Abstract:
Two sub-assemblies in a fiber optic device are fitted to respective end faces of a central section, along a longitudinal axis. The end faces of the central section are non-parallel. Butting the sub-assemblies to respective ends of the central section permits relative adjustment of the two sub-assemblies in substantially decoupled degrees of freedom. This results in a simpler adjustment procedure for aligning the two sub-assemblies. Furthermore, the mounting of the sub-assemblies using angled faces permits the use of relatively thin layers of adhesive that reduce misalignment problems arising from mismatched thermal expansion when the temperature changes.

Description:
FIELD OF THE INVENTION 
     The present invention is directed generally to fiber optic devices, and more particularly to a method and apparatus for aligning a fiber optic device that includes collimator sub-assemblies. 
     BACKGROUND 
     Optical fibers find many uses for directing beams of light between two points. Optical fibers have been developed to have low loss, low dispersion, polarization maintaining properties and can also act as amplifiers. As a result, optical fiber systems find widespread use, for example in optical communication applications. 
     However, one of the important advantages of fiber optic beam transport, that of enclosing the optical beam to guide it between terminal points, is also a limitation. There are several optical components, important for use in fiber systems or in fiber system development, that are not implemented in a fiber-based form where the optical beam is guided in a waveguide. Instead, these optical components are implemented in a bulk form and through which the light propagates freely. Examples of such components include, but are not limited to, filters, isolators, circulators, polarizers, switches and shutters. Consequently, the inclusion of a bulk component in an optical fiber system necessitates that the optical fiber system have a section where the beam path propagates freely in space, rather than being guided within a fiber. 
     Free space propagation typically requires use of collimation units, also known as collimator sub-assemblies, at the ends of the fibers to produce collimated beams. Therefore, a device may have a collimator sub-assembly at each end, defining one or more collimated beam paths to their respective fibers. Light from an input fiber is collimated by the first collimator unit and passes through free space to the second collimator unit, where it is focused into an output fiber. One difficulty in manufacturing a fiber optic device is ensuring that the collimated beam paths from the two collimator sub-assemblies are collinear. 
     Mechanically, many of the prior art approaches to aligning collimator sub-assemblies are less than elegant. Typically, the two sub-assemblies are adjusted in space by tooling until good optical coupling is achieved. They are then immersed in a “sea of glue” to fix their positions. (The “sea of glue” fills the space between the outside of the sub-assembly and the inside of the module housing.) There are typically no mechanical supports for the sub-assemblies except for the glue itself. One of the drawbacks to the “sea of glue” is that the thermal expansions of the glue and the housing may be different, and so any asymmetry in the glue distribution may produce some shifting of the components as the temperature changes. Also the glue lines are thick, uneven, and vary from assembly to assembly. This leads to complex and, therefore, often labor intensive, procedures for aligning modules that include sub-assemblies. 
     SUMMARY OF THE INVENTION 
     Generally, the present invention relates to a module where two sub-assemblies are fitted to respective end faces of a central section. The end faces of the central section are non-parallel, and permit the adjustment of the two sub-assemblies in substantially decoupled degrees of freedom. 
     One particular embodiment of the invention is directed to a fiber optic device having a longitudinal axis. The device includes a first sub-housing disposed on the longitudinal axis and has first and second end faces. The first end face defines a first plane parallel to a first transverse axis perpendicular to the longitudinal axis, where the first plane is non-parallel to i) the longitudinal axis and ii) a second transverse axis that is perpendicular to both the longitudinal axis and the first transverse axis. The second end face defines a second plane parallel to the second transverse axis, where the second plane is non-parallel to i) the longitudinal axis and ii) the first transverse axis. The device also includes a second sub-housing disposed on the longitudinal axis and has a third end face parallel to the first end face. The third end face is fitted to the first end face. The device also includes a third sub-housing disposed on the longitudinal axis. The fourth sub-housing has a fourth end face fitted to the second end face of the first sub-housing. 
     Another embodiment of the invention is directed to a method of aligning a fiber device. The method includes providing a first sub-housing on a longitudinal axis. The first sub-housing has first and second end faces, where the first end face defines a first plane parallel to a first transverse axis perpendicular to the longitudinal axis. The first plane is non-parallel to i) the longitudinal axis and ii) a second transverse axis perpendicular to both the longitudinal axis and the first transverse axis. The second end face defines a second plane parallel to the second transverse axis. The second plane is non-parallel to i) the longitudinal axis and ii) the first transverse axis. The method also includes fitting a third end face of a second sub-housing to the first end face of the first sub-housing and fitting a fourth end face of a third sub-housing to the second end face of the first sub-housing. The method further includes adjusting position of the second sub-housing with the third end face fitted to the first end face and adjusting position of the third sub-housing with the fourth end face fitted to the second end face. 
     The above summary of the present invention is not intended to describe each illustrated embodiment or every implementation of the present invention. The figures and the detailed description which follow more particularly exemplify these embodiments. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The invention may be more completely understood in consideration of the following detailed description of various embodiments of the invention in connection with the accompanying drawings, in which: 
     The invention may be more completely understood in consideration of the following detailed description of various embodiments of the invention in connection with the accompanying drawings, in which: 
     FIG. 1 schematically illustrates a fiber optic device that includes two single fiber collimator sub-assemblies; 
     FIG. 2 schematically illustrates a fiber optic device that includes two dual fiber collimator sub-assemblies; 
     FIG. 3 schematically illustrates one embodiment of a multiple fiber collimator sub-assembly; 
     FIG. 4 schematically illustrates another embodiment of a multiple fiber collimator sub-assembly; 
     FIG. 5 schematically illustrates to collimator sub-assemblies and a co-ordinate system used for describing alignment of the collimator sub-assemblies; 
     FIG. 6 presents a graph showing coupling between two single fiber sub-assemblies where each sub-assembly is adjustable in the same degree of freedom; 
     FIG. 7 presents a graph showing coupling between two single fiber sub-assemblies where the sub-assemblies are not adjustable in the same degree of freedom; 
     FIG. 8 schematically illustrates an embodiment of a device formed from two sub-assemblies, according to an embodiment of the present invention; 
     FIG. 9 schematically illustrates the central housing in the device of FIG. 8; 
     FIG. 10 schematically illustrates the device of FIG. 10 in a housing, according to an embodiment of the present invention; 
     FIGS. 11A,  11 B, and  11 C, schematically illustrates a central section of a device according to an embodiment of the present invention; 
     FIGS. 12A,  12 B, and  12 C schematically illustrate a co-ordinate system; 
     FIG. 13 schematically illustrates a co-ordinate transformation; and 
     FIGS. 14A,  14 B, and  14 C schematically illustrates a central section of the device according to the present invention with a transformed co-ordinate system. 
    
    
     While the invention is amenable to various modifications and alternative forms, specifics thereof have been shown by way of example in the drawings and will be described in detail. It should be understood, however, that the intention is not to limit the invention to the particular embodiments described. On the contrary, the intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the invention as defined by the appended claims. 
     DETAILED DESCRIPTION 
     Generally, the present invention relates to a method and apparatus for aligning collimator sub-assemblies. The invention arises from a realization that prohibiting the two collimator sub-assemblies from being adjusted in the same degree of freedom leads to faster and easier alignment than is possible using conventional approaches. 
     The present invention is related to the implementation of decoupled adjustments of optical sub-assemblies, described further in U.S. patent application Ser. No. 10/138,169 entitled “Alignment of Collimator Sub-Assemblies”, filed on even date herewith by R. Gerber and T. Gardner, and incorporated herein by reference. 
     A schematic illustration of one embodiment of a fiber optic device  100  is presented in FIG.  1 . The device includes left and right single fiber collimator (SFC) sub-assemblies  102  and  104  mounted in opposing directions. Each sub-assembly includes a fiber  106   a  and  106   b  mounted in a ferrule  108   a  and  108   b . A lens  110   a  and  110   b  is positioned to collimate light passing out of the respective fiber  106   a  and  106   b , or to focus light into the respective fiber  106   a  and  106   b . The lens  110   a  and  110   b  may be any type of suitable lens, including a gradient index (GRIN) lens, or a lens having a curved refractive surface, such as a spherical or aspherical lens. Typically, the ferrule end  112   a  and  112   b  and fiber end  114   a  and  114   b  are polished at a small angle to reduce back reflections. 
     Considering the example where light enters the device  100  through the left sub-assembly  102 , the light  116  from the sub-assembly  102  is collimated, may pass through the optical component  118 , disposed between the two sub-assemblies  102  and  104 , to the second sub-assembly. The optical component  118  may be any suitable type of optical component that operates on the light propagating in free space, including but not restricted to an isolator, a filter, a polarizer, an attenuator, a switch, a shutter, or the like. It will also be appreciated that the light may pass from the right sub-assembly  104  to the left sub-assembly  102 . 
     One or both of the sub-assemblies  102  and  104  may also include additional optical components not illustrated. For example, the left and/or right sub-assembly  102  and  104  may include a filter. Additionally, there may be no optical component  118  mounted within the housing separately from the sub-assemblies  102  and  104 , with the only optical component(s) within the device  100  being mounted within the sub-assemblies  102  and  104  themselves. 
     The sub-assemblies  102  and  104  are often disposed within a housing  120 . Typically, both the housing  120  and the sub-assemblies  102  and  104  are cylindrical in shape, so that the sub-assemblies  102  and  104  easily slip into the respective housing ends  122   a  and  122   b . The sub-assemblies  102  and  104  are mounted within the housing  120  using respective bands of adhesive  124   a  and  124   b . Likewise, the element  118  may be mounted in the housing  120  using adhesive  126 . Often, the only mechanical support to the sub-assemblies  102  and  104  is provided by the adhesive  124   a  and  124   b  itself, which may not be applied evenly around the sub-assemblies  102  and  104 . Due to the different thermal expansion coefficients of the adhesive  124   a  and  124   b  and the housing  120 , typically formed of metal, any asymmetry in the adhesive  124   a  and  124   b  results in shifting, and subsequent misalignment, of the components with temperature. 
     Other types of collimator sub-assembly are illustrated in FIGS. 2-4. In FIG. 2, a dual fiber collimator (DFC) sub-assembly  200  includes two fibers  202  and  204  held in a dual fiber ferrule  206 . Light  208  from the first fiber  202  is directed to a lens  210 . The first fiber  202  is typically positioned at a distance from the lens  210  of about the focal length of the lens  210 , so that the light  212  emerging from the lens  210  is approximately collimated. However, the first fiber  202  is not positioned on the axis  214  of the lens  210 , and so the collimated light  212  does not propagate parallel to the axis  214 . The light path  216  from the second fiber  204  to the lens  210  is likewise diverging and, following the lens  210 , the light path  218  is collimated, but off-axis. 
     The DFC  200  may optionally include an optical component  220 , such as an optical filter. In the particular embodiment illustrated, light  212  from the first fiber  202  is reflected as light  218  back to the second fiber  204  by the filter  220 , while some light  222  is transmitted through the filter  220 . There may also be a path  224  for light transmitted through the filter  220  that passes to the second fiber  204 . 
     A DFC such as the DFC  200  is useful for introducing a collimated, but off-axis, light beam to an optical element, such as a filter. For example, a device having two opposing DFCs may be used with an interference filter between the DFCs to combine or separate light of different wavelengths, and is commonly used as a multiplexer or demultiplexer in optical communications systems that use multiple channel optical signals. DFCs are further described in U.S. patent applications Ser. Nos. 09/999,891, and 09/999,553, both of which are incorporated by reference. 
     Another type of collimator sub-assembly  300  is schematically illustrated in FIG.  3 . This sub-assembly  300  uses two lenses to produce substantially collimated beams that propagate parallel to an axis, from two or more fibers. In the particular embodiment illustrated, two fibers  302  and  304  are mounted in a dual fiber ferrule  306 . The light path  308  from the first fiber  302  diverges to the first lens  310 . The first lens  310  focuses the light, reducing the divergence. Since the first fiber is not positioned on the lens axis  312 , the light path  314  emerging from the first lens  310  crosses the axis  312 . Likewise, the light path  316  from the second fiber diverges to the lens  310  and the light path  318  from the lens  310  is directed across the axis  312 . A second lens  320  parallelizes the light paths  314  and  318  so that they propagate in a direction parallel to the axis  312 . 
     This type of collimator sub-assembly may be used to produce substantially parallel beams from more than two fibers. Furthermore, with careful selection of the focal lengths of the lenses  310  and  320 , and with careful selection of the relative spacings between the two lenses  310  and  320 , and the fibers  302  and  304 , the parallelized light paths  322  and  324  may be substantially collimated. This type of collimator sub-assembly is described in greater detail in U.S. Pat. No. 6,289,152, which is incorporated by reference. 
     The second lens  320  may be replaced with a biprism. However, this is effective at paralellizing only light from fibers set at one particular distance form the optical axis  312 , whereas the approach using the second lens  320  is useful at parallelizing light from fibers set at different distances from the axis  312 . 
     The sub-assembly  300  is useful for optical devices that require multiple, parallelized beams, for example isolators, circulators, and the like. 
     Another type of collimator sub-assembly  400  is illustrated in FIG.  4 . The sub-assembly  400  includes at least two fibers  402  and  404  mounted in a ferrule  406 . Each fiber  402  and  404  has a respective lens  408   a  and  408   b  disposed at its output to collimate the light  410   a  and  410   b  produced from the fibers  402  and  404 . The lenses  408   a  and  408   b  may be GRIN lenses, as illustrated, or may be lenses having a curved refractive surface. 
     Like the sub-assembly  300  shown in FIG. 3, the sub-assembly  400  produces multiple parallel collimated beams from multiple fibers. However, this sub-assembly needs a single lens for each fiber, whereas the sub-assembly  300  is capable of producing collimated, parallel light paths using two fibers, irrespective of the number of fibers present. 
     It will be appreciated that in the different types of sub-assemblies illustrated in FIGS. 1-4, a lens described as collimating or focusing light emerging from a fiber may also be used to focus light into the fiber where the light propagates in the opposite direction from that described. 
     Fiber optic devices may be constructed using any of the collimator sub-assemblies discussed above. Furthermore, other collimator sub-assemblies, not described here, may be used in a fiber optic device. Additionally, a central section may be positioned within the housing between the sub-assemblies, for example to hold additional optical elements. 
     One problem common to devices that use collimator sub-assemblies is in the relative alignment of the sub-assemblies, since there are so many degrees of freedom available for adjusting the sub-assemblies. This is schematically illustrated in FIG. 5, which shows two opposing sub-assemblies  502  and  504  aligned on an axis  506 . According to the adopted co-ordinate system, the axis  506  lies parallel to the z-direction. Each sub-assembly  502  and  504  has the following four degrees of freedom: x, y, θ x , and θ y . The angle θ x  refers to orientational adjustment in the x-z plane and θ y  refers to orientational adjustment in the y-z plane. Since each sub-assembly  502  and  504  may have each of these four degrees of freedom, the device may be aligned by aligning each degree of freedom for each sub-assembly, which may be a long and tedious process. According to the present invention, a simplified approach to aligning the sub-assemblies may be reached by prohibiting the two collimator sub-assemblies from being adjusted in the same degree of freedom. 
     It can be shown mathematically that the x-direction and the y-direction are decoupled, and so x adjustments (x, θ x ) may be made independently of y adjustments (y, θ y ). Initially, we consider only x adjustments. Combinations for aligning the two sub-assemblies, labeled Left and Right, are listed in the following table. 
     
       
         
               
             
               
               
               
             
           
               
                 TABLE I 
               
             
             
               
                   
               
               
                 One Dimensional Alignment Combinations for Two Sub-assemblies 
               
             
          
           
               
                 Combination No. 
                 Left 
                 Right 
               
               
                   
               
               
                 1 
                 x 
                 x 
               
               
                 2 
                 θ x   
                 θ x   
               
               
                 3 
                 θ x   
                 x 
               
               
                 4 
                 x, θ x   
                 &lt;no adjust&gt; 
               
               
                   
               
             
          
         
       
     
     Combination No. 1 may be ignored, because it provides no guarantee of aligning the sub-assemblies. According to Combination No. 2, the orientation angle of each sub-assembly is adjusted. The pivot points may be, for example, roughly about the exit face of the sub-assembly. There is no translation in this alignment scheme, just goniometric rotation. In practice, this approach to alignment entails adjusting θ x  for each sub-assembly alternately, first adjusting the left sub-assembly, then the right sub-assembly, then the left sub-assembly again and so on, while monitoring the amount of light coupled through the device from one sub-assembly to the other. 
     A graph showing calculated contours of equal coupling values is illustrated in FIG.  6 . The abscissa shows the value of θ x  in degrees, for the right sub-assembly while the ordinate shows the value of θ x , in degrees, for the left sub-assembly. 
     A straightforward approach to aligning the sub-assemblies, which involves adjusting the value of θ x , for only one assembly at a time, is to set the value of θ x  for one sub-assembly to a first value, optimize the optical coupling to a first optimized value by adjusting θ x  for the other sub-assembly, optimize the optical coupling to a second optimized value by adjusting θ x  for the first sub-assembly, and continuing on, in this fashion, alternating between sub-assemblies until the point of maximum coupling is reached. 
     This approach is partially illustrated in FIG.  6 . An arbitrary start point for the initial alignment is given by point A. Rotation of the left sub-assembly takes the alignment to point B, where the line AB is tangent to one of the contour lines. Rotation of the right sub-assembly will take the alignment to a second optimal point between B and F where the line BF is tangent to a second contour line. The coupling value at this second point will be higher than at point B. Rotation of the sub-assemblies continues to alternate in this fashion, following a series of steepest ascent paths, via points F, J, and K, that eventually leads to the point of optimal coupling, at point L. It was assumed for generating these plots that the light beam had a 1/e 2  half width of 140 μm and that the sub-assemblies were separated by 6 mm. 
     Because the elliptical contours are very narrow, the change in rotation angle and coupling efficiency from one optimal point to the next tend to be small. It is difficult for alignment stages and coupling measurement instruments to resolve these small changes with the result that no discernment may be made between sequential optimum points and further iteration is impossible. Even with ideal instrumentation, the small steps from optimal point to optimal point results in a large number of iterations, therefore increasing the time taken to perform the alignment, before convergence to the maximum coupling value. Coupling contours with elliptical aspect ratios approaching that for a circle reduce the demands on instrument resolution and result in rapid convergence to the point of maximum coupling. 
     The goal of these two procedures may be viewed as moving the device&#39;s operating point from a random starting point on the graph, set by the initial alignment between the two sub-assemblies, “up the hill” to the maximum possible value of optical coupling. The center of the elliptical contours represents optimal coupling between the sub-assemblies, and the alignment process should guarantee that the the final operating point is set at the center of the ellipses regardless of the position of the initial operating point. Also, it is advantageous for the alignment process to reach the point of maximum coupling with a small number of steps. 
     The problem with this alignment process is that movement is made only in horizontal and vertical steps. An adjustment of θ x  for the left sub-assembly moves the value of optical coupling to a local peak value. The narrowness of the elliptical contours results in making many small alignment steps. The resolution of these these small steps may be difficult for many alignment tools to achieve. Futhermore, the large number of alignment steps increases the length of time requried to aligne the fiber optic device. 
     We now consider alignment Combination No. 3, in which one of the sub-assemblies is translated, and the other sub-assembly is rotated. A plot showing calculated contours of equal optical coupling between sub-assemblies for this alignment option is displayed in FIG.  7 . The abscissa shows the value of x for the right sub-assembly, in microns, while the ordinate shows the value of θ x  for the left sub-assembly. 
     The contours  702 ,  704  and  706  are in the form of ellipses whose axes are nearly aligned with the horizontal and vertical axes of the plot, and therefore the alignments are nearly decoupled. From any starting location in the plane, the alignment corresponding to maximum optical coupling between the sub-assemblies may be reached in just a few iterations. For example, if the initial alignment of the sub-assemblies is at point A, then the operator may rotate the left sub-assembly to move the device alignment to point B. Translation of the right sub-assembly may bring the alignment to point C, and further rotation of the left sub-assembly brings the operating point to position D, which is close to optimal. 
     The slight misalignment of the elliptical contours arises because there is a separation between the pivot point of one sub-assembly and the back focal plane of the lens in the other sub-assembly. The greater the separation, the more these axes of ellipses are tilted relative to the axes of the graph, resulting in greater coupling between these two adjustments in x and θ x . It is advantageous for the separation to be zero, in which case the axes of the ellipses are aligned parallel to the axes of the graph, and the adjustments in x and θ x  are completely decoupled. A separation of 6 mm between the pivot point of the left sub-assembly and the back focal plane of the right sub-assembly was assumed to generate the contours illustrated in FIG. 7, while the 1/e 2  half beam width was 140 μm, and the wavelength of light was 1.55 μm. 
     Since the alignments for the (x, θ x ) alignment scheme are almost decoupled, this scheme is preferred over the (θ x , θ x ) scheme: it is much simpler to align using the (x, θ x ) scheme than the (θ x , θ x ), there are fewer steps involved and the alignment may be performed faster. Furthermore, the alignment may be performed with operators that are less highly trained. 
     Combination No. 4 is similar to Combination No. 3, except that in this case the x and θ x  adjustments are both performed on the same sub-assembly. It is a matter of choice as to whether both adjustments should be done on one sub-assembly, or one adjustment should be done on each sub-assembly. 
     The above description of alignment in x and θ x  also holds for y-adjustments, in other words translations parallel to the y-axis and rotations of θ y . Therefore, combining the different options for making x- and y-adjustments, the following alignment options listed in Table II have substantially decoupled adjustments. 
     
       
         
               
             
               
               
               
             
           
               
                 TABLE II 
               
             
             
               
                   
               
               
                 Two Dimensional Alignment Combinations for Two Sub-assemblies 
               
             
          
           
               
                   
                 Left 
                 Right 
               
               
                   
                   
               
               
                   
                 x 
                 y, θ x , θ y   
               
               
                   
                 y 
                 x, θ x , θ y   
               
               
                   
                 θ y   
                 x, y, θ x   
               
               
                   
                 θ x   
                 x, y, θ y   
               
               
                   
                 x, y 
                 θ x , θ y   
               
               
                   
                 x, θ x   
                 y, θ y   
               
               
                   
                 x, θ y   
                 y, θ x   
               
               
                   
                 x, y, θ x , θ y   
                 &lt;no adjust&gt; 
               
               
                   
                   
               
             
          
         
       
     
     The choice of which alignment option to use is left to the designer. It will be appreciated that the right and left sub-assemblies may be exchanged for each other with no significant effect. Thus, for example, a device in which the left sub-assembly is adjustable in x, while the right sub-assembly is adjustable in y, θ x , and θ y , is equivalent to a device in which the right sub-assembly is adjustable in x, while the left sub-assembly is adjustable in y, θ x , and θ y . 
     One approach to implementing a device  800  in which the two sub-assemblies are adjusted in decoupled degrees of freedom is illustrated schematically in FIG. 8, which includes an outer housing  802  that houses a first sub-assembly housing  804 , a central section housing  806  and a second sub-assembly housing  808 . In the illustrated embodiment, the sub-assemblies  804  and  808  and the central section housing  806  are cylindrical in cross-section, although this is not a requirement. The housings  804 ,  806  and  808  are shown separated along the device axis  809 , although this need not be the case, and the housings  804 ,  806  and  808  may be advantageously in contact. Contact between the housings reduces the thickness of the adhesive between the housings, thus reducing the problems arising due to the differential expansion of thick, uneven portions of adhesive under increasing temperatures. 
     The first sub-assembly housing  804  has an angled face  810  and the central section housing  806  has a first angled face  812  opposing the angled face  810 . A first interface is formed between the first sub-assembly housing  804  and the central section housing  806  by the angled faces  810  and  812 . The central section housing  806  has a second angled face  814  and the second sub-assembly housing  808  also has an angled face  816  opposing the second angled face  814 . A second interface is formed between the second sub-assembly housing  808  and the central section housing  806  by the angled faces  814  and  816 . 
     The geometry with the angled interface between adjacent sections resembles a miter joint. Where the central section  806  remains fixed within the outer housing  802 , the following adjustments may be applied to the different sub-assemblies  804  and  808  as follows: 
     1) the first sub-assembly  804  pivots about the normal to the faces  810  and  812  (small rotations result in θ y  adjustment); 
     2) the first sub-assembly  804  translates at the interface  810  in the y-direction (up/down in the figure); 
     3) the second sub-assembly  808  pivots about the normal to the faces  814  and  816  (small rotations result in θ x  adjustment); and 
     4) the second sub-assembly  808  translates at the interface  812  in the x-direction (into/out of the figure). 
     Two other translations are possible, namely: 
     5) the first sub-assembly  804  translates in the x direction (into/out of the figure); and 
     6) the second sub-assembly  808  translates in the y-direction (up/down in the figure). 
     Adjustments Nos. 5) and 6) are less preferable for aligning the three units  804 ,  806  and  808 , because they change the axial spacing between the sub-assemblies  804  and  808 , whereas translations 2) and 4) preserve the axial spacing between the sub-assemblies  804  and  808 . One potential advantage of adjustments Nos.  5 ) and  6 ) is that they may be used in an initial aligning step in which the light beam passing through the device  800  is centered on an aperture in the central section housing  806 . 
     The effect of the two rotations, adjustments 1) and 3) is explained further with reference to FIG. 9, which shows the central section housing  806  in perspective view and lines  818  and  820  from the faces  812  and  814  that are parallel to y and x-axes respectively. The first sub-assembly  804  may be rotated about a normal to the angled face  812  of the central section  806  so that its angled face  810  stays parallel with the angled face  812 . For example, the angled face  810  may be in contact with the angled face  812 . If the first sub-assembly is rotated 360 ° about the normal to the angled face  812 , then the first sub-assembly  804  traces out an ellipse  824 , shown in a dashed line. Likewise, the second sub-assembly  808  may be rotated about a normal to the angled face  814  of the central section  806  so that its angled face  816  stays parallel with the angled face  814 . For example, the angled face  816  may be in contact with the angled face  814 . If the second sub-assembly  808  is rotated 360° about the normal to the angled face  814 , then the second sub-assembly  808  traces out an ellipse  822 , shown in a dashed line. 
     As a practical matter, however, only small rotations of the subassemblies  804  and  808  are required for aligning the device  800 . The dark arcs  826  and  828  respectively represent the range of angles about which the first and second sub-assemblies  804  and  808  are rotated in order to achieve alignment. The arc  826  represents rotation primarily of θ y , while the arc  828  represents rotation primarily of θ x . 
     After the two sub-assemblies  804  and  808  have been aligned and efficient optical coupling between the two sub-assemblies  804  and  808  has been achieved, the sub-assemblies  804  and  808  may be bonded to the center section  806 . For example, an epoxy or other suitable type of adhesive may be used about the peripheries of the angled faces  810 ,  812 ,  814  and  816 . Also, the sub-assemblies  804  and  808  may be attached to the center section  806  by any other suitable method, including welding or soldering. One or more of the central section  806  and the sub-assemblies  804  and  808  may also be supported within the outer housing  802  by an adhesive. For example, a first glue line  1002  about the interface between the faces  810  and  812 , and another glue line  1004  about the interface between the faces  814  and  816 , as illustrated in FIG. 10 may protrude radially beyond the sub-assemblies  804  and  808  , and the central section  806 , to adhere to the inner wall  1006  of the outer housing  802 . Thus the two glue lines  1002  and  1004  may suffice to hold the sub-assemblies  804  and  808 , and the central section  806  in place within the housing  802 . An advantage of this approach is that the “sea of glue” present in previous devices is avoided, and so problems due to thermal expansion mismatches are reduced. 
     There now follows a physical analysis of the device  800 . In order to obtain the exiting angles of light in one arm of the device  800 , we perform three coordinate transformations. First, the initial coordinates (x,y,z) are aligned with the central section  806  portion of the housing, as illustrated in FIGS. 11A-11C which show orthogonal views of a portion of the central section  806 , along with the second angled face  814  that is angled in the y-z plane. The light beam is initially assumed to propagate along the z-direction. The initial coordinates (x,y,z) may be transformed into the surface coordinates (n x ,n y ,n z ), as shown in FIGS. 12A-12C, using the transformation:          (                   n   ^     x                 n   ^     y                       n   ^     z           )     =       (         1       0       0           0         cos                 C             -   sin                   C             0         sin                 C           cos                 C           )          (           x   ^               y   ^               z   ^           )                              
     The surface normal is n z . Initial coordinate x becomes n x , and both y and z are rotated by cut angle C into n y  and n z , respectively. 
     For adjustment, a part is rotated by angle T around the surface normal n z . Denoting rotated coordinates by a prime (′), the surface coordinates (n x ,n y ,n z ) are transformed into rotated surface coordinates (n x ′,n y ′,n z ′), illustrated in FIG. 13, using the transformation:          (             n   ^     x   ′                 n   ^     y   ′                 n   ^     z   ′           )     =       (           cos                 T           sin                 T         0               -   sin                   T           cos                 T         0           0       0       1         )          (                   n   ^     x                 n   ^     y                       n   ^     z           )                              
     Coordinate n z  becomes n z ′ directly, and n x  and n y  are rotated by tilt angle T to become n x ′ and n y ′, respectively. 
     Finally, the rotated surface coordinates (n x ′,n y ′,n z ′) are transformed into a coordinate system (x′,y′,z′) aligned with the adjustable arm, for example the second sub-assembly  808 , as illustrated in FIG. 14, using the transformation:          (             x   ^     ′                 y   ^     ′                 z   ^     ′           )     =       (         1       0       0           0         cos                 C           sin                 C             0           -   sin                   C           cos                 C           )          (             n   ^     x   ′                 n   ^     y   ′                 n   ^     z   ′           )                              
     Thus, the full coordinate transformation may be written as follows:          (             x   ^     ′                 y   ^     ′                 z   ^     ′           )     =       (         1       0       0           0         cos                 C           sin                 C             0           -   sin                   C           cos                 C           )          (           cos                 T           sin                 T         0               -   sin                   T           cos                 T         0           0       0       1         )          (         1       0       0           0         cos                 C             -   sin                   C             0         sin                 C           cos                 C           )          (           x   ^               y   ^               z   ^           )                              
     One important quantity is the unit vector z′ in the transformed space. The components in x and y give the angular offsets of the beam as the subassemblies are adjusted by an angle T: 
     
       
           {circumflex over (z)} ′[sin  C  sin  T]{circumflex over (x)} +[cos  C  sin  C (1−cos  T )] ŷ +[cos 2   C +sin 2   C  cos  T]{circumflex over (z)}   
       
     
     For small angles T, sin T=T, and cos T=1−T 2 /2, where the angle T is measured in radians. Thus, the component of the rotated z′ direction that lies along the original x direction, {circumflex over (z)}′ x , and the component of the rotated z′ direction that lies along the original y direction, {circumflex over (z)}′ y , are given by:            Z   ^     y   ′     =       T   2     ×       cos                 C                 sin                 C     2                              
     The z′ x  term is particularly interesting, since it shows that, for a cut angle C, there is a demagnification of (sin C) between the tilt angle T and the output arm pivot component z′ x . The z′ y  term is undesirable, and describes how much of the desired rotation leaks into the wrong component. For small T, this component is quite small, and poses no problems in an alignment scheme. 
     For a cut angle of C=15°, the demagnification factor is sin C=0.26 and, therefore, the tilt required to sweep out a beam pivot of 1° is T=3.9°. The undesirable beam pivot associated with this adjustment in the wrong direction is 0.033°, and is negligibly small, especially during an iterative alignment step. 
     If the analysis is repeated with a cut angle of C=30°, sin C=0.5, then the tilt required to sweep out a beam pivot of 1° is T=2°. The undesirable beam pivot associated with this adjustment is only 0.015°. Thus, the amount of undesired rotation constitutes less than 2% of the desired rotation. 
     Therefore, use of a miter joint provides effective decoupling between adjustments of θ x  and θ y , permitting the decoupled adjustment discussed above. It also enables contact between sub-assemblies and the central housing, thus avoiding thick portions of adhesive that may give rise to misalignment problems due to unmatched thermal expansion. 
     It will be appreciated that the entire end face of the central section and the sub-assemblies is not needed to define the parallel surfaces between the sub-assemblies and the central section that lie at an angle relative to the longitudinal axis of the device. Instead, only portions of these end faces may be used to define the parallel surfaces. 
     Another approach to providing separate, decoupled adjustment to a device having two collimator sub-assemblies is discussed in U.S. patent application Ser. No. 10/138,168, entitled “Compact Optical Module with Adjustable Joint for Decoupled Alignment”, filed on even date herewith by T. Schmitt, J. Treptau, R. Gerber, T. Gardner, E. Gage and K. Batko, and incorporated herein by reference. 
     The invention may be practiced with any type of collimator sub-assembly, and is not restricted to use with those sub-assemblies described above. 
     As noted above, the present invention is applicable to aligning sub-assembly modules and is believed to be particularly useful for providing orthogonal degrees of freedom for easier alignment of sub-assembly modules. The present invention should not be considered limited to the particular examples described above, but rather should be understood to cover all aspects of the invention as fairly set out in the attached claims. Various modifications, equivalent processes, as well as numerous structures to which the present invention may be applicable will be readily apparent to those of skill in the art to which the present invention is directed upon review of the present specification. The claims are intended to cover such modifications and devices.