by referring to fig1 - 5 , along with the following detailed discussion , the overall construction and operation of the present invention can best be understood . as will become evident to one of ordinary skill in the art , fig1 - 5 depict the preferred embodiment of the present invention . however , alternate constructions and variations of this invention can be made without departing from the scope of this invention . consequently , it is to be understood that the construction shown in fig1 - 5 is provided for exemplary purposes only and is not intended to limit the present invention thereto . as is well - known in the industry , every speaker system &# 39 ; s performance is affected by seven basic acoustical modes of operation . these seven modes are reflections , diffraction , refraction , diffusion , coupling , loading , and summation . in order to produce a true hemispherical wavefront from a single loudspeaker enclosure , each of these modes must be carefully balanced and applied to the designs . since many of these modes are competing , each must be controlled and defined in their own unique characteristic way , as they apply to the wavelength of the frequency being transmitted . by integrating these acoustical modes as well as the inherent natural wavefront shape of various frequencies , the desired operation and preferred wavefront pattern can be created . as shown in fig1 loudspeaker system 20 of the present invention comprises at least one driver 21 , spherical enclosure 22 and cooperatively associated reflector 23 . in the present invention , driver 21 is designed for optimum sensitivity or efficiency , bandwidth or frequency response , linearity or flatness of response , transient response , lack of distortion or coloration , power handling and maximum sound pressure level capability . in order to function in the intended manner , all of these qualities must be present in speaker or driver 21 , since spherical enclosure 22 and cooperating reflector 23 function as passive wave shaping and controlling devices , and cannot add to the purity , quality or fidelity of the acoustical signal generated by driver 21 . spherical enclosure 22 and reflector 23 are constructed using generally well known forming technology in order to achieve the desired shape and the desired diameter . typically , spherical enclosure 22 and / or reflector 23 may be formed from a wide variety of fabrication materials . although any desired material may be employed , the preferred materials for fabricating spherical enclosure 22 , and reflector 23 comprises one selected from the group consisting of fiberglass , plastics , structural foams , aluminum bonded to sound dampening materials , and steel bonded to sound dampening materials . in addition , although a wide variety of plastics made be effectively employed , the preferred plastics for forming these components are selected from the group consisting of acrylics , styrenes , polyvinyl chlorides and polycarbonates . reflector 23 is a principal component of the present invention in providing the desired hemispherical wavefront . as shown in fig1 - 5 , reflector 23 comprises a radial concave shaped surface 26 extending from apex 24 at the center thereof and terminating at outer peripheral rim 25 . in addition , in this embodiment of the present invention , concave shaped surface 26 incorporates a plurality of reflector vanes 30 formed on surface 26 and radially extending from apex 24 . as detailed herein , vanes 30 provide a substantial enhancement to the dispersion of high frequency waves . as depicted in fig1 - 5 , the cross - sectional profile forming radically extending concave shaped surface 26 is not linear , but comprises a geometric form which defines an exponentially progressive curve . the form of the curve begins at the center or apex 24 of reflector 23 and proceeds in a radial fashion outwardly to rim 25 . the curve is symmetrical both radially and annularly about the entire circumference of reflector 23 . in addition , each reflector vane 30 is constructed with an exponential cross - section that is continuously variable over its entire length and with an axial profile that is also exponential . the feature of each vane being continuously variable over its profile is a function of , and an adjunct to , the ray analysis and wavelength propagation of the reflector surface profile . in analysis , the individual vane profiles emulate a specific section of the ( host ) reflector with the exception that they are physically positioned to cause acoustical reflections or secondary ray patterns at higher angles of incidence thereby supplementing the acoustical reflection properties of the reflector . the practical design of the vanes is in accordance with simple ray analysis based on the incidental and coincidental reflection properties of every wavelength of concern . the reflector is somewhat limited in its mathematically theoretical configuration to effectively allow both ideal lower frequency wave shaping and . at the same time , provide the ideal high frequency dispersion . therefore , in order to avoid a significant compromise in reflector design , the reflector is primarily designed to control the reflections of the lower frequencies . then , the vanes , as supplemental reflectors , can be designed to control the higher frequencies . when appropriate profile curves are designed for the reflector and the vanes , a synergistic harmony of full hemispherical reflections results . in accordance with the present invention , the progression of radially extending concave shaped surface 26 of reflector 23 comprises a form / factor that is complementary to spherical enclosure 22 . since the diameter of the spherical enclosure 22 is fixed , the diameter thereof becomes the reference baseline for calculating the profile shape of surface 26 of reflector 23 . since the shape of surface 26 comprises a continuous exponentially progressive curve , the exponential form must become a variable in its progression in order to affect the desired result . this continuous exponential curve is best defined by the following formula : de = linear axial distance between reflector and sphere at any p 1 , p 2 . . . p n = linear axial distance of any expressed as the expansion factor of the prime parameter a c / p l in addition , any linear distance between reflector 23 and spherical enclosure 22 , at any mutual point along the radial dimension , is a numerical factor in the exponential progression . accordingly , the specific exponential shape of surface 26 of reflector 23 , along with reflecting ray patterns between the diaphragm of driver 21 and reflector 23 , combine together to define the performance qualities of the ultimate objective , namely the acoustical spatial wave shaping which , in turn , describes a hemispherical polar coverage pattern within the system &# 39 ; s power bandwidth at a point of summation of approximately eight times the reflector &# 39 ; s diameter . furthermore , in this embodiment , vanes 30 are strategically placed about apex 24 of reflector 23 with the position and size of vanes 30 being determined by calculations based upon the wavelengths or frequencies of particular concern . the top or point end of each vane 30 is designed to represent the highest practical frequency of the system &# 39 ; s power bandwidth , while the radiused or wide end of the vane is designed for the lowest or the cutoff frequency . in accordance with the present invention , the cooperation of driver 21 , spherical enclosure 22 , and reflector 23 with vanes 30 on surface 26 establishes the final shape and coverage patterns of all of the frequencies produced by driver 21 . by constructing surface 26 of reflector 23 and secondary reflector vanes 30 in the manner detailed above , an optimum , highly desirable , hemispherical sound wave pattern is achieved . as discussed above , by forming the plurality of secondary reflector vanes 30 on surface 26 of reflector 23 , high frequency dispersion is substantially enhanced and greater polar coverage linearity is achieved . as detailed above , the particular size , shape , number , and position of reflector vanes 30 are determined by the construction of surface 26 of reflector 23 and the polar coverage characteristics which result in conjunction with the acoustical energy source , namely driver 21 . in practice , secondary reflector vanes 30 function in exactly the same way as surface 26 of reflector 23 . however , reflector vanes 30 are variable in profile at different angular positions . as a result , as is clearly depicted in fig4 ( a )- 4 ( d ), the performance achieved by reflector 23 incorporating vanes 30 is substantially enhanced . by referring to fig4 ( a ), the acoustical ray pattern produced by surface 26 of reflector 23 is depicted . as shown therein , as the acoustic wave front impinges upon surface 26 of reflector 23 , the waves or rays reflect off of surface 26 at different angles , with the reflected rays converging at a point away from reflector 23 . in order to eliminate or reduce the convergence of the reflected rays , it has been found that the incorporation of secondary reflector vanes 30 produce the desired enhanced result . in fig4 ( b )- 4 ( d ), the reflected ray pattern at different cross - sectional positions along vanes 30 are clearly shown . as is evident from a review of these figures , vanes 30 produce a substantial enhancement to surface 26 of reflector 23 . in this regard , the acoustical rays are reflected from vanes 30 on surface 26 of reflector 23 in an ever increasing parallel configuration , depending upon the radial position along the vanes 30 being considered . as a result , the convergence of the rays is substantially reduced or effectively eliminated . in effect , vanes 30 represent segmented sections of surface 26 of reflector 23 , with the acoustical near field being substantially unchanged . however , in the acoustical far field , passed the point of summation , the effect of incorporating vanes 30 on surface 26 is substantial . in this regard , the lobes produced by the incorporation of vanes 30 are summed and averaged , providing a smoothing condition due to the convex shape along the entire length of each vane 30 . as shown in fig5 by incorporating vanes 30 on surface 26 of reflector 23 , with vanes 30 being properly designed , correctly oriented , a substantially improved total or overall effect is achieved . in this regard , the high frequency band acoustical energy output is increased at the more obtuse or off - axis coverage angles of the hemispherical polar coverage pattern . it will thus be seen that the objects set forth above , among those made apparent from the preceding description , are efficiently attained and , since certain changes may be made in the above article without departing from the scope of the invention , it is intended that all matter contained in the above description or shown in the accompanying drawings shall be interpreted as illustrative and not in a limiting sense . it is also to be understood that the following claims are intended to cover all of the generic and specific features of the invention herein described , and all statements of the scope of the invention which , as a matter of language , might be said to fall therebetween .