Renaud Goullioud

Micro-pixel accuracy centroid displacement estimation and detector calibration

Conventional centroid estimation fits a template point spread function (PSF) to image data. Because the PSF is typically not known to high accuracy, systematic errors exist. Here, we present an accurate centroid displacement estimation algorithm by reconstructing the PSF from Nyquist-sampled images. In absence of inter-pixel response variations, this method can estimate centroid displacement between two 32×32 images to sub-micropixel accuracy. Inter-pixel response variations can be calibrated in Fourier space by using laser metrology. The inter-pixel variations of Fourier transforms of the pixel response functions can be conveniently expressed in terms of powers of spatial wavenumbers. Calibrating up to the third-order terms in the expansion, the displacement estimation is accurate to a few micro-pixels. This algorithm is applicable to a new mission concept of performing mirco-arcsecond level relative astrometry using a 1 m telescope for detecting terrestrial exoplanets and high-precision photometry missions.

Results from the TOM3 testbed: thermal deformation of optics at the picometer level

Future space-based optical interferometers, such as the space interferometer mission (SIM), require thermal stability of the optical wavefront to the level of picometers in order to produce astrometric data at the micro-arc-second level. In SIM, the internal path of the interferometer will be measured with a small metrology beam whereas the starlight fringe position is estimated from a large concentric annular beam. To achieve the micro-arc-second observation goal for SIM, it is necessary to maintain the optical path difference between the central and the outer annulus portions of the wavefront of the front-end telescope optics to a few tens of picometers for an hour. The thermo-opto-mechanical testbed (TOM3) was developed at the Jet Propulsion Laboratory to measure thermally induced optical deformations of a full-size flight-like beam compressor and siderostat, the two largest optics on SIM, in flight-like thermal environments. A common path heterodyne interferometer (COPHI) developed at JPL was used for the fine optical path difference measurement as the metrology sensor. The system was integrated inside a large vacuum chamber in order to mitigate the atmospheric and thermal disturbances. The siderostat was installed in a temperature-controlled thermal shroud inside the vacuum chamber, creating a flight-like thermal environment. Detailed thermal and structural models of the test articles (siderostat and compressor) were also developed for model prediction and correlation of the thermal deformations. Experimental data shows SIM required thermal stability of the test articles and good agreement with the model predictions

A heterodyne interferometer for angle metrology

We have developed a compact, high-resolution, angle measurement instrument based on a heterodyne interferometer. Common-path heterodyne interferometer metrology is used to measure displacements of a reflective target surface. In the interferometer set up, an optical mask is used to sample the laser beam reflecting back from four areas on a target surface. From the relative displacement measurements of the target surface areas, we can simultaneously determine angular rotations around two orthogonal axes in a plane perpendicular to the measurement beam propagation direction. The device is used in a testbed for a tracking telescope system where pitch and yaw angle measurements of a flat mirror are performed. Angle noise measurement of the device shows 0.1 nrad/square root of Hz at 1 Hz, at a working distance of 1 m. The operation range and nonlinearity of the device when used with a flat mirror is approximately +/-0.15 mrad, and 3 microrad rms, respectively.

SIM astrometric demonstration at 24 picometers on the MAM testbed

Future space-based optical interferometers, such as the Space Interferometer Mission (SIM), require fringe measurements to the level of picometers in order to produce astrometric data at the micro-arc-second level. To be more specific, it is necessary to measure both the position of the starlight central fringe and the change in the internal optical path of the interferometer to a couple of tens of picometers. The internal path is measured with a small metrology beam, whereas the starlight fringe position is estimated with a CCD sampling and a large concentric annular beam. One major challenge for SIM is to align the metrology beam with the starlight beam to keep the consistency between these two sensors at the system level while articulating the instrument optics. The Micro-Arcsecond Metrology testbed (MAM) developed at the Jet Propulsion Laboratory features an optical interferometer with a white light source, all major optical components of a stellar interferometer, and heterodyne metrology sensors. The setup is installed inside a large vacuum chamber in order to mitigate atmospheric and thermal disturbances. Recent data show agreement between the metrology and starlight paths to better than 24 pm in the one-degree narrow-angle field of regard of SIM. This paper describes how MAM processes its narrow-angle data, the testbed performance, and how it relates to SIM.

Piezoelectric stack actuator life test

Future NASA interferometer missions require actuators for precision positioning to accuracies of the order of nanometers. For this purpose, commercially available multilayer piezoelectric stack actuators are being considered for driving these precision positioning mechanisms. These mechanisms have potential mission operational requirements that exceed 5 years and the nominal actuator requirements for the most critical actuators on the these missions were estimated from the Modulation Optics Mechanism (MOM) and Pathlength control Optics Mechanism (POM) mechanisms which were developed for the Space Interferometry Mission (SIM). At a nominal drive frequency of two hundred and fifty hertz one mission life is calculated to be 40 Billion cycles. In order to test the feasibility of using these commercial actuators for these applications and to determine the reliability and the redundancy requirements of these actuators a life test study was undertaken. In this study a set of commercial PZT stacks configured in a potential actuator flight configuration (pre-stressed and bonded in flexures) were tested for up to 100 billion cycles. The test flexures allowed for two stacks to be mechanically connected in series. The tests were controlled using an automated Lab-View control and data acquisition system that set up the test parameters and monitored the waveform of the stack electrical current and voltage. The samples were driven between 0 and 20 Volts at 2000Hz to accelerate the life test and mimic the voltage expected to be applied to the stacks during operation. During the life test the primary stack was driven while the redundant stack was open circuited. The stroke determined from a strain gauge and the temperature and humidity in the chamber and the temperature of each individual stack were recorded. In addition other properties of the stacks were measured at specific intervals. These measurements included the displacement from a Capacitance gap sensor and impedance spectra. The degradation in the stroke over the life test was found to be small (<3%) for the primary stacks and estimated to be < 4% for the redundant stacks. It was noted that about half the stroke reduction occurred within the first 10 billion cycles. At the end of the life test it was found that by applying DC voltage levels (100 V) above the life test voltage we could initially recover about half of the lost stroke with again some degradation in the long term. The data up to 100 billion cycles for these tests and the analysis of the experimental results will be presented in this paper. 1,2

Piezoelectric multilayer actuator life test

Potential NASA optical missions such as the Space Interferometer Mission require actuators for precision positioning to accuracies of the order of nanometers. Commercially available multilayer piezoelectric stack actuators are being considered for driving these precision mirror positioning mechanisms. These mechanisms have potential mission operational requirements that exceed 5 years for one mission life. To test the feasibility of using these commercial actuators for these applications and to determine their reliability and the redundancy requirements, a life test study was undertaken. The nominal actuator requirements for the most critical actuators on the Space Interferometry Mission (SIM) in terms of number of cycles was estimated from the Modulation Optics Mechanism (MOM) and Pathlength control Optics Mechanism (POM) and these requirements were used to define the study. At a nominal drive frequency of 250 Hz, one mission life is calculated to be 40 billion cycles. In this study, a set of commercial PZT stacks configured in a potential flight actuator configuration (pre-stressed to 18 MPa and bonded in flexures) were tested for up to 100 billion cycles. Each test flexure allowed for two sets of primary and redundant stacks to be mechanically connected in series. The tests were controlled using an automated software control and data acquisition system that set up the test parameters and monitored the waveform of the stack electrical current and voltage. The samples were driven between 0 and 20 V at 2000 Hz to accelerate the life test and mimic the voltage amplitude that is expected to be applied to the stacks during operation. During the life test, 10 primary stacks were driven and 10 redundant stacks, mechanically in series with the driven stacks, were open-circuited. The stroke determined from a strain gauge, the temperature and humidity in the chamber, and the temperature of each individual stack were recorded. Other properties of the stacks, including the displacement from a capacitance gap sensor and impedance spectra were measured at specific intervals. The average degradation in the stroke over the life test was found to be small (≪3%) for the primary stacks and ≪4% for the redundant stacks. It was noted that about half of the stroke reduction occurred within the first 10 billion cycles. At the end of the life test, it was found that the actuator could recover about half of the lost stroke by applying a dc voltage of 100 V at room temperature. The data up to 100 billion cycles for these tests and the analysis of the experimental results are presented in this paper.

SIM PlanetQuest white-light fringe modeling: picometer accuracy calibration and estimation algorithms

SIM PlanetQuest will perform narrow-angle astrometry with microarcsecond accuracy using starlight interferometry requiring tens of picometers accuracy in estimating the optical path difference change between observing two stars. One challenge is to accurately model the white-light fringes and calibrate the required model parameters. Previous studies have developed algorithms based on a CCD-pixel-level calibration scheme assuming slowly varying phase-dispersion functions. However, recent measurements from the SIM PlanetQuest Spectral Calibration Development Unit (SCDU) showed that wavefront aberrations caused the phase-dispersion functions to vary by tens of nanometers across the bandwidth of a CCD pixel, making the previous CCD-pixel-based calibration scheme inadequate. We present a white-light fringe model including the extra phase dispersions caused by the wavefront aberrations together with a calibration and estimation scheme using long-stroke fringe measurements to resolve the bandwidth of pixels. Using simulated data, we show that the total systematic errors in the calibration and estimation scheme are less than a picometer. With SCDU experimental data, we demonstrate that the end-to-end accuracy of the calibration and estimation algorithm is better than 20 pm, achieving the SIM PlanetQuest Engineering Milestone 4.

Looking for Earth-like Planets with the SIM Planet Quest Light Mission

The Space Interferometry Mission Planet Quest Light (SIM PQL) is a new concept for a space borne astrometric instrument. It will be located in a solar Earth-trailing orbit. SIM PQL utilized technology developed for the space interferometry mission planet quest (SIM PQ). The instrument consists of two Michelson stellar interferometers and a telescope. The first interferometer chops between the target star and a set of reference stars. The second interferometer monitors the attitude of the instrument in the direction of the target star. The telescope monitors the attitude of the instrument in the other two directions. SIM PQL will be capable of one micro-arc-second narrow angle astrometry, over a two-degree field of regard for magnitude 6 and brighter target stars. During the 5-year mission, SIM PQL would search 50 nearby stars for planets of mass down to one Earth mass, in the Habitable Zone, which have orbit periods of less than 3 years. SIM PQL will also perform global astrometry on a variety of astrophysics objects, reaching 6 micro-arc-seconds absolute position and parallax measurements. As a pointed instrument, SIM PQ will maintain its astrometric accuracy on fainter objects. This paper will describe the instrument, how it will do its astrometric measurements and the expected performance based on the current technology.

Space Interferometry Mission System testbed-3: architecture

The Space Interferometry Missions System testbed-3 has recently integrated its precision support structure and spacecraft backpack (bus) on a pseudo free-free 0.5 Hz passive isolation system. The precision support structure holds a 3-baseline stellar interferometer instrument. The architecture of the instrument is based on the current flight system design, and its main purpose is to demonstrate nanometer class fringe stabilization using the path length feed forward technique. This work describes the overall instrument architecture, brief theory of operation, and preliminary measurements.

MAM testbed detail description and alignment

Future space-based optical interferometers, such as the Space Interferometer Mission (SIM), require fringe measurements to the level of picometers in order to produce astrometric data at the micro-arc-second level. To be more specific, it is necessary to measure both the position of the starlight central fringe and the change in the internal optical path of the interferometer to a couple of tens of picometers. The internal path is measured with a small metrology beam, whereas the starlight fringe position is estimated with a CCD sampling and a large concentric annular beam. One major challenge for SIM is to align the metrology beam with the starlight beam to keep the consistency between these two sensors at the system level while articulating the instrument optics. The Micro-Arcsecond Metrology testbed (MAM) developed at the Jet Propulsion Laboratory features an optical interferometer with a white light source, all major optical components of a stellar interferometer, and heterodyne metrology sensors. The setup is installed inside a large vacuum chamber in order to mitigate atmospheric and thermal disturbances. Recent data show agreement between the metrology and starlight paths to better than 24 pm in the one-degree narrow-angle field of regard of SIM. This paper describes the MAM optical setup and the precision alignment.