Transverse beam profile reconstruction using synchrotron radiation interferometry

Transverse beam size measurements in new generation of synchrotron light sources is a challenging task due to their characteristic small beam emittances and low couplings. Since the late 1990s, synchrotron radiation interferometry (SRI) has been used in many accelerators to measure the beam size through the analysis of the spatial coherence of the synchrotron light. However, the standard SRI using a double-aperture system provides the beam size projection in a given direction. For this reason, the beam shape is not fully characterized because information about possible transverse beam tilts is not determined. In this report, we describe a technique to fully reconstruct the transverse beam profile based on a rotating double-pinhole mask, together with experimental results obtained at ALBA under different beam couplings. We also discuss how this method allows us to infer ultrasmall beam sizes in case of limitations of the standard SRI.

Figure 1

Beam tilt angle for three different settings of the skew quads at ALBA in Sector 1.

Figure 2

Sketch ALBA diagnostic beamline, Xanadu. The synchrotron radiation beam is selected by a photon shutter located at 1.64 m from the source point. The in-vacuum extraction mirror is located 7 m downstream, 7 mm above the orbit plane. Seven other mirrors (already out of vacuum) bring the light from the tunnel to the Xanadu optical table.

Figure 3

Sketch of the SRI experimental setup: the synchrotron radiation (SR) produced by the beam passes through the double pinhole system and is imaged through a lens and an objective ocular to the CCD. The radiation polarization and the wavelength are selected through a polarizer (Pol.) and a color filter (Col. Filt.).

Figure 4

Interferograms at minimum and maximum coupling used to measure the vertical beam size, and the data analysis to obtain the results. Black dots represent the projection of the central slice of the interferogram, while the black line is obtained fitting the data using Eq. (1). Note the different visibilities leading to different beam sizes.

Figure 5

Interferograms rotated at 0°, 45°, 90°, and 135° to measure the size of the projection of the beam along the respective axis. White lines are oriented in the direction of the pinholes axis, rotated at angle $\theta$, and represent the slices selected for the fitting process.

Figure 6

Sketch of the transverse beam shape reconstruction using tangent lines calculated according to Eq. (6). Black lines represent the laboratory reference system, black dashed lines are drawn considering $\theta =0°$ and $\theta =90°$, and provide the projection along the $x$ and $y$ axis, ${\sigma }_x$ and ${\sigma }_y$. The red solid line represents the rotation direction of the double-pinhole axis of a generic angle $\theta$, while red dashed lines are the tangent lines calculated taking into account ${\sigma }_p$ (the distance PQ in the drawing).

Figure 7

In the first plot the full reconstruction of the transverse beam shape using tangents lines, in the second only the lines obtained by the projections at 0°, 45°, 90°, and 135° are considered. The red ellipses are drawn using the results of the fit presented in Fig. 9.

Figure 8

General tilted ellipse: $(x,y)$ is the laboratory reference system (in black), $(u,v)$ refers to the reference system in which the ellipse is not tilted (in red), while $(p,q)$ refers to the one rotated by an angle $\theta$ with respect to the laboratory system (in blue).

Figure 9

Beam projection as a function of the pinhole rotation angle $\theta$. In the first plot all the 40 measurements, while in the second the projections at 0°, 45°, 90°, and 135° are presented. The third plot (black line) is the difference between the fits obtained with 40 and 4 points as a percentage of the 40 points curve.

Figure 10

Mean value of the difference between the curve obtained by fitting 200 projections and the one fitting only 4 projections as a percentage of the first.

Figure 11

Fit of projections taken at 0°, 45°, 90°, and 135° to reconstruct the ellipse taken at different couplings ($K$). Black dots are real data, while the red lines are obtained by fitting.

Figure 12

Reconstruction of the beam at different couplings. Black lines are calculated from real data while the red ellipse is drawn from the result of the fit.

Figure 13

Comparison of the SRI reconstruction with the results from LOCO for the horizontal and vertical beam size and the beam tilt at the Xanadu location.

Figure 14

Simulated $5\mu \mathrm{m}$ vertical beam size reconstruction using the rotated SRI technique using SRW. Black dots are the SRW simulated data, the error bar is fixed to $1.5\mu \mathrm{m}$, and red line is the result of the fit using Eq. (12). The black cross indicates the result from the fit for the ${\sigma }_v$.

Figure 15

Results for $2\mu \mathrm{m}$, $5\mu \mathrm{m}$, $7\mu \mathrm{m}$, and $10\mu \mathrm{m}$ beam size reconstruction for SRI beam size measurement statistical errors of $0.5\mu \mathrm{m}$, $1\mu \mathrm{m}$, $1.5\mu \mathrm{m}$, and $2\mu \mathrm{m}$. Black dots are the obtained values, the error bar is given by the standard deviation of 100 smeared reconstructions, the black dashed line is the theoretical value, while the red dashed line is the result obtained performing rotating SRI SRW simulations.