Spectral Astrometry Mission for Planets Detection

Erskine & Edelstein, SPIE 4852, Conference on Astronomical Instrumentation, Hawaii, Aug. 2002 1

Spectral Astrometry Mission for Planets Detection

David J. Erskinea and Jerry Edelsteinb

aLawrence Livermore Nat. Lab., 7000 East Ave, Livermore, CA 94550bSpace Sciences Lab. at Univ. of Calif., Berkeley, CA 94720-7450

ABSTRACT

The Spectral Astrometry Mission is a space-mission concept that uses simultaneous, multiple-star differentialastrometry to measure exo-solar planet masses. The goal of SAM is to measure the reflex motions of hundredsof nearby (∼50 pc) F, G and K stars, relative to adjacent stars, with a resolution of 2.5 µ-arcsec. SAM is anew application of Spectral Interferometry (SI), also called Externally Dispersed Interferometry (EDI), thatcan simultaneously measure the angular difference between the target and multiple reference stars. SI hasdemonstrated the ability to measure a λ/20, 000 white-light fringe shift with only λ/3 baseline control. SAM’sstructural stability and compensation requirements are therefore dramatically reduced compared to existinglong-arm balanced-arm interferometric astrometry methods. We describe the SAM’s mission concept, long-baseline SI astrometry method, and technical challenges to achieving the mission.

Keywords: Astrometry, Externally Dispersed Interferometry, Spectral Interferometry, Exoplanet Search

1. INTRODUCTION

We describe a space-based differential astrometry mission concept for measuring exo-solar planet masses. Themission concept, called the Spectral Astrometry Mission or SAM, has as its goal the detection of the motions ofhundreds of nearby (∼50 pc) F, G and K stars, relative to adjacent stars, with a resolution of 2.5 µarcsec (µ”).SAM is based on the new application of an existing interferometric technique called Spectral Interferometry (SI).The SAM SI instrument can simultaneously measure target and reference stars. Light collected by telescopes,separated by a long-baseline, is combined and measured by SI’s hybrid of an unbalanced-arm interferometerand a classical spectrometer. Because the SI technique has demonstrated1, 2 visible phase shifts resolutionof λ/20, 000 with a baseline control of only λ/3, the requirements for SAM’s large-scale structural stabilityor compensation are dramatically reduced compared to existing balanced-arm, single-target interferometricastrometry methods such as those proposed for space interferometry mission3 (SIM). The SAM is compact,using 50 cm telescopes separated by a 2-m ‘flexible’ baseline. The SAM mission concept offers a promising newpath for space-based differential astrometry.

1.1. The Search for Extra-solar Planets

The search for extra-solar planets is one of the most visible areas of science today.4, 5 Ground based mea-surements of radial stellar velocity reflex have led to the discovery of scores of planets. Important questionsregarding the statistical distribution of planet masses and orbital axis remain because the radial velocimetrymethods are inherently biased toward the detection of large mass planets with small axes, and because themethods establish only lower planet-mass limits due to undermined orbital inclination. In particular, key ques-tions remain regarding the population of Earth like planets within habitable zones and the population of Jupiterlike planets at large distances. It is unclear whether our kind of planetary system is typical or atypical. Theseissues have profound impact upon the predicted evolution of habitable planets and their atmospheres.

Further author information:D.J.E.: E-mail: [email protected], Telephone: 1 925 422 9545J.E.: E-mail: [email protected], Telephone: 1 510 642 0599


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J

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SAM 5-Yr Mission

2.5 µarcsec

SAM 5 pc

PTI 5-Yr Mission50 µarcsec @ 10 pc

SAM 25 pc

Keck 13-Yr Mission10 µarcsec @ 10 pc

1 µarcsec @ 3 pc

E

SIM 5-Yr Mission5 µarcsec @ 10 pc

N

Figure 1. Discovery space. Data taken from SIM report.3

Shaded area shows SAM sensitivity from 5–25 pc.

The limitations of radial-velocimetry measurementshave inspired efforts to find new methods of directlymeasuring exo-planets. One method being activelypursued for space-missions is wide-angle astrometry tomeasure a star’s circular reflex motion due to the pres-ence of a planet(s), (such as the SIM concept). Thewide-angle astrometry method uses long baseline in-terferometry (LBI) to measure the positional shift of atarget star’s centroid relative to other reference stars.By making repeated measurements over time of the tar-get’s differential position, the actual reflex orbital mo-tion can be mapped, the orbital inclination estimated,and the planetary mass derived given the target massdue to the stellar type.

The observations required for planetary populationinvestigations are to survey for Earth-like and largerplanets around hundreds of Sun-like stars, and to di-rectly determine the masses of the detected planets.The science requirements propagate into inter-relatedobservatory and instrument requirements. The desiredrange for planet mass and axis measurements deter-mines the minimum (∼2-3 months) and maximum mea-surement interval (∼5 years) and so establishes require-

ments for mission life and number of exposures per tar-get. The planet mass and axis, together with the targetspace distribution, establish the astrometric resolutionrequirements and, taken together with the requirednumber of target measurements, determines the in-strument flux sensitivity requirements. The target dis-tribution is derived from the 3-dimensional space dis-tribution (luminosity function) of Sun-like stars (heretaken as F, G, and K dwarfs).

The relationship between several of these parame-ters is shown in “discovery space” in Fig. 1. The as-trometric resolution needed to detect planets of givenorbital axes and masses at specific distances are shown.We conclude that an intermediate, 2.5 µ” resolution,sufficient to detect the reflex motion of an Earth-likeplanet at 1.2 pc, will provide a sufficient sampling ofthe discovery space to obtain essential science data. Asummary of the SAM mission concept parameters areshown in Table 1.

1.2. Existing Method: BalancedLong-Baseline Interferometry (e.g. SIM)

We briefly describe the LBI astrometry method usedby SIM6 for planet finding. SIM uses a long-baselinebalanced-arm interferometer. Light from two collec-tors at the baseline ends is interfered. The opticalpath lengths of the two input arms must be preciselymatched so that their difference (called the delay τ) isnearly zero. In this balanced-path configuration, thefringe phase (φ = τ/λ) does not vary strongly withwavelength (λ). The method requires exquisite dimen-sional stability or characterization of the large opticalpaths because as τ departs from 0 the fringes becomeunresolvable. For example, the SIM6 plans a 7 m base-line rigid truss to mount open-beam optics, and usesmultiple control and metrology loops to stabilize ormeasure the entire optical path with a total error bud-get of 340 pico-m, or λ/1500 at 5000 A. Limiting di-mensional tolerances to this precision over multi-meterbaselines is extremely challenging, stretching the stateof the art, and budgets.

With this method, a minimum of three separate orsequentially interferometer baseline measurements arerequired to obtain the relative angular position of thetarget to two reference stars. This is because balancedLBI techniques cannot distinguish between multiplesources if their starlight is superimposed within a sin-gle common path. The inability to use a common pathoccurs because different objects within the field willgenerate a similar spectral fringe pattern7 that cannot


Fringe phase

Line

-out

alo

ng

#waves

0°

Figure 2. Long baseline measurement of an object off-axisat angle θ creates an unbalanced interferometer having non-zero τ , producing fringes that vary along the wavelengthdirection with a density proportional to θ.

be accurately distinguished. Some conventional LBI in-struments use up to a few tens of wavelength channelsto help retain fringe visibility under parasitic disper-sion effects, however this is insufficient to distinguishamong multiple simultaneous objects.

1.3. SAM Method: UnbalancedLong-Baseline Spectral Interferometry

1.3.1. System Description

The SI astrometry system (see Fig. 2) is a long-baselineunbalanced-arm, white-light interferometer that sam-ples the delay τ (corresponding to illumination angle)between its two apertures over a large number of phasecycles by using dispersion to separate the spectrallyvarying fringes emanating from a Michelson interfer-ometer. By inserting a reference absorption cell in thebeam, a low spatial frequency Moire pattern results onthe detector because of the heterodyning of the twohigh spatial frequency spectra. This heterodyning re-lieves the need for a high-resolution spectrometer andexpands the measurement range of τ , effectively in-creasing the angular field of view for a given detectorpixel size. Multiple stars can be viewed simultaneouslyin the enlarged field of view. Each star has a differentMoire pattern that will beat with the other stars pat-tern. Phase stepping techniques provide robust andaccurate determination of the beat pattern phase. Si-multaneous multiple reference star observation elimi-nates the dependence of the baseline length and ro-tation angle knowledge from the phase determination.Common mode changes in the pathlength of the mul-tiple stars are unimportant, dramatically reducing thestability requirements of the instrument for the largecommon-path baseline distances.

1.3.2. Fringe Formation

Light from two collectors at the baseline B ends arejoined in a Michelson interferometer. The optical pathdifference, τ , of the two inputs are made intentionallylarge (e.g. many thousands of wavelengths, λ). In this,unbalanced -path configuration the fringe phase variesstrongly with λ. The light from the interferometer isimaged to the slit of a conventional spectrograph andthe overlapping phases in the interfered light are dis-persed. The sinusoidal fringes form a spectrally depen-dent comb transmission function,

T (ν) = (1/2)[1 + cos(2πτν)] , (1)

(where ν = 1/λ in cm−1), that modulates (multiplies)the input spectrum. The spectral dispersion allowsmeasurement of the Michelson fringes.

1.3.3. Simultaneous angle measurement

An essential characteristic of SI is its ability to measureseveral stars simultaneously. The SI can be used tomeasure the source position angle to the baseline, θ,because θ effects the total inter-arm delay by

δτ = B sin θ ∼ Bθ , (2)

and therefore the density of fringes per unit of fre-quency. Hence, for small θ, the target angle is propor-tional to, and uniquely determines, the spatial fringefrequency across the bandwidth (∆ν) of the spectro-graph:

θ = (#fringes)/(B∆ν) . (3)

This is significant because multiple targets, observedsimultaneously at different position angles, will gen-erate multiple spatial frequencies that can be readilyseparated using post-detection Fourier decomposition(see Fig. 3 for a laboratory demonstration of this phe-nomena). Differential angular measurement betweensimultaneous targets are robust to changes over thelong baseline because light from all of the stars travelsimultaneously through this common path. Therefore,common optical element changes such as detector dis-tortions, focal spot shape, and temporal changes in thestellar spectrum or intensity are negated.

1.3.4. Importance of simultaneousmeasurements

SI’s capability to simultaneously measure stars has sev-eral very important ramifications.(1) The need for long-path baseline stability is relievedbecause the differential angle measurements are not af-fected by deviations (typically environmental) in the


common-conduit path.(2) The determination of differential position angle canbe made independent of the value of the baseline lengthif two reference stars are simultaneously measured againstthe target. Hence, δθ can be measured to high accuracyeven if the baseline shifts within or between measure-ments (see Eq. 11, which shows δθ is independent ofB).(3) Determining δθ can also be made independent ofabsolute baseline rotation-angle if three reference starsare simultaneously measured against the target becausethe new reference coordinates allow for a recursive es-timation of roll errors. Consequently, the need for crit-ical control or measurement of observatory rotationalpointing is decoupled from the interferometric result.(4) Simultaneous measurements of both target and ref-erence stars present an observing efficiency advantagecompared to sequential observations.

1.3.5. Spatial heterodyning of anglemeasurement

Because the spectral fringe frequency increases withposition angle, the maximum measurable angle is pro-portional to the resolution of the spectrograph (and thepixel size of the detector). In order to measure largeangles, while keeping the spectral resolution R = λ/δλmodest and the consequent payload size, mass andcomplexity low, a Moire or heterodyning process isused. The light, after interference, is passed through awavelength reference cell (comb) that imprints (multi-plies) a known spectrum against the input spectrum.The reference spectrum imprints the light with thou-sands of stable spectral fiducials. The sinusoidal fringesdue to angular position (Eqs. 1 & 2 beat against thefeatures of the reference spectrum to form a Moire pat-tern on the detector. These Moire patterns rotate inphase with position angle in the same way as its un-derlying spectral fringes.

1.3.6. Beat phase measurement

For spectral astrometry, the position-angle induced Moirepattern for one star is measured simultaneously withthe Moire pattern for another star. The phase of thebeats formed between the two patterns is a highly sen-sitive measurement of the differential angle δθ betweenthe two stars. The beat phase, is independent of driftsin the common path delay. The δθ measurement is in-sensitive to the absolute position angle because, whilethe underlying fringe pattern frequency changes withθ, the beat pattern frequency does not. Because theMoire patterns are large compared to the spectral fringes

Beats in fringingspectra yield ∆

CCD

B

1

2

∆

1

2

a) Both sources

b) Source 1

c) Source 2

Figure 3. Laboratory data demonstration of multi-objectSI. Two stars observed by the spectral interferometer eachwould produce a unique fringe pattern, which manifestsbeats when summed at the detector. The white light fringepatterns shown were obtained using the prototype SI mod-ified to have a baseline B, and two white light pinholesources simulating stars, both together (#a with beats) andseparately (#b, #c). Pinholes were separated by 0.5◦ withB=6 mm and spectrum bandwidth 350 A over 5400 A.


themselves, the system is quite insensitive to the opti-cal quality of the common path system. For example,while variable or aberrant spectrometer resolution orfocus may change or reduce the Moire pattern con-trast, it will not degrade the structure of the patternitself.

1.3.7. Phase Stepping improvements

We implement a phase-stepping method to provide ac-curate phase determination and to allow for a straight-forward data-analysis algorithm to eliminate fixed pat-tern instrument noise and delay drifts up to λ/3. Wearrange for the interferometer delay τ to linearly varyslightly along the spectrometer input slit axis (calledthe vertical axis) by tilting one interferometer mirroracross the spectral dispersion plane. The resultingslanted interferometer comb pattern can be analyzedalong the vertical axis at each spectral channel. Thus,the real and imaginary components of the fringe phasecan be derived by using a series of self-referenced phasemeasurements of the Moire fringe within a single expo-sure. Although this cross-dispersion sinus phase vari-ation itself allows for phase determinations, additionalphase stepping is still advantageous because it removesfixed pattern noise such as detector flat-field variations.Hence, we introduce delay modulation with a PZT-transduced mirror by taking four exposures with de-lay steps of about λ/4. A proven, sophisticated phasealgorithm8 does not require knowledge of the phasestepping size. The step size is found as part of a min-imization procedure that takes advantage of the inde-pendence of the fringing wavelength channels.

2. DEMONSTRATION OF SPECTRALINTERFEROMETRY PERFORMANCE

We have demonstrated a compact spectral interferom-eter in our laboratories to have a phase resolution of∆τ = 27 picometers or λ/20, 000.1, 2 This SI wasdesigned for a Doppler velocimetry application. The-ory of the Moire fringe formation and phase steppingdata processing technique common to both the Dopplerand astrometry applications is in Refs. 8–10. Figure 5shows the SI. Light from a source fiber passes throughan iodine vapor cell used as a spectral reference. Hencethe light now consists of both the potentially Doppler-affected source spectra and the stationary iodine ab-sorption spectrum (5000–5800 A). The light transitsan unbalanced Michelson interferometer, with a τ ∼ 1cm delay, and is then dispersed by a commercial R =20k spectrograph to a CCD detector. Fringes were ob-served with various sources including sunlight, bright

Slit

a) Model

Slanted Interferometer comb

Narrow Absorptionlines

c) Iodine data

or

b) After blurring

Broad Moirefringes

c) Measured iodine fringing spectrum

Figure 4. Demonstration of Moire or heterodyning effecton actual iodine absorption spectrum c) recorded by SI pro-totype for a fixed delay of about 1.1 cm. Each delay createsa unique Moire pattern which can be used to determine thedelay to 27 pm precision with a 0–6 cm range. a) Model. b)Blurring due to spectrograph slit does not prevent detectionof Moire fringes.

CCDDetector

GratingSpectrograph

Wide angleInterferometer

Iodine vaporcell

Input Fiber

a)

Wide angleinterferometer

I2 vapor cell

Slit

Spectrograph

CCD

Light source

FiberPZT

Detector

Glass plate Mirrors

Few cm

Grating

(insertable)

(vertical)

Figure 5. Photo and schematic of EDI (SI) prototype usedto take solar, iodine and bright starlight velocimetry data.


starlight, and simulated stationary starlight consistingof a backlit bromine vapor cell. Figure 4 shows SI’sMoire fringes resulting from beating an iodine refer-ence spectrum against the comb from a τ = 1.1 cmunbalanced interferometer. The relative shift betweena stationary “bromine stellar source” and the refer-ence iodine cell spectra were measured repeatedly1, 2 tofind an instrument noise-limited performance of 0.76m/s, which is equivalent to λ/20, 000. Although thevelocimetry and astrometry data analysis techniquesslightly differ, the λ/20, 000 performance result can bedirectly applied to our astrometry application.

The Doppler SI suffered a long period (2 week) zero-point velocity drift (∼4 m/s), a small magnitude thatis quite remarkable given that the instrument was notthermally or optically stabilized. Regardless, astrom-etry requires repeated precision across long measure-ment intervals. Fortunately, these zero-point drifts areimmaterial to our astrometry because the SAM ap-proach uses a differential method that obtains a newzero-point template spectra for each measurement.

The broadband nature of SI is a primary reasonfor the order of magnitude fringe-shift precision im-provement compared to conventional monochromaticinterferometers. The presence of thousands of wave-length channels, each having independent, evenly sam-pled fringe phase, means that systematic phase errorsare statistically diminished. In fact this type of multi-channel spectral method has been applied, using 32channels, to improve group-delay fringe tracking forthe ground based Navy Prototype Optical Interferom-eter.11

3. THEORY3.1. Spectral beats for astrometryThe angular difference ∆θ between two objects in theSI is detected through the presence of beats in thefringing spectra vs. ν (Fig. 3). First consider a singletarget. As τ increases, the fringing spectra twists (lin-early increasing phase angle change ∆φ versus ν) be-cause ∆φ is wavelength dependent, ∆φ = ∆τ/λ. (Ouranalysis, which determines the absolute τ that createsa given fringing spectrum, is not confused by integerfringe skips, as is a monochromatic system. Now con-sider two temporally incoherent broadband sources #1and #2. Assume that θ1 and θ2 are widely separatedso that (τ1 − τ2)ν > 1, i.e. so that at least 1 fringe ex-ists over the spectrograph bandwidth. Then these twofringe patterns will not be confused, as we show. Sinceboth star light 1 and 2 travel through the same refer-ence spectrum cell, they each make a similar fringing

spectrum but having different amounts of twist. Fring-ing spectra are represented by complex waves, whosephase and magnitude vs. ν represent the phase andvisibility for a given spectral channel. Let W1(ν) andW2(ν) be fringing spectra for stars 1 and 2 measuredalone, and W0(ν) the spectra for the reference cell alone(i.e. the instrument at θ = 0, τ = 0). It can be shownthat the fringing spectra are related to the intrinsicspectrum W0(ν) by a phasor

Wk(ν) = W0(ν)ei2πντk (4)

which applies the spiral twist. The addition of two dif-ferent amounts of twists on the same fringing spectrumcreates beats in net amplitude and phase, depending onthe relative intensity a of the sources:

W1 + αW2 = W0(ν)ei2πντ1 + αW0(ν)ei2πντ2 (5)= W0(ν)ei2πντ1(1 + αei2πν∆τ ) . (6)

The second term contains the beats in both phaseand magnitude. The number of beats across the band-width (BW) is

n = (∆τ/λ)(BW/λ) (7)

and is proportional to the difference in source angle,

n = ∆θ(B/λ) cos θ(BW/λ) . (8)

The expected angular displacements created by aplanet tugging a star will produce fringes from obser-vation to observation that change by much less thana single revolution of twist. Because the whole num-ber of beats changes so slightly, we choose to measurethe phase of the beats for a fixed n to determine ∆θ.The use of spectral beats for astrometry has been the-oretically discussed by James, Kandpal and Wolf.12, 13

Our method differs by the inclusion of the referencecell that greatly increasing the maximum measurabledelay, and by the use of phase stepping techniques thatvery precisely measure the beats in both amplitude andphase.

3.2. Independence from Baseline

The SI measures the fraction angular position of thetarget relative to the spacing between the two referencestars. Using small angles (the conclusion is valid forlarger angles), each star’s delay is due to its angle plusthe common pathlength offset C:

τ1 = Bθ1 + C ; τ2 = Bθ2 + C ; τ3 = Bθ3 + C . (9)


1

10

2

0.1 1 10Relative Intensity ofTarget Star

Pho

ton

nois

e fa

ctor

Stars measured separatelyand sequentially

Stars measured simultaneously

3-3 0Magnitude of Target Star Relative to Reference Stars

PNFSA

PNF*SA

PNF0

Simultaneous and attenuate the brightest

Figure 6. Photon noise component of angular precision vsintensity of target star relative to two other reference stars.

If the target is #2 and the reference #1 and #3, thenthe baseline is

B = (τ1 − τ3)/(θ1 − θ3) (10)

and

δθ = (θ2 − θ3) = (θ1 − θ3)(τ2 − τ3)(τ1 − τ3)

. (11)

Hence, two or more simultaneous reference stars re-move the baseline value B from determination of δθ.

3.3. Photon-limited SensitivityThe single star photon limited angular resolution of aSI interferometer is

δθ =√

2λ

πBVPNF (12)

where V is fringe visibility (0.2 to < 1 typical) and thephoton noise factor

PNF =√

1/Nph (13)

where Nph is the number of photons. For multiple starsmeasured separately the PNF is described by

PNF0 =√

1/N1 + 1/N2 + 1/N3 (14)

which is plotted in Fig. 6 as thin curve for a case wherethe target star magnitude is varied relative to two ref-erence star intensities. In comparison, for measuring 3stars simultaneously, the PNF is described by

PNFSA =√

N1 + N2 + N3

√1/N2

1 + 1/N22 + 1/N2

3

(15)

which is plotted in Fig. 6 as dashed curve. It is benefi-cial to make all 3 stars equal intensity. The bold curve,PNFSA, shows when the brightest stars of a triad areattenuated to minimize the PNF. To maximize sensi-tivity, the range of target and reference star flux shouldbe limited. This can be accomplished by target selec-tion (as we have done for our target estimates) or byrelative attenuation which, in theory, could be instru-mentally implemented. Note that measuring the starsseparately means measuring them sequentially. For afixed total integration time, Nph will be reduced 3×,raising PNF0 by

√3. Hence sequential and simulta-

neous observations produce similar photon limited be-havior when the stars are of similar intensity.

3.4. Multi-Star Target Statistics

We have examined the Tycho and Hipparcos stellar cat-alogs to find candidate target stars with nearby refer-ence stars suitable for differential astrometry measure-ments. We identified all dwarf stars of type F, G andK as possible targets. We counted as candidates thenumber of target stars with magnitude ≤ mv , within adistance ≤ d, and with 3 or more reference stars withina certain angular distance to the target star. The cat-alogs completeness begins to limit the population formv < 10. Our results are summarized in the Table 2.Our analysis shows that an SI with a 0.5◦ to 1◦ FOVwith sensitivity to detect mv < 9 or 10 should be ableto observe the desired number of science targets. Ourcandidate values are not estimates, but actual catalogcounts. Not all of these stars may be ideal targets forSAM science however. We have not yet tested the rela-tive separation and orthogonal alignment, parametersthat can effect the astrometric uncertainty.

4. PRELIMINARY INSTRUMENTDESIGN

Figure 7 shows our straw-man adaptation for the SAMSI instrument. Two telescopes, separated by a base-line distance B, collect coherent broadband light beamsfrom distant targets. Given SI’s demonstrated λ/20, 000wavefront precision, then the 2.5 µ” angular resolutiongoal can be achieved with a 2 meter baseline.

4.0.1. Telescope size

Sensitivity requirements determine the telescope sizeand bandpass. From our prior analysis (Eq. 12), weestimate that a total ∼700 million events must be de-tected to achieve 2.5 µ” resolution with a 2-m baselineassuming a 50% fringe visibility and reference and tar-get stars with similar intensity. These events may be


OptionalI2 ref. Ref.

comb

Delay offsetFringe trackingPhase stepping

CavityStabilization

Spectrograph & CCD

Figure 7. Simplified schematic of a spectral interferom-eter used in simultaneous astrometry of multiple sources.Light from sources are collected by two input telescope sys-tems (not shown) and injected into the ends of left andright conduits separated by a baseline B. The left & rightbeams are interfered at the beam splitter and dispersedto a CCD detector. The angle θ of each source creates atime delay between the left & right arms, which manifestsfringes vs. wavelength across the recorded spectrum hav-ing density (1/spacing) proportional to source angle. Mul-tiple sources travelling the same common path through theconduit create beats in spectrum. These measure the dif-ferential source angle ∆θ12 independent of conduit length.Coarse (λ/3) fringe tracking prevents fringe skips. A spec-tral reference is used to heterodyne dense fringe spacing toa lower density resolvable by spectrograph. The referencecould either be an iodine absorption cell or a laser stabilizedinterferometer.

accumulated in any series of independent observation.To observe 150 targets four times per year then eachobservation may accumulate a total integration timeof ∼25,000 s, assuming an observational efficiency of50%. To measure orthogonal angular positions on thesky, two observations per star are needed unless a sec-ond, two-telescope SI is included in the payload design.We presume SAM includes a pair of SI’s for both ob-servational efficiency and redundancy. Assuming rea-sonable component efficiencies (7*M 93%, G 80%, Q70%, BS 50%, 4*T 95%, fiber coupling 50%), the to-tal throughput is ∼8%. Presuming a 50-cm telescopeaperture with 70% obscuration, we derive that a 600A bandpass is required to observe a 9th magnitude G2star.

4.0.2. Focal plane fiber collector

At the focal plane, four fiber collectors are shuttled toa fixed position to collect each star’s light. We envi-sion that co-aligned star-trackers per telescope actuatean “anti-jitter” mirror system that stabilizes starlightin the correct focal plane position for beam collection.The four fiber paths from each telescope must be com-bined into a single beam or fiber optical conduit in acommon mode mixer (e.g. via a pinhole or single modefiber). We envision using single-mode joiners similar tothose commercially available.

For each star, the path from the first telescope sur-face to the point of beam combination is non-common.Consequently, great care must be taken to control ormeasure relative shifts between each of the stars’ opti-cal path. The focal plane collection and non-commonpath treatment represent the primary technical chal-lenges to be mastered. We describe methods of resolv-ing these issues below, and note the happy fact thatthe dimensional control issue must be resolved over thesize scale of an individual telescope, not over the multi-meter baseline scale.

4.0.3. Flexible Baseline Conduit

A long baseline conduit carries mixed light from eachfocal plane to the interferometer. The conduit can con-sist of flexible optical fiber because using simultaneousreference stars negates any changes in the common-path baseline. Once the individual fibers have beenforced to share the same wavefront by, say travel througha pinhole or short length of single mode fiber, then anysubsequent path shares a common wavefront and canbe of any type such as a large diameter multimode fiberor an open beam. Our straw-man uses multimode fiberfor the long common path between the input optics andinterferometer. Flexible conduit allows greater freedomin the mechanical design and layout of the payload andeliminates the need for a large rigid (subwave) base-line truss. While single mode fibers produce a morecontrolled fringe phase at the spectrometer, multimodefibers tend to have a larger transparency bandwidth.

4.0.4. Gross Optical Delay

An optical delay line trombone is actuated over manycm in one arm to allow for an adjustable non-zero delayoffset, which is also equivalent to a FOV pointing offsetthat allows for compensation of large-scale observatorypointing errors. We anticipate launching the fiber lightto a small, collimated open beam prior to entering thedelay line.


During each individual exposure, the arm path lengthmust be stable to λ/3 or net fringe visibility will bediminished. This can be accomplished using a conven-tional, small-motion optical-path stabilizing (λ/3) ac-tuator in one of the two arms. A huge advantage of SIis that the relative stellar angle precision is de-coupledfrom the phase precision (φ) so pathlength stabiliza-tion < λ/3 is not necessary. (The SIM method mustachieve λ/1500 phase precision because, in this case, φdirectly sets the angular resolution.) The small-motionactuator also can be used to provide ∼ λ/4 phase step-ping per exposure. The optical-path actuator(s) finepositioning is controlled (typically piezoelectrics) by afringe phase sensor.

4.0.5. Field of View

The light from both arms are combined with a beamsplitter and passed through a reference cell. The max-imum angle that can be measured in a single obser-vation is θmax = τcoh/B where τcoh is the coherencelength of the reference cavity. For an iodine cell (τcoh ∼6 cm) and a 2 m baseline θmax is 1.7◦. However, thefield of view of the SAM will also be constrained bythe input optics design and the statistics of the distri-bution of the target and reference stars. We illustratethe choice of either a stabilized interferometric cavitycell, and a gas absorption cell. Interferometric cavitiestend to have much higher fringe visibility and coher-ence lengths than gas cells and, in principle, can havetheir fringe spacing actively tuned to provide the opti-mum comb function for observations. The gas cell, canprovide an absolute fiducial wavelength grid that canbe used to calibrate the tunable cavity or to extracta wavelength-calibrated high resolution spectrum fromand individual star.

4.0.6. Spectrometer and CCD

A spectrometer’s slit is at the focus of the reference celloutput beam. The R=20,000 spectrometer dispersesthe fringes to a wide (∼4000 pxl) CCD detector thatcovers the 600 A bandwidth centered at 5000 A. TheCCD need not be as tall (128 pxl) because the non-dispersion axis is used to read low spatial frequencyMoire pattern phase.

Exposures per target are taken in sequence for eachλ/4 phase. Maximum exposure time will be bound bythe depth of the CCD well and by the ability of the SIsystem to maintain fringe stability. The phase steppingalgorithm removes high frequency fixed pattern noiseand fringe patterns from the data image and eventuallyreturns the Moire beat complex phase.

1

2

3

Fiber joiner

To spectral interferom.

Common pathNon-commonpath

Pathlengthcalibrant

1 ≠ 2 ≠ 3

Figure 8. Schematic of white light calibration of non-common path delay. Light from fiber creates fringes dueto the deliberately differing lengths of the input fibers. Fora Cassegrain, a tripod of fibers determines the XYZ loca-tion of each fiber input.

5. FURTHER DESIGNCONSIDERATIONS

5.1. Reference cells

In principal, any stable spectrum can be used for a fidu-cial spectral reference, such as an I2 absorption spec-trum or the periodic spectrum provided by a stabilizedinterferometer or cavity (e.g. Michelson, Fabry Perotor Lyot cell). The reference cell’s spectral comb sta-bility must match the desired SI system fringe resolu-tion. The technology to meet cell stability requirementis tractable. Gas absorption cells (e.g. I2, Br2) have> λ/20, 000 stability for ∼6 cm cavities. A Fabry-Perot (FP) has been demonstrated in a 1-cm cell with∼ λ/20, 000 stability using a using semiconductor-laserstabilization (Connes14, 15). In principle, this FP stabi-lization technique should be applicable to much longercoherence lengths.

5.2. Internal phase calibration system

Light from each star must be joined into a commonmode in a way that does not cause uncorrectable changesto the relative pathlength for each star. That meansthat the entire uncommon path from the first telescopesurface to the mixed fiber must be stable or measurableto the wavefront resolution requirement of λ/20, 000.This requirement is the key technical challenge to theSAM’s implementation.


Our approach to the problem is to directly measure any differences in the individual star beam pathlengthsin situ with the same SI used for the stellar measurements. White light is inserted by one of three narrow fibersaffixed about the primary surface (Fig. 8). A spherically expanding wavefront propagates through the optics toeach collecting fiber. The fibers have pathlengths that differ by more than the light coherence length to avoiddata confusion between the fibers. The calibrant light creates a fringing spectrum and the fibers’ differentialpathlengths are determined using the same apparatus and method as for starlight. The exact location of theemitting fibers does not matter, since offsets generate a pathlength error linear in θ are eliminated by using tworeference stars. Using three fibers in a tripod allows all 6 dimensions of differential rotation and translationto be determined. Then only non-linear temporal mirror figure distortions between the fiber locations must becontrolled or calibrated. The calibration would occur separately for each input arm and the three fibers wouldbe energized sequentially. The source need not be exactly white, and could be a high-brightness photo-diode sothat calibration exposures would be rapid.

5.2.1. Telescope induced phase errors

Telescope illumination effects and temporal optical excursions could induce differential phase errors to the starbeam paths. Since only differences in pathlengths between the individual stars matters, then only higher ordereffects are generally important. For example, a non-spherical wavefront at the fibers focus is, in itself, notdetrimental, because as the telescope pointing wanders all the fibers will move over the focal spot in the sameway. Secondly, wavefront differences do not matter if they are linear in position, because such terms can beshown to be equivalent to a change in baseline B to form an effective baseline B†, an uncertainty eliminated byusing two simultaneous reference stars (Eqs. 9–11). Only a secondary-induced, quadratic wavefront distortioncan cause significant differential beam path changes. An offending quadratic term in the data difference,

(Dataj − Datak) = B†(θj − θk) + β(θ2j − θ2

k) , (16)

could be eliminated by subtracting instantaneous white light calibration. If the calibrations bracket the stellarexposure in time, then the offense will be cancelled. (However, subtle errors can arise if β is varying, such asdue to thermal effects.)


Table 1. SAM Straw-Man Parameters

Mission

Mission Duration 5 yearsPayload Envelope 3m × 3m × 1.5mSpacecraft Mass 600–800 kg (approximate)Science Data 0.5–1 Gbit /day, unreduced

5–10 observations / orbit @ 6.4 Mbit/orbit

Science

Angular resolution 2.5 µarcsecFringe Sensitivity λ/20,000 for 9th Magnitude G star in 25,000 sec.Targets per year ∼150 stars × 4 observations in orthogonal axesCandidates Mv ≤ 9 FGK 1000 / 2600 stars within 50 pc (30’ / 60’ FOV)Reference stars Minimum 3 per field within 30’ / 60’

Instrument

Baseline 2 meter length (2 each, orthogonal)Optical delay line ±5 cm travel(±1.5◦ pointing compensation)Fringe Stabilizer λ/3 stability, 250 µm rangePhase Stepping, λ/10 resolution, 1λ range

Telescopes 2 × 50cm primary, F/10 R-C, 85cm p-s, 30 cm bflField of View (FOV) 30’ diameter nominal, ∼15 µm focal sizeImage stabilization Combined spacecraft + active siderostat ±1”Telescope Focal Plane 4@ move and forget fiber shuttle on focal curve(for 30’ FOV) 50µm lenslets to fiber, ∼5 µm accuracy on 5 cm

(or 10× field reducer to fiber, 0.5 µm on 5mm)Fiber optics Single mode, 6 µm core to combiners

Multi-mode for common pathBeam splitter Transmissive, open beam, 1cmReference cell(s) Stabilized cell (Fabry-Perot or similar), I2 cavityGrating Spectrometer Reflection 5cm, 2000/mm, 50cm fl @ 10 A/mm

λ/∆λ= 20,000 @ 5000A, 600A bandwidthDetector CCD– 70% QE at 5000A, 4028 (λ) × 128

(Standard readout rates, noise <10e- per pixel)5–10 readouts per orbit

Table 2. a) Number of candidate F, G, K targets with 3 reference stars within a Field of View (FOV). b) Planet massinducing detectable motion on a G star by distance to star.

Target d ≤ (pc) Target mv ≥ (mag) 60’ FOV 30’ FOV Mass of planet at 2 AUCandidates Candidates causing 2.5 µ” motion(N stars) (N stars) of a G star. (MEarth)

50 9 / 10 2653 / 3293 1004 / 1415 2125 9 / 10 370 / 435 116 / 162 1010 10 15 5 4


ACKNOWLEDGMENTS

Thanks to John Vallerga for assistance with the manuscript, Pat Jelinsky for statistics of star distribution,and John Mather for fruitful discussions. Work was partially supported by CalSpace/Lockheed, and NASASARA research grants NAG5-9091 and NAG5-3051. This work was performed under the auspices of the U.S.Department of Energy by the University of California, Lawrence Livermore National Laboratory under contractNo. W-7405-Eng-48.

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