the present invention involves a method and apparatus for reducing interactions between charged particles in a particle beam imaging system , for example electron - electron interactions in an electron beam projection system , which interactions can contribute to image blurring , or , in other words , degradation of image resolution at the work piece . for purposes of clarity and to avoid prolixity the description of the present invention uses an electron beam system as an example . however , a person of ordinary skill in the art would understand that the invention is not limited to electron beam projection systems , but would encompass any particle beam imaging system . the solution to the problem of electron - electron interactions , lies in part , in recognizing that not all parts of the beam trajectory between the electron gun and the image at the workpiece contribute equally to image blurring . in an e - beam projection system there are a series of planes within the envelope of electron trajectories in the beam path and normal to the central axis in which the beam cross - sectional area is locally minimal . with reference to fig1 examples of such planes include the planes located by points 124a , 124b and 124c . the image in the planes located by points 124b and 124c are conjugate to the crossover 124a of the electron gun 101 . the average distance between electrons is much smaller at crossover images 124b and 124c than at other points along the electron beam . thus , effects due to electron - electron interactions are much greater at the crossover images 124b and 124c than at other points along the electron beam . therefore , a significant portion of the overall electron - electron interaction effects arises from the beam path in the vicinity of such crossover images . with reference to fig2 a there is shown in schematic form an exemplary e - beam projection system which embodies the present invention . in fig1 a and 2a like numerals indicate similar features . the system of fig2 a includes illumination optics 212 and imaging optics 214 disposed about a central axis 210 , and separated by a reticle ( e . g . mask ) 220 disposed normal to the central axis 210 . the illumination optics 212 and imaging optics 214 have functions that are similar to their prior art counterparts discussed above with reference to fig1 . included within the illumination optics 212 is an electron gun 201 including cathode 216 and associated electrodes 202 , condenser 217 and illuminator 218 . interposed between condenser 217 and illuminator 218 , at crossover image 224b and normal to the central axis 210 , is an aperture 240 . the aperture 240 functions to alter the crossover image 224b so as to increase the average distance between electrons at conjugate crossover images , for example , crossover image 224c . the aperture 240 is preferably annular , having a central circular area which is substantially opaque ( non - transmissive ) to electrons surrounded by a ring - shaped area which is substantially transparent to electrons and an outer periphery which is substantially opaque to electrons . the transparent portion of the aperture 240 may be in the form of a membrane thin enough to be effectively transparent , and in this case the central opaque portion may be supported by the membrane . alternatively , the transparent portion may be an open area , in which case the central opaque portion must be supported , for example , by struts extending from the outer opaque portion of the aperture . methods of fabricating annular apertures having struts are known and will not be discussed in detail herein . the aperture 240 is preferably formed from a refractory metal or from a noble metal having a high melting point , for example platinum , because the power dissipation at the annular aperture may be high . the annular aperture 240 changes the electron beam from solid to hollow , thereby increasing the average distance between electrons in the electron beam at cross - over image 224b and subsequent conjugate images ( e . g . 224c ). with reference to fig2 b there are shown the beam current distributions ( e . g . beam current as a function of radial position from central axis 210 ) at various points along the central axis 210 of the system 200 . beam current distribution 242 shows a solid beam formed by the electron gun 201 at the gun crossover point 224a which may be an approximately gaussian distribution . beam current distribution 242 indicates that the beam current is maximum at the central axis 210 and falls off as radial distance from the axis increases . therefore the average distance between electrons is smallest near the central axis 210 and increases as the radial distance from the axis increases . hollow beam current distributions 244 and 246 show the effect on the current distribution of the respective crossover images 224a and 224c when an annular aperture is placed as described above . more particularly , the electrons closest to the central axis at crossover image 224b are not transmitted by the aperture 240 , thus increasing average distance between electrons at crossover image 224a and conjugate image 224c . it should be noted that the annular aperture 240 also has the effect of reducing the overall current of the electron beam , as compared to the solid beam . however , this reduction in beam current should be compensated for by increasing the emission current ( e . g . current magnitude exiting the electron gun 201 ), such that the desired current arrives at the workpiece . for example , if the desired beam current at the workpiece is i and the annular aperture 240 removes 50 % of the beam current , the magnitude of the emission current should be 2i . such compensation maintains the throughput of the system , while simultaneously enhancing resolution . numerical calculations comparing a conventional electron beam projection system and a system according to the present invention , each having the same beam current incident on the workpiece , show up to approximately a 30 % reduction in trajectory displacement aberration of the system according to the present invention over the conventional system . the preferred placement of the aperture 240 may change depending on the particular characteristics of the overall system 200 . for instance , if in a particular system the boersch effect contributes more to overall aberrations than does trajectory displacement , the aperture 240 is preferably placed at the first crossover image in the illumination optics 212 , that is , the crossover image nearest the cathode 216 . on the other hand , if for a particular system trajectory displacement is found to be more significant than the boersch effect , it is sufficient that the aperture 240 be placed at any crossover image in the illumination optics 212 such that the crossover image 224c in the imaging optics 214 is hollow . moreover , while the envelope of electron trajectories of the exemplary system depicted in fig2 shows parallel illumination of the reticle 220 , wherein the crossover image 224c of the imaging optics 212 is at the back focal plane of lens 222 , the invention can also be practiced on systems employing non - parallel illumination . in a system employing non - parallel illumination , the crossover image in the imaging optics will appear at a different position . however , the crossover image in the imaging optics will still be hollow if the annular aperture has been properly positioned at a crossover image in the illumination optics as described above . while the invention has been particularly shown and described with reference to preferred embodiments thereof , it will be understood by those skilled in the art that various other changes in form and detail may be made therein without departing from the spirit and scope of the invention .