An Eight-Octant Phase-Mask Coronagraph

Transcription

1 PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF THE PACIFIC, 12: , 28 October 28. The Astronomical Society of the Pacific. All rights reserved. Printed in U.S.A. An Eight-Octant Phase-Mask Coronagraph NAOSHI MURAKAMI National Astronomical Observatory of Japan, Osawa, Mitaka, Tokyo , Japan; RYOSUKE UEMURA AND NAOSHI BABA Division of Applied Physics, Hokkaido University, Sapporo , Japan JUN NISHIKAWA AND MOTOHIDE TAMURA National Astronomical Observatory of Japan, Osawa, Mitaka, Tokyo , Japan NOBUYUKI HASHIMOTO Citizen Technology Center Co., 84 Shimotomi, Tokorozawa, Saitama , Japan AND LYU ABE Laboratoire Hippolyte Fizeau, UMR 6525, Université de Nice-Sophia Antipolis, 28, avenue Valrose, F-618 Nice, France Received 28 June 6; accepted 28 August 4; published 28 September 24 ABSTRACT. We present numerical simulations and laboratory experiments on an eight-octant phase-mask (EOPM) coronagraph. The numerical simulations suggest that an achievable contrast for the EOPM coronagraph can be greatly improved as compared to that of a four-quadrant phase-mask (FQPM) coronagraph for a partially resolved star. On-sky transmission maps reveal that the EOPM coronagraph has relatively high optical throughput, a small inner working angle, and large discovery space. We have manufactured an eight-segment phase mask utilizing a nematic liquid-crystal device, which can be easily switched between the FQPM and the EOPM modes. The laboratory experiments demonstrate that the EOPM coronagraph has a better tolerance of the tip-tilt error than the FQPM one. We also discuss feasibility of a fully achromatic and high-throughput EOPM coronagraph utilizing a polarization interferometric technique. 1. INTRODUCTION An attempt to discover and characterize extrasolar Earth-like planets is one of the most challenging issues in modern astronomy. For direct detection of the extrasolar planets, many concepts of high-contrast imagers have been proposed, especially in the context of the Terrestrial Planet Finder Coronagraph (TPF-C) mission. It is necessary for the high-contrast imagers to realize extremely high dynamic range over a broad spectral bandwidth, together with high optical throughput, a small inner working angle (IWA), and large discovery space. For a practical aspect, in addition, technically simple instrumentation would be preferable because of a severe environment of space observations. A classical Lyot coronagraph is a precursory work for the high-contrast imager aiming at observing a solar coronal prominence by using an opaque mask on a focal plane (Lyot 1939). Recently, more advanced focal-plane masks, such as a four-quadrant phase mask (FQPM), a band-limited mask, and an optical vortex mask, have been proposed for planet detection (Rouan et al. 2; Kuchner & Traub 22; Kuchner et al. 25; Foo et al. 25). These techniques have the ability to strongly suppress both stellar diffraction core and halo, and tend to have relatively small IWAs. Pupil-apodization techniques, such as an apodized square aperture and binary shaped masks, have been proposed to suppress only the stellar diffraction halo (Nisenson & Papaliolios 21; Kasdin et al. 23; Enya et al. 27). An apodized pupil Lyot coronagraph (APLC), a combination of the pupil-apodization and the classical Lyot coronagraph, has also been proposed for realizing the highcontrast imaging with arbitrary aperture shapes of telescopes (Soummer 25). The pupil apodizations are less sensitive to tip-tilt errors and/or finite stellar angular sizes than the focalplane mask coronagraphs. However, these techniques tend to have relatively large IWAs and low optical throughputs. A phase-induced amplitude apodization (PIAA) has been proposed to achieve a small IWA without a loss of the optical throughput (Guyon 23). A comprehensive evaluation of theoretical capabilities for extrasolar planet detection has been conducted for several promising concepts (Guyon et al. 26). For direct detection of the extrasolar Earth-like planets, the high-contrast imagers must be 1112

2 EIGHT-OCTANT PHASE-MASK CORONAGRAPH 1113 tolerant of the tip-tilt error and the stellar angular size problem. For the FQPM coronagraph, however, residual stellar noise increases rapidly with δ 2, where δ is the tip-tilt error. This second-order behavior for the tip-tilt error would be insufficient for direct detection of the Earth-like planets around nearby stars. For this reason, the FQPM coronagraph has been excluded from the candidates for the TPF-C mission. Note that it is possible to realize the higher-order insensitivities to the tip-tilt error by using the other focal-plane mask (the band-limited mask and the optical vortex mask) coronagraphs. Nevertheless, the FQPM coronagraph is still attractive because of its ability to realize a perfect stellar suppression, a high optical throughput, a large discovery space, and a small IWA together with technically simple instrumentation. Rouan et al. (27) point out that it is possible to realize more efficient stellar suppressions by multiplying the number of sectors of the phase mask. We have also been paying attention to an eight-octant phase mask (EOPM) because of its acceptable optical throughput, IWA, and discovery space. We expect that it is easy to manufacture and achromatize the high-performance EOPM, because it has neither continuous phase retardation like the optical vortex masks nor complex and fine structure like the bandlimited masks. We have manufactured a chromatic version of the phase mask by using a nematic liquid crystal device, which can be easily switched between the FQPM and the EOPM modes. In this paper, we present numerical simulations and preliminary laboratory experiments on the EOPM coronagraph comparing it with the FQPM one. In 2, we show the results of the coronagraphic numerical simulations for a partially resolved star. On-sky transmittances of both the coronagraphs are also shown for evaluating their optical throughputs, IWAs, and discovery spaces. In 3, we describe the manufactured phase mask, and show results of the laboratory experiments on both the coronagraphs for various tip-tilt errors. In 4, we discuss feasibility of a fully achromatic and high-throughput EOPM coronagraph utilizing a polarization interferometric technique. Finally, our conclusions are summarized in NUMERICAL SIMULATIONS Similar to the FQPM, the EOPM is put on a focal plane to divide a stellar image into eight-octant regions, and provides a -phase difference between the adjacent octants. This causes a self-destructive interference inside the pupil area on a following reimaged pupil plane, where a Lyot stop is put to block stellar light diffracted outside the pupil. A transmittance of the EOPM is defined as MðψÞ ¼ð 1Þ k ; k 4 ðk þ 1Þ ψ < ; (1) 4 where ψ is an azimuth angle in the focal plane, and k is an arbitrary integer. The transmittance can be expressed by using a Fourier expansion as MðψÞ ¼ 2 i X m¼ e 4ð2mþ1Þiψ 2m þ 1 X m¼ e 4ð2mþ1Þiψ : (2) 2m þ 1 The above equation shows that the EOPM can be written as a weighted sum of evenly charged optical vortex masks, each of which causes zero intensity within the pupil in a Lyot-stop plane for a pointlike star (Jenkins 28). Thus, the EOPM coronagraph realizes perfect stellar elimination for unresolved stars as well as the FQPM one does. In practice, however, observed stars will have finite angular sizes, and residual stellar noise will increase due to off-axis light from a rim of the stellar disk. We carry out numerical simulations for evaluating coronagraphic performance of both the coronagraphs for partially resolved stars. In Figure 1, we show the results of the numerical simulations, together with illustrations of the FQPM and the EOPM. In the numerical simulations, we assume a uniform-disk star with an angular diameter of :2λ=D as an example. This angular size roughly corresponds to a Sun-like star seen from 1 parsec away from the Earth assuming D ¼ 3 m and λ ¼ :6 μm. A Lyot-stop size is set to be 9% of an entrance pupil. Two images show the coronagraphic images for a model planetary system around the partially resolved star. The model planetary system is composed of three model planets at 1.5, 3., and 5:λ=D from the central star with star/planet intensity ratios of 2 1 9, 1 1 1, and 2 1 1, respectively. The model planetary images can be clearly detected by the EOPM coronagraph as pointed by arrows, while these images are buried in the residual stellar noise for the FQPM-coronagraphic image. Note that instrumental defects (chromatism, phase and amplitude FIG. 1. Drawings of phase masks and simulated coronagraphic images for FQPM (left) and EOPM coronagraphs (right). A partially resolved central star (angular diameter of :2λ=D) and three model planets (indicated by arrows) are assumed in the numerical simulation. 28 PASP, 12:

3 1114 MURAKAMI ET AL. aberrations, misalignment, a pointing error of a telescope, an effect of a central obscuration of a secondary mirror, and so on) are not included in the numerical simulations. We also evaluate coronagraphic performance for partially resolved stars of various angular diameters. Figure 2 shows halo intensity (mean intensity over 4 6λ=D) as a function of the stellar diameter in λ=d unit. A ratio of the halo intensities of both the coronagraphs is also shown in the graph. The results suggest that the coronagraphic performance can be greatly improved by using the EOPM especially for smaller stars. For example, the coronagraphic performance can be 1 4 times improved for stars with a diameter less than :4λ=D, and a contrast greater than 1 9 will be achieved at the angular distance around 5λ=D even for a stellar diameter of :1λ=D. Next, we show on-sky transmission maps for both the coronagraphs to evaluate their IWAs and discovery spaces. Figure 3 shows the transmission maps with a field of view of 2 2λ=D, in which we calculate peak intensities of an off-axis light source from each on-sky position normalized by those without the phase masks. Two plots (shown by diamonds and crosses) in Figure 3 show the azimuthally averaged transmission for both the coronagraphs as a function of an angular distance in unit of λ=d from a center of the phase mask. Two curves in the graph show the transmittances along highthroughput axes between the boundaries of the phase masks. The high-throughput axes for both the phase masks are shown by dashed arrows in each transmission map. Note that the peak intensities exceed unity because a loss of intensity due to a Lyot stop is not considered in these results. The loss due to the Lyot stop becomes D 4 L, where D L is a relative size of the Lyot stop to an entrance pupil. In the case of the numerical simulation shown here, the loss becomes D 4 L ¼ :66 because we set the Lyot-stop size to D L ¼ :9. From the transmission maps, we conclude that the FQPM has an IWA of 1:1λ=D while that of the EOPM is 1:9λ=D. Here, we Halo intensity e-6 1e-8 1e-1 1e-12 1e-14 EO/FQ FQPM EOPM Stellar diameter [ λ D ] FIG. 2. Normalized halo intensity (mean intensity over 4 6λ=D) as a function of a stellar diameter in unit of λ=d. Ratios between FQPM and EOPM are also shown. FIG.3. Calculated on-sky transmission maps for the FQPM and EOPM coronagraphs (a field of view of 2 2λ=D). Two plots in the graph are radial profiles of the transmission maps (diamonds for the FQPM, and plus signs for the EOPM), while two curves show the profiles along the high-throughput axes (shown by dashed arrows in the maps). define the IWA as an angular distance at which the transmission along the high-throughput axis including the loss due to the Lyot stop reaches 5%. Note that the transmission of 5% corresponds to.76 in Figure 3, because the numerical simulations do not include the loss due to the Lyot stop. Although we estimate the IWA of the EOPM as 1:9λ=D here, faint companions imaged at inner region (e.g., 1:5λ=D) would be detectable as demonstrated in Figure 1. We also evaluate the discovery spaces as 81% and 71% for the FQPM and EOPM coronagraphs, respectively. Here, we define the discovery space as a fractional region, with respect to a full field of view of 2 2λ=D, in which the transmission exceeds 5%. Note that planetary images are strongly suppressed on the boundary of the phase masks, and thus rotations of the phase masks (45 for the FQPM and 22.5 for the EOPM) are required for obtaining a full-sky coverage. 3. LABORATORY DEMONSTRATIONS We have manufactured an eight-segment phase mask utilizing a nematic liquid crystal (NLC) device with homogeneous alignment. Figure 4 is a picture of the manufactured phase mask. The NLC device is subdivided into eight segments, L1 L4 and R1 R4, which can be connected to function generators separately via flexible printed circuits (FPCs) for applying desired voltages to each segment. When a linearly polarized (LP) light along x-direction (parallel to the alignment of the NLC) enters, the resultant polarization is unchanged, while the phase can be modulated by the applied voltage V. The phase of the resultant LP light can be written as ϕðv Þ¼2nðVÞd=λ, where n and d are a refractive index and thickness of the NLC device, and λ is an operational wavelength. For realizing a coronagraphic phase mask, the applied voltages V a and V b to the appropriate segments (e.g., V a to segments [L1, L3, R2, R4] and V b to [L2, L4, R1, R3] for the EOPM-mode) must be 28 PASP, 12:

4 EIGHT-OCTANT PHASE-MASK CORONAGRAPH 1115 FIG.4. A picture of a manufactured NLC phase mask. A liquid-crystal cell is subdivided into eight segments (R1 R4 and L1 L4, as shown by an inset), to which the flexible printed circuits (FPCs) are connected for applying voltages separately. A coronagraphic phase mask can be realized for a linearly polarized light along x- direction by adjusting the applied voltages appropriately. adjusted so that the phase difference Δϕ ¼ ϕðv a Þ ϕðv b Þ is ð2m þ 1Þ (m is an arbitrary integer). In our laboratory demonstrations, we choose the applied voltages (a rectangular wave of 1 khz) of V b ¼ 2:73 V rms and V a ¼ : V rms for realizing Δϕ ¼ 3 (i.e. m ¼ 1). It should be noted that the manufactured phase mask cannot be used for a broadband light because of a chromatic property of the NLC device although it can be optimized for an arbitrary wavelength by adjusting the applied voltages. An issue of an achromatization of the phase mask will be discussed in the following section. We have carried out laboratory demonstrations of the FQPM and the EOPM coronagraphs with a monochromatic light source (He-Ne laser with λ ¼ :633 μm) to acquire coronagraphic images with various tip-tilt errors. Figure 5 shows experimental results. The top panels are acquired images with the tip-tilt errors δ of.5 and :4λ=D. White arrows and dotted lines indicate the tip-tilt directions and the boundaries of the phase masks, respectively. We show the experimental results for two tip-tilt directions; one is that between the boundaries (FQ-1 and EO-1) and the other is that along the boundary (FQ-2 and EO-2). For evaluating a residual intensity due to the tip-tilt error, we subtract a zero tip-tilt coronagraphic image from each image to eliminate residual speckle noise. We assume that the residual speckle noise comes especially from an optical surface roughness of the NLC phase mask itself, which is measured to be around :1 λ rms over a diameter of 5.4 mm. For on-sky observations, the speckle subtraction will be carried out by subtracting a reference pointlike star of a similar spectral type to a target. Note that the speckle noise can also be suppressed by using the differential techniques (Racine et al. 1999; Baba & Murakami 23; Murakami et al. 27) or the speckle nulling technique (Trauger & Traub 27). We calculate a total intensity IðδÞ of the coronagraphic images over a field of view of 7:4 7:4λ=D. The bottom graph in Figure 5 shows the result. Four plots are the measured intensities IðδÞ for the FQPM (diamonds and plus signs) and the EOPM (squares and crosses). The residual intensity for the FQPM coronagraph rapidly increases with the tip-tilt error, while that for the EOPM one can be well suppressed even for large tip-tilt errors. We also fit the experimental data with a function IðδÞ ¼aδ b, where a and b are fitting parameters. The fittings are carried out by using the data for small tip-tilt errors (δ < :3 for the FQPM and δ < :7 for the EOPM). The fitting results and the fitted parameters for both the coronagraphs with two different tip-tilt directions are also shown in Figure 5. Consequently, we obtain the values b ¼ 2:41 and 2.18 for the FQPM coronagraph, while b ¼ 4:9 and 4. for the EOPM one. These results demonstrate that the EOPM coronagraph has a tolerance of the tip-tilt error (a fourth-order response) as compared to the FQPM one (roughly a secondorder response). 4. DISCUSSION The manufactured phase mask cannot be used for a broadband light because of the chromatic effect of the NLC device. We estimate that, when an acceptable phase error is set to 5 mrad, an effective spectral bandwidth at λ ¼ 65 nm is restricted to only 16 nm (that is, Δλ=λ ¼ :25). For our future work, we are planning to design and manufacture an achromatic EOPM. We expect that it would be much easier to manufacture the achromatic EOPM than the other focal-plane coronagraphic masks, because the EOPM has neither a continuous phase shift nor complex and fine structure. Many techniques for the achromatic phase mask have been proposed in the context of the FQPM coronagraph that can be directly applied to the EOPM one. Riaud et al. (21) propose to use a reflective phase mask with a quarter-wave multilayer coating of high- and low-optical indices. Abe et al. (21) propose a phase-knife coronagraph, in which a white-light Airy image is dispersed to provide -phase shift separately for each wavelength. A zero-order grating has also been proposed, which makes use of a form birefringence of subwavelength surfacerelief gratings (Mawet et al. 25). Mawet et al. (26) propose to use a two stage stack of birefringence half-wave plates (HWPs) with two materials. Baudoz et al. (28) propose a mul- 28 PASP, 12:

5 1116 MURAKAMI ET AL. FIG. 5. Top figures show the acquired FQPM- and EOPM-coronagraphic images with tip-tilt errors of.5 (top) and :4λ=D (bottom). The tip-tilt directions and boundaries of the phase masks are shown by white arrows and dotted lines in the top images. Zero tip-tilt images are subtracted from each image for suppressing residual speckle noise. Plots in a bottom graph show normalized intensities IðδÞ integrated over a field of view as a function of the tip-tilt error δ. Curves show fitting results of each data with a function IðδÞ ¼aδ b. Fitted parameters a, b for each situation are also shown in the graph. tistage FQPM coronagraph by constructing chromatic phasemask coronagraphs in cascade. Note that the manufactured NLC-mask might be advantageous to this technique because of its adjustable operational wavelength. An application of the manufactured NLC-mask to the multistage FQPM coronagraph will be an interesting future work. A FQPM by utilizing a polarization interferometry (a fourquadrant polarization-mask; FQPoM) has been proposed (Baba et al. 22), and very high contrast has been demonstrated (Murakami et al. 28). The FQPoM is composed of four HWPs made of a ferroelectric liquid crystal (FLC) device with different angles of optical axes between quadrants. These HWPs rotate an input LP light to opposite directions by 45 (Murakami et al. 23). This method requires two polarizers, one in front of and one behind the FQPoM, whose orientation angles are 45 and 45, respectively. By utilizing the polarization interferometry, it is possible to realize a fully achromatic phase mask in spite of the chromatic characteristic of the FLC device. However, this original design has very low optical throughput, which is restricted to be at most.25 because of the two polarizers (intensity losses of.5 at each polarizer assuming unpolarized planetary signal). This problem can be solved by replacing the first 45 polarizer with a polarizing beam splitter to construct a twochannel configuration for utilizing both 45 and 45 LP components (LP A and LP B, respectively) (Baba & Murakami 23). Furthermore, the optical throughput can also be greatly improved by changing the angles of the LP rotation from 45 to 9 as mentioned in Murakami et al. (26). Figure 6 shows a fully achromatic and high-throughput design of the EOPM coronagraph, which we call an eightoctant polarization mask (EOPoM). When the LP A light enters top the phase mask, whose Jones vector can be written as E in ¼ 1 ffiffi 2 ½1 1Š ( means transposed matrix), Jones vectors of the output beams from two segments of the EOPoM (segments 1 and 2 in Fig. 6) can be written as E out;1 ¼ 1 p 2 ffiffi 1 2 e iβ ; E out;2 ¼ 1 p 2 ffiffiffi eiβ : (3) 2 1 Here, β is a retardation of the FLC device, which must ideally 28 PASP, 12:

6 EIGHT-OCTANT PHASE-MASK CORONAGRAPH 1117 E in Segment 2 Segment 1 x E out,2 y y Analyzer ( 45 ) E in E out,2 EOPoM LP A ( 45 ) x E out,1 be (EOPoM is regarded as perfect HWPs), but in general, depends strongly on a wavelength. Equation (3) suggests that both the output light beams become 45 LP light when the retardation β ¼. On the other hand, the outputs become circular polarizations of opposite directions when the EOPoM is regarded as quarter-wave plates (QWPs; β ¼ =2). After passing though the EOPoM, output Jones vectors from the 45 analyzer are calculated as E out;1 ¼ 1 p 2 ffiffiffi 1 e iβ 2 1 þ e iβ ; E out;2 ¼ 1 p 2 ffiffiffi 1 þ eiβ 2 1 e iβ : (4) E out,1 FIG.6. A schematic design of a fully achromatic and high-throughput eightoctant polarization mask. Implementation of the EOPoM is also shown for input LP A (45 linearly polarized) light beams passing through two segments (segments 1 and 2). Equation (4) clearly shows that the resultant light beams satisfy E out;2 ¼ e i E out;1 for any values of β. Thus, a fully achromatic phase mask can be realized despite the chromatic property of the FLC device. In Figure 6, we describe states of polarization before and after the EOPoM and after the analyzer for two cases (solid lines for β ¼, and dotted lines for β ¼ =2), assuming the input LP A light beams. Almost all photons of a planetary image pass through one segment of the phase mask (e.g., segment 1). Thus, an optical throughput for the planetary signal can be written as T ¼ je out;1 j 2 =je in j 2, and becomes T ¼ 1 2ð1 cos βþ: (5) Therefore, a lossless EOPM coronagraph (that is, T ¼ 1:) can be realized when β ¼, but the optical throughput decreases as β deviates from. For achieving high throughput of T>:8, a deviation of the retardation β from must be less than :92 radian. We measured the retardation βðλþ of a FLC device used in FQPoM-coronagraphic demonstrations reported in Murakami et al. (28). From the measurements, we roughly estimate that the throughput of T>:8 can be achieved for a broad bandwidth of Δλ=λ ¼ :4 in a visible spectral range. We expect that the achromatic EOPoM can also be realized by utilizing a twisted-nematic liquid crystal (TNLC) device with twist angles of 9, because this kind of device can also rotate an input LP light to 9. Evaluations of the achromaticity and the optical throughput of the FLC- and TNLC-based phase masks will be our future works. 5. CONCLUSIONS In this paper, we report the numerical simulations and the laboratory experiments on the EOPM coronagraph. The numerical simulations show that the EOPM coronagraph greatly improves the achievable contrast as compared to the FQPM one for partially resolved stars. In addition, on-sky transmission maps reveal that the EOPM coronagraph has a relatively small IWA and a large discovery space. We manufactured the eightsegment phase mask by using the NLC device, which can be easily switched between the FQPM and EOPM modes. Our laboratory experiments confirm that the EOPM coronagraph has the fourth-order response to the tip-tilt error, which is better than that of the FQPM one (expected to be second-order). This higher-order behavior of the EOPM coronagraph could enable us to detect extrasolar Earth-like planets around nearby stars with relatively large apparent sizes. We also discuss feasibility of a fully achromatic and highthroughput EOPM coronagraph. We expect that the polarization interferometric phase mask by using the FLC device (so-called EOPoM) and the two-channel optical configuration to improve the achromaticity and the optical throughput. The two-channel configuration is also useful for obtaining polarization differential images to suppress residual stellar speckle noise and to carry out polarimetric measurements of extrasolar planets (Baba & Murakami 23). For our future work, we are planning to design and manufacture the achromatic EOPoM by using the FLC (or possibly by the TNLC) device, and conduct on-sky high-contrast observations of circumstellar disks and faint companions around nearby stars. We thank T. Inabe and H. Shibuya of Hokkaido University for their experimental assistance. We are grateful to K. Oka of Hokkaido University for his valuable comments and support. We thank the Advanced Technology Center of the National Astronomical Observatory of Japan for helpful support. This research was partly supported by the National Astronomical Observatory of Japan and by a Grant-in-Aid for Scientific Research (B) from the Japan Society for the Promotion of Science (193636). This research was also partly supported by the 28 PASP, 12:

7 1118 MURAKAMI ET AL. Japanese Ministry of Education, Culture, Sports, Science and Technology, through a Grant-in-Aid for Scientific Research on Priority Areas, Development of Extra-solar Planetary Science. N. M. is financially supported by the Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists. REFERENCES Abe, L., Vakili, F., & Boccaletti, A. 21, A&A, 374, 1161 Baba, N., & Murakami, N. 23, PASP, 115, 1363 Baba, N., Murakami, N., Ishigaki, T., & Hashimoto, N. 22, Opt. Lett., 27, 1373 Baudoz, P., Galicher, R., Baudrand, J., & Boccaletti, A. 28, preprint (astro-ph/ ) Enya, K., Tanaka, S., Abe, L., & Nakagawa, T. 27, A&A, 461, 783 Foo, G., Palacios, D. M., & Swartzlander, G. A., Jr. 25, Opt. Lett., 3, 338 Guyon, O. 23, A&A, 44, 379 Guyon, O., Pluzhnik, E. A., Kuchner, M. J., Collins, G., & Ridgway, S. T. 26, ApJS, 167, 81 Jenkins, C. 28, MNRAS, 384, 515 Kasdin, N. J., Vanderbei, R. J., Spergel, D. N., & Littman, M. G. 23, ApJ, 582, 1147 Kuchner, M. J., Creep, J., & Ge, J. 25, ApJ, 628, 466 Kuchner, M. J., & Traub, W. A. 22, ApJ, 57, 9 Lyot, B. 1939, MNRAS, 99, 58 Mawet, D., Riaud, P., Baudrand, J., Baudoz, P., Boccaletti, A., Duppis, O., & Rouan, D. 26, A&A, 448, 81 Mawet, D., Riaud, P., Surdej, J., & Baudrand, J. 25, AO, 44, 7313 Murakami, N., Abe, L., Tamura, M., & Baba, N. 27, ApJ, 661, 634 Murakami, N., Baba, N., Ishigaki, T., & Hashimoto, N. 23, Proc. SPIE, 486, 343 Murakami, N., Baba, N., Tate, Y., Sato, Y., & Tamura, M. 26, PASP, 118, 774 Murakami, N., Uemura, R., Baba, N., Sato, Y., Nishikawa, J., & Tamura, M. 28, ApJ, 677, 1425 Nisenson, P., & Papaliolios, C. 21, ApJL, 548, 21 Racine, R., Walker, G. A. H., Nadeau, D., Doyon, R., & Marois, C. 1999, PASP, 111, 587 Riaud, P., Boccaletti, A., Rouan, D., Lemarquis, F., & Labeyrie, A. 21, PASP, 113, 1145 Rouan, D., Baudrand, J., Boccaletti, A., Baudoz, P., Mawet, D., & Riaud, P. 27, C. R. Physique, 8, 298 Rouan, D., Riaud, P., Boccaletti, A., Clénet, Y., & Labeyrie, A. 2, PASP, 112, 1479 Soummer, R. 25, ApJL, 618, 161 Trauger, J. T., & Traub, W. A. 27, Nature, 446, PASP, 12:

8 Laboratory experiments on the 8-octant phase-mask coronagraph Naoshi Murakami, a,*1 Ryosuke Uemura, b Naoshi Baba, b Hiroshi Shibuya, b Jun Nishikawa, a Lyu Abe, a,*2 Motohide Tamura, a and Nobuyuki Hashimoto c a National Astronomical Observatory of Japan, Osawa, Mitaka, Tokyo , Japan; b Division of Applied Physics, Hokkaido University, Sapporo , Japan; c Citizen Technology Center Co., 84 Shimotomi, Tokorozawa, Saitama , Japan ABSTRACT A four-quadrant phase-mask (FQPM) coronagraph can suppress perfectly stellar light when a star can be regarded as a point-like source. However, the FQPM coronagraph is highly sensitive to partially resolved stars, and shows second-order sensitivity to tip-tilt error leakage. Higher-order sensitivity is required for extremely high-contrast imaging of nearby stars. We propose an eight-octant phase-mask (EOPM) for achieving fourth-order sensitivity to tip-tilt errors. We manufactured the phase-mask utilizing a nematic liquid crystal (LC) device, which is composed of eight segments. A phase retardation of the LC can be adjustable by an applied voltage to the device. The LC phase-mask can be switched between FQPM-mode and EOPM-mode by applying appropriate voltages to the segments. We carry out experiments on the phase-mask coronagraph with various tip-tilt errors. The experimental results show the higher-order behavior of the EOPM compared to the FQPM. We present a current status of the laboratory experiments on the EOPM coronagraph, and also show coronagraphic performance of the EOPM derived from numerical simulations. Keywords: coronagraph, high-contrast imaging, extrasolar planet, laboratory experiment, liquid crystal device 1. INTRODUCTION Various concepts of high-contrast imagers have been proposed for direct detections and characterizations of extrasolar planets. Among the high-contrast imagers, focal-plane mask coronagraphs can suppress both bright stellar diffraction core and halo. 1-4 A four-quadrant phase-mask (FQPM) coronagraph is one of the most promising approaches. The FQPM is put on a focal plane to divide a stellar image into four-quadrant regions and provide a -phase difference between the adjacent quadrants. This causes destructive interference inside the pupil area on a following reimaged pupil plane, where a Lyot-stop is put to block stellar light diffracted outside the pupil. Theoretically, it is possible to achieve perfect stellar elimination by using the FQPM coronagraph. The FQPM coronagraph will also be advantageous because *1 naoshi.murakami@nao.ac.jp, *2 Current affiliation is Laboratoire Hippolyte Fizeau, UMR 6525, Université de Nice-Sophia Antipolis, 28, avenue Valrose, F-618 Nice, France Space Telescopes and Instrumentation 28: Optical, Infrared, and Millimeter, edited by Jacobus M. Oschmann, Jr., Mattheus W. M. de Graauw, Howard A. MacEwen, Proc. of SPIE Vol. 71, 711J, (28) X/8/$18 doi: / Proc. of SPIE Vol J-1

9 it has a relatively small inner working angle (IWA), large discovery space, and high optical throughput with technically simple instrumentation. For coronagraphic observations with a broad spectral range, many concepts for an achromatic phase-mask have been proposed, such as a two stage stack of birefringence half-wave plates 5, a zero-order grating 6, a polarization interferometric technique 7, a multi-layer reflective phase-mask 8, a phase-knife coronagraph 9, and so on. On-sky observations with the FQPM coronagraph have also been carried out and some interesting scientific results have been reported One of the most critical problems of the FQPM coronagraph is its low-order sensitivity to tip-tilt errors or finite angular sizes of the target stars. This effect might cause leakage of stellar noise and prevent us from detecting faint companions around partially resolved nearby stars. To solve this problem, multi-segment phase-masks (eight-, 16-, or more) have been proposed for providing higher-order sensitivities. 13 We present results of preliminary coronagraphic experiments with an eight-segment phase-mask (hereafter eight-octant phase-mask, EOPM). We manufactured the EOPM by using a liquid crystal (LC) device. In section 2, we describe the manufactured LC phase-mask. Results of laboratory experiments are shown in section 3. In Section 4, we summarize our conclusions. 2. MANUFACTURE OF THE LIQUID-CRYSTAL EIGHT-OCTANT PHASE-MASK Figure 1 shows the manufactured eight-segment phase-mask and its implementation. A left figure shows a picture of the manufactured phase-mask by using a nematic LC device with homogeneous alignment. The LC cell is subdivided into eight segments (L1-L4 and R1-R4), each of which is connected to flexible printed circuit (FPC) for applying voltage separately. The LC device is regarded as a variable retarder, and the retardation can be modulated by changing the applied voltage V. Thus, when a linearly polarized (LP) light beam, whose direction is parallel to the alignment of the liquid crystal (x-axis in figure 1), enters to the phase-mask, the resultant polarization is unchanged and phase can be modulated as 2n ( ) ( V ) d φ V =. (1) λ Here, n is a refractive index for the LP of the x-direction, and λ, d are a wavelength and a thickness of the LC device, respectively. Note that the LC mask can be utilized as both the FQPM and the EOPM by applying two voltages V a and V b to the desired segments (e.g., V a to the segments [L1, L3, R2, R4] and V b to [L2, L4, R1, R3] for the EOPM-mode). To realize -phase difference between the segments, the two voltages must be adjusted to satisfy the following condition: 2 ( ) ( ) { n( Va ) n( Vb )} d φ V φ V = = ( 2m + 1), (2) a b λ where m is an arbitrary integer. It should be noted that the LC phase-mask has chromatic characteristic in its retardation, and cannot be used for broadband light. Development of an achromatic EOPM is our important future work. Figure 2 shows the phase difference ( V ) φ( ) φ as a function of the applied voltage Va (a rectangular voltage wave a V b with 1 khz frequency), assuming that another voltage Vb is set to zero and the operational wavelength is 65 nm. It is Proc. of SPIE Vol J-2

10 m= m= 1 possible to realize the coronagraphic phase-masks when the voltage Va is set to V (about 1.7 Vrms) and V (about 3.1 Vrms), respectively. The former case corresponds to the phase difference of (m=) and the latter case corresponds to 3 (m=1). a a LC Cell Out-of-phase.1 Applied voltages Output FPC III I I L1 L2 L3 L4 R1 R2 R3 R4 In-phase y x FPC Input polarization FPC Applied voltages Figure 1: A picture of manufactured LC phase-mask and its implementation. The LC cell is subdivided into eight segments (L1-L4 and R1-R4), each of which is connected to a flexible printed circuit (FPC) for applying voltage separately. A -phase difference between segments can be realized for one polarization (along x-axis) by modulating the applied voltages appropriately λ 2 1 Phase Difference [nm] λ 2 2 m= m= 1 V a V a Voltage [Vrms] Figure 2: An estimated phase difference between segments of a LC phase-mask as a function of an applied voltage V a assuming another voltage V b is set to zero. Proc. of SPIE Vol J-3

11 3. LABORATORY EXPERIMENTS In this section, we present laboratory demonstrations of the EOPM coronagraph. Figure 3 shows the experimental setup. As a light source, we use a monochromatic He-Ne laser (λ =633 nm) because of the chromatic characteristic of the phase-mask. A model star is imaged onto the LC phase-mask after passing through an entrance pupil (diameter of D=1. o mm), a focusing lens L2 (focal length of f=1 mm), and a polarizer P ( θ = ). Thus, a scale of λf/d on the phase-mask plane corresponds to 633 µm, which seems to be large enough compared to width of boundaries between segments of the phase-mask (estimated to be about 5 µm). The phase-mask is mounted on an xz-stage to move accurately for introducing tip-tilt errors instead of tilting the incident light beam. A re-imaged pupil is formed by a lens L3 (f=5 nm) with a magnification of.5 on a Lyot-stop plane. A size of the Lyot-stop is set to.4 mm, which corresponds to 8% of the entrance pupil. A final coronagraphic image is formed on a CCD camera by a lens L4 (f=7 mm). A Lyot-stop image can also be obtained by replacing lens L4 with another one L5 (f=2 mm). Figure 4 shows the acquired Lyot-stop images for the (a) FQPM- and (c) EOPM-modes, which are similar to those of numerical simulations (b, d). Figure 5 shows EOPM-coronagraphic performance as a function of a phase-difference error from radian. Two plots m= m= 1 show experimental results around the applied voltages V (diamonds) and V (crosses), and a curve shows a a result of a numerical simulation. Corresponding applied voltages are also shown in the graph. In these experiments, we measure total intensity over the Lyot-stop normalized by the intensity over the entrance pupil. The best performance can be obtained when the voltages are set to V am= = Vrms and V am=1 = Vrms, respectively. Note that the m= 1 voltage V for the He-Ne laser (λ =633 nm) is different from that estimated in figure 2 for λ =65 nm, because of a the chromatic effect of the LC device. The experimental results show that a slightly better performance can be obtained m= 1 for the voltage V. Thus, we use this voltage for the following experiments. It should also be noted that the a coronagraphic performance cannot reach to the theoretical limit derived from the numerical simulation, probably because of defects of the LC phase-mask (for example, optical surface roughness, phase retardation error, non-uniformity of the LC device, and so on) P a HeNe Laser L1 (f=6) L2 (f=1) L3 (f=5) L4/L5 (f=7/2) Objective Lens Pinhole Entrance Pupil LC Phase-Mask Lyot Stop (D=5micron) (D=1.) on xz-stage (D=.4) CCD Camera Function Generator Figure 3: Experimental setup for demonstrating the FQPM and EOPM coronagraphs with various tip-tilt errors. A monochromatic light source (He-Ne laser, 633 nm) is used. Proc. of SPIE Vol J-4

12 Next, we carry out coronagraphic demonstrations by introducing various tip-tilt errors. Top images in figure 6 are acquired FQPM- and EOPM- coronagraphic images for the tip-tilt errors from. to.4λ/d. White arrows show a direction of the tip-tilt errors. As can be seen in these results, leakage due to the tip-tilt error increases rapidly for the FQPM coronagraph, while that for the EOPM one can be well suppressed even for the large tip-tilt errors. A bottom graph shows the halo-intensity level at 3λ/D as a function of the tip-tilt error for two tip-tilt directions. Tip-tilt 1 means a tip-tilt direction along x-axis, while tip-tilt 2 is that between boundaries of the segments of the phase-mask o o ( 45 with respect to the x-axis for the FQPM, and 22.5 for the EOPM as illustrated in the graph). The graph suggests that the FQPM and the EOPM coronagraphs have second-order and forth-order sensitivity to the tip-tilt error, respectively. The higher-order characteristic of the EOPM will enable us to detect directly faint extrasolar planets around partially resolved nearby stars. (a) Experiment (FQPM) (b) Simulation (FQPM) (c) Experiment (EOPM) (d) Simulation (EOPM) Figure 4: Laboratory experiments and numerical simulations of the FQPM- and EOPM-coronagraphic images on the Lyot-stop plane. 1 m= m=1 Simulation Normalized Intensity Vrms 1.8 Vrms 2.68 Vrms 2.76 Vrms Phase Error [rad] Figure 5: EOPM-coronagraphic performance as a function of a phase-difference error from radian by modulating the applied voltages around m= V (diamonds) and a m=1 V (crosses). The corresponding applied voltages are shown in the graph. A vertical a axis shows coronagraphic performance, that is, total intensity over the Lyot-stop normalized by that over the entrance pupil. A result of a numerical simulation is also shown. Proc. of SPIE Vol J-5

13 Tip-tilt error /[ λ /D] FQPM EOPM 5e-4 y x FQPM Tip-tilt 2 EOPM (Tip-tilt 1) EOPM (Tip-tilt 2) FQPM (Tip-Tilt 1) FQPM (Tip-Tilt 2) Halo Intensity at 3 lambda/d e-5 Tip-tilt 1 EOPM Tip-tilt 2 Tip-tilt Tip-Tilt Error [lambda/d] Figure 6: Top images are acquired FQPM- and EOPM coronagraphic images with tip-tilt errors from. to.4λ/d. Bottom graph shows halo intensity at 3 λ/d as a function of the tip-tilt error. 4. CONCLUSION We manufactured the eight-segment phase-mask by using the LC device, which can be easily switched between the FQPM- and EOPM-modes. By using the manufactured phase-mask, we carried out the laboratory experiments of the both coronagraphs with the monochromatic He-Ne laser. We obtained the Lyot-stop images of the FQPM and EOPM coronagraphs, and confirmed that the obtained images are well similar to those of the numerical simulations. We also carried out the coronagraphic demonstrations by introducing various tip-tilt errors. The results show that the halo intensity for the FQPM coronagraph increases rapidly with the tip-tilt error, while that for the EOPM one can be well suppressed even for a large tip-tilt error. We estimated that the FQPM coronagraph has the second-order sensitivity to the tip-tilt error, while the EOPM one has the forth-order one. This higher-order characteristic of the EOPM coronagraph will make it possible to detect extrasolar planets around partially resolved nearby stars. We could not obtain extremely high contrast as predicted by the numerical simulation as Proc. of SPIE Vol J-6

14 shown in figure 5. We are now checking the whole system, especially the operation of the LC phase-mask, for improving the achievable contrast. Achromatization of the EOPM is one of the most important future works for us. We expect that the polarization interferometric phase-mask is one noticeable solution because of its fully achromatic design. We have manufactured a four-quadrant polarization mask (FQPoM) by utilizing a ferroelectric LC device, and achieved very high contrast. 14 As a next step, we are planning to manufacture an eight-octant polarization mask (EOPoM) for preparing for future on-sky observations aiming at directly detecting and characterizing extrasolar planets around nearby stars. ACKNOWLEDGMENTS We thank T. Inabe of Hokkaido University for his experimental assistance. We thank the Advanced Technology Center of the National Astronomical Observatory of Japan for helpful support. This research was partly supported by the National Astronomical Observatory of Japan and by a Grant-in-Aid for Scientific Research (B) from the Japan Society for the Promotion of Science (193636). This research was also partly supported by the Japanese Ministry of Education, Culture, Sports, Science and Technology, through a Grant-in-Aid for Scientific Research on Priority Areas, "Development of Extra-solar Planetary Science". N. M. is financially supported by the Japan Society for the Promotion of Science for Young Scientists. REFERENCES 1. F. Roddier and C. Roddier, Stellar coronagraph with phase mask, Publ. Astron. Soc. Pac. 19, pp , D. Rouan, P. Riaud, A. Boccaletti, Y. Clénet, and A. Labeyrie, The four-quadrant phase-mask coronagraph. I. Principle, Publ. Astron. Soc. Pac. 112, pp , M. J. Kuchner and W. A. Traub, A coronagraph with a band-limited mask for finding terrestrial planets, Astrophys. J. 57, pp. 9-98, G. Foo, D. M. Palacios, and G. A. Swartzlander, Jr., Optical vortex coronagraph, Opt. Lett. 3, pp , D. Mawet, P. Riaud, J. Baudrand, P. Baudoz, A. Boccaletti, O. Dupuis, and D. Rouan, The four-quadrant phase-mask coronagraph: white light laboratory results with an achromatic device, Astron. Astrophys. 448, pp , D. Mawet, P. Riaud, J. Surdej, and J. Baudrand, Subwavelength surface-relief gratings for stellar coronagraphy, Appl. Opt. 44, pp , N. Baba, N. Murakami, T. Ishigaki, and N. Hashimoto, Polarization interferometric stellar coronagraph, Opt. Lett. 27, pp , P. Riaud, A. Boccaletti, D. Rouan, F. Lemarquis, and A. Labeyrie, The four-quadrant phase-mask coronagraph. II. Simulations, Publ. Astron. Soc. Pac. 113, pp , L. Abe, F. Vakili, and A. Boccaletti, The achromatic phase knife coronagraph, Astron. Astrophys. 374, pp , 21. Proc. of SPIE Vol J-7

15 1. A. Boccaletti, P. Riaud, P. Baudoz, J. Baudrand, D. Rouan, D. Gratadour, F. Lacombe, and A. M. Lagrange, The four-quadrant phase mask coronagraph. IV. First light at the Very Large Telescope, Publ. Astron. Soc. Pac. 116, pp , D. Gratadour, D. Rouan, A. Boccaletti, P. Riaud, and Y. Clénet, Four quadrant phase mask K-band coronagraphy of NGC 168 with NAOS-CONICA at VLT, Astron. Astrophys. 429, pp , P. Riaud, D. Mawet, O. Absil, A. Boccaletti, P. Baudoz, E. Herwats, and J. Surdej, Coronagraphic imaging of three weak-line T Tauri stars: evidence of planetary formation around PDS 7, Astron. Astrophys. 458, pp , D. Rouan, J. Baudrand, A. Boccaletti, P. Baudoz, D. Mawet, and P. Riaud, The Four Quadrant Phase Mask Coronagraph and its avators, Comptes Rendus - Physique 8, pp , N. Murakami, R. Uemura, N. Baba, Y. Sato, J. Nishikawa, and M. Tamura, Four-quadrant phase mask coronagraph with a Jacquinot-Lyot stop, Astrophys. J. 677, pp , 28. Proc. of SPIE Vol J-8

16 Virtual wavefront compensation and speckle reduction in coronagraph by unbalanced nulling interferometer (UNI) and phase and amplitude correction (PAC) J. Nishikawa* a, K. Yokochi b, L. Abe c, N. Murakami a, T. Kotani d, M. Tamura a, T. Kurokawa b, A.V. Tavrov** a, M. Takeda e a Exoplanet Project, Division of Opt/IR Astronomy, NAOJ, Mitaka, Tokyo , Japan b Tokyo University of Agricalture and Technology, Koganei, Tokyo , Japan c Laboratoire Hippolyte Fizeau, Universite de Nice-Sophia Antipolis, F-618 Nice, France d LESIA, Observatoire de Paris, section Meudon, 5 Place Jules Janssen, Meudon, France e Univ. of Electro-Communications, Chofu, Tokyo , Japan ABSTRACT We proposed a novel method based on a pre-optics setup that behaves partly as a low-efficiency coronagraph, and partly as a high-sensitivity wavefront aberration compensator (phase and amplitude). The combination of the two effects results in a highly accurate corrected wavefront. First, an (intensity-) unbalanced nulling interferometer (UNI) performs a rejection of part of the wavefront electric field. Then the recombined output wavefront has its input aberrations magnified. Because of the unbalanced recombination scheme, aberrations can be free of phase singular points (zeros) and can therefore be compensated by a downstream phase and amplitude correction (PAC) adaptive optics system, using two deformable mirrors. In the image plane, the central star's peak intensity and the noise level of its speckled halo are reduced by the UNI-PAC combination: the output-corrected wavefront aberrations can be interpreted as an improved compensation of the initial (eventually already corrected) incident wavefront aberrations. The important conclusion is that not all the elements in the optical setup using UNI-PAC need to reach the lambda/1 rms surface error quality. In the experiments, we observed the aberration magnification of more than 5 times and compensated to about lambda/7 rms which is the current limit of the AO system. This means that we reached to lambda/35 level virtually. We observed the speckle reduction in the focal plane with a coronagraph. Keywords: Wavefront, nulling interferometer, coronagraph, adaptive optics 1. INTRODUCTION Nulling interferometry and coronagraphy are useful methods to achieve high dynamic range observations for the direct detection of exoplanets. In these techniques, the required dynamic range of 1-1 for direct detection of earth-like planets at optical wavelengths can only be achieved with a very high quality wavefront of about lambda/1 rms and an intensity uniformity of about 1/1 rms. A dynamic range close to the requirement within a limited area of the focal plane is reported by a dark-hole coronagraph with very precise wavefront control by an adaptive optics (AO) system in a lab 1. However, wavefront accuracy including telescope mirrors is not guaranteed yet for a long integration time of exposing planets and reducing residual speckles at low light level. The wavefront compensation, i.e., the speckle noise reduction, remains an issue in very high dynamic range optics for direct detection of extra-solar planets. Recently a coronagraphic stage is shown to be used to reproduce a perfect flat wavefront in spite of the central obscuration and spider arms at the entrance pupil itself by Abe et al. 2. A two-beam nulling interferometer has been shown to be used as a coronagraphic stage whose output flat wavefront can be led to a downstream coronagraph by Nishikawa et al. 3 By using useful characteristics of these pre-optics concepts, a novel technique for very precise wavefront error reduction is developed by Nishikawa et al. 4,5, which uses an unbalanced nulling interferometer (UNI) and phase and amplitude correction (PAC) by a normal wavefront sensor and a two-mirror AO system. *jun.nishikawa.naoj.8@gmail.com; phone ; fax **current address Moscow Power Engineering Institute (Technical University) and Space Research Institute (IKI) , 84/32 Profsoyuznaya Str, Moscow, Russia Space Telescopes and Instrumentation 28: Optical, Infrared, and Millimeter, edited by Jacobus M. Oschmann, Jr., Mattheus W. M. de Graauw, Howard A. MacEwen, Proc. of SPIE Vol. 71, 712A, (28) X/8/$18 doi: / Proc. of SPIE Vol A-1

17 2. PRINCIPLE A brief description of the principle is as follows although detailed descriptions with formalism can be seen in a paper 5. The (intensity) unbalanced nulling of the two beams provides some order of extinction of the central star light. Since the wavefront of the UNI output has still enough large amplitude without phase singularity and wavefront errors are magnified by the reduction of the unaberrated electric field, a normal wavefront sensor and a deformable mirror can be applied at the PAC stage, where two mirrors are required to compensate for the amplitude error as well as the phase error. The wavefront error correction at the error-magnified stage is equivalent to very precise wavefront compensation at the initial wavefront which can be seen in the drawing of the electric field in Fig. 1. After the UNI-PAC method is applied, the peak intensity of the central star is dimmed and speckle noise level is also reduced relative to off-axis planet intensity. When the UNI-PAC is used as pre-optics, a down stream coronagraph can achieve better planet detection. The intensity changes of the star and speckle noise are shown in Fig.2 with a candidate optics configuration. Im Wavefront 1 Re UNI Im Re Im Wavefront 2 Re Im PAC Re unaberrated electric field distribution of aberration component Fig. 1. The electric field changes of the star light through UNI and PAC stages. 2 WFS 2 WFS log(normarized Intensity) AO UNI PAC Coronagraph Starimage λ / 1 Speckle λ / 1 λ / 1 λ / 1 λ / 1 Planet Fig. 2. The intensity changes of the star and speckle noise through a coronagraph system which consists of a telescope, first AO, UNI, PAC, and a coronagraph. Proc. of SPIE Vol A-2