We present the recent developments of a study aimed at measuring the transverse beam profile using the Heterodyne Near Field Speckles (HNFS) method. The HNFS technique works by illuminating a suspension of Brownian nanoparticles with synchrotron radiation and studying the resulting interference pattern. The transverse coherence of the source, and therefore, under the conditions of validity of the Van Cittert and Zernike theorem, the transverse electron beam size is retrieved from the interference between the transmitted beam and the spherical waves scattered by each nanoparticle. We here describe the fundamentals of this technique, as well as the recent experimental results obtained with 12 keV undulator radiation at the NCD beamline at the ALBA synchrotron. The applicability of such a technique for future accelerators (e.g. CLIC or FCC) is also discussed

A.A. Nosych

B. Paroli

C.S. Kamma-Lorger

F. Roncarolo

G. Trad

M. Potenza

M. Siano

S. Mazzoni

U. Iriso

English

Mazzoni S.

Roncarolo F.

Trad G.

Paroli B.

Potenza M.

Siano M.

Iriso U.

Kamma-Lorger C. S.

Nosych A. A.

AIR Universita degli studi di Milano

PROGRESS ON TRANSVERSE BEAM PROFILE MEASUREMENT USING THE HETERODYNE NEAR FIELD SPECKLES METHOD AT ALBA S. Mazzoni, F. Roncarolo, G. Trad, CERN, Geneva, Switzerland B. Paroli, M. Potenza, M. Siano, Università degli Studi di Milano, Milan, Italy U. Iriso, C. S. Kamma-Lorger, A. A. Nosych, ALBA, Barcelona, Spain Abstract We present the recent developments of a study aimed at measuring the transverse beam profile using the Hetero-dyne Near Field Speckles (HNFS) method. The HNFS technique works by illuminating a suspension of Brownian nanoparticles with synchrotron radiation and studying the resulting interference pattern. The transverse coherence of the source, and therefore, under the conditions of validity of the Van Cittert and Zernike theorem,  the transverse electron beam size is retrieved from the interference be-tween the transmitted beam and the spherical waves scat-tered by each nanoparticle. We here describe the funda-mentals of this technique, as well as the recent experi-mental results obtained with 12 keV undulator radiation at the NCD beamline at the ALBA synchrotron. The applica-bility of such a technique for future accelerators (e.g. CLIC or FCC) is also discussed.  INTRODUCTION The HNFS method is a powerful, yet conceptually sim-ple and inexpensive method to measure the transverse co-herence properties of a light source. It is described mathe-matically by the Complex Coherence Factor (CCF):  𝝁ሺ𝒙𝟏, 𝒙𝟐ሻ ൌ  〈𝑬ሺ𝒙𝟏,௧ሻ𝑬∗ሺ𝒙𝟐,௧ሻ〉ሾூభூమሿభ/మ     (1)  where 𝑬ሺ𝒙𝒊, 𝑡ሻ is the electric field at a given point in space and time, 𝐼௜ ൌ 〈𝑬ሺ𝒙𝒊, 𝑡ሻ𝑬∗ሺ𝒙𝒊, 𝑡ሻ〉 is the intensity of the electric field and 〈… 〉 denotes time averaging. The abil-ity to measure the CCF of a light source is of interest for beam diagnostics as, under the conditions of validity of the Van Cittert and Zernike (VCZ) theorem [1], the CCF is the Fourier transform of the source intensity distribution. As a consequence, when Synchrotron Radiation (SR) is used as the light source, a measurement of its transverse coherence allows the transverse profile of the beam at the emission plane to be retrieved.  The traditional method for measuring the beam size through the CCF is Young’s two slit interferometer [2], where SR impinges on a pair of narrow slits forming an interference pattern. In this case, the CCF is retrieved from the visibility V of the fringes:  𝑉 ≝ ூ೘ೌೣିூ೘೔೙ூ೘ೌೣାூ೘೔೙ ൌ  ଶඥூభூమூభାூమ |𝝁𝟏𝟐|   (2) where 𝐼௜ is the time averaged intensity at slit i and 𝝁𝟏𝟐is a short form for the CCF as defined in Eq. 1. The HNFS method is an alternative to Young’s double slit method that offers some potential advantages. HNFS does not require the almost completely blocking of SR radiation as in the Young’s slits configuration, and it does not require the challenging fabrication of narrow slits in a medium that must be opaque to X-rays. While HNFS is known a well-known particle sizing technique, it has never, to our knowledge, been used for beam size monitoring in particle accelerators. We will report of the status of a proof of con-cept experiment at ALBA to measure beam size using X-ray radiation.  THE HNFS TECHNIQUE A typical HNFS setup using X-ray radiation (see Fig. 1) is composed of a suspension of nanoparticles in water po-sitioned at a distance 𝑧ଵ from the source, which can be a dipole or insertion device. The transmitted and scattered fields propagate for a distance 𝑧ଶ where they impinge on a YAG scintillator that produces visible light at 550 nm with the same intensity modulations as the incident X-ray radi-ation. The visible signal is extracted from the X-ray beam path by means of a mirror at 45º. A highly magnified image of the YAG screen is then produced on a sensor by means of a microscope objective.   Figure 1: A typical HNFS setup for X-rays (shown in red). a) target composed of a suspension of nanoparticles in wa-ter. b) YAG screen with visible light shown in green. c) microscope objective. d) sensor Heterodyne Near Field Scattering (HNFS) is an interfer-ometric technique where the incident light beam 𝑬𝟎 im-pinging on the target generates a large number of weak spherical waves (𝑬𝒔, |𝑬𝒔| ≪ |𝑬𝟎|) that interfere with the transmitted field. The resulting intensity distribution is known as a speckle field and it is recorded onto the scintil-lator plane at a distance 𝑧ଶ downstream the scattering sam-ple.  The coherence properties of the source are determined from analysis of the stochastic interferogram formed at the scintillator plane with the resulting light intensity distribu-tion given by:  𝐼 ൌ  |𝑬𝟎 ൅ 𝑬𝒔|ଶ ൌ  |𝑬𝟎|ଶ ൅ 2𝑅𝑒|𝑬𝟎∗𝐸௦|  (3) 7th Int. Beam Instrumentation Conf. IBIC2018, Shanghai, China JACoW PublishingISBN: 978-3-95450-201-1 doi:10.18429/JACoW-IBIC2018-THOA03THOA03538ContentfromthisworkmaybeusedunderthetermsoftheCCBY3.0licence(©2018).Anydistributionofthisworkmustmaintainattributiontotheauthor(s),titleofthework,publisher,andDOI.6. Transverse profiles and emittance monitorswhere the multiple scattering term |𝑬𝒔|ଶ is neglected be-cause of the weak scattering. The second term of Eq. 3 is reminiscent of the CCF (Eq. 1), and represents the sum of the many interference patterns generated by the overlap of the transmitted wave and the weak spherical waves gener-ated by single nanoparticles. However, due to the random position of the nanoparticles, the intensity 𝐼 results in a sto-chastic speckle field where the information about the single interferogram is lost.   Figure 2. Principle of the HNFS method. The single parti-cle simulated interference pattern (a) is stochastically over-lapped for a large (b) and very large (c) number of nano-particles, resulting in a speckle field. The single particle interferogram is retrieved from the square modulus of the 2D Fourier transform This can be seen in Fig. 2, where the simulated interfer-ence pattern resulting from the interference of a single par-ticle (spherical wave) and a plane wave is shown in (a). When the pattern is overlapped according to the random distribution of a very large number of particles, infor-mation about the single interferogram is lost. However, by computing the square modulus of the two-dimensional Fourier transform of the image 𝐼ሺ𝑞ሻ, the square modulus of the CCF can be retrieved in the reciprocal space. It can be shown [3] that in the reciprocal space with coordinates 𝑞 ൌ |𝒒| ൌ 2𝑘 sin ణଶ ൎ 𝑘𝜗 (k being the radiation wavenumber, 𝜗 the scattering angle):   𝐼ሺ𝑞ሻ ൌ  |𝝁ሺ𝑞ሻ|ଶ𝑇ሺ𝑞ሻ𝐻ሺ𝑞ሻ ൅ 𝑃ሺ𝑞ሻ  (4)  where 𝑇ሺ𝑞ሻ is a single particle interferogram, 𝐻ሺ𝑞ሻ com-bines the Instrument Transfer Function (ITF) – mainly the phosphor and particle form factor (the latter being essen-tially a constant in our case), and 𝑃ሺ𝑞ሻ the shotnoise and other spurious contributions. Since 𝑇ሺ𝑞ሻ is known theoret-ically quite precisely and the other terms can be measured, the 2D power spectrum of the image yields the square mod-ulus of the CCF expressed in reciprocal space. The relation between Eq. 4 and Eq. 1 is given by the spatial scaling Δ𝑥ሺ𝑞ሻ ൌ  𝑞𝑧 𝑘ଶ⁄  [3, 4] (in Eq. 1, we assume that the radia-tion CCF depends only on Δ𝑥 ൌ  𝑥ଵ െ 𝑥ଶ). Then, a simple two dimensional Fourier transform of the square root of 𝐼ሺΔሺ𝑥ሺ𝑞ሻሻ allows the two dimensional intensity distribu-tion of the source to be recovered.  THE EXPERIMENTAL SETUP An HNFS setup has been installed in the NCD-SWEET beamline at ALBA (see Table 1).    Table 1: NCD-SWEET Beamline Parameters Source type In vacuum undulator Period 21.3 mm Number of periods 92 Gap 5.86 mm Resonant energy 12.4 KeV Beam current 150 mA Bandpass 3.1x10-4 (@ 10 keV) SR source size (RMS) 131x8 m2 (HxV)  A channel cut silicon monochromator is positioned 22 m away from the centre of the in-vacuum undulator. The sam-ple position can be adjusted to be between 30 and 33 metres from the source, and was fixed at 32.5 m for the measure-ment here presented. The target is composed of a series of capillaries of 1.5 mm diameter positioned on a motorised stage. The capillaries are filled with a suspension of silica nanoparticles of 500 nm of diameter, with a 10% volume fraction concentration. A reference capillary filled with dis-tilled water without nanoparticles is also present. The scin-tillator is a YAG:Ce crystal of 0.1 mm thickness, mounted on a long translation stage that allows the distance 𝑧ଶ(see Fig.1). The measurements here presented were performed at a distance 𝑧ଶ ൌ 252 mm The optical system is mounted on the same YAG support and is composed of a 45º mirror, and a 20X microscope objective that forms the image on a Basler scA1300-32gc CCD camera.   RESULTS AND DISCUSSION The typical result of a 2D power spectrum obtained through HNFS for a 12.4 keV X-ray beam at NCD-SWEET is shown in Fig. 3. The interference is more prominent along the direction with the larger transverse coherence length (vertical), as expected from theory [4, 5]. This can be understood from the beam shape (smaller size in the ver-tical direction) and the fact that there exist a Fourier trans-form relation between the transverse intensity of the source and the far-field transverse coherence. The poor horizontal coherence induces an almost complete lack of single parti-cle interferogram fringes along the corresponding direc-tion, as can be seen in Fig. 3b and 3c. For completeness the horizontal and vertical profile of the shot-noise contribu-tion, can be inferred from the power spectrum of the capil-lary filled with only distilled water.  Due to limitations in the set-up, it is not possible to ac-cess sample-YAG distances smaller than a few cm where we would be sensitive to the phosphor Transfer Function (TF), and where the power spectrum would be perfectly symmetric [5], before coherence effects start to be domi-nant.  7th Int. Beam Instrumentation Conf. IBIC2018, Shanghai, China JACoW PublishingISBN: 978-3-95450-201-1 doi:10.18429/JACoW-IBIC2018-THOA036. Transverse profiles and emittance monitorsTHOA03539ContentfromthisworkmaybeusedunderthetermsoftheCCBY3.0licence(©2018).Anydistributionofthisworkmustmaintainattributiontotheauthor(s),titleofthework,publisher,andDOI. Figure 3: Two dimensional power spectrum of the speckles field (a) with its horizontal (b) and vertical (c) profiles (or-ange curves). Surveying the literature [6,7], the transfer function of crystal scintillators is measured to be a negative exponen-tial 𝐻ሺ𝑞ሻ ൌ  𝐻଴ expሺെ 𝑞 𝑞௦௖௜௡௧⁄ ሻ, with 𝑞௦௖௜௡௧ ranging from 0.6 um-1 [6] to 0.8 um-1 [7]. If we assume a similar TF for our YAG phosphor then we can produce corrected plots for different values of 𝑞௦௖௜௡௧ (0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0). Results for values 0.7-1 are reported in Fig. 4 for the verti-cal direction.   Figure 4: Vertical profiles corrected with an exponential  phosphor transfer function 𝐻ሺ𝑞ሻ for four different values of the characteristic exponential decay, 𝑞௦௖௜௡௧ . Horizontal profiles are not shown for brevity If we had truly measured the H(q) of the optics, the re-duced curves T(q) |𝝁ሺ𝑞ሻ|ଶ would be normalized to a max-imum value of 1 at q=0. Here, the first Talbot maximum appears at roughly q=0.8? m-1, corresponding to a trans-verse displacement Δ𝑟 ൌ  𝑞𝑧ଶ 𝑘⁄  = 4 m. This value lies well within the extent of the coherence in the vertical di-rection, meaning that the corresponding curves T(q) |𝝁ሺ𝑞ሻ|ଶ along the vertical direction would have a value of 1 in normalized units. The same analysis applies to horizontal profiles. We thus normalize the corrected hor-izontal and vertical profiles according to the value of the first Talbot maximum along the vertical direction  𝐼௖௢௥௥ሺ𝑞ሻ ൌ  ଵூబூሺ௤ሻுሺ௤ሻ  ∝ |𝝁ሺ𝑞ሻ|ଶ𝑇ሺ𝑞ሻ  (5)  We do not consider the three power spectra (correspond-ing to 𝑞௦௖௜௡௧ = 0.4, 0.5, 0.6) since the normalised coherence function of the radiation exceeds 1, an unphysical result that points to an incorrect value of 𝑞௦௖௜௡௧. Let us discuss separately the horizontal and vertical pro-files. Fig. 5 shows the normalized horizontal profile 𝐼௖௢௥௥ሺ𝑞ሻ, together with a fitting function which assumes a Gaussian CCF 𝜇ሺ𝑞ሻ ൌ exp െሺ𝑞ଶ 2𝜎ଶ⁄ ሻ where 𝜎, express-ing the width of 𝜇ሺ𝑞ሻ depends on the distance 𝑧ଶ [5] (252 mm in our case – see Fig. 1). We define the transverse co-herence length as   𝜎௖௢௛ ൌ  න |𝜇ሺΔ𝑟ሻ|ଶ𝑑Δ𝑟ାஶିஶ  according to [1], where Δ𝑟 is a radial transverse displace-ment from the optical axis defined in the previous para-graph. Under Gaussian approximation, 𝜎 can be related to the transverse coherence length of the source as measured at the target plane:  𝜎௖௢௛ ൌ √గ௞ 𝑧ଶ𝜎   (6)  Figure 5: Horizontal profile of 𝐼௖௢௥௥ሺ𝑞ሻ with a 𝑞௦௖௜௡௧ = 0.7 m fitted with the single particle interferogram 𝑇ሺ𝑞ሻ mod-ulated by a Gaussian CCF In principle, our “manual” data reduction should lead to a value of 𝜎௖௢௛  which is related to the choice of 𝜎௦௖௜௡௧ used to calculate the corrected intensity. We find however that 𝜎௖௢௛ shows a very weak dependence on the un-known 𝑞௦௖௜௡௧ , its value changing by only 2% for values of 𝑞௦௖௜௡௧ from 0.7 – 1.0. This means that the envelope of the single particle interferogram fringes along the horizontal direction is entirely dictated by the coherence properties of the source. We therefore consider  𝑞௦௖௜௡௧ = 0.7 m-1, for which we obtain   7th Int. Beam Instrumentation Conf. IBIC2018, Shanghai, China JACoW PublishingISBN: 978-3-95450-201-1 doi:10.18429/JACoW-IBIC2018-THOA03THOA03540ContentfromthisworkmaybeusedunderthetermsoftheCCBY3.0licence(©2018).Anydistributionofthisworkmustmaintainattributiontotheauthor(s),titleofthework,publisher,andDOI.6. Transverse profiles and emittance monitors𝜎௛௖௢௛ ൌ 7.6 േ 0.3 m.   (7)  This value is in fair agreement with the expected results from simulations assuming perfect resonance conditions and no energy spread effects [4], for which 𝜎௛௖௢௛= 7.1 m. Under the conditions of validity of the VCZ theorem, we finally retrieve the transverse horizontal size of the source as 𝜎௛௦௜௭௘ ൌ √గ௞௭భఙ೓೎೚೓ ൌ 111 േ 10 m  (8)  which is in fair agreement with the expected value of 131 m.  Figure 6: Vertical profile of 𝐼௖௢௥௥ሺ𝑞ሻ for 𝑞௦௖௜௡௧ = 0.7 m. A similar procedure cannot be applied to the vertical pro-files since the envelope of the single particle interferogram is not Gaussian but rather exhibits a sort of echo at q=3 m-1, as shown in Fig 6 for the case of 𝑞௦௖௜௡௧ = 0.7 m . Here the dashed red line is drawn simply to guide the eye. Such a peculiar behavior is not predicted by theory for free-space propagation [4] and might be ascribed to “de-fective” optics, as was similarly reported in previous ob-servations [3]. In particular it can be caused by the mono-chromator, whose surface is known to be corrugated. Fur-ther measurements are however needed in order to under-stand this peculiar modulation in the vertical envelope of the Talbot oscillations. Following [3], the coherence func-tion could be given by the overall envelope curve of such echoes. The 𝜎 of such curves ranges from 3 to 7 m-1, cor-responding to a transverse beam size 𝜎௩௦௜௭௘ between 17 and 38 m in the vertical direction, a range of values that is quite far from the expected 8 m. This could be due to a poor correction for the phosphor TF, which is expected to influence the vertical power spectrum much more than the horizontal one [5]. Beam energy spread might also affect the coherence properties of SR from an undulator in the vertical direction, as mentioned in [4]. CONCLUSIONS We have reported recent measurements of transverse co-herence length of a 12.4 keV X-rays beam at the NCD-SWEET beamline at ALBA. Under the conditions of valid-ity of the VCZ theorem, the transverse beam size of the source was determined. The horizontal beam size is in good agreement with the expected value of 131 m, while the vertical is affected by large experimental uncertainties that result in a value from 2 to 5 times larger than the expected 8 m. The cause of such discrepancy is still under investi-gation, but is believed to be partly related to the approxi-mate knowledge of the phosphor transfer function. HNFS is still a relatively new technique in accelerator beam diagnostics using X-rays. Our ongoing studies aim at understand its experimental advantages and limitations when compared to the more established two-slit interfer-ometer. In particular, we plan to optimise the HNFS target to produce a high contrast speckles field for an improved measurement of the coherence length and beam size. This could be achieved by using different nanoparticles, or al-ternatives to a suspension like masks or membranes. Future work also aims at testing HNFS on dipole SR with possible applications on future machines such as the Future Circular Collider.  REFERENCES [1] J. W. Goodman, Statistical Optics. New York, NY, USA, John Wiley, 2000 [2] T. Mitsuhashi, “Beam Profile Measurement by SR Interfer-ometers”, in Proceedings of the Joint U.S.-CERN-Japan- Russia School on Particle Accelerators, Montreux, Switzer-land, 1998 [3] M. D. Alaimo, M. A. C. Potenza, M. Manfredda, G. Geloni, M. Sztucki, T. Narayanan, and M. Giglio, “Probing the transverse coherence of an undulator X-ray beam using brownian nanoparticles”, Phys. Rev. Lett. Vol. 103, p. 194805, 2009 [5] G. Geloni, E. Saldin, E. Schneidmiller, and M. Yurkov, “Transverse coherence properties of X-ray beams in third-generation sources”, Nucl. Instrum. Methods Phys. Res., Sect. A, vol 588, p. 463, 2008 [4] M. Siano, B. Paroli, M. A. C. Potenza, U. Iriso, A. A. Nosych, L. Torino, S. Mazzoni, G. Trad, A. N. Goldblatt, “Characterizing temporal coherence of visible synchrotron radiation with heterodyne near field speckles”, Phys. Rev. Accel. Beams, vol. 20, p. 110702, 2017. [6] R. Cerbino, L. Peverini, M. A. C. Potenza, A. Robert, P. Bosecke, and M. Giglio, “X-ray scattering information ob-tained from near-field speckle”, Nat. Phys., vol 4, p. 238 2008, Supplementary Materials.  [7] Y. Kashyap, H. Wang, and K. Sawhney, “Two-dimensional transverse coherence measurements of hard X-ray beams using near-field speckle”, Phys. Rev. A, vol. 92, p. 033842 2015. 7th Int. Beam Instrumentation Conf. IBIC2018, Shanghai, China JACoW PublishingISBN: 978-3-95450-201-1 doi:10.18429/JACoW-IBIC2018-THOA036. Transverse profiles and emittance monitorsTHOA03541ContentfromthisworkmaybeusedunderthetermsoftheCCBY3.0licence(©2018).Anydistributionofthisworkmustmaintainattributiontotheauthor(s),titleofthework,publisher,andDOI.

Progress on transverse beam profile measurement using the heterodyne near field speckles method at Alba

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Progress on transverse beam profile measurement using the heterodyne near field speckles method at Alba

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