Beam Diagnostics for FACET Page: 3 of 3
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[um x 6.45 um. An image taken at f/11 is shown in Figure
5 with added texts to illustrate the group and element
numbers in the pattern.S-lemt 2 flu
3 = II
4 . 1u= I iii
5=1 .2
6 EIIiII = 1Figure 5: An image of the central part of the USAF1951
test pattern captured by a Nikkor 105mm f/2.8D lens at a
magnification of 1:1 and an aperture of f/11.
The spatial frequency F represents the spacing of lines
in the test pattern and can be calculated by
2Group+(Element-1)/6 in unit of line pairs per mm (lp/mm).
A rough and subjective estimate of the resolution can be
established by identifying the smallest element in which
an observer can distinguish all the line pairs in the test
pattern. Nevertheless, resolution can be quantified. A
contrast transfer function (CTF) is the black and white
contrast at a particular spatial frequency, normalized to
contrast at the lowest frequency. The CTF can be
determined directly from a square wave test pattern such
as the USAF1951 resolution target. However, the
performance of a lens is typically referenced by a
modulation transfer function (MTF) that can be obtained
from a sine pattern. Alternatively, the MTF can also be
derived [8] from the CTF:
MTF(F) = 4 + CTF(3F) _ CTF(SF) + CTF(7F) +
CTF(11F) CTF(13F) CTF(15F) _
11 13 15 I
The latter method is used to calculate the MTF results
presented in Figure 6. For example, for the case where no
window and no filter were used, the 50% MTF frequency
is about 17 lp/mm corresponding to 29.2 um and the 10%
MTF frequency is about 45 lp/mm or 11.1 um.
The resolution test compares the effect on resolution
with the use of diamond or sapphire window, as well as
red or blue filter. The diamond window is 1.2" in
diameter and 250 um thick while the sapphire window is
ultraviolet grade with 0.94" view diameter and about 2.03
mm thick. The response curves suggest that sapphire
provides better resolution than diamond.
The nominal beam size at the upstream OTR location is
Gaussian with ao = 550 um and o = 55 [um. Note that at
large apertures, the MTF is limited by optical
imperfections and limited by diffraction at small
apertures. The aperture of f/11 appears to be optimal in
our optical system. Using the formula given in [9], the
maximum f-number to resolve a resolution of 55 um
beam is much larger than 11. Therefore, our opticalsystem provides sufficient resolution to resolve the OTR
image of the beam.
Dliancndwidicut[ilte Di od with red 1l1e Diariondwvit bluetier
08 9 08 23u 89
0404 04
c2 02 04
0( 0 10 00 50 100 5 10
5patial Frequency( p/m.) Spatial-rquny (Ip/mm) SpatialFrquecy(lp/ )widow w [h blue [Ilzr
0 m
06
a0
\S #
02
kFigure 6: Resolution of the Nikkor 105mm f/2.8D lens at
a magnification of 1:1 and an aperture of f/11. Solid lines
are third order polynomial fits to the CTF data (*) and
dashed lines are the MTF curves derived from CTF.
SUMMARY
Beam diagnostic measurements not only provide
valuable insights to the running and tuning of the
accelerator but also are crucial for the PWFA experiments
in particular. Beam diagnostic devices are being set up at
FACET and will be ready for beam commissioning in
summer 2011.
REFERENCES
[1] C. Barnes, "Longitudinal Phase Space Measurements
and Application to Beam-Plasma Physics", Stanford
University Ph.D thesis, (2005).
[2] J. Seeman, et. al., "SLC Energy Spectrum Monitor
Using Synchrotron Radiation", SLAC-PUB-3945.
[3] The pco.edge camera data sheet, www.pco.de.
[4] I. Blumenfeld et. al., Nature 445, 741-744 (2007).
[5] M. J. Hogan, et. al., Phys. Rev. Lett. 95, 054802
(2005).
[6] H. Loos, et. al., "Relative Bunch Length Monitor for
the Linac Coherent Light Source (LCLS) Using
Coherent Edge Radiation", PAC 2007.
[7] R. Ischebeck, et. al., "Resolution of Transverse
Electron Beam Measurements Using Optical
Transition Radiation", PAC 2005.
[8] J. W. Coltman, J. Opt. Soc. Am. 44, 468-469 (1954).
[9] M. Castellano and V. A. Verzilov, PRST-AB 1,
062801(1998).*. w dww~rdfle
. - "
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Li, S. Z. & Hogan, M. J. Beam Diagnostics for FACET, article, August 19, 2011; United States. (https://digital.library.unt.edu/ark:/67531/metadc840821/m1/3/: accessed April 23, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.