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Resolution of Field-Emission X-Ray Sources

1

Radiation Physics

Francis M. Charbonnler, Ph.D., John P. Barbour, M.A., and Walter P. Dyke, Ph.D. The physical designs of field-emission and conventional x-ray tubes are compared, and the physical and geometric source properties are translated into optical and resolution characteristics using modulation transfer functions calculated for idealized and practical sources and verified by star test pattern measurements. The field-emission design has several advantages: axial symmetry, circular shape, and a relatively favorable Intensity distribution of the focal spot; in addition, the focal spot size is independent of the tube current. These advantages greatly enhance uniformity over the field of view and may increase resolution by a factor of 2 for a given nominal source size, thus largely offsetting the greater physical size of present field-emission sources. INDEX TERMS: Focal Spots. Line Spread Function. Modulation Transfer Function • Radiography, apparatus and equipment

Radiology 117:165-172, October 1975

NEW FIELD-EMISSION x-ray tube is now available for

A

use in radiology. Its small size has made possible new x-ray machines for pediatric (8) and stereotaxic surgery (25), while its ability to operate economically at higher voltages has enabled the development of a new machine for 350-kV chest radiography (9) which has had favorable clinical evaluation (13). Since an increasing number of field-emission x-ray sources are being used, we wish to compare the geometric and optical characteristics of field-emission and conventional x-ray sources as well as the lateral resolution obtainable with each type of system. Although present field-emission sources are generally larger than thermionic sources, the axially symmetrical design of the field-emission x-ray tube yields important benefits: (a) the circular shape of the focus and its relatively favorable intensity distribution enhance resolution for a source of a given size; (b) the size of the source is independent of the tube current and remains the same over the field of view; (c) there are no first-order variations in x-ray beam intensity and hardness over the field of view; and (d) there is no appreciable off-focus radiation, so that exposure and resolution are more uniform over the film and the improvement in center-field resolution can be a factor of 2 for a source of a given size. We calculated the lateral resolution for field-emission x-ray sources and oheckedlt experimentally with star test patterns; depth resolution is discussed elsewhere (9). Our studies showed that present field-emission source sizes are satisfactory for routine chest films. A forthcoming paper (7) will analyze in detail the conditions for optimizing visibility in chest films. PHYSICAL DESIGN AND PROJECTED X-RAY SOURCES

The basic geometries of the x-ray tube and source 1

are compared in Figure 1 for conventional and fieldemission types, and the corresponding projected x-ray source configurations and intensity distributions for the two tube types at the film planes are shown in Figure 2. X-ray sources with the same projected size are illustrated in order to facilitate discussion of relative variations over the field of view; in practice, the field-emission source would generally be larger. In the field-emission tube, the cathode consists of sharp metallic needle assemblies surrounding a conical tungsten target. Pulsing the target briefly to high voltage causes the cathode to emit a high-current electron stream which bombards the target and produces a burst of x rays whose intensity increases rapidly with voltage. The tube requires no heater and is much smaller than conventional tubes, particularly those capable of high voltage. A single submicrosecond pulse is used for flash radiography of high-speed events, while a fast stream of pulses (typically 1,000 pulses per second) is preferred for medical applications. In hot-cathode tubes, the target is a plane slanted at an angle 'l/; to the axis of the x-ray beam. The focal spot is ndrmally an elongated rectangle which is seen as a square when viewed from the center of the film. The typical 'l/; value of approximately 20° is a compromise: a smaller angle would increase the area of the focal spot and improve heat dissipation, but it would also aggravate the "heel effect," i.e., undesired variations in x-ray beam intensity and projected source size over the film area. A 15 % variation in x-ray intensity and a 30 % degradation of resolution at the upper corners of the film are typical. These disadvantages of conventional tubes, which have been discussed in detail in recent papers (3, 15, 18, 21), are essentially eliminated by the symmetry of revolution of the field-emission tube. The cone half-angle of 7°, while sufficient to ensure almost uniform illumination and res-

From Hewlett-Packard Co., McMinnville Division, McMinnville, Ore. Accepted for publication in October 1974.

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FRANCIS

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M. CHARBONNIER AND OTHERS

October1975

THERMAL CATHODE

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Fig. 1. Comparison of x-ray source geometries for tubes with a thermal or field-emission cathode. The shaded area represents the x-ray source. A thermal tube uses a plane target and usually produces a line focus with a strong edge intensity. A fieldemission tube uses a conical target with a small half-angle 1f; and produces an axially symmetrical focus.

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elution over a 35.6 X 43.2-cm (14 X 17-in.) film at 1.8 m (6 ft.), remains small enough to produce a large focal spot (8X the projected area vs. 3X for the conventional tube). The large ratio between actual and projected area increases the rate of heat diffusion to the center of the target and enhances the short-term heat dissipation capability of the tube; however, the lack of a massive target surrounding the focal spot makes extremely small ones impractical and limits the total heat dissipation capability of present field-emission tubes for long exposures. These general characteristics indicate that the present field-emission x-ray tube design is particularly well suited for chest radiography, where short exposure, uniform illumination of a large subject, and high voltage (for mediastinal penetration) are required, rather than for applications such as serial angiography which require a very fine focal spot and a large total output. OPTICAL CHARACTERISTICS AND RESOLUTION

In evaluating geometric unsharpness due to the x-ray

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Fig. 2. Variations of x-ray intensity and projected source size for typical chest x-ray geometry: 35.6 X 43.2-cm (14 X 17-in.) film 1.8 m (6 ft.) from the x-ray source. Sources of the same physical size are illustrated to facilitate display of relative variations over the field of view, though present field-emission focal spots are generally larger than conventional-tube focal spots. The asymmetry of the thermal x-ray tube causes large variations over the field of view; these are essentially eliminated by the axial symmetry of the field-emission x-ray tube.

source, it is necessary to consider not only the size of the source but also its shape, the distribution of x-ray intensity across it, and possible changes in these parameters with x-ray technique (e.g., current or voltage) or with the location on the film. Calculations based entirely on the nominal size of the source may be in error by a factor of 2 or even more (2, 4, 5, 16, 17, 19). The geometric unsharpness resulting from the characteristics of the focal spot can be expressed in terms of the linespread function (LSF), which basically represents the x-ray intensity in the image of an infinitely long and narrow slit (19, 23). Once this has been done, it is necessary to determine the lateral and depth resolution of the entire recording system, i.e., the unsharpness of the x-ray source must be combined with other factors associated with the film, screens, quantum mottle, and depth resolution. The modulation transfer function (MTF) approach is generally favored, as it makes these determinations more precise and takes all focus characteristics into account; the overall MTF of a complex imaging system is simply the product of the MTFs of each component (19, 23, 24). Figure 3 illustrates the geometry and parameters used in calculating LSF and MTF. The reference spatial frequency used in calculating the MTF is

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where 0 is the basic reference dimension of the projected x-ray focus, i.e., the diameter for a circular source or the side for a square source. Square (Conventional) Sources: Figure 4 compares MTFs for several simple source-intensity distributions, which are identified by the LSFs in the lower part of the figure. In order to facilitate comparisons, the projected

167

RESOLUTION OF FIELD-EMISSION X-RAY SOURCES

Vol. 117

1.0

Radiation Physics

INTENSITY OISTRIBUTION

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Fig. 5. MTFs illustrating the loss of resolution caused by the hollow intensity distribution of the x-ray source commonly found in thermal x-ray tubes.

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Fig. 4. Modulation transfer functions (MTF) iIIustra~ing the effect of x-ray source intensity distribution on resolution. An abrupt source cut-off is undesirable.

focal-spot widths at half maximum intensity have all been normalized to the same value X o. The MTF for a uniform square spot (Case 1) was first given by Morgan (20):

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and other MTFs can readily be calculated in a similar manner. An MTF of 1 represents perfect imaging, while the gradual departure from 1 with increasing spatial frequency represents a progressive loss of contrast in the image. An MTF of 0 corresponds to a complete loss of resolving capacity, and the negative or phase-reversal region which follows is particularly troublesome because it represents "spurious resolution," i.e., the occurrence of false images (11, 19). These features are readily observed in radiographs of test patterns and in maqniflcation angiography. The "cut-off" frequency f c (corresponding to the first o value of the MTF) provides a useful measure of the relative resolution of various sources and geometries. Since high cut-off frequency and minimum phase reversal are desired for high resolution, MTF analysis shows that a sharp cut-off at the outer edge of the focal spot and a relatively hollow distribution with low intensity at its center are particularly detrimental to resolution and should be avoided if possible. The effect of the x-ray intensity distribution near the outer edge of the focal spot is shown in Figure 4. Even though the intensity distributions for Cases 2, 3, and 4 represent total source widths which are much larger

than the width Xo of the square distribution, their overall resolution capability remains quite comparable: the cutoff frequency is decreased by less than 10%, and the strong reduction in phase reversal more than compensates for the moderate decrease of image contrast at low spatial frequencies. The gaussian intensity distribution (Case 4) completely eliminates the phase reversal region and has therefore been particularly recommended for applications such as magnification angiography, where spurious resolution is very detrimental (11, 12, 19). Conventional tubes with more nearly gaussian focal spots are now being made available (10). The effect of a hollow distribution has been investigated theoretically (5, 6, 19) and is illustrated in Figure 5, which compares the MTFs of several focal spots having a gradually increasing concentration of emission near the edges, as illustrated by the LSFs shown in the lower part of the figure. Case 3, which may be considered fairly representative of most current thermionic focal spots, shows a 15 % loss in cut-off frequency and a doubling in phase reversal amplitude compared to a spot with uniform intensity. For the extreme case of two thin bands (Case 5), the cut-off frequency (and therefore the resolution) is reduced to half, and the problem of spurious resolution is acute. Circular (Field-Emission) Sources: Two limiting cases are a circular source with uniform intensity and an infinitely thin ring with all of the emission concentrated at the periphery. The normalized LSFs for these two cases are, respectively,

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where x < xo/2. The MTFs are derived from these LSFs by the standard expression for symmetrical LSFs:

168

FRANCIS

CASE 1 : CIRCULAR SOURCE WITH UNIFORM INTENSITY CASE 2: INFINITELY THIN RING SOURCE CASE 3: " DOUGHNUT" SOURCE

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M. CHARBONNIER AND OTHERS

October1975

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Fig. 6. Calculated MTFs for x-ray sources with the circular shape characteristic of field-emission x-ray tubes.

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