Special Problems in Measuring the Modulation Transfer Function of X-Ray Image Intensifiers

Special Problems in Measuring the Modulation Transfer Function of X-Ray Image Intensifiers INGEBORG STAHNKE and HANS HEINRICH Siemna-Reiniger-Werke AU, Erlangen, Uermany

INTRODUCTION The advantages of using the modulation transfer function (m.t.f.) for the evaluation of image transfer properties are well known. However, the m.t.f. is not only a measure of how details of different sizes and contrast are transferred, it is also the expression which relates the image transfer properties of the individual elements of a system to the equivalent property of the complete system. Furthermore, if the image transfer of an individual element is caused by a single process, the m.t.f. gives some indication of what this process is. Geveral publications have dealt with m.t.f. theory and its application to various systems.l-* I n applying the m.t.f. theory to X-ray image intensifiers and their individual elements, special problems occur. Some m.t.f.’s are not in agreement with m.t.f. theory, since their initial values are below unity, and their measured values depend on parameters such as the diameter of the lead diaphragm used and the X-ray quantum energy. Above all the product of the m.t.f.’s of the individual elements is sometimes not equal to the overall m.t.f. of the intensifier. One may conclude from these facts that the premises on which the theory is based are not fulfilled. To examine this problem one has to know first what processes occur within the intensifier and then to check which premises of the m.t.f. theory are not met. Finally, one has t o look for a solution of the problem. THE X-RAY IMAGE INTENSIFIER USED FOR THE TESTS Figure 1 shows the construction of the X-ray image intensifier used, its mode of operation, and a list of some of the internal processes. The X-rays leaving the X-ray tube are modulated by the object in a way depending on its absorption and scattering power, and the X-ray pattern so formed undergoes a number of transformations and imagings within the intensifier. The X-ray quanta are absorbed and light is generated within the phosphor layer of the input screen and is transferred through the glass foil to the photocathode. The photoelectrons emitted are accelerated and focused, by means of the electron optics, on 355

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the phosphor of the output screen where the electrons (now having an energy of 25 keV) are absorbed and generate light. However, these imaging processes are not the only ones occurring within the intensifier since there are others which, while not participating in the image transfer itself, are inevitably present in an X-ray image intensifier. For example, X-rays are scattered by the bulb and the electrodes, light is conducted within the glass carriers of the screens and reflexion of light occurs at the electrodes. These processes are collectively called disturbing processes.

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Fxo. 1. Schematic diagram of X-ray image intensifier.

For measuring the m.t.f., a rectangular lead grid is used as the object. This is placed in front of the centered diaphragm and is moved slowly in a direction perpendicular to its bars. The image of the lead grid at the output screen of the intensifier is magnified 20 times by optical means. In the plane of this magnified image a narrow slit is positioned parallel to the bars and the light passing through this slit is received by a photomultiplier, whose signal is recorded. The focus of the X-ray tube, the 20-mm lead diaphragm, the intensifier, the optical system and the slit are centered on the same axis. CONVERSION OF X-RAYSINTO LIGHT

It is necessary to look now for the assumptions which are not

justified. There are two. First it is assumed that the transformations within the intensifier are linear. This assumption is not always fulfilled when X-rays are converted into light. Figure 2 shows the brightness of an X-ray screen as a function of the dose-rate in the case of attenuation with lead filters, for two X-rays having different quantum energies. For exampIe, a lead foil of 60 pm thickness (which is the thickness

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nsTF MEASUREMENT OF X-RAY IMAQE INTENSIFIERS

used for making the lead grids) attenuates an X-ray beam from a

60-kV source with no additional filter, to 22.7% brightness and 12.1% dose-rate,while an X-ray beam from an 85-kVsource,with an additional 20-mm aluminium filter is attenuated to 69% brightness and 72.6% dose-rate. These values and the slope of the two curves demonstrate that the brightness of the input screen is not proportional to the incident dose-rate, when this is varied by filtering. The reason is IOC

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FIG.2. Brightness of the input screen as a function of the dose-rate.

that the spectral energy distribution of the X-rays is changed in passing through the filter and, therefore, the absorption process and the distribution of the generated light are changed too. The brightness and dose-rate values (B min, D min) for the above two X-rays beams with a 60-pm lead foil are shown in Table I together with the brightness and TABLEI Ratio y6 of brightness and dose-rate contrast for two X-ray sources

X-Ray Bource

60 86

0

20

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100 100

12-1 72.6

Brightness

100 100

22.7

0.806

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1-16

dose-rate values (B max, D max) without the lead foil. With these values one can calculate two different values for the contrast of the

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object, the first defined in terms of dose-rate (object dose-rate contrast), and the second in terme of the brightness of the X-ray screen (object brightness contrast). Let the ratio of these two be y E , then

Dmax

+

Dmin

where B refers to the brightness and D to the dose-rates. According to the last column of Table I, ys can be greater or less than 1, depending on the X-ray spectral energy distribution. Of course, y E depends also on the filter material and its thickness, the luminescent material, and the thickness and the method of making of the screen. From these facts, the following conclusion can be drawn. In order to be independent of the X-ray spectral energy distribution, and also of the filter material used for making the grid, the X-ray absorption properties of the input screen, and the object brightness contrast of each screen and tube, have to be measured and applied for determining the m.t.f. The effect of the foregoing considerations of the m.t.f. is illustrated in Fig. 3, curves 1 and 2, assuming the same contrast in the final image at 1.0

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FIQ.3. The m.t.f. of an X-ray image htenei6er.

the output of the intensifier. Curve 1 refers tothe object dose-rate contrast and curve 2 t o the object brightness contrast.

Effect of the background Curves 2 and 3 demonstrate that a further effect influences the m.t.f. The two m.t.f.’s were measured under the same conditions, and only the diameter of the diaphragm was different. Curve 2 is h r a diaphragm

MTF MEASUREMENT OF X-RAY IMAGE INTENSIFIERS

359

diameter of 170 mm and curve 3 for one of 20 mm. This dependence of the m.t.f. on the diaphragm diameter indicates that processes with large ranges are responsible for this effect. I n order to put this effect on a mathematical basis and determine how large the ranges of the participating processes may be, the expression for the m.t.f. is given as

&P) = Jfrnf(z) cos (2nPz)dz, --m

where f ( s )is the normalized line-spread function:

1::

f ( z )dz = 1.

I n actual fact, the integration limits are not plus and minus infinity but are given by the aperture of the diaphragm. The second assumption is therefore that +(P)is measurable only if f(z)is sufficiently small outside these real limits. If this ip not the c a m the measured m.t.f. is only an approximation. For this reason, it is necessary to consider how large are the ranges of all the processes, and how ranges which are too large can be taken into account by calculation and measurement. With image resolutions of 1 lp/mm and above, the image details are much smaller than the 20-mm diameter of the diaphragm, and consequently the m.t.f.’s of the imaging processes are measurable. But the ranges of the disturbing processes are comparable to or larger than the diaphragm. I n order to allow for the effect of these processes on the m.t.f. of the imaging processes proper the following method is applied and illustrated for the example of light conduction within the X-ray screen carrier. Figure 4 shows the brightness of an input screen

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at its centre as a function of the diameter of the diaphragm, extrapolated and related to a diaphragm of zero diameter. Then (Nd- 1) is a measure for the increase of brightness caused by light conduction within the glass foil, briefly cdled the background u d . I n the presence

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I. STAHNKE AND H. HEINRICR

of a lead grid, the background at the measuring point is lowered and depends also on the location of the lead grid with respect to the measuring point. (A more extensive treatment of these calculations and of the problems described will be published elsewhere.6) First of all, this lowered background was found by calculation. It was then theoretically superimposed on the image of a sinusoidal grid and finally the altered m.t.f. was calculated. The effect of these calculations and others necessary to obtain +(P) is illustrated in Fig. 6. Curve 1 represents the measured m.t.f. of an

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FIO.5. The m.t.f. of the input soreen.

input screen. Curve 2 shows the m.t.f. corrected for background and converted to a sinusoidal grid. As the measuring set-up has its own inherent m.t.f. this curve must be corrected once more. The result is shown in curve 3. This last curve is the real modulation transfer function of the phosphor layer of the input screen and is independent of the measuring conditions, such as X-ray spectral energy distribution, diaphragm diameter, lead grid used, and measuring set-up.

M.T.F.OF AN X-RAYIMAQE INTENSIFIER AND ITS COMPONENTS The m.t.f.'s of the components of an X-ray image intensifier are represented in Fig. 8. Curve 1 is the m.t.f. of the glass foil-the carrier of the input screen. For measuring this function an opalescent disc was used as the light source. The receiver was a thin, smoky magnesium oxide layer on the glass foil and the m.t.f. of this was calculated too. Curve 2 shows the m.t.f. of the electron optical system. Its shape was found by assuming a certain electron distribution (lineare DreieckaVerteilung) within the image area of an object point, and from measure-

36 1

MTF MEASUREMENT OF X-RAY IMAQE INTENSIFIERS

ments on image intensifiers without an X-ray screen. From the m.t.f. of the electron optical system, the resolution for different demagnifications and tube potentials was calculated. A comparison was made between this calculated behaviour and the measured one, and the agreement was found to be good.

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The m.t.f. of the input screen, curve 3, was measured and corrected as described above. The m.t.f. of the output screen, curve 4, was measured in vacuum using electron excitation and bar grids of tungsten wire up to 40 lp/mm. The measured m.t.f. was corrected in a similar way to that of the input screen. As the thickness of the photocathode is less than 1000 A, its m.t.f. in 1 for the range of frequencies used. 12-2

362

I. STAIINKE AND € HEINRICH I.

The product of these functions-the combined modulation transfer function of the whole tube-is represented in curve 1 of Fig. 7. Curve 2 shows the measured and corrected m.t.f. of the same X-ray image intensifier. The conformity of both curves is satisfactory. This comparison of the measured m.t.f. and the combined m.t.f. of the individual elements was carried out with about 20 X-ray image intensifiers. We are of the opinion that the agreement found is a confirmation of the correctness of our considerations and calculations. CONCLUSION The measured m.t.f.’s of X-ray image intensifiers can be combined by multiplication of those of the individual elements, provided that the non-linearity of the input screen and the influences of the disturbing processes are corrected by measurement and calculation. The m.t.f.’s then have initial values of unity and they are independent of the measuring conditions. The image transfer itself is determined by three functions: yE as a function of the X-ray spectral energy distribution and filter material, +(P)and the background function U,.

REFERENCES 1. 2. 3. 4. 6.

Molitz, H., Fhotogr. Korrespondent 95, 3 (1969). Wittmann, F. and Rohler, It., Optik 19, 234 (1962). Rosenhauer, K. and Rosenbruch, K. J., 2. Inetrumkde 67, 179 (1969). Rossmann. K., J. Opt. SOC.Anzer. 54, 187 (1964). Stahnke, I. and Heinrich, H., Optik (in press).

DISCUSSION T. c. RINDFLEIBCH: You have measured square-wave response and converted the measurements to sine-wave response. This is a diffcult calculation to do accurately. What error in your results do you think is due to this difficulty, i.e. in the comparison of cascaded sine-wave response function calculations to actual sine-wave response measurements? H. HEINRICH: The error is less than 1-2% as the measured square-wave response functions of the main individual elements, i.e. the screens, drop very sharply at the frequency range corresponding to the limiting resolution of the tube. Y. DOCHET: What was the thickness of the primary screen and of the intermediate glms? H. HEINRICH: The thickness of the primary screen was 300 pm and that of the intmmediate glass 200 pm.