PROBA-3 Mission Research Articles

GLADE: Gravitational Light-Bending Astrometry Dual-Satellite Experiment

Light bending is one of the classical tests of general relativity and is a crucial aspect to be taken into account for accurate assessments of photon propagation. In particular, high-precision astrometry can constrain theoretical models of gravitation in the weak field limit applicable to the Sun neighborhood. We propose a concept for experimental determination of the light deflection close to the Sun in the 10−7 to 10−8 range, in a modern rendition of the 1919 experiment by Dyson, Eddington and Davidson, using formation flying to generate an artificial long-lasting eclipse. The technology is going to be demonstrated by the forthcoming ESA mission PROBA3. The experimental setup includes two units separated by 150 m and aligned to the mm level: an occulter and a small telescope (0.3 m diameter) with an annular field of view covering a region 0∘.7 from the Sun. The design is compatible with a space weather payload, merging several instruments for observation of the solar corona and environment. We discuss the measurement conditions and the expected performance.

PROBA-3 mission and the Shadow Position Sensors: Metrology measurement concept and budget

PROBA-3 is a space mission of the European Space Agency that will test, and validate metrology and control systems for autonomous formation flying of two independent satellites. PROBA-3 will operate in a High Elliptic Orbit and when approaching the apogee at 6·104 Km, the two spacecraft will align to realize a giant externally occulted coronagraph named ASPIICS, with the telescope on one satellite and the external occulter on the other one, at inter-satellite distance of 144.3 m. The formation will be maintained over 6 hrs across the apogee transit and during this time different validation operations will be performed to confirm the effectiveness of the formation flying metrology concept, the metrology control systems and algorithms, and the spacecraft manoeuvring. The observation of the Sun’s Corona in the field of view [1.08;3.0]RSun will represent the scientific tool to confirm the formation flying alignment. In this paper, we review the mission concept and we describe the Shadow Position Sensors (SPS), one of the metrological systems designed to provide high accuracy (sub-millimetre level) absolute and relative alignment measurement of the formation flying. The metrology algorithm developed to convert the SPS measurements in lateral and longitudinal movement estimation is also described and the measurement budget summarized.

Influence of surface roughness on diffraction in the externally occulted Lyot solar coronagraph

Context. The solar coronagraph ASPIICS will fly on the future ESA formation flying mission Proba-3. The instrument combines an external occulter of diameter 1.42 m and a Lyot solar coronagraph of 5 cm diameter, located downstream at a distance of 144 m. Aims. The theoretical performance of the externally occulted Lyot coronagraph has been computed by assuming perfect optics. In this paper, we improve related modelling by introducing roughness scattering effects from the telescope. We have computed the diffraction at the detector, that we compare to the ideal case without perturbation to estimate the performance degradation. We have also investigated the influence of sizing the internal occulter and the Lyot stop, and we performed a sensitivity analysis on the roughness. Methods. We have built on a recently published numerical model of diffraction propagation. The micro-structures of the telescope are built by filtering a white noise with a power spectral density following an isotropic ABC function, suggested by Harvey scatter theory. The parameters were tuned to fit experimental data measured on ASPIICS lenses. The computed wave front error was included in the Fresnel wave propagation of the coronagraph. A circular integration over the solar disk was performed to reconstruct the complete diffraction intensity. Results. The level of micro-roughness is 1.92 nm root-mean-square. Compared to the ideal case, in the plane of the internal occulter, the diffraction peak intensity is reduced by ≃0.001%. However, the intensity outside the peak increases by 12% on average, up to 20% at 3 R⊙, where the mask does not filter out the diffraction. At detector level, the diffraction peak remains ≃10−6 at 1.1 R⊙, similar to the ideal case, but the diffraction tail at large solar radius is much higher, up to one order of magnitude. Sizing the internal occulter and the Lyot stop does not improve the rejection, as opposed to the ideal case. Conclusions. Besides these results, this paper provides a methodology to implement roughness scattering in the wave propagation model for the solar coronagraph.

Interpolation methods for tracking spacecraft in ultratight formation

By measuring the centroid of a beam on a detector, one can track the movement of that beam across the detector. By tracking this movement, one can track the object encompassing the detector, for example, a spacecraft. A variety of system-specific performance inhibitors can make this a challenge, requiring a robust method. The goal of this investigation is to model the true beam position of the instrument in terms of the measured beam position. For this, a mathematical model is created that interpolates and corrects the measured beam position using precollected position data—a calibration model. The real-world scenario for this investigation is the flight-representative model of the fine lateral and longitudinal sensor (FLLS) instrument, built by Neptec Design Group and Neptec UK for the European Space Agency mission PROBA-3. Performance inhibitors for FLLS are cropping of the beam, imperfect optics, and a varying distance the beam has traveled (up to 250 m). Using bivariate spline interpolation for the FLLS model gives the best performance, achieving a measurement accuracy well within the mission requirement of <300 μm.

Modeling and removal of optical ghosts in the PROBA-3/ASPIICS externally occulted solar coronagraph

Context. ASPIICS is a novel externally occulted solar coronagraph, which will be launched onboard the PROBA-3 mission of the European Space Agency. The external occulter will be placed on the first satellite ∼150 m ahead of the second satellite that will carry an optical instrument. For 6 h per orbit, the satellites will fly in a precise formation, constituting a giant externally occulted coronagraph. The large distance between the external occulter and the primary objective will allow observations of the white-light solar corona starting from extremely low heights ∼1.1 R⊙. Aims. We aim to analyze the possible influence of optical ghost images formed inside the telescope and to develop an algorithm for their removal. Methods. We implement the optical layout of ASPIICS in Zemax and study the ghost behavior in sequential and nonsequential regimes. We identify sources of the ghost contributions and analyze their geometrical behavior. Finally we develop a mathematical model and software to calculate ghost images for any given input image. Results. We show that ghost light can be important in the outer part of the field of view, where the coronal signal is weak, since the energy of bright inner corona is redistributed to the outer corona. However, the model allows for the ghost contribution to be removed. Due to the large distance between the external occulter and the primary objective, the primary objective does not produce a significant ghost. The use of the Lyot spot in ASPIICS is not necessary.

Principle of Fredholm image reconstruction in the vignetting zone of an externally occulted solar coronagraph

Aims.This study is carried out in the context of data processing of the solar coronagraph ASPIICS of the future formation-flying mission Proba-3, which is expected to provide images of the corona very close to the limb. There will be a transition zone of the order of 100 arcsec close to the limb, where the telescope aperture suffers a strong vignetting by the external occulter (a disc of 1.42 m at 144 m). The instrument response in this region will vary rapidly both in shape and in integrated intensity, the latter being particular to the external occultation. The aim of this paper is to propose a technique to recover as much as possible of the image of the corona very close to the limb in the vignetting zone.Methods.The object image relationship in this zone is not defined by the usual convolution but by the more general Fredholm integral of the first kind. Theoretical aspects of the problem are detailed in the context of a matrix formalism for the inversion of the Fredholm integral, formalism that we maintain up to the end of the numerical simulations, which is specific to the present work. The iterative Richardson-Lucy algorithm, specially written for the non-constant integrated intensity of the responses is used here for reconstruction. A study of the effect of noise on a photodetected image is made.Results.An important part of the work consisted in calculating the elements of the transfer matrix between the object and the image for a simulation on a small region of size 100 × 100 arcsec sampled over 128 × 128 pixels. This is obtained propagating the light through the system using a previously published approach. On a toy object, the reconstruction is excellent down to about 60 arcsec from the limb, corresponding to a vignetting of 50%. The drawback is that the recovery of aN × Nobject requires the handling of aN2 × N2matrix, i.e. a 16384 × 16384 transfer matrix here. However, taking into account radial symmetries of the experiment, we propose the use of a transformation from Cartesian to polar coordinates which allows to apply the same procedure all around the sun as for a small region.

Influence of misalignments on the performance of externally occulted solar coronagraphs

Context. The ASPIICS instrument is a novel externally occulted coronagraph that will be launched on board the PROBA-3 mission of the European Space Agency. The external occulter will be placed on one satellite ~150 m ahead of the second satellite that will carry an optical instrument. During 6 h out of 19.38 h of orbit, the satellites will fly in a precise (accuracy around a few millimeters) formation, constituting a giant externally occulted coronagraph. The large distance between the external occulter and the primary objective will allow observations of the white-light solar corona starting from extremely low heights ~ 1.1R⊙. Aims. We intend to analyze influence of shifts of the satellites and misalignments of optical elements on the ASPIICS performance in terms of diffracted light. Based on the quantitative influence of misalignments on diffracted light, we provide a recipe for choosing the size of the internal occulter (IO) to achieve a trade-off between the minimal height of observations and sustainability to possible misalignments. Methods. We considered different types of misalignments and analyzed their influence from optical and computational points of view. We implemented a numerical model of the diffracted light and its propagation through the optical system and computed intensities of diffracted light throughout the instrument. Our numerical approach is based on a model from the literature that considered the axisymmetrical case. Here we extend the model to include nonsymmetrical cases and possible misalignments. Results. The numerical computations fully confirm the main properties of the diffracted light that we obtained from semi-analytical consideration. We obtain that relative influences of various misalignments are significantly different. We show that the internal occulter with RIO = 1.694 mm = 1.1R⊙ is large enough to compensate possible misalignments expected to occur in PROBA-3/ASPIICS. Besides that we show that apodizing the edge of the internal occulter leads to additional suppression of the diffracted light. Conclusions. We conclude that the most important misalignment is the tilt of the telescope with respect to the line connecting the center of the external occulter and the entrance aperture. Special care should be taken to co-align the external occulter and the coronagraph, which means co-aligning the diffraction fringe from the external occulter and the internal occulter. We suggest that the best orientation strategy is to point the coronagraph to the center of the external occulter.

Theoretical performance of serrated external occulters for solar coronagraphy

Context. This study is made in the context of the future solar coronagraph ASPIICS of the ESA formation-flying mission Proba-3. Aims. In the context of solar coronagraphy, we provide a comparative study of the theoretical performance of serrated (or toothed) external occulters by varying the number and size of the teeth, which we compare to the sharp-edged and apodized disks. The tooth height is small (a few centimeters), to avoid hindering the observation of the solar corona near the limb. We first analyze the diffraction pattern produced by such occulters. In a second step, we compute the umbra profile by integration over the Sun. Methods. We explored a few methods to compute the diffraction pattern. Two of them were implemented. The first is based on 2D fast Fourier transformation (FFT) routines and a multiplication by the Fresnel filter of the form exp(−iπλzu2). Simple rules were derived and discussed to set the sampling conditions. The Maggi–Rubinowicz representation is then proposed as an alternative method, and is proven to be very efficient for this study. Results. Serrated occulters tend to create a two-level intensity pattern, the inner being the darker, which perfectly matches a previously reported geometrical prediction. The diffraction in this central region is lower by two to four orders of magnitude when compared to the sharp-edged disk. The achieved umbra level at the center ranges from 10−4 to below 10−7, depending on the geometry of the teeth. Conclusions. Our study shows that serrated occulters can achieve a high rejection and can almost reach the performance of the apodized disk when very many teeth are used. We prove that shaped occulters must be preferred to simple disks in solar and stellar coronagraphy.

Performance of the hybrid externally occultedLyotsolar coronagraph

Context. High-contrast hybrid coronagraphs, which combine an external occulter and a Lyot-style coronagraph became a reality in recent years, despite the lack of analytic and numerical end-to-end performance studies. The solar coronagraph ASPIICS which will fly on the future ESA Formation Flying mission Proba-3 is a good example of such a hybrid coronograph. Aims. We aim to provide a numerical model to compute theoretical performance of the hybrid externally occulted Lyot-style coronagraph, which we then aim to compare to the performance of the classical Lyot coronagraph and the externally occulted solar coronagraph. We will provide the level and intensity distribution of the stray light, when the Sun is considered as an extended source. We also investigate the effect of different sizes for the internal occulter and Lyot stop. Methods. First, we have built on a recently published approach, to express the diffracted wave front from Fresnel diffraction produced by an external occulter at the entrance aperture of the coronagraph. Second, we computed the coherent propagation of the wave front coming from a given point of the Sun through the instrument. This is performed in three steps: from the aperture to the image of the external occulter, where the internal occulter is set, from this plane to the image of the entrance aperture, where the Lyot stop is set, and from there to the final image plane. Making use of the axis-symmetry, we considered wave fronts originating from one radius of the Sun and we circularly average the intensities. Our numerical computation used the parameters of ASPIICS. Results. The hybrid externally occulted Lyot coronagraph rejects sunlight below 10E-8Mean Solar Brightness from 1,3 solar radius - in the particular configuration of ASPIICS. The Lyot coronagraph effectively complements the external occultation. We show that reducing the Lyot stop allows a clear gain in rejection, being even better than oversizing the internal occulter, that tends to exclude observations very close to the solar limb. As an illustration, we provide a graph that allows us to estimate performance as a function of the internal occulter and Lyot stop sizes. Conclusions. Our work consists of a methodological approach to compute the end-to-end performance for solar coronagraph.

Performance Assessment of a Gyroless 3-Axis Stabilised Sun Pointing Mode on a Highly Elliptical Orbit

This paper investigates the feasibility of a concept for acquisition and maintenance of a gyroless three-axis stabilized Sun pointing attitude from tumbling conditions on a Highly Elliptical Orbit (HEO) in the presence of sunlight, based on the sole utilisation of Sun sensors and reaction wheels. It uses the ESA PROBA-3 mission as a study case. Based on candidate algorithms identified in the literature, suitable Guidance, Navigation, and Control (GNC) functions are designed to meet the PROBA-3 Sun Acquisition Mode pointing requirements. The proposed GNC loop is validated in a high fidelity closed-loop simulation environment and is found to be reliable provided observability conditions are met. These conditions and other limitations are discussed.

Four Reaction Wheels Management: Algorithms Trade-Off and Tuning Drivers for the PROBA-3 Mission

Reaction Wheels (RW) are common actuators for three-axis stabilized satellites. This paper deals with the management of a RW assembly where four or more skewed RW are used simultaneously. Four-wheel control is commonly used on spacecraft. This paper contributes to this field by providing an efficient algorithm for attitude control torque distribution with RW angular rate constraint management and by providing the rationales that guide the tuning of this algorithm. Moreover, it defines an algorithm for the angular momentum management of this reaction wheels assembly. Eventually, as proof of concept, it applies these algorithms to a realistic scenario of the PROBA-3 mission using a high fidelity simulator. Results demonstrate that the suggested algorithms are operational and efficient. They can be used and adapted to several types of missions.

GPS-based relative navigation for the Proba-3 formation flying mission

The primary objective of the Proba-3 mission is to build a solar coronagraph composed of two satellites flying in close formation on a high elliptical orbit and tightly controlled at apogee. Both spacecraft will embark a low-cost GPS receiver, originally designed for low-Earth orbits, to support the mission operations and planning during the perigee passage, when the GPS constellation is visible. The paper demonstrates the possibility of extending the utilization range of the GPS-based navigation system to serve as sensor for formation acquisition and coarse formation keeping. The results presented in the paper aim at achieving an unprecedented degree of realism using a high-fidelity simulation environment with hardware-in-the-loop capabilities. A modified version of the flight-proven PRISMA navigation system, composed of two single-frequency Phoenix GPS receivers and an advanced real-time onboard navigation filter, has been retained for this analysis. For several-day long simulations, the GPS receivers are replaced by software emulation to accelerate the simulation process. Special attention has been paid to the receiver link budget and to the selection of a proper attitude profile. Overall the paper demonstrates that, despite a limited GPS tracking time, the onboard navigation filter gets enough measurements to perform a relative orbit determination accurate at the centimeter level at perigee. Afterwards, the orbit prediction performance depends mainly on the quality of the onboard modeling of the differential solar radiation pressure acting on the satellites. When not taken into account, this perturbation is responsible for relative navigation errors at apogee up to 50m. The errors can be reduced to only 10m if the navigation filter is able to model this disturbance with 70% fidelity.

PROBA-3: Precise formation flying demonstration mission

Formation Flying (FF) has generated a strong interest in many space applications, most of them involving a significant complexity for building for example on-board large “virtual structures or distributed observatories”.The implementation of these complex formation flying missions with critical dependency on this new, advanced and critical formation technology requires a thorough verification of the system behaviour in order to provide enough guarantees for the target mission success. A significant number of conceptual or preliminary designs, analyses, simulations, and HW on-ground testing have been performed during the last years, but still the limitations of the ground verification determine that enough confidence of the behaviour of the formation flying mission will only be possible by demonstration in flight of the concept and the associated technologies.PROBA-3 is the mission under development at ESA for in-flight formation flying demonstration, dedicated to obtain that confidence and the necessary flight maturity level in the formation flying technologies for those future target missions. PROBA-3 will demonstrate technologies such as formation metrology sensors (from very coarse to highest accuracy), formation control and GNC, system operability, safety, etc.During the last years, PROBA-3 has evolved from the initial CDF study at ESA, to two parallel phase A studies, followed by a change in the industrial configuration for the Bridging step between A and B phases. Currently the SRR consolidation has been completed, and the project is in the middle of the phase B. After the phase A study SENER and GMV were responsible for the Formation Flying System, within a mission core team completed by OHB-Sweden, QinetiQ Space and CASA Espacio.In this paper an overview of the PROBA-3 mission is provided, with a more detailed description of the formation flying preliminary design and results.

Formation flying and mission design for Proba-3

The Proba-3 mission is an ambitious European mission to test the design, implementation and operation of a two-spacecraft formation flying system with a high degree of autonomy with a launch foreseen in the 2015/2016 time-frame. It comprises two spacecraft, the coronagraph and the occulter, which are to be inserted into a highly elliptical orbit. It is intended to perform the formation flying demonstration around the apogee and use the perigee pass for telemetry, orbit determination, orbit correction, and formation configuration manoeuvres. The design of the target orbit is driven by the minimisation of disturbances to the spacecraft formation, and is constrained by the rather low Δv capability of the spacecraft of less than 100ms−1 as well as the characteristics of the selected launch vehicle. The secondary mission objective of Proba-3 is to operate the formation as a coronagraph with one spacecraft being the occulter and the other carrying the optics and detectors. The alignment of the formation with the Sun-direction has as a consequence that the geometry of the formation relative to the orbit is prescribed for the perigee pass. This geometry also determines the relative dynamics of the formation. The relationship between formation configuration and orbital parameters is typical for formation flying missions on elliptical orbits and requires a careful choice of the launch time such that the constraints on the angle between the Sun-direction and the orbital plane are fulfilled. Here we present the design of the operational orbit and transfer phase of Proba-3 together with an analysis of the separation, formation acquisition, and target formation maintenance. Also the benefit of available tracking data for contingency situations in the Proba-3 missions is discussed.

A Matching Pursuit Algorithm Approach to Chaser-Target Formation Flying Problems

In this brief we present a new approach to fine relative position control in satellite formation flying. We focus on a situation involving two spacecraft, one of which (the “chaser”) is actively controlling its position with respect to the other (the “target”). The goal of the approach is to use the minimum number of thruster firings in order to keep the chaser following its reference position within a certain tolerance. We first present a method based on the matching pursuit (MP) algorithm, which proves to provide a solution to this problem in the open-loop case. Moreover, we show that a closed-loop version of the controller can be obtained as well by turning the method into a model predictive control (MPC) strategy, thanks to the fact that the computational cost of the method is small. An example of application is shown at the end for a mission scenario inspired by the PROBA3 mission, which is currently under development.

A Matching Pursuit Algorithm Approach to Chaser-Target Formation Flying Problems with Linear Time-Invariant Dynamics

AbstractIn this article we present a new approach to satellite formation flying problems involving two spacecraft, one of which (the “chaser”) is actively controlling its relative position with respect to the other (the “target”). The goal of this controller is to use the minimum number of thruster firings in order to keep the chaser following its reference position within a certain tolerance. We show an approach based on the Matching Pursuit algorithm (MP), which proves to provide a solution to this problem in the open-loop case. A feedback version of the controller can be obtained by turning the method into a Model Predictive Control (MPC) strategy, thanks to the fact that the computational cost of the method is small.An example of application is shown at the end for a mission scenario inspired by the PROBA3 mission, which is currently under development.