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Home , Gamma (agency), Pinhole camera

FRESNEL 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 -ray image. Systems such as the Anger nately transparent and opaque to the gamma rays, (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 , 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- is that here the "hologram" was formed ray lens is impossible because gamma rays are not by shadowing rather than by . appreciably refracted by matter. However, this paper Decoding or reconstruction is accomplished with describes a "coded" aperture which performs the a 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 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 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 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. A reconstruction of a 10 /xCi simulated 1S1Ithy in the zone plate case. Exactly how many more is still to be resolved. Experimental and theoretical roid phantom is shown in Fig. 3. A total of 110,000 counts were collected by the Anger camera* in a investigation of this problem is underway, but results 3-min with S, = 30 cm and S2 = 15 cm. to date are inconclusive. Another advantage of the zone plate camera is The counting rate could be increased about an order that three-dimensional information about the object of magnitude, if this were important, simply by using is recorded in a single exposure on a single hologram, S, = 10 cm and S2 = 5 cm. Further reduction in just as in optical holography. For the zone plate these values would result in a loss in resolution due camera, the reconstruction is tomographic—only a to the finite crystal thickness. thin slice of the object is in focus at once. Different The phantom has two cold nodules, one of which planes can be brought into focus simply by changing shows up as a shortened right lobe. The other is not focal distances in the optical processing system. The detected because of inadequate resolution. The the , defined as the range in S, which an oretical resolution 8 is about 2 cm, and inspection object must move for a two-fold decrease in resolu of Fig. 3 shows that the actual value is not substan tion, is given by tially worse. Figure 3 also indicates that 110,000 counts are AS, 3 S, (10) completely adequate for this object with the zone S, 8N S2 plate aperture, and probably fewer could have been used. A pinhole image of the same object required As the numerical examples in Table 1 show, this about 15,000 counts for comparable image quality. fractional depth of field is usually quite small. How ever, if an extended absolute depth of field is desired, * Nuclear-Chicago Pho/Gamma III, without high per rather than a tomographic display, it can be obtained formance modifications.

384 JOURNAL OF NUCLEAR MEDICINE FRESNEL ZONE PLATE IMAGING

A useful variation on the system described above liver, there are definite limitations which we will is an off-axis zone plate to aid in separating the DC delineate more carefully in forthcoming publications. and information-bearing components of the light Future research in this field should include the in beam (11). This approach, which is analogous to vestigation of other possible aperture codes and asso using an off-axis reference beam in optical hologra ciated decoding methods, extension to other types phy, gives much cleaner images but poorer object of radiation, and most importantly, clinical evalu resolution for a given camera resolution*. Therefore ation. it is much more suitable for image-intensifier cam eras than for an Anger camera. Comparative per ACKNOWLEDGMENTS formance figures are given in Table 1. The author is grateful to F. A. Horrigan for many in The Fresnel zone plate aperture is but one mem valuable suggestions and for continuing advice and encour ber of a large class of possible coding functions agement. G. D. DeMeester and D. T. Wilson were in large measure responsible for obtaining the experimental results which can be used to image incoherent radiation. reported here. Discussions with J. Sage and R. W. Bierig Dicke (12) has proposed a random array of pinholes were also very valuable. Melvin Farmelant was most help for the same purpose. Also, the author (13) has ful in permitting us to use his laboratory and in providing described the use of a linear array of pinholes with insight into the medical aspects of this development. varying spacing, or essentially a one-dimensional off-axis zone plate. Here the decoding was done REFERENCES electrically with a dispersive filter rather than opti /. ANGER HO: Scintillation camera. In Instrumentation in Nuclear Medicine, vol 1, HiñeCJ, ed. New York, Aca cally. An excellent discussion of the requirements on demic Press, 1967, pp 485-552 the codes is given by Mertz (77). 2. BENDER MA, BLAU M: The autofluoroscope. Nucle onics 21 : No. 10, 52-56, 1963 3. MALLARD JR, WILKS RJ: The Aber gammascope, an SUMMARY image intensifier camera. In Medical Radioisotope Scintig- In summary, we have shown that a Fresnel zone raphy, vol 1, Vienna, IAEA, 1969, pp 3-12 plate aperture permits the recording of a gamma- 4. THOMAS FD, BEIERWALTES WH, KNOLL GF, et al: A new scintillation camera. In Medical Radioisotope Scin- ray image in a coded form, analogous to a hologram, tigraphy, vol 1, Vienna, IAEA. 1969, p 43 but with an enormous increase in gamma-ray col 5. YOUNGNO: Sky and Telescope 25: 8-9, 1963 lection efficiency compared to a pinhole or collimator. 6. MERTZ L, YOUNG NO: Fresnel transformation of This advantage can be used by the physician to either images. In Proc International Conf on Optical Instruments, reduce the administered dose of radiopharmaceuticals London, Chapman and Hall, p 305, 1961 7. JENKINS FA, WHITE HE: Fundamentais of , or to decrease the time required to obtain an image. New York, McGraw-Hill, 1957 The practicality of the scheme has been demonstrated 8. SHULMAN AR: Optical Data Processing, New York, for small objects such as the thyroid gland. For high- John Wiley, 1970 resolution imaging of large objects, such as the 9. STROKEGW: An Introduction to Coherent Optics and Holography, New York, Academic Press, 1966 10. STIGLIANI DJ, MITTRA R, SEMONIN RG: Resolving * The resolution, field of view, and depth of field of a zone power of a zone plate. / Opt Soc Amer 57: 610-613, 1967 plate camera using an off-axis zone plate are the same as //. MERTZ L: Transformations in Optics, New York, those of a camera using an equivalent on-axis plate having John Wiley, 1965 the same diameter and . However, the off-axis 12. DICKE RH: Scatter-hole for x-rays and plate will have a minimum zone width Arx which is smaller by a factor of 2 to 3 (depending on how far off-axis the gamma rays. Astropliys J 153: L101, 1968 plate is) and therefore requires a smaller dram. The equations 13. BARRETT HH: Pulse compression techniques in nu given in the text hold only for an on-axis zone plate. clear medicine. Submitted to Proc. IEEE

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