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APPLICATION OF A FRESNEL ZONE PLATE TO -RAY IMAGING

W. L. Rogers, K. S. Han, L. W. Jones, and W. H. Beierwaltes University of Michigan, Ann Arbor, Michigan

The fundamental principles of were be constructed for a collection of point sources and first set forth by Gabor in 1948 (7). Rogers de small objects. Also, since sources located at different scribed the hologram in terms of a generalized Fresnel distances from the zone plate will cast different size zone plate in 1950 (2). In 1961, Mertz and Young shadows, the images will be reconstructed at different realized that a Fresnel zone plate could be used to distances from the hologram, thus giving rise to a construct a hologram using incoherent radiation (3). three-dimensional image. They applied the principle to imaging x-ray stars. The theoretical limiting resolution of the zone plate This technique has now been applied to imaging is determined by the width of the smallest, or outer gamma-ray sources at the suggestion of Barrett (4). most, ring (3). This width is given by The properties of a Fresnel zone plate are de W = Fi(Vn^—Vn —1). (2) scribed in almost any elementary optical textbook (5). A zone plate pattern consists of alternating Here n "is the number of zones and r, is the radius opaque and transparent rings whose bounding radii of the central zone. It is seen that W may be de are in the ratio of the square roots of successive whole creased either by increasing n or scaling down r,. numbers. It behaves as a with the principal Under the assumption that all radiation passing given by through the zone plate falls upon a detector, the detection efficiency is given by integration over the (1) open solid angle. For sources at a distance A greater than r„from a zone plate of radius rn, the solid angle Parallel, coherent light, of A, incident on efficiency, r¡,is given by a zone plate whose central zone has a radius r,, will be brought to a on the axis of the zone plate (3) 8A2 at a distance f in front of the zone plate. There is also a virtual image corresponding to the This includes the fact that the zone plate area is focal length in Eq. 1 located a distance f behind the 50% open. In practice the maximum zone plate zone plate. radius is limited because the plate must be con The method of Mertz and Young may best be structed with a finite absorber thickness to stop the understood by considering a point source of radia gamma rays. This limits the field of view for the tion which is allowed to illuminate a large Fresnel smaller rings. zone plate. If the shadow of this zone plate is photo METHOD graphed on transparency film at a suitable reduction In order to adapt the zone plate to the imaging of in size, a miniature zone plate image results which gamma sources, our high-resolution image intensifier simulates the hologram of a point source. This simi was used as the basic imaging system (6). larity to an interference hologram formed with co Figure 1 shows the image intensifier camera with the herent light is due to the fact that the interference normal parallel-hole collimator replaced by the lead pattern of a plane wave and spherical wave is just a zone plate pattern. Upon illuminating the pseudo hologram with plane coherent light, one reconstructs Received Dec. 17, 1971; revision accepted Apr. 3, 1972. For reprints contact: W. Leslie Rogers, Nuclear Medicine the image of the original point source at the focus Div., University of Michigan Medical Center, Ann Arbor, of the hologram. In a similar manner an image may Mich. 48104.

612 JOURNAL OF NUCLEAR MEDICINE ZONE PLATE SHADOW PATTERN ON CRYSTAL IMAGE AMPLIFIER LENS

RADIOACTIVE POINT SOURCES

FIG. 1. Diagram of ¡mage intensifier camera with Fresnel zone plate. Shadow pattern is focused onto photocathode of image intensifier and output is photo SODIUM IODIDE graphed with 35 mm camera. SCINTILLATOR

Fresnel zone plate. (This zone plate is not being They were located 25 cm from the 10-ring lead zone used to produce effects but only to cast plate, and the Michigan image tube camera was a geometric shadow.) utilized as shown in Fig. 1. The integration time was Two zone plates were constructed of 1-mm-thick 10 sec. This image demonstrates a resolution of be lead for use with »»Tc.The first had ten open zones tween 7 and 10 mm at 25 cm as opposed to the with r, = 1 cm, r20= 4.5 cm, and W = 1 mm, while theoretical resolution of 6 mm. The approximate the second had 30 open zones with r, = 1.6 cm, number of photons incident on the detector may be r«,,= 12.4, and W = 1 mm (W refers to the width calculated using the efficiency given by Eq. (3). In of the outermost open ring). The theoretical limiting this instance 10" photons were incident on the object resolution is related to W by the relative dis crystal. tances between object, zone plate, and crystal: The final two images, C and D, demonstrate the tomographic effect and were made using the 30-ring A + B R = W, (4) zone plate on the image intensifier camera. An IAEA B head phantom was located 50 cm from the zone where A and B are as noted in Fig. 1. For an object plate and the four lesions were filled with "ftniTcwith distance A = 25 cm from either of the above zone specific activity of 1.7 mCi/cc. No background ac plates and B = 5 cm, the resolution is 6 mm. This tivity was used. Both images were reconstructed from limiting resolution will only be reached if the reso lution for the rest of the optical system is substantially better than the zone plate. The image intensifier camera has a line spread function 1.5 mm FWHM for a 9!)1"Tcsource and the zone plate was designed to be compatible with this. Light from a He-Ne laser was used to illuminate the hologram when reconstructing the image. The real image was magnified and brought to a focus on a rear projection screen where it was photographed.

RESULTS Figure 2 shows four images reconstructed from incoherent holograms. Image A was formed op tically using visible light and without using the image intensifier camera. Shadows of a 10-ring emulsion zone plate with W = 0.75 mm were cast on a screen by the back lighted letters. The source-to-zone plate and zone-plate-to-screen distances were 22.5 and FIG. 2. Images reconstructed from incoherent holograms. (A) Reconstruction from hologram formed optically without image in 7.5 cm, respectively. The pattern was photographed tensifier camera. A = 22.5 cm, B = 7.5 cm, W =: 0.75 mm. (B) Image of two 1-cc syringes located 25 cm from zone plate. Each from the screen at about 30:1 reduction. The theo syringe contained 2.8 mCi of """'Tc. Integration time, 10 sec. A retical resolution of 3.0 mm is clearly achieved as 25 cm, B = 5 cm, W — 1 mm. (C) Tomographie section through the center of the "0" is 6 mm diam, and it is sup 13.5- and 0.51-cc lesions of IAEA head phantom located 50 cm from zone plate. Small lesion is just barely visualized while 4- and ported by a 1.5-mm-wide tab which is just visualized. 1.8 cc lesions are defocused but visible. A 50 cm, B - 10 cm, Image B, formed with gamma rays, is of two W 1 mm. (D) Tomographic section through 4- and 1 8 cc lesions. 1-cc syringes each containing 2.8 mCi of 9!)mTc. A — 50 cm, B = 10 cm, W - 1 mm. Depth separation of tomo graphic sections, 5 cm.

Volume 13, NumberS 613 ROGERS, HAN, JONES, AND BEIERWALTES the same hologram. Image C shows the 13.5-cc out that the number of overlapping shadows for a lesion in focus and a hint of the coplanar 0.51-cc given distribution of point sources is governed by lesion. The two other lesions, 4 and 1.8 cc, are visi the diameter of the zone plate and the relative dis ble but defocused. In image D these lesions which tances between object, zone plate, and detector. are coplanar are brought into focus. The two planes Thus the signal amplitude in the hologram for an are separated by 5 cm in depth. increased number of point sources may be main tained at the expense of efficiency by decreasing the DISCUSSION zone plate diameter. It is also evident that a con The resolution obtained was surprisingly close to tinuous source distribution must be broken up into that predicted considering the line spread function a finite number of source elements of dimensions of the image tube camera along with the fact that commensurate with the object resolution. The dy the magnetically focused image tube introduces some namic range problem might be overcome by digital "S" distortion which has a defocusing effect on the recording and reconstruction of the holograms. Al hologram. though the Fresnel transformation is readily accom It is useful to compare the performance of a zone plished in an analog manner with coherent light, plate to that of a pinholc. For the same conditions other transformations may well be better suited to of source, , and detector location a pinhole digital processing. of diameter W will give the same spatial resolution In reconstruction of the image from the hologram as a zone plate with outer ring width W. The zone in our application, background arises from the fol plate solid angle, however, is greater than that of lowing sources: the pinhole by VzM2, where M is the ratio of zone 1. Undiffractcd plane wave transmitted by the plate diameter to pinhole diameter. For imaging a hologram. point source the zone plate will give an increased 2. Defocused light from the virtual image. signal-to-noise ratio of M/V2. Comparing the 9-cm- 3. Light diffracted from the edge of the hologram. diam zone plate used to obtain the image in Fig. 4. Light diffracted by the image of a burned re 2(b) to a 1-mm-diam pinhole which would give gion on the image tube photocathode. equal resolution, it is seen that there is a factor of 5. Film grain and intermodulation noise arising 4,050 gain in solid angle for the zone plate over the from nonlinear film response. pinhole with a corresponding increase of 64 in signal The general background seen in all images is due to noise. predominantly to transmitted plane wave and the The hologram used to generate Fig. 2B was re defocused virtual image. The circular fringe pattern corded with an estimated overall efficiency of 3%. which is just visible in A and which is evident in That is, of the 10°gammas impinging on the detec B is the diffraction pattern from the edge of the holo tor, approximately 3 X IO4 counts were recorded gram. The vertical fringe pattern in B comes from on film. When the time was reduced by a the burned region of the photocathode. Background factor of 10, the image became very noisy and ap originating from the transmitted plane wave and the peared to be badly limited by poor statistics. Since virtual image may be reduced by using spatial filter ing and off-axis techniques described by Leith et al 3,000 counts in an image of this size should yield a fairly clean image, it is clear that the actual efficiency (8). No processing was done on the images shown. of the zone plate in this instance is less than that The preliminary study reveals evidence that a predicted for a point source. Fresnel zone plate shows promise for gamma imag The causes of image degradation are to be found ing in nuclear medicine. The promise appears greatest both in the hologram and in the reconstruction proc for imaging small sources with good resolution and ess. As a direct consequence of the incoherent forma high efficiency. Although there exists a wide range tion of the hologram both a theoretical and ex of problems to be explored both experimentally and perimental limitation is placed on the maximum theoretically before this promise can be realized, it information density which may be recorded. Leith is felt that this approach may stimulate significant et al point out (7) that the signal amplitude in the advances in isotope imaging. holograms decreases as 1/VN, where N is the num ber of point source holograms which are being in ACKNOWLEDGMENTS coherently superposed. As the number of point The authors are indebted to Emme« Leith and Jerry sources is increased, the contrast is reduced and Shapiro for their help and advice. We also wish to acknowl severe demands are made on the dynamic range of edge similar work which is presently in progress at the Raytheon Research Division. This work was supported in the recording medium. Although these considerations part by the National Institutes of Health Grant GM have not yet been fully evaluated, it should be pointed 16188-03, and the Nuclear Medicine Research Fund.

614 JOURNAL OF NUCLEAR MEDICINE USE OF FRESNEL ZONE PLATE FOR GAMMA IMAGING

REFERENCES 5. JENKINS FA, WHITK HE: Fundamentals of Optics. New York, McGraw-Hill, 1950, p 355 /. GABOR D: Microscopy by reconstructed wave-fronts. 6. ROGERSWL, THOMASFD, BEIERWALTESWH, et al: Proc Roy Soc (London) Biol A197, 454-487, 1949 The U.M.-Bendix scintillation camera. Biomed Sei Instrum 6: 248-255, 1969 2. ROGERSGL: Gabor diffraction microscopy: the holo gram as a generalized zone plate. Nature (London) 166: 237, 7. LEITH EN, UPATNIEKSJ: Recent advances in hologra phy. In Progress in Optics 6, Wolf E, ed, Amsterdam, North- 1950 Holland Publishing Co, 1967, pp 46-48 3. MERTZ L, YOUNG NO: Fresnel transformation of 8. LEITH EN, UPATNIEKS J: Reconstructed wavefronts images. In Proc Int Conf Optical last, London. 1961. p 305 and communication theory. J Opt Soc Am 52: 1123-1130, 4. BARRETT H: Personal communication, July 1971 1962

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