Abstract

The imaging characteristics of diagnostic x-ray systems are dependent, in part, upon the size, shape, and intensity distribution of the x-ray source. These properties, however, vary with such parameters as kVp (tube mA (tube current), and, because of the steep anode face, field position. We have investigated the voltage), characterization of the focal spot using the image of a random array of small radiopaque objects. The Fourier transform of this image is, to a good approximation, the modulation transfer function (MTF) of the focal spot. We have compared the accuracy and reliability of this technique with both pinhole and star imaging Focal spot variations with kVp, mA, and field position have been measured, and the use of this techniques. technique with microfocus x-ray sources has been demonstrated.

© 1976 Optical Society of America

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References

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  1. K. Doi, Am. J. Roentgenol. 94, 712 (1965).
  2. K. Doi, “Measurement of Dimensions of Focal Spots of Diagnostic X-ray Tubes,” National Electrical Manufacturers Association Standards Publication XR5 (1974).
  3. J. E. Gray, M. P. Capp, F. R. Whitehead, Invest. Radiol. 9, 252 (1974).
    [CrossRef] [PubMed]
  4. M. Braun, W. W. Stoner, Abstract: Med. Phys. 2, 173 (1975).
  5. G. Groh, E. Klotz, H. Weiss, Appl. Opt. 12, 1693 (1973).
    [CrossRef] [PubMed]
  6. J. E. Gray, M. Trefler, Med. Phys. in press.
  7. E. L. Chaney, W. R. Hendee, Med. Phys. 1, 141 (1974).
    [CrossRef] [PubMed]

1975 (1)

M. Braun, W. W. Stoner, Abstract: Med. Phys. 2, 173 (1975).

1974 (3)

E. L. Chaney, W. R. Hendee, Med. Phys. 1, 141 (1974).
[CrossRef] [PubMed]

K. Doi, “Measurement of Dimensions of Focal Spots of Diagnostic X-ray Tubes,” National Electrical Manufacturers Association Standards Publication XR5 (1974).

J. E. Gray, M. P. Capp, F. R. Whitehead, Invest. Radiol. 9, 252 (1974).
[CrossRef] [PubMed]

1973 (1)

1965 (1)

K. Doi, Am. J. Roentgenol. 94, 712 (1965).

Braun, M.

M. Braun, W. W. Stoner, Abstract: Med. Phys. 2, 173 (1975).

Capp, M. P.

J. E. Gray, M. P. Capp, F. R. Whitehead, Invest. Radiol. 9, 252 (1974).
[CrossRef] [PubMed]

Chaney, E. L.

E. L. Chaney, W. R. Hendee, Med. Phys. 1, 141 (1974).
[CrossRef] [PubMed]

Doi, K.

K. Doi, “Measurement of Dimensions of Focal Spots of Diagnostic X-ray Tubes,” National Electrical Manufacturers Association Standards Publication XR5 (1974).

K. Doi, Am. J. Roentgenol. 94, 712 (1965).

Gray, J. E.

J. E. Gray, M. P. Capp, F. R. Whitehead, Invest. Radiol. 9, 252 (1974).
[CrossRef] [PubMed]

J. E. Gray, M. Trefler, Med. Phys. in press.

Groh, G.

Hendee, W. R.

E. L. Chaney, W. R. Hendee, Med. Phys. 1, 141 (1974).
[CrossRef] [PubMed]

Klotz, E.

Stoner, W. W.

M. Braun, W. W. Stoner, Abstract: Med. Phys. 2, 173 (1975).

Trefler, M.

J. E. Gray, M. Trefler, Med. Phys. in press.

Weiss, H.

Whitehead, F. R.

J. E. Gray, M. P. Capp, F. R. Whitehead, Invest. Radiol. 9, 252 (1974).
[CrossRef] [PubMed]

Abstract: Med. Phys. (1)

M. Braun, W. W. Stoner, Abstract: Med. Phys. 2, 173 (1975).

Am. J. Roentgenol. (1)

K. Doi, Am. J. Roentgenol. 94, 712 (1965).

Appl. Opt. (1)

Invest. Radiol. (1)

J. E. Gray, M. P. Capp, F. R. Whitehead, Invest. Radiol. 9, 252 (1974).
[CrossRef] [PubMed]

Med. Phys. (1)

E. L. Chaney, W. R. Hendee, Med. Phys. 1, 141 (1974).
[CrossRef] [PubMed]

National Electrical Manufacturers Association Standards Publication XR5 (1)

K. Doi, “Measurement of Dimensions of Focal Spots of Diagnostic X-ray Tubes,” National Electrical Manufacturers Association Standards Publication XR5 (1974).

Other (1)

J. E. Gray, M. Trefler, Med. Phys. in press.

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Figures (9)

Fig. 1
Fig. 1

Geometry of typical x-ray imaging system showing the cathode (C), anode (A), and object and image planes. Note the steep anode angle (usually 10–20° from the central ray).

Fig. 2
Fig. 2

(a) Pinhole image of a typical 1.0-mm x-ray focal spot using a 0.030-mm pinhole, (b) contact radiograph of a star pattern, and (c) a magnified radiograph of this star pattern taken with the 1.0-mm focal spot.

Fig. 3
Fig. 3

(a) Contact radiograph of 100-μm lead random object distribution, (b) magnified radiograph of the random distribution, and (c) pinhole image of an x-ray focal spot used for (b). (Note the reproductions of the focal spot in Figure 3b.)

Fig. 4
Fig. 4

Schematic of optical processor.

Fig. 5
Fig. 5

(a) Two-dimensional MTF of focal spot in Fig. 3 and (b) stylized one-dimensional profile through the origin of (a).

Fig. 6
Fig. 6

Focal spot size measured (a) parallel to the anode–cathode axis and (b) perpendicular to the anode–cathode axis as a function of mA.

Fig. 7
Fig. 7

Focal spot size measured perpendicular to the anode–cathode axis as a function of kVp.

Fig. 8
Fig. 8

Variation of imaging properties of a focal spot with field position from anode end (upper left) to cathode end (lower right), a total distance of 43 cm (17 in.) in the image plane.

Fig. 9
Fig. 9

Fourier transforms of a 0.3-mm focal spot using (a) 40-μm Bi random distribution and (b) 20-μm Bi random distribution.

Equations (6)

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( x , y ) = h ( x , y ) * s ( x , y ) ,
a = M o / [ ξ o ( M o - 1 ) ] ,
i ( x ) = h ( x ) * s ( x ) ,
I ( ξ ) = H ( ξ ) S ( ξ ) ,
I ( ξ ) = - i ( x ) exp ( - j 2 π ξ x ) d x .
a = ( 2 λ f ) / ( M p D ) ,

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