Segmented Vortex Telescope and its Tolerance to Diffraction Effects and Primary Aberrations

4.1 MB·English

by  Juan P. Treviño

Segmented Vortex Telescope and its Tolerance to
Diffraction Effects and Primary Aberrations.
Accepted Jan. 24th 2013 scheduled for for publication in the OE Vol. 52, No. 8.
Juan P. Trevin˜o, Omar L´opez-Cruz, and Sabino Cha´vez-Cerda ∗
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0 January 29, 2013
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Abstract

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WeproposethesegmentedLargeMillimeterTelescope(LMT/GTM),asthelargestspatiallightmodulator
2
capable of producing vortex beams of integer topological charge. This observing mode could be applied

] for direct exoplanet searches in the millimeter or submillimeter regimes. We studied the stability of the
M vortex structure against aberrations and diffraction effects inherent to the size and segmented nature
of the collector mirror. In the presence of low order aberrations the focal distribution of the system
I
. remains stable. Our results show that these effects depend on the topological charge of the vortex and
h
the relative orientation of the aberration with respect to the antenna axis. Coma and defocus show no
p
- large effects in the image at the focal plane, nevertheless the system is very sensitive to astigmatism.
o Heat turbulence, simulated by random aberrations, shows that the system behaves in a similar way as
r astigmatism dissociating the vortices. We propose the Segmented Vortex Telescope as a novel approach
t
s for the detection of giant planets outside circumstellar disks around nearby stars. Since our results are
a
applicable to other facilities with segmented surfaces, we suggest that this idea should be considered as
[
a regular observation mode complementary to interferometric methods.

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keywords: aberrations, astronomy, diffraction, millimeter waves, phase modulators, planets, spatial light
v
4 modulators, telescopes.
3
4 1 Introduction scopes equipped with coronagraphs [4, 5, 6, 7, 8, 9].
6
Vortex fields have been recently introduced to in-
.
1 In general, waves with phase singularities and a rota- crease the number of independent channels available
0
tional flow around the singularity are called vortices. to transmit data signals. By reshaping a common
3
Vortexfieldsariseinnature[1]andenjoyalargenum- parabolic antenna, a phase vortex can be induced on
1
: ber of technological applications. Vortex fields are a transmitted wave, creating a set of channels which
v
found in physical systems covering the widest range areindependenttothoseofaregularantenna[10,11].
i
X of scales, from single photons to astronomical black The number of channels that can be transmitted us-
r holes [2]. Applications of vortex fields have been ing a single frequency is, in principle, unbounded.
a found in optics, acoustics, telecommunications, as- This application has the potential of revolutionizing
tronomy, and other fields [3]. telecommunications.
Inastronomy, lightvorticityhasattractedalotof In this work, by combining the ideas above, we
attentionsinceithasshowntobeanelegantandeffi- explore the feasibility of turning the Large Millime-
cient way to reject light from a bright source on axis, ter Telescope (LMT/GTM) [12] into a coronagraph
allowing the study of its surroundings. Remarkable atmillimeterwavelengthsbyreshapingitssegmented
results have been obtained by the direct imaging of collector mirror into a vortex generator. The main
exoplanetary systems using ground-base optical tele- purpose is to investigate the potential of this system
∗Allauthors: InstitutoNacionaldeAstrof´ısica,OpticayElectr´onica,ApartadoPostal51/216,Puebla,M´exico72000. First
authorcontactaddress: [email protected]
1
as a regular observational mode able to detect giant Generating a vortex at the exit pupil creates a
exoplanets or giant proto-exoplanets outside circum- doughnut-like field distribution at the focal plane.
stellar disks. Given the lower luminosity contrast of Such setup is the reverse of the signal transmission
such objects in millimeter wavelengths, this device implemented in [10, 11]. The detection device cur-
would be very suitable for this application. We have rently used at the LMT/GTM is a bolometer array
investigatedthestabilityofthesystemagainstdiffrac- composed of 144 pixels [15]. The beam size is re-
tion effects induced by the segmented nature of the duced before it reaches the bolometer array. This
primarysurfaceandpossibledamagetoitssegments. wayifthevortexdistributionhadalargerradiusthan
We took into account the effects of aberrations in- the bolometer array, a further beam reduction would
herent to such large structure, as those produced by be necessary, however, this adjustment is straight-
deformations on the primary mirror due to its own forward. This configuration was first explored as a
weight or by temperature variations on its 50 meters means to reject light form bright sources by opening
diameter surface and its surroundings [13]. a window to observe incoherent background. In prin-
ciple, the achievable contrast depends on the vortex
order and the size of a field stop located at the focal
2 Optical Vortices and Phase
plane. Fortwoincoherentsources,theachievablecon-
Modifying Devices trast could be of the order of 105, so it is possible to
detect Super-Jupiters as we will see below. Although
notcommoninnature, forapairofcoherentsources,
A vortex coronagraph is created by placing a phase
bothonaxisandoffaxissourceswillcomeacrossthe
modifying device at the focal plane of an optical sys-
same vortex. However, some basic rules can be given
tem [4, 6, 7, 8, 9]. At a relayed pupil plane most
for the detection of secondary sources [5].
of the radiation from on axis sources is concentrated
in a sharp ring that can be easily filtered away by
means of a stop known as Lyot stop. This setup is 3 The Vortex collector mirror
usefulbecauseitallowstofilteroutlightfromonaxis
sources. Radiation from off axis sources remains al-
An optical vortex is a wavefield with an azimuthally
mostunchangedwhenitgoesthroughthesystem. In
varying phase factor of the form eimϕ. The number
this way it is possible to explore the vicinity of very
m (cid:54)= 0 must take only integral values and is known
bright objects and even to produce images of objects
as the topological charge of the vortex. The argu-
dimmer and angularly close to the primary one.
ment mϕ in the exponential represents an azimuthal
For telescopes at millimeter wavelengths, any
linear variation of the phase which generates a he-
component intended to be implemented at the focal
lical wavefront. The corresponding Poynting vector
plane poses a technical challenge, since any element
fieldfollowshelicaltrajectoriesaswell. Thesekindof
at this plane will attenuate the already low intensity
wavefields are known to carry Orbital Angular Mo-
signals. Additionally, detection devices need to be
mentum (OAM) [3, 17]. As a consequence, part of
kept at low temperatures to maximize their sensitiv-
theradiationinthecenterofthebeamisdrivenaway
ity [14], so any additional element absorbs some of
from the propagation axis and a dark core is created
the incident radiation and requires cooling which im-
at its center.
plies a higher cost of the entire system. Therefore,
A Cassegrain telescope like the LMT/GTM is de-
a vortex phase mask at the focal plane would not be
scribed by a complex pupil function whose mathe-
thebestoptionforradioandmillimetersignals,hence
maticalrepresentationincludesinformationaboutthe
we explore the possibility to locate the vortex on the
optical power and aberrations of the system. If the
primary surface.
vortexisintroducedattheexitpupilofthetelescope,
The LMT/GTMhas aCassegraindesign thatop-
the mathematical expression of the field in this plane
eratesatmillimeterwavelengths[12]. Ourproposalis
is
toreshapethesegmentedprimarysurfacetoproduce
vortices at the working wavelengths of this telescope, (cid:26) (cid:18)r2(cid:19)(cid:27)
U (r,ϕ)=T (r,ϕ) exp −ik eikW(r,ϕ)eimϕ,
which are 1.1, 1.4 and 2.1, mm. [15, 16]. The inde- 0 0 2f
pendentcontrolofthesegmentsintheprimarymirror (1)
can be configured to produce integral order vortices where W(r,ϕ)is theaberrationfunction andf isthe
at such wavelengths. focaldistanceofthemirror. Thewavenumberisgiven
2
by k = 2π/λ for the wavelength λ, while m is an in- feasible to implement our study to the current size of
teger defining the topological charge of the vortex. the primary, hence we have adjusted our simulations
Thecomparativesizesbetweentheworkingwave- to the current diameter (see Fig. 1). Considering the
lengthsandthegapsoftheLMT/GTMaresuchthat full 50m aperture is straightforward.
diffraction effects can be neglected. However, diffrac- Currently, each segment of the primary mirror
tion effects caused by gaps between segments have in the LMT/GTM is controlled by three actuators
been investigated here including different gap sizes withamaximumdisplacementof5,200µm. Thetotal
and configurations. wavefront error of the LMT/GTM design is of 75µm
The field U at planes approaching the neighbor- rms which means (cid:15) < λ/20 at 1.5mm. The collector
hood of the focal plane z =f− is obtained by a Fres- alone should have a 55µm rms error which represents
neldiffractionintegral, whileatthefocalplanez =f (cid:15) ≈ λ/18 at one millimeter. For longer wavelengths
theintegraltransformsintotheFrounhoferdiffraction the error decreases. The secondary mirror is a hy-
integral given by perbolic surface with a diameter of 2,570mm which
represents a central obscuration of less than 10% the
(cid:90) π (cid:90) ∞
U (ρ,θ)=C T (r,ϕ)eikW(r,ϕ)eimϕ radius of the exit pupil. The secondary has six de-
f 0
−π 0 grees of freedom.
(cid:26) (cid:27) Tocreateavortexofordermatthecollectormir-
2π
exp i rρcos(ϕ−θ) rdrdϕ, (2) ror, the reflected converging wave must have an ad-
λf
ditional azimuthal phase mϕ. For this reason, the
where C is a complex constant related to the ampli- collector must have a linear azimuthal deformation
tude of the field. For a continuous mirror and in with a maximum of mλ/2 additional to its parabolic
the total absence of aberrations, the field at the fo- profile. For every ring, each one of the N junctions
cal plane is radially symmetric and it reduces to the between sectors should be displaced by mλ n, where
2 N
Hankeltransformofordermofthetransmissionfunc- n = 0,1,...N, and N is the number of segments in
tion T (r). In the general case that we will study the corresponding ring. The maximum possible dis-
0
here a 2D Fourier transfrom will be necessary as the placement of the segments allows for the creation of
circular symmetry of T may be broken by arbitrary anm=5vortexatλ=2mm. However,ifthedesired
0
aberrationsordiffractioneffectsduetolargegapsand vortex order and corresponding wavelength required
damaged panels. For non symmetric cases, we eval- a maximum displacement larger than the maximum
uate numerically equation (2) by means of a Fast possible for a single segment, there is an option of
Fourier Transform algorithm. In order to calibrate creating a multiple pitch vortex, as shown in Fig 2.
ournumericalsimulationweevaluatedfirstthem=0 This configuration gives the same reflected wavefront
caseandothercasesforwhichanalyticalsolutionsare but the physical displacements required are smaller.
available, with known parameters. For other values It is worth mentioning that these calculations are
of m we also checked the phase of the focal field for independent of the number of segments in the collec-
consistency. tor mirror because the surface produced has a ramp-
like profile in the azimuthal direction, which in turn
produces a true spiral wavefront. Deforming the pri-
4 Reshaping the LMT/GTM
marysurfaceoftheLMT/GTMasproposedheredoes
Primary Surface notinduceaberrations,itreshapesthewavefrontinto
a convergent helicoid affected by diffraction due to
In the original design the collector mirror of the segmentgaps. Therigidityofthecollectormirrorseg-
LMT/GTM has a 50m diameter and a radius of cur- mentsmightcauseerrorswhenachievingthevalueof
vatureof35m. Itiscomposedby180panelsarranged m,howeverthesurfaceaccuracyisbelowtheerrorthe
in five rings. The innermost ring is formed of twelve systemtolerates(approximately5%)andtheycanbe
segments, the second ring has 24, and the remain- neglected. This procedure to produce vortices might
ing three are composed by 48 panels. The length of be compared to a step spiral phase mask [18] with N
each panel is 5m and the corresponding angular ex- steps. The latter approximates the ideal spiral wave-
tentdependsontheringwherethesegmentislocated. front by superposing N plane waves with a relative
Currently, only the first three inner rings are opera- retardation. Thisapproximationcausesadependence
tional, the corresponding diameter is of 32m. It is on N for such device, as opposed to the deformation
3
of the primary segmented mirror studied here. differently.
Vortexdissociationisclearlyappreciatedifweob-
servethephaseofthefield,butitcouldbedifficultto
5 Stability analysis to diffrac-
see with intensity detectors because the phase infor-
tive perturbations mationislostandvorticesmanifestaslocalminimma.
Howeverwemightdefineacriteriontodeterminevor-
As mentioned before, in the LMT/GTM the gaps tex dissociation depending on the contrast resolution
are sufficiently small compared to the wavelengths at of the detection device.
which the system operates, nevertheless we present The vortex dissociation effect is also observed for
simulations to evaluate the diffraction effects that damaged segments as small as ϕ ∼ 10◦ which is a
would appear for larger gaps. We split the problem very small value for the angular extent of the real
to study radial and angular gaps separately. LMT/GTM segments. In this case the vortex struc-
We first evaluate pupils formed from several con- tureisunstablebecausesymmetryisbroken(Fig.5).
tinuousringshavingavariableseparation. Thetrans- The focal distribution can be recovered to some ex-
mittance function of such a pupil is represented as tent if the opposite segment is darkened since some
a sum of circ functions. Given the linearity of the symmetry is recovered. We can see in the figure that
Fourier transform, the focal field of this multiple ring form=4theoriginalprofileisrecoveredintheverti-
pupil is a sum of the corresponding Fourier trans- calsection. Thecaseform=2isnotfullyrecovered,
forms. For any value of m, the effect on the focal howeverthehorizontalsectionremainswiththesame
distribution is very similar to what happens with a profile but a lower contrast.
simple annular pupil: the focal distribution shrinks Next,weexaminewhenmanyoppositesectorsare
radially,andthemainmaximumdecreasesrelativeto lostorobscuredasshowninFig.6. Atransversesec-
the secondary maximum as the radius of central ob- tion of the amplitude at the focal plane shows that
scuration increases(Fig. 3). Thiseffect isinterpreted although the maximum decreases, the profile of the
as having an increase of resolution of the system but central dark area caused by the vortex remains un-
a contrast decrease. For different values of m the changed. The same effects happen for the second
maximumfieldamplitudevaluesdropalmostlinearly or third rings composed of more segments. In these
as the size gap increases. Nevertheless, the profile outer rings there is a larger number of segments that
appears to be a scaled version of the original one, contribute to the focal field, and although the ob-
therefore the resulting distribution can be always ap- scuredproportionmightbehigh,theoppositereflect-
proximated by a power law rm in the vicinity of the ing sectors reconstruct a more symmetrical pattern.
vortex core. If the missing panels are considered to be radial
Nextwewillconsiderthecaseinwhichacomplete as shown in the figure, the maximum field amplitude
sector of angle ϕ is lost or darkened. For topological decreases linearly for m = 0, but for larger values of
charges m > 1 an obscured sector causes the vortex m, the behavior departs slightly from linearity. In all
to dissociate and generate m dark regions in the fo- cases the drop is proportional to the non-reflecting
cal image. The topological charge of a vortex must area.
be preserved along propagation, therefore these dark We have analyzed diffraction effect due to gaps
regionsareassociatedtoindividualvorticeswithuni- size and found out that the central annular field is
tarycharge. Ingeneral,vorticeswithoppositecharge stable up to a ten to one ratio between the panel and
might cancel each other upon propagation while vor- the gap. In the LMT/GTM the real proportion is
ticeswiththesamechargemighttravelalongsideeach much smaller than the aforementioned ratio, for this
otherforlongdistances. Detailedinformationonvor- reason, the effect can be neglected.
tex propagation might be found in [19, 20]. In the We now consider the effects of damaged panels.
case presented here vortex dissociation happens as We model this situation by leaving out randomly se-
the m order phase singularity separates into m first lecting panels (Fig. 7). We observe again that the
order singularities as shown in Fig. 4. A similar ef- basic vortex structure due to the azimuthal phase is
fect happens when the system is illuminated by two maintained. Similarsituationsinvolvingpartiallyob-
separate coherent sources [5]. However, the relative structed optical vortices have shown that this type
position of the dark regions due to the existence of of fields are stable upon propagation [21]. Even the
multiple sources and that due to aberrations behave absence of a complete ring, which is a special case of
4
concentric ring pupil was considered. It can be seen sal sections of the focal distribution of amplitude to
thatthiscanhavesmalleffectsontheexpectedimage show how the zeros are separated depending on the
(Fig. 7). value of A . For larger values of astigmatism the
a
radiation distribution is deformed into a set of in-
tensity lobes related to Hermite-Gaussian modes. It
6 Stability analysis under aber-
is known that Hermite-Gaussian modes can be con-
rations verted to and from Laguerre-Gaussian (L-G) modes
by means of an astigmatic mode converters. The lat-
ter are a type of vortex wavefields [25]. The system’s
So far we have analyzed how robust the segmented
response to aberration of coma (W = r3cosφ) was
vortex telescope can be considering diffraction per-
morestablesincenovortexdissociationwasobserved
turbations due to gaps between panels or assuming
foraberrationcoefficientsA <0.35whilethecritical
damages of the collector surface. We now draw the c
value for a 0.8 Strehl ratio is A =0.21.
attention to the presence of aberrations e.g. Seidel c
or balanced aberrations [22, 23]. Typically, the at- A system with randomly damaged panels and a
mospheric turbulence is modeled by a distribution of Seidelaberrationcombinedshowsthattheeffectsob-
aberrations. For the LMT/GTM, in addition to at- served are closer to those produced by aberration
mospheric turbulence, gravitational effects cause de- alone. The dark region at the focal plane dissoci-
formations of the collector mirror and also tempera- ates for aberration coefficients similar to those with-
turefluctuationsacrossits50metersdiametersurface out segment loss. Fig. 9 shows the collector mirror
causeaberrations[13]. Forthisreason,weanalyzethe with obscured panels and Ac = 0.15 along with the
focal distribution of the vortex telescope given Sei- focal image and transverse section. The image shows
del and balanced aberrations and also random phase vortex dissociation and small diffraction effects.
aberrations. For the large area of the collector mirror it is ex-
We introduce the wave aberration of the system pected that inhomogeneities of air density caused by
as a factor eikW(r,ϕ), with W(r,ϕ) = A Φ (r,ϕ) and atmosphericfluctuationsorheatturbulence,willgen-
j j
Φ could be either a Seidel or a balanced (Zernike) erateahighorderrandomaberrationoftheincoming
j
aberration [22, 23]. The aberration coefficient A is wavefront. The thermal design of the LMT/GTM al-
n
given in units of the wavelength λ. We used Seidel lows to evaluate and compensate deformations of the
sphericalaberration, SeidelandZernikeastigmatism, primary due to heat turbulence [13]. However, the
and finally Seidel and Zernike coma. Different aber- small fluctuations might not be possible to compen-
rationcoefficientswereselectedtoevaluatethestabil- sate. Inordertoinvestigatetheinfluenceofthistype
ity of the central vortex structure at the focal plane of perturbation on the system, we produced a sur-
as in the previous cases. The aberration coefficients face with random distributions of various frequencies
were chosen according to acceptable Strehl ratio cri- (Fig. 10). Each case was modeled for Seidel aber-
teria [24] selecting coefficients A ≤0.30. Symmetric rations and the aberration free case. In each case
i
aberrations such as defocus or first and second order we found out vortex dissociation for a phase aberra-
spheres cause variations in the contrast of the focal tion of a quarter wavelength measured peak to peak
image. Nevertheless the central profile of dark re- (Fig. 11). The sensitivity of the system to this type
gions remains the same in the sense that a power law of aberration requires a careful calibration and wave-
fit in the radial variable is still possible in the vicin- front compensation of the system.
ity of the vortex core. If the symmetry is broken by Sincetheantennafollowsobjectsinthesky,astig-
aberrations, the vortex dissociates in a similar way matismcausedbydeformationofthecollectormirror
as with perturbations due to diffraction. Astigmatic due to gravity, is constantly changing. If we wanted
aberration given by W = r2cosφ generated visible to distinguish between the presence of aberrations
vortex dissociation for low values, A = 0.03. Nev- and double coherent sources, we might have to an-
a
ertheless, the proportion of the inner maxima to the alyze the behavior of the dark regions as the antenna
mainringwasabout5%. Wesetthisproportionhere scans a given object in the sky. Aberrations caused
to define a visible dissociated vortex. Vortex disso- by changes in the antenna position would cause the
ciation occurs in an angle π/4 from the astigmatism dark regions to move as the antenna moves. On the
axis,andasectionperpendiculartothiskeepstherm other hand, if the dark regions remain unchanged as
power law profile. The simulations include transver- the scanning goes on, it would mean that there is a
5
double source. More precise schemes are being inves- the case of stellar systems with multiple components
tigatedbyourgroupatthemoment,andareportwill (starsandplanets),thismodecanincreasetheresolu-
be developed. tion up to 0.5(cid:48) at 1.1mm, which can only be attained
withinterferometricarrays. Moreover, thehighmap-
pingspeeds(0.55deg2/hr/mJy2 forLMT/GTMwith
7 Astronomical Application AzTEC) of large single dish telescopes make them
more efficient than interferometric arrays. Therefore,
Consider the LMT/GTM working at 1.1 mm, at this we suggest that future large millimeter single dish
wavelength the field of view is 1.5(cid:48) (minutes of arc) telescope should consider SVT as an regular obser-
and a beam size of 5(cid:48)(cid:48) (seconds of arc) with a point- vational mode, which would guide follow up observa-
ing accuracy is 1(cid:48)(cid:48). The specified final surface accu- tions with interferometric arrays.
racyof70µm,thisresultsinanAntennaEfficiencyof
46% at this wavelength. In the mm regime the con-
8 Conclusions
trast between the luminosity of a solar-like host star
(T ∼ 6000 K) and a Super-Jupiter (T ∼ 1700
eff S−J
K, R ∼ 1.5R , see e.g. [26]) becomes WehaveinvestigatedthepropertiesoftheLargeMil-
S−Jupiter Jupiter
of the order of 103, while in the optical regime the limeter Telescope as the largest spatial electromag-
contrast could be several times higher, ∼ 108. How- netic wavefront light modulator capable of producing
ever, cold dust in circumstellar disks becomes the vortexbeamsofintegertopologicalchargeatselected
dominant source of radiation at 1 mm, hence the wavelengths. We studied its stability against diffrac-
contrast between a face-on circumstellar disk (mean tion and aberration perturbations.
T ∼ 50K, see below for average size) e.g., [27] Diffraction caused by gaps between segments and
Disk
andaSuper-Jupitercouldbeaslargeas10−6. These by possible mechanical damages of the LMT/GTM
are rough figures under the assumption that the host panelsisnotcriticalsincethemainfeaturesofthevor-
star, the circumstellar disk, and the planet emit as tex structure at the focal plane remain unaffected by
black bodies. the segmented nature of the telescope even in highly
The mode of the diameter distribution of circum- perturbed cases.
stellar disks [28] is about 300 AU (1 Astronomical Regarding to aberrations, for small values of de-
Unit= 149,597,870.691 km). A disks of about this focus and coma, the focal distribution of the system
size, would appear unresolved at 60 pc (1 parsec= remains stable. As expected, we observed that the
206265 AU); hence we can use LMT/GTM in the system is very sensitive to astigmatism. Non-radially
SVT mode as a coronagraph to search for exoplan- symmetric aberrations cause the vortex to dissociate
ets orbiting around star-circumstellar disks systems into m vortices, and as a result, dark zones appear
at distances larger than 60 pc. The LMT/GTM’s in the focal distribution. The values at which this
fieldofviewwouldcoverseparationslargerthan5000 happensdependonmandontherelativeorientation
AU from the host star. Guided by previous observa- of the aberrations. The dark zones of a single source
tions [29], we found that exoplanetary systems have always appear perpendicular to the aberration axis.
shownawidevarietyofconfigurations. Massiveplan- For aberrations with random wavefront distribu-
ets have been found to orbit their host stars at wide tion, simulating heat turbulence, the system shows
orbits, ranging from several hundreds to over a thou- a high sensitivity which must be taken into account
sand AU, from their host stars [30]. A comprehen- since even single sources produce vortex dissocia-
sive survey for massive planets at wide orbits could tion generating similar focal distributions as those
helptoimposeconstraintsontheoriginofexoplanets produced by two coherent sources. In general, sin-
and their relation with the environment [31]. Super- gle sources produce multiple dark regions at the fo-
Jupiter have properties similar to low mass brown cal plane when the symmetry of the system is bro-
dwarf, hence LTM/GTM working as SVT could also ken either by diffraction or by the presence of non-
help to study the frequency of brown dwarfs in mul- symmetric aberrations.
tistellar systems. TheLMT/GTMworkingasaSVTcouldofferun-
The geometry of circumstellar disks can be ex- precedented opportunities for exoplanetary studies.
plored using sub-Rayleigh resolution [32] in classi- TheSVTcanhelptosearchforgiantplanets(Super-
callyresolved,orunresolvedcircumstellardisks,orin Jupiters) outside debris disks [33] and also work in
6
the sub-Rayleigh [32] mode to resolve multiple com- [9] G. J. Ruane and G. A. Swartzlander Optical
ponents. vortex coronagraphy with an elliptical aperture.
Appl. Opt., 2:52, 2013
Aknowledgements [10] F. Tamburini, E. Mari, A. Sponselli, B. Thid´e,
A.Bianchini,andF.Romanato. Encodingmany
channels on the same frequency through radio
The authors would like to acknowledge the reviewers
vorticity: First experimental test. New Journal
ofthismanuscripts. Theirvaluablecommentshelped
of Physics, 14:033001, 2012.
us to improve significantly our work.
[11] B. Thide, F. Tamburini, E. Mari, F. Ro-
ThefirstauthorwouldliketoacknowledgeAlfredo
manato, and D. Barbien. Radio beam vor-
AgustnMontan˜aBarbanoforthevaluablesourcesfor
ticity and optical angular momentum. arXiv,
the development of this work. He would also like
(arXiv:1101.6015v1 [astro-ph.IM]), 2011.
to acknowledge Jesus Emmanuel Gomez-Correa for
fruitful discussion. [12] W.M. Irvine, E. Carrasco, and I. Aretxaga. The
Large Millimeter Telescope: Neighbors Explore
the Cosmos. 2005.
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8
Authors
• Juan Pablo Trevino: Is a PhD candidate at Instituto Nacional de Astrof´ısica, Optica y Electr´onica.
His main research interests are the mathematical modeling of light modal propagation and its applica-
tions to imaging systems as the human eye and telescopes. He is also interested in the modeling and
compensation of aberrations with adaptive optics systems for various applications.
• Omar Lopez-Cruz: Omar Lpez-Cruz is a researcher at Instituto Nacional de Astrof´ısica, Optica y
Electr´onica,andvisitingscientistattheAstrophyisicsGroupoftheUniversityofBristolintheUK.His
researchinterestsrangefromstellarastrophysics,extragalacticastronomy,andobservationalcosmology.
Forthisaim,heusesallsortoftelescopes,interferometricarrays,andvirtualobservatories. Heisleading
a Mexican team of scientists and engineers to build a single-antenna experiment to search for the signs
oftheformationofthefirststarsintheuniverseusingthe21cmhyperfinetransitionofneutralhydrogen
as a tracer.
• SabinoCh´avez-Cerda: IsafulltimeresearcheratInstitutoNacionaldeAstrof´ısica,OpticayElectr´onica
intheOpticsdepartment. HeobtainedhisPhDdegreefromtheImperialCollegeandhasbeenrecently
appointed as Fellow of the Optics Society of America. His main research fields are propagation of non
diffractive fields and rigorous mathematical physics aspects of optics.
9
Figures
Figure 1: A: Complete setup with five rings as originally designed. Segments in black are currently not
active. B:ThecollectormirroroftheLMT/GTMgeneratesawaveftontwiththisshape. Thelinescorrespond
tothegapsbetweenthetelescopesegments. C:Frontviewofthetransmittancefunctionofthecurrentthree
rings of the collector.
Figure 2: Multiple pitch mirror for the segmented vortex telescope.
10