Enhancing Direct Exoplanet Spectroscopy with Apodizing and Beam Shaping Optics
Benjamin Calvin, Nemanja Jovanovic, Garreth Ruane, Jacklyn Pezzato, Jennah Colborn, Daniel Echeverri, Tobias Schofield, Michael Porter, J. Kent Wallace, Jacques-Robert Delorme, Dimitri Mawet
DDraft version February 24, 2021
Typeset using L A TEX twocolumn style in AASTeX63
Enhancing direct exoplanet spectroscopy with apodizing and beam shaping optics
Benjamin Calvin , Nemanja Jovanovic , Garreth Ruane ,
1, 2
Jacklyn Pezzato, Jennah Colborn, Daniel Echeverri, Tobias Schofield, Michael Porter, J. Kent Wallace, Jacques-Robert Delorme ,
1, 3 andDimitri Mawet
1, 2 California Institute of Technology, 1200 E. California Blvd., Pasadena, CA 91125, USA Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA W. M. Keck Observatory, Kamuela, HI 96743, USA (Received; Revised; Accepted)
Submitted to PASPABSTRACTDirect exoplanet spectroscopy aims to measure the spectrum of an exoplanet while simultaneouslyminimizing the light collected from its host star. Isolating the planet light from the starlight improvesthe signal-to-noise ratio (S/N) per spectral channel when noise due to the star dominates, which mayenable new studies of the exoplanet atmosphere with unprecedented detail at high spectral resolution( > ∼ Keywords: astronomical instrumentation: high angular resolution, techniques: high angular resolution,exoplanets INTRODUCTIONWith over 4000 exoplanets confirmed to date, detec-tion has given way to the era of characterization, crit-ical to understanding the properties of these systems.In this vein, high contrast imagers (HCI), which isolatethe light from the planet, offer numerous advantagesover indirect techniques that rely on the signal fromthe host star alone. Typically, HCI use advanced wave-front control techniques combined with coronagraphs toextinguish the star light and minimize contamination
Corresponding author: Benjamin [email protected], [email protected] to the planet signal (Macintosh et al. 2014; Jovanovicet al. 2015; Males et al. 2018; Beuzit et al. 2019). Thesesystems often exploit low to medium resolving power(R ∼ a r X i v : . [ a s t r o - ph . I M ] F e b Calvin et al. observer to constrain the nature of the orbiting object.This technique has been exploited to detect or char-acterize both planets (Barman et al. 2015) as well asdisks (Currie et al. 2017).Recently, the field has shifted focus towards muchgreater resolving power (R > High dispersion Coronagraphy(HDC) , optimally combines high contrast imaging tech-niques such as adaptive optics/wavefront control pluscoronagraphy to high resolution spectroscopy (Wanget al. 2017; Mawet et al. 2017). One approach thathas been explored is to use an optical fiber to route thelight of the known planet from the focal planet to thespectrograph. A single-mode fiber (SMF) is the idealtransport vehicle owing to the fact it has a field-of-view(FOV) that can be matched to the 1 λ/D width of thepoint spread function (PSF), enabling efficient couplingfor the planet light and suppression of unwanted starlight. Its small core size only allows light to be guidedin a single mode providing spatial filtering, which furthersuppresses starlight speckles from coupling in and moreimportantly delivers an ultra stable output beam pro-file, highly desired by many instruments (Schwab et al.2012; Woillez et al. 2003; Crass et al. 2020). In addition,its narrow FOV reduces the amount of sky backgroundinjected into the spectrograph, which can be several or-ders of magnitude greater in the case of a seeing-limitedspectrograph.HDC provides the ability to do species-by-speciesmolecular characterization (e.g. oxygen, water, car-bon dioxide, methane), thermal (vertical) atmosphericstructure, planetary spin measurements (length ofday), and potentially Doppler imaging of atmospheric(clouds) and/or surface features (continents versusoceans) (Wang et al. 2017). As such several projectshave been initiated to realize this new technique fromthe ground including: the Keck Planet Imager andCharacterizer (KPIC) (Jovanovic et al. 2019), whichcombines Keck AO and NIRSPEC, the Rigorous Exo-planetary Atmosphere Characterization with High dis-persion coronography instrument (REACH) (Jovanovicet al. 2017a), which combines SCExAO and IRDand High-Resolution Imaging and Spectroscopy ofExoplanets (HiRISE), which combines SPHERE andCRIRES+(Vigan et al. 2018). The phase I version ofKPIC and the REACH instrument are both transition-ing from commissioning to early science at the time ofwriting of this article and offer complimentary wave-length coverage across the near-IR (NIR) on Maunakea(REACH operates from y-H and KPIC operates in K and L bands), while HiRISE is still in the developmentstage.Key to being able to disperse the faint planet signalacross many pixels and maintain signal-to-noise (S/N),as is the case in a high resolution spectrograph, is max-imizing the planet throughput. This can be done byimproving the adaptive optics (AO) correction to boostthe Strehl ratio and hence coupling efficiency, reshap-ing the PSF to better match the fiber mode (Jovanovicet al. 2017b), or minimizing the number of optics in thesystem. In addition, it is also important to minimize thestellar leakage into the planet fiber to reduce the photonnoise contribution from the star. Improved AO correc-tion can also help here, but specific focal plane wavefrontcontrol techniques such as speckle nulling (Bottom et al.2016; Sayson et al. 2019) or the use of a pupil planeapodizing mask (Zhang et al. 2018), are better suitedto reducing speckle noise. Although these technologiesachieve different goals, they are used to reduce total ex-posure time, which is critical when characterizing faintexoplanets with high spectral resolution on large tele-scopes.The technology or approach of choice depends on theparameters of the system being observed, such as planet-to-star flux ratio, angular separation, and the wavebandof observation. In this paper, we present the develop-ment of two technologies that can help boost the per-formance of HDC on KPIC and similar instruments,namely: Phase Induced Amplitude Apodization (PIAA)optics for re-shaping the beam and boosting couplingand a grayscale microdot apodizer (MDA) for suppress-ing diffraction features at small angular separations. Weaim to deploy these as part of the phase II upgrade ofthe KPIC instrument in late 2021. In Section 2 we out-line the two technologies and present the design andsimulated performance of such devices. In Section 3 wepresent the experimental setup and procedures to eval-uate the two technologies and in Section 4 we summa-rize and compare the results to simulations. Section 5compares the two technologies in the context of a hypo-thetical observing scenario to highlight the benefits ofeach in their respective domains and Section 6 roundsout the paper with some concluding thoughts. APODIZATION OPTICSThis section provides an overview of the two technolo-gies that we have developed to enhance the S/N of di-rect spectroscopic, or HDC, observations of exoplanets:PIAA (see Fig. 1) and MDA (see Fig. 2) optics. Eachhas been employed previously in apodized coronagraphsin the context of high-contrast imaging (Watson et al.1991; Nisenson & Papaliolios 2001; Kasdin et al. 2003; podizers in KPIC Figure 1. a) A ray trace through the PIAA optics. Here,the 50 mm represents the inner spacing between the poweredsurfaces of the PIAA optics. b) An image of the first lens,which refracts the beam to reshape it. c) An image of thesecond lens in the pair, which re-collimates the light afterbeam shaping. d) The radial sag profile for the first lens. e)The radial sag profile for the second lens. Both sag profilesare azimuthally invariant.
Soummer et al. 2003), where the PIAA (Guyon 2003)or MDA (Dorrer & Zuegel 2007; Martinez et al. 2009a)modifies the shape of the beam at, or near, the re-imagedtelescope pupil to reduce diffracted starlight at smallangular separations where exoplanets may be directlyimaged. These pupil-plane optics do not require any fo-cal plane masks to work for our purposes with KPIC.Our application differs from conventional high contrastimaging in that we aim to maximize the S/N in themeasured spectrum of an exoplanet using a diffraction-limited spectrograph that is fed by a SMF. As such, thePIAA and MDA optics that we developed for KPIC areoptimized to maximize the coupling efficiency for planetlight, η p , and minimize the fraction of the starlight thatis coupled into the SMF, η s .The coupling efficiency of a coherent, scalar field, E ( r ), into a fiber mode Ψ( r ) is given by: η = (cid:12)(cid:12)(cid:82) E ∗ ( r )Ψ( r ) dA (cid:12)(cid:12) (cid:82) | E ( r ) | dA (cid:82) | Ψ( r ) | dA , (1) Figure 2. (Left) Design for the MDA. It consists of a500 ×
500 grid of 25 µ m chrome squares forming a 12.3 mmannulus of transmission. The white areas show the regionof high transmission, while the black parts are covered withchrome. For scale, the outer black edge of the MDA is 15mm. (Right) A white-light photograph of a device manufac-tured for KPIC placed on textured background showing thetransmission function in the visible regime appears similarto the design. where r is the coordinate in the plane transverse to thebeam at the fiber. We use Eqn. 1, often referred to asthe overlap integral, to compute η p and η s by pluggingin the field at the fiber, E ( r ), due to the planet andstar, respectively. When stellar photon noise dominates, S/N ∝ η p / √ η s , while in most other cases S/N ∝ η p .In essence, the PIAA optics are designed for the latterscenario, whereas the MDA is optimized for the former.The PIAA optics consist of a pair of beam shapinglenses designed to alter the effective distribution of lightat the pupil, in order to reshape the PSF in the focalplane. In the original implementation, PIAA lenses wereused to reduce the Airy rings in coronagraphs (Guyon2003). Later, PIAA optics were used to optimize thecoupling to a SMF (Jovanovic et al. 2017b).The KPIC PIAA optics consist of two aspheric lensesfabricated from CaF because of its high transmissionacross the wavelength regime that KPIC operates ( K and L bands; 2.0-4.2 µ m). AR coatings for this spectralregion were optimized and deposited on both sides ofeach optic to minimize Fresnel reflections. Figure 1(a)shows a ray diagram of the PIAA lenses, which aredesigned to re-distribute an annular intensity distribu-tion, similar to the centrally-obscured Keck pupil, into aquasi-Gaussian profile. As a result, the PSF is a bettermatch to the fundamental mode (LP ) of a SMF and,therefore, the coupling efficiency is improved.The lenses each consist of one flat surface (facing out-wards) and one aspheric surface (facing inwards). As thelight propagates from the first aspheric surface to thesecond 50 mm away, the collimated beam is remappedand recollimated. In this way the PIAA optic pair canbe inserted into a collimated beam without modifying Calvin et al.
Figure 3.
Theoretical, monochromatic beam shapes and PSFs for the Keck telescope (Top row) without apodization, (Middlerow) with the PIAA lenses, and (Bottom row) with the MDA. (Column 1) Beam intensity before focusing onto the SMF.(Column 2-4) Log base-10 PSF intensity for (Column 2) an on-axis source as well as sources with an angular separation of(Column 3) 5 λ/D and (Column 4) 10 λ/D from the optical axis (white cross). All are normalized to the peak intensity in thenon-apodized case and using the corresponding central design wavelength (3.8 µ m for the PIAA and 2.2 µ m for the MDA). the downstream focusing optics. The sag profiles ofthe two lenses were designed by solving the differentialequation in Guyon (2003), which leverages Snell’s lawto achieve the desired remapping. Figure 1(b) and (c)show the fabricated lens pair while (d) and (e) show thecross-section of the rotationally-symmetric sag profiles.We chose the sag profiles to achieve the desired remap-ping function at the central wavelength in the L (cid:48) band( λ = 3.8 µ m) because we expect the S/N to be lim-ited by thermal background in the longest wavelengthfilters. However, the PIAA can be used over the fullKPIC range with slightly degraded coupling efficiencyin the shorter wavelength filters.One limitation of the PIAA optics is that theremapped intensity depends on the position of the sourcewith respect to the optical axis. While the lenses aredesigned to provide a quasi-Gaussian beam shape foran on-axis source, the exiting wavefront deviates fromthis and becomes heavily aberrated when the source isoff-axis by even a few resolution elements (i.e. λ/D ,where λ is the wavelength and D is the beam diame-ter at the pupil). Figure 3 shows the beam shape andcorresponding PSFs without any alteration (Fig. 3, top row) and with (Fig. 3, middle row) the PIAA optics.The PIAA modifies the PSF favorably in the case of anon-axis source by concentrating more light into the PSFcore. However, the off-axis PSFs suffer from a strongcoma aberration with a magnitude that increases withthe the angular separation (Fig. 3 shows offsets of 5 and10 λ/D ). Due to the rotational symmetry of the PIAAdesign, the direction of the coma aberration will alwayspoint radially away from the core.To utilize PIAA optics for HDC, the planet must bealigned to the optical axis of the PIAA lenses to receivethe coupling boost. The star would then be off axis, andfor the separations depicted in the figure, would diffracta small amount of light onto the location of the planetmarked by the white cross. This is where its importantto note that Fig. 3 displays the intensity of the PSF,which does not necessarily indicate the amount of lightthat will couple into a SMF. So although there may bestar light of non-zero intensity at the location of theplanet fiber, we need to compute the coupling of thatspeckle pattern to the SMF to understand the stellarleakage term. Figure 4 shows an azimuthally averagedline profile taken from a 2D coupling map computed for podizers in KPIC µ m squaresin a 200 nm thick chrome layer on an AR-coated CaF substrate (seen in Fig. 2). The size of the microdots waschosen to maintain a ∼ S/N fora planet spectrum assuming the measurement is domi-nated by stellar photon noise. For computational con-venience, rather than maximizing the η p / √ η s ratio, weminimize η s /η p , which is proportional to the requiredexposure time to achieve a given S/N in a stellar pho-ton noise limited regime.To optimize the effective transmittance of the MDA,we assumed a polynomial radial apodization functionwith field amplitude A ( r ) = N (cid:88) j =0 c j ( r/a ) j , (2)where c j are constants, r is the radial coordinate, and a is the beam radius. In our simulations, we multi-plied A ( r ) by the expected Keck pupil function, whichis not rotationally-symmetric. However, using a one-dimensional apodization function simplifies the opticalsystem by not requiring a rotational alignment betweenthe apodizer and the beam. For each set of c j coeffi-cients, we computed the fraction of on-axis planet lightthat couples into the SMF, normalized to the total en-ergy incident on the apodizer. This slightly modifieddefinition of η p includes both losses in coupling efficiencyand the semi-transparent design of grayscale mask. Theeffective η s was defined as the fraction of starlight thatcouples into the on-axis SMF when the star is imagedoff-axis (see Fig. 4), averaged over planet-star separa-tions of 3-15 λ/D . Using these metrics, we found theoptimal apodization function by minimizing η s /η p witha simplex algorithm (see Fig. 3, bottom left). We re- Figure 4.
Azimuthal average of the coupling efficiency ofan off-axis PSF shown in Fig. 3 at the central design wave-length and assuming no other aberrations. A coupling of100% means that all of the light of the PSF couples intothe on-axis fiber. We can see that the PIAA does not sig-nificantly affect the off-axis coupling of the clear Keck pupil.We can also see that the MDA decreases the off-axis couplingfrom 3-12 λ /D, excluding two localized regions of 4.5-6 and8.5-9. peated the optimization for various values of N andopted to use N = 5 since adding more terms did notsignificantly improve performance.We converted the continuous apodization functioninto a binary microdot pattern using the Floyd-Steinberg error diffusion algorithm (Floyd & Steinberg1976; Dorrer & Zuegel 2007; Zhang et al. 2018) tak-ing into account the relative transmission of the 200 nmthick chrome layer and the exposed substrate. Figure 2shows the designed pattern and a photo of the fabricatedMDA, which has approximately 500 microdots acrossthe expected 12.3 mm beam size. The full coated regionis 15 mm in diameter. Given that the S/N is more likelyto be stellar photon noise limited at the shorter wave-lengths, we optimized the MDA for the central wave-length of K band ( λ = 2.2 µ m), but the MDA cantechnically be used with any KPIC filter. At the longestwavelengths, where thermal background tends to dom-inate, the MDA is not likely to improve performancebecause of the reduced throughput and potentially highemissivity of the opaque regions.Figure 5 shows azimuthally averaged line profiles ofeach on-axis PSF, normalized to the non-apodized case.The PIAA increases the flux in the core of the PSF,which leads to improved fiber coupling. On the otherhand, the MDA reduces the diffraction from the starat angular separations beyond 3 λ/D , but at the costof adding the semi-transparent optic and lowering thecoupling efficiency. These technologies provide the abil- Calvin et al.
KeckPIAAMDA
Angular coordinate ( /D) -6 -5 -4 -3 -2 -1 N o r m a li z ed i n t en s i t y a t c en t r a l w a v e l eng t h Figure 5.
Azimuthal average of the on-axis PSFs shownin Fig. 3 at the central design wavelength and assuming noaberrations. The intensities in all cases are normalized to thepeak of the Keck PSF. The top panel shows the intensity atthe PSF core on a linear scale and the bottom panel showsthe diffracted intensity further from the source on a log scale. ity to enhance the performance of KPIC in two dif-ferent regimes. However, each has a significant down-side. While the PIAA increases the throughput for anon-axis source, the source and PIAA must be carefullyaligned to the optical axis of the system; the off-axisPSF becomes heavily aberrated. The MDA suppressesdiffracted starlight and thereby reduces stellar photonnoise in the measurement of the planet spectrum, butat the cost of overall throughput. EXPERIMENTAL CHARACTERIZATIONIn this section we describe the experimental setup andtests carried out to characterize the fabricated devices.The key properties to examine for the two technologiesare the PSF shape, the throughput, and the couplingefficiency. To specify, we use throughput in this paperto refer to the throughput of the individual optics andnot the overall effect that the optic has on the system’sthroughput. The throughput of the individual optics is less than 100% as a result of Fresnel reflections, absorp-tion, and reflections from the micro-dots in the case ofthe MDA. Testing the throughput will help ensure thatthere were no errors in the manufacturing of the opticsand that the AR coatings are performing according tospec. In addition, we will measure what effect thesetechnologies have on the light coupled to a SMF on/offaxis and compare this to simulations.3.1.
Experimental Setup
Figure 6 shows the experimental setup with the PIAAmechanics in the beam. The setup to characterize andmeasure the MDA is equivalent, but with the KPICcoronagraph module at the “Test Optic” location.This testbed can be separated into 4 main compo-nents. First, there is the “telescope simulator,” whichcollimates light injected by a SMF. The SMF can beswapped between a 2 µ m laser and a blackbody lightsource that is single mode across the 2-5 µ m wavelengthregion. The collimating optic is an AR coated CaF2lens, with f=200 mm. Its distance from the light sourcecan be adjusted with a translation stage to ensure thatthe light is collimated regardless of the wavelength. Thebeam then passes through a pupil mask, which imitatesthe Keck pupil. Given the long focal length of the col-limating lens, the beam can be approximated as havinga flat top illumination after passing through the mask.The second component to the testbed is the test optic.These are located in the beam immediately following thetelescope simulator in collimated space. Both the PIAAand MDA are mounted on stages that can repeatablymove the optics in/out of the beam path. This allows forcomparative measurements to be taken quickly betweenthe apodized beam and the non-apodized beam.Following the test optics is the third component, thecoupling arm. This begins with a field-steering pick-off mirror (FSM1) that directs light toward the off-axis parabola (OAP) used to couple the light. FSM1is mounted on a magnetic plate that can be removedand repeatably replaced to give quick access to the twomain functionalities of the testbed. This turning mir-ror is complemented by a second, fixed steering mirror(FSM2). The two in combination can translate the col-limated beam and adjust its angle of incidence with re-spect to the OAP (inside of the OAP block). This allowsfor coupling to be efficiently optimized into the SMF.The OAP is a protected gold coated mirror with an off-axis focal length of 36.6 mm, which injects the light intoa ZBLAN fiber (Le Verre Fluor´e, MFD = 7 . µ m at a2 . µ m wavelength, core diameter = 6 . µ m, claddingdiameter = 125 µ m). With the pupil mask diameterof 12.3 mm, this creates an F .
0, which closely podizers in KPIC Figure 6.
Image of the experimental lab bench in the PSF imaging mode. The red line indicates the beam path for the PSFimaging mode. The orange line indicates the beam path for fiber coupling mode after the objects circled in orange have beeninserted into the beam path. Inset in the bottom left corner is the pupil mask emulating the Keck telescope pupil. matches the measured ZBLAN fibers numerical aper-ture of 0.175 ± µ m, and needs tobe liquid nitrogen cooled. It has 240 x 318 pixels and apixel pitch of 30 µ m. The PSF formed by the F . µ m laser and do K s measurements, a K s -band filter (Asahi-Spectra) is used.For L band measurements, we use a 3-5 micron bandpassfilter. 3.2. Procedures
Before the camera could be used to make quantitativemeasurements, it required us to linearize its response,maximize its dynamic range and do a one-point non-uniformity correction (NUC) flat fielding. The camera’sexposure time and video offset were coarsely adjustedto match the expected flux levels for the experiments.Then, they were carefully tuned and the response ofthe camera to varying flux levels was compared to thereading of a power meter. This resulted in a linear cam-era response with the maximum possible dynamic range.The next step was to perform a one-point NUC to ensurea uniform response across the detector. This was donewith the camera entrance window blocked by a blackpiece of metal, such that a uniform thermal backgroundfrom the plate filled the camera’s entire field-of-view,while running the NUC correction algorithm built intothe camera. 3.2.1.
PSF Imaging
We recognize that the shape of the PSF is criticaland that the faint wings can only be revealed at a highSNR. With the beam of interest projected onto the cam-era, the exposure time and video offset were adjustedboth to bring the background counts down to around50-100 ADUs and to maximize the signal. The 1 pointNUC was applied as outlined above. The light sourcewas blocked and a cube of 100 frames that constitutesthe background were collected. The light source wasunblocked and a cube of 100 frames with signal was col-lected. Finally, the light source was blocked once againand another cube with 100 background frames was col-
Calvin et al. lected. The two sets of background frames, bracketingthe signal frames, were used to construct a backgroundthat was as similar to the background when the signalwas acquired as possible.3.2.2.
Throughput
To make quantitative measurements of the flux usingthe camera, aperture photometry/radiometry was con-ducted. To obtain the throughput of a given opticalelement (e.g. PIAA or MDA), the flux from the PSFgenerated when the optic was in the beam was normal-ized by the flux of the PSF when the optic was out of thebeam. As such, it was important to keep the exposuretime and other camera settings constant between thetwo measurements to assure an accurate comparison.We take the same pattern of 100 background frames,100 signal frames, and then another 100 backgroundframes both when the optics were in and out of thebeam. 3.2.3.
Coupling Efficiency
To determine the coupling efficiency to the ZBLANoptical fiber, we again compare the flux between twostates: 1) light transmitted through the SMF re-imagedonto the detector and 2) the PSF that was directly in-cident on the fiber before being imaged onto the detec-tor. These two states have non-common optics and sothe throughputs of those optics had to be accounted forduring the analysis.To photometrically measure the coupling efficiency ina given band, we:1. Adjust the light source power, exposure time, andvideo offset to maximize the signal from the re-imaged coupling fiber,2. Image, with backgrounds, the re-imaged fiber,3. Carefully remove the re-imaging system and FSM1to reconfigure into PSF imaging mode,4. Image, with backgrounds, the PSF without adjust-ing any settings.After normalizing out the differential losses in eacharm, we can take the ratio between the extracted fluxesand determine the coupling efficiency in isolation.3.3.
Data Acquisition and Analysis
There are multiple things we can do with the imagedPSF to analyze and quantify it’s properties in compar-ison to the model. For example, one can compute theoverlap integral (Eqn 1) between the model and the ex-perimental PSFs to assess their similarity. For all other forms of analysis (i.e. throughput or coupling), we mustfirst extract the fluxes from the detector by carefullyremoving the background. The PSF is localized to, atmost, a region with a radius of 25 pixels. Meanwhile thethermal background is a non-zero bias across the frame,that can be assumed to be uniform following the 1 pointNUC. When using the single-mode blackbody source,the signal is small, so this background subtraction mustbe done carefully. To accurately only extract the fluxfrom the PSF, we follow a two step process: 1) subtracta background frame collected close in time to the dataand 2) model out the remainder of the background.To achieve step 2, we take measurements of the totalenclosed aperture flux at increasing aperture radii. Be-yond the extent of the PSF, the encircled flux increasesor decreases linearly (for a uniform background) withthe total enclosed pixels, F internal = F P SF + α · n pix ,where α is the average background flux. Thus, in or-der to get F P SF , we fit the linear part of the curve andsolve to determine the y-intercept, which is the back-ground free flux. The uncertainty in this measurementis the relevant value from the covariance matrix of thefit.With the flux’s extracted, the throughput can next becalculated. It is the ratio of the fluxes: ξ = F in /F out The coupling efficiency is mathematically very similarto the throughput, the ratio of the flux coupled into themode of the SMF and the flux incident on the fiber face.However, there is more involved with getting to this step.As was stated in the procedure, there are many non-common optics between the fiber re-imaging block andthe focusing arm of the bench. Once those are accountedfor, the coupling efficiency is as well: η = F coup /F in The key to qualifying the experimental measurementsis to be able to compare them to accurate models. Toensure we get the highest degree of agreement, we repli-cate the parameters of Fig. 6 in a simulator. Thereare uncertainties in some of the physical parameters inthe coupling arm of the setup: the NA of the couplingfiber and the effective focal length of the coupling OAPare known only to ∼ RESULTSHere we summarize the measurements of the parame-ters outlined in the methods section and compare themto simulations. 4.1.
PSF profiles
The critical feature for both technologies is the struc-ture of the PSFs and specifically the faint structure in podizers in KPIC µ m laser had enough power toreveal the faint structure on the MIR camera. Figure 7and 8, present the PSFs obtained from the Indigo cam-era side-by-side with the corresponding simulations andthe residual difference between the two. This enablesqualitative comparison between the two, which is impor-tant to building confidence in both the manufacturingand design process. Figure 7.
PSFs for the PIAA shown in both linear (top) anda base-10 logarithmic (bottom) space with the same spatialextent. (Left) Experimental, (Center) Simulated, (Right)Residual of difference between the model subtracted from theexperimental PSF. The linear scaling residuals emphasize thehigh degree of agreement between the model and experiment,while the logarithmic scaling shows the structural differencesbetween the two. All PSFs are shown at 2 µ m. It can be seen from both figures, that there is astrong similarity between the experimental and simu-lated PSFs. The right hand panel in both figures showsthat the residuals of the difference between the modeland the experimental PSFs are very low, with a peakaround the 10 − or 1% intensity level. Further, we canalso use the overlap integral as a quantitative compar-ison tool for the PSFs. To account for misalignment’sin the peaks of the two PSFs, we scan the model PSFacross the experimental PSF in 2D and compute an over-lap integral map as shown in Fig. 9. From the overlapintegral maps, we can see that both technologies have apeak greater than 99.8%, indicating a high level of con-sistency between the experimental and simulated PSFs,validating the design and manufacturing process.We can also compare the azimuthally averaged lineprofiles of the PSFs. By over plotting the line profile ofthe experimental PSF with the simulated PSF, we can Figure 8.
PSFs for the MDA shown in both linear (top) anda base-10 logarithmic (bottom) space with the same spatialextent. (Left) Experimental, (Center) Simulated, (Right)Residual of difference between the model subtracted from theexperimental PSF. The linear scaling residuals emphasize thehigh degree of agreement between the model and experiment,while the logarithmic scaling shows the structural differencesbetween the two. All PSFs are shown at 2 µ m. Figure 9.
Overlap integral maps between experimental andmodelled PSFs for (Left) PIAA and (Right) MDA. The fig-ures show a high level of consistency between the imagedPSFs and the simulated ones. identify locations where the flux is unexpectedly high orlow. In Fig. 10, we show these line profiles of the twotechnologies. The shaded regions indicate the standarddeviation in the azimuthal direction of the imaged PSF.We can see that both the PIAA and MDA closely followthe simulated curves, once again emphasizing the simi-larity between the design and the characterized devices.4.2.
Throughput
The throughput is defined as ξ = F out /F in , where F in is the flux at the input to the test optic and F out isthe flux at the output of the test optic. The simulationswere carried out in discrete monochromatic bands, whilethe experimental measurements, aside from the 2 µ m0 Calvin et al.
Figure 10.
Azimuthally averaged line profile of the a) PIAAPSF and b) MDA PSF. The shaded region accounts for theuncertainty in the measurements. laser, were taken using a broadband black-body lightsource combined with bandpass filters. The simulatedand measured throughputs are shown in Fig. 11, wherethe horizontal error bars represent the bandwidth of thelab filters.As can be seen from the figure, both technologies metthe expected throughput to within uncertainty. ThePIAA is designed to reshape the pupil in a lossless fash-ion as described in Section 2. The throughput is wellabove 90% in both K and L bands as expected, and anysystematic losses can be easily explained through resid-ual reflections across the four AR coated surfaces.We can see that the MDA had a throughput consis-tent with simulations of ∼
50% in K-band. However, wesee it begin to roll off in the experimental results in theL band. This is due to the AR coating on the MDA notbeing optimized for L band, because the losses associ-ated with the MDA reduce the L-band flux to the pointwhere the thermal background dominates. Therefore,the MDA was not expected to be scientifically useful inL band and hence the coating was not optimized in thisrange. 4.3.
Coupling Efficiency
Figure 11.
A comparison of throughput curves betweensimulations and our experimental measurements for thePIAA and MDA optics.
The simulations for the coupling efficiency were alsoproduced in discrete monochromatic bands, and com-pared to the polychromatic results obtained with a fil-tered black-body light source in the laboratory. Thecoupling efficiencies for the two technologies are shownin Fig. 12. The expected coupling for the non-apodizedpupil is overlaid on these figures for reference.It can be seen that the coupling for the PIAA opticsmatches our simulation well. We can also see that thecoupling for the MDA matches the simulation quite well,except for the measurement with the 2 µ m laser. We areunsure why this data point is off, but believe it has todo with the increased coherence of the 2 µ m laser andinterference effects generated by the MDA. To ensurethat this was not merely an effect of the camera, themeasurement was repeated by placing a Thorlabs S148cpower meter near the final focal plane and making thesame flux comparison as the camera. The power meterconfirmed the higher than expected coupling when usingthe MDA and the 2 µ m laser beam. While this is notwell understood, it is not an undesirable result in thecontext of KPIC.From the figure it is clear that the PIAA boosts thecoupling from ∼
60% in K and L bands without anyadditional optics to ∼
70% in K and 84% in L band. Incomparison, the MDA reduces the coupling in K bandto ∼
48% and in L band to 45%. It should be madeclear that these results are for the Keck like pupil maskin our experiments, which has oversized spiders, and atthe Keck telescope, the coupling will be 3 −
4% greaterin all cases.Looking at the impact of the optics at the system levelby combining the throughput and coupling efficiency,the PIAA has a total system throughput of 66% in K podizers in KPIC Figure 12.
A comparison of coupling efficiency curves be-tween the simulation and our experimental measurements forboth test optics. band and 77% in L band while the MDA is closer to ∼
24% in both K and L bands. The impact of theseefficiencies will be discussed in the following section. DISCUSSIONIt is clear from the results that the PIAA and MDAhave different characteristics that will be useful in dif-ferent contexts, so we will address them individually.5.1.
Beam Shaping Optics
The PIAA are lossless beam-shaping optics. We cansee from the Ks and L band measurements that there isan increase in coupling efficiency, from ∼
60% withoutthe PIAA to ∼
75% with PIAA in K band and ∼ ∼ Micro-dot Apodizer
The MDA’s effect is more subtle. The role of the MDAis to decrease the amount of contaminating light froman off-axis source that gets coupled into the SMF. Ascan be seen from the line profiles (Fig. 5), the PSF fromthe apodizer has nearly an order of magnitude less fluxbetween 3 and 12 λ /D compared to the PSF from anon-apodized pupil. So, in situations where the lightfrom the on-axis host star is drowning out the signalfrom the off-axis planet, using the MDA can help iso-late the planet light. One drawback of the MDA is, toachieve such starlight suppression, the apodizer must de-crease the throughput of the on-axis (star) and off-axis(planet) objects to ∼ Exposure Time Calculation
In this section we look at the impact of the two tech-nologies on the exposure time of a simulated observ-ing scenario of the planetary system 51 Eridani b, withKPIC, in both K and L band. Although the star istypically on-axis during acquisition, a tip/tilt mirror inthe injection unit is adjusted in the final steps of ac-quisition to put the known planet on-axis and align itwith the SMF. In this scenario, the exposure time ( τ exp )of an observation to reach a given SNR is proportionalto the coupling efficiency of the stars PSF ( η s ) and ap-proximately inversely proportional to the square of thecoupling efficiency of the planet PSF ( η p ): τ exp ∝ η s /η p To see how each technology effects the exposure time,the properties of KPIC were included in a realistic ex-posure time calculator (ETC). η s and η p were scannedacross a grid of reasonable values for the case of observ-ing 51 Eridani b. Figure 13 shows the contour maps ofexposure time vs raw contrast and throughput to achievea cross-correlation function (CCF) S/N=10. On thesefigures, discrete points can be seen for the case of thenative PSF (red dots), the PIAA (white dots) and theMDA (gold dots) PSFs. In addition, the cyan dots high-light the phase I level of performance of KPIC on-skybefore deploying these technologies in phase II.It can be seen that in the case of 51 Eridani b, thePIAA optics offer little improvement in K-band com-pared to the expected phase II performance, while theMDA can reduce the exposure time by ∼
33% from 3 to2 hrs. Despite the fact the MDA decreases the planet’sthroughput, it also suppresses the star light, improvingcontrast and the net effect is an improvement in thedetection exposure time. However, in L-band, whichis dominated by thermal background, the PIAA opticsoffer the advantages in exposure time, reducing the ex-2
Calvin et al.
Figure 13.
Exposure time contours for S/N=10 detection of 51 Eri b using the different technologies in K-band and L-bandin units of hours. Left, we can see in the K-band how the MDA decreases the planet’s throughput, but the resultant increasein star contrast creates a net improvement in detection exposure time. Right, we can see how the increased throughput of thePIAA helps to decrease the detection exposure time. posure time of the expected phase II system by ∼ CONCLUSIONWe have demonstrated the design, fabrication, char-acterization and accurate simulation of both PIAA andMDA optics in the context of HDC. The optics wereoptimized to operate in the K and L bands, which over-laps with the operating spectral bands of the KPIC in-strument. The PSFs, throughput and coupling efficien-cies all matched expectations from simulations, provid-ing a high level of confidence in both the simulation toolsand manufacturing capabilities. In a simulated observ-ing scenario of 51 Eridani b, it was determined thatthe MDA would offer a reduction in exposure time of ∼
33% in K-band, while the PIAA would offer a sim-ilar level of reduction for L-band observations. Suchreductions in exposure time are important on 8-10 mclass telescopes and are necessary to be able to targeteven fainter objects in future. The application of a par- ticular technology to a given observation will depend onwaveband of choice, the flux ratio of the star/planet andtheir angular separation, and needs to be determined ona case-by-case basis.ACKNOWLEDGMENTSThis work was supported by the Heising-Simons Foun-dation through grants
Facilities:
KeckIIREFERENCES
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