TMT-AGE: wide field of regard multi-object adaptive optics
for TMT
Masayuki Akiyamaa , Shin Oyab , Yoshito H. Onoa,b , Hideki Takamic , Shinobu Ozakic , Yutaka
Hayanob , Ikuru Iwatab , Kazuhiro Haned , Tong Wud , Tomoyasu Yamamuroe and Yuji Ikedaf
a Astronomical Institute, Tohoku University, 6-3 Aramaki, Aoba-ku, Sendai, Japan;b Subaru Telescope, National Astronomical Observatory of Japan, 650 North A’ohoku Place,

Hilo, HI, USA;c National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo, Japan;d Department of Nanomechanics, Tohoku University, 6-6 Aramaki, Aoba-ku, Sendai, Japan;
e OptCraft, 3-16-8-101 Higashi-Hashimoto, Midori-ku, Sagamihara, Japan;f Photocoding Inc., 460-102 Iwakura-Nakamachi, Sakyo-ku, Kyoto, Japan;

ABSTRACT
We introduce current status of the feasibility study on a wide ﬁeld of regard (FoR) Multi-Object Adaptive
Optics (MOAO) system for TMT (TMT-AGE: TMT-Analyzer for Galaxies in the Early universe). MOAO is
a system which realize high spatial-resolution observations of multiple objects scattered in a wide FoR. In thisstudy, we put emphasise on the FoR as wide as 10′ diameter. The wide FoR is crucial to eﬀectively observe very
high-redshift galaxies, which have low surface number density. Simulations of an MOAO system with 8 LGSs
show close-to-diﬀraction-limited correction can be achieved within 5′ diameter FoR and moderate AO correction
can be achieved within 10′ diameter FoR. We discuss overall system design of the wide FoR MOAO system
considering the constraint from the stroke of small-size deformable mirror (DM). We also introduce current
status of developments of key components of an MOAO system; high-dynamic range wavefront sensor (WFS)
and large-stroke small-size DM, and real time computer (RTC) with fast tomographic reconstruction.
Keywords: Adaptive Optics, TMT, Multi-Object Adaptive Optics, simulation

1. INTRODUCTION
Multi-Object Adaptive Optics (MOAO) is an AO system that delivers close-to diﬀraction-limited images ofmultiple objects scattered in a wide Field of Regard (FoR) simultaneously.1 The 3D volume structure of theatmospheric turbulence is estimated by tomographic reconstruction with wavefront measurements of multiple
laser guide stars (LGSs). The estimated 3D structure of the atmospheric turbulence is integrated along the lineof-sight of each target and the optimised correction for each target is determined. Multiple targets are picked
up by multiple science paths. The optimised correction for each science path is applied to a deformable mirror(DM) in the science path. The control of the DM is made in open-loop manner. Because Tip-Tilt (TT) andfocus components cannot be sensed with the LGSs, natural guide stars (NGSs) are necessary to measure thecomponents. Because TT component also has anisoplanatism, we need multiple NGSs within the wide FoR toestimate TT component of each science path. Bright NGSs within the wide FoR can also be used for high-orderwavefront measurements.2
Multiple deployable integral ﬁeld units (IFUs) assisted with the MOAO system is a powerful instrument
to obtain high-resolution 3D (two spatial and one wavelength dimension) information of statistical numberof galaxies. For Thirty Meter Telescope (TMT), two feasibility studies have been done for MOAO-assisted
multiple-IFUs NIR spectrograph under the name of Infrared Multi-Object Spectrograph (IRMOS).3 One isdone by members of University of Florida (UF) and Herzberg Institute of Astrophysics (HIA), IRMOS-UF/HIA
concept4–6 and the other one done by members of Caltech and Laboratoire d’Astrophysique de Marseille (LAM),
Further author information: (Send correspondence to M.A.)
M.A.: E-mail: akiyama@astr.tohoku.ac.jp, Telephone: +81 (0)22 795 6511

Figure 1. Observed wavelength of strong rest-frame UV lines for galaxies at z = 5−12. Green solid lines, blue dashed lines,
and red dotted lines represents strong emission, low-ionization inter-stellar absorption, and high-ionization inter-stellar
absorption lines observed in Lyman Break Galaxies at z ∼ 38 and galaxies at z ∼ 2.9

IRMOS-Tipi concept.7 Both of these feasibility studies conducted following the IRMOS speciﬁcation with neardiﬀraction-limited PSF within 5′ diameter FoR.
Following the feasibility studies on IRMOS, we started a feasibility study of an MOAO system covering
even wider FoR up to 10′ diameter under the name of TMT-AGE (TMT-Analyzer for Galaxies in the Early
universe). The wide FoR is crucial to eﬀectively observe very high-redshift galaxies at z > 5, whose surface
number density is rather low. In this paper, we describe the science drivers for a wide FoR MOAO system and
MOAO performance simulations in the wide FoR. Then, we describe overall system considerations emphasising
requirements for DMs. Finally we mention on-going developments related to components of the MOAO system;high dynamic range wavefront sensors (WFS), large stroke DMs, and fast tomography real time controller.

2. SCIENCE DRIVERS AND AO PERFORMANCE FEASIBILITY
2.1 Exploring the galaxies in the high-redshift universe with an ELT MOAO system
In this study, we put emphasis on the three science cases that can be tackled with an ELT MOAO system;1) revealing the history of establishment of the internal structure of galaxies, 2) revealing the physical process
associated with the violent star-formation during the formation phase of galaxies, and 3) identifying the galaxies
in the early universe.
For the ﬁrst science case, the history of the establishment of the internal structure of galaxies seen in thecurrent universe, i.e. Hubble sequence, will be revealed by spatially resolved spectroscopy of galaxies at up to
redshift 5. Recent studies on morphology of galaxies in the high-redshift universe10 suggest that morphological
mixture of galaxies at z > 1 is diﬀerent from that seen in the local universe. Dynamical structure of the galaxies
at z ∼ 1 − 2 is also diﬀerent, they show systematic rotation, like disk galaxies in the local universe, but they
have large velocity dispersion component as well.11 High-spatial and high-sensitivity observations supported by
AO system on ELT is crucial to reveal gas dynamics, gas metallicity, and stellar populations in each region of
the high-redshift galaxies. The average half-light radius of galaxies at redshifts z = 2 and 4 are 2.5 and 1.5
kpc,12 which are 0.3′′ and 0.2′′ for each redshift In reality, the dynamical structure of a galaxy at z ∼ 3 revealed
thanks to Gravitational lensing eﬀect shows steep velocity gradient within 1kpc scale.13 In order to resolve such
structure of galaxies at z = 2 − 4 with at least 3 spatial elements, spatial resolution as small as 0.05′′ × 0.05′′ isnecessary.5 Moreover, considering the diversity of the physical properties of galaxies, observations of statisticalnumber of high-redshift galaxies are important.

For the second science case, the physical process of violent star-formation in the very high-redshift galaxies
at z > 5 will be addressed by observing their integrated rest-frame UV spectra. Rest-frame UV emission andabsorption lines of star-forming galaxies provide us important information on the properties of high-mass starformation and inﬂowing and outﬂowing gas associated with the galaxies.8 Strength of the HeII emission line
can be used to constrain the slope of initial mass function in the high-mass end. The strength and velocity
of low-ionization and high-ionization inter-stellar absorption lines can be used to constrain the distribution andkinematics of neutral and ionized gas around the galaxies. The observed wavelength of the redshifted UV lines are
summarised in Figure 1. Most of the strong UV lines of very high-redshift galaxies can be observed in the J- andH-bands up to redshift 10, and high-sensitivity spectroscopy of faint galaxies is crucial for this science case. The
observed circularized half-light radius of the UV-luminous (MUV < −20mag) galaxies at z ∼ 7 − 8 is 0.6 kpc inthe rest-frame UV wavelength,14 which corresponds to 0.11′′ . For UV-luminous galaxies at z ∼ 10, the half-lightradius can be as small as 0.3 kpc,14 which is 0.07′′ . They are much smaller than typical seeing size at MaunaKea, and moderate AO correction can help signiﬁcantly improve the sensitivity for integrated spectroscopy under
the sky-background limited condition. The equivalent width of these rest-frame UV absorption lines are 1∼2 Å
in the rest-frame, therefore spectroscopy with moderate resolution with R ∼1,000 is important.
The targets for the third science case are candidates of galaxies in the early universe found by ALMA andfuture wide-ﬁeld NIR survey satellite missions, like Euclid, WFIRST, and WISH. For example, Ultra Deep
Survey of WISH will cover 100 deg2 down to 28 AB magnitude in 1-5µm (wishmission.org) with 3σ and provide
candidates of galaxies at z ≥ 8. These candidates can be identiﬁed with Lyα emission line in NIR (Figure 1).
Considering the strong redshift evolution of Lyα emission line luminosity function of galaxies possibly due tohigh neutral fraction in the early universe,15 we may need to identify the candidates with absorption lines andcontinuum break.
In Figure 2, detection limits of J-, H-, K-band spectroscopic observations with TMT are summarised. We
compare the detection limit of R = 500 spectroscopy with MOAO PSF, moderately-corrected PSF by Groundlayer Adaptive Optics (GLAO) system, and seeing-limited PSF. The PSFs are evaluated with average of PSFs
within 5′ diameter ﬁeld corrected by each AO mode. We assume ﬁxed square aperture observation, and thehorizontal axis represent the area of the ﬁxed aperture. Ensquared Energy (EE) is calculated for each PSF. For
the point source observation (left panel) MOAO PSF with small aperture can achieve highly sensitive observations
thanks to the reduced background emission. On the other hand, for the extended galaxies (right panel), because
their sizes are larger than the diﬀraction-limit PSF, reducing the size of the aperture do not help to increase
sensitivity. GLAO-like moderately corrected observations with 0.1′′ -0.2′′ aperture can be only ∼0.2mag shallower
than observations with MOAO PSF. As can be seen in Figure 1, J-band observations are important for the second
and third science cases. R = 500 ﬁxed aperture spectroscopy with MOAO and GLAO modes can reach 25.7
and 25.6 mag with SN=10 with 10h integration in the J-band. The expected sensitivities can be fainter thanthose of NIRspec on James Webb Space Telescope (JWST): JAB = 25.2mag with R = 1, 000 and SN=10 in
27.7h integration within 3′ × 3′ FoV (NIRSpec pocket guide), therefore moderate resolution spectroscopy of faintgalaxies supported by wide-ﬁeld AO correction can be one of the unique capability of ground-based TMT.
The sensitivity for spatially-resolved emission-line spectroscopy is also estimated with the same assumption
used in Figure 2. The limits for ﬂux density and line ﬂux are summarized in Table 1. The detection limits forline ﬂux are derived assuming the lines are not resolved with the resolution. The J-, H- and K-band detection
limits for line ﬂux with R = 3, 000 are 2.5 × 10−20 , 1.7 × 10−20 , 3.6 × 10−20 erg s−1 cm−2 per 0.05′′ × 0.05′′
spatial pixel with SN=10 by 10h integration. The detection limit corresponds to Hα emission line of 0.002 M⊙
yr−1 and 0.01 M⊙ yr−1 per spatial pixel for galaxies at z = 1.5 and z = 2.5, respectively.
The number densities of the targets for the second and third science cases are not very high. For example thenumber densities of the UV-bright z ≥ 5 galaxies that are brighter than the detection limits are 0.41 per arcmin2
for z ∼ 5 galaxies with Y < 25.5mag picked up by V -dropout method, 0.17 per arcmin2 for z ∼ 6 galaxies with
Y < 25.9mag picked up by i-dropout method, and 0.10 per arcmin2 for z ∼ 7 galaxies with J < 26.0mag picked
up by z-dropout method.16 The expected number density of the candidates of very high-redshift galaxies at z ≥ 8
is 0.5 per arcmin2 . Considering the low surface number density, wide FoR as wide as 10′ diameter is crucial toachieve eﬃcient observations of statistical number of very high-redshift galaxies utilising high multiplicity of an
MOAO system: 0.25 targets per arcmin2 is required to eﬀectively feed 20 science paths per 10′ diameter FoR.

23

Total MAB [mag]J-band (1250nm), Extended Source (Re=0.1")

J-band (1250nm), Point Source

22

24

900[s]x40[frames]=10[h]R=3000 binned to R=500
SN=10
Read Noise = 1.0 [e/pixel]
Total throughput = 0.22

Seeing
GLAO
MOAO

0.1
0.15
Aperture Area [arcsec2]

0.2

900[s]x40[frames]=10[h] Seeing
R=3000 binned to R=500 GLAO
SN=10
MOAO
Read Noise = 1.0 [e/pixel]
Total throughput = 0.22

25
26
27
28
29

0

0.05

0.05

0.1
0.15
Aperture Area [arcsec2]

0.25

SeeingGLAO
MOAO

Seeing
GLAO
MOAO

23

0.2

H-band (1650nm), Extended Source (Re=0.1")

H-band (1650nm), Point Source

22

Total MAB [mag]0.25 0

24
25
26
27
28
29

0

0.05

0.1
0.15
Aperture Area [arcsec2]

0.250

0.05

0.1
0.15
2
Aperture Area [arcsec ]Seeing
GLAO
MOAO

23

0.2

0.25

K-band (2200nm), Extended Source (Re=0.1")

K-band (2200nm), Point Source

22

Total MAB [mag]0.2

Seeing
GLAO
MOAO

24
25
26
27
28
29

0

0.05

0.1
0.15
Aperture Area [arcsec2]

0.2

0.250

0.05

0.1
0.15
2
Aperture Area [arcsec ]

0.2

0.25

Figure 2. J-, H-, K-bands magnitude limits of spectroscopic observations with TMT MOAO, GLAO, and seeing-limited
observations. The horizontal axis represents area of square aperture on the sky, i.e. 0.04 arcsec2 corresponds to 0.2′′ ×0.2′′
aperture. We assume ﬁxed aperture spectroscopy to obtain an integrated spectrum. Spatial sampling on the detector
is ﬁxed with 0.025′′ per pixel. EE in the aperture for each AO mode is calculated with average PSF shape within 5′
diameter ﬁeld. In the calculation, the continuum sky-background emission is considered, we assume observation between
strong OH-airglow lines with moderate spectroscopic resolution with R ∼ 3, 000, and binnig down to R ∼ 500 after
the removal of the eﬀect of the OH-airglow. Total throughput, including telescope, AO-system, IFU, spectrograph anddetector quantum eﬃciency, of 0.22 is assumed. Left) For point sources, Right) extended galaxy with eﬀective radius of
0.1′′ exponential-law, i.e. disk-like, galaxies.

Table 1. Detection limits for spatially-resolved spectroscopy with 0.05′′ × 0.05′′ aperture. We assume extended sourcethat have constant surface brightness and limits are for ﬂux density and line ﬂux within the aperture with SN=10 and
10h integration. Other assumptions are same as in Figure 2

R = 3, 000 ﬂux density (erg s

−1

cm

−2

Hz

−1

R = 3, 000 line ﬂux (erg s−1 cm−2 )R = 500 ﬂux density (erg s−1

cm

R = 500 line ﬂux (erg s−1 cm−2 )

−2

Hz

−1

)

)

J(1250nm)

H(1650nm)

K(2200nm)−31

3.2 × 10−31

2.9 × 10

7.7 × 10−31

2.5 × 10−20

1.7 × 10−20

3.6 × 10−20−31

1.2 × 10−31

1.1 × 10

2.7 × 10−31

5.8 × 10−20

4.0 × 10−20

7.0 × 10−20

Figure 3. Tip-Tilt anisoplanatism as a function of distance from a guide star. The vertical axis is the 3 σ scatter ofdiﬀerences of TT component from the center in each simulation run. Diﬀerent points at the same distance represent
results from diﬀerent simulation runs.

2.2 AO performance simulation within a wide FoR
The performance of an MOAO system in wide FoR is evaluated through AO simulation. The critical parameterof an MOAO system is the conﬁguration of LGSs and NGSs. Laser Guide Star Facility (LGSF) for TMT isdesigned to support the early-light AO system, NFIRAOS (Narrow Field InfraRed Adaptive Optics System17 ),with 6 LGSs with 1 at the center and 5 equally spaced on a circle with radius of 35′′ . The LGSF is designed
to accept future upgrades with 9 LGSs radii up to 510′′ .18 Nominal asterism considered for the TMT-IRMOS
system is 3 equally spaced on a circle with radius of 70′′ and 5 equally spaced on a circle with radius of 150′′(Subsystem Requirements Document for the Laser Guide Star Facility as of 2010 Apr.). In the current study,
we simulate two patterns, 1) 5 LGSs on a circle and one LGS at its center, and 3 NGSs on a triangle, and 2) 3
LGSs on a inner circle and 5 LGSs on a outer circle, and 3 NGSs on a triangle, as shown in Figure 4. We change
the radius of the LGS asterisms from 140′′ to 280′′ . The smallest asterism with 8 LGSs corresponds to that of
the nominal TMT-IRMOS case.
In both patterns, we use NGSs for measuring TT and focus components only. We locate three NGSs in atriangle with r = 120′′ in the simulations. Figure 3 shows amount of TT anisoplanatism as a function of distancedetermined with the simulations described below. In order to keep the TT error as small as 0.025′′ , we need a
TT guide star within 120′′ . The number density of 3 NGSs within the d = 5′ FoR corresponds to 550 per deg2 .
We estimate number density of stars based on the Galaxy star count model TRILEGAL.19 In the high-galactic
latitude regions, stars as faint as RAB = 17.5mag, JAB = 15.5mag, and KAB = 15.0mag have the required surface
number density.

6 Laser Guide Stars

8 Laser Guide Stars

3 Natural Guide Stars

3 Natural Guide Stars

PSF evaluation

PSF evaluation

along the direction

along the direction

Figure 4. The conﬁguration of the LGSs and NGSs in the performance simulations. We assume 6 LGSs at the centerand pentagon, and 3 NGSs at the triangle, the radius of the conﬁguration is changed. The PSFs are evaluated along theevaluation direction.

Figure 5. RMS wavefront error (WFE) as a function of distance from the FoR center. Filled squares, crosses, and open
squares represent total WFE, TT WFE, and WFE without TT component, respectively. The horizontal solid line indicate
WFE of which corresponds to Strehl ratio of 0.5 in the H-band. The vertical dashed and dotted lines represent radiusof LGSs and NGSs asterism. For the top row, one LGS at the center and 5 LGSs on a circle with radius of 140′′ , 175′′ ,and 280′′ from left to right. For the bottom row, 3 LGSs and 5 LGSs on circles with radii of (70′′ and 150′′ ), (100′′ and210′′ ), and (140′′ and 280′′ ). In all cases, 3 NGSs are located at 120′′ from the center. The lower left panel corresponds
to the nominal TMT-IRMOS LGS conﬁguration.

The simulations are conducted with Multi-threaded Adaptive Optics Simulator (MAOS) AO simulation
code.20 We assume moderate seeing condition with r0 = 0.186m at 500nm and 7 layer turbulence for 13N TMTsite on Mauna Kea. Turbulence outer scale L0 of 30m is assumed in all of the simulations. The 7 layer model
has layers at 0m and 500m to represent ground layer turbulence component. Further consideration of the eﬀectof the detailed modelling of the ground layer proﬁle21 to the wide FoR performance will be made in future. The
performance evaluation is done along the direction shown with an arrow in the ﬁgure.
The wavefront error (WFE) as a function of distance from the FoR center is shown in Figure 5. We show thetotal WFE (ﬁlled squares) as well as TT WFE (crosses) and WFE after removal of TT WFE (open square). In
the TMT-IRMOS study, 0.05′′ ×0.05′′ EE larger than 50% in the H-band is considered as scientiﬁc requirement.5

50% EE within 0.05′′ ×0.05′′ aperture typically corresponds to Strehl Ratio (SR) of 0.5.22 SR of 0.5 in the J-, H-,
and K-bands corresponds to rms WFE of 159nm, 211nm, and 291nm, respectively. The criteria in the H-bandis shown with horizontal solid lines in the panels. The criteria can be met with the TMT-IRMOS LGS asterism
within 120′′ from the center. If a wider conﬁguration of LGSs is assumed, the TT-removed WFE in the outerregion become smaller, but TT-removed WFE in the central region become larger.
EE within 0.05′′ × 0.05′′ aperture is shown in Figure 6 as a function of distance from the center. 0.9µm,
J-, H-, and K-band EE are shown with crosses, open squares, ﬁlled squares, and open circles, respectively.
Diﬀraction-limited PSF have 0.92, 0.90, 0.89, 0.85 EE in 0.9µm, J-, H-, and K-bands, respectively. More than
50% EE in the aperture in the H-band within 5′ diameter FoR can be achieved only with the nominal TMTIRMOS conﬁguration as expected from the WFE plot. This is consistent with previous studies.6 In the K-band,
more than 50% EE within 0.05′′ × 0.05′′ EE can be achieved within 6.5′ diameter FoR if we use wider asterism
with 8 LGSs.
EE in wider aperture with 0.2′′ × 0.2′′ is shown in Figure 7. More than 50% EE can be achieved almost
all regions within 10′ diameter FoR in the wavelength range longer than J-band with 8 LGSs. The nominal
TMT-IRMOS conﬁguration on the lower left panel shows the best results in the almost entire FoR. The EE is
2.5 times larger than the seeing-limited case (0.14, 0.21, 0.21, 0.27 for 0.9µm, J, H, K-bands) even at the edgeof the FoR.
These AO simulation results show, we can achieve good AO correction within 5′ diameter FoV and moderate
AO correction within 10′ diameter FoV with standard tomographic reconstruction method with 8 LGSs conﬁgured
within 150′′ radius.
We are also considering the atmospheric tomography algorithm that utilise WFS measurement at previous
time steps with the wind proﬁle as a function of altitude.23 The current simulation results of the algorithm arepromising: better AO correction than standard tomography can be achieved within 8′ diameter FoR with equallyspacing 5 LGSs on the 270′′ circle and 3 LGSs on the 120′′ circle. The assumed condition is rather ideal in thecurrent simulations; turbulence layer heights are known and perfectly frozen ﬂow holds within 0.1s. Althoughfurther realistic simulations with information on the accuracy of estimation of the heights of the turbulence layers
and the frozen ﬂow time-scale, the results show there is a possibility that better AO correction can be made in
the wide 10′ diameter FoR. Details of the algorithm and the simulation results, see Ono et al. (2014) in thisvolume.

Figure 6. EE within 0.05′′ × 0.05′′ aperture as a function of distance from the FoR center. Crosses, open-squares,
ﬁlled-squares, and open circles represent EE in the 0.9µm, J-, H-, and K-bands, respectively. The vertical dashed anddotted lines represent radius of LGSs and NGSs asterism. The lower left panel corresponds to the nominal TMT-IRMOS
conﬁguration.

Figure 7. Same as Figure 6 for 0.20′′ × 0.20′′ aperture.

3. OVERALL SYSTEM CONSIDERATION
3.1 MOAO system design and requirements for DM
Large optical path diﬀerence within 30m aperture due to the atmospheric turbulence demands large stroke for
DMs in TMT AO system. Requirements for the DM stroke are critical system constraints on an MOAO systemdesign for ELTs. In order to achieve the close to diﬀraction limited PSF, at least 60 × 60 DM covering the 30m
aperture is necessary for each science path, but the mechanical stroke for such large element number DM is still
limited.
We evaluate requirements for the mechanical stroke of the DM in an MOAO system through numericalsimulations with AO simulation code developed by one of the authors (Y.O.). In the results below, we assume
moderate condition with seeing of r0 = 0.156m and zenith angle of 0 deg, and bad condition with seeing of
r0 = 0.121m and zenith angle of 60 deg (equivalent to r0 = 0.08m at zenith) with 7 layer atmosphere modelsof Mauna Kea.23 We derive two values for each condition and setup, one is the Peak-to-Valley (PV) stroke
value of low spatial frequency mode for each DM sampling after removal of the TT component, and the otheris the maximum inter-actuator (IA) stroke which is the diﬀerence between neighbouring actuators. Resulting
values below represent mechanical stroke and are half of the corresponding values of the wavefront optical path
diﬀerence. These values are derived as an upper 2σ envelope of 100 simulations for each condition and setup.
If all of the wavefront distortion component is corrected by one 60×60 DM, we require 5.5µm PV stroke and2.5µm IA stroke for the moderate condition and 10.0µm PV stroke and 4.0µm IA stroke for the bad condition,
they are consistent with previous estimates.22 These values are signiﬁcantly larger than the currently available
30mm-size >3000-elements MEMS DM. For example, 4092-elements MEMS DM from Boston Micromachines
have 3.5µm PV stroke and 1.5µm IA stroke.24
One way to fulﬁll the stroke requirements is using the Woofer-Tweeter DMs in each science path. WooferDM corrects for low-spatial frequency modes with large amplitudes and following Tweeter-DM corrects forhigh-spatial frequency modes with small amplitude. If we assume 30×30 DM as a Woofer-DM, the required
strokes for the Woofer-DM are 5.5µm PV and 2.5µm IA strokes for the moderate condition and 10.0µm PV
and 4.5µm IA strokes for the bad condition. Most of the required strokes for the Woofer-DM, except for the IA
stroke under bad condition, can be fulﬁlled by the currently available small-size DMs, for example, 277-element
electromagnetic DM from ALPAO (www.alpao.fr) have 25µm Tip-Tilt and 3.0µm inter-actuator strokes. The
number of elements needs to be increased to meet the 30×30 requirement. In this case, the strokes of the Tweeter
DM for correcting the remaining high spatial frequency modes are 1.0µm (2.0µm) PV and 1.0µm (1.5µm) IA
for the moderate (bad) condition. Currently available MEMS DM realize all of the stroke requirements.
Another solution for the stroke requirements is proposed in IRMOS-Tipi feasibility study. In the design,
modiﬁed Oﬀner relay is inserted before the pick-oﬀ optics for each science path. The secondary mirror of themodiﬁed Oﬀner relay is a DM that corrects the common wavefront distortion in all of the science path. The
residual wavefront distortion for each science path is corrected by an individual DM in each science path. We
calculate the stroke requirements for the common DM and DM in each science path. We assume the common
DM corrects average wavefront distortion measured by the multiple LGSs and works like a GLAO system. In
this calculation the strokes 5′ away from the center is considered, but the diﬀerence in the stroke requirements insmall FoR is small, less than 1µm. The number of elements in the common DM aﬀects the stroke requirementsof the individual DM. If the number of elements in the common DM becomes larger up to 30×30, the required
stroke for the individual DM gets smaller. The trend saturate at 30×30 and increasing the number of elements
above 30×30 do not reduce the required stroke for the individual DM. Therefore, we choose 30×30 elements forthe common DM. In this case, the requirements for the common DM is 5.0µm (8.0µm) PV and 2.5µm (3.5µm)
IA strokes for moderate (bad) condition. For the individual DM, the requirements are 3.0µm (5.5µm) PV and
1.0 (2.0µm) IA strokes for moderate (bad) condition. Because the common DM can be as large as 300-400mm
diameter depending on the optical design, the required large stroke can be fulﬁlled with the piezo-stack DM. The
requirements for the PV stroke of the individual DM is larger than the Woofer-Tweeter case, because low-orderdistortion modes of high altitude atmospheric layers are not corrected by the common DM. The required PV
stroke is larger than the stroke of the currently available MEMS DM.
The above stroke requirements for the DMs are summarised in Table 2.

Table 2. Requirements for DM PV and inter-actuator strokes in three diﬀerent systems in µm. Values are upper 2σ valuesof 100 simulations with the moderate condition. Values in parenthesis are for the bad conditions. Tip-tilt component is
not included.

System30×30 DM

60×60 DM

PV

IA

PV

IA

—

—

5.5 (10.0)

2.5 (4.0)

30 × 30 Woofer- 60 × 60 Tweeter DMs for each path

5.5 (10.0)

2.5 (4.5)

1.0 (2.0)

1.0 (1.5)

Common 30 × 30 DM and one 60 × 60 DM for each path

5.0 (8.0)

2.5 (3.5)

3.0 (5.5)

1.0 (2.0)

One 60 × 60 DM for each path

3.2 Optical design for a common DM system
The common DM design can have a few advantages over the Woofer-Tweeter system in each science path,3
especially, part of the AO correction can be applied in closed-loop and images of the TT-guide stars can be
partly corrected. Such correction for TT-guide star can improve the limiting magnitude of TT WFS and increase
the sky coverage of the system. Considering the advantages, though the required PV strokes for the 60 × 60
DMs are larger than that of Woofer-Tweeter system and that of the currently available MEMS DMs, we further
investigate the feasibility of the common DM system of 10′ diameter FoR in the optical design point of view.
One extreme case of the common DM system is using the adaptive secondary mirror as the common DM.
Adaptive secondary mirror is considered as a possible future upgrade in the TMT project.3 Considering thediﬃculty associated with fabricating the adaptive secondary mirror with 3.0m diameter, we do not further
evaluate the possibility in this study.
At ﬁrst, we consider modiﬁed Oﬀner system following the IRMOS-Tipi feasibility study. In the optical design,
the common DM is conjugated to the primary mirror. We put emphasis on the size of the blur of the pupil
image on the common DM; it should be as small as half of the subaperture of 30×30 common DM, i.e. 1.7%,
within 5′ diameter FoR, and as small as the subaperture, i.e. 3.3%, within 10′ diameter FoR. Strictly speaking,pupil shift with 17% of subaperture size can introduce wavefront residual as large as ﬁtting error of 30×30 DM,
that means, the blur of the pupil image is better to be as small as 0.6%. The eﬀect of the blur of the pupil tothe performance inside wide FoR should be examined following the optical designs in the future. One opticaldesign by Optcraft (T.Y.) is shown in the left panel of Figure 8. In the optical design, the primary mirror of
the modiﬁed Oﬀner relay is spherical and has diameter of 4720mm. The secondary mirror corresponds to thecommon DM and has diameter of 400mm. The secondary mirror is also spherical and has curvature. In thisdesign, small glass plates in front of the focal plane are inserted to correct astigmatism for each science direction
individually. Such correction can be made by the individual DM in each science path, but the PV value of the
wavefront distortion is 5.8µm at the edge of the FoR and consume the stroke of the individual DM. The blur ofthe pupil on the common DM meet the speciﬁcation, less than 1.7% in most of the FoR except for the upperedge of 10′ FoR. The overall size of the design is 8436mm and close to the limit of the TMT Nasmyth platform
accepting 10m length system.
In order to reduce the size of the entire system, as well as the size of the largest optical component, we also
consider an optical design with free curve mirrors. The optical design by Photocoding (Y.I.) is shown in theright panel of Figure 8. In this design, all of the mirrors are free form curve except for the ﬂat DM. The resulting
size of the envelope is about half of that of the modiﬁed Oﬀner design. The largest mirror has 1.7m diameterand the DM has 280mm diameter. The distortion at the focal plane is within ±1.5µm. The blur of the pupil on
the common DM is 11% at most for the edge of the FoR. The blur is larger than the speciﬁcation at the edge.
In summary, there is an optical design for the common DM AO foreoptics that meets the requirements in the
10′ FoR. Further opt-mechanical consideration of the system will be made as a next step.

TMT focal planeDM
TMT focal plane

8436mmDM

800mm
by Photocoding

by Optcraft

Figure 8. The optical design for the common DM AO optics. Left) modiﬁed Oﬀner design by Optcraft. Right) Free curve
mirror array design by Photocoding.

4. DEVELOPMENTS FOR INDIVIDUAL COMPONENT
4.1 Requirements for high-dynamic range wavefront sensor
Because wavefront measurements in an MOAO system are done in open-loop manner, required dynamic range for
LGS WFS in the MOAO system is larger than a WFS in a closed-loop system. Assuming Shack-Hartmann (SH)
WFS, 5′′ FoV per subaperture is necessary to cover 5-sigma scatter of the wondering of spots under bad seeing
condition with r0 = 0.08m and measurement wavelength of 589nm. If we assume each spot of 60×60 SH WFS has
900 e− , which is the speciﬁed brightness of LGS for NFIRAOS,18 simple simulation with threshold-centroiding
suggests that pixel sampling of 0.25′′ is necessary to determine the position of each spot with 1σ accuracy of
0.01′′ . If we simulate the wavefront reconstruction through SH LGS WFS with 30m aperture considering the
spot elongation due to the Na-layer height proﬁle, 0.4′′ - 0.5′′ sampling is the optimised sampling for 60×60 LGS
WFS. With the setup, wavefront reconstruction accuracy is 150nm rms WFE including ﬁtting error. Therefore,
we require at least 10×10 pixels for each subaperture and 600×600 pixels in total.

4.2 Large stroke MEMS deformable mirror
As summarised in Section 3.1, the strokes of the currently available MEMS DMs cannot meet the required
speciﬁcation for 60×60 DM inside the common DM system design. In order to realize the large stroke MEMS
DM, we are conducting a development of a large stroke (20µm) MEMS deformable mirror.22, 25–27 We propose anew MEMS structure design with a bimorph-spring structure made by a HfO2 crystallisation process and Au-Si
eutectic bonding process. We fabricated 2×2 and 4×4 elements prototypes with 200µm length bimorph springsand 500µm spacing. By the bimorph-spring structure, the gap between the facesheet and the electrode as wide
as 20µm can be realized. The 2×2 prototype shows 7.6µm PV stroke with 110V and 4×4 prototype shows 3.5µm
PV stroke with 115V voltage. The response time of the DM is less than 0.5ms. The details of the structure andresults are shown in Wu et al. (2013).27

4.3 Tomography calculation with GPGPU
Fast tomographic reconstruction within 1ms is another key component of an MOAO system. In order to realize
the fast tomographic reconstruction, we apply parallel calculation with General Purpose Graphic Processor
Unit (GPGPU). The required time for the tomographic reconstruction with GPGPU through AO simulation
is evaluated. In the simulation, atmospheric turbulence structure in 7 layers is estimated by 8 60×60 LGS
WFSs measurements. The estimation is derived based on the minimum variance solution of the tomographic
reconstruction solved by conjugate gradient method (CG method).23
We use NVIDIA GTX Titan to solve the tomographic reconstruction in the simulation. One iteration of
the CG method takes 0.7ms with the current setup. The solution converges with 300 iterations with the CG
method, and it takes about 200ms in total to determine the solution. The required time is much longer than
the speciﬁcation currently. However the required number of iterations can be reduced to several times by using
the solution from the previous time step as the initial guess. Therefore improvement with the initial guess andfurther speed up of the GPGPU processing may meet the speciﬁcation.
The required time for data transfer from and to GPGPU can be another bottleneck for the fast tomographyreconstruction. Through the current setup with PCIe2.0 bus, transferring slope data to GPGPU and transferringreconstructed solution from GPGPU take 0.2ms and 0.4ms, respectively. We conﬁrmed that the required time
for data transfer can be reduced with using PCIe3.0 bus by factor of 1.5.

5. SUMMARY
We introduce current status of the feasibility study on a wide FoR MOAO system for TMT (TMT-AGE). In
this study, we put emphasise on the FoR as wide as 10′ diameter. The wide FoR is crucial to eﬀectively observe
very high-redshift galaxies at z > 5, which have low surface number density.
Simulations of an MOAO system show close-to-diﬀraction-limited correction can be achieved within 5′ diameter FoR with 8 LGSs located within 140′′ . Furthermore, moderate AO correction can be achieved within
10′ diameter FoR with the same LGS asterism. The EE within 0.2′′ × 0.2′′ can be 2.5 times larger than theseeing-limited case within the FoR.
We discuss overall system design of the wide FoR MOAO system considering the constraint of the stroke ofsmall-size deformable mirror DM. We compare the stroke requirements for DM in the Woofer-Tweeter system
and in the common DM system. In the common DM system, required PV stroke is larger than Woofer-Tweeter
system. We show two optical designs for the common DM system, one based on modiﬁed Oﬀner relay and theother one based on three mirror array of free curve surfaces.
We also introduce current status of developments of key components of an MOAO system; high-dynamic
range WFS, large-stroke small-size MEMS DM, and fast tomographic reconstruction RTC with GPGPU.

ACKNOWLEDGMENTS
This work is supported by Japanese TMT oﬃce strategic research and development funding of FY2012, FY2013,
and FY2014. M.A. is supported by JSPS KAKENHI Grant-in-Aid for Young Scientists (B) 23740140 and
Grant-in-Aid for Scientiﬁc Research (B) 26287027.

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