Patent Publication Number: US-6661955-B1

Title: Kinematic and non-kinematic passive alignment assemblies and methods of making the same

Description:
INCORPORATIONS BY REFERENCE 
     Co-assigned U.S. patent application Ser. No. 09/855,305, entitled “Angled Fiber Termination And Methods Of Making The Same”, filed on May 15, 2001, is hereby incorporated by reference in its entirety. 
     Another co-assigned U.S. patent application Ser. No. 10/001092, entitled “Optical Element Support Structure And Methods Of Using And Making The Same”, filed on Nov. 15, 2001, is hereby incorporated by reference in its entirety. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates generally to optical devices, and more particularly to optical element alignment assemblies and methods of making the same. 
     2. Description of the Related Art 
     An optical component, such as a mirror, lens or fiber, in an optical instrument or device, such as an optical switch, should be accurately located/positioned with respect to another optical component in order for the optical instrument or device to function properly. Thus, optical devices may require their components to be placed with exacting tolerances to fulfill design objectives. 
     Conventional passive alignment assemblies for MicroElectroMechanical System (MEMS) devices are typically planar in nature and only align local elements, e.g., a fiber and ball lens collimator, where the two components are within a few millimeters of each other. Alignments over larger distances (e.g., greater than five millimeters), and three-dimensional optical systems typically use conventionally machined components. Such assemblies often fail to align optical components with high intrinsic precision. 
     SUMMARY OF THE INVENTION 
     Components generally need to be located in three dimensions, i.e., distributed in a volume of space, and have three rotations specified and/or controlled. Components located in a plane (two dimensions) with three or fewer rotations specified and/or controlled are a subset of the general case. Other design objectives may include: (1) locate components without induced strains, either from the process of mounting or through bulk temperature changes of constituent parts, and/or (2) support components as rigidly as possible. 
     In accordance with the present invention, alignment assemblies and methods of using and making the assemblies are provided. An important advantage of several embodiments of the invention is to completely orient one body with respect to another body to a high degree of precision by providing (1) precise mating features between bodies and connecting elements, and (2) precise distances between these features on all bodies and connecting elements. 
     In one embodiment, the alignment assemblies are passive, kinematic or non-kinematic, and micromachined. “Passive alignment” means the various parts or devices to be assembled have mating features such that when these features are engaged with each other, the correct alignment (typically optical) is attained. In some instances, the engagement of these mating features permanently controls the alignment. In other instances, some type of fixture will hold the parts with their mating features engaged while some additional fixation, e.g., glue or bolt, is added to make the engagement permanent. 
     For comparison, in “active” alignment, two parts or devices are maneuvered with respect to each other by some motion control mechanism, e.g., a motorized motion stage, shim set, etc., in one or more directions or degrees-of-freedom (DOF) until some metric, e.g., light through-put, optical beam quality, etc., is within a specified tolerance. At that point, the two parts are fixed rigidly with respect to each other by some means, e.g., glue, solder, bolt. 
     As defined and used herein, “kinematic mounting” relates to attaching two bodies, which may be called a base assembly or a payload assembly, together by forming a structural path and creating stiffness between the two bodies in six, and only six, independent degrees of freedom (“DOFs”) or directions. Each degree of freedom (DOF) kinematically controlled between two bodies is also a position defined, i.e., a specific value of that DOF, as a linear measurement, may be maintained. Six DOFs are desired because the location of any object in space is defined by three orthogonal coordinates, and the attitude of the object is defined by three orthogonal rotations. 
     A kinematic support has the advantage of being stiff, yet any strains or distortions in the base assembly are not communicated to the payload assembly. Thus, any sensitive optical alignments are not altered in the payload assembly if the base assembly undergoes deformation due to applied loads or bulk temperature changes. 
     In one embodiment, it is desirable to tailor a DOF based on the configuration of a “pseudo-kinematic” support. “Pseudo-kinematic” means that although there may be many DOFs connecting at least two bodies, such as two micromachined passive alignment assemblies, in a practical attachment scheme, the DOFs can be tailored such that only six DOFs have a relatively high stiffness, and substantially all other DOFs have a relatively low stiffness. 
     Thus, true “kinematic” support means only 6 stiff DOFs connecting two parts, and no other stiffness paths exist. “Pseudo-kinematic” means there are 6 DOFs with relatively high stiffness, and possibly many more with much lower stiffness (typically two to three orders of magnitude less). In some applications, it is desirable to have pseudo-kinematic DOFs with relatively low stiffness to be two to three orders of magnitude lower than DOFs with relatively high stiffness. 
     DOFs with different levels of stiffness may be accomplished using a flexure system to relieve stiffness in unwanted DOFs. Depending on the cross-sectional properties of elements in the flexure system, connecting elements between two bodies may attain the desired stiffness connectivities. 
     The alignment assemblies and methods of making the assemblies according to the invention may provide a number of advantages. For example, the micromachined passive alignment assemblies may be made with high intrinsic precision. Micromachining processes may form three-dimensional structures from a substrate wafer with high accuracy. In several embodiments, one micromachined passive alignment assembly may be oriented and spaced with respect to another assembly (e.g., with connecting elements) with lithographic precision, e.g., three-dimensional translational positioning to less than one micron and three-dimensional angular positioning to less than five arcseconds for an assembly with a 50-mm characteristic dimension. 
     The methods according to the invention may construct mating surfaces on micromachined passive alignment assemblies, such as a base assembly and a payload assembly, to control six independent DOFs between the assemblies and allow complete, high-precision specification of position and attitude. In some applications, it is desirable to have micromachined connecting elements with counterpart mating surfaces to mate with the mating surfaces on the base and payload assemblies. 
     The accuracy of micromachined passive alignment assemblies may be fully realized if there is a positive contact between a pair of mating features. Thus, some form of preload or force may be applied to maintain compressive contact between the pair of mating features. An external force may be applied to preload mating surfaces to contact each other prior to gluing. Glues that shrink on cure may be used to maintain the preload across mating surfaces after assembly. 
     In addition to or instead of an external force, any of the structural elements being assembled may have an internal flexure assembly that applies an internally-reacted force (preload). The internal flexure assembly may seat mating surfaces without a deadband. In one embodiment, the internal flexure assembly comprises a set of double parallel motion flexures, a preloader stage, and a hole on one side of the preloader stage for inserting a separate preloader pin. When the preloader pin is inserted into the hole of the internal flexure assembly, the preloader stage deflects and exerts a force on the pin, which exerts a preload against a mating surface. After the micromachined passive alignment assemblies are assembled, the mating surfaces may be glued or bonded if desired. 
     A connecting element may be configured to restrain the base assembly and the payload assembly with one or more desired DOFs. In some embodiments, a “degenerate” support or connecting element may be used where less than six constrained DOFs between a base and payload are desired. The degenerate support may allow some trajectory (i.e., a combination of Cartesian DOFs) of a payload assembly relative to a base assembly to be unconstrained. 
     A “redundant” support or connecting element may be used in applications where more than six DOFs are desired. The redundant support reinforces the base and payload assemblies and maintains their flatness. 
     As another example, a micromachined passive alignment assembly may have thermal compensation flexure assemblies for maintaining centration of optical elements in the presence of large bulk or local temperature differences. The optical elements may then be attached to at least three pads supported by these flexure assemblies to effect this stable positioning. In some applications, it is desirable to position a plurality of optical elements in a precise pattern in the presence of large bulk or local temperature differences. In some of these applications, it may be desirable to position a plurality of thermal compensation flexure assemblies concentric with respect to the center of an opening and equidistant with respect to each other. 
     One aspect of the invention relates to an assembly configured to support at least one optical element to a pre-determined position. The assembly comprises a first micromachined structure having at least a first mating part and a second micromachined structure having at least a second mating part. The second mating part is configured to contact the first mating part to constrain the second micromachined structure with respect to the first micromachined structure. The second micromachined structure is configured to support at least one optical element. 
     In one embodiment, the second mating part is configured to contact the first mating part to precisely position the second micromachined structure with respect to the first micromachined structure. In one embodiment, the optical element is then precisely positioned with respect to the first micromachined structure. In one embodiment, the first micromachined structure also supports one or more optical elements. 
     Another aspect of the invention relates to an assembly configured to support at least one optical element. The assembly comprises a first micromachined structure having at least a first attachment point and a second micromachined structure having at least a second attachment point. The second attachment point is configured to contact the first attachment point to restrain the second micromachined structure with respect to the first micromachined structure in at least one degree-of-freedom (DOF). The second micromachined structure is configured to support at least one optical element at a predetermined position. 
     In one embodiment, the second attachment point is configured to contact the first attachment point to restrain and align the second micromachined structure with respect to the first micromachined structure. In one embodiment, the optical element is then aligned to a pre-determined position with respect to the first micromachined structure. In one embodiment, the first micromachined structure also supports one or more optical elements. 
     Another aspect of the invention relates to a method of making an assembly configured to position an optical element to a pre-determined position. The method comprises using lithography to form a first pattern and a second pattern on a substrate for a first structure and a second structure. The first pattern outlines a first mating part of the first structure. The second pattern outlines a second mating part of the second structure. The method comprises etching the substrate to form the first and second structures according to the first and second patterns. The second mating part is configured to contact the first mating part to constrain the second structure with respect to the first structure. The second structure is configured to position at least one optical element. 
     One aspect of the invention relates to an assembly configured to support at least one optical element to a pre-determined position. The assembly comprises a micromachined base, a payload and a connecting structure. The base has a first mating part. The payload is configured to position the optical element. The payload has a second mating part. The connecting structure is configured to contact the first mating part of the base and the second mating part of the payload. The connecting structure constrains the payload in about five to about six degrees of freedom with respect to the base. 
     In one embodiment, the base also positions an optical element. 
     Another aspect of the invention relates to an assembly configured to position at least one optical element to a pre-determined position. The assembly comprises a base plate and at least one side plate configured to connect to the base plate. The base plate and the side plate are configured to support a plurality of payload plates. Each payload plate is configured to connect to the side plate and to the base plate. Each payload plate is configured to position at least one optical element. 
     Another aspect of the invention relates to a method of making an assembly configured to position at least one optical element to a pre-determined position. The method comprises using lithography to form a first pattern, a second pattern and a third pattern on a substrate for a base, a payload and a connecting structure. The first pattern outlines a first mating part of the base. The second pattern outlines a second mating part of the payload. The third pattern outlines third and fourth mating parts of the connecting structure. The method further comprises etching the substrate to form the base, the payload and the connecting structure according to the first, second and third patterns. The connecting structure is configured to contact the first mating part of the base and the second mating part of the payload. The connecting structure constrains the payload in about five to about six degrees of freedom with respect to the base. The payload is configured to position an optical element. 
     One aspect of the invention relates to a micromachined flexure assembly formed in a first structure that is a part of an optical element alignment assembly. The flexure assembly comprises a set of parallel motion flexures and a preloader stage coupled to the set of parallel motion flexures. The set of parallel motion flexures allows the preloader stage to deflect away from a second structure of the optical element alignment assembly and apply a load against the second structure to constrain the second structure in at least one degree of freedom with respect to the first structure. 
     Another aspect of the invention relates to a micromachined thermal compensation flexure assembly formed in a first structure that is a part of an optical element alignment assembly. The flexure assembly comprises a set of collinear flexures and a center stage coupled to the set of collinear flexures. The set of collinear flexures and the center stage are configured to limit distortions in one direction due to a temperature change in the first structure from affecting an optical element supported by the first structure. 
     In one embodiment, three or more such assemblies may completely support a second structure, e.g., an optical element or assembly, with respect to the first structure such that there are minimal internal stresses, and hence distortions, in the second structure in the presence of bulk temperature changes or substantial temperature differences between the structures. 
     Another aspect of the invention relates to a micromachined strain isolation flexure assembly formed in a first structure that is a part of an optical element alignment assembly. The flexure assembly comprises a set of collinear flexures and a center stage coupled to the set of collinear flexures. The set of collinear flexures and the center stage are configured to limit strains in one direction in the first structure from transferring to a second structure. 
     Three or more such assemblies may completely isolate a second structure, e.g., an optical element or assembly, with respect to the first structure such that there are minimal internal stresses, and hence distortions, in the second structure in the presence of mechanically or inertially induced distortions in the first structure. 
     Another aspect of the invention relates to a method of making a micromachined flexure assembly in a structure that is a part of an optical element alignment assembly. The method comprises using lithography to form a pattern on a substrate for the structure. The pattern outlines a set of collinear flexures and a center stage coupled to the set of collinear flexures. The method further comprises etching the substrate to form the structure according to the pattern. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1A is a three-dimensional view of one kinematic support configuration. 
     FIG. 1B is a three-dimensional view of another kinematic support configuration. 
     FIG. 2A is a side view of a monopod connecting element shown in FIG.  1 A. 
     FIG. 2B is a side view of a bipod connecting element shown in FIG.  1 B. 
     FIGS. 3A-3I are views of slip-fit joint assemblies with optical elements. 
     FIG. 4 is a three-dimensional view of another embodiment of a slip-fit joint assembly. 
     FIG. 5 is a three-dimensional view of one embodiment of a stiffness control flexure system and an attachment portion. 
     FIG. 6 is a three-dimensional view of one embodiment of a pseudo-kinematic bipod connecting element. 
     FIG. 7 illustrates an example of positional control using the pseudo-kinematic bipod connecting element in FIG. 6 attached to a base assembly and a payload assembly. 
     FIG. 8 is a side view of one embodiment of an internal flexure assembly. 
     FIG. 9 illustrates two examples of preloading using a tab and slot attachment scheme with the internal flexure assembly of FIG.  8 . 
     FIG. 10 is a three-dimensional view of one embodiment of a preloader pin. 
     FIG. 11 illustrates an example where a plurality of internal flexure assemblies are used to maintain contact at mating surfaces of a slot. 
     FIG. 12A is a three-dimensional enlarged view of one embodiment of a fiber termination array assembly. 
     FIG. 12B is a three-dimensional assembled view of the fiber termination array assembly in FIG.  12 A. 
     FIG. 13 is a side view of two embodiments of redundant connecting elements. 
     FIG. 14 is a three-dimensional view of the two redundant connecting elements and the plate of FIG.  13 . 
     FIG. 15 is a three-dimensional view of one embodiment of a pseudo-kinematic support system. 
     FIG. 16 is a three-dimensional view of one embodiment of a partially-degenerate support system. 
     FIG. 17 is a three-dimensional view of another embodiment of a partially-degenerate support system. 
     FIG. 18 is a three-dimensional view of one embodiment of a strain isolation flexure assembly. 
     FIG. 19 is a three-dimensional view of one embodiment of a thermal compensation flexure assembly. 
     FIG. 20 is a three-dimensional view of one embodiment of a micromachined passive alignment assembly with a plurality of chucks in the base assembly and payload assembly for aligning optical elements. 
     FIG. 21 is an enlarged three-dimensional view of one part of the micromachined alignment assembly in FIG.  20 . 
     FIG. 22 is a three-dimensional view of one embodiment of an assembly, which comprises a first structure, a plurality of connecting elements and a second structure. 
     FIG. 23 is an enlarged view of a redundant attachment point of one connecting element in FIG.  22 . 
     FIG. 24 is an enlarged view of a pseudo-kinematic attachment point of one connecting element in FIG.  22 . 
     FIG. 25 is a three-dimensional view of one embodiment of a megastack structure. 
     FIG. 26 is an enlarged view of some attachment points of the side plate and the base plate in FIG.  25 . 
     FIG. 27 is the top view of the megastack structure in FIG.  25 . 
     FIG. 28 is a side view of one embodiment of a side plate in FIG.  25 . 
     FIG. 29 is a three-dimensional view of a complete megastack structure, which is shown partially in FIG.  25 . 
     FIG. 30 is the three-dimensional bottom view of the megastack structure in FIG.  29 . 
     FIG. 31 illustrates one method of designing the three-dimensional structures and assemblies described above and translating the designs into masks for high precision microlithography/photolithography. 
     FIG. 32 illustrates one method of making high precision, three-dimensional structures described above. 
     FIG. 33 illustrates one method of assembling three-dimensional structures described above from planar parts. 
    
    
     DETAILED DESCRIPTION 
     FIG. 1A is a three-dimensional schematic view of one kinematic support configuration  100 A. The kinematic support configuration  100 A in FIG. 1A comprises a base assembly  102 , a payload assembly  104  and six monopod connecting elements  106 A- 106 F (individually or collectively referred to herein as “monopod connecting element  106 ”). In one configuration, the base assembly  102  is a base support structure, and the payload assembly  104  holds or aligns an optical element, such as an optical fiber, lens or mirror. The base assembly  102  is connected to the payload assembly  104  via the six monopod connecting elements  106 A- 106 F. 
     Each monopod connecting element  106  in FIG. 1A constrains one degree of freedom (hereinafter referred to as ‘DOF’) between the base assembly  102  and the payload assembly  104 , as shown by an arrow above the kinematic support configuration  100 A in FIG. 1A. A constrained DOF may be referred to as a ‘stiff’ DOF or a restrained DOF. The relevant reference parameter for translational stiffness or translational DOF is force, while the relevant reference parameter for rotational stiffness or rotational DOF is torque. 
     FIG. 1B is a three-dimensional schematic view of another kinematic support configuration  100 B. The kinematic support configuration  100 B in FIG. 1B comprises a base assembly  102 , a payload assembly  104  and three bipod connecting elements  108 A- 108 C (individually or collectively referred to herein as “bipod connecting element  108 ”). The base assembly  102  is connected to the payload assembly  104  via the three bipod connecting elements  108 A- 108 C. Each bipod connecting element  108  constrains two DOFs between the base assembly  102  and the payload assembly  104 , as shown by a pair of arrows near the kinematic support configuration  100 B in FIG.  1 B. In one embodiment, the kinematic support configurations  100 A,  100 B each have a structural path between the base assembly  102  and the payload assembly  104  in six independent DOFs, as shown by the arrows in FIGS. 1A,  1 B. Six DOFs of constraint may be desired for some optic alignment applications. 
     The kinematic support configurations  100 A,  100 B in FIGS. 1A and 1B have the advantage of being as stiff as the connecting elements  106 A- 106 F,  108 A- 108 C, but any strain or distortion in the base assembly  102  will not be transferred to the payload assembly  104  (although a positional or attitude change may occur). Thus, any sensitive optical elements aligned within the payload assembly  104  will not be affected if applied loads or bulk temperature changes deform the base assembly  102 . 
     Similarly, if the payload  104  grows or shrinks, there will be no forces transferred to the base assembly  102  because of the connecting elements  106 A- 106 F,  108 A- 108 C. But there may be a change in position or attitude between the base  102  and the payload  104 . For the symmetric support configurations shown in FIGS. 1A and 1B, the only change is in the vertical direction between the two bodies  102 ,  104 . The payload  104  may be rigidly supported and maintains position in the presence of environmental conditions, such as inertial loads. 
     The location of an object in space is defined by three orthogonal coordinates or vectors, and the attitude of the object is defined by three orthogonal rotations with respect to the three vectors. In accordance with the present invention, if the components of an assembly (e.g., base, payload, and connecting structure such as bipods or monopods) are formed using an extremely precise fabrication method (e.g., micromachining), then the location and attitude of a payload relative to a base may be specified as precisely by fabricating connecting structure to calculated dimensions along their support DOF(s) (e.g., a precise length for a monopod, or a precise vertical and horizontal point of contact for a bipod). 
     Degenerate Support 
     If there are fewer than six DOFs constrained between the base  102  and the payload  104 , there may be some trajectory, i.e., combination of Cartesian DOFs, of the payload  104  relative to the base  102  that is unconstrained. In this case, the support between the base  102  and the payload  104  may be called “degenerate,” and may occur when a connecting element  106  or  108  is missing or when certain connecting elements  106 ,  108  are parallel. Arbitrarily complex patterns of motion may be created or controlled by replacing one linear connecting element  106  or  108  with a linear actuator. 
     Redundant Support 
     If there are more than six DOFs constrained between the base  102  and payload  104 , and the base  102  distorts or warps, there will be no solution of payload position and attitude that does not also warp the payload  104 . This type of support may be called “redundant.” 
     Monopods and Bipods 
     FIG. 2A is a schematic side view of a monopod connecting element  106  shown in FIG.  1 A. The monopod connecting element  106  in FIG. 2A constrains the base and payload assemblies  102 ,  104  with point contacts  200 ,  202  at two ends. 
     FIG. 2B is a schematic side view of a bipod connecting element  108  shown in FIG.  1 B. The bipod connecting element  108  in FIG. 2B constrains the base and payload assemblies  102 ,  104  with one or more (ideally) frictionless point contacts  204 A,  204 B at one end and two point contacts  206 A,  206 B at the other end. 
     The DOFs restrained by the monopod and bipod connecting elements  106 ,  108  are indicated by arrows in FIGS. 2A and 2B. Six monopod connecting elements  106 A- 106 F may constrain six DOFs between the base and payload assemblies  102 ,  104 , as shown by the arrows in FIG.  1 A. Also, three bipod connecting elements  108 A- 108 C may constrain six different DOFs between the base and payload assemblies  102 ,  104 , as shown by the arrows in FIG.  1 B. 
     Both types of joints (point-in-groove joint in FIG.  2 A and circle-in-groove joint in FIG. 2B) may be used interchangeably. A preload may be used to maintain contact between the base  102 , connecting element  106  or  108  and payload  104  in FIGS. 2A and 2B. 
     Micromachining 
     The base and payload assemblies  102 ,  104  and the connecting elements  106 A- 106 F,  108 A- 108 C in FIGS. 1A,  1 B,  2 A and  2 B may be hereinafter referred to collectively as a “micromachined passive alignment assembly” or a “micromachined assembly.” Other micromachined alignment assemblies are described below. A micromachined assembly may be formed with methods described below with reference to FIGS. 31-33. 
     In general, each component in the micromachined assembly in FIGS. 1A,  1 B,  2 A and  2 B may be formed by first using a patterning process, such as lithography or photolithography, to form a desired pattern on a substrate wafer. The substrate wafer may comprise silicon or another suitable material, such as gallium arsenide or germanium. The lithography process may include applying a resist on a surface of a substrate wafer, aligning a mask with a desired pattern above the substrate wafer, exposing the resist to radiation, developing the resist, and hardbaking the resist. 
     The radiation used for patterning the substrate wafer may include, by way of example, an ultraviolet light, an X-ray beam, or a beam of electrons. In one embodiment, the mask is made of a mechanically rigid material that has a low coefficient of thermal expansion. For example, the mask may be made of quartz, borosilicates, metallic chrome, or iron oxide. Patterning may be accomplished using either negative or positive resists. In some applications, it is desirable to use positive resists with aspect ratios above unity. In some applications, a photolithographic process is used to form a desired pattern on the substrate wafer. In a photolithography process, a photoresist such as photo-sensitive film is used in the patterning process. 
     After developing a pattern on the resist, one or more micromachining fabrication processes, such as Deep Reactive Ion Etching (DRIE), Wire Electric Discharge Machining (Wire EDM or WEDM), LIGA (X-Ray lithographie, galvanoformung, und abformtechnik) (X-Ray lithography, electrodeposition, and molding), or SCREAM (Single Crystal Reactive Etching and Metallization) may be used to etch the substrate wafer according to the masked pattern. In some applications, it is desirable to etch deep and straight sidewalls in the substrate wafer. In other applications, it is desirable to form a three-dimensional structure from the patterned wafer. 
     After etching, the patterned wafer is cleansed. The photoresist and/or resist may be removed using a solvent such as acetone. If there are other fragile MEMs structures on the wafer, a plasma etch may also be used to clean the substrate wafer. 
     After the fabricated components are cleansed, the components are assembled to form a desired micromachined passive alignment assembly. The fabrication processes described above may be used for making any part, element, patterned wafer, or component of the micromachined passive alignment assemblies described herein. FIGS. 31-33 provide additional details on micromachining in accordance with the present invention. 
     Slip-Fit Joint 
     A slip-fit caged joint is a slip-together pair of features which control at least one DOF in both directions (which may be called “tension” and “compression”), where fit tolerance is added to intrinsic feature accuracy. Since fit tolerances can be held to 1-3 microns, the tolerance may be the dominant error. A slip-fit caged joint still forms a relatively high accuracy connection. 
     FIG. 3A is a three-dimensional view of one embodiment of a slip-fit joint assembly  300 . The slip-fit joint assembly  300  comprises a payload assembly  302  and a base assembly  304 . The payload assembly  302  has three protrusions (also called “tabs” or “male connectors”) with mating surfaces  306 A- 306 C,  308 A- 308 C and  310 A- 310 C (not all mating surfaces are visible in FIG.  3 A). The base assembly  304  has counterpart grooves (also called “slots” or “female connectors”) with mating surfaces  312 A- 312 C,  314 A- 314 C, and  316 A- 316 C (not all mating surfaces are visible in FIG.  3 A). 
     The mating surfaces  306 A- 306 C,  308 A- 308 C,  310 A- 310 C,  312 A- 312 C,  314 A- 314 C, and  316 A- 316 C are configured to engage together. The mating surfaces  306 A,  306 C,  308 A,  308 C,  310 A,  310 C of the payload assembly  302  that are normal to the payload plane are configured to slide past the corresponding mating surfaces  312 A,  312 C,  314 A,  314 C,  316 A,  316 C of the base assembly  304 . A protrusion such as protrusion  306  and a groove such as groove  312  control at least two DOFs  324 ,  326  with a preload as shown in FIG.  3 A and described below. A protrusion-groove pair may be called a kinematic positioning joint. Each groove has a pre-determined depth, which is less than a height of each protrusion. Each groove is configured to contact one of the protrusions and control the protrusion in two degrees of freedom when a preload is applied, as shown in FIG.  3 A and described below. FIG. 3A also shows that each protrusion has four sidewalls, where each sidewall is substantially perpendicular to a plane of the payload  302 . Each protrusion has a sidewall facing a center point of the payload  302 . 
     In one embodiment, there is a fit clearance between the mating surfaces  306 A,  306 C,  308 A,  308 C,  310 A,  310 C,  312 A,  312 C,  314 A,  314 C,  316 A,  316 C to assemble the slip-fit joint assembly  300  of FIG.  3 A. In some applications, it is desirable to have a fit clearance of about 1-3 microns For example, the distance between the mating surfaces  312 A,  312 C is equal to the distance between the mating surfaces  306 A,  306 C plus a few microns This fit clearance leads to positioning “slop” or “deadband” of a few microns in (1) the plane of the base assembly  304 , which is defined by two DOFs  318  and  320 , and (2) a few arcseconds in rotation about the normal of the base plane, which is shown as DOF  322 . For rotational DOF  322  in FIG.  3 A and other rotational DOFs described herein, such as DOFs  526 ,  528  in FIG. 5, the double arrows symbolize a rotation about the axis. Each double pair of mating surfaces  306 A,  306 C,  308 A,  308 C,  310 A,  310 C,  312 A,  312 C,  314 A,  314 C,  316 A,  316 C in FIG. 3A may contribute deadband (or free play) that is normal to their surfaces, which is shown as DOF  324 . 
     In one embodiment, a preload is applied to seat the mating surfaces  306 B,  308 B,  310 B,  312 B,  314 B,  316 B that are parallel to the payload and base planes without a deadband in DOF  326 . Thus, the position of the payload assembly  302  normal to the base plane, illustrated as DOF  328 , is specifically controlled, as well as the two orthogonal rotations shown as DOFs  330  and  332 , whose axis lie in the base plane. The DOFs  328 ,  330 ,  332  may be referred to as piston, tip, and tilt. 
     In embodiment of FIG. 3, the protrusions are square or rectangular in shape, while the female connectors are square or rectangular cavities. In other embodiments, other shapes may be used, such as cylindrical projections. With cylindrical projections, the restrained DOFs may be the same as described above, as specified by the base plane pairs  312 A,  312 C,  314 A,  314 C,  316 A,  316 C. 
     FIG. 3B is side view of a payload  302 B with three protrusions (similar to FIG.  3 A: one Protrusion  306  is shown in FIG.  3 B), a base  304 B and an optical element  341 , such as a lens. FIG. 3C is a side view and FIG. 3D is a too view of a payload  302 C (similar to FIG.  3 A), a base  304 C, an optical element  341 , and a hole or receptacle  344 , which the same as hole  2002  in FIGS. 20-21 described below. 
     FIG. 3E is a side view of a payload  302 E (similar to FIG.  3 A), a base  304 E, an optical element  351 , such as a lens, and a fiber  352 . FIG. 3F is the same as FIG. 3E except the base  304 F holds the fiber  352  at an angle, as described in co-assigned U.S. patent application Ser. No. 09/955,305, entitled “Angled Fiber Termination And Methods Of Making The Same” which was incorporated above. 
     FIG. 3G is a side view of a payload  302  (similar to FIG.  3 A), a base  304 , and a diode  371 . 
     FIG. 3H is a side view of a payload  302 H (similar to FIG.  3 A), a base  304 H, and an optical fiber  352 . 
     FIG. 3I is a side view of a payload  3021  (similar to FIG.  3 A), a base  304 I, and an optical element, such as a mirror  380 . 
     FIG. 4 is a three-dimensional view of another embodiment of a slip-fit joint assembly  400 . The slip-fit joint assembly  400  comprises a base assembly  404  and a payload assembly  402 . The payload assembly  402  has protrusions  406 ,  408  and  410  with mating surfaces, while the base assembly  404  has counterpart recesses  412 ,  414 , and  416  with mating surfaces. Like the slip-fit joint assembly  300  of FIG. 3, the protrusions  406 ,  408 ,  410  and recesses  412 ,  414 , and  416  with mating surfaces can engage together like male and female connectors. In this embodiment, the male connectors  406 ,  408  and  410  are inverted T-like projections, while the female connectors  412 ,  414 , and  416  are window openings in the base assembly  404 . In FIG. 4, the bottom plane of the base  404  replaces surfaces  312 B,  314 B,  316 B in FIG. 3, but the base  404  provides the same DOF constraints. 
     The slip-fit joint assemblies  300  and  400  in FIGS. 3 and 4 may be fabricated with the same manufacturing procedures described above and below with reference to FIGS. 31-33. For example, the lithography process and the micromachining process may fabricate the desired mating surfaces  306 A- 306 C,  308 A- 308 C,  310 A- 310 C,  312 A- 312 C,  314 A- 314 C,  316 A- 316 C of the male and female connectors. In some applications, it is desirable to include a metallization process after the substrate wafer is cleaned. A metal is deposited via sputtering onto the male (tabs) and female connectors (slots). The metallization process increases robustness and reduces debris formation at the mating surfaces of the male and female connectors. 
     In one embodiment, each element in an assembly is kinematically supported with respect to all other elements. If each connecting element (e.g., element  106  in FIG. 1A) is kinematically supported in addition to the base and payload, the DOFs controlled by the connecting elements are capable of more accurate positioning. Thus, there are no allowed trajectories of the connecting elements (degenerate support). An allowed trajectory (change of attitude) of a connecting element could disturb the desired DOF controlled by the connecting element. Also, there is no overconstraint (redundant support) that could warp the connecting elements. An overconstraint could change a controlled DOF position through applied strain. As a consequence of kinematic support, every structural element in an assembly can now be a “payload,” which could support one or more optical components to the same levels of accuracy previously described. 
     In addition, an unlimited number of structural elements may be attached (to form a “daisy chain”) in this manner to a high level of accuracy. Each successive payload may be the base for the next payload in the chain. Another valid topology is to have an unlimited number of payloads attached to one set of connecting elements using the same DOFs at each connecting element (see “megastack” in FIG.  25 ). Other topologies may be possible. 
     Pseudo-Kinematic Connecting Element, Flexure Systems, Ball Joints, Attachment Points 
     FIG. 5 illustrates a three-dimensional view of one embodiment of a pseudo-kinematic connecting element flexure system and an attachment point  500 . “Pseudo-kinematic” means that although there may be many DOFs connecting at least two bodies through a plurality of connecting elements, such as two micromachined passive alignment assemblies, in a practical attachment scheme, the DOFs can be tailored such that only six DOFs have relatively high stiffness, and substantially all other DOFs have relatively low stiffness. In some applications, it is desirable to have at least one DOF with low stiffness to be two to three orders of magnitude lower than a DOF with high stiffness. DOFs with different levels of stiffness may be accomplished using a flexure system, such as the flexure system  504  in FIG. 5, to relieve stiffness in unwanted DOFs. Hereinafter, “kinematic” may be used to refer to pseudo-kinematic attachments. 
     In FIG. 5, the pseudo-kinematic connecting element flexure system and attachment point  500  comprises a body  502 , a flexure system  504 , and an attachment portion  506 . The flexure system  504  couples the body  502  to the attachment portion  506 . The attachment portion  506  and the flexure system  504  may be collectively referred to herein as a “ball joint,” a “ball joint flexure” or a “flexured ball joint” in a planar structure. A ball joint is a useful pseudo-kinematic structure that is relatively stiff in substantially all translations and relatively soft in substantially all rotations. 
     One embodiment of the attachment portion  506  in FIG. 5 comprises a mounting tab  508  with mating surfaces (contact surfaces)  510 A,  510 B,  510 D,  510 E, which may provide high precision dimensional control to mating elements. The flexure system  504  comprises two flexure elements  512 ,  514  that form a bipod-like structure. Each flexure element  512 ,  514  is very stiff in at least an axial direction. Thus, each flexure element  512 ,  514  provides a very stiff connection between the attachment portion  506  and the body  502  in DOFs  516  and  518 , as shown in FIG.  5 . 
     Depending on the cross-sectional properties of the flexure system, the connecting elements may have compliant (or “soft”) rotations become stiff and tiff translations become soft. The cross-sectional properties of the flexure elements  512 ,  514  include blade depth  520 , blade length  522 , and blade thickness  532 . If the blade depth  520  of the flexure elements  512 ,  514  is significantly smaller (e.g., less than {fraction (1/10)}) than the blade length  522 , the attachment of the body  502  to the attachment portion  506  by the flexure elements  512 ,  514  may have two stiff DOFs  516 ,  518  (i.e., forming a bipod), and other relatively softer DOFs  524 ,  526 ,  528 ,  530 . 
     In other applications, if the flexure elements  512  and  514  have a blade depth  520  that is significant (e.g., greater than about {fraction (1/10)} of the blade length  522 ), then DOF  524  has significant stiffness, and the attachment has the properties of a ball joint. The rotational DOFs  526 ,  528  may become stiffer compared to DOF  530 , which is primarily controlled by the flexure blade width  532 . In one embodiment, DOFs  526 ,  528  are soft and DOF  530  is very soft compared to DOFs  516 ,  518 . Depending on the exact magnitude and the sensitivity of a particular design, the soft DOFs  526 ,  528  may not cause any problems. 
     The stiffness of DOFs is highly dependent on the exact cross-sectional properties (blade depth  520 , length  522 , and thickness  532 ) of the flexure elements  512 ,  514 . It would be relatively easy to make the “soft” rotational DOFs  526 ,  528  stiffer and make the “stiff” translation  524  softer by changing the cross-sectional properties. As long as the blade length  522  is much greater than the blade depth  520  and the blade thickness  532 , e.g., 10 to 1 ratio (other ratios may be used), the “very stiff” translations  516  and  518  and the “very soft” rotation  530  will remain unchanged for this configuration. 
     In one configuration, it is desirable to have a ball joint at both ends of the body  502  to form a monopod connecting element (not shown). This configuration would create an appropriate set of stiff DOFs to make the monopod connecting element act like a single DOF constraint between two bodies. 
     Pseudo-Kinematic Bipod Connecting Element 
     In another configuration, it is desirable to have three attachment portions, similar to the attachment portion  506 , coupled to the body  502  to form a pseudo-kinematic bipod connecting element, as shown in FIG.  6 . 
     FIG. 6 is a three-dimensional view of one embodiment of a pseudo-kinematic bipod (i.e., two-DOF support) connecting element  600 . The pseudo-kinematic bipod connecting element  600  comprises attachment points  602 ,  604 ,  606  and a body  608 . The two attachment points  602  and  604  of the connecting element  600 ,may connect to a base assembly (not shown). The attachment point  606  may connect to a (nominal) payload assembly (not shown). 
     Two of the attachment points  602  and  606  are coupled to the bipod body  608  via ball joint flexures, as described above with reference to FIG.  5 . The ball joint at attachment point  602  provides three DOFs  610 ,  612 ,  614  of connectivity to the body  608 . The ball joint at attachment point  606  provides three DOFs  616 ,  618 ,  620  of connectivity to the body  608 . The attachment point  604  connects to the bipod body  608  via a single flexure  622  that provides two DOFs of connectivity  624  and  626 . 
     In one embodiment, three bipod connecting elements, such as the element  600  in FIG. 6, are kinematic in their attachments to a base and a payload. The three bipod connecting elements also form a kinematic attachment between a base and a payload. 
     In FIG. 6, the pseudo-kinematic bipod connecting element  600  “borrows” several DOFs  610 ,  612 ,  614 ,  616 ,  624 ,  626  from the base assembly and the payload assembly to control the position and attitude of the bipod connecting element  600 . This set of DOFs  610 ,  612 ,  614 ,  616 ,  624 ,  626  forms a 3-2-1 support structure (3 DOFs at one point, two DOFs at another, one DOF at a third) that is kinematic or pseudo-kinematic. Thus, the pseudo-kinematic bipod connecting element  600  could itself be an optical bench. The remaining DOFs  618  and  620  are used by the pseudo-kinematic bipod connecting element  600  to control the payload assembly. 
     The DOFs  610 ,  612 ,  614 ,  616 ,  618 ,  620 ,  624  and  626  may depend on one or more assumptions described above. For example, it may be assumed that the payload assembly is fully constrained by other pseudo-kinematic bipod connecting elements  600 . Otherwise, the “borrowed” DOF  616  may not be constrained. 
     As another example, at each attachment point  602 ,  604 ,  606  connected to a base or payload, all six DOFs with the attached body may be constrained by an adhesive or a preload (discussed below) to seat the mating surfaces without a deadband. The flexure structures may then select a subset of these DOFs to connect (i.e., be stiff in) to the body  608  to create the kinematic condition. 
     The structures described herein may have high stiffness in certain DOFs and much lower stiffness in all other DOFs. Some DOFs may vary in a common fashion with changes in flexure system dimensions, possibly requiring that a design decision may be made between either (1) allowing extra stiff DOFs, where an attachment may no longer be pseudo-kinematic, or (2) allowing a desired stiff DOF to be soft, which leaves the assembly with a relatively low frequency vibration mode and any desired positional accuracy in that direction may be compromised. Each of the two choices may be a viable design. An extra stiff DOF means a redundant support, which may be undesirable for an optical bench connected to a poorly-controlled external structure, but may be acceptable for certain size scales or sets of assumptions. Low frequency vibration modes may be a problem, but if the low frequency is in the kilohertz range while the device operates in approximately the 100-Hertz range, there will not be a detrimental dynamic interaction. 
     The connecting elements  500  and  600  in FIGS. 5 and 6 may be fabricated with micromachining manufacturing methods described herein. For example, lithography and micromachining can fabricate the connecting elements  500  and  600  to the sub-micron level. To translate these highly accurate planar processes to highly accurate three-dimensional positioning accuracy requires the same DOF control used for kinematic attachment. In other words, the stiff constrained directions used to form a kinematic attachment (e.g., the directions constrained between a base and a payload by three bipod connecting elements) can also have a precisely-determined dimension associated with each of them, thereby uniquely and precisely specifying the position (translations) and attitude (rotations) between two bodies (e.g., a base and a payload). This precisely-determined dimension is shown in detail below in FIG. 7 for one bipod element. 
     FIG. 7 illustrates an example of the pseudo-kinematic bipod connecting element  600  (alignment features on a planar object) in FIG. 6 attached to a base assembly  702  and a payload assembly  704 . The attachment points  602 ,  604  and  606  engage into the base assembly  702  and the payload assembly  704  at the mating surfaces  706 A,  706 B,  706 D,  706 E,  708 A,  708 B,  708 D,  708 E and  710 A,  710 B,  710 D,  710 E, respectively. The bipod connecting element  600  has two constrained and precisely specified DOFs at the payload  704  (DOFs  618  and  620  in FIG.  6 ). 
     One alignment feature in FIG. 7 may be a precise separation distance  712  between the base assembly  702  and the payload assembly  704 , which is defined by a midpoint  714  of a line formed by mating surfaces  706 A and  706 E of attachment point  602  and another midpoint  716  of a line formed by mating surfaces  710 A and  710 E of attachment point  606 . This precise separation distance  712  precisely specifies the location of the payload assembly  704  relative to the base assembly  702  in the vertical direction (DOF  620  from FIG. 6) at the point of attachment between the connecting structure ( 600  from FIG. 6) and the payload assembly  704 . 
     Another alignment feature may be the lateral (horizontal) distance  718  between the mating surfaces  706 B and  7101 B, which may be zero, as shown in FIG.  7 . In one configuration, the mating surfaces  706 B,  710 B may be collinear. Thus, the mating surface  706 B forms a straight line with the mating surface  710 B. Each vertical mating surface  706 B,  710 B may set a lateral position reference between the attachment points  602 ,  606 . This precisely specifies the location of the payload assembly  704  relative to the base assembly  702  in the horizontal direction (DOF  618  in FIG. 6) at the point of attachment between the connecting structure ( 600  in FIG. 6) and the payload assembly  704 . 
     Another alignment feature may be a pair of collinear line segments (that are also mating surfaces)  708 A,  708 E that interface the base side  702 , are remote from point  714  and are collinear with  706 A,  706 E. The line segments  708 A,  708 E constrain the rotation of the planar object  600  about a normal to the plane of FIG.  7 . Note that attachment point  604  could also interface to the payload side  704 , and the constraint would be identical. This rotational constraint may completely restrain the connecting element  600  in the desired DOFs. Otherwise, rotation in-plane of FIG. 7 would nullify the proper function of the vertical and horizontal position reference features described above. 
     In summary, the base and payload planes in FIG. 7 are parallel and separated by a specific distance  712 . In this example, the sets of collinear line segments  706 A,  706 E,  710 A,  710 E that define the separation distance are also parallel, and the lateral position reference  718  is zero (collinear line segments  706 B,  710 B) between the two connected objects  702 ,  704 . 
     Thus, the connecting element  600  in FIG. 6 not only supports a payload  704  relative to a base  702  in  2  DOFs  618 ,  620 , but also precisely locates the payload  704  relative to a base  702  in these same DOFs. Hence, three of these structures  600  would not only provide kinematic attachment between a payload and a base, but also completely and precisely specify the location and orientation of the payload relative to the base. 
     The method of engaging attachment points  602 ,  604 ,  606  may be the same for the attachment portion  506  of the pseudo-kinematic connecting element  500  shown in FIG.  5  and described above. 
     The above described connecting structure also applies for the more general case of non-parallel base and payload plates. 
     Design/Fabrication Considerations 
     Since the alignment features of the connecting element  600  discussed above are all coplanar lines, a mask with the desired pattern can be made for the patterning process (e.g., lithography). The patterning process can locate alignment features with high precision in a substrate wafer plane immediately adjacent to the mask. 
     In some applications, it may be important to consider two design and fabrication points for connecting elements  500  (FIG. 5) and  600  (FIGS.  6  and  7 ). First, the mask sides or regions of a substrate wafer intended to form mating features should be substantially in contact with the mask sides of other elements for highest precision. For example, for highest precision, the mask sides in FIG. 7 should be the upper surface of the base assembly  702  and the lower surface of the payload assembly  704 . 
     Second, a micromachining process may either etch (cut) through the substrate wafer in a perfectly perpendicular manner or with a draft (e.g., inward draft). Etching the substrate in a perfectly perpendicular manner is the ideal case. If drafting occurs, it is recommended to have an inward draft with acute angles measured from the mask plane to the etched sides of the substrate wafer. It may be important to ensure contact at the masked side of the substrate wafer. In one embodiment, the amount of draft should be as small as practical, such as just enough draft to ensure there is nothing beyond a perpendicular cut (outward draft; obtuse angle) within the error of the micromachining process. For example, in one configuration, the draft is half a degree. 
     As a result of inward drafts, some of the ideal line contacts, shown in FIG. 7 as mating surfaces  706 B,  706 D,  708 B,  708 D,  710 B, and  710 D, may be reduced to point contacts with very shallow angles. The mating surfaces  706 A-E,  708 A-E, and  710 A-E for the base assembly  702 , the payload assembly  704  and the connecting element  600  may all experience drafts. Thus, the mating surfaces  706 B and  710 B (which define lateral position reference line segments  718 ) may actually be contact points on the mask sides of the base assembly  704  and the payload assembly  706 . Inward drafting may be acceptable because the two planes of two mating surfaces, which coincide at a point contact, form a very acute angle. Thus, if a load is applied, a substantial contact patch may be formed, and hence result in reasonable contact stresses. 
     Internal Load and Flexure Assembly 
     To obtain maximum accuracy, the mating features described herein may be preloaded together with an externally-applied load (e.g., to seat mating features during a bonding operation) or an internally-reacted set of loads. In the latter case, the preload may be permanently applied and bonding may not be necessary. Internally reacted loads may be created by deflecting a flexure assembly (see FIG. 8) that is micromachined into one or more of the connected planar structures. 
     FIG. 8 is a side view of one embodiment of an internal flexure assembly  800  (also referred to herein as an “internal preloader” or “preload”). The internal flexure assembly  800  comprises a set of double-parallel-motion flexures  802 A- 802 B,  804 A- 802 B (double-parallel-motion set) with outer ends connected to a wafer  806 . In one embodiment, the internal flexure assembly  800  may further comprise a preloader stage  808  connected to the inner ends of the flexures  802 A- 802 B and  804 A- 802 B. The stage  808  constitutes a linear motion control device and hence may be called a “stage.” In one embodiment, it is desirable to have a hole  810  on at least one side of the preloader stage  808  for inserting a preloader pin (see FIG.  10 ). 
     In some applications, it is desirable to use the internal flexure assembly  800  to provide internal preloading in a substrate wafer, thereby seating mating surfaces together without a deadband. Internal preloading occurs when the flexures  802 A- 802 B,  804 A- 804 B are deflected by the action of inserting a preloader pin, or more generally a mating feature of another planar structure. 
     Each flexure  802 A- 802 B and  804 A- 804 B constrains DOFs such that the preloader stage  808  is supported very stiffly in five DOFs, but is soft in the one remaining DOF  812  (i.e., forming a spring). This soft DOF  812  is in the direction where the preload is applied. An applied deflection  816  results from a force  814  applied at the preloader stage  808 . The force  818  is equal to and opposite to a resultant force  814  (internally reacted force) applied by the preloader stage  808  to the connected wafer  806  in the vertical direction in FIG.  8 . The force  818  is the preload force used to positively seat a mating element against reference features (see FIGS.  9  and  11 ). In one embodiment, a relatively large deflection  816  is required to generate a preload  818 . 
     The internal flexure assembly  800  in the planar structure of FIG. 8 may be micromachined with high accuracy. Thus, the flexures  802 A- 802 B,  804 A- 802 B may have highly-accurate stiffnesses. Thus, deflections  816  of the flexures  802 A- 802 B,  804 A- 802 B should generate very accurate, repeatable and/or predictable preloads from device to device. By internally reacting these accurately-defined preloads, negligible distortion may occur in mated structures. 
     A maximum deflection capability defined by a “deflection stop”  820  may be implemented to limit the motion of the preloader stage  808 . If the applied deflection  816  is close to the deflection stop  820 , then motions of an assembled structure (because of further elastic deflection of the preloader stage  808  due to inertial or external loads on the assembly) will be limited to the difference in height  822  between the applied deflection  816  and the maximum deflection  820 . 
     Tab and Slot 
     In some configurations, it is desirable to attach micromachined passive alignment assemblies using male and female connectors, such as by way of example, a tab and slot attachment scheme. 
     FIG. 9 illustrates two examples of preloading using a tab and slot attachment scheme with the internal flexure assembly  800  of FIG.  8 . The tab  902  may be used as an attachment point for a connecting element, or a male or female connector for a base or payload assembly. The tab  902  has two substantially vertical mating surfaces  904  and  906 , and two horizontal mating surfaces  908  and  910 . 
     In FIG. 9, a connecting object  912  (such as a horizontal wafer) has an opening or slot for inserting the tab  902  (FIG. 9 is a section view along the long axis of the slot, normal to the plane of object  912 , and in the plane of the tab  902 ). The connecting object  912  may have mating surfaces such as surfaces  914 ,  916  that serve as counterparts to the mating surfaces  904 ,  906  of the tab  902 . When the tab  902  is inserted into the slot, the vertical mating surfaces  904 ,  906  (horizontal constraint features) of the tab  902  rest against the ends  914 ,  916  of the slot in the connecting object  912 , and the horizontal mating surfaces  908 ,  910  (vertical constraint features) of tab  902  rest against the lower surface of object  912 . 
     In one example of preloading, if a lateral position/motion constraint is desired, one substantially vertical mating surface  904  of the tab  902  is made to bear against one end  914  of the slot. The other end  916  of the slot comprises a stage for a flexure preloader  934 . The substantially vertical mating surface  906  of the tab  902  may be formed at an angle  918  (angle relief) to enable initial vertical engagement against the end  916  of the slot. When the tab  902  is fully seated in the vertical direction in the slot of the connecting object  912 , the preloader stage  934  is displaced laterally (to the left, as indicated by an arrow  920 ) a sufficient amount to generate a desired load  922  (to the right) against the mating surface  906  of the tab  902 . 
     Another example of preloading in FIG. 9 involves the internal flexure assembly  924  (also called a flexure preloader) in the tab  902  as a vertical position/motion constraint. The internal flexure assembly  924  is micromachined into the tab  902  with a soft DOF  926  of the preloader stage  928  in the vertical direction. When the tab  902  is approximately seated vertically (i.e. surfaces  908  and  910  in approximate contact with connecting object  912 ), there is a hole  930  whose top edge is the preloader stage  928  and whose bottom edge and sides are in the tab  902 . 
     In one embodiment, the bottom edge of the hole  930  is a horizontal surface of a part  932  of the connecting object  912  (wafer). The shape of the hole  930  may be rectangular, circular, polygon or other shape, depending on the design of the micromachined passive alignment assembly. A separate structure called a preloader pin (see FIG. 10) may be inserted in the hole  930  in FIG. 9 to generate a vertical preload force pair  936 ,  938  (via upward displacement of the stage  928 ). The force  936  acts on the tab  902  and force  938  acts on the part  932  of connecting object  912  that forms the bottom of hole  930 . These forces  936 ,  938  are then reacted across the horizontal mating surfaces  908 ,  910  and the lower surface of object  912  by force pairs  940 ,  942  and  944 ,  946 , which forces these surfaces into intimate contact and creates a more precise (i.e. deadband free) vertical position constraint. At this point, in the absence of any flexured “ball joint” type structure attached to tab element  902 , a vertical constraint on the paired surfaces  908  and  910  also creates a (possibly redundant) rotational constraint out of the plane of FIG.  9 . This may be acceptable (see sections “Redundant Elements for Additional Stiffness / Planarity Enforcement” and “Optical Element Support Structure”). 
     FIG. 10 is a three-dimensional view of one embodiment of a preloader pin  1000 . The preloader pin  1000  may be fabricated using patterning and micromachining processes discussed herein. The preloader pin  1000  may be made of silicon, plastic or some other suitable substance. The cross-section of the preloader pin  1000  may be a rectangle, a circle, a square, a polygon or some other suitable shape. In one embodiment, the end of the preloader pin  1000  has a substantially square cross-section with four sides that are preferably about 500 microns in length. The shape of the right cross-section end of the preloader pin  1000  is configurable and may depend on the shape of the hole  930  in FIG. 9, such that when the preloader pin  1000  is fully inserted in the hole  930 , the preloader stage  928  is deflected vertically a desired amount. 
     Gently tapering the preloader pin  1000  in the vertical direction  1002  allows a low-force initial insertion and engagement. In some applications, the preloader pin  1000  is maintained in the hole  930  (FIG. 9) by friction. The frictional holding should be good to several hundred times gravitational acceleration. In other applications, it may be desirable to dispense an adhesive (e.g., spot of glue) on the preloader pin  1000  to restrain the pin  1000  in the hole  930 . 
     In FIG. 10, the preloader pin  1000  may comprise a stop flange  1004  to provide a positive stop location after inserting the preloader pin  1000  in the direction of insertion  1008 . The preloader pin  1000  may also comprise an edge relief  1006  to allow for any sharp corners of the mating surfaces in the preloader stage  928  (FIG. 9) or hole  930 . 
     In FIG. 9, the flexure preloader  934  and the other flexure preloader (internal flexure assembly  924 ) each form an internally-reacted set of loads. In the first example described above, the force reaction points are the two substantially vertical mating surfaces  904  and  906  of the tab  902  and the two ends  914  and  916  of the slot, where one end  916  comprises a stage of a flexure preloader  934 . The preload  920  causes simple compressive stress locally in the tab  902 , and a somewhat more complex yet still local tensile stress pattern around the slot. By virtue of the softness of the preloader  934 , the forces and hence stresses can be made very small in absolute value. Since strain is proportional to stress, and overall distortion is proportional to strain times a distance, small localized strains create negligible overall distortions. 
     FIG. 11 illustrates an assembly  1100  where two internal flexure assemblies  1102  and  1104  are used to maintain the 2-DOF, in-plane position of a tab  1106 , i.e., maintain contact at mating surfaces of a slot. The tab  1106  in FIG. 11 may represent a top view of the tab  902  in FIG. 9, and a planar object  1100  in FIG. 11 may represent a top view of the connecting object  912  in FIG.  9 . As in FIG. 9, the tab  1106  in FIG. 11 fits in a slot in the object  1100 . Thus, an internal flexure assembly  1102  in FIG. 11 may represent the flexure preloader  934  described above in the first preloading example of FIG.  9 . The internal flexure assembly  1102  in FIG. 11 controls the vertical position of the tab  1106  in FIG. 11 by preloading surface  1118  of tab  1106  against surface  1120  of planar object  1100 . These surfaces are analogous to  904  and  914 , respectively, in FIG.  9 . 
     The other internal flexure assembly  1104  in FIG. 11 controls the horizontal position of the tab  1106 . The internal flexure assembly  1104  has a hole  1108  configure to receive a preloader pin  1110 . FIG. 11 shows an end view of the preloader pin  1000  in FIG.  10 . When a preloader pin  1110  is inserted into the hole  1108 , the pin  1110  causes a horizontal deflection  1112  (to the right) of a preloader stage  1114 , which causes a horizontal force  1116  (substantially equal and opposite to the deflection  1112 ) applied by the preloader stage  1114  on the pin  1110  and the tab  1106 . This forces surface  1122  of tab  1106  into intimate contact with surface  1124  of planar object  1100 . 
     Partially-Degenerate, Partially-Redundant, Pseudo-Kinematic Designs 
     The level of stiffness or softness of a particular DOF depends on design factors such as plate stiffness of an attached structure, a desired precision of position, thermal and dynamic environment, etc. An alignment assembly may be designed to be partially-degenerate, partially-redundant or a pseudo-kinematic design with substantially six stiff DOFs. 
     To construct a partially-degenerate support, design analysis determines resonant modeshapes and frequencies and verifies that the modeshapes and frequencies do not negatively impact the design. 
     For a partially redundant support, an appropriate analysis involves application of dynamic and thermal environments to verify that distortions caused by the dynamic and thermal environments are less than the desired precision. 
     For many applications of these micromachined pseudo-kinematic structures, there may be two things in common: (1) all component structures may be made of silicon and (2) the payload and the base may be parallel. Where either of these conditions occur, it is possible to greatly relax the constraints of kinematicity. If a structure is all silicon, a highly redundant support system can be used. If redundant DOFs are properly chosen, the payload may only experience warping in the presence of high thermal gradients, which is unlikely given the high conductivity of silicon and the small dimensions involved. If a symmetric support is used and the base and payload are parallel, bulk temperature changes would cause only a piston shift (no lateral, tip, tilt, or roll shift). 
     The design and fabrication combination of solid modeling software and lithographic micromachining allows the construction of multi-part assemblies where the fit-up on assembly may be virtually perfect, even with complex geometries. The construction of multi-part assemblies where the fit-up on assembly may be virtually perfect may obviate the need for kinematic attachment in many cases. In the macroscopic world, much of the need for kinematic support is due to imperfections of the mounting surfaces. 
     An added benefit of a redundant support is greater stiffness of each of the component parts of the assembly. Extended line contacts effectively restrain out-of-plane deformations in a wafer. 
     Fiber Termination Array Assembly 
     FIG. 12A is a three-dimensional enlarged view of one embodiment of a fiber termination array assembly  1200  (also called a fiber alignment device). FIG. 12B is a three-dimensional assembled view of the fiber termination array assembly  1200  in FIG.  12 A. The fiber termination array assembly  1200  may be formed by one or more processes described in co-assigned U.S. patent application Ser. No. 09/855,305, entitled “ANGLED FIBER TERMINATION AND METHODS OF MAKING THE SAME”, which is hereby incorporated by reference in its entirety. The fiber termination array assembly  1200  comprises a fiber locator plate  1202 , a fiber termination plate  1204  and three connecting elements  1206 A- 1206 C. 
     The fiber termination plate  1204  has a polished optical surface  1216 , holes  1220  configured to support/align optical fiber ends and kinematic positioning slots  1208 ,  1214  (with mating surfaces). The slots  1208 ,  1214  are configured to receive a tab (with mating surfaces), such as tab  1210 , of the connecting elements  1206 A- 1206 C. The fiber locator plate  1202  also has holes  1218  configured to support/align optical fibers and slots, such as slot  1212 , configured to receive a tab of the connecting elements  1206 A- 1206 C. In one configuration, the connecting element protrusions  1222  form extended line contacts that effectively restrain out-of-plane deformations in the fiber termination plate  1204  and/or the fiber locator plate  1202 . 
     The three connecting elements  1206 A- 1206 C constrain the fiber termination plate  1204  to the fiber locator plate  1206  with about six DOFs. Each connecting element  1206  may control two DOFs of position and may have four to five DOFs of stiffness. Although one connecting element  1206 A may be redundant in a stiffness DOF in view of the other connecting elements  1206 B,  1206 C, each connecting element controls two DOFs of position and may precisely position the fiber locator plate  1202  with respect to the fiber termination plate  1204 . 
     In some applications, it may be desirable to connect the fiber termination plate  1204  and the fiber locator plate  1202  with more than six stiff DOFs. For example, more than six stiff DOFs are used to reinforce flatness, add stiffness, and prevent sagging under gravity or vibration for the fiber termination plate  1204  and the fiber locator plate  1202 . 
     In one embodiment, the assembly  1200  was analyzed for polishing pressure on an optical face on the fiber termination plate  1204  and found to have deformations on the nanometer level with typical polishing pressures. 
     As shown in FIGS. 12A and 12B, two objects, such as two planar silicon wafers, may be positioned precisely relative to each other in six DOFs (tip, tilt, piston, roll, and two in-plane DOFs (lateral to separation direction)) to lithographic levels of precision or exactness. The two objects may be positioned by using planar connecting structures, each with mating reference features to control one or more DOFs between the two objects for a total of six DOFs. The objects and connecting structures may all be fabricated using lithographic micromachining techniques, or their equivalents in precision. The two objects to be aligned may contain arrays of optical components, which are already precisely positioned within the plane such that the two arrays would be precisely positioned relative to each other. 
     If the above positioning concept has no internal preloading, some gaps are allowed between mating features to ensure assembly. These gaps may contribute to the overall error in the positions of objects in the assembly. 
     If the above positioning concept has internal preloading, internally reacted loads ensure contact between mating surfaces, remove any gaps and allow a very high assembly precision. 
     Redundant Elements for Additional Stiffness / Planarity Enforcement 
     Large pseudo-kinematically supported planar arrays may be designed with extra bending stiffness to resist inertial loads. To implement extra bending stiffness, redundantly-attached ribs may be added to a main wafer plane. The redundantly attached ribs may be designed to actually enforce the flatness of the main wafer. This enforcement may be done to lithographic precision. 
     FIG. 13 is a side view of two embodiments of redundant connecting elements  1302  (also called ribs) and  1304  and a plate  1306  (also called wafer). The wafer  1306  may be used as an optical bench to support optical elements  1308 ,  1309  such as fibers, lenses or mirrors. In one embodiment, a wafer  1306  (e.g., a base assembly or a payload assembly) is supported with more than six stiff DOFs to enforce flatness (i.e., planar surface control), add extra stiffness, resist inertial loads (e.g., sagging or bending under gravity or vibration of the wafer  1306 ), and/or resist externally-applied loads from the environment. Thus, less strains or distortions are communicated to the optical elements  1308  and their positions remain more precise. 
     The connecting elements  1302  and  1304  may be designed with redundant tabs  1310 A- 1310 C,  1314 A- 1314 C (also called attachment points). The connecting elements  1302  and  1304  may be fabricated with high precision using the patterning and micromachining processes discussed above. 
     In one embodiment, the connecting element  1302  has tabs  1310 A- 1310 C that may engage into slots  1312 A- 1312 C of the wafer  1306 . The attachment mechanism of the tabs  1310 A- 1310 C and slots  1312 A- 1312 C may encompass external preloading and gluing of the tab into the slot. FIG. 13 shows a tab  1320  of a connecting element, such as connecting element  1302 , that is flush with the top surface of the wafer  1306 . 
     In another embodiment, the connecting element  1304  has tabs  1314 A- 1314 C with internal flexure assemblies  1316  (with preloaders), which are micromachined in the tabs  1314 A- 1314 C. The attachment mechanism of the tabs  1314 A- 1314 C and slots  1312 A- 1312 C may follow the second example described above with reference to FIG  9 . FIG. 13 shows a tab  1318  of a connecting element, such as connecting element  1304 , protruding from a top surface of the wafer  1306 . Each tab  1318  may use a connecting pin (not shown). 
     FIG. 14 is a three-dimensional view of the two connecting elements  1302  and  1304  and the plate  1306  of FIG.  13 . FIG. 14 shows protruding, attached tabs  1318 A,  1318 B and attached tabs  1320  that are flush with the top surface of the wafer  1306 . The tabs  1318 A,  1318 B,  1320  are part of connecting elements underneath the plate  1306 . Each connecting element  1302 ,  1304  may have any number of tabs, such as six tabs, as shown in FIG.  14 . 
     Pseudo-Kinematic vs. Partially-Degenerate Support 
     FIGS. 15,  16  and  17  illustrate the difference between a pseudo-kinematic support system and partially-degenerate support systems. FIG. 15 is a three-dimensional view of one embodiment of a pseudo-kinematic support system  1500 . The pseudo-kinematic support system  1500  in FIG. 15 comprises a box-like structure  1510  and three pseudo-kinematic, planar, bipod connecting elements  1502 A- 502 C (referred to as “bipod connecting elements”). Each bipod connecting element  1502  may have two stiff or very stiff DOFs. For example, bipod connecting element  1502 A has two stiff DOFs  1504 A- 1504 B. Bipod connecting element  1502 B has two stiff DOFs  1506 A- 1506 B. Bipod connecting element  1502 C has two stiff DOFs  1508 A- 1508 B. Thus, the bipod connecting elements  1502 A- 1502 C may constitute a complete support (six stiff DOFs) for the box-like structure  1510  (e.g., base assembly or payload assembly). The remaining DOFs (not shown in FIG. 15) may be soft. To determine whether or not a set of support DOFs is kinematic, redundant, or degenerate, the directions and points of application of each set of support DOFs should be considered. Kinematic may also be referred to as “determinate” or “statistically determinate.” Redundant may also be referred to as “indeterminate” or “statistically indeterminate.” 
     In some applications, it is desirable to have a degenerate support system, for example, when building a motion control stage. A degenerate support system constrains base and payload assemblies with less than six DOFs. As a result, there may be some trajectory (i.e. combination of Cartesian DOFs) of the payload assembly relative to the base assembly that is unconstrained. A degenerate support system may occur when a connecting element is missing or when certain connecting elements are parallel. 
     Although a degenerate support and a partially-degenerate support constrain base and payload assemblies with less than six DOFs, a degenerate support will move in some trajectory direction that is unconstrained while a partially-degenerate support will move in some trajectory direction that is resisted by soft DOF(s) from the pseudo-kinematic connecting elements. The trajectory direction of the degenerate support would have no restoring force and zero resonant frequency. Meanwhile, the trajectory direction of the partially-degenerate support would have relatively little restoring force, and a relatively low resonant frequency. 
     FIG. 16 is a three-dimensional view of one embodiment of a partially-degenerate support system  1600 . The partially-degenerate support system  1600  in FIG. 16 comprises a box-like structure  1612 , two pseudo-kinematic, planar, bipod connecting elements  1602 A- 1602 B (referred to as “bipod connecting elements”) and one pseudo-kinematic, planar, monopod connecting element  1604  (referred to as “monopod connecting element”). While the two bipod connecting elements  1602 A- 1602 B each have two stiff DOFs  1606 A- 1606 B,  1608 A- 1608 B, the monopod connecting element  1604  has one stiff DOF  1610 . Because the bipod connecting elements  1602 A- 1602 B and the monopod connecting element  1604  are pseudo-kinematic, the remaining DOFs (not shown) may be soft. 
     Since the partially-degenerate support system  1600  restrains the structure  1612  with five stiff DOFs  1606 A- 1606 B,  1608 A- 1608 B, and  1610 , there may be some trajectory direction  1614  for the structure  1612 . Motion in this trajectory (motion direction)  1614  is resisted by out-of-plane bending of the bipod connecting elements  1602 A- 1602 B and in-plane or out-of-plane bending of the monopod connecting element  1604 , which are all fairly soft DOFs. Motion along trajectory direction  1614  would therefore have little restoring force, and thus would have a low resonant frequency. The compliance in trajectory direction  1614  would also mean any precise positioning features designed to control motion along the trajectory direction  1614  may have degraded performance. 
     FIG. 17 is a three-dimensional view of another embodiment of a partially-degenerate support system  1700 . The partially-degenerate support system  1700  comprises three connecting plates  1710 A- 1710 C and three pseudo-kinematic, planar, bipod connecting elements  1702 A- 1702 C (referred to as “bipod connecting elements  702 A- 1702 C”). Each bipod connecting element  1702 A- 1702 C has two stiff or very stiff DOFs. For example, bipod connecting element  1702 A has two stiff DOFs  704 A- 1704 B. Bipod connecting element  1702 B has two stiff DOF  1706 A- 1706 B. Bipod connecting element  1702 C has two stiff DOF  1708 A- 1708 B. 
     In one embodiment, where the three plates  1710 A- 1710 C are rigidly attached to each other, the system  1700  has a total of six stiff DOFs  1704 A- 1704 B,  1706 A- 1706 B,  1708 A- 1708 B. The remaining DOFs (not shown) may be soft. 
     Because the attachment points of the three bipod connecting elements  1702 A- 1702 C are collinear, one bipod connecting element  1702 A may be ineffective. Thus, the three connecting plates  1710 A- 1710 C with three bipod connecting elements  1702 - 1702 C may have only four stiff DOFs, including two trajectory directions  1712  and  1714  with very low stiffness. 
     Strain Isolation 
     As explained above, one or more internal flexure assemblies may seat mating surfaces together without a deadband. One or more internal flexure assemblies may also be used to resist load-induced or temperature-induced strains/distortions in a base assembly from transferring to a payload assembly, or vice versa. At most, there may be a position shift and/or an attitude shift of the base assembly with respect to a payload assembly, or vice versa. 
     FIG. 18 is a three-dimensional view of one embodiment of a strain isolation flexure assembly  1800 . The strain isolation flexure assembly  1800  in FIG. 18 comprises one or more payload assemblies  1810  and a base assembly  1808  with micromachined features, such as three micromachined outer internal flexure assemblies  1802 A- 1802 C (i.e., “strain-isolation mounting flexures” or “mounting flexures”), a plurality of holes  1814  and a set of inner internal flexure assemblies  1816 A- 1816 C around each hole  1814 . 
     The outer internal flexure assemblies  1802 A- 1802 C in FIG. 18 may be oriented 120 degrees apart, as shown in FIG. 18, or oriented at any arbitrary angle or distance from each other, preferably with the lines-of-action  1804 A- 1804 C (i.e., soft direction of the flexure system) meeting at some common point, such as point  1806 . In some applications, it may be desirable to have less than three or more than three outer internal flexure assemblies in the strain isolation flexure assembly  1800 . 
     Each outer internal flexure assembly  1802  controls two DOFs, such as DOF  1818 A (vertical, out-of-plane) and DOF  1818 B (in-plane). FIG. 18 illustrates three lines of action  1804 A- 1804 C that intersect at a centroid  1806 . The three lines of action  1804 A- 1804 C represent degrees of flexibility or soft DOFs provided by the outer internal flexure assemblies  1802 A- 1802 C. 
     Any distortion or strain in a foundation (not shown), to which the base assembly  1808  is attached via flexure assemblies  1802 A- 1802 C, can be accommodated by motion along the lines of action, thereby generating only minute forces in the base assembly  1808  from restoring forces in the flexure systems  1802 A- 1802 C. Thus, the outer internal flexure assemblies  1802 A- 1802 C may prevent load-induced strains/distortions in a foundation from communicating to the base assembly to  1808 , and hence maintain the relative location of one or more payload assemblies  1810 , which are attached to the base assembly  1808 . Thus, the flexure assemblies  1802 - 180 C may be called “strain isolation mounting flexures.” At most, there may be a position shift and/or an attitude shift of the base assembly  1808  with respect to the foundation, or vice versa. 
     The outer internal flexure assemblies  1802 A- 1802 C maintain a pseudo-kinematic state between the base assembly  1808  and the foundation. The pseudo-kinematic state may be particularly important when the base assembly  1808  is used as an optical bench to support payload assemblies  1810 . Maintaining a pseudo-kinematic state between the base assembly  1808  and the foundation reduces the amount of strains/distortions in the base assembly  1808 , hence maintaining the relative positions of the payload assemblies  1810 . 
     Thermal Compensation 
     FIG. 19 illustrates a part of the base assembly  1808  in FIG. 18, a payload assembly  1810 , an optical element  1812  supported by the payload assembly  1810 , an outer internal flexure assembly  1802 , a hole  1814  and a set of inner internal flexure assemblies  1816 A- 1816 C around the hole  1814 . One or more optical elements  1812  may be inserted in each hole  1814 . The payload assembly  1810  (e.g., silicon optical bench) in FIG. 19 is directly connected to the base assembly  1808 , and the connection points are flexured to attain a pseudo-kinematic state. 
     In other embodiments, there may be more than three or less than three inner internal flexure assemblies  1816 A- 1816 C. The inner internal flexure assemblies  1816 A- 1816 C may be oriented 120 degrees apart or oriented at any arbitrary angle or distance or angle from each other, preferably with the lines-of-action  1908 A- 1908 C meeting at a common point (e.g.1910). For example, the inner internal flexure assemblies  1816 A- 1816 C in FIG. 19 are oriented 90 degrees apart. 
     The inner internal flexure assemblies  1816 A- 1816 C in FIG. 19 may be referred to as thermal compensation flexures, which may be used to maintain hot die passive alignment. The inner internal flexure assemblies  1816 A- 1816 C together may be called a thermal compensation flexure assembly. 
     FIG. 19 illustrates three lines of action  1908 A- 1908 C that intersect at a centroid  1910 . The three lines of action  1908 A- 1908 C represent degrees of flexibility or soft DOFs provided by the inner internal flexure assemblies  1816 A- 1816 C. An optical element  1812 , such as a diode, will expand as the element  1812  rises in temperature (generates or absorbs heat). Thus, the optical element  1812  and its payload assembly  1810  will attempt to increase in size relative to the payload assembly&#39;s attachment points to the base assembly  1808 . Because the inner internal flexure assemblies  1816 A- 1816 C allow for or compensate temperature-induced distortions along the lines of action  1908 A- 1908 C, the expanding optical element  1812  and its payload assembly  1810  will not cause any warping or stresses to the base assembly  1808 . The optical element  1812  and the payload assembly  1810  will be at substantially the same temperature and hence will generate no internal stresses or distortions (other than simple expansion). 
     The inner internal flexure assemblies  1816 A- 1816 C also maintain the center of the expanding payload assembly  1810  (and optical element  1812 ) at the centroid  1910  of the flexure systems lines-of-action. In some applications, maintaining centration of the expanding optical element  1812  is critical. For example, an incident laser beam may be required to remain at a certain spatial position on a diode. The spatial position for instance, is the center of the diode. With a thermal compensation flexure assembly in FIG. 19, the laser beam will remain at its spatial position even when the diode expands or contracts. If the diode expands or contracts, the neutral point is the center of the diode, and the center of the diode will not move spatially laterally, relative to the base assembly  1808 . 
     Chuck Array 
     FIG. 20 is a three-dimensional view of one embodiment of a micromachined alignment assembly  2000 , which comprises a base assembly  2006  and a payload assembly  2004  (also called “chuck arrays” or “wafers” or “planar objects”). In another embodiment the top structure  2004  may be the base, and the bottom structure  2006  may be the payload. The micromachined alignment assembly  2000  in FIG. 20 may constitute a view of one-third of a two-piece, ring-shaped alignment assembly. The base assembly  2006  and payload assembly  2004  each comprise an array of micromachined chucks or holes  2002  for restraining and aligning arrays of optical elements  2008 , such as mounted lenses, fibers, or mirrors. The chucks  2002  may be formed by one or more processes described in the above-referenced U.S. Patent Application, entitled “OPTICAL ELEMENT SUPPORT STRUCTURE AND METHODS OF USING AND MAKING THE SAME” Ser. No. 10/001092, which is hereby incorporated by reference in its entirety. 
     FIG. 21 is an enlarged three-dimensional view  2100  of one part of the micromachined alignment assembly  2000  (“chuck array”) in FIG.  20 . FIG. 21 illustrates a bipod-style connecting element  2108  (e.g., a planar structure) with two tabs  2102 A- 2102 B for pseudo-kinematic (low distortion) or redundant (planarity enforcing) attachment of the base assembly  2006  and the payload assembly  2004 . An alignment assembly may comprise two ring-shaped structures, which are partially shown in FIGS. 20 and 21, and a plurality of bipod-style connecting elements (e.g., three), such as the bipod-style connecting element  2108  in FIG.  21 . 
     In one embodiment, each connecting tab  2102 A,  2102 B in FIG. 21 is a planar structure with two stiff DOFs. DOFs  2110 ,  2112 ,  2114  are controlled at the payload assembly  2004 . DOFs  2110 ,  2114  are used by the payload assembly  2004 , and DOF  2112  is used by the connector tab  2102 A. DOFs  2116 ,  2118  are redundant, which may or may not be used. DOF  2116  may be used by the payload assembly  2004  to enforce planarity, and DOF  2118  may be used by the connecting structure  2108  to enforce planarity. 
     With three bipod-style connecting elements, such as the bipod-style connecting element  2108  in FIG. 21, the payload assembly  2004  and the base assembly  2006  may be supported by a total of six stiff DOFs. The connector tabs  2102 A- 2102 B have internal flexure assemblies  2104 A,  2104 B that provide compliance in the vertical direction for preloader stages  2106 A,  2106 B, which in turn may be used (with a preloader pin, not shown) to provide preload to controlled DOFs  2110  and  2116 . Similar to the vertical preload example of FIG. 9, a possibly redundant rotational constraint normal to the plane of connecting structure  2108  may also be created. The micromachined alignment assembly  2000  shown in FIGS. 20 and 21 may accurately control the lateral positions of the payload assembly  2004  with respect to the base assembly  2006 , and thus control the lateral positions (desired orientation) of upper and lower portions of the optical elements  2008 . 
     In one embodiment, each bipod-style connecting element  2108  utilizes neighboring flexure systems in the base and payload wafers  2006 ,  2004  to provide preloading for the other DOFs indicated in FIG.  21 . For example, a first connecting tab  2102 A of the bipod-style connecting element  2108  in FIG. 21 has neighboring flexure systems  2120 A and  2120 B. FIG. 11 shows a top view of a connecting tab  1106  that may represent connecting tab  2102 A in FIG.  21 . The two flexure systems  2120 A and  2120 B, together with their respective preloader stages and preloader pins (not shown) allow for application of preload to control DOFs  2112  and  2114 . Flexure systems  2120 C,  2120 D provide similar capability at the attachment of  2108  to the base assembly  2006 . 
     The connecting structures between two objects (e.g., a base and a payload) disclosed herein may be pseudo-kinematically supported, which allows the connecting structures to be used for precision positioning and distortion free support of optical components. 
     Optical Element Support Structure 
     FIG. 22 is a three-dimensional view of one embodiment of an assembly  2200 , which comprises a first structure  2210  (e.g., a base assembly or a payload assembly), a plurality of connecting elements  2202 A- 2202 C and a second structure  2208  (e.g., a base assembly, a payload assembly or an optical element, such as a mirror). In one configuration, the assembly  2200  may be an all-silicon fold mirror. 
     Other embodiments of the assembly  2200  may have less than three or more than three connecting elements. The connecting elements  2202 A- 2202 C have redundant attachment points  2204 A- 2204 F on one end and pseudo-kinematic attachment points  2206 A- 2206 C on the other end. The six redundant attachment points  2204 A- 2204 F may connect to the first structure  2210 . The three pseudo-kinematic attachment points  2206 A- 2206 C may connect to the second structure  2208 . 
     Other embodiments of the connecting elements  2202 A- 2202 C may have less or more attachment points. 
     FIG. 23 is an enlarged view of a redundant attachment point  2204 A of one connecting element  2202 A in FIG.  22 . The redundant attachment points  2204 A- 2204 F of the connecting elements  2202 A- 2202 C in FIG. 22 attach to the base assembly  2210  collectively with more than six stiff DOFs. In FIG. 23, the redundant attachment point  2204 A is connected to the base assembly  2210  with two possibly stiff DOFs  2302 A- 2302 B, in addition to the DOFs (e.g., three translations) used for pseudo-kinematic attachment. Similarly, the redundant attachment points  2204 B- 2204 F are each connected to the base assembly  2210  with two additional possibly stiff DOFs (not shown). Therefore, the three connecting elements  2202 A- 2202 C attach to the base assembly  2210  with twelve additional possibly stiff DOFs. 
     In some applications, other designs for the connecting elements may be used to attach the base assembly in more than six DOFs. For example, a connecting element may have three redundant attachment points. The rationale for allowing these redundant DOFs in this assembly is the same as discussed in the section “Redundant Elements for Additional Stiffness/Planarity Enforcement” (e.g., enforcing the planarity of the base and/or connecting elements). 
     FIG. 24 is an enlarged view of a pseudo-kinematic attachment point  2206 A (also called mounting tab) of one connecting element  2202 A in FIG.  22 . The attachment point  2206 A in FIG. 24 may embody some or all of the principles of kinematic support and position control described above. The pseudo-kinematic attachment points  2206 A- 2206 C of the connecting elements  2202 A- 2202 C in FIG. 22 attach to the optical element  2208  collectively with six stiff DOFs. FIG. 24 illustrates one pseudo-kinematic attachment point  2206 A with two stiff DOFs  2402 A,  2402 B. Similarly, the other pseudo-kinematic attachment points  2206 B,  2206 C are connected to the optical element  2208 , each with two stiff DOFs (not shown). 
     In one embodiment, each pseudo-kinematic attachment point  2206  has a flexure system  2408 A and  2408 B (FIG. 24) that is designed to provide an appropriate stiffness to form a ball joint with stiff DOFs  2402 A,  2402 B,  2406 . DOFs  2402 A,  2402 B pseudo-kinematically support the mirror wafer  2208 , and DOF  2406  is a constraint borrowed back from the optical element  2208  to support the end of the connecting element  2202 A. 
     In one embodiment, the pseudo-kinematic attachment point  2206 A uses positive preloaders (or preloading stage) to attach the connecting element  2202 A to the optical element  2208  without deadband, such that DOFs  2402 A,  2402 B,  2406  are precisely specified and controlled (i.e., possess high stiffness). In one configuration, the pseudo-kinematic attachment point  2206 A uses three preloaders. One preloader  2412  applies a preload against a surface of the pseudo-kinematic attachment point  2206 A using a preloader pin (not shown) to precisely specify and control DOF  2406 . Another preloader  2414  applies a preload against another surface (e.g., end of the tab in the slot) of the pseudo-kinematic attachment point  2206 A without a pin (see FIGS. 9,  11 ) to precisely specify and control DOF  2402 B. 
     A vertical preloader (not shown) in an upper portion of the attachment point  2206 A that protrudes above the optical element  2208  is similar to the preloader stage  2304  in the redundant attachment point  2204 A in FIG.  23 . The vertical preloader stage in the pseudo-kinematic attachment point  2206 A provides a preload in DOF  2402 A. The vertical preloader stage uses a preloader pin. 
     The flexure system  2405  has two flexure elements  2408 A- 2408 B that form a bipod-like structure. The two flexure elements  2408 A- 2408 B intersect at a virtual point in the pseudo-kinematic attachment point  2206 A and hence form a “ball joint” as previously described. 
     In one embodiment, the flexure system  2405  in FIG. 24 is recessed using an extra micromachining step (an etch defined by the square area  2404 ), to decrease the depth  2410  of the flexure elements  2408 A- 2408 B. The flexure blade depth  2410  is then variable and not fixed as the thickness of the wafer. Thus, flexure properties may be more readily tailored to achieve a desired pseudo-kinematic stiffness connectivity. For example, if the flexure elements  2408 A- 2408 B are thinned sufficiently, they would behave more like rods, and thus more perfectly constrain only two DOFs, i.e., have larger separation of stiffness between desired and undesired constraint DOFs. 
     The connecting elements  2202 A- 2202 C in FIG. 22 may be fabricated using the manufacturing procedures described herein. For example, lithography and micromachining can fabricate the connecting elements  2202 A- 2202 C with high intrinsic precision. In one embodiment, a recessed flexure system (e.g.,  2408 A and  2408 B in FIG. 24) in each connecting element  2202  is formed by a patterning process, such as lithography, that forms a desired pattern, such as a rectangle, of the recessed flexure system  2405  on one side of a substrate wafer. Then the rectangular area is partially etched through the substrate wafer until a desired depth  2410  for the flexure elements  2408 A- 2408 B remains. The flexure system  2405  could then be etched from the other side using an appropriate mask pattern to form the flexure elements  2408 A- 2408 B. 
     In another embodiment, a patterning process such as lithography may be used to form a desired pattern of the flexure elements  2408 A- 2408 B on a substrate wafer. Next, a micromachining process such as an etching process may be used to etch through the substrate wafer to a pre-determined depth for thinning down the depth  2410  of the flexure elements  2406 A- 2406 B. After the micromachining process, the substrate wafer is cleansed. Next, the substrate wafer may be subjected to a second patterning process. Then, the substrate wafer may be subjected to a second micromachining process to etch through the whole substrate wafer. Finally, the substrate wafer is cleansed and then assembled to provide the desired micromachined passive alignment assembly. 
     Megastack 
     FIG. 25 is a three-dimensional view of one embodiment of a megastack structure  2500 . The megastack structure comprises a base plate  2502  and one or more side plates  2504 A,  2504 B. The configuration with one sideplate  2504  may be referred to as an “L-type megastack,” and the configuration with two side plates  2504 A,  2504 B, shown in FIG. 25, may be referred to herein as a “C-type megastack.” The megastack structure  2500  enables precise dimensional support of an arbitrarily large number of payload assemblies  2506 , which may comprise silicon wafers with MEMs devices or integral or mounted optical devices. Optical elements  2508  may be mounted, restrained, and/or aligned on a payload assembly  2506 . In some applications, a side plate  2504  may also serve as a payload assembly that mounts, restrains, and/or aligns optical elements. 
     As shown in FIG. 25, the megastack structure  2500  has precisely-formed attachment points  2510 A- 2510 C (also called “slots”) to support and align each payload assembly  2506 . Each attachment point  2510  provides two-DOF positioning control in the C type megastack configuration to attain a pseudo-kinematic support condition. 
     The side plates  2504 A- 2504 B may or may not be kinematically attached to the base plate  2502 . As shown in FIG. 25, DOFs  2512 A,  2512 B,  2514 ,  2516 ,  2518 A,  2518 B are used to kinematically support the side plate  2504 A. The DOF  2514  is “borrowed” from a payload assembly  2506  (or other structural element) to create a kinematic support condition. The side plate  2504 A is also attached to the base plate  2502  via redundant DOFs  2520 A- 2520 B. The redundant DOFs  2520 A,  2520 B may be allowable because their directions support the attached plates  2504 A- 2504 B in DOFs that have an associated soft stiffness of plate out-of-plane bending. The redundant DOFs  2520 A,  2520 B may therefore preserve the flatness in both the base plate  2502  and the side plate  2504 A. 
     In other embodiments, it may be desirable to have a degenerate or a redundant support system for a C-type or L-type megastack structure  2500 . If a degenerate support system is desired, the megastack structure  2500  may support and/or align the payload assembly  2506  using less than three attachment points  2510 . If a redundant support system is desired, the megastack structure  2500  may support and/or align the payload assembly  2506  using more than three attachment points  2510 . 
     The attachment points  2510 A- 2510 C (FIG. 25) are geometrically positioned such that two attachment points  2510 A and  2510 C are elevated above the base plate  2502 , and one attachment point  2510 B is in the plane of the base plate  2502 . This geometrical attachment arrangement, or other similar arrangements, when combined with the specific directions of local DOF support, produce a non-degenerate, non-redundant, pseudo-kinematic support for a payload plate  2506 . 
     As another example, an L-type megastack may have two attachments points on a base plate and one attachment point elevated above the baseplate plane on a sideplate. Here the local DOF supported at each attachment point are in different directions from the pictured C-type megastack  2500  in FIG.  25 . 
     FIG. 26 is an enlarged view of some attachment points  2510 A,  25101 B of the side plate  2504 A and the base plate  2502  in FIG.  25 . Given the geometric position of the attachment points  2510 A- 2510 C (FIG.  25 ), a C-type megastack payload assembly structure  2506  is pseudo-kinematically supported by two precisely-controlled DOFs  2602 A,  2602 B (FIG. 26) from attachment point  2510 A, two DOFs  2604 A,  2604 B from attachment point  2510 B, and two DOFs (not shown) from attachment point  2510 C (FIG.  25 ). The two DOFs (not shown) from attachment point  2510 C are similar to the two DOFs  2602 A,  2602 B (FIG. 26) from attachment point  2510 A. 
     In FIGS. 25 and 26, flexure systems with integral preloaders  2606 A,  2606 B,  2608 A,  2808 B may be implemented for maximum positioning precision. For example, preloader  2608 B preloads a tapered tab (not shown) of a payload assembly  2506  to seat the tab against the slot  25101 B in DOF  2604 A, which forms a tab-in-slot configuration as shown in FIGS. 9 and 11. Preloader  2608 A may use a tapered pin (not shown) to preload the tab (not shown) of a payload assembly  2506  against the slot  2510 B in DOF  2604 B. Similarly, the preloaders  2606 A,  2606 B may preload a tab, such as tab  2610 , in DOFs  2602 B,  2602 A, respectively. The tab  2610  may have a preloader  2612 . 
     FIG. 27 is the top view of the megastack structure  2500  in FIG.  25 . 
     FIG. 28 is the side view schematic of one embodiment of a side plate, such as the sideplate  2504 A in FIG.  25 . The side plate  2802  in FIG. 28 is another example of planar positioning accuracy. The side plate  2802  has three slots  2804 A- 2804 C for engaging three tabs  2806 A- 2806 C of three payload assemblies, such as the payload wafer  2506  in FIG.  25 . In FIG. 28, the slots  2804 A- 2804 C are open-ended at a top side. In FIG. 25, the side plates  2504 A,  2504 B have slots  2510 A,  2510 B that are closed-ended at all sides and form a window opening in the side plates  2504 A,  2504 B. Similarly, the base  2502  in FIG. 25 has slots  2510 B that are closed-ended at all sides and form a window opening in the base assembly  2502 . 
     The side plate  2802  in FIG. 28 may precisely control two DOFs on each of the three tabs  2806 A- 2806 C of attached payload wafers (FIG.  25 ). The vertical edges  2810 A- 2810 C of the slots  2804 A- 2804 C may allow precise definition of the horizontal separation  2808 A,  2808 B between the three tabs  2806 A- 2806 C (even more precise if the tabs  2806 A- 2806 C are preloaded against the slots  2810 A- 2810 C). The horizontal (bottom) edges of the slots  2804 A- 2804 C provide a vertical reference between the tabs  2806 A- 2806 C (again, even more precise when the tabs  2806 A- 2806 C are preloaded against the bottom edges). 
     The side plate  2802  in FIG. 28 may be used in conjunction with one or two other similar objects (each appropriately connected to the others) to completely define the positions and orientations of three payload wafers, which each have a plurality of tabs (FIG. 28 shows tabs  2806 A- 2806 C of three payload wafers). 
     In some applications, it is desirable to have the side plate  2802  with slots  2804 A- 2804 C that are equidistant from one another, as shown by distances  2808 A- 2808 B. An equidistant arrangement may allow proper alignment of the payload assemblies. 
     FIG. 29 is a three-dimensional view of a complete megastack structure  2900 , which is shown partially in FIG. 25, with a plurality of payload assemblies  2902 A- 2902 G. The complete megastack structure  2900  in FIG. 29 comprises side plates  2504 A,  2504 B, a base plate  2502 , tabs (such as tab  2610 ), slots, internal flexure assemblies, payload assemblies  2902 A- 2902 G, optical elements (collectively referred to as “components”), as described above. The attachment mechanisms maintain the complete megastack structure  2900  in a pseudo-kinematic state. 
     FIG. 30 is a three-dimensional bottom view of the complete megastack structure  2900  in FIG.  29 . FIG. 30 shows one side plate  2504 B, the base plate  2502 , one payload assembly  2506 , bottom tabs  3002 A- 3002 C of the side plate  2504 B and bottom tabs  3004 A- 3004 C of three payload assemblies. The bottom tabs  3002 A- 3002 C and bottom tabs  3004 A- 3004 C protrude from the bottom surface of the base plate  2502 . 
     The complete megastack structure  2900  in FIGS. 29 and 30 may be fabricated using the same manufacturing procedures described herein. For example, using the lithography process and the micromachining process to fabricate the tabs, slots, internal flexure assemblies, payload assemblies, sideplate assemblies, and base assemblies. 
     FIG. 31 illustrates one method of designing the three-dimensional structures and assemblies described above and translating the designs into masks for high precision microlithography/photolithography. The actions described in FIG. 31 may be performed in the order as shown or in alternative orders. Some of the actions may be skipped or combined with other actions. The method of FIG. 31 may include other actions in addition to or instead of the actions shown. 
     FIG. 32 illustrates one method of making high precision, three-dimensional structures described above. The actions described in FIG. 32 may be performed in the order as shown or in alternative orders. Some of the actions may be skipped or combined with other actions. The method of FIG. 32 may include other actions in addition to or instead of the actions shown. 
     FIG. 33 illustrates one method of assembling three-dimensional structures described above from planar parts. The actions described in FIG. 33 may be performed in the order as shown or in alternative orders. Some of the actions may be skipped or combined with other actions. The method of FIG. 33 may include other actions in addition to or instead of the actions shown. 
     The above-described embodiments of the present invention are merely meant to be illustrative and not limiting. Various changes and modifications may be made without departing from the invention in its broader aspects. The appended claims encompass such changes and modifications within the spirit and scope of the invention.