External occulter laboratory demonstrator for theforthcoming formation flying coronagraphs
Federico Landini,1,* Sébastien Vives,2 Mélanie Venet,2 Marco Romoli,1
Christophe Guillon,2 and Silvano Fineschi3
1Dipartimento di Fisica e Astronomia, Sez. di Astronomia—Università di Firenze, Largo Fermi 2, 20125 Firenze, Italy2Laboratoire d’Astrophysique de Marseille, Rue Frédéric Joliot-Curie, Marseille Cedex 13, France
3INAF-Osservatorio Astronomico di Torino, Strada Osservatorio 20, 10025 Pino Torinese, Italy
The observation of the inner corona (below 1.3 solarradii, being the solar radius, R⊙ equal to 7 × 108 m)is the major challenge the next generation ofwhite-light coronagraphs is going to face. Indeed, thecontrast between the inner corona and the solarphotosphere (i.e., the visible-light solar disk) is typi-cally ranging between 10−6 and 10−8, making coronalobservation very difficult. The visible-light corona isan optically thin medium, thus it is observable onlyout of the solar disk limb by occulting the bright disk
source with a suitable stop. On the basis of theoccultation concept, we can distinguish between in-ternally and externally occulted coronagraphs. In in-ternally occulted coronagraphs, the occulter is placedon the focal plane of the primary objective, which ishit by the direct solar disk light. These coronagraphsare particularly suited for the observation of the so-lar corona between 1.1 and 2R⊙. The observation be-low 1:1R⊙ down to the minimum distance achievablefrom the solar disk limb is prevented by the over-whelming level of stray light, which grows higherand higher by observing closer to the limb. Classicalexternally occulted coronagraphs are limited, too, inobserving the inner corona because of the stray-lightlevel behind the occulter and the very low resolution
due to the presence of the occulter in front of thepupil (vignetting effect). By increasing the distancebetween the occulter and the pupil, both effects arereduced. The optimal conditions for the observationof the inner corona occur during total solar eclipses;in fact, the large distance between the telescope (onEarth) and the occulter (the Moon) guarantees a verylow stray-light level and a minimum vignetting ac-tion of the occulter over the pupil. However, eclipsesare too rare (only one or two per year) and too short intime (only a few minutes) to allow intensive coronalobservations. A way of getting closer to total solareclipse conditions (thus to observe the inner coronaeven below 1:1R⊙ at high resolution) is to enlargeas much as possible the distance between the occul-ter and the rest of the telescope. The ideal answer tosuch a highly demanding request is to design, build,and operate two spacecraft (S/C) flying in formation,thus forming a giant solar coronagraph. New chal-lenges are generated by the novelty of the formationflying (FF) concept: by increasing the distance be-tween the S/C, bigger occulters are needed, thuscausing difficulties in managing such large opticalelements in space. The most critical issue in the de-sign of a white-light solar coronagraph is the reduc-tion of the stray light due to the diffraction andscattering of the solar disk light by the optics. Themain source of stray light is the occulting system thatmust be optimized in order to maximize its efficiency.As experimentally proven by Newkirk and Eddy [1]during a balloon flight, not-optimized occulters fail infulfilling their goal, since the light diffracted by theocculter edge and scattered by the telescope opticsconstitutes a contribution of the same order of mag-nitude of the coronal light. It has been demonstratedby all successive missions (see Section 2 for an his-toric list of the most successful ones) that an occulteredge shape optimization may lower the level ofdiffracted light by 2 or 3 orders of magnitude. Bycombining the FF concept to a suitable optimizationof the occulter shape, we satisfy all the requirementsin order to maximize the stray-light reduction. Inthis paper we describe our work on the optimizationof large external occulters for future FF corona-graphs, both from logic-theoretical and experimentalpoints of view. Space-borne coronagraph history ischaracterized by a long debate on the best optimizingshape for the occulter edge, as described in Section 2.The novelty of the FF coronagraph concept (i.e., thecoronagraph with the most Moon-like occulter everconceived, in terms of both occulter–pupil distanceand size) does not allow us to completely rely onliterature for a choice on the occulter optimization,since all space-borne coronagraphs that are ac-counted for are within 2m of length, and all dimen-sions are scaled more or less accordingly. Therefore,we performed a dedicated study. Although FF solarcoronagraphs are a relatively new argument, theyhave already been discussed by the scientific commu-nity, and some missions have been proposed. On thisbasis, we adopted a practical approach, by focusing
on a particular mission in order to make our consid-erations directly applicable to a concrete instrument.As a baseline for our investigation, we consideredthe observational requirements of the PROBA-3/ASPIICS FF coronagraph [2]. Association de Satel-lites Pour l’Imagerie et l’Interférométrie de la Cour-onne Solaire (ASPIICS) is a visible-light, externallyocculted coronagraph conceived to perform both highspatial resolution imaging and two-dimensionalspectrophotometry of the inner corona. It will beimplemented on the PROBA-3 mission [EuropeanSpace Agency (ESA)], which aims at validating de-velopments in space. ASPIICS is distributed on thetwo PROBA-3 S/C, separated by 150m. The entranceaperture of the telescope is protected from directsolar disk light by an occulting disk of 1:5m indiameter. This geometry guarantees an inner fieldof view of 1:015R⊙ (i.e., ∼14 arcsec overoccultationof the solar disk). The optical design of ASPIICS isadapted from the general principles of a classical ex-ternally occulted Lyot coronagraph [3]. Section 2 isdedicated to the comparison among pros and consof the optimization systems that can be found in lit-erature, by considering their performances in stray-light reduction and the issues connected with theirpossible implementation in the FF mission understudy. Sections 3 and 4 are dedicated to the measure-ments we performed at the Laboratoire d’Astro-physique de Marseille (LAM) to determine occulteroptimization performance and manufacturing toler-ances. The work described in this paper has beenperformed in 2010 in the framework of the ESASTARTIGER program supporting the developmentof future FF solar coronagraphs. The scientificand technical goals of our STARTIGER project aredetailed in [4].
2. Literature Heritage and FF CoronagraphRequirements
One of the pioneering papers that faced the occulteroptimization issue was by Newkirk and Bohlin [5];they called the optimization “apodization,” while ad-mitting that the phrasing is not entirely appropriatefor this kind of optical issue. From their paper: “Dif-fraction from the external occulting disk is the mainsource of this stray light. The light diffracted intothe objective may be reduced by removing the occult-ing disk to a great distance, as is the moon at totaleclipse, or by ‘apodizing’ or ‘softening’ the edge ofthe disk. (Although ‘apodization’ commonly refersto the alteration of the Fraunhofer diffraction pat-tern of an objective lens by means of a radiallygraded filter, it is here used to describe the modifica-tion of the Fresnel diffraction by an opaque disk.) Theserrated occulting disk developed by our colleaguesat the Naval Research Laboratory is one form ofapodization.”
Since then, many papers have described opti-mization systems and analyzed them both from the-oretical and experimental points of view. The threemost discussed and used systems are toothed disks,
triple disks (in general multiple disks), and a multi-threaded or polished frustum of a right cone (orbarrel).
There are five milestone papers on the analysis ofthe optimization techniques; in chronological order,the main authors are Newkirk [6], Fort [7], Lenskii[8], Koutchmy [9], and Bout [10]. The only systemtheoretically fully analyzed is the toothed disk [8],while the triple disk and the multithread solutionare only qualitatively explained and experimentallytested. In particular, Koutchmy and Bout reportedexperimental and theoretical (where possible) com-parisons among the different optimization systems.
A. Toothed Disk
This method was first proposed by Purcell andKoomen in 1962 [11], and consists of a single diskwith a serrated edge. The case has been theoreticallyanalyzed by Lenskii [8], and experimentally testedby Fort et al. [7] and Koutchmy [9]. A series of verytiny and sharp teeth was designed to spread dif-fracted light along the edge of the shadow of the diskitself, in order to escape the pupil. It is the only solu-tion that allows limiting the optimization shape tothe plane of the occulter itself, but it is not easilyachievable. The main challenge is to manufacturevery sharp teeth, which have to be kept very clean.Every single particle that settles on the teeth or inthe thin hollow between two successive teeth canscatter light and become a dominant stray-lightsource; anyway, scattering due to dust settling be-tween two successive teeth can be limited by couplingtwo disks dephased by half a tooth. Dust is not a ma-jor challenge for multiple disks (Subsection 2.B) andoptimizing shapes (Subsection 2.C), because they aredesigned to block light scattered by dust directlyexposed to the solar disk. The toothed disk solutionhas been adopted by several space-borne corona-graphic missions:
• 1963, a NRL team, led by Tousey, obtained thefirst image of the extended corona with a rocketflight [12];
• 1968–1970, Dollfus flew a coronagraph on aballoon [13];
• 1993–1998, the SPARTAN 201 mission flew anexternally occulted coronagraph/spectrometer with atoothed linear occulter to obtain the first UV obser-vation of the extended solar corona [14]; and
• 1995–present, SOHO-Ultraviolet CoronagraphSpectrometer uses the same design concept as theSPARTAN 201 instrument [15,16].
B. Multiple Disks
This system was first proposed and tested byNewkirk and Bohlin in 1963 [6]. A second disk, in theshadow of the first, with respect to the solar disk,blocks the radiation diffracted by the first disk edgeand limits the scattering from eventual dust on thefirst disk; a third disk, in the shadow of the secondone, blocks thediffractionproduced by the seconddisk
edge, and so on. Actually, all flown coronagraphsusing this solution mounted a three-disk system.Figure 1 describes the concept for amultiple-disk sys-tem, by designing just two disks; l is the disk interdis-tance and z the distance between the external occulterand the entrance pupil of the coronagraph. To addmore disks between the two drawn in Fig. 1, it is en-ough to apply the very same principle. If r2−1 < rFOV(and the same inequality holds also for successivedisks, if any), then themultiple-disk systemhas a bar-rel profile, while, if r2−1 ¼ rFOV, then the profile isconic. The conic occulter described in Subsection 2.Cis designed following this principle. Lenskii [8] per-formed a theoretical analysis of the stray-light levelbehind a two-disk system, and extended the resultto infer an estimate of the stray-light level behind athree-disk system, but without a proper theoreticalanalysis. This system has been employed by
• 1965, the balloon-borne Coronascope II ofNewkirk and Bohlin [5];
• 1971–1974, the white-light coronagraph inOSO-7 [17];
• 1995–present, LASCO-C3 aboard SOHO [18],that is producing visible-light images of the extendedsolar corona up to 30R⊙,
• 2006–present, Cor2 coronagraph and Helio-spheric Imager (which uses straight-edge multipleocculters) of the STEREO/SECCHI mission [19]; and
• 2009, HERSCHEL/SCORE [20,21] andHERSCHEL/HeCor [22] coronagraphs, the firsttwo coronagraphs that observed the extended coronain the HeII 30:4nm line.
Laboratory tests for the GOES-R coronagraph oc-culter, conducted for a multiple-disk system, demon-strated that, for compact coronagraphs, the barrelprofile is preferable to the cone one [23].
C. Cone or Barrel
The multithreaded cone or barrel is the logical exten-sion of the three-disk system; it is basically an im-provement of the number of disks, each one in theshadow of the previous, and each one blocking thelight diffracted by the previous disk edge. The ideawas proposed by Newkirk and Bohlin, but they didnot consider this solution very reliable, because ofthe “inevitable irregularities in the disk” that “throw
Pupil
R2A1 A2
Critical edge
r2−1 rFOV
R1
zl
Fig. 1. Concept for the first two disks of a multiple-disksystem. The principle is easily repeatable for any other diskthat may be inserted between those two. In our case, z ¼ 150m,rFOV ¼ 1:015R⊙.
spurious radiation into the objective aperture”[6]. This result was overturned by Koutchmyand Belmahdi in experimental tests in 1987 [24].LASCO-C2 aboard SOHO [18] is using this solutionwith excellent results. By increasing the number ofdisks to infinity, we get a polished cone or barrel,which has been compared with the multithreadsolution only by Bout et al. [10]: their result, whileconfirming Koutchmy and Belmahdi’s conclusion,emphasized a substantial equivalence between mul-tithreaded and polished surfaces in stray-light re-duction performance, thus suggesting the adoptionof polished surfaces, these being easier to manufac-ture and handle than multithreaded ones.
D. Trade-Off Solutions for the ASPIICS Case
Since the main objective of the coronagraph is tofulfill an observation of the solar corona as close aspossible to the limb, a priori we tend to exclude op-timization systems that increase the inner field ofview (FOV). The toothed disk is an example. In fact,while for a multiple-disk system (see Fig. 1) the op-timization geometry does not affect the FOV, theteeth of a serrated edge do increase the inner FOV.The toothed disk must be thought of as the baselinesharp disk of 1:5m diameter plus the thickness of theteeth. By using formula (12) from Lenskii’s paper [8],we estimated the diffracted flux on axis behind atoothed disk, normalized to the diffracted flux behindthe nominal simple disk for our reference FF corona-graph. Figure 2 shows the result as a function ofthe number of teeth, for three different tooth peak-to-valley heights (d in Fig. 2). Even in the case of d ¼5mm (which fixes the inner FOV at 1:022R⊙), to ob-tain a decrease in diffracted light comparable to the 2or 3 orders of magnitude that are typical for other
kinds of optimization, we should manufacture morethan 1 × 105 teeth along the disk circumference.Such a high number corresponds to a peak-to-peakdistance of 24 μm, which is really challenging to ma-chine. Other requirements that have to be matchedare the handling and manufacturing for such a hugeocculter. Alignment issues must be taken intoaccount, and even pointing stability must be consid-ered. These constraints suggest avoiding long occult-ing systems, such as the multiple disks, but also acone would have to be short, i.e., ∼10–15 cm at most.We are thus forced to discard a multiple-disk system.
To support this choice, we performed a simplesimulation, comparing together the performance ofdifferent instruments with a two-disk occulter, as afunction of the distance between the disks. Figure 3(top) shows the result. The y axis of the plot repre-sents the ratio I2=I1, where I2 is the normalized dif-fracted flux on axis on the entrance pupil planebehind a two-disk system, and I1 is the same quan-tity for a single disk. Both values are calculated withthe whole solar disk as a source and are given byformulas (8) and (6), respectively, from the Lenskiipaper [8].
Three instruments are compared: STEREO-SECCHI/Cor2, HERSCHEL/SCORE, and the 150mbaseline distance FF coronagraph. The x axis is dif-ferent for each instrument, since they have differentdimensions.
It is evident from Fig. 3 (top) that the stray-lightreduction due to a two-disk system is improved byincreasing the distance between the disks. On theother hand, moving the second disk far from the firstone implies an approach to the entrance apertureplane and, thus, a reduction in the instrument col-lecting area. In the limit of a second disk on the plane
d
Fig. 2. Ratio between on-axis diffracted light behind a toothed disk and a knife-edge disk, for three different peak-to-valley tooth heights.
of the entrance aperture, we would get a removalof the stray light, as well as of the coronal signal.A trade-off must be found.
A comparison between the diffraction level and apredefined threshold may not be an appropriatemethod, since the instruments have different FOVs:in general, at fixed geometry, the observation at high-er minimum FOV induces a lower level of stray lightbehind the disks, as confirmed by Fig. 3 (top). Thisis due to a fainter source (obtained by observingfarther from the solar disk limb) diffracted by theocculter edge.
A reasonable way of judging the effectiveness of asecond disk is to compute the derivative of the ratioI2=I1, which is shown in Fig. 3 (bottom).
Neither the Cor2 nor the SCORE disk interdis-tance was chosen by using these simulations; never-theless, this plot is evidence to support the goodnessof those choices. The interdistance of two disks is25 cm for SCORE and 5 cm for Cor2. Both disk inter-distances correspond to derivative values in therange (−3 × 10−4 ÷ 10−4), which can be seen as therange where the ratio slope starts smoothing, i.e.,the effectiveness of a second disk starts to be less
Fig. 3. Comparison among different coronagraphs on stray-light reduction performance (top) as a function of the disk interdistance. Thederivative of such performance is shown (bottom) in order to define a procedure to fix the more advantageous trade-off disk interdistance(see text).
advantageous. Moving disks farther beyond that in-terdistance would not bring the same improvementin stray-light reduction as for shorter interdistances.If we imagine applying the same principle to the cor-onagraph in FF, we would need an impracticable se-paration between the two disks of at least 12:5m.
As a rule of thumb, the conic occulter should alsokeep the same dimensions as the multiple-disk sys-tem, since they share the same design principle (seeFig. 1). But a conic occulter has never been simu-lated, so the previous statement cannot be con-firmed. Moreover, if we consider a conic surface (orbarrel) and not a multithread with a conic profile(or barrel), the material, the machining, and the sur-face finish can all affect the performance: laboratorytests are needed to assess these unexplored aspects.
Since polished or electro-eroded cones (or barrels)are more easily machined and less expensive thanmultithreaded ones while offering comparable per-formance [10], we decided to concentrate on theformer ones, leaving to future analyses a comprehen-sive evaluation.
Figure 4 shows that, if we draw a barrel followingthe same principle that we use for a multiple-disksystem (see Fig. 1), then, over a length of 15 cm, weget Rc − Rb ∼ 4 μm, which means that the cone or bar-rel has the same shape within the manufacturingtolerances. However, it is possible to investigate com-pact barrels with different design principles (seeSubsection 4.D).
3. Laboratory Setup
A test setup has been assembled at the LAM, insidea Class 100 clean room, using the solar simulatorimplemented for the tests of the LASCO-C2 corona-graph [10]. Since it is practically impossible to realizea full-scale model of the 150m baseline FF corona-graph, we designed a setup that is able to measurethe stray light behind a section of the whole occulter.The section of such a large occulter (1:5m diameter)can be well approximated by a small straight-edge piece.
We therefore measured the diffraction pattern be-hind a linear occulter and not behind a disk; thus, itis not possible to directly extrapolate our present re-sults to the actual coronagraph. Nevertheless, it ispossible to perform a relative analysis, by comparingstray-light reduction performance of linear occulters.
The light diffracted from a knife edge, beingeasily computable even for an extended source (seeSubsection 4.A), is the reference for all the sets ofmeasurements.
It is reasonable to measure the stray-light patternbehind the occulter in the same solid angle definedby the space real-model geometry. Figure 5 showsa comparison between laboratory and flight geome-tries. The stray light we are interested in is the por-tion of all the light scattered by the occulter edge thatis collected by the telescope entrance pupil. So wemeasured the stray-light pattern in the solid angleΩ subtended by the pupil as seen by the occulter edge(Fig. 5, top). This created some challenging issues inthe laboratory configuration, since we had to mea-sure the stray-light pattern very near to the solardisk critical edge (Fig. 5, bottom), which is definedby the ray coming from the solar limb, grazing theocculter edge.
A sketch of the measurement setup is representedin Fig. 6. A complete overview of the setup conceptis shown in Fig. 6(a): the source is a collimator thatsimulates the angular dimension of the real solardisk. Light from the source enters the Class 100clean room through an aperture. In the clean room,the stray-light measurement setup is assembled.
15 cm
RbR
aR
R1.015 R1.015
R1.004
lerraBenoC
15 cm
c
Fig. 4. Cone geometry compared to barrel: if we follow the sameprinciple in designing the two optimizations (see Figure 1), giventhe flight geometry, differences are negligible (Rc − Rb ∼ 4 μm).
Lab configuration: 80 cm
Flight configuration: 150 m
Critical edge (1 R )
Critical edge (1 R )
Occulter Pupil
Ω
Ω 3.8 mm4.3 mm
Occulter
1.5 m10 cm
Fig. 5. Comparison between flight (up) and laboratory (down)configurations. The critical edge is defined by the ray coming fromthe solar limb.
Fig. 6. Not to scale sketch of the measurement setup. (a) Over-view of the complete setup, divided into two separated rooms, com-municating only by the exit aperture of the source. (b) Particular ofthe optics setup for stray-light measurement behind the occulter.
The detector is a photodiode mounted on a transla-tion stage. In front of the photodiode is mounted abaffle, accommodating a 0:45mm pinhole, to allowa high spatial resolution sampling. A light trap isplaced very near to the detector to prevent direct “so-lar” disk light from illuminating the room. Stray-light measurements are performed behind the linearocculter along a direction perpendicular to the oc-culter edge. All measurements are relative to thesource unobstructed flux (i.e., without the occultermounted). A complete overview of the optical setupis shown in Fig. 7(a).
To achieve the conic angle of the optimized linearocculter, we used a metal plate mounted on a preci-sion steel tilting platform. This also allowed us to de-fine the tolerance we can afford in manufacturing theconic optimization shape, by repeating the stray-light measurement behind the occulter for severalconic angles (i.e., several tilting platform tilts, asdescribed in Subsection 4.C.4). Figure 7(b) showsthe tilting platform together with the whole linearocculter assembly, as seen from the top of the opticalbench.
4. Measurements
A. Knife Edge: Theory
The diffraction pattern behind a linear occulter isrelatively easy to compute, even considering an ex-tended source like the solar disk.
Using the Huygens–Fresnel theory [25], the nor-malized diffracted light intensity pattern behind aperfect and infinite knife edge for a point source atinfinity is given by
Iðx; λÞ ¼ 12
12þ CðαÞ
2þ12þ SðαÞ
2; ð1Þ
where λ is the wavelength, x is the coordinate on theimage plane along the direction perpendicular to theocculter edge, α ¼ x
, with L distance be-tween the occulter and the image plane, i is the ima-ginary unit, and CðαÞ, SðαÞ are the Fresnel integrals.By integrating Eq. (1) over the solar disk, after somebrief analytical calculations, we get
ISðx; λÞ ¼1
πR2⊙
ZR⊙þx
−R⊙þxBðxSÞdxS
12þ CðαSÞ
2
þ12þ SðαSÞ
2; ð2Þ
where xS is the coordinate along the solardisk radius, αS ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2=ðλLÞp ðx − xSÞ, and BðxSÞ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiR2
⊙− ðxS − xÞ2
q. Figure 8 compares the diffraction
given by Eqs. (1) and (2) at a fixed wavelength of500nm. The 0 of the x axis corresponds to the pointwhere the line defined by the center of the Sun and
Fig. 7. (a) Overview of the whole optical setup. (b) Particular ofthe optical setup showing the occulter assembly, as seen from thetop of the optical bench: the tilt of the tilting platform is empha-sized by an arched white arrow.
Fig. 8. Theoretical diffraction at a fixed wavelength (500nm) behind a knife edge in case of point source at infinity (dashed curve) andextended source (solid curve).
the center of the occulter edge intersects the imageplane. It can be interesting to note that we can easilyrecognize the penumbra and umbra (i.e., diffraction)zones in the curves. The inflection point on the des-cent defines the border between umbra and penum-bra; in fact, in correspondence of that point, the lightabruptly changes its decreasing slope.
Actually, for rigor’s sake, we must consider thatthe photodiode integrates the signal on its wave-length range of responsivity, so, to get a proper simu-lated signal, we shall average over the wavelength,including the wavelength dependence of each opticalelement that the radiation goes through. We callTðλÞ ¼ RðλÞ ·WðλÞ · ΓðλÞ the total efficiency of the op-tical system as a function of the wavelength. RðλÞ isthe responsivity of the photodiode, ΓðλÞ is the spec-tral distribution emitted by the halogen lamp thatis the source of the solar simulator, and WðλÞ is thetransmittance of the two Wratten 80A filters used tochange the color temperature of the radiation; weconsider the transmission of the collimator as a con-stant over the wavelength. With these assumptions,Eq. (2) becomes
ISðxÞ¼1
πR2⊙
1R λfλi TðλÞdλ
Z λf
λi
ZR⊙þx
−R⊙þx
12þCðαSðxS;x;λÞÞ
2
þ12þSðαSðxS;x;λÞÞ
2TðλÞBðxSÞdxSdλ: ð3Þ
In the simulation we included the nominal curvesfor the spectral distribution of the lamp, thetransmittance of the Wratten 80A filters, and theresponsivity of the photodiode. Taking into account
the uncertainty provided by the manufacturers, wecomputed a tolerance of 20% on simulated data.Figure 9 shows the simulation as a range that takesinto account the uncertainty.
B. Knife Edge: Measurement
With the setup described in Section 3, we performeda measurement to check the agreement of the mea-sured diffraction pattern behind the knife edge andthe signal foreseen by Eq. (3). Figure 9 shows a verygood agreement between theory and measurements,thus confirming the reliability of the experimentalsetup. In particular, we may notice that, in the pe-numbra range, the simulation path is perfectly sym-metrical with respect to data values, while, in thediffraction range, the simulation slightly underesti-mates the measures. This effect can be interpretedas a contribution given by some stray-light sourcesstill present in the measurement environment: sincedata still fit the uncertainty-weighted simulationrange, we assume this stray-light contribution to benegligible. The measurement of diffracted light be-hind a knife edge is a major step in our analysis,since it validates the experimental setup and allowus to use the nominal values of the simulation as areference for all the successive tests.
C. Cone
With the setup described in Section 3, various conicconfigurations have been applied to the linear occul-ter. Even though we dealt with a tilted metal plate,we interpret it as a portion of a much bigger flightocculter; thus, in the following, we will always referto it as a cone. To understand how longitudinal
Fig. 9. Measurements of diffracted light behind a knife-edge occulter (black curve) compared to the simulation (gray pattern: the un-certainties provided by the manufacturers are included). A mean behavior of the simulation will be shown as a reference in all successiveplots.
dimension, materials, surface polishing, scratches,and assembly errors affect the stray-light reductionperformance of the optimized occulter, we performedseveral indicative tests, for each of which a differentocculter was designed and manufactured.
A1: aluminum, 10 cm long, surface roughnessσ ¼ 0:4 μm, which is compared with all the other conemodels.
A2: aluminum, 15 cm long, σ ¼ 0:4 μm, to investi-gate how length affects performance.
I1: Invar, 10 cm long, σ ¼ 0:4 μm, to compare differ-ent materials’ performance.
A3: aluminum, 10 cm long, σ ¼ 0:4 μm, separatedin two equal parts, A3G and A3D, to test if thereare differences in stray-light reduction performancebetween an occulter manufactured as one piece andan assembled one.
A4: aluminum, 10 cm long, σ ¼ 6:4 μm, to checkwhether a different surface finishing affects occulterperformance.
A5: a spare of A1, surface scratched at a depth of20 μm, to check at which level scratches start to affectocculter performance.
A6: a spare of A1, surface scratched at a depth of200 μm, with the same objective as A5.
Laboratory tests reveal that there is no differencein stray-light reduction among A1, I1, and A4. It isnot necessary to show such measurements, since thecurves are overlapped within the errors. This sug-gests that neither cone material nor its mechanicalsurface finishing affect stray-light reduction perfor-mance (see also Subsection 4.C.3). In any case, Fig. 10reveals that the conic optimization does indeedimprove stray-light performances with respect tothe simple knife edge.
1. Length
FromFig. 10wemay also conclude that an increase inthe occulter longitudinal length (i.e., along the opticalaxis) improves the performance, as is evident fromthe comparison between A1 and A2. This was some-how expected, as the ideal conic optimization for theocculting disk should be much longer than 15 cm,according to the design principle exposed inSubsection 2.B and to the comment in Subsection 2.D.
2. Bad Assembly
If the flight occulter will be made of smaller compo-nents, assembly errors may occur. To infer how muchassembly errors may affect the optimization perfor-mance, tests were made by bad assembly of A3Gand A3D on purpose. We define “radial” assemblyerror as a misalignment along the ideal radius ofthe flight occulter, i.e., perpendicular to the conicsurface. We define “longitudinal” assembly error asa misalignment perpendicular to the previous one,i.e., parallel to the conic surface. We applied a long-itudinal misalignment of 1:5mm and a radial misa-lignment of 0:5mm. Figure 11 shows that if theassembly error is radial, we completely jeopardizethe optimization effect, while if it is longitudinal,we have no significant impact on the stray-lightreduction performance.
3. Scratches
Figure 12 describes how scratches influence the per-formance of the optimized occulter. Scratches wererealized by means of a drill, with a depth of 20 μmon A5 and 200 μm on A6. This result allows us toestablish that scratches at least 20 μm deep do not
Fig. 10. Comparison among A1, A2, and the knife-edge reference (see Fig. 9 caption).
affect stray-light reduction performance of theoptimized occulter surface.
4. Cone Angle
Figure 13 shows how the cone angle influencesstray-light reduction performance. Strangely en-ough, it seems that we can manufacture a cone withan angle increase within 2 arcmin from the nominal34:05 arcmin (defined according to the nominal FOVof the instrument and to the principle of Fig. 1).To simulate different cone angles with our linear
optimizing plate, we performed several measuresby changing the angle defined by the tilting plat-form on which the linear occulter was mounted[see Fig. 7(b)]. We obtained a deviation from the nom-inal behavior (case of A1 in Fig. 10), only beyond36 arcmin. This result may sound queer since a puregeometric discussion would lead to the conclusionthat, by changing the cone angle from the nominalvalue, we would completely compromise the drawingprinciple, and thus the performance that it mayprovide. It may be an interesting result also for types
assembly error
of 1.5 mmerror of 0.5 mm
Radial assembly
Knife edge reference
A1
Longitudinal
Fig. 11. In the case of an assembled cone, radial assembly errors deeply affect optimization performance, while longitudinal assemblyerrors are practically ineffective.
Fig. 12. Comparison among two types of A1s with scratched surfaces and A1 (with no scratches).
of coronagraphs other than FF ones, for example,standard coronagraphs that are designed to observethe solar corona at different distances from the Sun,such as those aboard Solar Probe [26] or SolarOrbiter [27]. A unique geometry could guaranteegood stray-light reduction performance at differentdistances from the Sun (i.e., at different instrumen-tal FOV).
D. Toroidal Occulters
In Subsection 2.D, we noticed that, due to the geome-try of FF coronagraphs, when designing a barrel withthe principle of Fig. 1, we cannot deviate appreciablyfrom a cone. In any case, we can change arbitrarily
the barrel designing principle, and compare its per-formance with the conic occulter. We designed threedifferent linear occulters with a cylinderlike geome-try, that, if extended on the FF external occulterprofile, gives rise to toroidal shapes. These occultersdiffer in the radius of curvature. To investigate thewidest possible field of geometries, we chose to adopt1 cm, 10 cm, and 1m as radii. Figure 14 shows thethree manufactured occulters, together with a three-dimensional (3D) CAD model of the 1 cm occultermounted in the setup and a sketch showing thecurvature radius definition. All the three toroidal oc-culters were made of aluminum by electro-erosion.Figure 15 shows the performance of the three toroi-dal occulters compared with A1. The 1 cm toroidal oc-culter is the worst of the three, and performancesincrease by flattening the surface. The 100 cm radiusocculter, which is in fact almost flat, has a behaviorcomparable with the conic occulter. On the otherhand, sensitivity to occulter tilt is negligible for the1 cm toroid, and is the same as A1 for the 100 cm one.
5. Conclusions
In the framework of the ESA STARTIGER programfor coronagraphs in FF, a trade-off study was per-formed for the optimization of the 1:5m diameterexternal occulter of a 150m baseline distance FF cor-onagraph (such as ASPIICS). The analysis was bothqualitative (based upon theoretical and laboratorydescriptions in literature) and quantitative. In fact,several sets of measurements were performed atthe LAM (France), with a setup mounted in a Class100 clean room and using a solar simulator source.Since it is impossible to replicate in the laboratorythe flight configuration, the measurements wereperformed on linear occulters, thought of as small
Fig. 13. Analysis on the tolerance we can afford in manufacturing the cone angle. The box enhances a subrange of the main plot between1.1 and 2R⊙.
Fig. 14. Clockwise, from the top left: 3D CAD model showing the1 cm radius occulter mounted in the setup; sketch showing a sec-tion of the toroidal occulter, in order to define the curvature radiusR; picture of the three manufactured toroidal occulters.
portions of the big circular occulter. Therefore, it isnot possible to directly extrapolate our present re-sults to the actual coronagraph, even though the ob-tained results provide important information on thebest type of optimization and on the manufacturingtolerances. An improvement of the described work iscurrently ongoing, to confirm that scaled models ofthe big occulter give the same information as the lin-ear occulters. The results of the current project willbe the subject of a forthcoming publication.
All our results are relative to the unobstructedflux and to the knife-edge stray-light reductionperformance.
Figure 16 effectively summarizes the main resultwe obtained, by representing the ratios of each opti-mized solution performance and the knife-edge refer-ence. Within the limitations due to the use of linearocculters in place of actual disks, our analysis con-firms that an optimization improves the stray-lightreduction performance of a knife edge. If we thinkof the straight edge as a portion of a large circularocculter, we may infer that an optimized shapeimproves the simple disk performance, even in thecase of a huge occulter and for very compact shapesalong the optical axis.
Toroid 10 cm radius
Toroid 100 cm radius
A1
Knife edge reference
Toroid 1 cm radius
Fig. 15. Comparison among the three toroidal occulters, A1, and the theoretical knife-edge curve.
Fig. 16. Ratios among optimized solutions’ performance and knife-edge reference.
A conic shape is the best solution, and performanceimproves by increasing the length of the cone axis.The optimization is not deeply affected by the choiceof the material and the surface finishing: evenscratches (up to 20 μm of depth) do not change theoptimized occulter performance. Our analysis showsalso that such a system is relatively insensitive to tilt(within 2 arcmin) and scratches (at least 20 μm deep)on the conic surface. We tested also some toroidalapodizations, which are less efficient than the conicones.
This work was supported by European SpaceAgency (ESA) funding in the framework of theSTARTIGER program dedicated to formation flightmissions. Invaluable contributions were given byGuglielmo Rossi on technical drawings, Jose Garciaon mechanical machining, and Giuseppe Massone onboth.
References1. G. Newkirk, Jr. and J. A. Eddy, “A coronograph above the
atmosphere,” Sky & Telescope 24, 77–81 (1962).2. P. Lamy, L. Damé, S. Vives, and A. Zhukov, “ASPIICS: a giant
coronagraph for the ESA/PROBA-3 Formation Flying Mis-sion,” Proc. SPIE 7731, 773118 (2010).
3. J. W. Evans, “Photometer for measurement of sky brightnessnear the Sun,” J. Opt. Soc. Am. 38, 1083 (1948).
4. S. Vives, L. Damé, P. Lamy, A. Antonopoulos, G. Burton,G. Capobianco, G. Crescenzio, V. Da Deppo, M. Ellouzi,S. Fineschi, J. Garcia, C. Guillon, F. Landini, A. Marshall,A. Mazzoli, P. Rochus, T. Soilly, F. Stathopoulos, C. Tsiganos,K. Tsinganos, and N. Waltham, “The STARTIGER’s demon-strators: toward a new generation of formation flying solarcoronagraphs,” in 2010 International Conference on SpaceOptics (ICSO) (2010), paper 39, http://congrex.nl/icso/Papers/TPosters/39_VIVES_ICSO_PAPER.pdf.
5. G. Newkirk, Jr. and D. Bohlin, “Coronascope II: observation ofthe white light corona from a stratospheric balloon,” in Inter-national Astronomical Union Symposium (1965), Vol. 23,pp. 287–291.
6. G. Newkirk, Jr. and D. Bohlin, “Reduction of scattered light inthe coronagraph,” Appl. Opt. 2, 131–140 (1963).
7. B. Fort, C. Morel, and G. Spaak, “The reduction of scatteredlight in an external occulting disk coronagraph,” Astron.Astrophys. 63, 243–246 (1978).
8. A. V. Lenskii, “Theoretical evaluation of the efficiency ofexternal occulting systems for coronagraphs,” Sov. Astron.25, 366–372 (1981).
9. S. Koutchmy, “Space-borne coronagraphy,” Space Sci. Rev. 47,95–143 (1988).
10. M. Bout, P. Lamy, A. Maucherat, C. Colin, and A. Llebaria,“Experimental study of external occulters for the Large Angleand Spectrometric Coronagraph 2: LASCO-C2,”Appl. Opt. 39,3955–3962 (2000).
11. J. D. Purcell and M. J. Koomen, “Coronagraph with improvedscattered-light properties,” J. Opt. Soc. Am. 52, 596 (1962).
12. R. Tousey, “Observations of the white light corona by rocket,”Ann. d’Astrophys. 28, 600–604 (1965).
13. A. Dollfus, “La couronne solaire vue de ballon,” L’Astronomie82, 284 (1968).
14. J. L. Kohl, L. D. Gardner, L. Strachan, and D. M. Hassler, “Ul-traviolet spectroscopy of the extended solar corona during theSPARTAN 201 mission,” Space Sci. Rev. 70, 253–261 (1994).
15. J. L. Kohl, R. Esser, L. D. Gardner, S. Habbal, P. S. Daigneau,E. F. Dennis, G. U. Nystrom, A. Panasyuk, J. C. Raymond,P. L. Smith, L. Strachan, A. A. Van Ballegooijen, G. Noci,S. Fineschi, M. Romoli, A. Ciaravella, A. Modigliani, M. C.Huber, E. Antonucci, C. Benna, S. Giordano, G. Tondello, P.Nicolosi, G. Naletto, C. Pernechele, D. Spadaro, G. Poletto,S. Livi, O. Von Der Lühe, J. Geiss, J. G. Timothy, G. Gloeckler,A. Allegra, G. Basile, R. Brusa, B. Wood, O. H. Siegmund, W.Fowler, R. Fisher, and M. Jhabvala, “The ultraviolet corona-graph spectrometer for the solar and heliospheric observa-tory,” Sol. Phys. 162, 313–356 (1995).
16. M. Romoli, H. Weiser, L. D. Gardner, and J. L. Kohl, “Stray-light suppression in a reflecting white-light coronagraph,”Appl. Opt. 32, 3559–3569 (1993).
17. M. J. Koomen, C. R. Detwiler, G. E. Brueckner, H. W. Cooper,and R. Tousey, “White light coronagraph in OSO-7,”Appl. Opt.14, 743–751 (1975).
18. G. E. Brueckner, R. A. Howard, M. J. Koomen, C. M.Korendyke, D. J. Michels, J. D. Moses, D. G. Socker, K. P. Dere,P. Lamy, A. Llebaria, M. Bout, R. Schwenn, G. M. Simnett,D. K. Bedford, and C. J. Eyles, “The Large Angle SpectroscopicCoronagraph (LASCO),” Sol. Phys. 162, 357–400 (1995).
19. R. A. Howard, J. D. Moses, A. Vourlidas, J. S. Newmark, D. G.Socker, S. P. Plunkett, C. M. Korendyke, J. W. Cook, A. Hurley,J. M. Davila, W. T. Thompson, O. C. St. Cyr, E. Mentzell,K. Mehalick, J. R. Lemen, J. P. Wuelser, D. W. Duncan,T. D. Tarbell, C. J. Wolfson, A. Moore, R. A. Harrison, N. R.Waltham, J. Lang, C. J. Davis, C. J. Eyles, H. Mapson-Menard,G. M. Simnett, J. P. Halain, J. M. Defise, E. Mazy, P. Rochus,R. Mercier, M. F. Ravet, F. Delmotte, F. Auchère, J. P.Delaboudinière, V. Bothmer, W. Deutsch, D. Wang, N. Rich, S.Cooper, V. Stephens, G. Maahs, R. Baugh, D. McMullin, and T.Carter, “Sun Earth Connection Coronal and HeliosphericInvestigation (SECCHI),” Space Sci. Rev. 136, 67–115(2008).
20. M. Romoli, E. Antonucci, S. Fineschi, D. Gardiol, L. Zangrilli,M. A. Malvezzi, E. Pace, L. Gori, F. Landini, A. Gherardi, V. DaDeppo, G. Naletto, P. Nicolosi, M. G. Pelizzo, J. D. Moses, J.Newmark, R. Howard, F. Auchère, and J. P. Delaboudinière,“The ultraviolet and visible-light coronagraph of theHERSCHEL experiment,” in Solar Wind Ten (American Insti-tute of Physics, 2003), Vol. 679, pp. 846–849.
21. S. Fineschi, E. Antonucci, M. Romoli, D. Gardiol, G. Naletto,S. Giordano, M. Malvezzi, V. Da Deppo, L. Zangrilli, and G.Noci, “Ultraviolet and Visible-light Coronagraphic Imager(UVCI),” Proc. SPIE 4853, 162–171 (2003).
22. F. Auchère, M. F. Ravet-Krill, J. D. Moses, F. Rouesnel,J. P. Moalic, D. Barbet, C. Hecquet, A. Jérome, R. Mercier,J. C. Leclec’h, F. Delmotte, and J. S. Newmark, “HECOR: aHElium CORonagraphy aboard the Herschel soundingrocket,” Proc. SPIE 6689, 66890A (2007).
23. A. Thernisien, R. C. Colaninno, S. Plunkett, D. G. Socker,Q. Gong, and F. Landini, “Experimental and numerical opti-mization of a coronagraph external occulter. Application toSECCHI-COR2 and GOES-R SCOR,” Proc. SPIE 5901,366–376 (2005).
24. S. Koutchmy and M. Belmahdi, “Improved measurements ofscattered light level behind occulting systems,” J. Opt. 18,265–269 (1987).
25. M. Born and E. Wolf, Principles of Optics (CambridgeUniversity, 2001).
26. “Solar Probe Plus: report of the science and technologydefinition team,” Tech. Rep. TM-2008-214161 (NASA, 2008).
27. “Solar orbiter assessment study report,” Tech. Rep.SRE(2009)5 (European Space Agency, 2009).
