TMT-AGE：

Numerical simulation of a new tomographic
reconstruction method for wide FoR MOAO	
Yoshito H. Onoa,b, Masayuki Akiyamaa, Shin Oyab

( a : Tohoku University in Japan, b : National Astronomical Observatory of Japan )Email: ono@naoj.org

Introduction	

Results	
• Wind profiles for the new tomography method are derived using thetemporal auto correlation of estimated slope.
• Assuming 100% frozen-flow and perfect information of atmosphericlayer altitudes.
• The measurements at 0.1s previous time step are used, ∆t = 0.1s.
Tab.1: Atmosphere Model and Wind Estimation Error	

Fig.1: LGS
Configurations	
+200

Y (arcsec)

100• The solution for Eq.(1) is constructed with Minimum Variance
Reconstruction.

The Eq.(2) is solved with Conjugate Gradient Method.

◆ Estimation of Wind Speeds and Directions	wavefront,, + ,+-300

are influence matrices between
and, respectively, and is a noise vector.

Estimatedslope

++, ,+-300• The linear equation between current atmospheric turbulence andShack Hartmann wavefront sensor (WFS) measurements at both ofcurrent and previous time steps is given as follows.

Estimated phase map Extracted

0-200• Under the assumption of Taylor’s frozen-flow hypothesis, evolution ofatmospheric turbulences can be described as the shift of atmosphericlayers due to the wind. If the wind profiles are known, we can build
the relation between measurements at previous time steps andcurrent atmospheric turbulence.

and,+ ,-100◆ New Tomographic Reconstruction	

Here,and+Temporalauto correlation

• Tomographic reconstruction provides the phase map of atmosphericturbulence at each altitude. Wind profiles can be estimated from thetime variation of the phase on the maps.
• We use a temporal auto correlation of estimated slope for deriving
wind profiles, since a slope correlation has a sharper peak than awavefront correlation.
• Wind speed and direction at each altitude are calculated withtracking a peak of temporal auto correlation of estimated slope
which moves depending on wind speed and direction at this altitude
and a time delay for the temporal correlation..

-200-100
0100
X (arcsec)

200300

TMT-IRMOS configuration, ClassicalWider Configuration, Classical350
Wider Configuration, New

Residual WFE [nm]300,Methods	

400

300
250
200
150

Aperture size = 30m
r0 = 0.156m
L0 = 30m
Subaperture size = 0.5m
DM segment size = 0.5m

100

Fig.2: Residual WFE	
012

34

Distance from the center of FoR [arcmin]

0.8

Ensquared Energy in a 50mas square• We are conducting a concept study on a wide field of regard (FoR)
Multi-Object Adaptive Optics (MOAO) system for Thirty Meter
Telescope (TMT-AGE: TMT - Analyzer for Galaxies in the Early
universe [1]).
• Because the number density of high-redshift galaxies is small, which
are key science targets of TMT- AGE, enlarging the FoR of an
MOAO system up to around 10′ is critical.
• We propose a new tomographic reconstruction method which
increases a FoR of MOAO System. The new method use
atmospheric wind profiles, wind speeds and directions at each
altitude, and WFS measurements at previous time steps to increase
the number of virtual measurement points of atmospheric turbulencelayers for tomographic reconstruction.
• The wind profiles are derived using the atmospheric turbulence
structure estimated with tomographic reconstruction.

5TMT-IRMOS configuration, ClassicalWider Configuration, ClassicalWider Configuration, New

0.7
0.6
0.5
0.4
0.3
0.2

Fig.3: Ensquared Energy(J-band, 50mas)	

0.1
001

2

3

4

Distance from the center of FoR [arcmin]

5The new tomography method with the wider configuration (■ in Fig.2and 3) decreases WFE and increases a ensquared energy at outside of
the FoR compering to the result of the normal tomography with the TMTIRMOS configuration (○ in Fig.2 and 3).	

Discussion	• Since the displacement error within 0.1s due to wind estimation error
is less than 25cm, which is half of DM segment size, a tomographic
error due to the error of wind estimation is smaller than the fitting error.
• In reality, the time scale of frozen flow is limited and the correlation
peak becomes fainter with time [3]. This affects the accuracy of thedetection of the correlation peaks.
• We will evaluate the accuracy of the wind estimation method with theuncertainties of the altitudes of atmospheric layers, for example
uncertainty with estimation by SLODAR [4], in a future work.	

Conclusion	

We propose a new tomographic reconstruction method using
measurements at previous time steps and wind information to increase
the FoR of MOAO systems and evaluate the method with numericalsimulations. We also introduce a method to estimate wind speeds anddirections at each altitude. The wind profiles can be estimated with
sufficient accuracy under assumption of 100% frozen flow and perfect
Reference	knowledge of altitudes of atmospheric turbulences. With the estimate of[1] Akiyama et al, Proc. SPIE this volume, Adaptive Optics Systems IV (2014).
wind speeds and directions, the new tomographic reconstruction method[2] Ellerbroek, B. L., J. Opt. Soc. Am. A 19, 1803–1816 (2002).
reduces
WFE
toless
than
250nm
for
thewiderLGS
configurationin8′[3] Corts et al, [Proceedings of the Third AO4ELT Conference], Firenze (2013).
[4] Wilson, R. W., Monthly Notices of the Royal Astronomical Society 33, 103–108 (2002)	 FoR (Fig.2).