Design and simulation of interferometer for synchrotron radiation beam size measurement

Liangwei Sun; Qing Luo

doi:10.11884/HPLPB202133.210236

Journals >High Power Laser and Particle Beams >Volume 33 >Issue 8 >Page 084002 > Article

High Power Laser and Particle Beams
Vol. 33, Issue 8, 084002 (2021)

Design and simulation of interferometer for synchrotron radiation beam size measurement

Liangwei Sun and Qing Luo^*

Author Affiliations

National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hefei 230029, China

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DOI: 10.11884/HPLPB202133.210236 Cite this Article

Liangwei Sun, Qing Luo. Design and simulation of interferometer for synchrotron radiation beam size measurement[J]. High Power Laser and Particle Beams, 2021, 33(8): 084002 Copy Citation Text

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Fig. 1. Schematic diagram of interferometer

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Fig. 2. Schematic of the optical system of the interferometer

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Fig. 3. Change of beam size measurement error with coherence

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Fig. 4. Change of coherence with the slit separation

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Fig. 5. Schematic of RC focusing mirror

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Fig. 6. Relationship between the distance between the light source and the slit and the degree of coherence

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Fig. 7. Simulation diagram of interferometer

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Fig. 8. Vertical interference fringes and fitting graph (L=30 m, d=16 mm)

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Fig. 9. Horizontal interference fringes and fitting graph (L=40 m, d=18 mm)

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Fig. 10. Data points and fitted curve

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Fig. 11. Effect of intensity imbalance factor on coherence and beam size

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$ {L}_{{x}} $/m	$ {L}_{{y}} $/m	$ \lambda /\mathrm{n}\mathrm{m} $	$ \Delta \lambda $/nm	${w}_{{x} }\times {w}_{{y} }$		$ {d}_{{y}} $/mm	$ {d}_{{x}} $/mm	$ {f}_{1} $/mm	$ {f}_{2} $/mm
$ {L}_{{x}} $/m	$ {L}_{{y}} $/m	$ \lambda /\mathrm{n}\mathrm{m} $	$ \Delta \lambda $/nm	vertical	horizontal	$ {d}_{{y}} $/mm	$ {d}_{{x}} $/mm	$ {f}_{1} $/mm	$ {f}_{2} $/mm
40	30	500	10	$ 2\;\mathrm{m}\mathrm{m}\times 1\;\mathrm{m}\mathrm{m} $	$ 1\;\mathrm{m}\mathrm{m}\times 2\;\mathrm{m}\mathrm{m} $	16	18	1000	100

Table 1. Structure parameters of interferometer

	Airy disk radius/μm	RMS radius of spot diagram/μm	wave front error/ $ \lambda $	cut-off frequency of MTF/（lp·mm⁻¹）
original design	$ 56.55 $	$ 24.25 $	$ 0.207 $	$ 20.2 $
new design	$ 36.48 $	$ 0.05 $	$0.050$	$ 33.5 $

Table 2. Comparison of the results of interferometer optical path quality evaluation

	L/m	d/mm	$ \left\|\gamma \right\| $	$\sigma /{\text{μ}}\mathrm{m}$
vertical profile	30	16	0.56	160.7
	30	18	0.47	162.9
	30	20	0.40	161.5
horizontal profile	40	16	0.52	227.5
	40	18	0.40	239.4
	40	20	0.42	209.6

Table 3. Results of simulation

fitting value of visibility	true value of the degree of coherence	absolute error of visibility $ {u}_{\left\|\gamma \right\|} $	relative error of visibility $ {\delta }_{\left\|\gamma \right\|} $
$ {V}_{\rm{y}}=\dfrac{2\sqrt{\rho }}{1+\rho }\left\|{\gamma }_{\rm{y}}\right\| $	$ \left\|{\gamma }_{\rm{y}}\right\| $	$ \dfrac{2\sqrt{\rho }}{1+\rho }\left\|{\gamma }_{\rm{y}}\right\|-\left\|{\gamma }_{\rm{y}}\right\| $	$ \left(\dfrac{2\sqrt{\rho }}{1+\rho }\left\|{\gamma }_{\rm{y}}\right\|-\left\|{\gamma }_{\rm{y}}\right\|\right)/\left\|{\gamma }_{\rm{y}}\right\| $

Table 4. Error calculation table

L/mm	$ \lambda /\mathrm{n}\mathrm{m} $	d/mm	$ \left\|\gamma \right\| $
30000±10	500±10	16±0.01	0.6±0.06

Table 5. Parameters of vertical interferometer and measurement standard deviation

Liangwei Sun, Qing Luo. Design and simulation of interferometer for synchrotron radiation beam size measurement[J]. High Power Laser and Particle Beams, 2021, 33(8): 084002

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