- Email: [email protected]
Laboratory demonstration of a dual-stage vortex coronagraph
Optics Communications 379 (2016) 64–67
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Laboratory demonstration of a dual-stage vortex coronagraph Eugene Serabyn a,n, Kurt Liewer a, Dimitri Mawet b a b
Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA California Institute of Technology, 1200 E. California Blvd., Pasadena, CA 91125, USA
art ic l e i nf o
a b s t r a c t
Article history: Received 22 February 2016 Received in revised form 14 May 2016 Accepted 15 May 2016 Available online 1 June 2016
While an ideal optical vortex coronagraph operating behind a clear, circular, unaberrated telescope aperture can theoretically provide perfect rejection of the incident plane wave from an unresolved star, use of a telescope with an on-axis secondary mirror limits the rejection. In theory, a dual-stage vortex coronagraph can provide improved starlight rejection for an on-axis telescope, and here we provide experimental confirmation of the predicted distribution of the residual light in the output pupil plane of a dual-stage vortex coronagraph. In addition, a simple method of further improving the rejection of such a coronagraph is suggested: by slightly oversizing the first Lyot stop and phase-shifting the light within the exposed annulus by half a wave, the residual starlight within the pupil can be canceled to deeper levels. & 2016 Elsevier B.V. All rights reserved.
Keywords: Coronagraphy Starlight rejection High contrast imaging
1. Introduction The resolution of very faint exoplanets from their host stars requires deep suppression of the much brighter starlight. One promising technique in this regard is the optical vortex coronagraph [1–3], in which an azimuthal phase ramp applied to the stellar focal-plane Airy pattern expels the starlight from a subsequent pupil image. While the rejection should be perfect for an ideal, clear circular input aperture, on-axis secondary telescope mirrors degrade performance significantly [4,5]. Improved starlight suppression levels or suppression bandwidths can in some cases be obtained with cascaded, multi-stage coronagraphs [6,7], and the multi-stage vortex coronagraph [8] was proposed to mitigate the additional leakage in the centrally-obscured telescope case. Here we present a laboratory demonstration of the improved rejection provided by the dual-vortex coronagraph for a centrally obscured aperture. The theory of the dual-vortex coronagraph has already been presented in detail [8], and so here we quickly summarize the theory graphically (Fig. 1). Fig. 1 shows a schematic layout of a dual-stage vortex coronagraph, indicating all focal and pupil planes. Optical vortex phase masks (V1 and V2) lie in both internal focal planes. Below the layout are shown the theoretically expected light distributions in five near-pupil-plane locations along the coronagraphic beam train, with P being the input pupil; L1 & L1 þ the planes just before and after the first Lyot stop plane, L1, n
Corresponding author. E-mail address: [email protected] (E. Serabyn).
http://dx.doi.org/10.1016/j.optcom.2016.05.042 0030-4018/& 2016 Elsevier B.V. All rights reserved.
and L2 & L2 þ being the planes just before and after the second Lyot stop plane, L2. For simplicity, in the following we ignore the secondary supports, concentrating solely on the effects of the central obscuration. The discussion here is also limited to optical vortex phase wraps of topological charge 2, i.e., those in which the output optical phase wraps from 0 to 4π in one circuit about the center. With a uniform input-pupil field between diameters of d and D, passage of the coherent starlight from an unresolved star through the first optical vortex phase mask results in two components of residual starlight in the subsequent pupil plane, both with an r 2 field profile, where r is the radial coordinate. These components originate at the primary and secondary mirror edges (Fig. 1). The light external to the pupil can be blocked with an opaque “Lyot” stop, L1, but the residual light between the primary and secondary edges limits the rejection in a single-stage vortex coronagraph [8] to (d/D)2. However, passing the post-L1 residual starlight through a second focal-plane optical vortex phase mask (V2) again leads to a redistribution of the starlight in the subsequent pupil plane, L2. In L2, most of the residual starlight is concentrated inside d, where it can be blocked by a second, central, Lyot stop (L2 in Fig. 1). However, a smaller residue of light, of uniform field strength (d/D)2, remains between d and D, which limits the dual-vortex (intensity) rejection to (d/D)4. As the residual light in the output pupil plane L2 þ is an exact scaled replica of the input pupil P (see Fig. 1), the rejection is given directly by the ratio of the uniform intensities in the these two pupil planes, which is equivalent to, but simpler than, ratioing the Airy patterns in the two subsequent focal planes.
E. Serabyn et al. / Optics Communications 379 (2016) 64–67
65
2: Collimating OAP 1
1: Fiber source 3: Input pupil mask
8: Focusing OAP 2 4: Focusing OAP 1
5: Vortex mask 1
9: Vortex mask 2
6: Collimating OAP 2 7: Lyot stop 1
Fig. 1. Schematic of the dual-vortex coronagraph layout as used in our experiment. SM is a single-mode fiber input, P is the input-pupil mask, V1 and V2 are the two optical vortex phase masks located in two successive focal planes, L1 is the first pupil image plane and contains the first Lyot stop (clear inside D; opaque beyond D), and L2 is the second pupil plane and contains the second Lyot stop (clear beyond d; opaque inside d). For simplicity, the off-axis paraboloids are shown here as lenses. Shown below the layout are the theoretical pupils expected in the 5 planes: the input pupil, P, just before and after L1, and just before and after L2. Shown along the bottom are crosscuts of the initial and final pupil planes.
The rejection improvement from (d/D)2 to (d/D)4 in going from a single vortex coronagraph to a pair of vortices is best for small secondary/primary ratios, but large extant telescopes tend to have sizeable d/D ratios. (Note that this ratio actually refers to the central blockage, which tends to be somewhat larger than the secondary mirror diameter itself.) At one extreme, the Hale telescope at the Palomar Observatory, with d/D ¼0.36, would show a theoretical rejection improvement from 0.13 to 0.017 in going from one to two vortex stages. Even this single order of magnitude improvement is significant, as the extra stage decreases the residual diffracted starlight to levels near or below the stellar leakage caused by residual post-extreme-adaptive-optics atmospheric wavefront errors. Even larger ground-based telescopes typically have somewhat smaller d/D ratios (down to 0.1), for which the rejection improvement is more significant.
2. Experiment Our experiment was carried out on the Infrared Coronagraphic Testbed (IRCT), an open-air coronagraphic optical bench located at the Jet Propulsion Laboratory. This testbed has been used for several experiments, including the testing of coronagraphic masks for the James Webb Space Telescope's Near Infrared Camera [9], as well as for the Subaru and Keck telescopes. For this demonstration, a second coronagraphic optical relay was added to the IRCT. The IRCT consists of all-reflective optics (except for the optical vortex phase masks) up to the second coronagraphic focal plane, after which lenses are used in order to save space after the light rejection steps are completed. The light source was a diode laser at a wavelength of 795 nm coupled to the testbed through a singlemode fiber. The input pupil is defined by means of a metal mask in the collimated input beam with apertures that provide a scaled version of the Hale telescope at the Palomar Observatory (however, the support legs of the “secondary” blocker were larger than scale). The IRCT input pupil was then relayed through two focalplane optical vortex phase masks, as shown in Figs. 1 and 2. Both vortex phase masks, manufactured by Beam Engineering [10], were designed for a wavelength of 800 nm. The requisite Lyot stops were placed in the two pupil planes (Figs. 1 and 2), and the final pupil plane was relayed to our camera with additional lenses. To make a uniform and rapid set of directly comparable coronagraphic performance measurements, we found it best to avoid switching between focal plane images, in which the light is
13: CCD camera
12: 2:1 relay 11: Lyot stop 2
10: Re-imaging lens
Fig. 2. The Infrared Coronagraphic Testbed (IRCT), with all non-flat-mirror optics numbered in sequence. From the fiber launcher (1), the light proceeds through two sequential optical relays, each consisting of a pair of off-axis paraboloids (OAPs), that produce the focal planes in which the two optical vortex phase masks are located (5 & 9). An input pupil mask (3) and two pupil-plane Lyot stops (7 & 11) are also indicated. Flat fold mirrors are not indicated. All of the beam train optics up to the fold flat after the second focal-plane vortex mask (9) are reflective. Thereafter, lenses are used to generate the final pupil image and to transport it to the CCD camera.
intensely concentrated onto a small number of pixels, and pupil plane images, in which the light is spread over many pixels, as such switches would necessitate changing optical attenuators, electrical gain settings, and/or integration times. Changing optical attenuators within the source was found to be problematic, as insertion of different attenuators changed the coupling of the input beam into the input fiber (due to differing attenuator wedge angles), thus altering relative intensities in non-reproducible ways. We therefore decided to rely solely on pupil plane images, which provide the same rejection information as focal plane images (i.e., once flux is removed from the pupil plane, it is also removed from the subsequent focal plane), but which nicely obviate all dynamic range issues. The pupil plane images also provide a point-by-point comparison across the pupil. Moreover, because removing an optical element is a much simpler and quicker step than inserting and aligning an optical element, we decided upon the following uniform and efficient procedure to obtain the desired images of the five pupil planes of interest (P, L1 , L1 þ , L2 , and L2 þ ). First the full two-stage coronagraph was carefully and completely aligned to the limits achievable with our manual actuators. We then simply cycled through the five needed images in reverse, by removing in reverse order the already installed Lyot stops and vortices one by one. Specifically, starting from the image of L2 þ , removing L2 takes us to L2 ; removing V2 takes us to L1 þ , removing L1 takes us to L1 , and finally, removing V1 takes us to P, the input pupil. The five resultant dark-subtracted pupil plane images so obtained in a single sequence are shown in Fig. 3. Aside from the diffraction along the central blocker's support legs, the measured radial light distributions in these five images correspond rather well with the theoretical distributions shown in Fig. 2. Fig. 4 shows an image of the measured intensity ratio of the final output pupil plane (L2 þ ) to the input pupil plane (P), which, as mentioned earlier, directly gives the light rejection as a function of position within the pupil. The intensities in the clear areas of the 2nd Lyot plane are indeed relatively flat across much of the pupil area (except near some of the sub-aperture boundaries), and are much reduced compared to the input pupil, being on the order of 0.02 of the input pupil (see, e.g., the vertical crosscut through the pupil shown in Fig. 4), and reach down to near the theoretical value of 0.17 in the best regions of the pupil (e.g., near the top of
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E. Serabyn et al. / Optics Communications 379 (2016) 64–67
P
L1-
L1+
L2-
L2+
Fig. 3. Measured pupil-plane light distributions in the 5 planes labeled in Fig. 1. From left to right: the input pupil P, just before and after the first pupil plane, L1, and just before and after the second pupil plane, L2. The color scales range from 0 in all cases to maxima of roughly 55,000, 65,000, 65,000, 26,000 and 6000, from left to right. Note the residual light around the secondary in the L1 and L1 þ images, and the morphological similarity of the first and last images (the initial and final pupils). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 4. Left: The intensity ratio of the 2nd Lyot plane (L2 þ ) to the input pupil (P). The color scale ranges from 0 to 0.1. Right: Vertical crosscuts through the center of the L2 þ /P pupil plane ratio (bottom curve) and the L1 þ /P pupil plane ratio (top curve). The two light dotted vertical lines at the inner radius of the L2 þ pupil are guides for the eye. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
the image, corresponding to near pixel 337 in the bottom vertical cross-cut curve in Fig. 4). Low-level optical aberrations were the main limitation to the measured rejection, as residual patchy light (the reddish areas in Fig. 4) was seen to fluctuate across the final pupil as slight alignment adjustments were made, and the IRCT has no deformable mirror to reduce or remove wavefront aberrations. Indeed, in addition to wavefront and alignment errors, any other imperfections, such as imperfect vortices, slight differences between the two vortices, a mismatch between the vortex and laser wavelengths, and operation slightly outside the single mode regime of the injection fiber [which begins at 800 nm], should all serve to raise the level of light leakage within the pupil. In practice, the theoretically expected rejection ratio should thus serve as a lower limit to the measured intensity ratio, which does seem to be the case (Fig. 4). The measured dual-stage vortex intensity rejection is thus in line with theoretical expectations.
3. Potential for further rejection improvement For large d/D ratios, the residual light left within the unobscured pupil area by a dual-vortex coronagraph is still somewhat large, making further light rejection desirable in demanding high-contrast applications. Further gains could be made by adding additional stages [6–8], but this would lead to an increasingly large and unwieldy optical system. An alternative approach is the
single-stage ring-apodized vortex coronagraph [11], but this approach brings with it a significant throughput loss, and is not compatible with the speckle phase sensing scheme enabled by the dual-vortex coronagraph configuration [12]. On the other hand, as we suggest here, the rejection of the dual-vortex coronagraph can be improved via a slight optical modification, that being to further reduce the residual starlight inside the final dual-vortex coronagraph pupil (L2 þ ) by canceling it with a small amount of the starlight that lies beyond the rim of the upstream L1 pupil stop. Specifically, if the first Lyot stop were increased in diameter from D to a slightly larger diameter D0 (to be determined below), the small annulus of starlight between D and D0 (with an r 2 radial field dependence) would be converted upon passage through the 2nd vortex into an additional uniform field component in the L2 plane. In particular, since the amplitude of the (uniform) postvortex pupil-plane field is given by the value of the r 2 field at the aperture boundaries, the extra field component introduced by the oversized L1 stop is given by the difference term between the two edges of the additional light annulus, i.e., 1–(D/D0 )2. In addition, the slightly larger L1 stop slightly modifies the normal residual field term from (d/D)2 inside D to (d/D0 )2 inside D0 . (We note that any fields extending beyond D can be cut off again at the 2nd Lyot plane.) As both of these small fields are positive, they do not cancel, but if a relative half-wave phase shift were introduced between the regions interior and exterior to D in the L1 pupil plane, the relative signs of the two residual fields would be
E. Serabyn et al. / Optics Communications 379 (2016) 64–67
inverted, implying cancellation if D0 is chosen such that 2
2
1– ( D/D′) = ( d/D′) ,
Acknowledgment
(1)
i.e., if
(2)
D′ 2 = D2 + d2.
67
This work was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under contract with NASA, United States.
For small secondary/primary ratios, this can be approximated as
References 2
D′/D ≈ 1 + ½ ( d/D) .
(3)
In practice, an adjustable iris diaphragm at L1 would allow for optimization of the size of D0 to maximize rejection. The net rejection will then be limited by the next term in the expansion in powers of (d/D)2, i.e., by the (d/D)6 term. Moreover, practical issues such as aberrations and secondary supports will also limit rejection. Nevertheless, even for sizable secondaries, such as at Palomar, this additional step should lower the theoretical rejection to roughly the 10 3 level or better, at which point the raw rejection will typically be significantly better than that set by atmospheric wavefront residuals. The requisite half-wave phase shift can be introduced by a glass substrate (in transmission) or a mirror (in reflection) at L1 that is a half-wave thicker or thinner in optical path beyond D, which is relatively simple to implement, e.g., by etching the substrate to the correct depth. Although such approaches are essentially monochromatic half-wave implementations, typical astronomical filter passbands are sufficiently narrow, 10–20% full width at half maximum (FWHM), that optimizing for the passband center still yields a sizeable improvement in integrated rejection – specifically, a factor of (πf)2/12, where f is the filter's fractional FWHM – implying a rejection improvement of a factor of 30 even with a 20% FWHM filter.
[1] Mawet, P. Riaud, O. Absil, J. Surdej, Annular groove phase mask coronagraph, Astrophys. J. 633 (2005) 1191. [2] G. Foo, D.M. Palacios, G.A. Swartzlander Jr., Optical vortex coronagraph, Opt. Lett. 30 (2005) 3308. [3] G.A. Swartzlander Jr., The optical vortex coronagraph, J. Opt. A 11 (2009) 094022. [4] C. Jenkins, Optical vortex coronagraphs on ground-based telescopes, Mon. Not. Royal Astron. Soc. 384 (2008) 515. [5] D. Mawet, L. Pueyo, D. Moody, J. Krist, E. Serabyn, The vector vortex coronagraph: sensitivity to central obscuration, low-order aberrations, chromaticism, and polarization, Proc. SPIE 7739 (2010) 773914-1. [6] P. Baudoz, F. Assemat, R. Galicher, J. Baudrand, A. Boccaletti, Experimental results of multi-stage four quadrant phase mask coronagraph, Proc. SPIE 7735 (2010) 773581-1. [7] C. Aime, R. Soummer, Multi-stage apodized pupil Lyot coronagraph for high contrast imaging, Proc. SPIE 5490 (2004) 456. [8] D. Mawet, E. Serabyn, J.K. Wallace, L. Pueyo, Improved high-contrast imaging with on-axis telescopes using a multistage vortex coronagraph, Opt. Lett. 36 (2011) 1506. [9] J.E. Krist, K. Balasubramanian, R.E. Muller, S.B. Shaklan, D.M. Kelly, D.W. Wilson, C.A. Beichman, E. Serabyn, Y. Mao, P.M. Echternach, J.T. Trauger, K.M. Liewer, The JWST.NIRCam coronagraph flight occulters, Proc . SPIE, vol. 7731, pp. 77313J-1. [10] 〈www.beamco.com〉. [11] D. Mawet, L. Pueyo, A. Carlotti, B. Mennesson, E. Serabyn, J.K. Wallace, Ringapodized vortex coronagraphs for obscured telescopes. I. Transmissive ring apodizers, Astrophys. J. Suppl. 209 (2013) 7. [12] E. Serabyn, J.K. Wallace, D. Mawet, Speckle-phase measurement in a tandemvortex coronagraph, Appl. Opt. 50 (2011) 5453.
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Laboratory demonstration of a dual-stage vortex coronagraph Eugene Serabyn a,n, Kurt Liewer a, Dimitri Mawet b a b
Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA California Institute of Technology, 1200 E. California Blvd., Pasadena, CA 91125, USA
art ic l e i nf o
a b s t r a c t
Article history: Received 22 February 2016 Received in revised form 14 May 2016 Accepted 15 May 2016 Available online 1 June 2016
While an ideal optical vortex coronagraph operating behind a clear, circular, unaberrated telescope aperture can theoretically provide perfect rejection of the incident plane wave from an unresolved star, use of a telescope with an on-axis secondary mirror limits the rejection. In theory, a dual-stage vortex coronagraph can provide improved starlight rejection for an on-axis telescope, and here we provide experimental confirmation of the predicted distribution of the residual light in the output pupil plane of a dual-stage vortex coronagraph. In addition, a simple method of further improving the rejection of such a coronagraph is suggested: by slightly oversizing the first Lyot stop and phase-shifting the light within the exposed annulus by half a wave, the residual starlight within the pupil can be canceled to deeper levels. & 2016 Elsevier B.V. All rights reserved.
Keywords: Coronagraphy Starlight rejection High contrast imaging
1. Introduction The resolution of very faint exoplanets from their host stars requires deep suppression of the much brighter starlight. One promising technique in this regard is the optical vortex coronagraph [1–3], in which an azimuthal phase ramp applied to the stellar focal-plane Airy pattern expels the starlight from a subsequent pupil image. While the rejection should be perfect for an ideal, clear circular input aperture, on-axis secondary telescope mirrors degrade performance significantly [4,5]. Improved starlight suppression levels or suppression bandwidths can in some cases be obtained with cascaded, multi-stage coronagraphs [6,7], and the multi-stage vortex coronagraph [8] was proposed to mitigate the additional leakage in the centrally-obscured telescope case. Here we present a laboratory demonstration of the improved rejection provided by the dual-vortex coronagraph for a centrally obscured aperture. The theory of the dual-vortex coronagraph has already been presented in detail [8], and so here we quickly summarize the theory graphically (Fig. 1). Fig. 1 shows a schematic layout of a dual-stage vortex coronagraph, indicating all focal and pupil planes. Optical vortex phase masks (V1 and V2) lie in both internal focal planes. Below the layout are shown the theoretically expected light distributions in five near-pupil-plane locations along the coronagraphic beam train, with P being the input pupil; L1 & L1 þ the planes just before and after the first Lyot stop plane, L1, n
Corresponding author. E-mail address: [email protected] (E. Serabyn).
http://dx.doi.org/10.1016/j.optcom.2016.05.042 0030-4018/& 2016 Elsevier B.V. All rights reserved.
and L2 & L2 þ being the planes just before and after the second Lyot stop plane, L2. For simplicity, in the following we ignore the secondary supports, concentrating solely on the effects of the central obscuration. The discussion here is also limited to optical vortex phase wraps of topological charge 2, i.e., those in which the output optical phase wraps from 0 to 4π in one circuit about the center. With a uniform input-pupil field between diameters of d and D, passage of the coherent starlight from an unresolved star through the first optical vortex phase mask results in two components of residual starlight in the subsequent pupil plane, both with an r 2 field profile, where r is the radial coordinate. These components originate at the primary and secondary mirror edges (Fig. 1). The light external to the pupil can be blocked with an opaque “Lyot” stop, L1, but the residual light between the primary and secondary edges limits the rejection in a single-stage vortex coronagraph [8] to (d/D)2. However, passing the post-L1 residual starlight through a second focal-plane optical vortex phase mask (V2) again leads to a redistribution of the starlight in the subsequent pupil plane, L2. In L2, most of the residual starlight is concentrated inside d, where it can be blocked by a second, central, Lyot stop (L2 in Fig. 1). However, a smaller residue of light, of uniform field strength (d/D)2, remains between d and D, which limits the dual-vortex (intensity) rejection to (d/D)4. As the residual light in the output pupil plane L2 þ is an exact scaled replica of the input pupil P (see Fig. 1), the rejection is given directly by the ratio of the uniform intensities in the these two pupil planes, which is equivalent to, but simpler than, ratioing the Airy patterns in the two subsequent focal planes.
E. Serabyn et al. / Optics Communications 379 (2016) 64–67
65
2: Collimating OAP 1
1: Fiber source 3: Input pupil mask
8: Focusing OAP 2 4: Focusing OAP 1
5: Vortex mask 1
9: Vortex mask 2
6: Collimating OAP 2 7: Lyot stop 1
Fig. 1. Schematic of the dual-vortex coronagraph layout as used in our experiment. SM is a single-mode fiber input, P is the input-pupil mask, V1 and V2 are the two optical vortex phase masks located in two successive focal planes, L1 is the first pupil image plane and contains the first Lyot stop (clear inside D; opaque beyond D), and L2 is the second pupil plane and contains the second Lyot stop (clear beyond d; opaque inside d). For simplicity, the off-axis paraboloids are shown here as lenses. Shown below the layout are the theoretical pupils expected in the 5 planes: the input pupil, P, just before and after L1, and just before and after L2. Shown along the bottom are crosscuts of the initial and final pupil planes.
The rejection improvement from (d/D)2 to (d/D)4 in going from a single vortex coronagraph to a pair of vortices is best for small secondary/primary ratios, but large extant telescopes tend to have sizeable d/D ratios. (Note that this ratio actually refers to the central blockage, which tends to be somewhat larger than the secondary mirror diameter itself.) At one extreme, the Hale telescope at the Palomar Observatory, with d/D ¼0.36, would show a theoretical rejection improvement from 0.13 to 0.017 in going from one to two vortex stages. Even this single order of magnitude improvement is significant, as the extra stage decreases the residual diffracted starlight to levels near or below the stellar leakage caused by residual post-extreme-adaptive-optics atmospheric wavefront errors. Even larger ground-based telescopes typically have somewhat smaller d/D ratios (down to 0.1), for which the rejection improvement is more significant.
2. Experiment Our experiment was carried out on the Infrared Coronagraphic Testbed (IRCT), an open-air coronagraphic optical bench located at the Jet Propulsion Laboratory. This testbed has been used for several experiments, including the testing of coronagraphic masks for the James Webb Space Telescope's Near Infrared Camera [9], as well as for the Subaru and Keck telescopes. For this demonstration, a second coronagraphic optical relay was added to the IRCT. The IRCT consists of all-reflective optics (except for the optical vortex phase masks) up to the second coronagraphic focal plane, after which lenses are used in order to save space after the light rejection steps are completed. The light source was a diode laser at a wavelength of 795 nm coupled to the testbed through a singlemode fiber. The input pupil is defined by means of a metal mask in the collimated input beam with apertures that provide a scaled version of the Hale telescope at the Palomar Observatory (however, the support legs of the “secondary” blocker were larger than scale). The IRCT input pupil was then relayed through two focalplane optical vortex phase masks, as shown in Figs. 1 and 2. Both vortex phase masks, manufactured by Beam Engineering [10], were designed for a wavelength of 800 nm. The requisite Lyot stops were placed in the two pupil planes (Figs. 1 and 2), and the final pupil plane was relayed to our camera with additional lenses. To make a uniform and rapid set of directly comparable coronagraphic performance measurements, we found it best to avoid switching between focal plane images, in which the light is
13: CCD camera
12: 2:1 relay 11: Lyot stop 2
10: Re-imaging lens
Fig. 2. The Infrared Coronagraphic Testbed (IRCT), with all non-flat-mirror optics numbered in sequence. From the fiber launcher (1), the light proceeds through two sequential optical relays, each consisting of a pair of off-axis paraboloids (OAPs), that produce the focal planes in which the two optical vortex phase masks are located (5 & 9). An input pupil mask (3) and two pupil-plane Lyot stops (7 & 11) are also indicated. Flat fold mirrors are not indicated. All of the beam train optics up to the fold flat after the second focal-plane vortex mask (9) are reflective. Thereafter, lenses are used to generate the final pupil image and to transport it to the CCD camera.
intensely concentrated onto a small number of pixels, and pupil plane images, in which the light is spread over many pixels, as such switches would necessitate changing optical attenuators, electrical gain settings, and/or integration times. Changing optical attenuators within the source was found to be problematic, as insertion of different attenuators changed the coupling of the input beam into the input fiber (due to differing attenuator wedge angles), thus altering relative intensities in non-reproducible ways. We therefore decided to rely solely on pupil plane images, which provide the same rejection information as focal plane images (i.e., once flux is removed from the pupil plane, it is also removed from the subsequent focal plane), but which nicely obviate all dynamic range issues. The pupil plane images also provide a point-by-point comparison across the pupil. Moreover, because removing an optical element is a much simpler and quicker step than inserting and aligning an optical element, we decided upon the following uniform and efficient procedure to obtain the desired images of the five pupil planes of interest (P, L1 , L1 þ , L2 , and L2 þ ). First the full two-stage coronagraph was carefully and completely aligned to the limits achievable with our manual actuators. We then simply cycled through the five needed images in reverse, by removing in reverse order the already installed Lyot stops and vortices one by one. Specifically, starting from the image of L2 þ , removing L2 takes us to L2 ; removing V2 takes us to L1 þ , removing L1 takes us to L1 , and finally, removing V1 takes us to P, the input pupil. The five resultant dark-subtracted pupil plane images so obtained in a single sequence are shown in Fig. 3. Aside from the diffraction along the central blocker's support legs, the measured radial light distributions in these five images correspond rather well with the theoretical distributions shown in Fig. 2. Fig. 4 shows an image of the measured intensity ratio of the final output pupil plane (L2 þ ) to the input pupil plane (P), which, as mentioned earlier, directly gives the light rejection as a function of position within the pupil. The intensities in the clear areas of the 2nd Lyot plane are indeed relatively flat across much of the pupil area (except near some of the sub-aperture boundaries), and are much reduced compared to the input pupil, being on the order of 0.02 of the input pupil (see, e.g., the vertical crosscut through the pupil shown in Fig. 4), and reach down to near the theoretical value of 0.17 in the best regions of the pupil (e.g., near the top of
66
E. Serabyn et al. / Optics Communications 379 (2016) 64–67
P
L1-
L1+
L2-
L2+
Fig. 3. Measured pupil-plane light distributions in the 5 planes labeled in Fig. 1. From left to right: the input pupil P, just before and after the first pupil plane, L1, and just before and after the second pupil plane, L2. The color scales range from 0 in all cases to maxima of roughly 55,000, 65,000, 65,000, 26,000 and 6000, from left to right. Note the residual light around the secondary in the L1 and L1 þ images, and the morphological similarity of the first and last images (the initial and final pupils). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 4. Left: The intensity ratio of the 2nd Lyot plane (L2 þ ) to the input pupil (P). The color scale ranges from 0 to 0.1. Right: Vertical crosscuts through the center of the L2 þ /P pupil plane ratio (bottom curve) and the L1 þ /P pupil plane ratio (top curve). The two light dotted vertical lines at the inner radius of the L2 þ pupil are guides for the eye. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
the image, corresponding to near pixel 337 in the bottom vertical cross-cut curve in Fig. 4). Low-level optical aberrations were the main limitation to the measured rejection, as residual patchy light (the reddish areas in Fig. 4) was seen to fluctuate across the final pupil as slight alignment adjustments were made, and the IRCT has no deformable mirror to reduce or remove wavefront aberrations. Indeed, in addition to wavefront and alignment errors, any other imperfections, such as imperfect vortices, slight differences between the two vortices, a mismatch between the vortex and laser wavelengths, and operation slightly outside the single mode regime of the injection fiber [which begins at 800 nm], should all serve to raise the level of light leakage within the pupil. In practice, the theoretically expected rejection ratio should thus serve as a lower limit to the measured intensity ratio, which does seem to be the case (Fig. 4). The measured dual-stage vortex intensity rejection is thus in line with theoretical expectations.
3. Potential for further rejection improvement For large d/D ratios, the residual light left within the unobscured pupil area by a dual-vortex coronagraph is still somewhat large, making further light rejection desirable in demanding high-contrast applications. Further gains could be made by adding additional stages [6–8], but this would lead to an increasingly large and unwieldy optical system. An alternative approach is the
single-stage ring-apodized vortex coronagraph [11], but this approach brings with it a significant throughput loss, and is not compatible with the speckle phase sensing scheme enabled by the dual-vortex coronagraph configuration [12]. On the other hand, as we suggest here, the rejection of the dual-vortex coronagraph can be improved via a slight optical modification, that being to further reduce the residual starlight inside the final dual-vortex coronagraph pupil (L2 þ ) by canceling it with a small amount of the starlight that lies beyond the rim of the upstream L1 pupil stop. Specifically, if the first Lyot stop were increased in diameter from D to a slightly larger diameter D0 (to be determined below), the small annulus of starlight between D and D0 (with an r 2 radial field dependence) would be converted upon passage through the 2nd vortex into an additional uniform field component in the L2 plane. In particular, since the amplitude of the (uniform) postvortex pupil-plane field is given by the value of the r 2 field at the aperture boundaries, the extra field component introduced by the oversized L1 stop is given by the difference term between the two edges of the additional light annulus, i.e., 1–(D/D0 )2. In addition, the slightly larger L1 stop slightly modifies the normal residual field term from (d/D)2 inside D to (d/D0 )2 inside D0 . (We note that any fields extending beyond D can be cut off again at the 2nd Lyot plane.) As both of these small fields are positive, they do not cancel, but if a relative half-wave phase shift were introduced between the regions interior and exterior to D in the L1 pupil plane, the relative signs of the two residual fields would be
E. Serabyn et al. / Optics Communications 379 (2016) 64–67
inverted, implying cancellation if D0 is chosen such that 2
2
1– ( D/D′) = ( d/D′) ,
Acknowledgment
(1)
i.e., if
(2)
D′ 2 = D2 + d2.
67
This work was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under contract with NASA, United States.
For small secondary/primary ratios, this can be approximated as
References 2
D′/D ≈ 1 + ½ ( d/D) .
(3)
In practice, an adjustable iris diaphragm at L1 would allow for optimization of the size of D0 to maximize rejection. The net rejection will then be limited by the next term in the expansion in powers of (d/D)2, i.e., by the (d/D)6 term. Moreover, practical issues such as aberrations and secondary supports will also limit rejection. Nevertheless, even for sizable secondaries, such as at Palomar, this additional step should lower the theoretical rejection to roughly the 10 3 level or better, at which point the raw rejection will typically be significantly better than that set by atmospheric wavefront residuals. The requisite half-wave phase shift can be introduced by a glass substrate (in transmission) or a mirror (in reflection) at L1 that is a half-wave thicker or thinner in optical path beyond D, which is relatively simple to implement, e.g., by etching the substrate to the correct depth. Although such approaches are essentially monochromatic half-wave implementations, typical astronomical filter passbands are sufficiently narrow, 10–20% full width at half maximum (FWHM), that optimizing for the passband center still yields a sizeable improvement in integrated rejection – specifically, a factor of (πf)2/12, where f is the filter's fractional FWHM – implying a rejection improvement of a factor of 30 even with a 20% FWHM filter.
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