Design and simulation of interferometer for synchrotron radiation beam size measurement

$ {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 2. Comparison of the results of interferometer optical path quality evaluation

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

	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 3. Results of simulation
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Table 3. Results of simulation
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 4. Error calculation table

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Table 4. Error calculation table

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 5. Parameters of vertical interferometer and measurement standard deviation
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Table 5. Parameters of vertical interferometer and measurement standard deviation
L/mm $ \lambda /\mathrm{n}\mathrm{m} $ d/mm $ \left|\gamma \right| $
30000±10 500±10 16±0.01 0.6±0.06

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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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