Tilting positioner for a micropositioning device
BACKGROUND OF THE INVENTION 
     This invention relates to a small motion transducer positioner for use in a micropositioning device to control the position of a probe tip relative to the surface of a sample under observation and, more particularly, to an improved positioner for eliminating Abba offset error even though tilting of the positioner is effected. 
     Segmented piezoceramic tubes are commonly used as actuators to produce probe tip motion in micropositioning devices such as scanning probe microscopes and profilometers. Such actuators have the advantages of simplicity, long range, small size and stiffness. What is disadvantageous about these actuators is the unpredictable tilting of the end of the tube, which introduces motion that is difficult to measure. This problem, known in the field of dimensional metrology as Abba offset error, is described, for example, in the article &#34;Dimensional Metrology with Scanning Probe Microscopes&#34; J. Appl. Phys., Volume 74, No. 9, Nov. 1, 1993, pages 83-109. U.S. Pat. No. 5,306,919, issued Apr. 26, 1994, to Elings et al proposes a solution to the problem of unwanted tilting by bending a piezoelectric tube into an S shape. This proposed solution is not entirely satisfactory because the bending leads to unpredictable tilting. It is therefore a primary object of the present invention to provide a positioner for a micropositioning device which eliminates unpredictable tilting so that Abba offset error is eliminated. 
     It would also be desirable to provide such a positioner which magnifies actuator movement to achieve long range, is thermally compensated, can be used for two and three dimensional motion, and is of simple construction. It is therefore another object of the present invention to provide a positioner possessing all of these attributes. 
     SUMMARY OF THE INVENTION 
     The foregoing and additional objects are attained in accordance with the principles of this invention by providing a positioner for a micropositioning device to control one dimensional horizontal movement between a pair of elements. The positioner comprises a rigid elongated member having a first free end and a second pivot end. The first free end is rigidly coupled to the first element. At least one pair of actuators is pivotally coupled to the pivot end of the elongated member. One example of a suitable actuator is a small motion transducer. The pivotal couplings are affixed to the elongated member such that one coupling in the pair is on the opposing side of the longitudinal axis of the elongated member from the other coupling in the pair. One end of each actuator is affixed to its respective pivotal coupling via a rigid member intermediate support. The other end of each actuator is fixed to a rigid, fixed base (i.e., the second element). Each pair of actuators is controlled in concert to effect movement of the first element by pivoting the pivot end of the elongated member. Control means are provided for energizing the actuators to cause differential motion thereof. In a preferred embodiment, the movement of each small motion transducer actuator is in a direction that is parallel to the longitudinal axis of the elongated member when the elongated member is in an untilted position. Accordingly, the elongated member is caused to tilt in a controlled manner. 
     In one embodiment of this invention, the pivotal couplings are pivot balls secured to the pivot end of the elongated member and to one of the small motion transducer actuators via the rigid intermediate support member. 
     In another embodiment of this invention, the positioner is arranged for two dimensional horizontal movement and further includes at least one additional intermediate support member, at least one additional pivotal coupling, and at least one additional small motion transducer actuator. If is advantageous if an additional pair of rigid intermediate support members, an additional pair of pivotal couplings, and an additional pair of small motion transducer actuators are provided for this embodiment. These additional pairs are arranged similarly to the first pairs with a first line through the first and second pivotal couplings orthogonally intersecting a second line through the third and fourth pivotal couplings at the longitudinal axis of the elongated member. Accordingly, the elongated member can be tilted so that its free end partakes of two dimensional horizontal movement within an orthogonal axis coordinate system. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The foregoing will be more readily apparent upon reading the following description in conjunction with the drawings in which like elements in different figures thereof are identified by the same reference numeral and wherein: 
     FIG. 1 illustrates tilting movement using a lever principle which magnifies actuator movement; 
     FIG. 2 is a side view of a folded positioner constructed according to this invention using two small motion transducer actuators and arranged for one dimensional horizontal movement by tilting; 
     FIG. 3 is a schematic plan view of the folded positioner of FIG. 2 using four small motion transducer actuators and arranged for two dimensional horizontal movement by tilting; 
     FIG. 4 is a side view of an unfolded positioner similar to that shown in FIG. 2; 
     FIGS. 5 and 6 illustrate alternate pivots to the balls shown in FIGS. 2-4; and 
     FIG. 7 is a diagram useful for understanding the geometry of vertical motion of the probe tip during horizontal movement by tilting. 
    
    
     DETAILED DESCRIPTION 
     Before describing the invention in detail, it should be understood that where the description refers to a scanning probe microscope, this is not intended to be a term of limitation. A scanning probe microscope is merely an exemplary form of micropositioning device which is a suitable environment for this invention, another such device being a profilometer. Also, while the description specifically refers to piezoelectric material, other materials, such as electrostrictive and magnetostrictive materials, may also be utilized as small motion transducers. 
     The inventive design described herein uses the tilting of a moment arm to magnify the relatively short range of movement of small motion transducer actuators. FIG. 1 illustrates such tilting. As shown therein, a rigid elongated member 10 of length L has a free end 12 and a second end 14. The second end 14 is fixed to the center of a cross member 16 having an overall length of 2d. According to the present invention, a pair of opposing small motion transducer actuators (not shown in FIG. 1) are provided equidistant from the center of the cross member 16. One of the actuators is caused to move its end of the cross member 16 downwardly a small distance δz while the other actuator is caused to move its end of the cross member 16 upwardly the same distance δz. This differential motion minimizes vertical movement of the member 10. The vertical displacement δz of the ends of the cross member 16 is magnified into lateral motion δx of the free end 12 of the member 10 by the following relationship: 
     
         (δx/δz)=(L/d). 
    
     This can easily be more than a factor of ten. A second cross member can be provided orthogonal to the cross member 16, along with a second set of actuators, to effect lateral motion of the free end 12 into and out of the plane of the paper, resulting in two dimensional motion. 
     FIG. 2 illustrates an inventive physical implementation using the principle shown in FIG. 1 to provide a one dimensional positioner. Thus, FIG. 2 illustrates a folded positioner for controlling one dimensional horizontal movement between a pair of elements. In the illustrative environment of a scanning probe microscope, the first of the elements is the probe tip 18. The second element is the base 20. The sample under observation (not shown) is affixed to the base 20 via a support member (not shown) that permits the sample to be placed in close proximity opposite the probe tip 18. The probe tip 18 is rigidly secured to a first free end of a rigid elongated member 22 so as to prevent relative horizontal movement therebetween. Illustratively, the member 22 is a cylindrical tube of rigid material, such as quartz. While other rigid materials may be utilized, quartz has the advantage of having a low thermal expansion coefficient. The tube 22 has a central longitudinal axis 24 which extends between its opposite ends and the probe tip 18 lies along this axis. The positioner further includes first and second rigid intermediate support members 26, 28. Each of the support members 26, 28 is coupled to the second pivot end of the tube 22 opposite from the probe tip 18 by a respective pivot means 30, 32. Illustratively, each of the pivot means 30, 32 is a solid ruby sphere secured to the respective support 26, 28 and to the tube 22 by epoxy or some other suitable adhesive. In this embodiment, the flexibility of the epoxy allows the rigid tube 22 to pivot on the spheres 30, 32. The balls 30, 32 are on opposite sides of the longitudinal axis 24 and function to effect pivoting movement of the tube 22 relative to the respective one of the support members 26, 28 about respective parallel pivot axes 34, 36 (FIG. 3) orthogonal to the longitudinal axis 24. Small motion transducer actuators 38, 40 are each coupled between the base 20 and a respective one of the support members 26, 28 and are controllable for effecting relative movement between the base 20 and the respective support member 26, 28, each along a line orthogonal to the respective pivot axis 34, 36. In the folded design shown in FIG. 2, the member 22 and the actuators 38, 40 all extend on the same side of the support members 26, 28. 
     Illustratively, the small motion transducer actuators 38, 40 are hollow piezoceramic cylinders with internal and external electrodes 39,41, respectively. When a voltage of a first polarity is applied across the electrodes, the length of the actuator increases. When a voltage of the opposite polarity is applied across the electrodes, the length of the actuator decreases. Preferably, the actuators 38, 40 are identical and the controller 42, which may include a programmed computer, is connected to the electrodes of the actuators 38, 40 and applies voltages to those electrodes so as to cause one of the actuators 38, 40 to increase in length and the other of the actuators 38, 40 to decrease in length. This differential motion causes the tube 22 to tilt, as previously described with respect to FIG. 1. 
     FIG. 3 shows the addition of two more actuators to the arrangement shown in FIG. 2 so as to effect two dimensional motion of the probe tip 18. Thus, the actuators 38, 40 control motion along the x axis. Arranged symmetrically and orthogonally thereto, are identical actuators 44, 46, along with their respective intermediate support members 48, 50, and respective pivot balls 52, 54, having respective pivot axes 56, 58. The actuators 44, 46 are coupled to the controller 42 (FIG. 2), which controls their energizations so as to achieve a desired y axis component of horizontal movement. It is clear from FIG. 3 that the first and second pivot balls 30, 32 are positioned along a line parallel to the x axis of movement of the probe tip 18 and, likewise, the third and fourth pivot balls 52, 54 are positioned along a line parallel to the y axis of movement of the probe tip 18. These lines connecting their respective pivot ball pairs, as well as the x and y axes, intersect at the central longitudinal axis 24 of the tube 22. As shown, the pivot balls 30, 32, 52, 54 are equidistant from the longitudinal axis 24 so that they may be considered as being positioned at respective corners of a square centered at the longitudinal axis 24. However, although it is preferable that within each pair of opposed actuators the distances of the actuators from the axis 24 are equal, from pair to pair these distances need not be the same. 
     Preferably, movement of each of the actuators 38, 40, 44, 46 is in a direction that is parallel to the longitudinal axis 24 when the tube 22 is in an untilted position. In addition to the four actuator embodiment previously described, it is also contemplated that two dimensional motion of the probe tip 18 can be effected using three actuators. In the three actuator embodiment, the actuators are arranged in a triangular configuration about the longitudinal axis of the tube 22. 
     In addition to its long range, the aforedescribed positioner possesses at least two other significant advantages. A first of these advantages is that it reduces errors arising from Abbaoffset. Abbe offset occurs when a position sensor, such as a capacitive sensor in a scanning probe microscope, does not lie in the plane of the probe tip. Any uncontrolled tilting of the scan head can cause motion of the probe tip that may not be detected by the position sensor. The advantage of the aforedescribed inventive arrangement is that the tilt is very well controlled and predictable, so any necessary correction to the measured position can be easily made. A second of these advantages is that the folded design and symmetry of the inventive positioner reduces errors arising from thermal expansion (i.e., it is inherently thermally compensated). The thermal compensation is illustrated in FIG. 2. The system can be designed by taking advantage of the thermal expansion characteristics of its component parts so that the position of the probe tip 18 is held constant relative to the base 20 as the ambient temperature changes. This can be accomplished by arranging to have the ratio of the two lengths L 1  and L 2  inversely proportional to the ratio of the two thermal expansion coefficients E 1  and E 2 , where the subscript 1 refers to the tube 22 and the subscript 2 refers to one of the actuators 38, 40, 44, 46 (which are identical), since these make up the bulk of the different lengths. Thus: 
     
         (L.sub.1 /L.sub.2)=/E.sub.2 E.sub.1). 
    
     Accordingly, when the temperature changes the two lengths L 1  and L 2  change by the same amount. 
     While the folded design shown in FIG. 2 possesses the advantages of compactness and thermal compensation, there may be applications where these advantages are not needed. As shown in FIG. 4, the inventive concept is also applicable to an unfolded design. 
     Further, while solid ruby spheres have been cited as exemplary pivots, other pivots can be utilized. Thus, FIG. 5 indicates that generic flexures 64, 66, which bend at their narrow regions, can be utilized, and FIG. 6 indicates that stiff wires 68, 70 can also be utilized. 
     FIG. 7 illustrates the vertical motion of the probe tip as tilting occurs. Thus, when the tube 22 is tilted at an angle α, the vertical displacement of the probe tip caused by the tilting is equal to L 1  (1-cosα). For dimensions and motions typical in a scanning probe microscope, the total vertical displacement is on the order of 10 mm. This can be compensated in several ways. Referring to FIG. 2, a small expansion actuator 60 can be added to the tube 22 to counteract this motion. Alternatively, the main z axis actuator 62 can be controlled to counteract the motion. Also, the tilt actuators 38, 40, 44, 46 can be driven so as to counteract the vertical motion. 
     Accordingly, there has been disclosed an improved tilting positioner for a micropositioning device which eliminates Abbaoffset error. While illustrative embodiments of the inventive concept have been disclosed herein, it is understood that other embodiments and modifications may be apparent to those of ordinary skill in the art and it is intended that this invention be limited only by the scope of the appended claims.