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Optics Express

  • Editor: J. H. Eberly
  • Vol. 9, Iss. 1 — Jul. 2, 2001
  • pp: 36–41
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Exoplanet detection using a nulling interferometer

Manuel P. Cagigal and Vidal F. Canales  »View Author Affiliations


Optics Express, Vol. 9, Issue 1, pp. 36-41 (2001)
http://dx.doi.org/10.1364/OE.9.000036


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Abstract

The detection of extra solar planets is a topic of growing interest, which stretches current technology and knowledge to their limits. Indirect measurement confirms the existence of a considerable number. However, direct imaging is the only way to obtain information about the nature of these planets and to detect Earth-like planets, which could support life. The main problem for direct imaging is that planets are associated with a much brighter source of light. Here, we propose the use of the nulling interferometer along with a photon counting technique called Dark Speckle. Using a simple model the behavior of the technique is predicted. The signal-to-noise ratio estimated confirms that it is a promising way to detect faint objects.

© Optical Society of America

1. Introduction

In the last six years, more than fifty Jupiter-like planets have been reported. In every case their presence has been inferred from indirect measurements. Most of them have been found using the Doppler technique, which measures changes in the star’s velocity due to the planet’s gravitational force. However, direct imaging will offer information hidden to other detection techniques and will allow us to observe Earth-like planets, which cannot be detected using other techniques [1

1. J.R.P. Angel and N.J. Woolf, “An imaging nulling interferometer to study extrasolar planets,” Astrophys. J. 475, 373–379 (1997). [CrossRef]

]. The main problem for direct imaging is that planets are associated with a much brighter source of light. In the visible, where planets shine by reflection of starlight, the contrast ratio between a Jupiter-like planet and its parent star is about 109.

To reduce this ratio, Hinz et al. [2

2. P.M. Hinz, J.R.P. Angel, W.F. Hoffmann, D.W. McCarthy, P.C. McGuire, M. Cheselka, J.L. Hora, and N.J. Woolf, “Imaging circumstellar environments with a nulling interferometer,” Nature 395, 251–253 (1998). [CrossRef]

] suggested using infrared (IR) wavelengths between 5 and 10 µm. In this range of wavelengths many young giant planets are self luminous and the star/planet intensity ratio, R, is about 106. The advantages and drawbacks of the use of visible or IR light will be analyzed later on. In both cases, the star diffraction pattern at the planet location is still several orders of magnitude brighter than the planet peak [3

3. F. Roddier and C. Roddier, “Stellar coronagraph with phase mask,” Publ. Astron. Soc. Pac. 109, 815–820 (1997). [CrossRef]

]. Consequently, the star diffraction rings must be suppressed in order to detect a planet. As an example, for a wavelength of 600 nm and a 8 m telescope, a planet 1 AU from a star at 10 pc is located at the position of the fifth Airy ring of the star (0.1 arcsec). In the IR case, the resolution is lower and, thus, the planet is even closer to the star’s Airy core.

Several solutions have been proposed for the suppression of the star diffraction pattern, e.g. the nulling interferometer [4

4. R.N. Bracewell, “Detecting nonsolar planets by spinning infrared interferometer,” Nature 274, 780–781 (1978). [CrossRef]

,5

5. N. Woolf and J.R.P. Angel, “Astronomical searches for Earth-like planets and signs of life,” Annu. Rev. Astron. Astrophys. 36, 507–537 (1998). [CrossRef]

], a coronagraph with phase mask [3

3. F. Roddier and C. Roddier, “Stellar coronagraph with phase mask,” Publ. Astron. Soc. Pac. 109, 815–820 (1997). [CrossRef]

] or the use of a square transmission-weighted apodizing aperture in the telescope pupil [6

6. P. Nisenson and C. Papaliolios, “Detection of Earth-like planets using apodized telescopes,” Astrophys. J. 548, L201–L205 (2001). [CrossRef]

]. Each technique offers some advantages and, of course, some drawbacks. The main disadvantage of the phase mask is its bandwidth limitation, while the square aperture technique does not make use of all the energy arriving from the planet. The nulling interferometer requires extremely precise control although interferometric techniques offer high spatial resolution with small apertures. Hence, such an instrument could detect Earth-like planets and perform spectroscopic analysis to look for features of water or ozone, which would indicate that the planet supported life. Consequently, here we choose the nulling interferometer, although this does not mean that the other techniques should be discarded. It is worthwhile to perform an analysis of the other techniques similar to that developed here for the nulling interferometer. Thus, the most suitable conditions for each technique could be found. Even, the combination of different techniques should be considered [6

6. P. Nisenson and C. Papaliolios, “Detection of Earth-like planets using apodized telescopes,” Astrophys. J. 548, L201–L205 (2001). [CrossRef]

].

The main advantage of the nulling interferometer is that it allows the detection of light coming from the planet in a pixel where the light from the star is interfering in a destructive way. This is because the nulling interference condition is fulfilled for a particular scientific object, but for a different object this condition does not work. Most of the physical principles upon which a final nuller for exoplanet detection must be based, have already been experimentally validated. Hinz et al. have shown the feasibility of the nulling interferometer to suppress the star diffraction pattern: using images of Betelgeuse, light from an unresolved star almost disappears, while a source 0.2 arcsec apart remains [2

2. P.M. Hinz, J.R.P. Angel, W.F. Hoffmann, D.W. McCarthy, P.C. McGuire, M. Cheselka, J.L. Hora, and N.J. Woolf, “Imaging circumstellar environments with a nulling interferometer,” Nature 395, 251–253 (1998). [CrossRef]

]. Wallace et al. have achieved a deep and stable nulling of broadband thermal light [7

7. K. Wallace, G. Hardy, and E. Serabyn, “Deep and stable interferometric nulling of broadband light with implications for observing planets around nearby stars”, Nature 406, 700–702 (2000). [CrossRef] [PubMed]

].

We choose a scheme with two telescopes co-mounted on a rigid frame pointed at a star, with no need for path equalization. Although there are more complex configurations, such as that proposed by Angel to achieve good star suppression even when a long baseline is required (because the planet is close to the star or due to the use of IR wavelengths) [1

1. J.R.P. Angel and N.J. Woolf, “An imaging nulling interferometer to study extrasolar planets,” Astrophys. J. 475, 373–379 (1997). [CrossRef]

], our analysis of the dark speckle technique can be easily generalized for any configuration.

2. System gain

The technique consists of detecting the probability of zero counts in every pixel of the whole image plane. Deviations of the expected zero-count Probability Distribution will indicate the presence of a planet. The algorithm described by Labeyrie consists of the generation of a dark map by counting, in each pixel, the number of short exposures that contribute zero photons. As these contributions are accumulated in the dark map, a planet’s Airy peak is expected to emerge as a black dot among background noise. To obtain an image, the negative of these results can be displayed. Actually, the planet peak has a size comparable to a speckle and therefore contains several pixels. The optimal value of the number of pixels per speckle, j, to achieve very low-light-level detection, is j=0.62 R/G, where G is the system gain [9

9. A. Bocaletti, A. Labeyrie, and R. Ragazzoni, “Preliminary results of dark-speckle stellar coronography,” Astron. Astrophys. 338, 106–110 (1998).

].

It is possible to develop a simple model to predict the behavior of the Dark Speckle technique applied to an image obtained by a nulling interferometer. Let us consider two identical telescopes observing the same scientific object. In both telescopes the same compensation level is obtained using the corresponding adaptive optics system. Thus, each telescope would produce an image composed of a coherent Airy pattern plus an incoherent speckled halo. The energy at the coherent peak is a factor exp(-σϕ2) of the total energy [10

10. V.F. Canales and M.P. Cagigal, “Gain estimate for exoplanet detection with adaptive optics,” Astron. Astrophys. Suppl. Ser. 145, 445–449 (2000). [CrossRef]

], where σϕ2 is the average residual phase variance in the corrected wavefront, that can be obtained from experimental measurements [11

11. M.P. Cagigal and V.F. Canales, “Residual phase variance in partial correction: application to the estimate of the light intensity statistics,” J.Opt. Soc. Am. A. 17, 1312–1318 (2000). [CrossRef]

]. The energy at the halo is (1-exp(-σϕ2)) of the total energy. In these conditions, fields coming from both telescopes are superimposed to produce an interferometric image. The coherent part of the electromagnetic field interferes and the star diffraction pattern vanishes. However the incoherent halo intensities are added, giving a residual halo twice the halo at a single telescope.

The system gain is the key parameter for describing the system performance and for comparing with other techniques. In the nulling interferometer it can be defined as the ratio between twice the intensity at the core in each of the single telescopes and the residual intensity at the halo of the nulling interferometer. Consequently, the gain provided by the nulling interferometer is the same as the gain between the core and halo in each single telescope [10

10. V.F. Canales and M.P. Cagigal, “Gain estimate for exoplanet detection with adaptive optics,” Astron. Astrophys. Suppl. Ser. 145, 445–449 (2000). [CrossRef]

]:

GNI=2IcoreTELIhaloNI=(Dlc)2exp(σϕ2)(1exp(σϕ2))
(1)

where lc is the correlation length, and is a function of the number of actuators, a, of the compensating system, lc =0.286- a -0.362 D, and (D/lc )2 is the number of speckles [12

12. M.P. Cagigal and V.F. Canales, “Generalized Fried parameter after adaptive optics partial wave-front compensation,” J.Opt. Soc. Am. A. 17, 903–910 (2000). [CrossRef]

]. This is a meaningful gain definition for exoplanet detection, because the planet light does not interfere destructively, as is the case for starlight.

For the task of finding extrasolar planets it is usually considered that the adaptive optics system must at least provide a gain of 106 [13

13. J.R.P. Angel, “Ground-based imaging of extrasolar planets using adaptive optics,” Nature 368, 203–207 (1994). [CrossRef]

]. In the visible, this value of the gain is necessary to retain a reasonable value of the number of pixels per speckle j=0.62 R/G [9

9. A. Bocaletti, A. Labeyrie, and R. Ragazzoni, “Preliminary results of dark-speckle stellar coronography,” Astron. Astrophys. 338, 106–110 (1998).

]. This need for a high gain value requires the use of a nulling interferometer to suppress the Airy rings, which would otherwise impede the obtention of such a gain value at the planet location.

3. Signal to noise ratio

Up to this point, we have described the system performance through the gain. From now on, the feasibility of the Dark Speckle technique to detect exoplanets is analyzed. The SNR and the integration time required will be estimated.

PNI(0)=(1+tN*0.62R[1exp(σϕ2)])1
(2)

Now, this technique can be applied to detect a planet close to a star. The probability of zero-counts in pixels without a planet is given by Eq.(2) but in those pixels where a planet appears the zero-count probability is given by P NI(0)P o(0), where P o(0) is the zero-count probability corresponding to the planet. As the Adaptive Optics system provides a high gain, the intensity at the planet PSF core can be considered almost constant. Consequently, the number of photons follows a Poisson distribution. By comparing statistics in pixels with and without a planet, small differences can be detected. The difference function used to detect the planet presence is Dp =P NI(0)-P o(0)

Its SNR can be determined as a function of the number of frames n:6

SNR=(1Po(0))nPNI(0)=N*exp(σϕ2)RtTG0.62R+tN*exp(σϕ2)
(3)

where T is the total integration time. In this equation, it has been taken into account that the planet peak has a size comparable to a speckle and, therefore, contains several pixels, j=0.62R/G, which contribute as if they were independent exposures on a single pixel.6 The dependence of the SNR with the photon flux and with compensation level (through the gain and the residual phase variance) is clear. It is necessary to point out that Eq.(3) represents the behavior of the SNR of the difference function derived for the case of low-light-level. The low-light-level condition means that the probability of detecting zero photocounts in the interferometric image when the star is being detected, P NI(0), must be close to unity, that actually corresponds to the case when searching for extrasolar planets with a nulling interferometer.

4. Discussion and results

From Eq.(3) the number of frames required to detect a faint companion can be derived. In this analysis, we have considered that diffraction pattern vanishes with nulling, but we have not addressed some of the hard problems that arise in ground-based nulling interferometers to achieve the high gain required, with requisite broadband and dual-polarization. Phase equalization of the paths in the interferometer’s arms must be extremely precise and stable, and amplitudes must also be matched to over 0.1%. Several solutions have been proposed for this task [5

5. N. Woolf and J.R.P. Angel, “Astronomical searches for Earth-like planets and signs of life,” Annu. Rev. Astron. Astrophys. 36, 507–537 (1998). [CrossRef]

], but a thorough analysis of them is beyond the scope of this paper. The technological evolution leads us to the assumption that the interferometer will provide a good enough null [1

1. J.R.P. Angel and N.J. Woolf, “An imaging nulling interferometer to study extrasolar planets,” Astrophys. J. 475, 373–379 (1997). [CrossRef]

,5

5. N. Woolf and J.R.P. Angel, “Astronomical searches for Earth-like planets and signs of life,” Annu. Rev. Astron. Astrophys. 36, 507–537 (1998). [CrossRef]

,7

7. K. Wallace, G. Hardy, and E. Serabyn, “Deep and stable interferometric nulling of broadband light with implications for observing planets around nearby stars”, Nature 406, 700–702 (2000). [CrossRef] [PubMed]

].

For visible wavelengths r 0 is rarely greater than 20 cm. If a 10 m telescope assisted by an adaptive optics system with 104 actuators is considered, a 106 gain could be achieved, provided scintillation effects are compensated. This condition on the gain stresses current technology to its limits. The star photon flux per second at this aperture is 1010 ph/s taking q=0.2, 100 nm bandwidth and mν =3. As a consequence, to obtain a SNR=5, with typical values of exposure time of 20 ms, and contrast ratio 109, a total integration time of 3.2 hours is necessary.

In the IR case, for a detection wavelength between 5 and 10 µm the size of the Fried parameter is typically between 3 and 7 m. Hence, it is much easier to build an adaptive optics system with the desired 106 gain. If a bandwidth of 1µm is used, the number of detected photoelectrons from the star is 1012 ph/s. Furthermore, the brightness ratio in the IR is typically smaller than in visible wavelengths. Consequently, the total integration time would be dramatically reduced. However, the actual integration time would be increased because of the thermal noise in the devices and noise from the zodiacal dust. We consider extrazodiacal dust effects negligible, because models of formation of the solar system show that systems with much less dust than ours can be expected, although it would be an important error source for most planetary systems. In spite of these problems, the achievable goals are so relevant, that a great effort to prepare the Dark Speckle technique in the IR should be developed as soon as photon counting detectors are available for wavelengths between 5 and 10 µm.

5. Conclusion

We have shown that cancellation of the star diffraction pattern is required to apply the Dark Speckle technique to direct imaging of exoplanets. From a simple model for the energy distribution in partially compensated images, we have analyzed the behavior of this Speckle technique in a ground-based nulling interferometer assisted by adaptive optics. We conclude that combination of the nulling interferometer and the Dark Speckle technique would allow the ground-based imaging of exoplanets either in the visible, if the technological challenges to achieve the required high gain are solved, or in the IR, if photon-counting detectors for this range of wavelengths are developed.

Fig. 1. Integration time necessary to obtain a SNR=5 as a function of the number of actuators in each adaptive optics system, if the diameter of both telescopes is 10 m and with a total flux from the star of 1010 ph/s. The exposure time is 20 ms. The solid curve corresponds to values of R=109 and D/r 0=50 (visible wavelengths) and the dashed blue curve to value of R=5 108 and D/r 0=2 (mid IR).

Acknowledgments

This work has been supported by the Dirección General de Investigación.

References and links

1.

J.R.P. Angel and N.J. Woolf, “An imaging nulling interferometer to study extrasolar planets,” Astrophys. J. 475, 373–379 (1997). [CrossRef]

2.

P.M. Hinz, J.R.P. Angel, W.F. Hoffmann, D.W. McCarthy, P.C. McGuire, M. Cheselka, J.L. Hora, and N.J. Woolf, “Imaging circumstellar environments with a nulling interferometer,” Nature 395, 251–253 (1998). [CrossRef]

3.

F. Roddier and C. Roddier, “Stellar coronagraph with phase mask,” Publ. Astron. Soc. Pac. 109, 815–820 (1997). [CrossRef]

4.

R.N. Bracewell, “Detecting nonsolar planets by spinning infrared interferometer,” Nature 274, 780–781 (1978). [CrossRef]

5.

N. Woolf and J.R.P. Angel, “Astronomical searches for Earth-like planets and signs of life,” Annu. Rev. Astron. Astrophys. 36, 507–537 (1998). [CrossRef]

6.

P. Nisenson and C. Papaliolios, “Detection of Earth-like planets using apodized telescopes,” Astrophys. J. 548, L201–L205 (2001). [CrossRef]

7.

K. Wallace, G. Hardy, and E. Serabyn, “Deep and stable interferometric nulling of broadband light with implications for observing planets around nearby stars”, Nature 406, 700–702 (2000). [CrossRef] [PubMed]

8.

A. Labeirye, “Images of exo-planets obtainable from dark speckles in adaptive optics,” Astron. Astrophys. 298, 544–548 (1995).

9.

A. Bocaletti, A. Labeyrie, and R. Ragazzoni, “Preliminary results of dark-speckle stellar coronography,” Astron. Astrophys. 338, 106–110 (1998).

10.

V.F. Canales and M.P. Cagigal, “Gain estimate for exoplanet detection with adaptive optics,” Astron. Astrophys. Suppl. Ser. 145, 445–449 (2000). [CrossRef]

11.

M.P. Cagigal and V.F. Canales, “Residual phase variance in partial correction: application to the estimate of the light intensity statistics,” J.Opt. Soc. Am. A. 17, 1312–1318 (2000). [CrossRef]

12.

M.P. Cagigal and V.F. Canales, “Generalized Fried parameter after adaptive optics partial wave-front compensation,” J.Opt. Soc. Am. A. 17, 903–910 (2000). [CrossRef]

13.

J.R.P. Angel, “Ground-based imaging of extrasolar planets using adaptive optics,” Nature 368, 203–207 (1994). [CrossRef]

OCIS Codes
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(350.1260) Other areas of optics : Astronomical optics

ToC Category:
Research Papers

History
Original Manuscript: May 21, 2001
Published: July 2, 2001

Citation
Manuel Cagigal and Vidal Canales, "Exoplanet detection using a nulling interferometer," Opt. Express 9, 36-41 (2001)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-9-1-36


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References

  1. J.R.P. Angel and N.J. Woolf, "An imaging nulling interferometer to study extrasolar planets," Astrophys. J. 475, 373-379 (1997). [CrossRef]
  2. P.M. Hinz, J.R.P. Angel, W.F. Hoffmann, D.W. McCarthy, P.C. McGuire, M. Cheselka, J.L. Hora, N.J. Woolf, "Imaging circumstellar environments with a nulling interferometer," Nature 395, 251-253 (1998). [CrossRef]
  3. F. Roddier and C. Roddier, "Stellar coronagraph with phase mask," Publ. Astron. Soc. Pac. 109, 815-820 (1997). [CrossRef]
  4. R.N. Bracewell, "Detecting nonsolar planets by spinning infrared interferometer," Nature 274, 780-781 (1978). [CrossRef]
  5. N. Woolf and J.R.P. Angel, "Astronomical searches for Earth-like planets and signs of life," Annu. Rev. Astron. Astrophys. 36, 507-537 (1998). [CrossRef]
  6. P. Nisenson and C. Papaliolios, "Detection of Earth-like planets using apodized telescopes," Astrophys. J. 548, L201-L205 (2001). [CrossRef]
  7. K. Wallace, G. Hardy, E. Serabyn, "Deep and stable interferometric nulling of broadband light with implications for observing planets around nearby stars," Nature 406, 700-702 (2000). [CrossRef] [PubMed]
  8. A. Labeirye, "Images of exo-planets obtainable from dark speckles in adaptive optics," Astron. Astrophys. 298, 544-548 (1995).
  9. A. Bocaletti, A. Labeyrie, R. Ragazzoni, "Preliminary results of dark-speckle stellar coronography," Astron. Astrophys. 338, 106-110 (1998).
  10. V.F. Canales and M.P. Cagigal, "Gain estimate for exoplanet detection with adaptive optics," Astron. Astrophys. Suppl. Ser. 145, 445-449 (2000). [CrossRef]
  11. M.P. Cagigal and V.F. Canales, "Residual phase variance in partial correction: application to the estimate of the light intensity statistics," J. Opt. Soc. Am. A. 17, 1312-1318 (2000). [CrossRef]
  12. M.P. Cagigal and V.F. Canales, "Generalized Fried parameter after adaptive optics partial wave-front compensation," J. Opt. Soc. Am. A. 17, 903-910 (2000). [CrossRef]
  13. J.R.P. Angel, "Ground-based imaging of extrasolar planets using adaptive optics," Nature 368, 203-207 (1994). [CrossRef]

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