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Calibration method for microscale stereo X-ray imaging system

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Abstract

Calibration of an X-ray imaging system involves estimation of the 3D geometrical configuration of the system components. Here, we propose a calibration method for stereo X-ray imaging systems, which capture two X-ray images at two orthogonal positions. The calibration parameters include the relation between image coordinates and world coordinates, the relative 3D positions of the X-ray source and detector, and the rotational axis of the stereo X-ray system. The average error of the proposed calibration method was determined to be approximately 0.03% in evaluation tests.

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Abbreviations

Π f :

front plane near the X-ray source of the two calibration planes of the calibration cube

Π b :

back plane in contact with the detector of the two calibration planes of the calibration cube

cp f,i (cp b,i ):

calibration points on Π f (Π b ) (i=1,...,n)

cp′ f,i :

cp f,i ’s projected points on the detector

l i :

projecting lines passing both cp f,i and cp′ f,i

State 1 :

State of stereo X-ray system before rotating 90°

State 2 :

State of stereo X-ray system after rotating 90°

I 1 (I 2 ):

X-ray image at State 1 (State 2)

CF :

calibration frame

fp i :

calibration points of CF (i=1,...,n)

fp 1,i :

image coordinates of fp i in actual radiograph I 1

fp′ 1,i :

image coordinates computed by projecting fp i onto the detector at any assumed position of CF

Ω:

rotating axis of stereo X-ray system

Ω* dir (Ω* pivot ):

direction vector (pivot point) of estimated Ω

t f * (r f *):

estimated translations (rotations) of CF

I′ 2 :

X-ray image obtained from hypothesized X-ray system

fp′ 2,i :

image coordinates calculated after projecting fp i in I′ 2

fp 2,i :

image coordinates of fp i in actual radiograph I 2

X n,src :

X-ray source position at State n (n=1,2)

D n,cen :

center of detector at State n (n=1,2)

D n,up :

upvector of detector at State n (n=1,2)

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Authors and Affiliations

  1. Bionics Research Group, Korea Institute of Science and Technology, 39-1 Hawolgok-dong, Seongbuk-gu, Seoul, South Korea, 136-791

    Youngjun Kim & Sehyung Park

  2. K & I Technology Co., 1586-6 Seocho-dong, Seocho-gu, Seoul, South Korea, 137-070

    Wontae Kim

  3. Institute for Industrial Technology Policy, Seoul National University of Science & Technology, 232 Gongneung-ro, Nowon-gu, Seoul, South Korea, 139-743

    Jong-Hyeong Kim

Authors
  1. Youngjun Kim
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  2. Wontae Kim
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  3. Sehyung Park
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  4. Jong-Hyeong Kim
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Correspondence to Jong-Hyeong Kim.

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Kim, Y., Kim, W., Park, S. et al. Calibration method for microscale stereo X-ray imaging system. Int. J. Precis. Eng. Manuf. 13, 877–882 (2012). https://doi.org/10.1007/s12541-012-0114-3

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  • DOI: https://doi.org/10.1007/s12541-012-0114-3

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