one embodiment of a mechanism 20 formed in accordance with the present invention is depicted in the figures . the mechanism 20 includes two generally annular mounting members , hereafter referred to as a lower mounting member 22 and upper mounting member 24 . the designation of “ lower ” and “ upper ” is for reference purposes only . the mounting members 22 , 24 are nearly identical in construction and are interchangeable . the following description focuses on the upper mounting member 24 with the understanding that the lower mounting member 22 is similarly constructed except where otherwise specified . the upper mounting member 24 is metal and is generally annular with a depth ( measured vertically in fig2 ) that is about one - half of its radius ( as measured in a plan view ). a notch 26 ( fig1 ) is cut through the mounting member 24 . an open end of a somewhat elongated enclosure 28 is attached to the mounting member at the notch 26 to protrude radially outwardly therefrom . ( the corresponding enclosure of the lower mounting member 22 is shown at 128 .) it is noteworthy that the mounting member may also be formed of rigid plastic , such as delrin ®. this would be a useful configuration when the mechanism is used in a magnetic field as occurs , for example , in tokomak polarimeter applications . a primary function of each mounting member 22 , 24 is to support the optical assembly of a photoelastic modulator ( pem ) 30 . the primary components of the pem &# 39 ; s optical assembly include an optical element 32 formed of fused silica . other material , such as fused quartz , calcium fluoride , zinc selenide , silicon and others may be used to form the optical element . ( the corresponding optical element supported in the lower mounting member 22 is shown at 132 .) the optical element 32 is a generally square - shaped member but having beveled corners that define flat support surfaces 34 , the function of which is described below . the optical element also has an entry surface 36 against which an incident light beam is directed while the pem is operating . a quartz piezoelectric transducer 38 ( fig1 ) is bonded to one of the four sides of the optical element 32 . electrical leads ( not shown ) from the transducer are connected to a driver circuit for vibrating the optical element 32 . the optical element 32 is supported so that its entry surface 36 extends across the central aperture 40 of the upper mounting member 24 . preferably , the center of the entry surface is aligned with the central axis 41 of that aperture 40 ( fig2 and 3 ). the optical element 32 is free to vibrate when driven as described above . in this regard , the optical element 32 is mounted to the upper mounting member 24 by somewhat flexible supports 42 ( fig1 ) that secure the optical element 32 at each support surface 34 so that the optical element is substantially suspended within the central aperture 40 of the upper mounting member 24 . each one of the supports 42 includes an elastomeric rod 44 that may be formed , for example , from extruded silicone ( polysiloxane ) cords that are cut to a specified length to define the rod 44 . one of the two , flat ends of the rod 44 is attached , as by an adhesive , to one of the support surfaces 34 on the optical element 32 . the other , free end of the rod 44 fits within a sleeve 46 that is carried inside of a cylindrical slider 48 . the sleeve 46 has a cylindrical axial bore formed through one end to receive the elastomeric rod 44 . the sleeve 46 is a rigid , externally threaded member that is threaded into an internally threaded bore 50 ( fig3 ) of the slider 48 . each on of the four sliders 48 fits inside of a radial hole 52 ( fig3 ) formed through the curved side 56 of the upper mounting member 24 . the slider 48 , with the sleeve 46 threaded into its bore 50 , is slid with the radial hole 52 until the rod 44 is received in the bore of the sleeve 46 . the slider 48 is secured in place via a setscrew 54 that is threaded vertically ( fig1 ) through the upper mounting member 24 to bear against the slider . with the slider secured in place , the sleeve 46 is advanced until the free end of the rod 44 ( that is , the end not bonded to the optical element support surface 34 ) is completely received within the bore of the sleeve . the sleeve 46 may be advanced by hand or with a tool . in this regard , the outer end of the sleeve 46 may be shaped to define a socket for an allen - type wrench or the like that can be extended into the bore 50 of the slider to reach the socket in the sleeve 46 . the foregoing description of an exemplary support 42 applies to all four supports 42 on both mounting members 22 , 24 . as depicted in fig1 , four supports are employed to secure the optical element 32 in place relative to the upper mounting member 24 . the supports are thus arranged in diametrically opposed pairs . alternative configurations of such supports 42 are contemplated , such as those described in u . s . pat . no . 7 , 800 , 845 owned by the assignee of this application . as another alternative , the rod 44 could be replaced with a glass or plastic conical member with the base of the cone bonded to the support surface 34 and the pointed end seated in the central opening of an annular elastomeric grommet that is mounted on the end of a cylindrical barrel that is secured in the hole 52 . in the figures , the grommet and barrel would appear as the sleeve 46 and slider 48 respectively . the setscrew 54 would hold the barrel and grommet combination in place . the transducer 38 is attached to the optical element 32 , and not otherwise supported by the upper mounting member 24 . the transducer 38 is an elongated , bar - like member that extends from the optical element 32 and into the enclosure 28 that protrudes radially outwardly from the outer , curved surface 56 of the upper mounting member 24 . the longitudinal axis 58 of the transducer 38 is aligned with the center of the optical element 32 and , as such , this axis 58 coincides with the optical axis of that optical element . for purposes of this description , the projection of the optical axis of the optical element 32 of the pem 30 onto the structure of the upper mounting member 24 is illustrated by axis line 58 , which will hereafter be referred to as the optics axis 58 of the upper mounting member 24 . the lower mounting member 22 has a similarly defined optic axis 158 , as shown in fig1 , 3 and 4 . the angle between these two optics axes 58 , 158 ( as viewed along the central axis 41 ( see fig1 and 4 ) is referred to as the optics angle 60 . it will be appreciated that the optics angle 60 ( and the associated adjustments to that angle discussed below ) corresponds directly to the angle between the optical axis of the optical element 32 in the upper mounting member 24 and the optical axis of the optical element 132 in the lower mounting member 22 . any minor variations between those two axes ( which may be attributable to , for example , a slight misalignment of the supports 42 that secure the optical elements 32 , 132 in place ) can be accounted for as will be discussed below . as best shown in fig1 and 2 , each mounting member 22 , 24 , includes three , spaced - apart , elongated guide slots 62 , 162 that , in plan view , are curved about the central axis 41 . the guide slots 62 , 162 are counterbored into the opposite flat surfaces of the upper and lower mounting members 22 , 24 . the counterbored portions 64 , 164 of the guide slots thus provide recesses within which the opposite ends of shoulder bolts 66 are received . as shown in the figures , the upper mounting member 24 and lower mounting member 22 are stacked together , concentric with the central axis 41 . the guide slots 62 , 162 are precisely , concentrically aligned so that the smooth , shoulder portion 68 of each shoulder bolt 66 fits vertically through the stacked mounting members ( see fig2 ) to serve as guide pins so that one mounting member can be precisely rotated relative to the other about the central axis 41 . the head of each shoulder bolt 66 fits inside a counterbored portion 64 . the threaded end of the bolt , to which a flanged nut 70 is fastened , also fits inside of a counterbored portion 164 of the guide slots . the nuts 70 are sized so that they will not rotate with the bolt 66 . when the precise , desired optics angle 60 is established , the shoulder bolts 66 are tightened ( as by an allen wrench applied to the hex socket in the bolt head ) to lock the upper mounting member 24 to the lower mounting member 22 , thereby fixing the optics angle . in a preferred embodiment , the upper and lower flat surfaces of the stacked upper mounting member 24 and lower mounting member 22 are provided with thin cover plates 72 , the uppermost plate being added after the bolts 66 are all tightened . the underside of the radially protruding portion of the enclosure 28 of the upper mounting member 24 has a cover plate 73 , and the upper side of the radially protruding portion of the enclosure 128 of the lower mounting member 22 has a cover plate 75 ( fig3 ). it is contemplated that once the upper and lower mounting members 24 , 22 are stacked but not rotatably fixed together by bolts 66 , any one of a variety of actuators may be employed for precisely rotating one mounting member relative to the other until the desired optics angle 60 is established . the actuator may be applied to any part of one mounting member to force rotation of that mounting member relative to the other . the actuator can be connected to a work surface adjacent to the rotated mounting member . alternatively , the actuator can be connected to one mounting member ( which member is secured to be stationary ) and operable to apply force to the other mounting member . the actuator may be a permanent component of the overall mechanism , or be configured for removal once the precise optics angle is established , and the mounting members locked together . the actuator can be manually operated or mechanically driven under computer control . in a preferred embodiment , an actuator 74 ( fig1 ) for providing precise rotation of one mounting member relative to the other comprises a fine adjustment screw assembly 76 . that assembly includes and elongated screw 78 , one end of which 80 is rounded and engages an exterior surface of the enclosure 28 that protrudes radially from the upper mounting member 24 ( fig1 ). the screw 78 is threaded through a bushing 82 that is mounted within a base 84 of the assembly . the base 84 ( hence the assembly ) is connected to the cover plate 75 of the lower mounting member enclosure 128 via fasteners that are threaded into mounting holes 86 ( fig4 ). rotation of the ultra fine pitched screw is transferred via the contact of end 80 with the enclosure 28 into rotation of the upper mounting member 24 relative to the lower mounting member 22 , which member 22 may or may not be secured in place while this adjustment is made . as noted above , the angle between the two optics axes 58 , 158 ( namely ; the optics angle 60 ) that is adjusted as just described corresponds directly to the angle between the optical axes of the optical elements 32 , 132 in the respective upper mounting member 24 and lower mounting member 22 . any minor variations between one optic axis 58 , 158 and the corresponding optical axis of the associated optical elements 32 , 132 ( which variations may be attributable to , for example , a slight misalignment of the supports 42 securing the optical elements 32 , 132 in place ) can be addressed while the mechanism 20 is located in an optical setup with light passing though the optical elements of both pems and detected . this approach can be referred to as the pems optical angle calibration . one approach to this calibration is schematically depicted in fig2 , where the mechanism 20 is part of a setup that includes a light source 86 , adjustable polarizer 88 , an adjustable analyzer 90 , photodetector 92 and an associated lock - in amplifier 94 . the procedure discussed next is for precisely establishing the angle between the optical axes of the two pems to be 45 °, although other angles may be selected . the polarizer 88 is set at 0 ° and the analyzer 90 is set at 45 °. the upper mounting member 24 is rotated as described above until the optics axis 60 is at 45 °. this angle can be measured in any of a number of ways , including the use of angular graduations on the exposed , adjacent surfaces of the mounting members . next , the pem 30 in the upper mounting member 24 is operated at a peak retardation of one - half wave while the pem in the lower mounting member 22 remains off . the 2f signal on the detector 92 is monitored using the lock - in amplifier 94 . the mechanism 20 is then employed to precisely rotate the upper mounting member 24 relative to the lower mounting member 22 until the 2f signal reads “ 0 ,” at which point the upper mounting member 24 and lower mounting member 22 are locked together using the shoulder bolts 66 as described above . while the foregoing description was made in the context of a preferred embodiment , it is contemplated that modifications to the embodiment may be made without departure from the invention as claimed . for example , it is contemplated that the preferred embodiment of the actuator 74 may include the application of a spring or latch member extending between the adjustment screw and enclosure 28 so that the enclosure will move with both the extension and retraction of the adjustment screw 78 . further , the actuator may be configured to act on any portion of the mounting members to impart the relative rotation , such portions can be considered protrusions but need not be the radially protruding enclosures discussed above .