Proceedings of IBIC2012, Tsukuba, JapanWECC03

INTENSITY IMBALANCE OPTICAL INTERFEROMETER BEAM SIZEMONITOR∗
M.J. Boland, Australian Synchrotron, Clayton, Victoria, Australia
T. Mitsuhashi, T. Naito, KEK, Ibaraki, Japan
K.P. Wootton, The University of Melbourne, Victoria, Australia
The technique of measuring the beam size in a particle accelerator with an optical interferometer with the Mitsuhashi apparatus is well established and one of the only
direct measurement techniques available. However, oneof the limitations of the technique is the dynamic range
and noise level of CCD cameras when measuring ultra low
emittance beams and hence visibilities close to unity. Anew design has been successfully tested to overcome theselimitations by introducing a known intensity imbalance in
one of the light paths of the interferometer. This modiﬁcation reduces the visibility in a controlled way and lifts themeasured interference pattern out of the noise level of theCCD, thus increasing the dynamic range of the apparatus.
Results are presented from tests at the ATF2 at KEK andon the optical diagnostic beamline at the Australian Synchrotron storage ring.

OPTICAL INTERFEROMETRY
The Mitsuhashi apparatus [1] for measuring the ﬁrst order spatial coherence of a beam of charged particles thatemit synchrotron radiation is well established and used on
many accelerators. The technique samples two parts of thediverging visible light beam using a double slit type conﬁguration.
Using a focussing mirror the beams from each slit arebrought together to form an interference pattern that isrecorded with a CCD camera. A mirror is currently used
to focus the beams since mirrors can be constructed witha larger aperture and with better roughness and dig-scratch
performance than a lens of the same aperture. A parabolic
mirror can be made with relatively few aberrations drawing
on the experience of astronomical mirrors for telescopes.
In essence to start to construct an interferometer the ﬁrst
step is to build a telescope to image the beam. Once a good
optical path has been established the interferometer components can be added step by step to construct the Mitsuhashi
apparatus for measuring the ﬁrst order spatial coherence. Anarrow bandpass ﬁlter is added to simplify the analysis, forexample ω = 500 nm, Δω = 10 nm. A polariser is used toselect the σ-mode of the synchrotron radiation so as to distinguish it from the π-mode which produces a interference
pattern with a phase shift that washes out the interferogram.
If more intensity is needed for low beam currents it is possible to use a wider bandpass ﬁler of 80 nm to increase thelight, however the analysis of the data will have to take this
into account.
∗ Work supported by a JSPS Travel Fellowship.

A typical example of an interference pattern producedwith the Mitsuhashi apparatus is shown in Fig. 1:

Figure 1: A typical interference pattern created by the Mitsuhashi apparatus for measuring beam sizes.

LIMITATIONS OF A CONVENTIONALINTERFEROMETER
In modern accelerators where the vertical emittance isbeing pushed lower and lower, towards sub-picometre radian level, the beam size becomes very small and is highly
spatially coherent. This means that the visibility of theinterference pattern is very close to unity and the troughs
dip down into the noise ﬂoor of the CCD that is recording
the pattern. As a consequence the Mitsuhashi apparatus ispractically limited by the signal to noise ratio of the CCDcamera. At ATF2 optical beamline in the injection area thebeam size was measured by the interferometer to be 5 μm
with an error of less than 1 μm [2], which was mostly due tothe CCD noise. The CCD by Hamamatsu [3] is one of thebest performing on the market, with a low noise level and avery linear response across the range required for the interferometer, so a modiﬁcation of the technique was required
to improve the performance at very high spatial coherence.

INTENSITY IMBALANCE TECHNIQUE
The intensity distribution of the interference pattern created by light of wavelength λ passing through a double slitof hieght a, slit separation D and a distance R from thesource with a certain polarisation is given by [2]2 
2πa
2πD
yy+φ ,
1 + |V| cos
I(y) = I0 sincλR
λR

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Copyright ○Abstract

WECC03

Proceedings of IBIC2012, Tsukuba, Japan

ATF2 MEASUREMENTS

Visibility





Imbalance Ratio I1 /I2

Figure 2: Visibility plotted again the imbalance ratio ρ =I2 /I1 in the interferometer.

Light is extracted just after the injection point of theATF2 damping ring using a mirror that captures the lightsymmetrically above and below the optical axis. The beamis then reﬂected out of the tunnel and onto an optical hutchon the roof of the damping ring and directed into the interferometer on the optical table as shown in Fig. 3.
Firstly the beam size was measured using the standard
interferometer and the slit size varied to check the distribution of the visibility function. Using the 20 mm slit separation the visibility was quite high around 0.95, so the imbalance method could be put to good use. Figure 4 shows
the interferogram for the balanced interferometer, whileFig. 5 shows the interferogram from the intensity imbalanced measurement.
c 2012 by the respective authors — cc Creative Commons Attribution 3.0 (CC BY 3.0)
Copyright ○√2 I1 I2|γ|.
I1 + I2

In most cases one can assume V = |γ| since for I1 ≈ I2
this assumption is valid. For a symmetrical visible radiation fan with the interferometer sampling the beam at thetop and bottom of the optical axis, it can be assumed thatthe intensity is the same at each slit opening. Figure 2
shows that for an imbalance of up to 10% the visibility onlychanges by less than 1%.
This leads to two situations; one where the intensity isimbalanced due to the beam or beamline conditions; thewhere an imbalance is introduced in a controlled way, i.e.
the intensity imbalance interferometer. An optical ﬂat withthe top half fully transmissive and the bottom half with anattenuation coating can be introduced to create the imbalance and reduce the visibility for a given beam size. Thetrue beam size can then be determined as follows by correcting the measured visibility to the complex degree ofcoherence using the imbalance ratio ρ = I2 /I1|γ| = V

(1 + ρ)√ ,2 ρand then computing the beam size from the Fourier pair ofthe visibility distribution using (again following [2])πDσy =λR

1ln21.
|γ|Using this method with a value of ρ = 0.2 gives a visibility reduction of 0.745 and achieves the aim of lifting thefringes in the interference pattern above the noise. The following section demonstrates the intensity imbalance technique using beam size measurements from ATF2 at KEK.

intensity [a.u.]

V=[

dataﬁt|γ| = 0.953



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






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pixel

Figure 4: Interferogram from the balanced interferometerwith a slit separation of 20 mm.



dataﬁtintensity [a.u.]where the visibility V is related to the complex degree ofcoherence by a factor involving the intensity of each beam
I1 and I2 given by
V = 0.693|γ| = 0.930






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pixelFigure 5: Interferogram from the balanced interferometerwith a slit separation of 20 mm also showing the visibility
corrected to derive the complex degree of coherence.
The ﬁt to the interferogram produces some inconsistent
beam sizes as seen in Table 1, indicating a problem withthe signal to noise or a shot to shot beam size variation.
The measurements were repeated using the intensity imbalance setup and as expected the visibility was reduced(compare Fig. 4 and Fig. 5). When the complex degree

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WECC03slit separation (mm) |γ| σy ( μm)200.953
9300.868
10400.854
8of coherence was computed using the known intensity imbalance, similar beam sizes were extracted from the data,
however there were some inconsistencies across the rangeof slit separations measured.



Table 2: Summary of ATF2 Imbalanced Interferometer
Measurements
slit separation (mm)
V|γ| σy ( μm)200.693 0.930
11300.640 0.858
10400.592 0.794
10The inconsistencies may be due to ﬁtting errors or shot toshot variations in the beam but it is worth noting the intensity imbalance measurements are more consistent. Whenplotted against the slit separation 6 the complex degreeof coherence for the imbalance measurement is consistent
with the 10 μm beam size proﬁle, while the balanced measurement has a larger spread, perhaps due to the problemsof measuring high visibilities.
In an attempt to reduce the shot to shot variations introduced by the damping ring injection cycle, measurements
were performed using a similar setup at the Australian Synchrotron storage ring.

imbalance databalance dataσy = 10 μm proﬁle









Slit Separation (mm)Figure 6: The complex degree of coherence for various slit
separations for the imbalance interferometer.

ASLS MEASUREMENTS
The optical diagnostic beamline on the AS storage ringhas a stable beam, unfortunately the pick-off mirror conﬁguration is not optimal for interferometry. At ATF2 thevisible light pick-off mirror captures the light symmetrically above and below the optical axis. However, Fig. 7shows how the narrow opening angle of the ASLS optical
diagnostic beamline and the pick-off mirror that only samples the top half of the beam introduces an imbalance in theintensity of the two beams in the interferometer. The imbalance ratio is ≈ 0.6 which means it needs to be corrected
for in the analysis of the interferogram in order to achieve
an accurate measurement; we cannot use the assumptionthat I1 = I2 . This was done by measuring individually theISBN 978-3-95450-119-9
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Copyright ○Table 1: Summary of ATF2 Balanced Interferometer Measurements

Complex Degree of Coherence |γ|

Figure 3: The currently used conﬁguration of the Mitsuhashi aparatus interferometer as used at the ATF2 at KEK (March2012).

WECC03

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V
0.795
0.546
0.707
0.484

|γ| σy ( μm)
0.804
58
0.790
61
0.734
69
0.70474

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top and bottom beam intensity by blanking them off in turnand capturing an image. This measured intensity data isthen used to unfold the complex degree of coherence fromthe interference pattern.
Another disadvantage of the AS storage ring is that thenominal beam size at the optical diagnostic beamline is
not very small to begin with; a nominal beam height of
σy = 58 μm for a 1% emittance coupling ratio. An attempt
was made to reduce the coupling by turning off the skew
quadrupoles (which are set during user beam to increase
the coupling in order to increase the beam lifetime).
Measurements were taken using a slightly different conﬁguration than at ATF2 and the AS setup is shown in Fig 8.

dataﬁt

V = 0.795|γ| = 0.804







pixel

Figure 9: Interferogram with the skew quadrupoles off.

Figure 8: The refractive optics setup of the intensity imbalance interferometer on the optical diagnostic beamline at
the Australian Synchrotron.
Two beam conﬁgurations were created; one at nominal
1% emittance coupling for a large beam size; and one withthe skew quadrupoles off. For each beam conﬁguration
the beam size was measured with the interferometer andwith the intensity imbalanced interferometer. The results
are summarised in Table 3. The intensity of the two beams
were measured for each interferogram that was taken since
we cannot use the I1 = I2 assumption. The interference
pattern was ﬁt to obtain V, then |γ| was computed and ﬁnally the beam size determined.
The measurements are in reasonable agreement but due
to the small opening angle of the beamline the slit separation is limited to up to 10 mm. At 10 mm separation thevisibility changes very little with beam size so the anal-dataﬁtintensity [a.u.]c 2012 by the respective authors — cc Creative Commons Attribution 3.0 (CC BY 3.0)
Copyright ○Figure 7: The ASLS optical diagnostic beamline visible
radiation fan. The blue circles indicade the angular position
the interferometer slits sample the beam.

ysis is very sensitive to ﬁtting errors. This highlighted aproblem with the ASLS data that the CCD has an internal
threshold for removing background which results in an unphysical absolute zero background. As a result a DC shift
is introduced to the data that will give the wrong value forthe visibility. This can be see in Fig. 9 and Fig. 10 where
the minima of the sinc envelope has a series of data points
at exactly zero.

intensity [a.u.]

í




V = 0.546|γ| = 0.790














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pixel

Figure 10: Interferogram taken with the intensity imbalance interferometer with the skew quadrupoles turned off.
This problem was not observed at ATF2 at KEK where
the CCD used gave the raw counts in the pixels including
the dark counts due to noise.

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VIRTUAL BEAM MEASUREMENTACKNOWLEDGMENT

The vertical beam size at the ASLS optical diagnostic
beamline is more than an order or magnitude larger thanfor future damping ring and light source storage ring designs. Very small beam sizes producing visibilities close tounity are required to properly test the intensity imbalanceinterferometer, so a 24 time demagniﬁed virtual source wascreated at the ASLS optical diagnostic beamline by placing
a concave lens directly in front of the slits. The nominal
beam size at the optical diagnostic beamline source pointis 58 μm (for a calibrated lattice and 1% coupling), so thevirtual source was ≈ 2.4 μm. The beam size was measured
with the intensity imbalance interferometer to be 2.6 μm,
demonstrating the true advantage of the technique.

The Japanese Society of the Promotion of Science (JSPS) is gratefully acknowledged for providing
M. J. Boland with a Short-term Travel Fellowship to perform measurements at KEK, Japan.

REFERENCES[1] T. Mitsuhashi, Proceedings of the Particle Accelerator Conference 1997, p. 766 (1998).
[2] T. Naito and T. Mitsuhashi, Rhys. Rev. ST-AB 9, 122802(2006).
[3] Hamamatsu CCD model number C5985.

The intensity imbalance interferometer achieved the aimof reducing the visibility in a controlled way and still measuring the correct beam size. This technique improves
the sensitivity of the Mitsuhashi apparatus and can measure very small beam sizes with less than 1 μm accuracy.
Two experimental setups were tested with the imbalancemethod, however neither had the ideal conditions of a verysmall beam size and stable beam to demonstrate the fullpotential of the apparatus. It remains one of the best direct measurements of beam sizes in accelerators and further work will attempt to improve the optical beamline at
the Australian Synchrotron to take advantage of the interferometer.

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Copyright ○CONCLUSION