TPF-I SWG Report - Exoplanet Exploration Program - NASA

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C HAPTER 4 therefore increasing the dark field of view seen from the combiner spacecraft. Strategies for minimizing stray light have been detailed by Noecker et al. (2004, 2005). 4.8 Instability Noise and Mitigation In an ideal nulling interferometer, the electric fields of the light from the collecting telescopes are combined with a prescribed set of amplitudes and phases that produce a perfect null response at the star (Figure 4-17a). In this case the integration times needed for planet detection and spectroscopy depend on the planet signal strength and the level of photon shot noise (from local and exozodiacal emission, stellar leakage around the null, and instrument thermal emission). a) Ideal stellar E-fields b) Amplitude and phase errors c) Dynamic errors 2 2 2 1 4 3 1 4 3 1 4 3 Figure 4-17. a) Summation of electric fields in the spatial filter for an ideal Dual Chopped Bracewell nulling configuration. b) Amplitude and phase errors in the contributions from the different collectors lead to a residual leakage of photons. c) As the amplitude and phase errors vary with time, the residual photon leakage rate fluctuates and can mimic the presence of a planet. 4.8.1 Origin of Instability Noise In practice, it will not be possible to maintain the exact set of amplitudes and phases – vibrations and thermal drifts result in small path-length errors and time-variable aberrations. The null “floor” is degraded, and there is a time-variable leakage of stellar photons that can mimic a planet signal (Fig. 4-17b and c). This is known as ‘instability noise’ (previously “systematic error” or “variability noise”), and it increases the integration time required. The analysis of instability noise is somewhat complex (Lay 2004). Some components are removed by phase-chopping. Others, such as the “amplitude-phase cross terms” and the “co-phasing error,” are not removed and result in leakage photon rates proportional to δA i δφ j and δφ j , respectively, where δA i represents an amplitude error from the i th collector and δφ j is a phase error from the j th collector. The analysis shows that a null depth of ~10 -5 is generally sufficient to control the level of photon noise from the stellar leakage, but that a null depth of ~10 -6 is needed to prevent instability noise from becoming the dominant source of noise. A 10 -6 null requires rms path control to within ~1.5 nm, and rms amplitude control of ~0.1%. It is therefore instability noise, not photon noise that drives the performance of the instrument. Table 4-1 lists the mechanisms responsible for amplitude and phase errors, along with their spectral dependence and temporal nature. For example, vibrations in the optical path difference (OPD) result in a phase error that scales as the inverse of wavelength and are inherently time varying. Beam shear also 78
D ESIGN AND A R C H I T E C T U R E T RADE S TUDIES gives a time-varying amplitude error (less light is coupled to the detector) but is approximately independent of wavelength. Mismatches in dispersion, birefringence, and reflectivities between the collector beams may have a more complex spectral dependence, denoted by f (λ), but are inherently static. These static effects can be compensated by an adaptive nuller (Peters et al. 2006) or similar device. The dynamic terms combine via amplitude-phase (δAδφ) and co-phasing (δφ) mechanisms to form the timevariable instability noise: −1 −2 −3 () = ⎡α () λ + α ( ) λ + α ( ) λ ⎤ ( λ) IN t ⎣ 1 t 2 t 3 t ⎦F* 2 3 () t () t () t ⎤F ( ) = ⎡ ⎣β1 ν + β2 ν + β3 ν ⎦ * ν (1) where ν is the optical frequency, the α and β coefficients vary randomly with time, and F * is the stellar flux (since the star is the source of these leakage photons). Other instability mechanisms, such as an unbalanced chop, may also be important, but will have a similar spectral dependence. The important conclusion is that at any given time the instability noise has a spectral signature that varies slowly with wavelength. This slow dependence with wavelength forms the basis of the first mitigation strategy, described in the following section. Ben Lane has proposed an alternative scheme described in Section 4.8.3. Table 4-1. Sources of Instability Noise and Their Spectral Dependence Phase Amplitude Mechanism Spectrum Static / dynamic Mechanism Spectrum Static / dynamic OPD Vibration λ -1 dynamic Tip / tilt λ -2 dynamic Fringe tracker offset λ -1 dynamic Focus λ -2 dynamic Control noise λ -1 dynamic Higher order λ -2 dynamic Dispersion mismatch f 1 (λ) static Beam shear λ 0 dynamic Birefringence mismatch f 2 (λ) static Reflectivity / transmittivity f 3 (λ) static 79
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JPL Publication 07-1 Terrestrial Pl
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Abstract Over the past two years, t
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Acknowledgements Twenty-two represe
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Table of Contents 1 Introduction...
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4.8.3 Post-Nulling Calibration.....
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6.4.5 Double Fourier Interferometry
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I NTRODUCTION 1 Introduction Over 2
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I NTRODUCTION et al. 2004), and res
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I NTRODUCTION Standard Interferomet
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I NTRODUCTION 1.4 References Angel,
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C HAPTER 2 0.7 to 1.5 AU scaled by
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C HAPTER 2 Table 2-2. Illustrative
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C HAPTER 2 Classical interferometry
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C HAPTER 2 trivial in the absence o
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C HAPTER 2 Figure 2-3. Simulated mi
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C HAPTER 2 would be in atmospheres
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C HAPTER 2 Figure 2-6. The mid-infr
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C HAPTER 2 Lines of constant stella
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C HAPTER 2 presence of zodiacal clo
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Page 48 and 49: C HAPTER 2 Beichman, C. A., Fridlun
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Page 52 and 53: C HAPTER 2 Reach, W. T., Franz, B.
Page 54 and 55: C HAPTER 3 3.1.1 Darwin/TPF-I Prope
Page 56 and 57: C HAPTER 3 clouds or an OB associat
Page 58 and 59: C HAPTER 3 Figure 3-3. Three possib
Page 60 and 61: C HAPTER 3 the circumstellar disk,
Page 62 and 63: C HAPTER 3 Figure 3-6. (Left panel)
Page 64 and 65: C HAPTER 3 Continuum interferometry
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Page 68 and 69: C HAPTER 3 3.3 Conclusions Darwin/T
Page 70 and 71: C HAPTER 3 Nguyen, H. T., Kallivaya
Page 73 and 74: D ESIGN AND A R C H I T E C T U R E
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Page 132 and 133: C HAPTER 5 a) c) b) d) IWA = 43 mas
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Page 138 and 139: C HAPTER 5 5.8.4 Angular Resolution
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C HAPTER 5 The optimization works b
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T E C H N O L O G Y R OADMAP FOR TP
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F UTURE D EVELOPMENTS 7 Preparatory
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F UTURE D EVELOPMENTS • To comple
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F UTURE D EVELOPMENTS Table 7-1. Pr
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D ISCUSSION AND C ONCLUSION 8 Discu
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Appendices 167
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T E C H N O L O G Y A DVISORY C O M
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F L I G H T S YSTEM C ONFIGURATION
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F L I G H T S YSTEM C ONFIGURATION
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A PPENDIX C 2. Identical FACS fligh
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A PPENDIX C 2. Recall that the coef
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A PPENDIX C Once the formation has
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A PPENDIX C Figure C-3. Example of
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A PPENDIX C Figure C-4. FAST Flight
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A PPENDIX C The “true” time of
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A PPENDIX C References Cohen, S., a
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A PPENDIX D DC DCB DM DM DOCS DOD D
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A PPENDIX D NaCl NAR NASA NASTRAN N
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A PPENDIX E Appendix E TPF-I Review
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A PPENDIX F Alice Quillen, Universi
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A PPENDIX F Figure 3-1 - Original f
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