FRESNEL ZONE PLATE IMAGING IN NUCLEAR MEDICINE Harrison H. Barrett Raytheon Research Division, Waltham, Massachusetts Considerable progress has been made in recent so that there is essentially no collimation. The zone years in detecting the scintillation pattern produced plate has a series of equi-area annular zones, alter by a gamma-ray image. Systems such as the Anger nately transparent and opaque to the gamma rays, camera (7) and Autoflouroscope (2) give efficient with the edges of the zones located at radii given by counting while an image intensifier camera (3,4) rn = n = 1,2, N. gives better spatial resolution at some sacrifice in (D efficiency. However, the common means of image To understand the operation of this aperture, con formation, the pinhole aperture and parallel-hole sider first a point source of gamma rays. Then collimator, are very inefficient. Only a tiny fraction the scintillation pattern on the crystal is a projected (~0.1-0.01%) of the gamma-ray photons emitted shadow of the zone plate, with the position of the by the source are transmitted to the detector plane shadow depending linearly on the position of the (scintillator crystal), and this fraction can be in source. The shadow thus contains the desired infor creased only by unacceptably degrading the spatial mation about the source location. It may be regarded resolution. It would be desirable, of course, to have as a coded image similar to a hologram. Indeed, a a large-aperture, gamma-ray lens so that good col Fresnel zone plate is simply the hologram of a point lection efficiency and good resolution could be ob source (9). The essential difference from normal tained simultaneously. Strictly speaking, a gamma- holography is that here the "hologram" was formed ray lens is impossible because gamma rays are not by shadowing rather than by diffraction. appreciably refracted by matter. However, this paper Decoding or reconstruction is accomplished with describes a "coded" aperture which performs the a laser beam as in optical holography. The scintilla same function and permits an increase in collection tion pattern on the crystal is detected, in our ex efficiency of two to three orders of magnitude over periments with an Anger camera, and the output a pinhole or parallel-hole collimator. It was first pro display is photographed as a positive transparency. posed by Mertz and Young (5,6) for use in x-ray This transparency is then the optical hologram cor astronomy. responding to the coded gamma-ray image. The basic concept is illustrated in Fig. 1. The When a coherent light beam passes through the aperture is a Fresnel zone plate (7,8), thin enough transparency, some of the light is diffracted by the zone plate into a small focal spot which is the image Scinlillotor of the original gamma-ray point source. If two point Polaroid camera with sources were present, two distinct focal points would transparency film Display be produced. Then, to the extent that linear super position holds, any general object may be considered ff to be made up of point sources and will be correctly Radioactive object imaged. / Scintillation camera The major practical problem is the undiffracted or (e.g.Anger camero or image intensifier) DC light which results from the incoherent nature FIG. 1. Fremei zone plate camera. Zone plate is heavy metal such as lead mounted on backing plate of light metal such as Received Dec. 15, 1971; revision accepted Jan. 25, 1972. aluminum and machined into zones which are alternately transparent For reprints contact: Harrison H. Barrett, Research Di and opaque to radiation. vision, Raytheon Co., 28 Seyon St., Waltham, Mass. 02154. 382 JOURNAL OF NUCLEAR MEDICINE of the gamma radiation and the fact that a shadow is recorded rather than a diffraction pattern. In optical holography the diffraction amplitude recorded in the hologram has both positive and negative values with a zero average value. The gamma-ray flux plays Transform the role of the amplitude in the present case, but, of lens ~ / Transparency ( reconstruction plane) course, cannot be negative. Much of the difficulty from figure I with the DC light is eliminated by placing a Schlieren stop in the focal plane of a lens as shown in Fig. 2. FIG. 2. Reconstruction system for decoding image obtained with zone plate camera. The optical amplitude distribution in this plane is the Fourier transform of the hologram transparency Usually it is desirable to have a point source project (8). Therefore the DC light is concentrated near the zone plate so that it about fills the crystal: the axis and is blocked by the stop. However, some of the desired information in the hologram also con 2r.,A Dïtal- (5) tains low spatial frequencies which are blocked by the stop, particularly for large objects. In addition, If Fjj is much smaller than this, collection efficiency there are fluctuations associated with the DC trans is sacrificed. If it is much larger, resolution must be parency of the zone plate which cannot be blocked sacrificed if Eq. 4 is to be satisfied. and which contribute additional noise to the recon Equation 5 implies that the collection aperture struction. The net result is that small objects are varies with position in the field. We may define a more easily imaged than large ones. field of view (FOV) as the diameter of a circle in The characteristics of this imaging system are the object plane for which the center of the zone derivable from the well-known focusing properties plate projects to the edge of the crystal. The efficiency of a zone plate (7,8). A detailed treatment will be at the edge of this field will be somewhat less than published separately. The minimum resolvable (Ray- one half of its value at the center. Then by simple leigh criterion) separation of two point sources, 8, geometry, is given by S, FOV = D,UI (6) S = /9(N) ArN (2) which is the same as for a pinhole camera except in which /Î(N)is a parameter of order unity which there the falloff in efficiency at the edge of the field depends on the number of rings in the zone plate is abrupt while for the zone plate camera it is grad (10), S, is the distance from object to zone plate, and ual. Furthermore the resolution also varies over the S2 is the distance from zone plate to camera. ArN is field of a zone plate camera, being only about one the width of the narrowest (outermost) zone in the half as good at the edge defined by Eq. 6 as at the plate, i.e., center. If flatness of efficiency and resolution over ArN= rN —rN_, «r,/2(N)V» = rs/2N. (3) the field is important, it can be achieved at the ex pense of center efficiency and resolution by reducing The scintillation camera should be capable of re rN below the value given in Eq. 5, or at the expense solving this outer ring since an unresolved ring con of center resolution alone by increasing rx. As with tributes noise but no image information. Therefore a pinhole camera, very small objects can be well re the camera should satisfy the condition solved by making Si/S2 or ArNsmall enough, but the s. + s2 price must be paid in FOV or efficiency. Ar.v o ucan (4) Note that Eqs. 4 arid 5 fix the maximum number of rings (opaque plus transparent) in the zone plate, in which donm is the intrinsic camera resolution. since Equation 2 shows that the zone plate aperture has a resolution equivalent to a pinhole aperture where J_ (7) the pinhole diameter is equal to ß(N)ArN-.The final 2rs 4N image resolution with a zone plate camera may be independent of S,/S2. It is desirable to make N as somewhat degraded by film nonlinearities and lens large as possible for maximum resolution. Therefore aberrations in the reconstruction system, but our we should have experience has been that the theoretical limiting res Dxt olution, Eq. 2, can be closely approached in practice. N (8) The other properties of the zone plate camera re late to the diameter of the scintillator crystal, Dxtnl. which for an Anger camera means that N 6-7. Volume 13, Number 6 383 BARRETT TABLE 1. CALCULATEDCAMERASZonePARAMETERS OF FRESNEL ZONE PLATE parametersAssumed plate propertiesResolution(i) detectorparametersAnger width(N)66ó25252567*67«7oneof zones field(AS,/Si)<%)9.312.418.62.253.04.56.75913.5Relativeefficiency(»J«p/7)ph)170170170330033003300367367367of (mm)3.35.06.70.671.01.330.671.01.33including(mm)6.413291.2244.93.87.215through cameradcftm cmDn.i= 1 cmImage= 24 intensifiera, mmDxt.imi — 2 cmImage= 20 intensifiera mD.i.,1ct tu —2 in cm(with-. 20 off-axiszone plate)* Off-axis zone plateSpacingratio(5,/S,)%12%12%12shiftedbySmallestNo.diameter.(Art») zones 8Imaging 75.FOV(cm)122448102040102040Depth The gamma-ray collection efficiency ijivof the zone plate camera relative to a pinhole of the same reso lution and same spacings S, and S2, is i;phi?,p ~_ transparentarea of equivalentarea of zonepinholeplate I/2(2rN)2 = *gr (it) For N = 7 this ratio is 230, which means that for a point source, an image with a given signal-to-noise FIG. 3. Reconstructed image of 10-/uCi thyroid phantom taken ratio can be obtained 230 times faster with a zone with lead zone plate (on-axis) and Anger camera. plate camera than with a pinhole. For more com plicated objects the advantage is less since more at the expense of sensitivity by increasing Si and S2 counts are required to get a comparable image quality in the same proportion.