Centroiding experiment for
determining the positions ofstars with high precision
ADASS2009 Sapporo
October 7, 2009 Renaissance Sapporo Hotel Sapporo, Japan

Taihei Yano, Hiroshi Araki, Hideo Hanada, Seiichi Tazawa,Naoteru Gouda, Yukiyasu Kobayashi (NAOJ), Yoshiyuki
Yamada (Kyoto Univ.), Yoshito Niwa (Kyoto Univ./NAOJ),JASMINE-WG

Table of Contents
1. Introduction
Infrared Astrometry Satellite (JASMINE project)

2. Centroiding Experiment
Algorithm
Result3. Summary

Introduction• JASMINE project- Japan Astrometry Satellite Mission for INfrared Exploration・Infrared Astrometry Satellite
・Mainly in progress at the National Astronomical Observatory of JapanThe objective
investigate the bulge components of the Milky Way galaxy

Introduction
In order to accomplish these objectives,• JASMINE will measure positions, proper motions, and the annual
parallaxes of bulge stars with the precision of 10µas.
(10µas is needed for determining the distance of bulge stars.)

Introduction
Specifications

Aperture
Wavelength

Small-JASMINE
30cm
2micronPlanned〜2015
Launch date

JASMINE80cm
2micron2020s

Observational Method
JASMINE will observe the bulge stars inthe following procedure.
• We take star image and measure thepositions of stars with the precision of
about 10-2 pixel for one exposure.
• We continue to take many images
during the mission time and estimate
the positions of stars with the precisionof about 10 microarcsec, that is, ofabout 10-4 pixel for all the observations.

To the 10 microarcsec in theexperiment

In the experiment we must show the following two points.
• the positional error is about 10-2 pixel for one exposure.
• the position of a star is estimated with a precision of
about 10-4 pixel for all the observations.
If we can remove or estimate the systematic error
adequately, the error of the position decreases as therandom error.

Experiment 1
1．Determination of the position with a
precision of about 10-2 pixel for one
exposure
2. Determination of the position with a
precision of about 10-4 pixel using about 104
imagesDetermination of the position
It is difficult to determine the position of stars with high accuracy.

・If we substitute photon-weighted mean for the position of a star, weobtain the position with a precision of a few tenth of pixels.
・However it is difficult to estimate the position with a precision of about
10-2 pixel level.
So we need some idea to estimate the accurate position.
photon-weighted mean : positional mean using the number of photons

Algorithm
We need to estimate a center of a star image
On the other hand, it is easy to calculate photon-weighted mean.
So, we estimate a center of star from the photon-weighted meanNote) Photon weighted mean of a star is different from the center of the star.

Schematic picture of the CCD and the star image

AlgorithmProcedure
1. Select two stars to measure the distance
2. Pick up a square subset of 5x5 pixels around the peak pixel of each star image
peak pixel : the pixel in which the number of photons is maximum

3. Calculate the photon-weighted mean of each star (xc, yc)
4. Assume that the difference between the photon-weighted mean and the realposition is proportional to the deviation of the photon-weighted mean from thecenter of the pixelxa - xc = k xc (Linear correction)
xc: photon weighted meanxa: real position of a star

5. Estimate the parameter k from the several images using the least square method

Experimental Equipment

Light sources

OpticsCCD

Result 1■Distance between the photon-weighted mean of two stars◆Estimated distance between two stars (linear Correction)
We obtained the variance of less than 10-2pixel for one exposure.

Experiment 2
１．Determination of the position with a
precision of about 10-2 pixel for one
exposure
2. Determination of the position with a
precision of about 10-4 pixel using about 104
images

To the 10 microarcsec
We would like to determine a position of a star witha precision of about 10-4 pixel using about 104images.
However if there exist systematic error which we do
not realize, variance does not decrease according
to 1/√N.
We must remove the systematic errors using a modelor control them so that we can neglect them.
In our experiment, we control the systematic errors.
control: ex. chromaticity effect ⇒we use same colors for all stars

Method・Obtain many images（In this case, 8000 images）
・Calculate the mean distance and variance from one set of 10 images.
・Calculate the mean distance and variance from one set of the above 10 values….

Result 2 (Variance vs. Number of images)••

variances decrease according to the slope in the case of random error.
We do not find a systematic error which we do not realize.

Summary and the Future plan
Summary• We obtained the precision of less than 10-2pixel for one
measurement.
• positional error decrease according to the slope in the case ofrandom error (1/√N).
Future plan
• We will obtain much more data to improve the statisticalerrors.
• We will remove the systematic errors, such as the distortionof the image, chromaticity effect, irregularity of pixels usinga model.
• We will experiment using a different algorithm, such as PSF
fitting method.