Deep Space Exploration

2014. Vol.*, No.*, **-**

P u b l i s h e d O n l i n e * * * * 2 0 1 4 i n * * * * * * D O I : * * * * *

Copyright © 2013 SciRes. 1

Present status of ILOM, VLBI and LLR for future lunar

missions *

H. Hanada1,2

, S. Tsuruta1, K. Asari

1, H. Araki

1,2, H. Noda

1,2, S. Kashima

1, K. Funazaki

3, F. Kikuchi

1, K. Matsumoto

1,2, Y. Kono

4,2, H.

Kunimori5, S. Sasaki

6

1RISE Project, National Astronomical Observatory, Oshu, Japan

2Department of Astronomical Science, The Graduate University for Advanced Studies (SOKENDAI), Mitaka, Japan

3Faculty of Engineering, Iwate University, Morioka, Japan

4Mizusawa VLBI Observatory, National Astronomical Observatory, Mitaka, Japan

5Wireless Network Research Institute, National Institute of Information and Communications Technology,

Koganei, Japan 6Department of Earth and Space Science, Osaka University, Toyonaka, Japan

Email: hideo.hanada@nao.ac.jp

Received Month Day, Year (2014).

We investigated basic characteristics of the telescope for In-situ Lunar Orientation Measurement (ILOM),

such as the centroid accuracy and the effects of temperature change, tilt and ground vibrations, by labora-

tory experiments using a Bread Board Model and by simulations. We have a prospect to observe the lu-

nar rotation on the lunar surface with the accuracy of 1 milliarcsecond. We will make test observations

on the ground in order to evaluate overall characteristics with the target accuracy of better than 0.1

arcseconds.

Keywords: Moon, Rotation, ILOM, Telescope, PZT, Mercury pool

Introduction

Geodetic observation of the Moon, such as the lunar rota-

tion, the gravitational fields and tidal deformation, is one of

the essential and basic observations for investigating the

interior of the Moon. We are developing instruments for

study of internal structure of the Moon in SELENE-2 and

future missions., They are radio sources for differential VLBI (Very Long Baseline Interferometer), a retro-reflector

for Lunar Laser Ranging (LLR), and a telescope for In-situ

Lunar Orientation Measurement (ILOM).

VLBI is effective and promising method for orbit deter-

mination of artificial satellites. Kaguya mission employed

the differential VLBI for orbit determination and gravity study, and attained the accuracy of 1 ps in the differential

phase delay of the X-band signal, which resulted in the orbit

accuracy of around 10 m (Kikuchi et al., 2009). We can

expect that the differential VLBI between artificial radio

sources on a lunar lander and a lunar orbiter will measure the

doubly-differenced ranges more accurately than Kaguya because there is more chance of the same beam observations

(Kikuchi et al., 2014). An S/X-band two-beam system on a

ground station can increase the chance for simultaneous ob-

servations of the two spacecraft, and we are developing a

phase array system using self-complementary antennas.

We have also developed an antenna which has a gain of -5 dBi for beam-width of 60 degrees and for bandwidth of 140

MHz in temperature range of -200 to +120 degrees for future

landing mission (Kikuchi et al., 2014).

We are proposing to put a new retro-reflector on the

Moon in order to expand the network of retro-reflectors and

to make it possible for many ground stations to participate in

the observations, and thus to improve the accuracy of LLR

(Sasaki et al., 2012). The reflector on the Moon of not in an

array but of a single large one will improve the ranging ac-curacy up to 1mm order because it will not be affected by the

shift of the optical center due to change of the incident angle.

We should set dihedral angles which are the angles created

by two intersecting surfaces with the accuracy of better than

0.1 arcseconds in order to receive return energy effectively

(Otsubo et al., 2011). Therefore Manufacturing method is under development and bonding of three mirrors or integral

molding are two alternatives.

We are developing also a small telescope like Photo-

graphic Zenith Tube (PZT) for observations of the lunar

rotation through positioning of stars on the Moon with a

target accuracy of 1 milliarcsecond (mas) as an ILOM pro-ject. Since the observation is not affected by orbital motion

of the Moon and the rotation of the Earth, the observed data

are independent to observations by LLR. Observations for

longer than one year have a potential to detect small compo-

nents of the physical librations and the lunar free librations

which are related to the lunar interior (Heki, 2000; Petrova & Hanada, 2013). We have already made a bread board mod-

el (BBM) and are in a stage of test observations on the

ground as the basis for a future lunar telescope.

Development of mainly a telescope for ILOM is presented

in this paper.

Development of a Telescope for ILOM

Bread Board Model

A. NAME (an abbreviation of the first author’s name) ET AL.

2 Copyright © 2013 SciRes.

The PZT is a kind of zenith telescope with a mercury pool as

a reflector at the middle point of the focal length of the objec-

tive. Stellar images on the focal plane at the nodal-plane of

the objective does not shift in principle even if the tube inclines

a little except the effect of aberration, since the optical path

reflected at the mercury surface does not change by the tilt.

We have already developed a bread board model (BBM) of a

telescope for basic experiments of ILOM. Technical devel-

opment for improvement of accuracy, environmental test of key

elements were made by using the BBM in cooperation with

JASMINE project of National Astronomical Observatory of

Japan (NAOJ) and Iwate University. The optical system of

PZT is shown in Figure 1 and the specification is shown in

Table 1.

We succeeded in determination of star position with the ac-

curacy of about 1/300 pixel, which corresponds to about 3 mas

for the PZT with 1m focal length and CCD with pixels of

5μm×5μm (Yano et al., 2004).

Effect of tilt is compensated according to the principle of

Photographic Zenith Tube (PZT). The error of the compensa-

tion is less than 1 mas if the tilt is within about 80 arcseconds

from the vertical (Hanada et al., 2012). The attitude control

system can make the tube vertical within an error of 0.006 de-

grees (or about 20 arcseconds) (Funazaki et al., 2008).

Ray tracing simulations showed that the effect of tempera-

ture change, which is expected to be about 3 mas per degree for

an objective with conventional lenses, can be reduced to about

0.1 mas per degree by adopting a diffractive element (DOE) in

the objective (Kashima et al., 2012; Kashima et al., 2013).

We made laboratory experiments by using the BBM and an

artificial light source in order to know the effect of ground

vibrations upon the stellar position on the focal plane. It is

anticipated that the mercury surface as a reflector may magnify

the effect through the surface vibrations. Three copper ves-

sels of 84 mm diameter with a conical bottom surface of dif-

ferent depth, 0.25 mm, 0.5mm and 1mm, were used for the

experiments. Copper amalgam is formed inside of the vessel

for reducing the effect of surface tension of mercury (Tsuruta et

al., 2014).

Ground Experiment Model We improved the BBM for aiming at observations on the

ground and developed so called Ground Experiment Model or Ground Model in short as shown in Figure 2. A new tripod makes it possible to set the telescope on the slope of less than 30 degrees. PZT has a potential to observe deflection of the verti-cal (DOV) with an accuracy better than 0.1 arcsecond (Hirt & Bürki, 2002; Li et al., 2005). It is not always possible, however, to observe DOV with such a high accuracy on the ground since the environments such as the atmosphere, ground vibrations and the air temperature can perturb the images of stars. It is im-portant to confirm how accurately we can observe DOV under the condition on the ground.

Spacial resolution of a telescope generally depends on astro-nomical seeing, diffraction limit and pixel size of CCD. The latter two factors are inherent in the optical system and detectors and do not depend on environments.

The diffraction limit, which is represented as the radius of the Airy disk, is the best focused spot of light through a perfect lens with a circular aperture, limited by the diffraction of light. The diffraction limit θ [rad] is expressed as θ = 1.22λ/D with λ of

Figure 1.

Optical system of PZT. 1: objective, 2: plain parallel, 3:

prism, 4: CCD, 5: mercury surface.

Table 1.

Specification of the telescope

Aperture 0.1m

Focal Length 1m

Type PZT

Detector CCD

Pixel Size 7.4μm×7.4μm (1.5″×1.5″)

Number of Pixels 512×512

Angle of View 0.0035×0.0035 rad (12′× 12′)

Figure 2.

The Ground Experiment Model.

A. NAME (an abbreviation of the first author’s name) ET AL.

Copyright © 2014 DeepSpace. 3

wavelength and D aperture. It becomes 7.32×10-6 (1.5 arcsec-onds) when D = 0.1m and λ = 600nm. It is possible to deter-mine stellar position better than the diffraction limit by centroid estimation which fits the stellar image to a point spread function. We assume the centroid estimation as well as the pixel size of CCD in setting the target accuracy of ILOM of 1 mas. The diffraction limit and the pixel size of CCD are not important in comparison between the observations on the lunar surface and those on the ground.

The astronomical seeing or the seeing in short, on the other hand, is an index how much the Earth's atmosphere perturbs the images of stars as seen through a telescope, and depends on the place, season and time of the day. The seeing is normally about 1” even under a good condition on the ground, and the seeing of 0.4” was attained at the top of a high mountain such as Mauna Kea in Hawaii which is one of the best places for astronomical observations. There are two alternatives; to increase integration time or to adopt the adaptive optics, for reducing the effect of the atmosphere. The adaptive optics, however, is not adequate for astrometry such as ILOM since it can shift the stellar position in the course of compensation using a tip tilt mirror and deformable mirrors.

We can reduce the effect of atmospheric turbulence by lengthen the integration time if we suppose the flickers are ran-dom phenomena. Roughly speaking, the standard error of the mean will be 1/10 of the standard deviation if we get 100 data during the integration time. Long integration time contribute also to improve the signal to noise ratio (SNR), which results in

improvement of the accuracy in determination of stellar position. There is a limit, however, in the integration time for observa-

tions using PZT since it does not track the stars. Stars move in the field of view according to the rotation of the Earth. Time when a star is within a field of view corresponds to the maximum integration time in this case. The maximum integration time depends on the rotation rate of the Earth. It is estimated that the maximum integration time is 48 s from the angular velocity of the rotation of the Earth of 7.3 rad/s and the angle of view of 0.0035 rad. Considering the integration time of longer than 100 s assumed in ILOM (Hanada et al., 2012), we cannot expect to attain the accuracy of the observation on the ground comparable to that on the Moon by lengthening the integration time far long-er than 100s. Eventually, it will be possible to reduce the effect of atmospheric turbulence to be smaller than 0.1” although fur-ther improvement is difficult in this situation.

Preliminary Experiment

Ground vibration is also the factor which can affect the ac-

curacy of astronomical observations as has pointed out above,

and it is inevitable if we carry out the observations on the

ground. We must pay special attention to the mercury pool in

the telescope relating to the ground vibrations (Tsuruta et al.,

2014). We investigated how CCD image of a star moves by ground

vibration through vibration of the mercury surface as a prelim-

inary experiment to observations on the ground. We recorded

Figure 3

Variations of stellar position observed by the Ground Model with

the mercury pool of 0.5mm depth. Upper : X-component, Low-

er : Y-component. Time : 2013/12/3 15:51:30 – 15:52:30

Figure 4

Variations of stellar position observed by the Ground Model without a mercury pool. Upper : X-component, Lower :

Y-component. Time : 2013/12/3 14:55:16 – 14:56:16

Figure 5

Power Spectra of the variation of stellar position in the case with a

mercury pool of 5mm depth (upper), and that with a mirror instead of

it (lower).

Figure 6

Power Spectra of ground vibrations for the period corresponding to

the experiment with the mercury pool (upper) and that with a mirror

instead of it (lower).

A. NAME (an abbreviation of the first author’s name) ET AL.

4 Copyright © 2013 SciRes.

the variation of the centroid of artificial stellar images fitted to

Gaussians for 60 s with 30 Hz sampling frequency. Ground

vibrations were observed by 3 components of velocity seismo-

meters with a natural frequency of 1 Hz. Figure 3 shows the

variation of the centroids when the mercury pool of 0.5 mm

depth was used. We also observed the variation of the cen-

troids in the case when the mercury pool was not used but a

plane mirror was used as a reference (Figure 4).

There is no big difference between the two sets of records.

Then, we compared them in power spectra as shown in Figure

5. There is also no big difference between them except that

the power between 0.5 and 1 Hz are relatively larger in the case

with the mercury pool. Further, there are no strong peaks at

around 0.5, 1.0 and 2.0 Hz as been seen before (Hanada et al.,

2014). The possible causes for the no noticeable difference

are that the amplitude of ground vibrations is not big enough to

excite the mercury surface, that there is no power in the ground

vibrations near the resonance frequency of the mercury surface,

and that we made a stronger frame for a mirror which guides

the beam from a light source (artificial star) to the telescope.

The ground vibrations, on the other hand, are almost similar in

both cases (Figure 6).

With respect to the amplitude of the variation of the centroid,

it exceed 5×10-7 m in the frequency range lower than 0.5 Hz.

This large amplitude seems to be related to the ground vibra-

tions since the spectra of the centroid and ground vibrations are

similar in this range. More specifically, the peaks at about

0.06, 0.16, 0.35, 0.45, 0.48, 0.65 and 0.74 are seen both in the

centroid and ground vibrations. We can confirm the similar-

ity also from time series data. Figure 7 shows the comparison

between the centroid data and vibration data for 20 s in which

the variations are larger and more remarkable. There are long

period variations with the periods of a few seconds in both data.

There are stronger correlations between (x, y) components of

the centroid data and (NS, EW) components of the vibration

data, respectively.

It seems to be possible to reduce the effect of the ground vi-

brations to be less than 5×10-7 m if we correct for the variation

of the centroid by using vibration data. The relation between

the centroid variation and the ground vibrations, however, can

be different for the future observations on the ground since the

configuration for the preliminary experiment in a laboratory

using an artificial star and that for the observation on the

ground outside are different. The effective method for the cor-

rection is future issues.

Concluding Remarks

We will perform observations on the ground by using the

Ground Model in order to check the total system of the tele-

scope and the software. It is also important to evaluate the

effect of the ground vibrations and temperature change upon

the stellar position on CCD. The goal of the observations on

the ground is to attain the accuracy of better than 0.1 arcsec-

onds. There are important targets for the observations, such

as the variation of DOV caused by seismic or volcanic activity.

Verification of 1 mas on the Moon will be possible in a spe-

cially equipped laboratory in the future.

Acknowledgements

The experiments in this work were supported by Advanced

Technology Center (No.2013-031). This work was supported

by Grant-in-Aid for Scientific Research (A) (No.20244073)

from Japan Society for the Promotion of Science. This re-

search was also supported by JSPS Bilateral Joint Research

Projects between Japan and Russia (14037711-000085).

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