Linear iterative near-field phase retrieval (LIPR) for dual-energy x-ray imaging and material discrimination

Heyang (Thomas) Li; Andrew M. Kingston; Glenn R. Myers; Levi Beeching; Adrian P. Sheppard

doi:10.1364/JOSAA.35.000A30

Journal of the Optical Society of America A
Vol. 35,
Issue 1,
pp. A30-A39
(2018)
•https://doi.org/10.1364/JOSAA.35.000A30

Linear iterative near-field phase retrieval (LIPR) for dual-energy x-ray imaging and material discrimination

Heyang (Thomas) Li, Andrew M. Kingston, Glenn R. Myers, Levi Beeching, and Adrian P. Sheppard

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Heyang (Thomas) Li, Andrew M. Kingston, Glenn R. Myers, Levi Beeching, and Adrian P. Sheppard, "Linear iterative near-field phase retrieval (LIPR) for dual-energy x-ray imaging and material discrimination," J. Opt. Soc. Am. A 35, A30-A39 (2018)

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Abstract

Near-field x-ray refraction (phase) contrast is unavoidable in many lab-based micro-CT imaging systems. Quantitative analysis of x-ray refraction (a.k.a. phase retrieval) is in general an under-constrained problem. Regularizing assumptions may not hold true for interesting samples; popular single-material methods are inappropriate for heterogeneous samples, leading to undesired blurring and/or over-sharpening. In this paper, we constrain and solve the phase-retrieval problem for heterogeneous objects, using the Alvarez–Macovski model for x-ray attenuation. Under this assumption we neglect Rayleigh scattering and pair production, considering only Compton scattering and the photoelectric effect. We formulate and test the resulting method to extract the material properties of density and atomic number from single-distance, dual-energy imaging of both strongly and weakly attenuating multi-material objects with polychromatic x-ray spectra. Simulation and experimental data are used to compare our proposed method with the Paganin single-material phase-retrieval algorithm, and an innovative interpretation of the data-constrained modeling phase-retrieval technique.

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Equations (14)

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Method	L2 Error in $C$ (Edges 1, 2, 3, and 5) $(\times 10^{- 2} mg / {mm}^{2})$				L2 Error in $P$ (Edges 1, 2, 3, and 5) $(\times 10^{2} mg \cdot Z^{3} / {mm}^{2})$
No Ret.	149	58	94	255	37	16	24	41
Sing. mat.	18	50	43	39	7	148	140	24
DCM	15	6	9	21	43	18	28	56
LIPR	3	1	2	8	8	6	8	5

Method	L2 Error in $C$ (Edges 1, 2, 3, and 5) $(\times 10^{- 2} mg / {mm}^{2})$				L2 Error in $P$ (Edges 1, 2, 3, and 5) $(\times 10^{2} mg \cdot Z^{3} / {mm}^{2})$
No Ret.	231	191	196	290	41	24	29	45
Sing. mat.	62	78	74	70	8	148	140	80
PC-DCM	66	66	59	68	50	29	35	60
LIPR	68	67	63	61	11	12	11	19

Method	L2 Error in $C$ (Edges 1, 2, 3, and 5) $(\times 10^{- 2} mg / {mm}^{2})$				L2 Error in $P$ (Edges 1, 2, 3, and 5) $(\times 10^{2} mg \cdot Z^{3} / {mm}^{2})$
No Ret.	149	58	94	255	37	16	24	41
Sing. mat.	18	50	43	39	7	148	140	24
DCM	15	6	9	21	43	18	28	56
LIPR	3	1	2	8	8	6	8	5

Method	L2 Error in $C$ (Edges 1, 2, 3, and 5) $(\times 10^{- 2} mg / {mm}^{2})$				L2 Error in $P$ (Edges 1, 2, 3, and 5) $(\times 10^{2} mg \cdot Z^{3} / {mm}^{2})$
No Ret.	231	191	196	290	41	24	29	45
Sing. mat.	62	78	74	70	8	148	140	80
PC-DCM	66	66	59	68	50	29	35	60
LIPR	68	67	63	61	11	12	11	19

Abstract

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Equations (14)

Journal of the Optical Society of America A