Abstract

The evanescent wave coronagraph (EvWaCo) is a specific kind of band-limited coronagraph using the frustrated total internal reflection phenomenon to produce the coronagraphic effect (removing starlight from the image plane in order to make the stellar environment detectable). In this paper, we present a theoretical and experimental study of the EvWaCo coronagraphic mask. First, we calculate the theoretical transmission and we show that this mask is partially achromatic. Then, we present the experimental results obtained in unpolarized light at the wavelength λ≈900 nm and relative spectral bandwidth Δλ/λ≈6%. In particular, we show that the coronagraph provides a contrast down to a few 10−6 at an angular distance of about ten Airy radii.

© 2017 Optical Society of America

1. Introduction

The small-angle coronagraphs dedicated to the direct detection and characterization of exoplanets can be classified in three main families: the improvement on the Lyot coronagraph with amplitude or phase masks, the phase and amplitude pupil apodization and the interferometers. The advantages and the drawbacks of each family of coronagraph have been intensively discussed in detail in previous papers [1,2]. One efficient improvement of the Lyot coronagraph is the so-called “Band-limited coronagraph” [3] that consists of placing in the image plane an amplitude mask with a transmission specifically designed to achieve as complete as possible an elimination of the on-axis light, while simultaneously maximizing the transmission for the stellar environment. The difficulties are to manufacture a circularly-symmetric mask with the appropriate transmission profile with minimum defects and discretization effects [4]. In particular, the fabrication errors induce a difference between the theoretical and the effective profile of the mask transmission as well as a spurious phase error that could degrade the performance [5].

In this paper, we propose an innovative coronagraphic mask for the “Band limited coronagraph” that consists of masking the center part of the stellar image (or Point Spread Function, PSF in the following) by relying on the Frustrated Total Internal Reflection (FTIR) phenomenon [6] to separate the light from the star placed on-axis and the light from an off-axis companion. The” mask” is made of a right angle prism and a glass medium, such as a single convex lens, put in contact. The concept of such a coronagraph was proposed by one of us in 2003 [7] and has been called the Evanescent Wave Coronagraph “EvWaCo”. This system is in principle partially achromatic since the working diameter (occulting diameter) of the mask increases with the wavelength. Another interesting property is that the starlight remains available, for example to sense the wavefront at the mask (for example to correct for tip-tilt effect) and/or to apply some “lucky imaging” algorithms [8].

This paper presents the characteristics and the preliminary performance of the simplest form of the Evanescent Wave coronagraph that involves a spherical surface put in contact with the diagonal face of a right-angle prism to produce the coronagraphic effect. In this case, the transmission of the occulting mask is gaussian and the coronagraph is not purely “band-limited”. However, this simple version demonstrates that the gap between two surfaces can be used to create an efficient coronagraphic mask. More efficient profiles could be properly designed and tuned to get the optimized transmission shapes corresponding to the so-called “4th order band limited coronagraph, BL4” and “8th order band limited coronagraph, BL8” [3] as discussed in the conclusion of the present paper. Furthermore, it was demonstrated in a previous published paper that the contrast obtained by using a mask with a gaussian transmission are significantly better than the contrast obtained with a classical Lyot “Top Hat” coronagraph [9].

In section 2 we describe the generic principle underlying the proposed concept and we introduce the mask theoretical properties. In particular, we show that the mask transmission profile, is nearly gaussian. In section 3 we present the setup used to verify the capability of the mask to efficiently eliminate the central area of a PSF over a disk which radius covers a few Airy radii. First, we present the results of the mask profile measurement that confirm the theoretically expected ones. In particular, we show that i) the attenuation profile is close to a gaussian, ii) the active area of the mask covers a few Airy rings and iii) the on-axis attenuation of the mask is fainter than 10−5. Second, we present the results obtained by placing, as usually done, a Lyot stop with a diameter equal to 55% of the pupil diameter: namely, a contrast C ≈3x10−6 at a distance of roughly 10 λ/D is obtained with unpolarized light at the wavelength λ = 880 nm with a relative spectral bandwidth Δλ/λ ≈6%. In section 4, we discuss the performance we have obtained. First, we discuss the optimal mask design and we analyze the fundamental limitation of the proposed approach. Then, we compare the performance with an existing coronagraph and finally, we discuss the possibility to use the proposed system to monitor and control the low order aberrations of the wavefront incident on the coronagraphic mask.

2. Mask theoretical reflection

2.1 Generic principle

The principle is inspired by the historical Newton’s rings and by the tunneling effect for evanescent waves. The on-axis beam from a telescope (Fig. 1) is focused on the oblique face inside of a prism of glass at such an incidence that the beam undergoes a total reflection on this face, unless a glass medium is placed in contact at the focus and allows the beam to be transmitted by means of captured evanescent waves (FTIR phenomenon). Besides, total reflection applies for an off-axis beam as soon as an air gap is set, in giving an appropriate shape (curvature for example) to the medium placed in contact (see Figs. 1 and 2). Thus, respective beams from the star and its companion can be separated, and the couple prism-medium acts as a rejecting mask.

 figure: Fig. 1

Fig. 1 Illustration of EvWaCo coronagraphic mask generic principle.

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 figure: Fig. 2

Fig. 2 EvWaCo mask principle. O is the point of contact between PMask and LMask and h(x,y) is the air thickness in the mask. The reflection and transmission coefficients of the mask, in intensity are denoted as R and T respectively.

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2.2 The model

The mask appearing in Fig. 2 comprises a prism PMask and a plano-convex lens LMask. The on-axis beam is focused on O, point of contact between PMask and the apex of LMask and is transmitted. Since the air thickness in the mask is increasing away from the point of contact and the total reflection process depends on both the air thickness and the wavelength (the larger the wavelength, the farther from contact it works) we have a kind of self-adaptation of the mask to the wavelength, so that we nearly have an achromatic rejection process.

In the diffraction-limited regime, the diameter DPSF of the Point Spread Function (PSF) at point O in a plane perpendicular to the optical axis is:

DPSF2.44×λ×F#

Where λ is the wavelength and F# is the aperture number of the beam incident on PMask. In the case of our setup (described in section 3) we use λ ≈880 nm and F# ≈37 that yields DPSF ≈80 μm. So, the size of the PSF is much larger than the wavelength, thus allowing the used approach. We have calculated the mask transmission by applying locally the reflection coefficient of the FTIR phenomenon [6] in the case of a thin, homogeneous air gap of optical index n2 between two glasses of optical indices n1 and n3 (Fig. 3).

 figure: Fig. 3

Fig. 3 Model of EvWaco mask for the calculation of the coefficient of reflection in intensity. The glass medium LMask is represented by a succession of thin, homogeneous air gap of optical index n2 between two glasses of optical indices n1 and n3.

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In this model, the angle between the incident star beam chief ray and the normal to the hypotenuse is equal to 45°. This angle is a critical parameter that is involved in the calculation of the amplitude and phase reflection coefficients and in the shape of the mask projected on the PSF. For this reason, the model is valid only close to the optical axis and for small aperture numbers where the angle of incidence is close to 45°.

In our case, the maximum distance from the PSF center is equal to 1 mm at the focal plane of an optics with a focal length of 300 mm. This correspond to a 0.2° variation of the angle of incidence on the prism. Since the beam aperture is equal to F# ≈40, the corresponding beam cone semi-angle is equal to 0.8°. Hence, we have considered that the proposed model can be used to calculate at first approximation the properties of the occulting mask involved in our setup.

We consider two axes in the plane of the oblique face of the prism, OX in the plane of incidence and OY perpendicular, where O is the contact point (coordinates 0, 0) as represented in Fig. 3 and Fig. 4. A running point denoted by M over the hypotenuse of the prism has coordinates (x, y), and the air-gap, h(x, y), seen by M, is measured perpendicular to the hypotenuse. We denote n1, n2 and n3 as the refractive indices of PMask, air, and LMask, respectively. The angle of incidence on the prism hypotenuse is denoted Φ1. The expression of the reflection coefficient is [6]:

 figure: Fig. 4

Fig. 4 Left-side: PMask, OX in the plane of incidence and OY perpendicular. The footprint of the PSF on PMask hypotenuse is represented in yellow. The PSF beam footprint is larger by a factor equal to 21/2 along the OX axis due to the angle of incidence of the beam being equal to 45°. Right-side: close-view of the coronagraphic mask that comprises the prism PMask and the lens LMask. This lens is glued on a prism that transmits the starlight as represented in Fig. 10.

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R(x,y,λ)=11αsinh2[(2πh(x,y)/λ)(n12sin2ϕ1n22)1/2]+β

Where α and β are the coefficients defined in (Zhu et al., 1986) [6] that depend on the incident polarization and on the refraction indices. The evolutions of the reflection coefficients, R and R//, corresponding to the polarization perpendicular and parallel to the plane of incidence, respectively, with respect to h are represented on Fig. 5. We notice that R and R// vary from 0 at h = 0 when the two glass medium are in contact (beam fully transmitted by the FTIR phenomenon) to 1 at h ≈1 μm (total reflection). We also notice that the variations of R and R// are different and that the coronagraph performance may be polarization dependent as discussed in section “2.3.1 Polarization effects”.

 figure: Fig. 5

Fig. 5 Variation of the reflection coefficients R and R// corresponding to the polarization perpendicular and parallel to the plane of incidence, respectively. This is the case for a thin, homogeneous air gap of thickness, h, delimited by two identical glass media made of BK7. We have used the wavelength λ = 880 nm, n1 = n3≈1.51 (BK7 optical index) and n2 = 1.

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2.3 Mask reflection coefficients

Figure 6 shows the mask theoretical reflection factors, R// and R, for the polarizations parallel and perpendicular to the plane of incidence, respectively, versus the “y” coordinate. We have considered in this case that LMask is a convex lens of material N-BK7 and of radius of curvature RC = 15.5 mm. The expression of the air thickness is thus:

 figure: Fig. 6

Fig. 6 PSF irradiance distribution and EvWaCo mask theoretical reflection coefficients R// and R along the Y axis at x = 0 for λ = 880 nm, Φ1 = 45°, n1 = n3 = 1.51 (N-BK7) and n2 = 1 (air). We have also represented the Full Width at Half Maximum, FWHM// and FWHM, of the mask.

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h(x,y)(x2+y2)/2.RC

We have also represented in Fig. 6 the PSF at the point O (0,0) in a plane perpendicular to the optical axis. Let us mention that the angle between the optical axis and (OX) is equal to 45°. Along (OX), the PSF amplitude distribution is thus dilated by a factor 21/2 (Fig. 4) while the shape of the LMask remains identical. We thus deduce that the projection of the mask on the PSF is asymmetrical and smaller by a factor 21/2 along the X axis. We notice on Fig. 6 that the mask reflection coefficients vary continuously from 0 at the PSF center to 1 at Y ≈+/− 200 μm with a rather smooth profile” and incidentally provides an apodization of the point spread function also shown (dotted line). Since DPSF ≈80 μm, we deduce that the Inner Working Angle (IWA) of this kind of coronagraph is roughly of a few elements of resolution.

2.3.1 Polarization effects

We notice on Fig. 6 that the reflection coefficients are unequal for the two polarizations. In particular, the Full Width at Half Maximum (FWHM) of the mask reflection are FWHM// ≈200 μm and FWHM ≈168 μm. We thus deduce that the mask slightly polarizes the reflected wave and the contrast depends on the polarization. However, the values we have obtained in unpolarized light are encouraging and indicate that the impact of this effect on the performance is likely to be negligible.

Let us note that the proposed mask induces a spatial variation of the phase of the reflected wave. We have calculated at the point M(x,y) the expression of the delay Φr at reflection on the mask by using the expression of the reflected amplitude as presented in (Zhu et al., 1986) [6]. In Fig. 7, we show the variation of phase delays, δΦ and δΦ//, with respect to the distance to the optical axis along the Y at the wavelength λ = 880 nm. We notice that δΦ varies between –π/2 and -π/5 rad, representing a significant variation of the phase delay over the mask active surface. We also notice that the spatial variation of δΦ// is less extended varying between –π/2 and −0.45 π.

 figure: Fig. 7

Fig. 7 Variation of the phase delays δΦ// and δΦ at reflection on the EvWaCo mask for the polarizations respectively parallel and perpendicular to the incident plane at the wavelength λ = 880 nm.

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We deduce that the mask induces a birefringence on the reflected wave that varies over the active area of the mask. We assess that the potential impact of this birefringence spatial variation on the wave propagation is to modify the distribution of irradiance in the Lyot stop plane thus modifying the contrast performance and/or the throughput. This effect will be studied in details during the next steps of the setup development by measuring the pupil plane irradiance distributions and the starlight extinctions in polarized and unpolarized light.

2.3.2 Chromatic variation of the mask reflection coefficient

Figure 8 shows the variation of the coefficients of reflection of the coronagraph at the two wavelengths, λ1 = 800 nm and λ3 = 1 μm. We have also represented the Full Width at Half Maximum FWHM(λ1) and FWHM(λ3) at these wavelengths. We notice that FWHM(λ1) is slightly larger than FWHM(λ3) and we thus observe that the dimension and the shape of the active area of the mask vary with the wavelength as expected. In Fig. 9, the variation of the FWHM versus λ and the variation of the diameter of the Airy disc are shown. We notice that: i) the mask FWHM increases almost linearly with λ over the full spectral band [0.4 μm, 1 μm], and ii) the slopes of the mask FWHM and of the Airy diameter spectral variations are identical. Thus both the active area and the Airy pattern are nearly matched at every wavelength and this illustrates the self-adaption capability of the system and a quasi-achromatization of the mask response.

 figure: Fig. 8

Fig. 8 EvWaCo mask theoretical reflection coefficients R(λ1) and R(λ3) at the wavelengths λ1 = 0.8 μm and λ3 = 1 µm. We have also represented: the PSF irradiance distribution cross-section along the Y axis at the wavelength λ2 = 0.9 μm.

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 figure: Fig. 9

Fig. 9 Variations versus the wavelength of the FWHM (blue curve) and of the Airy disk diameter (red curve) for the EvWaCo mask in unpolarized light.

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3. The setup and results

3.1 The setup

The experimental setup used to measure the characteristics of the mask and the contrast performance is composed of a point-like source to mimic the star, a collimator to make a parallel beam on-axis, a focusing lens, a right angle prism of glass, a plano-convex lens (for frustration of the total reflection) and a train of relay optics to form an image on the camera.

The source is composed of a fiber-coupled LED from Thorlabs (Model M880F2) of central wavelength λ ≈900 nm and relative bandwidth Δλ/λ ≈6%. This source injects the light inside a single-mode optical fiber. The fiber output end is placed on an XYZ translation stage to accurately locate the exit face at the focus of the lens L1. The light collimated by L1 passes through the aperture stop (AS) of diameter DAS = 8 mm. The lens L2 forms the image of AS at infinity and focuses the beam on the mask (described hereafter) which transmits the on-axis beam (star) and reflects an off-axis beam (companion). The beam reflected by the mask is then reflected by the mirrors, M1 and M2. These mirrors are used to adjust the direction and the transverse position of the beam reflected by the mask.

The beam reflected by M1 and M2 is collimated by the lens L3 and reflected by the mirror M3 toward the camera through the Lyot stop. The beam transmitted by the Lyot stop is reflected by the mirror M4 and focused by the lens L4 on an Apogee U9000 camera cooled at the temperature TCCD = −14°C with a pixel size equal to 12 μm. The experimental setup is shown in Fig. 10 and Fig. 11.

 figure: Fig. 10

Fig. 10 Optical setup used for the demonstration of principle of the proposed coronagraphic mask.

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 figure: Fig. 11

Fig. 11 Photograph of the setup optical components comprised between L2 and L3. The coronagraphic mask separates the incident beams in two distinct beams: the “star beam” transmitted by the mask and the “companion beam” reflected by the mask.

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3.2 Spatial variation of the mask reflection coefficient

We have measured the spatial variation of the mask reflectivity by placing a white screen between the exit end of the optical fiber and the lens L1, and by illuminating the screen with another optical fiber, thus producing a flat-field illumination of the coronagraphic mask. It is important to precise that this screen has been positioned at 300 millimeters from the source fiber exit end to ensure that the screen surface is not directly imaged on the camera. In Fig. 12, we represent the image of the illuminated mask obtained at the wavelength λ = 880 nm (left-side) and the cross-sections along the X and the Y axes (right-side).

 figure: Fig. 12

Fig. 12 Image of the coronagraphic mask (left) and normalized transmission profile of the mask along the X and the Y axes (right). The data have been acquired by performing a flat-field illumination at the wavelength λ = 880 nm with relative spectral bandwidth Δλ/λ ≈6% in unpolarized light.

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The normalization consists of setting the maximum and the minimum values of the mask reflectivity equal to 1 and to 0 respectively. Indeed, the on-axis and off-axis PSF profiles presented in the next paragraph demonstrate that the on-axis mask reflectivity is lower than 10−5 and can be neglected in the present analysis. We notice that the mask reflectivity profile is close to the theoretical prediction represented in Fig. 6. The FWHM of the mask along the X and the Y axes are equal to FWHMX ≈280 μm (8 λf2/D) and FWHMY ≈380 μm (11 λf2/D) that is larger than the predicted FWHM of the mask which should be around 200 μm along the Y axis.

We attribute this enlargement to the pressure applied by LMask on PMask that increases the contact area with a size that is in the 200 μm range. It is also important to notice that the ratio FWHMX/FWHMY is thus equal to 1.4 that is in very good agreement with the theoretical expectation that predicts a ratio of 1.4.

3.3 On-axis and off-axis PSF profiles without a Lyot stop

We have represented on Fig. 13 the irradiance distribution of the on-axis PSF centered on the mask. In Fig. 14 we show the PSF irradiance cross sections along the X and Y axes respectively. We notice that the mask blocks the light of the PSF central section as expected (cf section “3. Mask theoretical reflection”). We notice that the profile of the PSF centered on the mask is asymmetrical: the diffraction rings seem to be slightly distorted and that, far from the center of the coronagraphic mask, the irradiance distribution is not uniform.

 figure: Fig. 13

Fig. 13 On-axis PSF irradiance distribution centered on the mask in unpolarized light. This image has been acquired at the wavelength λ = 880 nm with a relative spectral bandwidth λ ≈6% with an integration time Δτ = 3s. We attribute the PSF irradiance profile asymmetries to the presence of contaminants between LMask and PMask, to the optical aberrations of the optical system and to the stray light effects.

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 figure: Fig. 14

Fig. 14 PSF normalized irradiance profiles along the X (left-hand side) and along the Y axis (right-hand side). The blue curves represent the cross-section of the PSF profile in the case of an on-axis source centered on the coronagraphic mask. The orange curves represent the case of a source located off-axis and far from the mask The represented signals are normalized with respect to the off-axis PSF maximum signal. The condition of acquisition of the on-axis images are identical to the Fig. 13. The off-axis images have been acquired in identical conditions by placing an optical density of transmission T = 0.0024 in front of the CCD.

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We attribute these asymmetries to several causes that could corrupt the FTIR phenomenon: the optical aberrations, the presence of contaminants between LMask and PMask, the stray light induced by the spurious reflections on the optical lens surfaces (ghost images) and the non-uniformity of the coatings as well. Indeed, these asymmetries are located at a distance larger than the mask active area. Furthermore, the measurements of the mask reflectivity (Fig. 12) shows that this reflectivity is uniform at distance larger than 200 μm from the optical axis. For these reasons, we are confident that the mask is not the origin of this asymmetrical irradiance distribution of the PSF. In order to improve the performance of our setup, we plan to identify the origin of these asymmetries by performing wavefront measurements, stray light calculations and measurements to conduct the relevant corrections and get a fully symmetrical PSF.

We notice on Fig. 14 that the ratio between the irradiances before and after masking at X = 0 is IM/I0 > 105 thus illustrating the to-date efficiency of the proposed coronagraphic mask to extinguish the PSF central section. In particular, we conclude that the residual air thickness at the contact area between the lens and the prism due to the material roughness and the particulate and molecular contamination is negligible and does not impact significantly the performance.

3.4 On-axis and off-axis PSF profiles with a Lyot stop

We installed a Lyot stop of diameter equal to 55% of the pupil diameter (Fig. 10) and measured the on-axis and the off-axis irradiance distributions. We have represented in Fig. 15 the on-axis and off-axis PSFs and in Fig. 16 the cross-sections along the X and the Y axes in unpolarized light at the wavelength λ = 880 nm with a relative spectral bandwidth Δλ/λ ≈6%. The PSF is located at a distance equal to 30 λ.f2/DAS from the mask center. We have also represented in Fig. 16 the variance of the background noise σBack ≈2.10−7. We have measured that the inner working angles respectively along the X and the Y axes are IWAX ≈6 λ.f2/DAS and IWAY ≈8 λ.f2/DAS. We thus deduce that IWAY/ IWAX ≈1.3 is close to the theoretical expectation and to the results of the mask reflectivity measurements (Fig. 12).

 figure: Fig. 15

Fig. 15 On-axis and off-axis PSF irradiance distribution in unpolarized light at the wavelength λ = 880 nm with relative spectral bandwidth Δλ/λ ≈6%. The off-axis PSF is located at a distance equal to 30 λ.f2/DAS from the mask center. Identical visualization levels for the two images: Imin = 1300 ADU and IMax = 65469 ADU. Each image is the result of a median combination of 101 images acquired at integration time Δτ = 7s. The radius of the inner and outer green circles are equal to 10 λ.f2/DAS and 20 λ.f2/DAS respectively.

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 figure: Fig. 16

Fig. 16 Left –side: cross-section along X-axis represented in logarithmic scale of the following signals: off-axis PSF (distance from mask center: 30 λ.f2/D) measured with a density of transmission TD = 3x10−3 and measured without density (grey and orange curves respectively); On-axis PSF centered on the mask measured without density (blue curve). Right –side: cross-section along Y-axis represented in logarithmic scale of the following signals: off-axis PSF (distance from mask center: 30 λ.f2/D) measured with a density of transmission TD = 3x10−3 and measured without density (grey and orange curves respectively); On-axis PSF centered on the mask measured without density (pink curve). The dash black line represents the variance of the background noise σBack ≈2.10−7. We have also represented in green lines the location of IWAX and IWAY. The data have been acquired in unpolarized light at the wavelength λ = 880 nm with a relative spectral bandwidth λ ≈6% with an integration time Δτ = 7s.

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The maximum contrast along the X axis is roughly equal to 10−4 at a distance X ≈6 λ.f2/DAS (IWAX). This contrast decreases constantly as X increases to reach roughly C ≈5.10−7 at X ≈20 λ.f2/DAS. Similarly, the contrast along the Y axis roughly decreases from C ≈7.10−5 at Y≈8 λ.f2/DAS (IWAY) to C ≈7.10−7 at Y ≈20 λ.f2/DAS. We consider that these results are very encouraging and demonstrate that this coronagraph is able to reject efficiently the starlight. In particular, it is remarkable that a contrast close to 10−6 is reached by using “off-the-shelf components” only.

We also notice in Figs. 15 and 16 that the residual energy is distributed near an annulus region of radius equal to IWAX (respectively equal to IWAY) along the X axis (respectively along the Y axis) and of angular extension equal to a few element of resolutions. It is therefore not possible to make efficient observations of faint companion located at a distance lower than 10 λ.f2/DAS from the PSF center where C > 10−5. This is a clear limitation of the proposed concept and we suspect that the origin of this phenomenon is the mask transmission profile. The next steps will thus aim at defining the shape of LMask that produces a mask transmission that optimizes the distribution of the residual energy to enable the observation of faint companion located at a distance equal to the IWA as discussed in the next section.

4. Discussion

4.1 Optimal mask design

In the previous section, we have presented the performance of the simplest version of EvWaCo that involves an occulting mask with a gaussian transmission. This is not the optimal mask design to get the best contrasts at the smallest IWA values. The main drawback is that the residual energy is concentrated on an annulus area of radius equal to the IWA and of angular extension equal to a few element of resolutions. The detection of a faint companion can be performed on at distances higher than 10 elements of resolution from the PSF center. In order to optimize the distribution of the residual irradiance to enable observations of faint companion at the IWA location, we plan to calculate the shape of the optical medium that frustrates the total internal reflection to get an attenuation profile that optimize the contrast performance. These particular attenuation profiles have been calculated in a previous work in the framework of the former Terrestrial Planet Finder TPF-C [3,10] to obtain higher contrasts compatible with the detection of earth-like exoplanets.

We assess that the development of a coronagraphic mask with a transmission for the band-limited mask functions described in Kuchner and Traub [3] will require the manufacturing of a micro-optics component with a precision in the λ/100 range to induce a precision of the transmission equal to a few percent. That correspond to a precision of few nanometers in the visible light and few ten nanometers in the mid-infrared. The current manufacturing capabilities [11] in micro-optics are able to manufacture components with a maximum surface error in the Δh ≈50 nm range. For example, in the K band where λ ≈2 μm, we assume by applying the equations presented by S. Zhu [6] that this error would induce a maximum error of the reflection coefficient of coronagraphic mask ΔR = +/− 0,1. However, the impact of the surface error on the mask reflectivity will not be constant over the mask active area. The estimation of the surface error impact on the mask transmission and on the contrast performance will thus require dedicated analyzes and developments that will be addressed in the future developments of EvWaCo.

4.2 Fundamental limitation of the proposed approach

We suspect that the following potential contributors limit the contrast performance: the wavefront errors due to the optical quality of the components, the stray light induced by the spurious reflections on the optical components and the mask transmission profile and phase effect. It is commonly accepted that the wavefront quality is one of the major limitation of a coronagraph contrast performance [12]. For example, in order to reach contrasts lower than 10−7 in visible light, the maximum wavefront error of a coronagraph setup must be equal to a few nanometers as discussed in a previous paper [13].

In our case, the optical components have commercial quality with a surface error that is typically equal to λ/4 PTV over the useful optical surface of diameter in the 20 mm range. In the current setup, the part of the beam from the source to the Lyot stop has a diameter varying between 8 mm and 13 mm. We thus expect that the optical components will induce non-negligible aberrations to the optical beam propagating through the coronagraph and thus impacting the performance. In order to improve the wavefront quality and thus the performance, we plan in a first time to replace the off-the-shelves achromatic doublets with high-precision reflective optics. In a second time, we plan to install a deformable mirror in the aperture stop plane to correct both low and high frequencies defects of the wavefront.

We also suspect that the stray light due to the ghost images is a major adverse contributor to the current performance. Indeed, the aperture number of the beam incident on the coronagraphic mask is F# ≈40. It means that this beam is quasi-collimated. The optical surfaces of L1, L2, L3 and of the prism are coated with an anti-reflective coating with a reflectivity RAR ≈2 x10−3. After two spurious reflections on the optical element surfaces, the ratio between the ghost image and the science beam radiances should be IGhost/IScience ≈4x10−6.

That is the order of magnitude of the contrast measured on EvWaCo at distances between 10 and 20 λ.f2/DAS from the PSF center. In a first time, we will perform stray light analyses of the setup by using the ZEMAX software in order to identify the most critical elements. In a second time, we will upgrade the setup by replacing the critical lenses by mirrors.

4.3 Comparison with an existing coronagraph

In this section, we compare the contrast performance of EvWaCo with an existing coronagraph. As presented in the previous section, EvWaCo provides some contrasts equal to few 10−6 at distances between 10 and 20 Airy radii in unpolarized light with a spectral bandwidth equal to 6%.

In the framework of the development of “extreme adaptive optics” (ExAO) systems for the Gemini and for the Very Large Telescope, the University of Arizona has developed and tested several reflective Gaussian Coronagraphs involving various masks of gaussian transmissions of various FWHM between 3.8 and 15.8 λ/D [9]. The masks were manufactured by using microlithographic techniques. The performance of these masks have been tested in monochromatic light with a doubled Nd:YAG polarized laser emitting at the wavelength λ = 532 nm by using “Laser grade optics”. In this section, we focus on the results obtained by using a gaussian mask of FWHM equal to 7.4 λ/D what is close to the FWHM of our occulting mask. We also consider the case without extra mask designed to block the diffracted “spot of Arago”, or “Poisson’s spot”, formed by light diffracting around the focal plane mask. This is similar to the current configuration of the EvWaCo setup.

At a distance equal to 6λ/D from the PSF center, the University of Arizona obtained a contrast close to 10−5. Between 6 and 20 λ/D, the contrast value decreases continuously from 10−5 to 10−7. We conclude that the performance obtained with EvWaco is comparable to this performance. The main difference is the performance obtained around the IWA since EvWaCo provides a contrast close to 10−4 at a distance equal to 8 λ/D. We conclude that the contrast performance of EvWaco is close to the performance obtained at a distance between 10 and 20 λ/D in polarized monochromatic light with a gaussian mask manufactured by using microlithographic techniques.

4.2 Optical centering and low order optical aberrations control

The control of the low-order aberrations is a critical point of the small-angle coronagraphs to reach the contrasts required for exoplanet direct detection and characterization. It is thus particularly important to measure the wavefront as close as possible to the occulting mask [1]. The proposed concept presents the advantage of clearly separating the star and the planet lights. The wavefront incident on the occulting mask can be measured by placing a wavefront sensor on the transmitted star light. The correction of this wavefront can be performed by placing a deformable mirror in a pupil plane as represented in Fig. 17.

 figure: Fig. 17

Fig. 17 Example of a setup to measure the wavefront of the star light transmitted by the occulting mask and control a deformable mirror placed in a pupil plane to adjust the center the star on the mask. The required resolution on the fast steering mirror angle is equal to 5 arcsecond typically to guaranty the contrast performance at the level presented in the section “3.4 On-axis and off-axis PSF profiles with a Lyot stop”.

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One of the most critical aspect is the centering of the star on the occulting mask. During the adjustment of the setup, we have noticed that the position of this PSF must be controlled with a resolution better than10 μm to get reproducible contrasts at a level equal to few 10−6 at an angular distance of about 10 to 20 Airy radii. With the focal length of the lens L2 equal to 300 mm, we deduce that the precision of the beam angle in the pupil plane must be controlled with an accuracy of typically 5 arc second, typically. This level of accuracy can be reached by using “off-the-shelves” fast-steering mirrors that usually propose an angular resolution better than 1 arcsecond [14] We thus conclude that the centering of the star on the occulting mask can be reached at the requested level of performance by using the star light and by controlling a common fast-steering mirror controls.

5. Conclusions and perspectives

In this paper we have presented the theoretical and experimental studies of EvWaCo coronagraphic mask. The theoretical calculations have demonstrated that EvWaCo mask apodizes the star profile and is almost achromatic. The experimental results performed in the near-infrared in unpolarized light and with a relative spectral bandwidth of a few percent confirmed the theoretical expectations. We have measured a contrast equal to few 10−6 at a distance of roughly ten elements of resolution from the PSF center by placing a Lyot stop with a diameter equal to 55% of the pupil diameter. This illustrates the capability of the EvWaCo to provide high starlight rejection at reasonable distances from the star center. By extrapolating our results to the K band where λ ≈2μm, we assess that our coronagraph placed on the focal plane of a 8 meter-class telescope equipped with an adaptive optics would provide contrasts in the 10−6 range at a distance equal to 1” from the star center. A potential application of our coronagraph could thus be the detection of warm Jupiter-like planets that will require contrasts between 10−6 and 10−7 in the near infrared domain [15].

The next steps of the development of EvWaCo setup will aim at measuring contrasts less than or equal to 10−7 at a distance close to the IWA from the PSF center. First, we plan to design and manufacture optimized mask to reach this performance. In parallel, we plan to upgrade our setup to reduce the wavefront errors and the level of stray light. Our objective is to reach some contrasts equal to 10−7 thus implying a maximum wavefront error equal to a few nm RMS. We will also replace the “off-the shelves” achromatic doublets by high-precision reflective optics. Next, we will install an adaptive optics in the plane of the aperture stop to control the low and high frequency errors which affect the wavefront.

Acknowledgments

The authors would like to thank the anonymous reviewers for their insightful comments and suggestions that helped improve the paper.

References and links

1. D. Mawet, L. Pueyoc, P. Lawson, L. Mugnier, W. Traub, A. Boccaletti, J. Trauger, S. Gladysz, E. Serabyn, J. Milli, R. Belikov, M. Kasper, P. Baudoz, B. Macintosh, C. Marois, B. Oppenheimer, H. Barrett, J.-L. Beuzit, N. Devaney, J. Girard, O. Guyon, J. Krist, B. Mennesson, D. Mouillet, N. Murakami, L. Poyneer, D. Savransky, C. Verinaud, and J. K. Wallace, “Review of small-angle coronagraphic techniques in the wake of ground-based second-generation adaptive optics systems,” Proc. SPIE 8442, 844204 (2012). [CrossRef]  

2. O. Guyon, E. A. Pluzhnik, M. J. Kuchner, B. Collins, and S. T. Ridgway, “Theoretical limits on extrasolar terrestrial planet detection with coronagraphs,” ApJS 167(1), 81–99 (2006). [CrossRef]  

3. M. Kuchner and W. A. Traub, “A coronagraph with a band-limited mask for finding terrestrial planets,” Astrophys. J. 570(2), 900–908 (2002). [CrossRef]  

4. P.R. Lawson, “Exoplanet Exploration Program Technology Plan, Appendix 2013,” JPL document D-81562, 2014.

5. E. Sidick and D. W. Wilson, “Behavior of imperfect band-limited coronagraphic masks in a high-contrast imaging system,” Appl. Opt. 46(9), 1397–1407 (2007). [CrossRef]   [PubMed]  

6. S. Zhu, A. W. Yu, D. Hawley, and R. Roy, “Frustrated total internal reflection: A demonstration and review,” Am. J. Phys. 54(7), 601–607 (1986). [CrossRef]  

7. C. Aime, R. Soumer, and Y. Rabbia, “Shared constraints and specific characters in Very High Dynamics Imaging,” in Proceedings of Astronomy with High Contrast Imaging, C. Aime and R. Soummer, eds., 8 (EAS Publication Series, 2003), pp. 65–78.

8. C. Mackay, “High-efficiency lucky imaging,” Mon. Not. R. Astron. Soc. 464, 680–687 (2017).

9. R. Park, L. M. Close, N. Siegler, E. L. Nielsen, and T. Stalcup, “A reflective Gaussian coronagraph for ExAO: laboratory performance,” Proc. SPIE 6272, 20–27 (1998). [CrossRef]  

10. J. Crepp, “High-Contrast Imaging with a band-limited coronagraphic mask,” PhD thesis, University of Florida (2008).

11. R. Voelkel, “Wafer-scale micro-optics fabrication,” Adv. Opt. Technol. 1, 135–150 (2012).

12. C. Cavarroc, A. Boccaletti, P. Baudoz, T. Fusco, and D. Rouan, “Fundamental limitations on Earth-like planet detection with extremely large telescope,” A&A. 447(1), 397–403 (2006). [CrossRef]  

13. J. W. Evans, G. Sommargren, B. A. Macintosh, S. Severson, and D. Dillon, “Effect of wavefront error on 10-7 contrast measurements,” Opt. Lett. 31(5), 565–567 (2006). [CrossRef]   [PubMed]  

14. Optics In Motion, “Standard Fast Steering Mirrors”, http://www.opticsinmotion.net/fast_steering_mirrors.html (2012).

15. A. Burrows, M. Marley, W. B. Hubbard, J. I. Lunine, T. Guillot, D. Saumon, R. Freed-man, D. Sudarsky, and C. Sharp, “A nongray theory of extrasolar giant planets and brown dwarfs,” Astrophys. J. 491(2), 856–875 (1997). [CrossRef]  

References

  • View by:

  1. D. Mawet, L. Pueyoc, P. Lawson, L. Mugnier, W. Traub, A. Boccaletti, J. Trauger, S. Gladysz, E. Serabyn, J. Milli, R. Belikov, M. Kasper, P. Baudoz, B. Macintosh, C. Marois, B. Oppenheimer, H. Barrett, J.-L. Beuzit, N. Devaney, J. Girard, O. Guyon, J. Krist, B. Mennesson, D. Mouillet, N. Murakami, L. Poyneer, D. Savransky, C. Verinaud, and J. K. Wallace, “Review of small-angle coronagraphic techniques in the wake of ground-based second-generation adaptive optics systems,” Proc. SPIE 8442, 844204 (2012).
    [Crossref]
  2. O. Guyon, E. A. Pluzhnik, M. J. Kuchner, B. Collins, and S. T. Ridgway, “Theoretical limits on extrasolar terrestrial planet detection with coronagraphs,” ApJS 167(1), 81–99 (2006).
    [Crossref]
  3. M. Kuchner and W. A. Traub, “A coronagraph with a band-limited mask for finding terrestrial planets,” Astrophys. J. 570(2), 900–908 (2002).
    [Crossref]
  4. P.R. Lawson, “Exoplanet Exploration Program Technology Plan, Appendix 2013,” JPL document D-81562, 2014.
  5. E. Sidick and D. W. Wilson, “Behavior of imperfect band-limited coronagraphic masks in a high-contrast imaging system,” Appl. Opt. 46(9), 1397–1407 (2007).
    [Crossref] [PubMed]
  6. S. Zhu, A. W. Yu, D. Hawley, and R. Roy, “Frustrated total internal reflection: A demonstration and review,” Am. J. Phys. 54(7), 601–607 (1986).
    [Crossref]
  7. C. Aime, R. Soumer, and Y. Rabbia, “Shared constraints and specific characters in Very High Dynamics Imaging,” in Proceedings of Astronomy with High Contrast Imaging, C. Aime and R. Soummer, eds., 8 (EAS Publication Series, 2003), pp. 65–78.
  8. C. Mackay, “High-efficiency lucky imaging,” Mon. Not. R. Astron. Soc. 464, 680–687 (2017).
  9. R. Park, L. M. Close, N. Siegler, E. L. Nielsen, and T. Stalcup, “A reflective Gaussian coronagraph for ExAO: laboratory performance,” Proc. SPIE 6272, 20–27 (1998).
    [Crossref]
  10. J. Crepp, “High-Contrast Imaging with a band-limited coronagraphic mask,” PhD thesis, University of Florida (2008).
  11. R. Voelkel, “Wafer-scale micro-optics fabrication,” Adv. Opt. Technol. 1, 135–150 (2012).
  12. C. Cavarroc, A. Boccaletti, P. Baudoz, T. Fusco, and D. Rouan, “Fundamental limitations on Earth-like planet detection with extremely large telescope,” A&A. 447(1), 397–403 (2006).
    [Crossref]
  13. J. W. Evans, G. Sommargren, B. A. Macintosh, S. Severson, and D. Dillon, “Effect of wavefront error on 10-7 contrast measurements,” Opt. Lett. 31(5), 565–567 (2006).
    [Crossref] [PubMed]
  14. Optics In Motion, “Standard Fast Steering Mirrors”, http://www.opticsinmotion.net/fast_steering_mirrors.html (2012).
  15. A. Burrows, M. Marley, W. B. Hubbard, J. I. Lunine, T. Guillot, D. Saumon, R. Freed-man, D. Sudarsky, and C. Sharp, “A nongray theory of extrasolar giant planets and brown dwarfs,” Astrophys. J. 491(2), 856–875 (1997).
    [Crossref]

2017 (1)

C. Mackay, “High-efficiency lucky imaging,” Mon. Not. R. Astron. Soc. 464, 680–687 (2017).

2012 (2)

D. Mawet, L. Pueyoc, P. Lawson, L. Mugnier, W. Traub, A. Boccaletti, J. Trauger, S. Gladysz, E. Serabyn, J. Milli, R. Belikov, M. Kasper, P. Baudoz, B. Macintosh, C. Marois, B. Oppenheimer, H. Barrett, J.-L. Beuzit, N. Devaney, J. Girard, O. Guyon, J. Krist, B. Mennesson, D. Mouillet, N. Murakami, L. Poyneer, D. Savransky, C. Verinaud, and J. K. Wallace, “Review of small-angle coronagraphic techniques in the wake of ground-based second-generation adaptive optics systems,” Proc. SPIE 8442, 844204 (2012).
[Crossref]

R. Voelkel, “Wafer-scale micro-optics fabrication,” Adv. Opt. Technol. 1, 135–150 (2012).

2007 (1)

2006 (3)

O. Guyon, E. A. Pluzhnik, M. J. Kuchner, B. Collins, and S. T. Ridgway, “Theoretical limits on extrasolar terrestrial planet detection with coronagraphs,” ApJS 167(1), 81–99 (2006).
[Crossref]

C. Cavarroc, A. Boccaletti, P. Baudoz, T. Fusco, and D. Rouan, “Fundamental limitations on Earth-like planet detection with extremely large telescope,” A&A. 447(1), 397–403 (2006).
[Crossref]

J. W. Evans, G. Sommargren, B. A. Macintosh, S. Severson, and D. Dillon, “Effect of wavefront error on 10-7 contrast measurements,” Opt. Lett. 31(5), 565–567 (2006).
[Crossref] [PubMed]

2002 (1)

M. Kuchner and W. A. Traub, “A coronagraph with a band-limited mask for finding terrestrial planets,” Astrophys. J. 570(2), 900–908 (2002).
[Crossref]

1998 (1)

R. Park, L. M. Close, N. Siegler, E. L. Nielsen, and T. Stalcup, “A reflective Gaussian coronagraph for ExAO: laboratory performance,” Proc. SPIE 6272, 20–27 (1998).
[Crossref]

1997 (1)

A. Burrows, M. Marley, W. B. Hubbard, J. I. Lunine, T. Guillot, D. Saumon, R. Freed-man, D. Sudarsky, and C. Sharp, “A nongray theory of extrasolar giant planets and brown dwarfs,” Astrophys. J. 491(2), 856–875 (1997).
[Crossref]

1986 (1)

S. Zhu, A. W. Yu, D. Hawley, and R. Roy, “Frustrated total internal reflection: A demonstration and review,” Am. J. Phys. 54(7), 601–607 (1986).
[Crossref]

Barrett, H.

D. Mawet, L. Pueyoc, P. Lawson, L. Mugnier, W. Traub, A. Boccaletti, J. Trauger, S. Gladysz, E. Serabyn, J. Milli, R. Belikov, M. Kasper, P. Baudoz, B. Macintosh, C. Marois, B. Oppenheimer, H. Barrett, J.-L. Beuzit, N. Devaney, J. Girard, O. Guyon, J. Krist, B. Mennesson, D. Mouillet, N. Murakami, L. Poyneer, D. Savransky, C. Verinaud, and J. K. Wallace, “Review of small-angle coronagraphic techniques in the wake of ground-based second-generation adaptive optics systems,” Proc. SPIE 8442, 844204 (2012).
[Crossref]

Baudoz, P.

D. Mawet, L. Pueyoc, P. Lawson, L. Mugnier, W. Traub, A. Boccaletti, J. Trauger, S. Gladysz, E. Serabyn, J. Milli, R. Belikov, M. Kasper, P. Baudoz, B. Macintosh, C. Marois, B. Oppenheimer, H. Barrett, J.-L. Beuzit, N. Devaney, J. Girard, O. Guyon, J. Krist, B. Mennesson, D. Mouillet, N. Murakami, L. Poyneer, D. Savransky, C. Verinaud, and J. K. Wallace, “Review of small-angle coronagraphic techniques in the wake of ground-based second-generation adaptive optics systems,” Proc. SPIE 8442, 844204 (2012).
[Crossref]

C. Cavarroc, A. Boccaletti, P. Baudoz, T. Fusco, and D. Rouan, “Fundamental limitations on Earth-like planet detection with extremely large telescope,” A&A. 447(1), 397–403 (2006).
[Crossref]

Belikov, R.

D. Mawet, L. Pueyoc, P. Lawson, L. Mugnier, W. Traub, A. Boccaletti, J. Trauger, S. Gladysz, E. Serabyn, J. Milli, R. Belikov, M. Kasper, P. Baudoz, B. Macintosh, C. Marois, B. Oppenheimer, H. Barrett, J.-L. Beuzit, N. Devaney, J. Girard, O. Guyon, J. Krist, B. Mennesson, D. Mouillet, N. Murakami, L. Poyneer, D. Savransky, C. Verinaud, and J. K. Wallace, “Review of small-angle coronagraphic techniques in the wake of ground-based second-generation adaptive optics systems,” Proc. SPIE 8442, 844204 (2012).
[Crossref]

Beuzit, J.-L.

D. Mawet, L. Pueyoc, P. Lawson, L. Mugnier, W. Traub, A. Boccaletti, J. Trauger, S. Gladysz, E. Serabyn, J. Milli, R. Belikov, M. Kasper, P. Baudoz, B. Macintosh, C. Marois, B. Oppenheimer, H. Barrett, J.-L. Beuzit, N. Devaney, J. Girard, O. Guyon, J. Krist, B. Mennesson, D. Mouillet, N. Murakami, L. Poyneer, D. Savransky, C. Verinaud, and J. K. Wallace, “Review of small-angle coronagraphic techniques in the wake of ground-based second-generation adaptive optics systems,” Proc. SPIE 8442, 844204 (2012).
[Crossref]

Boccaletti, A.

D. Mawet, L. Pueyoc, P. Lawson, L. Mugnier, W. Traub, A. Boccaletti, J. Trauger, S. Gladysz, E. Serabyn, J. Milli, R. Belikov, M. Kasper, P. Baudoz, B. Macintosh, C. Marois, B. Oppenheimer, H. Barrett, J.-L. Beuzit, N. Devaney, J. Girard, O. Guyon, J. Krist, B. Mennesson, D. Mouillet, N. Murakami, L. Poyneer, D. Savransky, C. Verinaud, and J. K. Wallace, “Review of small-angle coronagraphic techniques in the wake of ground-based second-generation adaptive optics systems,” Proc. SPIE 8442, 844204 (2012).
[Crossref]

C. Cavarroc, A. Boccaletti, P. Baudoz, T. Fusco, and D. Rouan, “Fundamental limitations on Earth-like planet detection with extremely large telescope,” A&A. 447(1), 397–403 (2006).
[Crossref]

Burrows, A.

A. Burrows, M. Marley, W. B. Hubbard, J. I. Lunine, T. Guillot, D. Saumon, R. Freed-man, D. Sudarsky, and C. Sharp, “A nongray theory of extrasolar giant planets and brown dwarfs,” Astrophys. J. 491(2), 856–875 (1997).
[Crossref]

Cavarroc, C.

C. Cavarroc, A. Boccaletti, P. Baudoz, T. Fusco, and D. Rouan, “Fundamental limitations on Earth-like planet detection with extremely large telescope,” A&A. 447(1), 397–403 (2006).
[Crossref]

Close, L. M.

R. Park, L. M. Close, N. Siegler, E. L. Nielsen, and T. Stalcup, “A reflective Gaussian coronagraph for ExAO: laboratory performance,” Proc. SPIE 6272, 20–27 (1998).
[Crossref]

Collins, B.

O. Guyon, E. A. Pluzhnik, M. J. Kuchner, B. Collins, and S. T. Ridgway, “Theoretical limits on extrasolar terrestrial planet detection with coronagraphs,” ApJS 167(1), 81–99 (2006).
[Crossref]

Devaney, N.

D. Mawet, L. Pueyoc, P. Lawson, L. Mugnier, W. Traub, A. Boccaletti, J. Trauger, S. Gladysz, E. Serabyn, J. Milli, R. Belikov, M. Kasper, P. Baudoz, B. Macintosh, C. Marois, B. Oppenheimer, H. Barrett, J.-L. Beuzit, N. Devaney, J. Girard, O. Guyon, J. Krist, B. Mennesson, D. Mouillet, N. Murakami, L. Poyneer, D. Savransky, C. Verinaud, and J. K. Wallace, “Review of small-angle coronagraphic techniques in the wake of ground-based second-generation adaptive optics systems,” Proc. SPIE 8442, 844204 (2012).
[Crossref]

Dillon, D.

Evans, J. W.

Freed-man, R.

A. Burrows, M. Marley, W. B. Hubbard, J. I. Lunine, T. Guillot, D. Saumon, R. Freed-man, D. Sudarsky, and C. Sharp, “A nongray theory of extrasolar giant planets and brown dwarfs,” Astrophys. J. 491(2), 856–875 (1997).
[Crossref]

Fusco, T.

C. Cavarroc, A. Boccaletti, P. Baudoz, T. Fusco, and D. Rouan, “Fundamental limitations on Earth-like planet detection with extremely large telescope,” A&A. 447(1), 397–403 (2006).
[Crossref]

Girard, J.

D. Mawet, L. Pueyoc, P. Lawson, L. Mugnier, W. Traub, A. Boccaletti, J. Trauger, S. Gladysz, E. Serabyn, J. Milli, R. Belikov, M. Kasper, P. Baudoz, B. Macintosh, C. Marois, B. Oppenheimer, H. Barrett, J.-L. Beuzit, N. Devaney, J. Girard, O. Guyon, J. Krist, B. Mennesson, D. Mouillet, N. Murakami, L. Poyneer, D. Savransky, C. Verinaud, and J. K. Wallace, “Review of small-angle coronagraphic techniques in the wake of ground-based second-generation adaptive optics systems,” Proc. SPIE 8442, 844204 (2012).
[Crossref]

Gladysz, S.

D. Mawet, L. Pueyoc, P. Lawson, L. Mugnier, W. Traub, A. Boccaletti, J. Trauger, S. Gladysz, E. Serabyn, J. Milli, R. Belikov, M. Kasper, P. Baudoz, B. Macintosh, C. Marois, B. Oppenheimer, H. Barrett, J.-L. Beuzit, N. Devaney, J. Girard, O. Guyon, J. Krist, B. Mennesson, D. Mouillet, N. Murakami, L. Poyneer, D. Savransky, C. Verinaud, and J. K. Wallace, “Review of small-angle coronagraphic techniques in the wake of ground-based second-generation adaptive optics systems,” Proc. SPIE 8442, 844204 (2012).
[Crossref]

Guillot, T.

A. Burrows, M. Marley, W. B. Hubbard, J. I. Lunine, T. Guillot, D. Saumon, R. Freed-man, D. Sudarsky, and C. Sharp, “A nongray theory of extrasolar giant planets and brown dwarfs,” Astrophys. J. 491(2), 856–875 (1997).
[Crossref]

Guyon, O.

D. Mawet, L. Pueyoc, P. Lawson, L. Mugnier, W. Traub, A. Boccaletti, J. Trauger, S. Gladysz, E. Serabyn, J. Milli, R. Belikov, M. Kasper, P. Baudoz, B. Macintosh, C. Marois, B. Oppenheimer, H. Barrett, J.-L. Beuzit, N. Devaney, J. Girard, O. Guyon, J. Krist, B. Mennesson, D. Mouillet, N. Murakami, L. Poyneer, D. Savransky, C. Verinaud, and J. K. Wallace, “Review of small-angle coronagraphic techniques in the wake of ground-based second-generation adaptive optics systems,” Proc. SPIE 8442, 844204 (2012).
[Crossref]

O. Guyon, E. A. Pluzhnik, M. J. Kuchner, B. Collins, and S. T. Ridgway, “Theoretical limits on extrasolar terrestrial planet detection with coronagraphs,” ApJS 167(1), 81–99 (2006).
[Crossref]

Hawley, D.

S. Zhu, A. W. Yu, D. Hawley, and R. Roy, “Frustrated total internal reflection: A demonstration and review,” Am. J. Phys. 54(7), 601–607 (1986).
[Crossref]

Hubbard, W. B.

A. Burrows, M. Marley, W. B. Hubbard, J. I. Lunine, T. Guillot, D. Saumon, R. Freed-man, D. Sudarsky, and C. Sharp, “A nongray theory of extrasolar giant planets and brown dwarfs,” Astrophys. J. 491(2), 856–875 (1997).
[Crossref]

Kasper, M.

D. Mawet, L. Pueyoc, P. Lawson, L. Mugnier, W. Traub, A. Boccaletti, J. Trauger, S. Gladysz, E. Serabyn, J. Milli, R. Belikov, M. Kasper, P. Baudoz, B. Macintosh, C. Marois, B. Oppenheimer, H. Barrett, J.-L. Beuzit, N. Devaney, J. Girard, O. Guyon, J. Krist, B. Mennesson, D. Mouillet, N. Murakami, L. Poyneer, D. Savransky, C. Verinaud, and J. K. Wallace, “Review of small-angle coronagraphic techniques in the wake of ground-based second-generation adaptive optics systems,” Proc. SPIE 8442, 844204 (2012).
[Crossref]

Krist, J.

D. Mawet, L. Pueyoc, P. Lawson, L. Mugnier, W. Traub, A. Boccaletti, J. Trauger, S. Gladysz, E. Serabyn, J. Milli, R. Belikov, M. Kasper, P. Baudoz, B. Macintosh, C. Marois, B. Oppenheimer, H. Barrett, J.-L. Beuzit, N. Devaney, J. Girard, O. Guyon, J. Krist, B. Mennesson, D. Mouillet, N. Murakami, L. Poyneer, D. Savransky, C. Verinaud, and J. K. Wallace, “Review of small-angle coronagraphic techniques in the wake of ground-based second-generation adaptive optics systems,” Proc. SPIE 8442, 844204 (2012).
[Crossref]

Kuchner, M.

M. Kuchner and W. A. Traub, “A coronagraph with a band-limited mask for finding terrestrial planets,” Astrophys. J. 570(2), 900–908 (2002).
[Crossref]

Kuchner, M. J.

O. Guyon, E. A. Pluzhnik, M. J. Kuchner, B. Collins, and S. T. Ridgway, “Theoretical limits on extrasolar terrestrial planet detection with coronagraphs,” ApJS 167(1), 81–99 (2006).
[Crossref]

Lawson, P.

D. Mawet, L. Pueyoc, P. Lawson, L. Mugnier, W. Traub, A. Boccaletti, J. Trauger, S. Gladysz, E. Serabyn, J. Milli, R. Belikov, M. Kasper, P. Baudoz, B. Macintosh, C. Marois, B. Oppenheimer, H. Barrett, J.-L. Beuzit, N. Devaney, J. Girard, O. Guyon, J. Krist, B. Mennesson, D. Mouillet, N. Murakami, L. Poyneer, D. Savransky, C. Verinaud, and J. K. Wallace, “Review of small-angle coronagraphic techniques in the wake of ground-based second-generation adaptive optics systems,” Proc. SPIE 8442, 844204 (2012).
[Crossref]

Lunine, J. I.

A. Burrows, M. Marley, W. B. Hubbard, J. I. Lunine, T. Guillot, D. Saumon, R. Freed-man, D. Sudarsky, and C. Sharp, “A nongray theory of extrasolar giant planets and brown dwarfs,” Astrophys. J. 491(2), 856–875 (1997).
[Crossref]

Macintosh, B.

D. Mawet, L. Pueyoc, P. Lawson, L. Mugnier, W. Traub, A. Boccaletti, J. Trauger, S. Gladysz, E. Serabyn, J. Milli, R. Belikov, M. Kasper, P. Baudoz, B. Macintosh, C. Marois, B. Oppenheimer, H. Barrett, J.-L. Beuzit, N. Devaney, J. Girard, O. Guyon, J. Krist, B. Mennesson, D. Mouillet, N. Murakami, L. Poyneer, D. Savransky, C. Verinaud, and J. K. Wallace, “Review of small-angle coronagraphic techniques in the wake of ground-based second-generation adaptive optics systems,” Proc. SPIE 8442, 844204 (2012).
[Crossref]

Macintosh, B. A.

Mackay, C.

C. Mackay, “High-efficiency lucky imaging,” Mon. Not. R. Astron. Soc. 464, 680–687 (2017).

Marley, M.

A. Burrows, M. Marley, W. B. Hubbard, J. I. Lunine, T. Guillot, D. Saumon, R. Freed-man, D. Sudarsky, and C. Sharp, “A nongray theory of extrasolar giant planets and brown dwarfs,” Astrophys. J. 491(2), 856–875 (1997).
[Crossref]

Marois, C.

D. Mawet, L. Pueyoc, P. Lawson, L. Mugnier, W. Traub, A. Boccaletti, J. Trauger, S. Gladysz, E. Serabyn, J. Milli, R. Belikov, M. Kasper, P. Baudoz, B. Macintosh, C. Marois, B. Oppenheimer, H. Barrett, J.-L. Beuzit, N. Devaney, J. Girard, O. Guyon, J. Krist, B. Mennesson, D. Mouillet, N. Murakami, L. Poyneer, D. Savransky, C. Verinaud, and J. K. Wallace, “Review of small-angle coronagraphic techniques in the wake of ground-based second-generation adaptive optics systems,” Proc. SPIE 8442, 844204 (2012).
[Crossref]

Mawet, D.

D. Mawet, L. Pueyoc, P. Lawson, L. Mugnier, W. Traub, A. Boccaletti, J. Trauger, S. Gladysz, E. Serabyn, J. Milli, R. Belikov, M. Kasper, P. Baudoz, B. Macintosh, C. Marois, B. Oppenheimer, H. Barrett, J.-L. Beuzit, N. Devaney, J. Girard, O. Guyon, J. Krist, B. Mennesson, D. Mouillet, N. Murakami, L. Poyneer, D. Savransky, C. Verinaud, and J. K. Wallace, “Review of small-angle coronagraphic techniques in the wake of ground-based second-generation adaptive optics systems,” Proc. SPIE 8442, 844204 (2012).
[Crossref]

Mennesson, B.

D. Mawet, L. Pueyoc, P. Lawson, L. Mugnier, W. Traub, A. Boccaletti, J. Trauger, S. Gladysz, E. Serabyn, J. Milli, R. Belikov, M. Kasper, P. Baudoz, B. Macintosh, C. Marois, B. Oppenheimer, H. Barrett, J.-L. Beuzit, N. Devaney, J. Girard, O. Guyon, J. Krist, B. Mennesson, D. Mouillet, N. Murakami, L. Poyneer, D. Savransky, C. Verinaud, and J. K. Wallace, “Review of small-angle coronagraphic techniques in the wake of ground-based second-generation adaptive optics systems,” Proc. SPIE 8442, 844204 (2012).
[Crossref]

Milli, J.

D. Mawet, L. Pueyoc, P. Lawson, L. Mugnier, W. Traub, A. Boccaletti, J. Trauger, S. Gladysz, E. Serabyn, J. Milli, R. Belikov, M. Kasper, P. Baudoz, B. Macintosh, C. Marois, B. Oppenheimer, H. Barrett, J.-L. Beuzit, N. Devaney, J. Girard, O. Guyon, J. Krist, B. Mennesson, D. Mouillet, N. Murakami, L. Poyneer, D. Savransky, C. Verinaud, and J. K. Wallace, “Review of small-angle coronagraphic techniques in the wake of ground-based second-generation adaptive optics systems,” Proc. SPIE 8442, 844204 (2012).
[Crossref]

Mouillet, D.

D. Mawet, L. Pueyoc, P. Lawson, L. Mugnier, W. Traub, A. Boccaletti, J. Trauger, S. Gladysz, E. Serabyn, J. Milli, R. Belikov, M. Kasper, P. Baudoz, B. Macintosh, C. Marois, B. Oppenheimer, H. Barrett, J.-L. Beuzit, N. Devaney, J. Girard, O. Guyon, J. Krist, B. Mennesson, D. Mouillet, N. Murakami, L. Poyneer, D. Savransky, C. Verinaud, and J. K. Wallace, “Review of small-angle coronagraphic techniques in the wake of ground-based second-generation adaptive optics systems,” Proc. SPIE 8442, 844204 (2012).
[Crossref]

Mugnier, L.

D. Mawet, L. Pueyoc, P. Lawson, L. Mugnier, W. Traub, A. Boccaletti, J. Trauger, S. Gladysz, E. Serabyn, J. Milli, R. Belikov, M. Kasper, P. Baudoz, B. Macintosh, C. Marois, B. Oppenheimer, H. Barrett, J.-L. Beuzit, N. Devaney, J. Girard, O. Guyon, J. Krist, B. Mennesson, D. Mouillet, N. Murakami, L. Poyneer, D. Savransky, C. Verinaud, and J. K. Wallace, “Review of small-angle coronagraphic techniques in the wake of ground-based second-generation adaptive optics systems,” Proc. SPIE 8442, 844204 (2012).
[Crossref]

Murakami, N.

D. Mawet, L. Pueyoc, P. Lawson, L. Mugnier, W. Traub, A. Boccaletti, J. Trauger, S. Gladysz, E. Serabyn, J. Milli, R. Belikov, M. Kasper, P. Baudoz, B. Macintosh, C. Marois, B. Oppenheimer, H. Barrett, J.-L. Beuzit, N. Devaney, J. Girard, O. Guyon, J. Krist, B. Mennesson, D. Mouillet, N. Murakami, L. Poyneer, D. Savransky, C. Verinaud, and J. K. Wallace, “Review of small-angle coronagraphic techniques in the wake of ground-based second-generation adaptive optics systems,” Proc. SPIE 8442, 844204 (2012).
[Crossref]

Nielsen, E. L.

R. Park, L. M. Close, N. Siegler, E. L. Nielsen, and T. Stalcup, “A reflective Gaussian coronagraph for ExAO: laboratory performance,” Proc. SPIE 6272, 20–27 (1998).
[Crossref]

Oppenheimer, B.

D. Mawet, L. Pueyoc, P. Lawson, L. Mugnier, W. Traub, A. Boccaletti, J. Trauger, S. Gladysz, E. Serabyn, J. Milli, R. Belikov, M. Kasper, P. Baudoz, B. Macintosh, C. Marois, B. Oppenheimer, H. Barrett, J.-L. Beuzit, N. Devaney, J. Girard, O. Guyon, J. Krist, B. Mennesson, D. Mouillet, N. Murakami, L. Poyneer, D. Savransky, C. Verinaud, and J. K. Wallace, “Review of small-angle coronagraphic techniques in the wake of ground-based second-generation adaptive optics systems,” Proc. SPIE 8442, 844204 (2012).
[Crossref]

Park, R.

R. Park, L. M. Close, N. Siegler, E. L. Nielsen, and T. Stalcup, “A reflective Gaussian coronagraph for ExAO: laboratory performance,” Proc. SPIE 6272, 20–27 (1998).
[Crossref]

Pluzhnik, E. A.

O. Guyon, E. A. Pluzhnik, M. J. Kuchner, B. Collins, and S. T. Ridgway, “Theoretical limits on extrasolar terrestrial planet detection with coronagraphs,” ApJS 167(1), 81–99 (2006).
[Crossref]

Poyneer, L.

D. Mawet, L. Pueyoc, P. Lawson, L. Mugnier, W. Traub, A. Boccaletti, J. Trauger, S. Gladysz, E. Serabyn, J. Milli, R. Belikov, M. Kasper, P. Baudoz, B. Macintosh, C. Marois, B. Oppenheimer, H. Barrett, J.-L. Beuzit, N. Devaney, J. Girard, O. Guyon, J. Krist, B. Mennesson, D. Mouillet, N. Murakami, L. Poyneer, D. Savransky, C. Verinaud, and J. K. Wallace, “Review of small-angle coronagraphic techniques in the wake of ground-based second-generation adaptive optics systems,” Proc. SPIE 8442, 844204 (2012).
[Crossref]

Pueyoc, L.

D. Mawet, L. Pueyoc, P. Lawson, L. Mugnier, W. Traub, A. Boccaletti, J. Trauger, S. Gladysz, E. Serabyn, J. Milli, R. Belikov, M. Kasper, P. Baudoz, B. Macintosh, C. Marois, B. Oppenheimer, H. Barrett, J.-L. Beuzit, N. Devaney, J. Girard, O. Guyon, J. Krist, B. Mennesson, D. Mouillet, N. Murakami, L. Poyneer, D. Savransky, C. Verinaud, and J. K. Wallace, “Review of small-angle coronagraphic techniques in the wake of ground-based second-generation adaptive optics systems,” Proc. SPIE 8442, 844204 (2012).
[Crossref]

Ridgway, S. T.

O. Guyon, E. A. Pluzhnik, M. J. Kuchner, B. Collins, and S. T. Ridgway, “Theoretical limits on extrasolar terrestrial planet detection with coronagraphs,” ApJS 167(1), 81–99 (2006).
[Crossref]

Rouan, D.

C. Cavarroc, A. Boccaletti, P. Baudoz, T. Fusco, and D. Rouan, “Fundamental limitations on Earth-like planet detection with extremely large telescope,” A&A. 447(1), 397–403 (2006).
[Crossref]

Roy, R.

S. Zhu, A. W. Yu, D. Hawley, and R. Roy, “Frustrated total internal reflection: A demonstration and review,” Am. J. Phys. 54(7), 601–607 (1986).
[Crossref]

Saumon, D.

A. Burrows, M. Marley, W. B. Hubbard, J. I. Lunine, T. Guillot, D. Saumon, R. Freed-man, D. Sudarsky, and C. Sharp, “A nongray theory of extrasolar giant planets and brown dwarfs,” Astrophys. J. 491(2), 856–875 (1997).
[Crossref]

Savransky, D.

D. Mawet, L. Pueyoc, P. Lawson, L. Mugnier, W. Traub, A. Boccaletti, J. Trauger, S. Gladysz, E. Serabyn, J. Milli, R. Belikov, M. Kasper, P. Baudoz, B. Macintosh, C. Marois, B. Oppenheimer, H. Barrett, J.-L. Beuzit, N. Devaney, J. Girard, O. Guyon, J. Krist, B. Mennesson, D. Mouillet, N. Murakami, L. Poyneer, D. Savransky, C. Verinaud, and J. K. Wallace, “Review of small-angle coronagraphic techniques in the wake of ground-based second-generation adaptive optics systems,” Proc. SPIE 8442, 844204 (2012).
[Crossref]

Serabyn, E.

D. Mawet, L. Pueyoc, P. Lawson, L. Mugnier, W. Traub, A. Boccaletti, J. Trauger, S. Gladysz, E. Serabyn, J. Milli, R. Belikov, M. Kasper, P. Baudoz, B. Macintosh, C. Marois, B. Oppenheimer, H. Barrett, J.-L. Beuzit, N. Devaney, J. Girard, O. Guyon, J. Krist, B. Mennesson, D. Mouillet, N. Murakami, L. Poyneer, D. Savransky, C. Verinaud, and J. K. Wallace, “Review of small-angle coronagraphic techniques in the wake of ground-based second-generation adaptive optics systems,” Proc. SPIE 8442, 844204 (2012).
[Crossref]

Severson, S.

Sharp, C.

A. Burrows, M. Marley, W. B. Hubbard, J. I. Lunine, T. Guillot, D. Saumon, R. Freed-man, D. Sudarsky, and C. Sharp, “A nongray theory of extrasolar giant planets and brown dwarfs,” Astrophys. J. 491(2), 856–875 (1997).
[Crossref]

Sidick, E.

Siegler, N.

R. Park, L. M. Close, N. Siegler, E. L. Nielsen, and T. Stalcup, “A reflective Gaussian coronagraph for ExAO: laboratory performance,” Proc. SPIE 6272, 20–27 (1998).
[Crossref]

Sommargren, G.

Stalcup, T.

R. Park, L. M. Close, N. Siegler, E. L. Nielsen, and T. Stalcup, “A reflective Gaussian coronagraph for ExAO: laboratory performance,” Proc. SPIE 6272, 20–27 (1998).
[Crossref]

Sudarsky, D.

A. Burrows, M. Marley, W. B. Hubbard, J. I. Lunine, T. Guillot, D. Saumon, R. Freed-man, D. Sudarsky, and C. Sharp, “A nongray theory of extrasolar giant planets and brown dwarfs,” Astrophys. J. 491(2), 856–875 (1997).
[Crossref]

Traub, W.

D. Mawet, L. Pueyoc, P. Lawson, L. Mugnier, W. Traub, A. Boccaletti, J. Trauger, S. Gladysz, E. Serabyn, J. Milli, R. Belikov, M. Kasper, P. Baudoz, B. Macintosh, C. Marois, B. Oppenheimer, H. Barrett, J.-L. Beuzit, N. Devaney, J. Girard, O. Guyon, J. Krist, B. Mennesson, D. Mouillet, N. Murakami, L. Poyneer, D. Savransky, C. Verinaud, and J. K. Wallace, “Review of small-angle coronagraphic techniques in the wake of ground-based second-generation adaptive optics systems,” Proc. SPIE 8442, 844204 (2012).
[Crossref]

Traub, W. A.

M. Kuchner and W. A. Traub, “A coronagraph with a band-limited mask for finding terrestrial planets,” Astrophys. J. 570(2), 900–908 (2002).
[Crossref]

Trauger, J.

D. Mawet, L. Pueyoc, P. Lawson, L. Mugnier, W. Traub, A. Boccaletti, J. Trauger, S. Gladysz, E. Serabyn, J. Milli, R. Belikov, M. Kasper, P. Baudoz, B. Macintosh, C. Marois, B. Oppenheimer, H. Barrett, J.-L. Beuzit, N. Devaney, J. Girard, O. Guyon, J. Krist, B. Mennesson, D. Mouillet, N. Murakami, L. Poyneer, D. Savransky, C. Verinaud, and J. K. Wallace, “Review of small-angle coronagraphic techniques in the wake of ground-based second-generation adaptive optics systems,” Proc. SPIE 8442, 844204 (2012).
[Crossref]

Verinaud, C.

D. Mawet, L. Pueyoc, P. Lawson, L. Mugnier, W. Traub, A. Boccaletti, J. Trauger, S. Gladysz, E. Serabyn, J. Milli, R. Belikov, M. Kasper, P. Baudoz, B. Macintosh, C. Marois, B. Oppenheimer, H. Barrett, J.-L. Beuzit, N. Devaney, J. Girard, O. Guyon, J. Krist, B. Mennesson, D. Mouillet, N. Murakami, L. Poyneer, D. Savransky, C. Verinaud, and J. K. Wallace, “Review of small-angle coronagraphic techniques in the wake of ground-based second-generation adaptive optics systems,” Proc. SPIE 8442, 844204 (2012).
[Crossref]

Voelkel, R.

R. Voelkel, “Wafer-scale micro-optics fabrication,” Adv. Opt. Technol. 1, 135–150 (2012).

Wallace, J. K.

D. Mawet, L. Pueyoc, P. Lawson, L. Mugnier, W. Traub, A. Boccaletti, J. Trauger, S. Gladysz, E. Serabyn, J. Milli, R. Belikov, M. Kasper, P. Baudoz, B. Macintosh, C. Marois, B. Oppenheimer, H. Barrett, J.-L. Beuzit, N. Devaney, J. Girard, O. Guyon, J. Krist, B. Mennesson, D. Mouillet, N. Murakami, L. Poyneer, D. Savransky, C. Verinaud, and J. K. Wallace, “Review of small-angle coronagraphic techniques in the wake of ground-based second-generation adaptive optics systems,” Proc. SPIE 8442, 844204 (2012).
[Crossref]

Wilson, D. W.

Yu, A. W.

S. Zhu, A. W. Yu, D. Hawley, and R. Roy, “Frustrated total internal reflection: A demonstration and review,” Am. J. Phys. 54(7), 601–607 (1986).
[Crossref]

Zhu, S.

S. Zhu, A. W. Yu, D. Hawley, and R. Roy, “Frustrated total internal reflection: A demonstration and review,” Am. J. Phys. 54(7), 601–607 (1986).
[Crossref]

A&A. (1)

C. Cavarroc, A. Boccaletti, P. Baudoz, T. Fusco, and D. Rouan, “Fundamental limitations on Earth-like planet detection with extremely large telescope,” A&A. 447(1), 397–403 (2006).
[Crossref]

Adv. Opt. Technol. (1)

R. Voelkel, “Wafer-scale micro-optics fabrication,” Adv. Opt. Technol. 1, 135–150 (2012).

Am. J. Phys. (1)

S. Zhu, A. W. Yu, D. Hawley, and R. Roy, “Frustrated total internal reflection: A demonstration and review,” Am. J. Phys. 54(7), 601–607 (1986).
[Crossref]

ApJS (1)

O. Guyon, E. A. Pluzhnik, M. J. Kuchner, B. Collins, and S. T. Ridgway, “Theoretical limits on extrasolar terrestrial planet detection with coronagraphs,” ApJS 167(1), 81–99 (2006).
[Crossref]

Appl. Opt. (1)

Astrophys. J. (2)

M. Kuchner and W. A. Traub, “A coronagraph with a band-limited mask for finding terrestrial planets,” Astrophys. J. 570(2), 900–908 (2002).
[Crossref]

A. Burrows, M. Marley, W. B. Hubbard, J. I. Lunine, T. Guillot, D. Saumon, R. Freed-man, D. Sudarsky, and C. Sharp, “A nongray theory of extrasolar giant planets and brown dwarfs,” Astrophys. J. 491(2), 856–875 (1997).
[Crossref]

Mon. Not. R. Astron. Soc. (1)

C. Mackay, “High-efficiency lucky imaging,” Mon. Not. R. Astron. Soc. 464, 680–687 (2017).

Opt. Lett. (1)

Proc. SPIE (2)

R. Park, L. M. Close, N. Siegler, E. L. Nielsen, and T. Stalcup, “A reflective Gaussian coronagraph for ExAO: laboratory performance,” Proc. SPIE 6272, 20–27 (1998).
[Crossref]

D. Mawet, L. Pueyoc, P. Lawson, L. Mugnier, W. Traub, A. Boccaletti, J. Trauger, S. Gladysz, E. Serabyn, J. Milli, R. Belikov, M. Kasper, P. Baudoz, B. Macintosh, C. Marois, B. Oppenheimer, H. Barrett, J.-L. Beuzit, N. Devaney, J. Girard, O. Guyon, J. Krist, B. Mennesson, D. Mouillet, N. Murakami, L. Poyneer, D. Savransky, C. Verinaud, and J. K. Wallace, “Review of small-angle coronagraphic techniques in the wake of ground-based second-generation adaptive optics systems,” Proc. SPIE 8442, 844204 (2012).
[Crossref]

Other (4)

P.R. Lawson, “Exoplanet Exploration Program Technology Plan, Appendix 2013,” JPL document D-81562, 2014.

J. Crepp, “High-Contrast Imaging with a band-limited coronagraphic mask,” PhD thesis, University of Florida (2008).

C. Aime, R. Soumer, and Y. Rabbia, “Shared constraints and specific characters in Very High Dynamics Imaging,” in Proceedings of Astronomy with High Contrast Imaging, C. Aime and R. Soummer, eds., 8 (EAS Publication Series, 2003), pp. 65–78.

Optics In Motion, “Standard Fast Steering Mirrors”, http://www.opticsinmotion.net/fast_steering_mirrors.html (2012).

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Figures (17)

Fig. 1
Fig. 1 Illustration of EvWaCo coronagraphic mask generic principle.
Fig. 2
Fig. 2 EvWaCo mask principle. O is the point of contact between PMask and LMask and h(x,y) is the air thickness in the mask. The reflection and transmission coefficients of the mask, in intensity are denoted as R and T respectively.
Fig. 3
Fig. 3 Model of EvWaco mask for the calculation of the coefficient of reflection in intensity. The glass medium LMask is represented by a succession of thin, homogeneous air gap of optical index n2 between two glasses of optical indices n1 and n3.
Fig. 4
Fig. 4 Left-side: PMask, OX in the plane of incidence and OY perpendicular. The footprint of the PSF on PMask hypotenuse is represented in yellow. The PSF beam footprint is larger by a factor equal to 21/2 along the OX axis due to the angle of incidence of the beam being equal to 45°. Right-side: close-view of the coronagraphic mask that comprises the prism PMask and the lens LMask. This lens is glued on a prism that transmits the starlight as represented in Fig. 10.
Fig. 5
Fig. 5 Variation of the reflection coefficients R and R// corresponding to the polarization perpendicular and parallel to the plane of incidence, respectively. This is the case for a thin, homogeneous air gap of thickness, h, delimited by two identical glass media made of BK7. We have used the wavelength λ = 880 nm, n1 = n3≈1.51 (BK7 optical index) and n2 = 1.
Fig. 6
Fig. 6 PSF irradiance distribution and EvWaCo mask theoretical reflection coefficients R// and R along the Y axis at x = 0 for λ = 880 nm, Φ1 = 45°, n1 = n3 = 1.51 (N-BK7) and n2 = 1 (air). We have also represented the Full Width at Half Maximum, FWHM// and FWHM, of the mask.
Fig. 7
Fig. 7 Variation of the phase delays δΦ// and δΦ at reflection on the EvWaCo mask for the polarizations respectively parallel and perpendicular to the incident plane at the wavelength λ = 880 nm.
Fig. 8
Fig. 8 EvWaCo mask theoretical reflection coefficients R(λ1) and R(λ3) at the wavelengths λ1 = 0.8 μm and λ3 = 1 µm. We have also represented: the PSF irradiance distribution cross-section along the Y axis at the wavelength λ2 = 0.9 μm.
Fig. 9
Fig. 9 Variations versus the wavelength of the FWHM (blue curve) and of the Airy disk diameter (red curve) for the EvWaCo mask in unpolarized light.
Fig. 10
Fig. 10 Optical setup used for the demonstration of principle of the proposed coronagraphic mask.
Fig. 11
Fig. 11 Photograph of the setup optical components comprised between L2 and L3. The coronagraphic mask separates the incident beams in two distinct beams: the “star beam” transmitted by the mask and the “companion beam” reflected by the mask.
Fig. 12
Fig. 12 Image of the coronagraphic mask (left) and normalized transmission profile of the mask along the X and the Y axes (right). The data have been acquired by performing a flat-field illumination at the wavelength λ = 880 nm with relative spectral bandwidth Δλ/λ ≈6% in unpolarized light.
Fig. 13
Fig. 13 On-axis PSF irradiance distribution centered on the mask in unpolarized light. This image has been acquired at the wavelength λ = 880 nm with a relative spectral bandwidth λ ≈6% with an integration time Δτ = 3s. We attribute the PSF irradiance profile asymmetries to the presence of contaminants between LMask and PMask, to the optical aberrations of the optical system and to the stray light effects.
Fig. 14
Fig. 14 PSF normalized irradiance profiles along the X (left-hand side) and along the Y axis (right-hand side). The blue curves represent the cross-section of the PSF profile in the case of an on-axis source centered on the coronagraphic mask. The orange curves represent the case of a source located off-axis and far from the mask The represented signals are normalized with respect to the off-axis PSF maximum signal. The condition of acquisition of the on-axis images are identical to the Fig. 13. The off-axis images have been acquired in identical conditions by placing an optical density of transmission T = 0.0024 in front of the CCD.
Fig. 15
Fig. 15 On-axis and off-axis PSF irradiance distribution in unpolarized light at the wavelength λ = 880 nm with relative spectral bandwidth Δλ/λ ≈6%. The off-axis PSF is located at a distance equal to 30 λ.f2/DAS from the mask center. Identical visualization levels for the two images: Imin = 1300 ADU and IMax = 65469 ADU. Each image is the result of a median combination of 101 images acquired at integration time Δτ = 7s. The radius of the inner and outer green circles are equal to 10 λ.f2/DAS and 20 λ.f2/DAS respectively.
Fig. 16
Fig. 16 Left –side: cross-section along X-axis represented in logarithmic scale of the following signals: off-axis PSF (distance from mask center: 30 λ.f2/D) measured with a density of transmission TD = 3x10−3 and measured without density (grey and orange curves respectively); On-axis PSF centered on the mask measured without density (blue curve). Right –side: cross-section along Y-axis represented in logarithmic scale of the following signals: off-axis PSF (distance from mask center: 30 λ.f2/D) measured with a density of transmission TD = 3x10−3 and measured without density (grey and orange curves respectively); On-axis PSF centered on the mask measured without density (pink curve). The dash black line represents the variance of the background noise σBack ≈2.10−7. We have also represented in green lines the location of IWAX and IWAY. The data have been acquired in unpolarized light at the wavelength λ = 880 nm with a relative spectral bandwidth λ ≈6% with an integration time Δτ = 7s.
Fig. 17
Fig. 17 Example of a setup to measure the wavefront of the star light transmitted by the occulting mask and control a deformable mirror placed in a pupil plane to adjust the center the star on the mask. The required resolution on the fast steering mirror angle is equal to 5 arcsecond typically to guaranty the contrast performance at the level presented in the section “3.4 On-axis and off-axis PSF profiles with a Lyot stop”.

Equations (3)

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D PSF 2.44×λ×F#
R( x,y,λ )=1 1 αsin h 2 [ ( 2π h( x,y ) /λ ) ( n 1 2 sin 2 ϕ 1 n 2 2 ) 1/2 ]+β
h( x,y ) ( x 2 + y 2 ) / 2.RC

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