IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 43. NO. 2, APRIL 1994 295

Real-Time X-Ray Fan-Beam 2-Axis Position Measurement

Michael F. Gard, Senior Member, IEEE

Abstrad-Precise control of fan-beam position is important to the production of highest quality CT images; failure to maintain fan-beam orientation can produce image artifacts. This paper describes a special technique which provides accurate real-time measurement of fan-beam z-axis position. A geometrical mask set is used to modify the response of conventional detector cells. Data from the masked detector cells are used to form a self-consistent normalized position signal which is independent of radiological dose.

I. INTRODUCTION HE physical orientation of a typical third-generation CT T scanner, in which both detector and X-ray tube rotate

about the patient, is shown in Fig. 1. The X-ray tube emits radiation from the focal spot, a small area on the tube anode; radiation from the focal spot spreads as from a point source. Close to the X-ray tube is a collimator assembly which blocks radiation in all directions other than a thin, approximately planar, collection of rays passing through the patient. It may be seen that the radiation beam is fan-shaped and hence is called a fan beam. As the fan beam passes through the patient, detector channels register information related to attenuation of the fan beam by the patient. This attenuation information is used to form a tomographic image of patient anatomy. A very readable discussion of CT fundamentals is found in [l].

In the 3-D Cartesian coordinate system used in third- generation CT, the x-axis is parallel to the long axis of the detector arc, and the y-axis is parallel to the line from detector center to the focal spot. Thus, the X-ray fan beam includes the x-y plane and would define the x-y plane if a perfectly aligned fan beam were infinitesimally thin. In conventional axial scanning, the fan beam describes an approximately planar surface as the tube-detector combination rotates around the patient; this surface is called the scan plane and represents the anatomical level of the tomographic slice. The z-axis of the coordinate system is the patient axis. In simple axial scanning (i.e., no gantry tilt), the z-axis is normal to the scan plane. By convention, fan-beam width is defined at the center of rotation (isocenter) where it also describes the effective width of the tomographic slice through the patient. In contemporary CT scanners, slice width can vary in graduated steps from 1 mm to 10 mm. Because the fan beam is emitted from a small spot, a realizable beam is slightly wedge-shaped in cross section (see Fig. 1).

Conventional third-generation CT scanners are sensitive to position errors in all three dimensions, although to varying

Manuscript received May 18, 1993; revised October 25, 1993. The author is with General Electric Medical Systems, Milwaukee, WI 53201

IEEE Log Number 9216518. USA.

/ \

collimator-

fan beam - +

isocenter 1 detector-

Fig. 1. Cartesian coordinates of a third-generation CT scanner.

degrees. Focal spot misalignments in the x-axis direction are well studied and their clinical consequences are well known; tube alignment procedures are generally successful in providing proper x-axis focal spot position for optimal image quality. Y-axis errors produce sight magnification changes, but the clinical significance of y-axis error is widely held to be negligible [2]. This paper is concemed with position errors along the remaining axis, the z-axis.

Some z-axis position error artifacts are associated with the detector. A fan beam should occupy the same position on the detector face during a scan because detector arrays, whether xenon or solid-state, do not have completely uniform z-axis response to radiation. If the fan-beam location exhibits z-axis motion during a scan, the detector output will contain an error component associated with beam location changes.

Other errors arise at the patient level. If the fan beam moves across the detector face in the z-direction, there must be cor- responding z-axis scan-plane motion at the patient level. Such scan-plane deviations have the effect of moving inappropriate anatomy in and out of the ideal scan plane, giving rise to image errors known as partial volume artifacts. These artifacts are especially objectionable in thin-slice images.

Sources of z-axis fan-beam motion include mechanical displacements of the X-ray tube anode, small mechanical misalignments, and thermal effects in the tube, tube housing, collimator, and other structures. Tube heating is a primary cause of scan-to-scan fan-beam z-axis position changes, while gravitational and centrifugal forces during gantry rotation are causes of intrascan (i.e., within a scan) position changes. Detailed engineering attention has been given to X-ray tubes and associated structures with the objective of minimizing z- axis motion. Unfortunately, it is most difficult to guarantee the absence of focal spot motion in a thermally stressed

00 18-9456/94$04.00 D 1994 IEEE

2% IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 43. NO. 2, APRIL 1994

on of fan beam

Fig. 2. Total of 2N interdigitated detector cells with triangular masks in place. Arrangement of the mask material (shaded areas) forms altemately disposed tnangular apertures (unshaded areas), causing the detector response to be a linear function of z-axis position.

and rapidly rotating X-ray tube, no matter how carefully engineered it may be. Similarly, considerable attention has been directed to providing uniform z-axis detector response. However, production tolerances, nonuniformities, and certain physical effects (e.g., edge effects) in detector components make it unlikely that detector performance can be made completely uniform across the face of each detector cell.

At the same time, consistent and stable fan-beam z-axis position is important to the production of highest quality CT images for certain studies (e.g., thin-slice lung images). Failure to maintain z -axis fan-beam orientation can produce several types of image error arising from scan-plane inconsistencies and detector response nonuniformities, as noted above. The desire to maintain a consistent and stable fan-beam position strongly motivates real-time measurement of fan-beam z-axis position. Clearly, the ability to control fan-beam position requires a means to measure fan-beam position. Because some error sources are operative within a scan, the measurement should be capable of real-time operation.

Many z-axis alignment procedures and tools, developed around factory requirements, have regarded z-axis alignment as a mechanical operation to be done during system assembly and repeated only during a tube or detector change. As may be expected, these fundamentally mechanical procedures often rely on film and special test fixtures [3]. Such operations are cumbersome and inadequate for real-time operation.

This paper describes a technique providing accurate real- time z-axis fan-beam position measurement using an inter- digitated set of triangular masks over a conventional detector. The technique is the X-ray analog of a method used for optical sensing and beam position control. Masked detector channel data are used to form a self-consistent normalized position signal independent of radiological dose. Experimental results with narrow collimator apertures confirm the measurement’s accuracy for a wide range of radiological techniques. The

measurement apparatus is inexpensive and requires only initial mechanical alignment of the detector mask to the detector cells. The resulting position signal is ideally suited for addi- tional work to provide closed-loop control for fan-beam z-axis position.

n. MEASUREMENT APPARATUS AND CALCULATIONS

The measurement apparatus has three principal elements. The first element consists of multiple detector cells which convert incident X-ray flux to electrical current or voltage. This paper assumes conversion to electrical current, as by a scintillator and photodiode. For reasons which will become evident, it is preferable that an even number of contiguous detector cells be employed, although this is not a conceptual limitation. It is preferable that there be at least four detector cells, although a minimum of two is sufficient.

The second element is a special mask to occlude portions of each detector cell from X-ray radiation, thereby forming an oriented geometrical aperture for each detector cell. By controlling mask geometry, each detector cell output can be made a specific and (subject to matching and alignment tolerances) arbitrary function of z-axis beam position. This paper describes the use of triangular apertures.

The third element is an electronics package providing output signals proportional to detector signal currents. The difference of these signals is indicative of X-ray beam location in the z-axis of the detector array. The sum of these signals is used to normalize the difference signal, thereby making the z-axis position signal independent of radiological technique.

Fig. 2 illustrates a linear array of 2N individual detector cells, where N is an arbitrary integer. Altemate cells are connected in parallel, resulting in two interdigitated parallel combinations of N cells each. Because individual cells are not, in general, completely uniform in their z-axis response to X-ray radiation, multiple cells are used to provide a relatively

GARD: REAL-TIME X-RAY FAN-BEAM Z-AXIS POSITION MEASUREMENT

uniform composite z-axis response. For this reason, it is desirable to employ at least four detector cells to obtain two sets of at least two cells each ( N 2 2). As more detector cells are used, we expect the composite z-axis response to become increasingly uniform.

Fig. 2 also illustrates a useful mask arrangement. The mask forms a series of altemating elongated triangular apertures which modify individual detector cell responses by prefer- entially occluding portions of the fan-beam X-ray radiation. The apertures are oriented so that beam motion in the z-axis direction produces a linearly increasing or decreasing signal current from each detector cell. As illustrated, signal currents increase in the even-numbered detector cells as the fan beam moves in the positive z direction, while signal currents in the odd-numbered cells decrease. For convenience, we assign arbitrary numbers (0 to 2 N - 1) to the detector cells and define signal currents i (even) and i (odd) by summing individual photodiode signal currents i j from the even-numbered and odd-numbered detector channels, respectively. Thus,

N - 1 N-1 _ . - . -

i (even) = i 2 j and i (odd) = &+I. (1) j = O j = O

Note that signal currents i (even) and i (odd) are unipolar. Assume two generalized transimpedance amplifiers with

gain constants A producing output voltages according to the relationships

V,,,, = A[i(even)] and Vodd = A[i(odd)] . (2)

Once the voltage signals V,,,, and V o d d are available, it is a simple matter to form the difference and sum values Vdzff and V,,,:

V&ff = A[i(even) - i(odd)] and V,,, = A[i(even) + i (odd)] . (3)

The signals V,,,, and V o d d are formed by analog elec- tronics; photodiode signal currents are converted to voltage signals. Clearly, the formation of Vdzff and V,,, is a matter of design convenience and circumstances. In most cases, it will be desirable to digitize V,,,, and V o d d immediately so that all subsequent arithmetic can be done digitally. There are occasions when analog difference and summing amplifiers are a desirable alternative. To keep the discussion general, this paper assumes no particular implementation.

Finally, form the ratio of the difference and sum signals:

(4)

Equation (4) retains the gain constant A in the numerator and denominator to emphasize that the ratios of these quantities are obtained by using transimpedance amplifiers.

When a thin uniform fan beam lies in the exact center of the mask, the active areas of all detector cells are equally illuminated; the difference between i ( even) and i (odd) is zero. If the fan beam is at the extreme positive z direction of the detector, signal current z(even) is maximum while signal current i (odd) is minimum. Hence, at the positive z extreme the difference between the two signals, Vdzff, is maximum positive. Likewise, if the fan beam is at the extreme negative z direction of the detector, Vd,,, is maximum negative.

Vdzff = A[i(even) - i(odd)] V,,, A[i(even) + i(odd)]' v, = -

297

JeL i

Fig. 3. perimental data.

Schematic diagram of measurement electronics used to gather ex-

It may be shown that, for this mask geometry, V,,, remains constant as a fan beam of constant and spatially uniform X-ray fluence traverses a triangularly masked interdigitated detector set composed of cells with otherwise uniform response over the z-axis range of interest. Thus, the signal V,,, is a position- independent measure of X-ray fluence incident on the detector cells.

Recall that signal currents i (even) and z(odd) are unipolar; for this discussion they are considered to be nonnegative. The difference signal in (3) can range from a maximum positive value of Az(even) to a maximum negative value of -Ai(odd). When the difference signal is maximum positive, i (odd) = 0 and the sum signal is also Ai(even) . Similarly, when the difference signal is maximum negative, i (even) = 0 and the sum signal is given by -Ai(odd). At points between these extrema, the sum signal is constant for a constant and uniform fan beam. Thus, the ratio V, in (4) is normalized for all radiological techniques and will take on values in the range -1 5 v, 5 +l.

This result is ideal for closed-loop control. The normalized difference V, may be used as the input error signal for a control system which forces the input error (position relative to the detector centerline) to zero, thereby ensuring the fan beam occupies the exact center of the detector mask. The error signal V, depends only on z-axis position because normalization has made the error signal independent of radiological technique. Furthermore, the normalized position signal is said to be self- consistent, because the difference and sum signals are formed from the same information; there is no requirement for an ex- temal reference signal to provide the normalization operation.

111. EXPERIMENTAL RESULTS

The essential features of the experimental apparatus used in this experiment are shown schematically in Fig. 3. U1 and U2 are type OPAlIlAM amplifiers in a conventional transimpedance configuration. Feedback resistors R1 and R2 (20 M 0) produce a full-scale output of -10 V with 500 nA input current. Capacitors C1 and C2 (1000 pF) are used to limit the bandwidth of the transimpedance stage.

298 IEEE TRANSACTIOb

200 m A , 0.018'' 0.46 m m

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0 20 40 60 80 100 mm

(a)

10 mA. 0.018"(0.46 mm) 6 ~ ' " " " ' " " ' " ' " ' ~

1 1

4 t

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Fig. 4. Test results obtained at 120 KVp. (a) 200 mA, 0.018 in (0.46 mm) aperture, (b) 10 mA, 0.018 in (0.46 mm) aperture.

Amplifiers U3 and U4 are sections of an OP470GP quad amplifier. U3 is a conventional inverting summing ampli- fier (R3-R5=20 ka), while U4 is a conventional difference amplifier (R7-Rl0 = 20 k a). U5 is a type AD734BQ multiplier used in the divider-connected mode to perform the normalization given in (4). A limiter maintains U5's denominator voltage at a minimum of 50 mV to ensure stability and reasonable accuracy of the analog divider. Limiter details are not shown for brevity.

This apparatus is particularly convenient in that the out- puts of U1 and U2 are available for digitization, while the normalized analog position signal from U5 is available for rapid position waveform measurements by oscilloscope or other equipment.

The mask assembly was installed on a detector module typical of those employed in General Electric 9800 series scan- ners. Detector modules in this scanner family are composed of sixteen individual detector cells each approximately 1 mm wide (in the z direction) by 30 mm long (in the z direction). Ten contiguous detector cells were used (2N = lo), resulting in two interdigitated sets of five detector cells per set (N = 5). A computer-driven z-axis test fixture exposed the masked detector module to radiation from a collimated X-ray tube at 120 KVp with tube emission current varying from 10 mA to 200 mA. Most experiments employed a relatively narrow collimator aperture of 0.018 in (0.46 mm) to provide the greatest z-axis position resolution. These experiments clearly established that the normalized error signal V, was a linear function of z-axis position and that the z-axis position signal was independent of widely varying radiological techniques.

IS ON INSTRUMENTATION AND MEASUREMENT, VOL. 43, NO. 2, APRIL 1994

Experimental results for two test runs are shown in Fig. 4, which is a digitized record of the analog z-axis position signal. The output of U5 was scaled and level-shifted to fit the -5 V to +5 V input range of the test fixture. The test apparatus had a total travel of 100 mm. Data from the 30 rmn test module appears between roughly 40 mm and 80 mm in the test plots shown in Fig. 4. The first plot was obtained using 120 KVp, 200 mA, 0.018 in (0.46 mm) aperture, while the second was obtained using 120 KVp, 10 mA, 0.018 in (0.46 mm) aperture. It may be seen that the z-axis position signal V, is linear and virtually identical in both cases, despite the twentyfold difference in incident X-ray fluence.

IV. CONCLUSIONS

This paper has described a technique to measure the z-axis position of an X-ray fan beam in real time. The measurement used a special mask set which modified the normal response of conventional detector cells. Triangular apertures were used to generate an output signal which is a linear function of z- axis position. Other mask geometries may be used to obtain different transfer functions.

This paper has also presented experimental z-axis position measurements obtained by a special text fixture. The z-axis position signal was produced by an all-analog implementation using transimpedance amplifiers, conventional analog sum and difference amplifiers, and a divider-connected analog inultiplier. Experimental results from the test fixture were in very good agreement with theoretical predictions.

ACKNOWLEDGMENT

Special thanks are extended to four GE Medical System employees. G. Englert designed and installed the detector mask used in these studies, C. Shiley performed the z-axis position measurements reported in this paper, and M. Limkeman and J. Hsieh helped extract Fig. 4 from the computer network.

REFERENCES [ l ] L. L. Berland, Practical CT Technology and Techniques. New York:

Raven, 1987. [2] D. Parker et al., "Design constraints in computed tomography: A

theoretical review," Med. Phys., vol. 9, pp. 531-539, July-Aug. 1982. [3] Direction 46-018305, CT HISPEED ADVANTAGE SYSTEM, Rev. 6,

General Electric Medical Systems, Milwaukee, WI, p. 10-7.

Michael F. Gard (SM'84) was born in McPherson, Kansas, in 1949. He received the B.S. in electrical engineering (Magna Cum Laude) from Kansas State University Manhattan, KS, in 1971, the M.S. in electrical engineering (Interdepartmental Program in Biomedical Engineering) from Washington Univer- sity, St. Louis, MO, in 1972, and the Ph.D. degree in electrical engineering from Southern Methodist University, Dallas, TX. in 1992.

He is employed as a Senior Systems Engineer in CT Engineering, GE Medical Systems. Previous

employers include Beech Aircraft Corporation, the Veterans Administration Medical Center, St. Louis, MO, AMOCO Exploration Company, and ARC0 Oil and Gas. His primary professional interests are real-time data. acquisition. precision analog instrumentation for hostile environments, and combined analoddigital systems design. He is a registered professional engineer and holder of thirteen patents.