Angular Differential Imaging: a Powerful High-Contrast Imaging Technique

TL;DR: In this paper, the authors proposed an acquisition strategy and reduction pipeline for speckle attenuation and high contrast imaging is demonstrated to significantly get better detection limits with longer integration times at all angular separations.

Abstract: Angular differential imaging is a high-contrast imaging technique that reduces speckle noise from quasi-static optical aberrations and facilitates the detection of faint nearby companions. A sequence of images is acquired with an altitude/azimuth telescope, the instrument rotator being turned off. This keeps the instrument and telescope optics aligned, stabilizes the instrumental PSF and allows the field of view to rotate with respect to the instrument. For each image, a reference PSF obtained from other images of the sequence is subtracted. All residual images are then rotated to align the field and are median combined. Observed performances are reported for Gemini Altair/NIRI data. Inside the speckle dominated region of the PSF, it is shown that quasi-static PSF noise can be reduced by a factor {approx}5 for each image subtraction. The combination of all residuals then provides an additional gain of the order of the square root of the total number of images acquired. To our knowledge, this is the first time an acquisition strategy and reduction pipeline designed for speckle attenuation and high contrast imaging is demonstrated to significantly get better detection limits with longer integration times at all angular separations. A PSF noise attenuation of 100 was achieved from 2-hourmore » long sequences of images of Vega, reaching a 5-sigma contrast of 20 magnitudes for separations greater than 7''. This technique can be used with currently available instruments to search for {approx} 1 M{sub Jup} exoplanets with orbits of radii between 50 and 300 AU around nearby young stars. The possibility of combining the technique with other high-contrast imaging methods is briefly discussed.« less

Summary

1. Introduction

• Direct detections of very faint exoplanets and brown dwarfs near bright stars are essential to understand substellar formation and evolution around stars.
• Both ground- and space-based imaging are plagued with this stellar PSF calibration problem caused by imperfect optics and slowly evolving optical alignments.
• The Angular Differential Imaging Technique ADI is a PSF calibration technique that can, in principle, suppress the PSF quasi-static structure by a large factor (Marois 2004).
• For each image, a reference PSF obtained from other images in the sequence is subtracted to remove the quasi-static structure.

3. Noise Attenuation Theory with ADI

• For each image of an ADI sequence, a reference PSF has to be built from images of the same sequence.
• Thus this first method minimizes the noise in regions where the residuals are limited by pixel-to-pixel noise.
• The time τmin required for such field rotation is function of the separation angle from the target, the target azimuth A and zenith distance z and the telescope latitude φ.
• For simplicity, if the authors assume a single quasi-speckle source evolving over a single timescale τspeck, the speckle attenuation resulting from the combination of all difference images is function of the PSF speckle evolution timescale τspeck.
• (3) We emphasize that ADI guarantees a gain in detection with increasing observing time for both regimes.the authors.the authors.

4. Observations

• The ADI technique was first used at the Gemini north telescope using the Altair adaptive optic system (Herriot et al. 1998) and NIRI (Hodapp et al. 2000) in queue mode.
• Data for two other stars, HIP18859 and HD1405 will also be discussed for comparison since they have been acquired with a different technique.
• During this sequence, the filter was switched from the broadband H filter to a narrow band filter every fourth exposure to acquire unsaturated images.
• In total, 38 30s exposures were obtained.
• These observations will be used in section 6.3 for a comparison between ADI and classical observations.

5.1. Preliminary Data Reduction

• The data reduction consists of flat field normalization, bad pixel correction using a median over surrounding pixels, and distortion correction using software provided by the Gemini Staff (Trujillo, private communication) and modified to use the IDL interpolate function with cubic interpolation.
• Images were then copied into larger blank images to ensure that no FOV is lost when shifting and rotating images.
• The center of the PSF of the first image of the sequence was then registered to the image center by minimizing the diffraction spikes residuals after subtraction of a 180-degree rotation of the image.
• The rest of the images were then registered by cross-correlation of the diffraction spikes with the first image.
• An azimuthally symmetric intensity profile was finally subtracted from each image – 10 – to remove the smooth seeing halo.

5.2. ADI algorithm

• These two methods can be combined into a single algorithm that optimizes speckle subtraction and minimizes pixel-to-pixel noise.
• First, the median of all the images is subtracted from each individual image.
• An optimized reference PSF (second method) is then obtained for each image by median combining 4 images (two acquired before and two after) that have at least 1.5 λ/D field rotation.
• This choice insures that the average τ of the reference PSF is ∼0.
• Table 2 summarizes the entire ADI reduction algorithm.

6.1. PSF Evolution Time-Scale

• The PSF noise evolution timescale can be studied through the evolution of the noise attenuation [N/∆N ] for the difference of two images as a function of the time interval, τ .
• This step is necessary to prevent biasing the noise estimate N of single images and leaves only speckles that have a spatial scale of the order of λ/D. Images were subtracted two by two with increasing time interval.
• The stronger noise attenuation achieved on Vega and HD97334B for short time intervals could be explained by better seeing that stabilizes the structure and enables a better subtraction.
• This evolution of the PSF structure is probably due to the filter wheel not returning to its exact position after each change.

6.2. Contrast Performances

• Fig 3 shows for all ADI targets the noise attenuations [N/∆N ]S achieved in average for each image differences and the one obtained [N/∆N ] after median combining all image difference.
• Again, a 25×25 pixels unsharp mask and a 4×4 pixels median filter were applied to each image to produce this figure.
• To their knowledge, this is the first time that such behavior is clearly demonstrated for an acquisition and reduction technique designed for speckle attenuation.
• Fig. 4 shows detection limits (5σ) in magnitude difference as a function of angular separation obtained with the ADI technique for all three ADI targets.

6.3. Comparison between ADI and Classical Observations

• In the previous sections it was shown that the ADI technique can achieve high contrast given a sufficiently long integration time and good PSF stability.
• To compare the performances of ADI and classical observations the authors analyze the first 38 images of the HD97334B ADI sequence and the 38 images of the HD1405 “classical” sequence.
• For this analysis, both data sets have been reduced according to section 5.1. – 15 – An increasing number of images (differences for HD97334B) of both sequences were median combined to study the noise attenuation as a function of the total observing time at 2′′, the results are presented in Fig.
• For this example, ADI achieves 4 times better noise attenuation, it is thus at least 16 times more efficient.

7. Discussion

• ADI is a general high-contrast imaging technique that can be applied to any existing or upcoming large altitude/azimuth telescope.
• ADI performances at small separations (< 1′′) require long time intervals and thus suffer from important PSF variations that prevent good quasi-static speckle attenuations.
• It has been – 16 – shown that such instruments are ultimately limited by non-common path aberrations, which are expected to be stable over long periods of time as they come almost entirely from the instrument itself (Marois et al. 2005).
• Even a very good coronagraph cannot totally suppress the light from uncorrected quasistatic wavefront errors and some level of quasi-static speckle noise will inevitably be present in coronagraphic observations.
• Ideally, all the techniques mentioned above, ADI, SSDI, high-order AO and coronag- raphy, could be used together to form an extremely powerful tool to detect exoplanets and brown dwarfs around stars.

8. Conclusion

• The ADI observing technique was described and its performance using Altair/NIRI at Gemini were presented.
• The stability of the PSF plays a crucial role in ADI as it not only determines the speckle attenuation from the reference image subtraction but it also determines the regime in which the noise is attenuated with increasing observing time.
• Finally, ADI could easily and advantageously be combined with SSDI, high-order AO and coronagraphy to improve the detection limits of exoplanets and brown dwarfs at all separations.
• The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian community.
• This work is supported in part through grants from the Natural Sciences and Engineering Research Council, Canada and from the Fonds Québécois de la Recherche sur la Nature et les Technologies, Québec.

Figures

Table 2: ADI Data Reduction Algorithm

Fig. 1.— Interval of time required for a point source to move by 1 λ/D (1.6µm on a 8-m diameter telescope) at 1′′ as a function of hour angle for various declinations. Calculated for Mauna Kea, Hawaii.

Fig. 5.— Vega (August 26th) ADI data reduction. A: A single image after flat field normalization, bad pixel correction, distortion correction, registering and removal of an azimuthally symmetric profile. FOV is 22′′ × 22′′ using a linear intensity range of ±10−6 from the estimated PSF peak intensity. B: A single ADI difference image shown with the same intensity range. C: same as B with an intensity range 25 times smaller. D: The final combination of all ADI differences shown with the same intensity range as C.

Fig. 4.— Detection limits (5σ) as a function of angular separation for HD18803, HD97334B and Vega (August 26th). The three curves are bended upward for separations greater than 9′′ due to the Altair anisoplanatism correction.

Fig. 3.— Single ADI difference [N/∆N ]s and total ADI [N/∆N ] noise attenuations with separation for HD97334B, HD18803 and Vega. Dotted lines show attenuation from a single ADI difference while solid lines show the attenuation after median combining all ADI differences. The bottom panel shows the attenuation ratio of a single ADI difference SD and the one obtained from combining all ADI differences ADI divided by the square root of the total number n of images in each sequence.

Fig. 2.— Noise attenuation obtained by subtracting images two by two with increasing time interval for HD97334B, HD18803 and Vega acquired on the 26/08/04 and on the 01/09/04. Solid, dashed, dot-dashed and tripe dot-dashed lines are for 2′′, 4′′, 6′′ and 8′′ respectively. For Vega, there is no solid line for 2′′ since images are saturated at that separation. Small lines show the estimated noise attenuation limit imposed by photon, sky, read and dark noises.

Table 1: Observations

Fig. 6.— Normalized noise attenuation from the median combination of an increasing number of images (differences in the ADI case) at 2′′ separation. The dotted and dashed lines are respectively for the ADI reduction and the HD1405 without field rotation sequence. See section 6.3 for more details.

Full text

UCRL-JRNL-216949
Angular Differential Imaging: a
Powerful High-Contrast Imaging
Technique
C. Marois, D. Lafreniere, R. Doyon, B. Macintosh,
D. Nadeau
November 9, 2005
Astrophysical Journal

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Angular Differential Imaging: a Powerful High-Contrast Imaging
Technique
1
Christian Marois
2,3
, David Lafreni`ere
2
,Ren´eDoyon
2
, Bruce Macintosh
3
,
Daniel Nadeau
2
2
D´epartement de physique and Observatoire du Mont M´egantic, Universit´edeMontr´eal,
C.P. 6128, Succ. A,
Montr´eal, QC, Canada H3C 3J7
3
Institute of Geophysics and Planetary Physics L-413,
Lawrence Livermore National Laboratory, 7000 East Ave, Livermore, CA 94550
cmarois@igpp.ucllnl.org david@astro.umontreal.ca doyon@astro.umontreal.ca
bmac@igpp.ucllnl.org nadeau@astro.umontreal.ca
ABSTRACT
Angular differential imaging is a high-contrast imaging technique that reduces
speckle noise from quasi-static optical aberrations and facilitates the detection
of faint nearby companions. A sequence of images is acquired with an alti-
tude/azimuth telescope, the instrument rotator being turned off. This keeps the
instrument and telescope optics aligned, stabilizes the instrumental PSF and al-
lows the field of view to rotate with respect to the instrument. For each image,
a reference PSF obtained from other images of the sequence is subtracted. All
residual images are then rotated to align the field and are median combined.
Observed performances are reported for Gemini Altair/NIRI data. Inside the
speckle dominated region of the PSF, it is shown that quasi-static PSF noise
can be reduced by a factor ∼5 for each image subtraction. The combination of

–2–
all residuals then provides an additional gain of the order of the square root of
the total number of images acquired. To our knowledge, this is the first time an
acquisition strategy and reduction pipeline designed for speckle attenuation and
high contrast imaging is demonstrated to significantly get better detection limits
with longer integration times at all angular separations. A PSF noise attenuation
of 100 was achieved from 2-hour long sequences of images of Vega, reaching a 5-
sigma contrast of 20 magnitudes for separations greater than 7
00
. This technique
can be used with currently available instruments to search for ∼ 1M
Jup
exoplan-
ets with orbits of radii between 50 and 300 AU around nearby young stars. The
possibility of combining the technique with other high-contrast imaging methods
is briefly discussed.
Subject headings: Instrumentation: AO - planetary systems - stars: imaging
Suggested running page header: Angular Differential Imaging
1. Introduction
Direct detections of very faint exoplanets and brown dwarfs near bright stars are essential
to understand substellar formation and evolution around stars. This endeavor is now one
of the major goals for next generation 10-m telescope instruments and future 30- to 100-m
telescopes. The task is dauntingly difficult. The exoplanet or brown dwarf image is usually
1
Based on observations obtained at the Gemini Observatory, which is operated by the Association of
Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the
Gemini partnership: the National Science Foundation (United States), the Particle Physics and Astronomy
Research Council (United Kingdom), the National Research Council (Canada), CONICYT (Chile), the
Australian Research Council (Australia), CNPq (Brazil) and CONICET (Argentina).

–3–
much fainter than the background from the brilliant stellar point spread function (PSF)
image. Besides the Poisson noise limit, ground-based telescopes suffer from atmospheric
turbulence that produces random short-lived speckles that mask faint companions. If these
two limitations were the only ones, a simple solution would be to integrate longer to average
these random noises and gain as the square root of the integration time. But observations
have shown that, for integrations longer than a few minutes, the PSF noise converges to a
quasi-static noise pattern, thus preventing a gain with increasing integration time (Marois et
al. 2003, 2005; Masciadri et al. 2005). To achieve better detection limits, it is thus necessary
to subtract the quasi-static noise using a reference PSF. Both ground- and space-based
imaging are plagued with this stellar PSF calibration problem caused by imperfect optics
and slowly evolving optical alignments. For ground-based imaging, subtraction of a reference
PSF obtained from a star close to the target achieves a factor ∼ 4 of PSF noise attenuation,
leaving residuals that are also quasi-static and thus severely limiting detection of fainter
companions (Marois et al. 2005). For space telescopes that have a better PSF stability,
like HST, a partial solution was found by subtracting two stellar images acquired during the
same orbit with a different roll angle. This technique, called “roll deconvolution”, successfully
subtracts the stellar image by a factor 50 (Schneider & Silverstone 2003) but is also ultimately
limited by PSF evolution. A similar technique, called angular differential imaging (ADI),
can be used on ground-based altitude/azimuth telescopes to subtract a significant fraction
of the stellar quasi-static noise and can potentially achieve detection limits that improve as
the square root of the integration time.
In this paper, the ADI technique is described and its performances is analyzed using a
simple analytical model and Gemini Altair/NIRI data. The PSF stability with Altair/NIRI
is studied and its impact on ADI performances is discussed. Detection limits for three stars
of our ongoing young nearby star survey are then shown. A comparison between ADI and
classical observations is also presented. Finally, the possibility of using ADI with other

Frequently asked questions

Q1. What are the contributions in "Angular differential imaging: a powerful high-contrast imaging technique" ?

In this paper, the angular differential imaging ( ADI ) was used to detect the stellar point spread function ( PSF ) of a star close to the target. 

Q2. What is the noise attenuation of the reference PSF?

The noise attenuation obtained by the subtraction of the reference PSF, [N/∆N ]S (θ, τ, texp),is a function of the angular separation, θ, the time interval τ between the original and the reference image and the individual image exposure time texp (neglecting overheads). 

Q3. What did the ADI technique remove the low-frequency spatial noise?

No unsharp masks were used for the ADI reduction since multiple tests have showed that even if they removed the low-frequency spatial noise, they did not increase candidates S/N and were slightly biasing the photometry. 

Q4. How does the ADI technique attenuate the noise of a difference image?

The ADI technique attenuates the PSF noise in two steps: (i) by subtraction of areference image to remove correlated speckles and (ii) by the combination of all residual images after FOV alignment to average the residual noise. 

Q5. Why is the noise attenuation in the first regime decorrelated?

In the first regime, the residuals of consecutive image differences are decorrelated, eitherbecause the correlated structure of the PSF which lasts for long times has been removed, leaving only Poisson noise, or because the PSF structure was already uncorrelated between consecutive images in the first place. 

Q6. What is the way to improve the stability of the PSF?

Future high-contrast instrumentation for 8-10 m class or larger telescopes based onhigh-order adaptive optics (AO) systems (Macintosh et al 2004; Mouillet et al. 2004) will most likely improve the stability of the PSF. 

Q7. What is the effect of the frequent filter change on speckles?

12 –Analysis of the HIP18859 data set that included a frequent filter change to acquireunsaturated images shows that a drop by a factor of 2 in speckle attenuation occurs following each filter change. 

Q8. How many MJups are obtained for Vega?

Both HD18803 and HD97334B achieve detection limits of 1-2 MJup at 3 ′′ (60 AU for both targets), while ∼3 MJup is obtained for Vega at 7′′ (55 AU). 

Q9. How much noise is decorrelated between residual images?

It was shown that the gain in S/N with increasing total observing time for separation greater than 2′′ reaches more than 70% of the optimal case, indicating that the noise is mostly decorrelated between residual images for these separations. 

Q10. What is the explanation for the noise attenuation on Vega?

The stronger noise attenuation achieved on Vega and HD97334B for short time intervals could be explained by better seeing that stabilizes the structure and enables a better subtraction. 

Q11. How much noise is the second method for constructing the reference PSF?

The second method is to take the median of only a few images as close in time as possiblebut for which the displacement due to field rotation at a given separation is at least 1.5 PSF FWHM. 

Q12. What is the noise attenuation of the unsaturated PSF and residual images?

Both the unsaturated PSF and residual images are convolved by an aperture of diameter 2 PSF FWHM prior to this calculation; the unsaturated PSF is also flux normalized to account for exposure time differences. 

Q13. What is the funding for this work?

This work is supported in part through grants from the Natural Sciences and Engineering Research Council, Canada and from the Fonds Québécois de la Recherche sur la Nature et les Technologies, Québec. 

Q14. What was the filter used to acquire unsaturated images?

During this sequence, the filter was switched from the broadband H filter to a narrow band filter every fourth exposure to acquire unsaturated images. 

Q15. What is the noise attenuation function of the PSF?

For simplicity, if the authors assume a single quasi-speckle source evolving over a single timescaleτspeck, the speckle attenuation resulting from the combination of all difference images is function of the PSF speckle evolution timescale τspeck. 

Q16. What is the timescale of the noise evolution of the PSF?

11 –The PSF noise evolution timescale can be studied through the evolution of the noiseattenuation [N/∆N ] for the difference of two images as a function of the time interval, τ . 

Q17. What is the timescale of the noise evolution of the PSF?

11 –The PSF noise evolution timescale can be studied through the evolution of the noiseattenuation [N/∆N ] for the difference of two images as a function of the time interval, τ . 

Q18. How does the noise attenuation for Vega compare to the detector?

HD97334B and HD18803 noise attenuations are shown to improve at all separation down to the detector saturation limit and clearly below it if the authors extrapolate the performances shown at 0.7′′.