Proceedings of IBIC2012, Tsukuba, Japan

TUPA42DIAGNOSTICS BEAMLINE OPTIMISATION AND IMAGE PROCESSINGFOR SUB-PS STREAK CAMERA BUNCH LENGTH MEASUREMENTAbstract
For the low-alpha beam mode at Diamond, standard theory predicts rms bunch lengths as small as 0.6 ps with amomentum compaction factor set to α = 0.8·10−6 . In order
to be able to reliably measure such a short bunch, we havebeen optimising the optical design of the visible diagnostics beamline, and we have implemented image processing
to take into account the point spread function of the streakcamera. The optical design has reduced a large chirp of
15 ps to less than 2 ps over the 400-550 nm bandwidth. It
has also permitted the transport of almost all the available
power, increasing the power by a factor 30, yet maintaining
the possibility to focus the beam down to less than 20 μm
into the streak camera for the best static streak camera
point spread function. The implemented de-convolution
technique extends the performance of the streak camera tobunch length measurements of less than the 1 ps PSF of thestreak camera. In this paper we present these two essentialfeatures required to measure sub-ps bunches with a streakcamera.

INTRODUCTION
For the low-alpha beam mode at Diamond, rms bunchlengths based on synchrotron frequency measurement arecalculated to be as small as 0.6 ps. In special user low alpha beam mode the bunch length is set to be of the orderof 2.5 ps. Measuring such small bunch lengths reliably canbe quite challenging. For such a measurement we use a
streak camera1 (SC), for which the resolution as definedusing the Rayleigh criterion and specified by the manufacturer is 2 ps (measured using narrowband pulses with a few
photons per pulse). The corresponding rms resolution isthen 0.75 ps. This should allow the SC to be able to measure bunch lengths 2 ps or less. However, control of thebandwidth and the power of the photon pulse is fundamental: too much power will induce Coulomb explosion of theelectron bunch in the streak tube, and thus measurement ofa longer bunch. Too little power will render the measurement dependant on the jitter of the many pulses needed toform an image.
In addition to this, one needs to take into account the possible chirping of the pulse going through various lengths ofglass. To reach the photocathode of the SC, a pulse passes
through at least the 4.3 mm of quartz on the entry of theSC tube. In our case there is also 6.3 mm of fused silica from a vacuum-air separation window. But the beam
∗ cyrille.thomas@diamond.ac.uk
1 Optronis GmbHneeds to be transported and focussed onto the photocathode, and the use of lenses will cause any broadband pulse
to be chirped, potentially becoming longer than the electron bunch length that generated it. This is what we called
the dynamic point spread function of the SC [1]. It is measurable with the time resolved spectrum of the pulse whichshows the length and centroid of the pulse as function of
the spectrum. With the original refractive focussing optics
a non-linear chirp of 15 ps over 150 nm bandwidth with amaximum gradient of 140 fs/nm was measured. This chirp
induces a dynamic point spread function rms width of approximately 6.5 ps. Re-designing the focussing optics using mirrors reduced this chirp to less than 2 ps for the same
150 nm bandwidth, with a maximum gradient 30 fs/nm [2].
Control of the power and bandwidth of the pulse is a firststep, but with bunch lengths equal or less than the static
PSF width, a very accurate knowledge of the PSF is absolutely necessary to allow the deconvolution and so recover
the original bunch profile.
In this paper, we present which conditions are necessary
for the measurement of ps bunch lengths. We first present
the optical design of the Diagnostics beamline which allows the focussing of an un-chirped pulse with almost allthe available power from the bending magnet synchrotron
radiation onto the SC photocathode. Then we briefly introduce the Lucy-Richardson image deconvolution techniqueapplied to the SC images. Finally, before some concluding remarks we show measurement of ps bunch lengths after the optimisation and deconvolution technique presented
previously has been applied.

OPTICAL DESIGN
The improvement of the performance of the SC goes in
two steps. The first one is the re-design of the front focusing optics (FO), replacing the achromatic Nikkor lens by anassembly of mirrors (Fig. 1). The second one is a re-designof the beam transport from the source to the SC with theaim to transport the maximum available power. The new
design collimates the beam and reduces its transverse sizeat the same time, in order to transport the geometrical beamthrough the 30x50 mm aperture of the chicane in the radiation shield wall. A layout of the design is shown in Fig. 3.

Streak Camera Reflective Front Optics
The main objective of replacing the reflective FO of theSC by a refractive FO is to suppress the chirp induced by
the refraction index of the objective lens in the broad spectrum synchrotron radiation pulse. This way all the UVvisible power spectrum can be used for bunch length mea-

ISBN 978-3-95450-119-9
Longitudinal Diagnostics and Synchronization

1c 2012 by the respective authors — cc Creative Commons Attribution 3.0 (CC BY 3.0)
Copyright ○C.A. Thomas∗ , I. Martin, G. Rehm, Diamond Light Source, Oxfordshire, UK

TUPA42

Proceedings of IBIC2012, Tsukuba, Japan

Figure 1: Drawing of the reflective FO assembly. Mirror
M1 is parabolic concave, M2 is spherical convex, M3 isspherical concave, M4 is flat. The footprint of the assemblyis smaller than an A4 sheet of paper.

surement without the need of reducing the bandwidth andthus the power of the incoming pulse. The design of theFO has been done using ZEMAX software, looking at thefocussing performance of the assembly. The result showed
the possibility to focus the astigmatic synchrotron radiation beam in a 10x20 μm2 spot. The experimental verification is shown in Fig. 2, where the synchrotron radiation
is focussed on the SC with both FO. The PSF of the SC asshown in Table 1 is comparable in both cases.

0.

0.1

0.1

0.3

0.5

0.1

0.3

0.68

40

0.5

3

0.9
0.68
0.5
0.3

45

0.5
850

0.

0.6

55

0.1

0.3

0.1

60

0.1

165

0.1

Fast synchroscan sweep axis (pixels)

70

0.9
0.680.5
0.3

c 2012 by the respective authors — cc Creative Commons Attribution 3.0 (CC BY 3.0)
Copyright ○Table 1: PSF Width of the SC with the Refractive and theReflective Optics
Reflective Optics Refractive Optics
σ (pixel)
6.2
6.3
σ at 15 ps/mm (ps)
1.07
1.08
σ at 25 ps/mm (ps)
1.93
1.94
σ at 50 ps/mm (ps)
3.92
3.95

0.

13530304050607030

Slow sweep axis (pixels)

40506070

Slow sweep axis (pixels)

Figure 2: SC PSF measured with both refractive (left) andreflective FO (right).

Beamline Transport Design
The original design of the diagnostics visible beamline
is shown in Fig. 3. For several reasons including simplicityof alignment, robustness and cost, the design included only
flat mirrors of 50 mm diameter. The calculated geometricalfactor power loss, due to the divergence of the beam, was ofthe order of 20 to 30, and the additional loss through the reflectivity of the mirrors is 43% - each of the 8 mirrors withUV-enhanced Al coating providing 90% average reflectiv-

ity over the range 350-650 nm. In spite the power loss, theSC could be operated with the fastest sweep, recording images of a single turn, but only with the full power available.
In order to transport all the synchrotron radiation powerreflected by the first mirror (mirror [a] in Fig. 3), we designed a Z-fold mirror assembly, composed of a concave
parabolic and a convex spherical mirror ([I] and [II] in Fig.
3), which collimates the synchrotron radiation beam and reduces its transverse size by a factor ≈ 7. Also we changed
mirrors [b] and [c] for larger diameter ones (76 mm). Thisshould recover the geometrical loss from the original design, but may bring power loss through the additional two
reflections. For that we decided to change the coating todielectric multilayer, which provides an average 99% reflectivity over the bandwidth 400-750 nm. The total power
loss by reflection over 10 mirrors is expected to be 90%.
Measurements performed with and without the Z-fold assembly confirmed the prediction: with a filter at 550 nm
the power with the Z-fold assembly is approximatively 30
times larger than without the Z-fold. With this power, theSC can acquire images of a single bunch in single shot with
reduced bandwidth.

IMAGE DECONVOLUTION
In order to deconvolve the SC images, one needs to measure or to know perfectly the PSF of the instrument. We canmeasure the PSF at the time of the experiment by switching oﬀ the sweep electrodes of the SC as shown in Fig. 2.
Using the implementation of the Lucy-Richardson [3, 4]
algorithm in Matlab, we directly supply the measured PSF
to deconvolve the SC images. Not detailing the algorithm,
its main characteristics are that it is an iterative converging algorithm, and the noise on the image is assumed tobe Poisson distributed. These two features makes this algorithm appropriate to the deconvolution of SC images. A
demonstration is shown below where we acquired SC images of the Diamond bunches with a Low Alpha lattice, andin which we varied the momentum compaction factor from
0.8 to 6.8·10−6, expecting the bunch length to vary from
0.6 ps to 1.9 ps. The RF cavity voltage was kept constantat 3.4 MV. There were 900 bunches stored with an average
current of 1.6 μA.

BUNCH LENGTH MEASUREMENT
Knowing that the pulses with 400-650 nm bandwidth
have a 2 ps chirp, we restricted it to less than 0.3 ps by
selecting the 550 ± 20 nm bandwidth of the pulse to bemeasured with the SC. We measured the PSF by switching oﬀ the sweep electrodes of the SC. The image is similar to the one shown in Fig. 2. We set the momentum
compaction factor (α) and indirectly measured it by measuring the synchrotron frequency. For each value of α set,
10 SC image were acquired. The analysis performed on theSC images was, firstly, a Gaussian fit was performed on 13slices across each image, then each image was deconvolvedISBN 978-3-95450-119-92Longitudinal Diagnostics and Synchronization

Proceedings of IBIC2012, Tsukuba, Japan

TUPA4224time (ps)681012141620 40 60 80 100 20 40 60 80 100

50100Figure 4: SC images: Left, raw image with α ≈ 1.210−6;
Middle, same image but deconvolved; Right, SC PSF.
Horizontal axis represents the slow axis sweep set to 500
μs/mm. On each image a region of interest of 100x100
pixels is selected, equivalent to ≈ 17 ps x 600 μs.

frequency noise which can also excite randomly all thebunches through their energy spread. Another explanation
is of course the deconvolution didn’t converge to the expected value. However, from the many tests through simulation we performed with this deconvolution algorithm, wealways recovered the bunch length, even with very noisy
images. We also note other theoretical limits are placedon the minimum bunch length which have not been taken
into account. For instance, RF voltage phase noise throughdispersion can contribute to the longitudinal bunch distribution, the same way as the quantum excitation [5]. Pathlength dependance on the betatron motion could also contribute to the bunch length, as described in [6]. These possible contributions to the minimum bunch length need to beevaluated numerically, and perhaps also measured.
3bunch(ps)2.5σand a Gaussian fit performed on the same slices over eachdeconvolved image. An example of the devonvolved imageis shown in Fig. 4. The result of the Gaussian fit for all thevalues of α is shown in Fig. 5. An estimate of the bunch
length can be calculated using the quadratic subtraction of
the width given by the raw image Gaussian fit by the widthof the PSF, also fit with a Gaussian. In order to compare
the results, the theoretical near zero current bunch length isalso shown in the figure. One first notes that the raw image
is nearly a factor 2 larger than the theoretical value, and between 30% and 100% larger than the PSF width. The widthof the deconvolved images is closer to the theoretical nearzero current value, 10% to 20% for most of the measured
points, but gets 90% larger for the smallest values of α. The
bunch length obtained from the quadratic subtraction is ofcourse smaller than bunch length from the raw image, but
as observed it doesn’t come close to the deconvolved image
bunch lengths.
Several explanations can be brought to explain the difference to the theoretical predictions. The first one can berandom jitter of all the 900 bunches, due to synchrotron
oscillation of individual bunches. During all the time ofthe experiment, relatively strong synchrotron oscillation
were observed, which might support this first hypothesis. Another explanation might come from RF cavity high21.5
σ

raw imageσquadratic subtractionσdeconvolved

bunch

1bunchbunch

σbunch,00.5
01

2

3

4

−6

theory567

α (x 10 )Figure 5: Bunch length measured as function of α. The
dashed lines represent the standard deviation over the setof 10 images with 13 slices per image per measurement
point. The mean value of the bunch length is shown for
the fit of the raw images, the deconvolved images, and also
for the quadratic subtraction using the width of the PSF,
σPS F = 1.5 ps. The solid line is the expected theoreticalnear zero current bunch length value.

CONCLUDING REMARKS
We have shown the technique and setup of a streak camera to be able to measure bunch length of ≈ 1 ps. The pulse
to be measured should contain the most available power,

ISBN 978-3-95450-119-9
Longitudinal Diagnostics and Synchronization

3c 2012 by the respective authors — cc Creative Commons Attribution 3.0 (CC BY 3.0)
Copyright ○Figure 3: Design of the optical transport beamline. The total path length is ≈ 25 m. The original design includes mirrors[a] to [i], and the new design the addition of the Z-fold assembly, mirrors [I] and [II].

TUPA42

Proceedings of IBIC2012, Tsukuba, Japanbut also the minimum chirp induced by the material it has
traversed. To achieve this, we had to re-design the SC front
optics, but also the transport beamline. We then could afford to loose some power by filtering the pulse bandwidthin order to control the residual chirp. The resulting performance is a PSF width of 1 ps. Extremely small bunch
length in the 1 ps range could be measured with the SC
in the optimum condition, and also using a deconvolution
technique.

REFERENCES[1] C. A. Thomas, I. Martin, and G. Rehm. Investigation of extremely short beam longitudinal measurement with a streak
camera. In Proceedings of DIPAC 2009, pages 260–262, May2009.
[2] C. A. Thomas, I. Martin, and G. Rehm. Performance of astreak camera using reflective input optics. In Proceedings ofIPAC 2010, pages 1170–1173, May 2010.
[3] W. H. Richardson. Bayesian-based iterative method of imagerestoration. J. Opt. Soc. Am., 62(1):55–59, Jan 1972.
[4] L. B. Lucy. An iterative technique for the rectification of observed distributions. Astronomical Journal, 79:745, jun 1974.
[5] S. Daté, K. Soutome, and A. Ando. Equilibrium bunch lengthwith rf noises in electron storage rings. Nuclear Instruments
and Methods in Physics Research A, 355:199–207, feb 1995.

c 2012 by the respective authors — cc Creative Commons Attribution 3.0 (CC BY 3.0)
Copyright ○[6] Y. Shoji. Dependence of average path length betatron motion
in a storage ring. Phys. Rev. ST Accel. Beams, 8:094001, Sep
2005.

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