KEYWORDS: Data modeling, Systems modeling, Stars, Systems engineering, Instrument modeling, Space operations, Performance modeling, Observatories, Planets, Metrology
The SIM Lite Astrometric Observatory will be the first space-based Michelson interferometer operating in the visible
wavelength, with the ability to perform ultra-high precision astrometric measurements on distant celestial objects. SIM
Lite data will address in a fundamental way questions such as characterization of Earth-mass planets around nearby
stars. To accomplish these goals it is necessary to rely on a model-based systems engineering approach - much more so
than most other space missions. This paper will describe in further detail the components of this end-to-end performance
model, called "SIM-sim", and show how it has helped the systems engineering process.
This paper examines how narrow-angle (NA) processing of data from the SIM Lite optical interferometry mission can be
undertaken when realistic spacecraft and mission operational constraints are taken into account. Using end-to-end
mission simulations we show that the goal of 1 μas single measurement accuracy (SMA) is obtainable, and hence the
detection of earth-like planets is achievable with the SIM Lite mission.
This paper develops an observing and processing scheme for narrow angle astrometry using a single
baseline interferometer without the aid of "grid" stars to characterize the interferometer baseline vector in
inertial space. The basic concept derives from the recognition that over a narrow field the set of fundamental
unknown instrument parameters that arise because the interferometer baseline vector has large uncertainties
(since there are no grid star measurements) is indistinguishable from a particular set of unobservable errors in the determination of star positions within the field. Reference stars within the narrow field are used to circumvent these unobservable modes. Feasibility of the approach is demonstrated through analysis and example simulations.
KEYWORDS: Calibration, Spectral calibration, Data modeling, Fourier transforms, Wavefronts, Charge-coupled devices, Optical filters, Monte Carlo methods, Modulation, Signal detection
The SIM PlanetQuest Mission will perform astrometry to one microarcsecond accuracy using optical interferometers
requiring optical path delay difference (OPD) measurements accurate to tens of picometers. Success
relies on very precise calibration. Spectral Calibration Development Unit (SCDU) has been built to demonstrate
the capability of calibrating spectral dependency of the white light fringe OPD to accuracy better than 20pm.
In this article, we present the spectral calibration modeling work for SCDU to achieve the SIM PlanetQuest
Engineering Milestone 4. SCDU data analysis shows that the wave front aberrations cause the instrument phase
dispersions to vary by tens of nanometers over the bandwidth of a CCD pixel making the previous model inadequate.
We include the effect of the wave front aberrations in the white light fringe model and develop a
procedure for calibrating the corresponding model parameters using long stroke fringe data based on Discrete
Fourier Transform. We make the calibration procedure flight traceable by dividing the whole calibration into the
instrument calibration and the source spectral calibration. End-to-end simulations are used to quantify both
the systematic and random errors in spectral calibration. The efficacy of the calibration scheme is demonstrated
using the SCDU experimental data.
Precision white light interferometry performed at the picometer class level is an extremely challenging endeavor.
Over the past several years a combination of analysis, experiment, and reconciliation of the two has yielded
continued improvements and refinements of the process to bring this technology to fruition. This paper provides
an overview of several of the refinements of the interference models and algorithms developed for calibration and
fringe estimation that have evolved over this period.
KEYWORDS: Stars, Interferometers, Charge-coupled devices, Visualization, Superposition, Target detection, Photons, Signal detection, Error analysis, Signal to noise ratio
SIM PlanetQuest will measure star positions to an accuracy of a few microarcseconds using precise white light
fringe measurements. One challenge for the SIM observation scenario is "star confusion," where multiple stars
are present in the instrument field of view. This is especially relevant for observing dim science targets because
the density of number of stars increases rapidly with star magnitude. We study the effect of star confusion on
the SIM astrometric performance due to systematic fringe errors caused by the extra photons from the confusion
star(s). Since star confusion from multiple stars may be analyzed as a linear superposition of the effect from single
star confusion, we quantify the astrometric errors due to single star confusion surveying over many spectral types,
including A0V, F0V, K5III, and M0V, and for various visual magnitude differences. To the leading order, the
star confusion effect is characterized by the magnitude difference, spectral difference, and the angular separation
between the target and confusion stars.
Strategies for dealing with star confusion are presented. For example, since the presence of additional sources
in the field of view leads to inconsistent delay estimates from different channels, with sufficient signal to noise
ratio, the star confusion can be detected using chi-square statistics of fringe measurements from multiple spectral
channels. An interesting result is that the star confusion can be detected even though the interferometer cannot
resolve the separation between the target and confusion stars when their spectra are sufficiently different. Other
strategies for mitigating the star confusion effect are also discussed.
SIM PlanetQuest will be the first space-based interferometer and will allow astrometric measurements that are
several hundred times more accurate than the previous missions operating at optical wavelengths. SIM promises
to achieve microarcsecond accuracy for astrometry on objects as faint as 20th visual magnitude. One of the
challenges is to achieve this accuracy at these dim levels, in the presence of even dimmer stars inside the SIM's
FOV. Therefore it is important to investigate the effects of "confusion" fields on astrometric performance for
SIM. This study will look at effects of Angle Tracking Camera performance for SIM in presence of a crowded
or confusion field near a target star. This will lead to a study that predicts SIM astrometric performance in
a crowded field. Centroid displacements due to any perturbation including a crowded field cause a shift in the
fringe and reduce visibility and performance. In this work we will devise an estimator to estimate the bias in
the centroid of SIM Angle Tracking camera in presence of a crowded field. This analysis will examine pointing
accuracy performance by estimating Angle Tracking centroid under different parameter variations that affect
performance. These parameters are number of neighboring stars, stellar types, and angular separation as well
as their relative brightness.
The Space Interferometry Mission(SIM) will measure optical path differences (OPDs) with an accuracy of tens of picometers, requiring precise calibration of the instrument. In this article, we present a calibration approach based on fitting star light interference fringes in the interferometer using a least-squares algorithm. The algorithm is first analyzed for the case of a monochromatic light source with a monochromatic fringe model. Using fringe data measured on the Micro-Arcsecond Metrology(MAM) testbed with a laser source, the error in the determination of the wavelength is shown to be less than 10pm. By using a quasi-monochromatic fringe model, the algorithm can be extended to the case of a white light source with a narrow detection bandwidth. In SIM, because of the finite bandwidth of each CCD pixel, the effect of the fringe envelope can not be neglected, especially for the larger optical path difference range favored for the wavelength calibration. We eliminate the fringe envelope effect by "projecting away" the fringe envelope, i.e. working in a subspace orthogonal to the envelope signal. The resulting fringe envelope parameters are needed for subsequent OPD estimation in SIM. We show the sensitivities to various errors. The algorithm is validated using both simulation and the fringe data obtained on the MAM test bed.
The Space Interferometry Mission (SIM), scheduled for launch in early 2010, is an optical interferometer that will perform narrow angle and global wide angle astrometry with unprecedented accuracy, providing differential position accuracies of 1 uas, and 4 uas global accuracies in position, proper motion and parallax. SIM astrometric measurements are sythesized from pathlength delay measurements provided by three Michelson-type, white light interferometers. Two of the interferometers are used for making precise measurements of variations in the spacecraft attitude, while the third interferometer performs the science measurement. The ultimate performance of SIM relies on a combination of precise fringe measurements of the interfered starlight with picometer class relative distance measurements made between a set of fiducials that define the interferometer baseline vectors. The focus of the present paper is on the development and analysis of algorithms for accurate white light estimation, and on the preliminary validation of these aglorithms on the MicroArcsecond Testbed.
Global astrometry is the measurement of stellar positions and motions. These are typically characterized by five parameters, including two position parameters, two proper motion parameters, and parallax. The Space Interferometry Mission (SIM) will derive these parameters for a grid of approximately 1300 stars covering the celestial sphere to an accuracy of approximately 4uas, representing a two orders of magnitude improvemnt over the most precise current star catalogues. Narrow angle astrometry will be performed to a 1uas accuracy. A wealth of scientific information will be obtained from these accurate measurements encompassing many aspects of both galactic and extragalactic science. SIM will be subject to a number of instrument errors that can potentially degrade performance. Many of these errors are systematic in that they are relatively static and repeatable with respect to the time frame and direction of the observation. This paper and its companion define the modeling of the contributing factors to these errors and the analysis of how they impact SIM's ability to perform astrometric science.
The current design of the Space Interferometry Mission (SIM) employs a 19 laser-metrology-beam system (also called L19 external metrology truss) to monitor changes of distances between the fiducials of the flight system's multiple baselines. The function of the external metrology truss is to aid in the determination of the time-variations of the interferometer baseline. The largest contributor to truss error occurs in SIM wide-angle observations when the articulation of the siderostat mirrors (in order to gather starlight from different sky coordinates) brings to light systematic errors due to offsets at levels of instrument components (which include corner cube retro-reflectors, etc.). This is the external metrology wide-angle field-dependent error. Physics-based model of field-dependent error at single metrology gauge level is developed and linearly propagated to errors in interferometer delay. General formulation of delay error sensitivity to various error parameters is developed. The essence of the linear error model is contained in an errormapping matrix. A corresponding Zernike component matrix approach is developed in parallel with its advantages discussed. As a first example, dihedral error model is developed for the corner cubes (CC) attached to the siderostat mirrors. Average and worst case residual errors are computed when various orders of field-dependent terms are removed from the delay error. These serve as guidelines for arriving at system requirements given the error budget allocation. Highlights of the non-common vertex error (NCVE) model are shown as a second example followed by discussions.
The astrometric performance of the SIM relies on precise measurements of the optical pathlength difference of the starlight through the arms of the interferometers that comprise the SIM instrument, and on precise relative distance betweeen a set of fiducials that define the baselines of the interferometers. The accuracy of these measurements can be affected by various phenomena. Some of them are time-dependent, while others are relatively static and repeatable. In this work we are concerned with the instrument errors of the latter type and in their compensation. In particular, a procedure for on-orbit calibration of the instrument error function is defined, and a proof of concept of its viability is presented. On a given grid of stars, the proposed procedure generates approximations of the gradient of the instrument error function at a discrete set of field points corresponding to the star locations via a specialized set of maneuvers of the spacecraft. These gradient approximations are then used to estimate the error function via a least squares procedure in a manner that is very analogous to the wavefront reconstruction problem in adaptive optics systems. An error analysis of the procedure is presented providing further insights into the connections between instrument errors and the grid reduction solution. Finally, numerical results are presented on a randomly generated grid of stars that demonstrate the feasibility of the method.
This paper summarizes two different strategies envisioned for calibrating the systematic field dependent biases present in the Space Interferometry Mission (SIM) instrument. The Internal Calibration strategy is based on pre-launch measurements combined with a set of on-orbit measurements generated by a source internal to the instrument. The External Calibration strategy uses stars as an external source for generating the calibration function. Both approaches demand a significant amount of innovation given that SIM's calibration strategy requires a post-calibration error of 100 picometers over a 15 degree field of regard while the uncalibrated instrument introduces tens to hundreds of nanometers of error. The calibration strategies are discussed in the context of the wide angle astrometric mode of the instrument, although variations on both strategies have been proposed for doing narrow angle astrometry.
We have developed a technique that allows SIM to measure
relative stellar positions with an accuracy of 1 micro-arcsecond
at any time during its 5-yr mission. Unlike SIM's standard
narrow-angle approach, Gridless Narrow Angle Astrometry (GNAA)
does not rely on the global reference frame of grid stars that
reaches full accuracy after 5 years. GNAA is simply the
application of traditional single-telescope narrow angle
techniques to SIM's narrow angle optical path delay measurements.
In GNAA, a set of reference stars and a target star are observed
at several baseline orientations. A linearized model uses delay
measurements to solve for star positions and baseline
orientations. A conformal transformation maps observations at
different epochs to a common reference frame. The technique works
on short period signals (P=days to months), allowing it to be
applied to many of the known extra-solar planets, intriguing
radio/X- ray binaries, and other periodic sources. The technique's
accuracy is limited in the long-term by false acceleration due to
a combination of reference star and target star proper motion. The
science capability, 1 micro-arcsecond astrometric precision, is
unique to SIM.
MAM is a dedicated systems-level testbed that combines the major SIM subsystems including laser metrogy, pointing, and pathlength control. The testbed is configured as a modified Michelson interferometer for the purpose of studying the white-light fringe measurement processes. This paper will compare the performance of various algorithms using the MAM data, and will aid in our recommendation of how the SIM flight system should process the science and guide interferometer data.
An external calibration technique for SIM1,2,3 involves measurement of calibration stars whose positions must already be known to an accuracy of 2 milliarcseconds. We demonstrate a procedure that effectively 'bootstraps' calibration star positions from an ab initio catalog to the required accuracy by observing them with the uncalibrated SIM instrument.
The Space Interferometry Mission (SIM) is a space-based
long baseline optical interferometer designed to perform precision
astrometry to an unprecedented accuracy. Highly accurate white
light fringe estimation is an important enabling technology for
the success of SIM. To accomplish this, the combined light from
the two arms of the interferometer is sent through a prism so that
fringes formed at different wavelengths are dispersed across a
number of spectral channels. The relative optical path difference
(OPD) between the two arms is modulated so that an estimate of the
phase in each of the channels can be obtained using phase shifting
interferometry (PSI) techniques. The present paper presents
several of the difficulties encountered in white light fringe
estimation for SIM, and offers a number of alternatives for
mitigating them.
Like all astrometric instruments, the Space Interferometry Mission (SIM) suffers from field-dependent errors requiring calibration. Diffraction effects in the delay line, polarization rotations on corner cubes, and beam walk across imperfect optics, all contribute to field-distortion that is significantly larger than is acceptable. The bulk of the systematic error is linear across the field - that is, it results in magnification and rotation errors. We show that the linear terms are inconsequential to the performance of SIM because they are inseparable from baseline length and orientation errors. One approach to calibrating the higher-order terms is to perform 'external' calibration; that is, SIM periodically makes differential measurements of a field of bright stars whose positions are not precisely known. We describe the requirements and constraints on the external calibration process and lay the groundwork for a specific procedure detailed in accompanying papers.
Numerical techniques for a class of optimization problems associated with the thermal modeling of optomechanical systems are presented. Emphasis is placed on applications where radiation plays a dominant role. This work is motivated by the need for incorporating thermal analysis into integrated modeling of high-precision, space-borne optical systems. The specific problems of interest are thermal control to minimize the wavefront error by application of external heat loads, and the temperature estimation problem of predicting temperatures at arbitrary nodes of the model given noisy measurements on a subset of nodes. The proposed numerical techniques are briefly described and compared to existing algorithms. Their accuracy and robustness are demonstrated through numerical tests with models form ongoing NASA missions.
The Space Interferometry Mission (SIM) is a space-based long-baseline optical interferometer for precision astrometry. One of the primary objectives of the SIM instrument is to accurately determine the directions to a grid of stars, together with their proper motions and parallax, improving a priori knowledge by nearly three orders of magnitude. The basic astrometric observable of the instrument is the pathlength delay, a measurement made by a combination of internal metrology measurements that determine the distance the starlight travels through the two arms of the interferometer and a measurement of the white light stellar fringe to find the point of equal pathlength. Because this operation requires a non-negligible integration time to accurately measure the stellar fringe position, the interferometer baseline vector is not stationary over this time period, as its absolute length and orientation are time-varying. This conflicts with the consistency condition necessary for extracting the astrometric parameters which requires a stationary baseline vector. This paper addresses how the time-varying baseline is `regularized' so that it may act as a single baseline vector for multiple stars.
This study was undertaken at the JPL to identify salient features of two competing instrument designs and to select the design that best meets the goals of the Space Interferometry Mission. Features were examined in terms of meeting performance, cost, schedule and risk requirements. The study included the spacecraft, the space environment, metrology considerations, stabilization of optics with temperature, spacecraft structure, complexity, and end-to- end testing among other items. The most significant determinant was the fundamental implementation of the instrument's metrology system. The impact on the testbed program associated with the mission was considered the second most important issue. An error propagation formalism was developed to address various instrument geometries examined as part of this study. The formalism propagates metrology errors from the gauge readings through to the angle on the sky. An introduction to the formalism is presented.
This paper presents an adaptive optics (AO) system for a large IR telescope. The Keck Telescope on Mauna Kea is used as a case study. The system is designed to provide low-order wavefront correction using faint natural guide stars. It is shown that two innovations, namely the use of an AO-optimized CCD detector, and use of a variable control bandwidth, result in correction to a Strehl ratio of about 0.1 using guide stars of visual magnitude 18. Sky coverage is approximately 20% at this level of performance. Sky coverage rises to 100% at a Strehl ratio of 0.05.
This paper investigates and compares wavefront sensing options for a proposed natural guide star adaptive optics upgrade for the Keck telescope. The methods of curvature sensing and slope sensing with a Hartmann sensor are compared. A curvature sensor model is developed that includes nonlinear, diffraction, and noise effects. The analytical model is validated in simulation using the Keck optical prescription parameters. A comprehensive treatment of estimation/reconstruction is presented and used for the Hartmann sensor/curvature sensor comparisons.
KEYWORDS: Wavefronts, Sensors, Control systems, Adaptive optics, Monte Carlo methods, Algorithm development, Control systems design, Error analysis, Optical components, Wavefront reconstruction
This paper presents the development and analysis of a wavefront control strategy for the Space Laser Electric Energy (SELENE) power beaming system. SELENE represents a substantial departure from most conventional adaptive optics systems in that the deformable element is the segmented primary mirror and the signal that is fedback includes both the local wavefront tilt and the relative edge mismatch between adjacent segments. The major challenge in designing the wavefront control system is the large number of subapertures that must be commanded. A fast and near optimal algorithm based on the local slope and edge measurements is defined for this system.
KEYWORDS: Algorithm development, Computer architecture, Evolutionary algorithms, Matrices, Digital signal processing, Control systems, Adaptive optics, Wavefronts, Aluminum, Computing systems
Massively parallel algorithms and architectures for real-time wavefront control of a dense adaptive optic system (SELENE) are presented. We have already shown that the computation of a near optimal control algorithm for SELENE can be reduced to the solution of a discrete Poisson equation on a regular domain. Although this represents an optimal computation, due to the large size of the system and the high sampling rate requirement, the implementation of this control algorithm poses a computationally challenging problem since it demands a sustained computational throughput of the order of 10 GFlops. We develop a novel algorithm, designated as Fast Invariant Imbedding algorithm, which offers a massive degree of parallelism with simple communication and synchronization requirements. We also discuss two massively parallel, algorithmically specialized, architectures for low-cost and optimal implementation of the Fast Invariant Imbedding algorithm.
Future space telescopes seek to maximize collecting aperture for increased sensitivity and high spatial resolution yet are limited in mass due to launch weight restrictions. JPL has developed the Controlled Optics Modelling Package (COMP) to easily facilitate analyses of optical systems whose elements are perturbed. Development of the computer tool, IMOS (Integrated Modeling of Advanced Optical Systems) allows modeling of structurally and thermally induced deformations to interact with optical systems. Presented here are analyses on the Segmented Reflector Telescope, (SRT), to estimate and then minimize the effect of anticipated disturbances on the resultant optical performance. Such studies are a needed prerequisite for estimating the requirements for adaptive optics due to structural movements. A simulation study estimates the space-time power spectral density of the residual telescope phases from reaction wheel disturbances. Results show that significant disturbances are concentrated in the first few Zernike polynomials with 87% of all disturbances described by the first 11 terms leaving a 0.35 micrometers rms residual. The time bandwidth of the disturbances is between 20 - 25 Hz which placed the required corrections in the adaptive optics regime.
KEYWORDS: Stars, Space telescopes, Systems modeling, Telescopes, Mirrors, Reflector telescopes, Space operations, Integrated optics, Control systems design, Observatories
NASA has an ambitious plan for exploring the universe involving
many space-based observatories. The CSI program (Control
Structure Interaction) is a NASA funded project to design
microprecision spacecraft observatories from a multidisciplinary
approach by integrating the structural, control and optical
subsystems of these spacecraft. A Focus Mission lnterferometer
(FMI), representative of one of NASA's astrometric missions for
extrasolar planet detection was selected as the focus for developing
this multidisciplinary technology. Very early in this study it was
discovered that integrated modeling tools were necessary to predict
the on orbit performance of the FMI.
An optomechanical model of a segmented reflector telescope is developed. An image quality metric is used to optimize the placement of damping elements in the telescope backup truss. Comparisons with an alternative placement criteria are made.
A general framework is presented for the matrix-form, linear optical model analysis of controlled optomechanical systems; the models are conjoined with linear models of structures and controls to compute system performance as a function of optics, structures, and control parameters. Covariance analysis, optimization, and estimation/simulation are used. Attention is given to a tolerancing example for the Hubble Space Telescope's Wide Field and Planetary Camera, which involves the creation of a linear model of residual pupil shear.
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