Influence on imaging performance and evaluation of Wolter-I type mandrel fabrication errors

Kaiji Wu; Fei Ding; Yanji Yang; Duo Li; Zheng Qiao; Pengfei Qiang; Bo Wang

doi:10.1364/AO.460960

Applied Optics
Vol. 61,
Issue 22,
pp. 6617-6626
(2022)
•https://doi.org/10.1364/AO.460960

Influence on imaging performance and evaluation of Wolter-I type mandrel fabrication errors

Kaiji Wu, Fei Ding, Yanji Yang, Duo Li, Zheng Qiao, Pengfei Qiang, and Bo Wang

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Kaiji Wu, Fei Ding, Yanji Yang, Duo Li, Zheng Qiao, Pengfei Qiang, and Bo Wang, "Influence on imaging performance and evaluation of Wolter-I type mandrel fabrication errors," Appl. Opt. 61, 6617-6626 (2022)

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Abstract

The electroforming replication process has been widely used in the fabrication of nested x-ray telescopes. The imaging performance of the mirrors is determined largely by the shape accuracy of the mandrels. To predict the imaging performance of mirrors replicated from mandrels with different parameter and fabrication errors, a special Monte Carlo ray tracing model is established and verified by experiments. Then, based on ray tracing numerical calculation, the influence of each major fabrication error is discussed. Furthermore, according to the results obtained by the simulation of slope error, a method for evaluating the relationship between the mandrel full-band errors and imaging quality is proposed and then verified by experiments. The results show that the power spectral density (PSD) reference given by the method can well reflect the quality of the mandrels, and guide the fabrication process.

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Error type	Source	Magnitude (µm)
Nominal radius	Tool setting	$\pm 1$
error	Blank size, cutting thickness control	$\pm 30$
Roundness	Spindle rotation accuracy	PV 0.1
	Full-size polishing is uneven in azimuthal direction	$< P V 1$
Taper error	Parallelism of $z$ axis and spindle	$< \pm 10$
	Perpendicularity error of $x z$ axis	$< \pm 1$
Axial slope error	Generatrix error, residual medium, and high frequency error after polishing	—

	Inner Radius (mm)
Mirror Number	Front ( $z = 1750$ )	Middle ( $z = 1600$ )	Rear ( $z = 1450$ )	Grazing Incidence Angle (°)
#1	178.264	174.241	161.960	1.55
#27	83.868	81.970	76.183	0.73
#54	38.138	37.274	34.642	0.33

	HPD Test Results (^′′)
Mirror Number	Blu-Ray (450 nm)	X-Ray (1.25 keV, 1 nm)	Mandrel Status
#17	24.9	26.5	Finished
#18	27.6	27.8	Finished
#24	47.1	80.1	Pre-polished

Error type	Source	Magnitude (µm)
Nominal radius	Tool setting	$\pm 1$
error	Blank size, cutting thickness control	$\pm 30$
Roundness	Spindle rotation accuracy	PV 0.1
	Full-size polishing is uneven in azimuthal direction	$< P V 1$
Taper error	Parallelism of $z$ axis and spindle	$< \pm 10$
	Perpendicularity error of $x z$ axis	$< \pm 1$
Axial slope error	Generatrix error, residual medium, and high frequency error after polishing	—

	Inner Radius (mm)
Mirror Number	Front ( $z = 1750$ )	Middle ( $z = 1600$ )	Rear ( $z = 1450$ )	Grazing Incidence Angle (°)
#1	178.264	174.241	161.960	1.55
#27	83.868	81.970	76.183	0.73
#54	38.138	37.274	34.642	0.33

Abstract

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Applied Optics