High-contrast imaging systems with a stellar halo suppression level of 10−10 are required for direct detection of Earth-like extra-solar planets. We investigated a novel high-contrast imaging system with an unbalanced nulling interferometer (UNI) followed by phase and amplitude correction (PAC), which not only can reduce starlight but also can suppress the speckle level caused by wavefront aberrations. We successfully demonstrated that wavefront aberrations were sufficiently magnified by the UNI and the magnified aberrations were effectively corrected in amplitude and phase with two deformable mirrors. We confirmed that the suppression level of the speckle pattern with the proposed optics was beyond the limit of the adaptive optics performance.
©2011 Optical Society of America
A nulling interferometer is interesting technology for high-contrast imaging used to distinguish starlight in order to extract extremely faint signals of Earth-like extra-solar planets (exoplanets). A nulling interferometer was originally proposed for infrared stellar interferometry  but recently has been applied to visible observation systems [2–5]. Several designs of a “stellar coronagraph” based on diffraction optics and interferometry have also been proposed . Recently, giant and bright exoplanets at a large distance from central stars have been discovered directly by high-contrast imaging techniques [7–10].
In a high-contrast imaging system, the speckle level due to wavefront aberrations remains after the destructive interference of light. Adaptive optics (AO) is often used with a nulling interferometer or a stellar coronagraph to obtain high wavefront quality and to suppress the speckle level. The contrast (109 –1010 in the visible) required for direct detection of Earth-like planets can be achieved only by an optical system with a very high-quality wavefront of λ/10000 rms and an intensity uniformity of 1/1000 rms . However, the AO performance is limited by a non-common path (NCP) error that results from the difference between wavefront sensing and imaging optics, and then the speckle level remains at the final focal plane. Researchers proposed wavefront sensing at the focal plane to suppress the remaining speckle [12–14]. The focal plane speckle level, however, would be as dark as the exoplanet, which could be detected with a long exposure, during which the wavefront quality of the telescope should be maintained at a value less than λ/10000 rms.
To overcome these problems, some authors have proposed an amplitude UNI followed by phase and amplitude correction (PAC) . A zero amplitude point is avoided in the UNI result so that aberrations can be corrected further by a downstream conventional AO system. The main advantage of the UNI is the magnification of wavefront aberrations. For example, unbalanced nulling interference with an amplitude reduction of 1/10, i.e., extinction ratio of 10−2, produces approximately a 10-fold magnification of the aberrations, creating the possibility of correcting magnified aberrations by 1/10 times and of suppressing the speckle level by a factor 1/100 times beyond AO system capabilities. The wavefront sensing of the UNI-PAC system can be made with bright starlight, which still remains about 1/100 of the original intensity before the UNI stage. It would be possible to measure wavefront aberration quickly as compared to wavefront sensing of weak nulled light at the focal plane.
In this paper, we experimentally demonstrate the characteristics of aberration magnification with the UNI and PAC by AO using two deformable mirrors. We also confirm speckle level suppression at the focal plane beyond the limit of AO performance. We briefly review the principles of the proposed high-contrast imager with the UNI in Section 2, present a laboratory experimental setup in Section 3, and provide results and discussion in Section 4.
As shown in Fig. 1 , diverging light from a telescope focus is collimated and guided into a high-contrast imaging system. Functionally, the system is divided into four parts consisting of the first AO, the UNI, the second (PAC) AO, and the final-stage nulling interferometer (coronagraph).
The operations of wavefront correction and starlight rejection are repeated two times in the system, first with AO and then the UNI, respectively, and subsequently with PAC and the nulling interferometer (coronagraph). The last stage for starlight rejection can be selected from various nulling interferometers or coronagraphs. We briefly review the principles (see  for details). Figure 2 shows changes of the complex amplitude of the electric field at each stage in Fig. 1. Let us consider collimated stellar light from a telescope with a phase-error-dominant wavefront. The phase error is corrected by the first AO system; however, wavefront aberrations remain because of the limits of AO performance or the NCP error between the wavefront sensor (WFS) and the main optics. The collimated light exiting from AO with residual aberration is split into two beams (beam 1 and beam 2) in an interferometer. The amplitude of beam 2 is slightly attenuated by a neutral density filter and then π-phase shifted to destructively interfere with beam 1. This amplitude-unbalanced interference of the two light beams achieves nearly two orders of extinction of the light intensity (one order reduction of modulus). It is difficult to compensate for the phase around a zero-amplitude point by a deformable mirror because the phase aberration abruptly changes there. Therefore, we need to avoid a zero-amplitude point (phase singularity) in the UNI result. The two beams at the UNI stage are combined with a lateral shearing distance, which is equivalent to a baseline of the two-telescope interferometry . Off-axis planet light can survive by an optical path difference (OPD) due to the lateral shearing.
At the UNI stage, the wavefront aberrations are magnified about 10 times by attenuating the amplitude of beam 2 to 90%. The magnified wavefront aberrations then can be corrected further in the next PAC AO system. Here, two deformable mirrors (DMs) would be used for correcting both the magnified amplitude and phase aberrations. After the UNI and PAC operations, the stellar light (which forms a point spread function at the image plane) is reduced by a nulling interferometer or a coronagraph in the last stage.
The complex amplitude at one point in the collimated beam, , can be considered as the sum of unaberrated amplitude (defined by the average complex amplitude within the beam) and a residual complex aberration component (CAC), , such that
In the following explanations, we omit the position variables for simplicity. We define the normalized complex aberration (NCA) by the ratio of the CAC to the aberration-free amplitude, . For a small aberration, the real and imaginary parts of the NCA, , approximately represent the amplitude and phase aberrations, respectively. In each stage, the rms of the NCA modulus,
Let us consider the complex amplitudes in beam 1 and beam 2,
When the two wavefronts in Arms 1 and 2 have some correlation effect, the magnification ratio expressed by Eq. (9) should be modified as follows. Assuming that the variances of the and modulus are equal, and can be written as the sum of an independent term with a ratio of f and a term correlated to , i.e., , the variance of becomes . Then, the aberration magnification ratio is modified asEq. (11) becomes equal to Eq. (9). The value decreases with the fvalue. When , no magnification occurs for the same aberrations of .
The effect of the correlation between the two wavefront aberrations will be discussed in the next section. A further wavefront correction performed by the PAC AO is expressed by
The wavefront aberrations of beam 1 before and after the UNI operation and that after the PAC operation can be evaluated by , , and .The speckle levels caused by these aberrations are proportional to , , and , respectively.
3. Experimental Setup
We performed laboratory experiments of the UNI and PAC operations. Figure 3 shows the experimental setup. A star image was simulated by a pinhole (10 μm in diameter) illuminated by a diode-pumped solid-state laser (with a wavelength of 671 nm), and the light was collimated by a doublet lens (f = 400 mm) and stopped with a 6 mm diaphragm. The front-end AO system is still under development and was not in use in the present experimental setup. However, the wavefront quality of the collimated beam was sufficient, better than ../200 rms, to enable us to proceed with the experiment.
In the UNI stage, we introduced a modified Mach–Zehnder interferometer based on polarizing beam splitters (PBSs) with half-wave plates (HWPs). This part of the system is called the polarization interferometric nulling coronagraph (see  for details). Initially, a linear polarizer selected (nearly) + 45° linearly polarized light (LPL) from the collimated beam. This light was then split into 0° and 90° LPL by the first PBS (PBS1). The transmitted 0° LPL (p-polarization) through Arm 1 and the reflected 90° LPL (s-polarization) through Arm 2 were combined at the second PBS (PBS2). An HWP was inserted between the two mirrors of each arm to rotate the incident 0° (90°) LPL to 90° (0°) light. A polarizer was inserted just after the first PBS in each arm to improve the extinction ratio of the PBS. For an on-axis source, a destructive interferometric output was obtained achromatically when the last analyzer was set to −45°. On the other hand, constructive interferometric output could be obtained when the analyzer was set to + 45°. This interferometer can be operated in the wavelength region of 400–700 nm, which is limited by the optical components we used, including the PBS, HWP, and the polarizers. It could be extended to a much broader wavelength region from visible to infrared by using broadband optical components . By using this polarization interferometer, the unbalanced nulling interference could be achieved by slightly rotating the initial linear polarizer from + 45°. We found that among the optical components in the system, the polarizers had the worst wavefront quality of λ/160 within a 1.6 mm area among all the optics, causing the input wavefront aberration at the UNI. The amplitude difference, here expressed by parameter g, had to be adjusted so as to avoid the generation of a phase singular point, compensable by DMs. Parameter g also determined the magnification ratio of the wavefront aberrations of the UNI, and thereby affected the extra speckle-level suppression ratio after the PAC AO operation. One of the mirrors in Arm 2 was held on a mirror mount driven by a piezoelectric transducer- (PZT) driven mirror mount to correct any tip-tilt errors, whereas the other mirror in Arm 2 was mounted on a PZT-controlled linear translation stage to adjust the optical path difference (OPD) between the two arms.
The Mach–Zehnder interferometer introduced a lateral shear of about 10% of the entrance pupil diameter. However, this parameter was not used in the present paper since the demonstration of the concept was performed with only a central source without off-axis planet light. On the other hand, the lateral shearing of the beams reduced the correlations of the wavefront aberrations in the two arms, which may affect the magnification ratio of the aberrations.
After passing through the UNI, the light proceeded to the PAC AO system composed of two DMs (DM1 and DM2). The control resolution of the DMs was about 15 nm in OPD for each actuator and about λ/150 rms overall. The active element of the DM was a monolithic array of 32 actuators in a 6 × 6 square array with a 0.3 mm pitch except for the four corners (Mini-DM; Boston Micromachines Co.). The entrance pupil was reimaged on DM2 with a reduction of 0.4 by two lenses (f = 1000 mm and f = 400 mm). A 6 × 6 Shack–Hartmann WFS with a microlens array that had the same pitch as the DM was set on a conjugate plane to DM2 in a split path, with the other two lenses having the same focal length (f = 400 mm). Because DM2 and the WFS were placed in conjugate pupil planes, the amplitude remained unchanged by phase correction. DM1 was set 20 cm upstream of DM2, separated from the reimaged pupil plane to enable amplitude correction by surface curvature control of DM1, and combined with the light propagation effects between DM1 and DM2 on the beam intensity distribution. The λ/100 piston control of the DM1 actuator corresponded to about a 1.6% intensity change at the pupil plane. DM2 compensated for the additional phase change by DM1 together with the original wavefront aberrations. First, the amplitude aberration was corrected by DM1, and then the phase aberration was compensated by DM2 with closed-loop feedback control. The size of the area in the image plane, controllable with the DMs, was at maximum ± 3, which corresponds to the Nyquist frequency of the 6 actuators in the diameter, wherein λ is the wavelength and D is the diameter of the optics.
The electric field at the focal plane is the Fourier transform of the pupil-plane electric field. Therefore the focal-plane speckle pattern is the power spectrum of the wavefront aberration component after reducing the unaberrated pupil-plane field. We note that the total speckle intensity is equivalent to the integrated squared modulus of the wavefront aberration component of the pupil-plane field. We dealt with the only speckle intensity within the field of view, which was determined by the spatial frequency at the pupil plane controlled with the deformable mirrors. In this paper we do not discuss the photon noise of the speckle to find planets below the speckle level.
The lenslet array of the 6 × 6 Shack–Hartmann WFS created a spot field on the camera sensor, which was analyzed based on the location and intensity of the individual spots. The amplitude was calculated as the square root of the intensity, and the amplitude aberration was a deviation from the average amplitude of 32 spots except for four corners.
After the UNI-PAC, we placed a 3D Sagnac nulling interferometric coronagraph that achieved achromatic nulling of 1.4 × 10−6 at the peak and 10−6 around for two lasers of 532 nm and 633 nm wavelengths in our previous experiments . We constructed the 3D Sagnac interferometer of six commercially available Al-coated mirrors, a BS, and a PBS that would have a total surface accuracy of approximately λ/270 rms within a 1.6 mm circular aperture. An angle incident to the interferometer was adjusted accurately by a PZT-driven tip-tilt mirror. Destructive and constructive interference could be obtained at a nulled output and a bright output, respectively. After the 3D Sagnac interferometer, the pupil was reimaged on the Lyot stop with a reduction of 0.25 by two lenses (f = 1000 mm and f = 250 mm). The Lyot stop is used for removing the non-interfered light at the Mach–Zehnder and the Sagnac interferometers. Because the Mach–Zehnder has non-interfered areas at both sides of the laterally sheared pupils, the Sagnac also has non-interfered regions at the periphery of the imperfect circular pupil. Here, the Lyot stop was a circular aperture with a 0.4 mm diameter, which was equivalent to1.6 mm on the DM (corresponds to 5.4 actuators). We calculated the variance of the wavefront aberrations by putting a weight factor on each sub-aperture (microlens) proportional to the area within the Lyot stop and evaluated the speckle intensity within the 2.7 radius, which is a controllable area by the DM (up to Nyquist frequency). The nulled and bright outputs of the 3D Sagnac interferometer were focused with an imaging lens and observed with a cooled CCD camera.
Initially, we set flat voltages for the two DMs. The mirror surfaces of the DMs were recorded by measuring the reflected wavefront using a commercial WFS (Zygo, GPI), and the accuracy we obtained was better than λ/90 rms for both of the DMs. Next, we operated DM1 and DM2 with the WFS using closed-loop feedback control for each light of Arm 1 and Arm 2, and we obtained amplitude aberration levels of 4.0% rms and 3.3% rms and wavefront accuracies of λ/150 rms and λ/170 rms, respectively. We adopted an average of the two operation voltages as the initial condition; then, the wavefront qualities of the two beams became λ/118 rms and λ/104 rms, and the amplitude aberrations were 4.6% rms and 4.0% rms, as listed in Table 1 , along with their changes in the subsequent stages. The aberrations of the UNI were measured when the two arms were combined with the amplitude-unbalanced condition, and those of the PAC were measured after the PAC with DM1 and DM2. The aberrations in these and the Arm 2 stages were normalized by the unaberrated amplitude of Arm 1.
4. Results and Discussion
First, we demonstrated the characteristics of aberration magnification with the UNI and the PAC. The phase and the amplitude aberrations of the beams were measured by the WFS for each arm in the UNI (Arms 1 and 2 with a slight amplitude reduction) after the UNI operation and after the PAC AO operation. We measured the wavefront magnifications for various amplitude differences g and plotted the aberration magnification ratios against the amplitude differences, as shown in Fig. 4 . The wavefront magnifications were calculated as of the UNI divided by the averaged of Arms 1 and 2. The measured points were distributed between M and [obtained from Eq. (11) for ] curves. The measured aberration magnification ratios show that the two wavefronts have some degree of correlation with the f value of 0.5–1.
Figure 5 shows the measured wavefront data in terms of the complex amplitude when the amplitude difference between the two arms was set to g = 0.18. We found that the two amplitude-unbalanced wavefronts were interfered with destructively, and the aberrations were magnified and corrected according to the principles of the UNI and PAC AO operations.
Table 1 tabulates the amplitude aberration; the phase aberration; , , and ; and the integrated speckle intensity in each stage, and Fig. 6 plots the rms of the former three. The initial phase aberrations averaged at Arms 1 and 2 were magnified 6.9 times by the UNI operation. The PAC AO multiplied the aberration level by a factor 0.17. The amplitude aberrations were also magnified 3.7 times and corrected 0.34 times. The magnification of the NCA, the overall aberration of the amplitude, and the phase aberration was 6.7 times. While the theoretical value was 7.0 when there was no correlation between the two wavefronts, the two wavefronts here might have a slight correlation. The magnification of the amplitude aberration was 3.7, which might imply much correlation in the amplitude distribution. The magnified NCA was reduced by 0.18 times to 0.085 by the PAC operation, which is a similar wavefront quality of Arms 1 and 2. Table 1 also lists the magnification ratios by the UNI and the reduction ratios in the and columns, respectively. was calculated as the aberration of the UNI divided by the averaged one of arms 1 and 2. was obtained as the aberration of the PAC divided by the one of the UNI. The suppression ratios of after the PAC operation to at Arms 1 and 2 are indicated in column S of Table 1, and the speckle intensity reduction ratio is also indicated in column S. The wavefront aberration after the PAC operation normalized by the initial wave amplitude was calculated and expressed as the PAC column of Table 1. For the results, we obtained 0.99% rms for the amplitude, λ/550 rms for the phase, and 0.015 of .
Figure 7 shows the output images observed at the focal plane after the 3D Sagnac nulling interferometric coronagraph and their azimuthally averaged intensity profiles. We observed that the airy profile disappeared and the speckle level produced by the wavefront aberrations became obvious. We measured the speckle level of the beam before and after the UNI operation and after the PAC AO operation. Table 1 shows the integrated speckle intensities of the nulled output in 2.7 normalized by the integrated intensity of bright output.
Figure 8 shows the integrated speckle intensity and at each stage. Here, corresponds to the integrated intensity of the pupil-plane aberration component because all wavefront data were normalized by the unaberrated amplitude of Arm 1.The speckle noises in Arms 1 and 2 were induced by the wavefront of λ/110 rms accuracy achieved by the AO system before the UNI operation. Compared to the integrated speckle intensity of 9.5 × 10−3 of the two arms, the speckle level was reduced to 7.0 × 10−4 by a factor of 0.073 after the UNI and PAC AO operations. These results were a successful demonstration, showing that speckle level suppression was achieved beyond the limit of the AO capabilities.
The speckle intensity measured at the focal plane was expected to be proportional to as measured by the WFS. In fact, the speckle levels were in rough agreement with the variations, as shown in Fig. 8. Here, we consider the effects of the NCP aberrations between the WFS path and the 3D Sagnac. In the WFS optics, the optical elements inducing the NCP aberrations were a BS, two lenses, and a mirror. The surface quality of these elements was measured (by Zygo GPI), and their statistical sum was expected to be about λ/140 rms, while the surface quality of a microlens array was neglected because of the much smaller aberration of the WFS under severe calibration. In the 3D Sagnac optics, similarly, the surface quality of four lenses, two mirrors, a BS, and the 3D Sagnac interferometer itself were expected to be about λ/86 rms. In this discussion, we considered only the phase aberrations and neglected the amplitude aberrations due to no data. Table 1 and Fig. 8 show the calculated results of that considered the NCP effects. The calculated values of showed better consistency with the speckle intensity in the same order.
Optical throughput in the UNI and PAC stages is very important because the light from the planet is very faint. The total transmittance in the UNI and PAC stages was about 30% for the incidence of a linear polarized light in spite of a number of folding mirrors, and it could be improved to be about 70% if we reduced the number of optical elements under the appropriate optical design and used low-loss polarizers and mirrors.
We adopted the polarization interferometer, which was convenient in the demonstration to adjust the amplitude difference of the two beams by the rotation angle of the polarizer. This interferometer transmits one linear polarization component, but two-channel configuration could be introduced to treat two polarization components effectively [5,16]. We do not discuss the throughput of 3D Sagnac nulling interferometer (see ), which is out of the scope of the present paper, because the UNI-PAC method can select one from various candidates.
We successfully demonstrated that wavefront aberrations were sufficiently magnified by the UNI, and the magnified aberrations were effectively corrected with two deformable mirrors. We confirmed that a suppression level of the speckle pattern with the proposed optics was beyond the limit of adaptive optics performance. In fact, the extra speckle-level suppression after the UNI-PAC operation was 0.073 times below the best achieved speckle level in the AO system. We believe the UNI will be an essential technology for high-contrast imagers with AO systems.
This research was supported by grants-in-aid from the Ministry of Education, Culture, Sports, Science, and Technology (MEXT) of Japan (20656013, 21360037); by the JAXA/ISAS airborne and spacecraft instruments development program; and by the JSPS Fellows (20-4783). This experiment was performed in the optical experiment facility of the Advanced Technology Center of NAOJ. K. Yokochi is financially supported by the Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists.
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