Computer simulation of the geometric unsharpness ...

COMPUTER SIMULATION OF THE GEOMETRIC UNSHARPNESS EFFECT ON RADIOLOGIC IMAGES Márcio A. Marques'; Annie F. Frère2; Henrique J. Q. Oliveira'; Homero Schiabel2; Paulo M. Azevedo Marques2; Ricardo J. Ferrari2; Aledir S. Pereira'

'

Dept. FIsica e Informática - JFSC/TJSP 2 Dept. Eng. Elétrica - EESC-USP Av. Dr. Carlos Boteiho, 1465 - 13560-250 - Sâo Carlos (SP) - Brazil

ABSTRACT

The magnitude of the image geometric unsharpness depends on the location in the field where the object is hit by the X-ray beam. This phenomenon is known as field characteristic and is caused by the target plane angulation. This yields different effective focal spot sizes and shapes when it is "seen" from different

directions and locations in the X-ray field. Due to the effect of the field characteristic, a more detailed evaluation of focal spot behavior in radiology systems is needed. Hence the focal spot should be evaluated in

all field locations, which is very complex with experimental procedures, although feasible by computer simulation. This work describes an algorithm with the aim of determining the size and shape of effective focal spots in any location of the radiation field, on the basis of the focal spot size measurement in the field center. The results obtained by the program have agreed with those obtained by pinholes matrix exposures in several radiology faculties. The program has proved efficient in computing the size of the focal spot projections for mammography systems, with a standard deviation around 0.03-0.04 mm.

Keywords: geometric unsharpness; field characteristics in radiographic systems; computer simulation; X-ray tube focal spot.

1. INTRODUCTION It is known that shadow and penumbra of an object imaged by an X-ray source vary according to the variation of the size of focal spot throughout the radiation field", For this reason, many works are concerned to the development of methods with purposes of measuring the focal spot size and of finding the causes of measuring errors, as Kuntke4, Takenaka et a!.5, Bookstem & Steck6, Rao7, Robinson & Grimshaw8, Trefler & Gray9, Doi et al.'°, and, more recently, Kratzat", Kimme-Smith & Chatziioannou'2 and Law'3. Geometric unsharpness relative to X-ray imaging systems depends on the location where the object is placed in the field. This is known as field characteristics', and is caused by the target plane angulation, which makes that focal spot has different sizes and shapes when it is "seen" from different directions and positioning in the X-ray beam. One of the main causes of error in focal spot measurements is the positioning of the test device (pinhole or slit cameras, for example), since for displacement of 10 cm along the field, the focal spot size can change up to 300%, depending on the direction of measurement. Most of the X-ray tubes have rotative anode. The tube anode target area where the electrons hit is the true focal spot, which may be considered as being located in an inclined plane relative to the object and image planes. Due to the effect of the field characteristics3, however, a more detailed evaluation of focal spot behavior in radiology systems is needed. Hence we should evaluate the focal spot in all locations of the field, which is not quite possible with experimental means, though feasible by computer simulation. Therefore, this paper describes the development of a procedure which was designed to determine size and shape of the focal spots in any location of the radiation field by computer simulation. The algorithm is based on the knowledge of the focal spot size measured in the field center and on equations describing the field characteristics for radiographic imaging systems. Computed the focal spot variations, the effect of geometric unsharpness can be predicted for all field locations.

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2. GEOMETRIC UNSHARPNESS DUE TO THE X-RAY TUBE FOCAL SPOT SIZE As a good approximation, we can suppose a focal spot as a rectangle having equal sides a and b in the center of the field, as illustrated by Fig. 1. From the scheme of that figure, the new values of these sides (a' and b') in a given position which distances d from the origin and forms an angle B with an axis parallel to the anode-cathode axis can be found by following equation:

a" cosl3 cosy

(1)

where

y = arctan

4y

(2)

arctan4

(3)

(dfi tana)) ÷dx)

and

=

dfi

Cathode — anode Ax[3

direction

dfi

I

I

Fig. 1 - Illustration of the focal spot projection at the field center and at an arbitrary location.

We are calling a the size of the side of the focal spot in a direction perpendicular to a line connecting the target plane center and the image plane in each desired location. It is determined by equation (4):

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all=__-.sin(a÷p) s:Lntz

(4)

By analyzing the behavior of the focal spot geometric projection from Fig. 1, we can verify that side

b

of the focal spot does not change because it is in a plane parallel to the object and image planes. Thus, we

have: b'= b. From this analysis, we have developed an algorithm and subsequent program in order to calculate the size and to determine the shape of focal spots in radiology systems, in any field position. The program may be described as follows: firstly the user introduces the name of the file of data storage (the values representing the sizes of the sides of the effective focal spot computed in several positions in the field); next, the user introduces data related to the sides offocal spot measured in the field center (a and b), and the target inclination angle (cc); finally, the displacements dx and the field orientation angles () are introduced so that the software can calculate the values of focal spot dimensions in all the locations displaced dx from the center along an axis with a shift of 9 relative to the anode-cathode axis.

Therefore the software calculates the new value of the largest side of focal spot (side a) in different field locations for simultaneously displaying all the effective focal spots in all those locations on the monitor screen.

3. RESULTS To confirm the validity of the simulation, focal spot images were taken by using a device similar to the pinhole camera matrix used in some radiology facilities. This matrix was made of a lead plate with pinholes of 0. 1 mni in diameter. This device was designed to be placed at 25 cm from the focal spot and also 25 cm from the image plane in tests with radiographic equipments in order to assure accuracy of the angulation of

pinholes far from the center of the plate. Fig. 2 and Fig. 3 illustrate images obtained from mammographic systems with, respectively, 1.75 x 0.90 mm and with 1.20 x 0.75 mm focal spots measured in the center of the field. The first (which we are calling here as mammographic system 1) had a target inclination of 290; the second (mammographic system 2) had 23 0 of target angulation. We have used the program to simulate focal spot behavior in mammography systems. Fig. 4 and Fig.

5 illustrate these images obtained on monitor screen concerned the data from the same mammographic equipments used to exposure the pinhole matrix which yield the image shown in Fig. 2 and 3. Comparisons of both set of figures (Fig. 2 vs. Fig. 4 and Fig. 3 vs. Fig. 5) evidence the validity of the results obtained with the simulation procedure.

In addition, we have provided here a table where data measured from the actual images and from the simulated images are plotted for comparison. Thus, Table I shows some of the measured values for the side a (the side parallel to the anode-cathode axis) in the simulated images (first column) and in the actual radiographic images (second column). The third column shows the difference between both measured values in each case. Table 1(a) refers to the images shown in Fig. 2 and 4 (mammographic system 1) and Table 1(b) refers to the images shown in Fig. 3 and 5 (mammographic system 2).

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-

K'A.K T/Gi

CATHODE

ANODE

0 deg.

90 deg.

- Actual radiographic image obtained from exposure of the pinhole matrix for mammographic system I (printed reproduction from the original radiogram).

Fig.2

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0

CATHODE

ANODE

0 deg.

90 deg. ______________________

Fig.3

b/OiLL

/Lt.)

- Actual radiographic image obtained from exposure of the pinhole matrix for mammographic

system 2 (printed reproduction from the original radiogram).

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0

ANODE

CATHODE

Odeg.

9Odeg.

Fig.4 - Simulated image - Effective focal spot in several field locations for manimographic system 1 (computer screen)

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CATHODE

ANODE

Odeg.

9Odeg.

Fig.5 - Simulated image - Effective focal spot in several field locations for mammographic system 2 (computer screen).

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TABLE I Comparisons between some measured values for the side a of the effective focal spot in the simulated and actual images (Fig. 2 to 5)

MAMMOGRAPHIC SYSTEM 1

a' [mm]

MAMMOGRAPHIC SYSTEM 2

a' [mm] (actual image)

shift [mm]

a' [mm] (simulation)

a' [mm] (actual image)

shift [mm]

(simulation) 1.75

1.75

0.00

1.20

1.20

0.00

1.71

1.80

0.09

1.33

1.40

0.07

1.67

1.80

0.13

1.47

1.55

0.08

1.64

1.75

0.11

1.26

1.25

-0.01

1.55

1.60

0.05

1.40

1.40

0.00

1.47

1.45

0.02

1.23

1.25

0.02

1.38

1.45

0.07

1.27

1.30

0.03

1.32

1.40

0.08

1.32

1.35

0.03

1.61

1.65

0.04

1.16

1.20

0.04

1.47

1.50

0.03

1.13

1.15

0.02

1.34

1.25

-0.09

1.03

1.05

0.02

1.20

1.15

-0.05

1.07

1.05

-0.02

1.08

1.05

-0.03

0.95

0.95

0.00

0.97

0.95

-0.02

0.84

080

-0.04

1.43

1.45

0.02

0.72

0.75

0.03

1.28

1.25

-0.03

.063

0.55

-0.08

1.13

1.15

0.02

0.54

0.50

-0.04

0.97

0.90

-0.07

0.92

0.90

-0.02

0.81

0.80

-0.01

0.78

0.75

-0.03

1.61

1.65

0.04

0.64

0.70

0.06

1.47

1.50

0.03

0.50

0.50

0.00

1.20

1.15

-0.05

0.36

0.40

0.04

1.54

1.55

0.01

1.07

1.05

-0.02

1.46

1.45

-0.01

0.83

0.80

-0.03

average shift:

(0.04 0.03)

mm

average shift:

(0.03

0.02)

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mm

4. CONCLUSIONS As it can be verified by the values calculated of the deviations - summarized in the bottom of Table

I -, the simulation program is efficient to compute the size of focal spots of the illustrated mammography systems. Similar results could be observed with other radiology systems evaluated during tests carried out during the last few months. The computer screens showing focal spots in different X-ray field locations demonstrate to which extent their size and inclination differs.

Behavior of simulated focal spots is coherent with the theory described previously. The size of focal spots becomes smaller as it moves toward the cut-off" (the location after which there are no more X-rays because of the anode inclination) as shown in Fig. 1 , and outside the anode/cathode axis all focal spots are turned (inclined) toward this point. Regarding this feature, the simulation program has once again proven to be efficient as a result of good agreement between the actual images obtained throughout the pinhole camera matrix and the simulated images of focal spots throughout the field.

5. ACKNOWLEDGEMENT The authors are grateful to FAPESP and PADCT for the financial support.

7. REFERENCES 1. K. Doi, "Field characteristics of geometric unsharpness due to X-ray tube focal spots", Med. Phys.,

v. 4, p.15-20, 1977. 2. A. E. Nickoloff; E. Donnelly; L. Evel; J. V. Atherton; T. Ascht, "Mammographic resolution: influence of focal spot intensity distribution and geometry", Med.Phys., v. 17, p. 436-447, 1990. 3. A. E. Burgess, "Focal spots III: field characteristics", Invest.Radiol., v. 12, p.54-61, 1977. Kuntke4, Takenaka et al.5, Bookstein & Steck6, Rao7, Robinson & Grimshaw8, Trefler & Gray9, Doi et al.10 and,

more recently, Kratzat", Kimme-Smith & Chatziioannou'2 and Law'3 4. A. H. 0. Kuntke, "On the determination of Roentgen tube focal spot sizes by pinh-hole camera roentgenography", Acta Radiol., v. 47, p. 55-64, 1957. 5. E. Takenaka; K. Kinoshita; R. Nakajima, "Modulation transfer function of the intensity distribution of the Roentgen focal spot", Acta Radiologica, v. 7, p. 263-272, 1968. 6. J.J. Bookstein; W. Steck, "Effective focal spot size", Radiology, v. 98, p. 3 1-33, 1971 7. U. V. G. Rao, "A new method to determine the focal spot size of X-ray tubes", Am. J. Roentgen., V. III, p. 628-632, 1972. 8. A. Robinson; G. M. Grimshaw, "Measurement of the focal spot size of diagnostic X-ray tubes - a comparison of pinhole and resolution methods", Brit. J. Radiol., v. 48, p. 572-580, 1975. 9. M. Trefler; J. E. Gray, "Characterization of the imaging properties of X-ray focal spots", Appi. Optics, v. 15, p. 3099-3104, 1976.

10. K. Doi; L.-N. Loo; H-P. Chan, "X-ray tube focal spot sizes: comprehensive studies of their measurement and effect of measured size in angiography", Radiology, v. 144, p. 383-393, 1982. 11. M. Kratzat, "Evaluating the importance of focal spot sizes in mammography", Medicamundi, v. 33, p. 74-80, 1988. 12. C. Kimme-Smith; A. Chatziioannou, "Mammography focal spot measurement with a star pattern: techniques to avoid inaccuracies", Med. Phys., v. 20, p. 93-97, 1993. 13. J. Law, "Measurement of focal spot size in mammography X-ray tubes", Brit. J. Radio!., v. 66, p. 44-50, 1993.

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