the instrument to the science requirements. The best way to reach this stability is to minimize thermal and mechanical disturbancies of the OB environment. Causes of main thermal disturbances are: - Earth albedo, producing a rotating heat load on the S/C around the instrument boresight, occuring at almost the same frequency of the LTE, - constant heat leackage through the optical entrance aperture to CS - the payload elements heat dissipation These disturbances have all been minimized by an active thermal control, that takes care of the functional elements dissipation by maintaining their I/F temperature very stably. MLI shielding has permitted to reduce the radiative effects of Earth Albedo on the bench and the leakage to space has been cut out by inserting a temperature controlled quartz window in front of telescope. The remaining thermal disturbances come from a residual temperature change on the structural I/F to S/C, which occurs at the orbit frequency, and by the heat losses within the Fibre injectors and the retro reflecting mirrors. To evaluate their impact a FE model of the optical bench structure was constructed and its behaviour verified under these thermal loads. Figure 14 shows the Finite Element model of the Optical Bench. Page 15

16 Figure 14: 3D View of the Optical Bench Finite Element Model This model has been used to track the movement (generated by the thermal environment changes) of all the 63 points of interest for the requirements verification. To track the Telescope optical axis movement during one orbit, maintaining the number of data within acceptable limits, the rotating orbital loads have been divided in 8 positions, as shown in figure 15. Loads relevant to positions F to B (through A) are referring to both OB I/F to S/C temperature changes, of the order of 0.1 C, and to the heat injection from thermally uncontrolled functional elements. Loads from C to D show only the latter, being the Earth Albedo influence on the OB I/F shielded by the S/C structure. To each one of these positions the relevant thermal loads have been applied for three orbits, to reach a steady state. Figure 15: Orbit load steps: PST Boresight normal to figure plane Figure 16 shows the thermal surface behaviour of the OB under step H loads (temperatures in Kelvin), the maximum temperature gradient within the bench is 0. K. Figure 17 gives the relevant displacement profile (dimensions in mm) showing a maximum displacement of about 16 nm. Page 16

17 Figure 16: OB FEM thermal profiles for step H Figure 17: OB FEM displacements for step H As shown in figure 17, the maximum displacement (red / top left corner) is found at the opposite side of the fixed I/F point (blue / bottom right corner). These results are currently under evaluation. The maximum displacement dimension allows to be optimistic on the stability requirement compliance. CONCLUSIONS The HYPER feasibility study, with its extremely stringent requirements in terms of pointing accuracy and stability, allows to push the limits of Star Tracking technology and further expand the large precision sensing knowledge base in Galileo Avionica. The first results from this feasibility study, which is still to be completed, show great promise that the extremely stringent requirements demanded by the HYPER mission can be met. Page 17

18 ACKNOWLEDGMENT The authors would like to thank Astrium GmbH, who are running the HYPER study and were responsible for the mission requirement breakdown to the level of the Optical Bench and PST. The authors would also like to acknowledge the essential and longstanding contributions of Dr. Ernst Maria Rasel, Dr. Philippe Bouyer and Dr. Arnaud Landragin, who formed the core of the advisory science team. The key contributions to the study of the other members of the HYPER Scientific core team and the industrial feasibility study team are also gratefully acknowledged. REFERENCES 1. HYPER: Hyper Precision Atom Interferometry in Space ESA CDF-09, September 000. Ch. Borde : Atom interferometry and laser spectroscopy in Laser Spectroscopy X, World Scientific, 39 (1991) 3. J. Lense, H. Thirring, Phys Z. 19, 156 (1918) Page 18