Abstract:
An interferometer system includes a plane mirror interferometer, a turning mirror, a retardation plate assembly having a retardation plate that can be adjusted and then fixed, and a retroreflector. A light beam travels in a path comprising the plane mirror interferometer, the turning mirror, the retardation plate assembly, and the retroreflector. The retardation plate assembly may include a plurality of bearings, a ring riding on the bearings, the retardation plate mounted to the ring, and a plunger pushing the ring against the bearings. The retardation plate may be fixed by adhesive after determining an orientation that produces little polarization leakage in the system.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is related to U.S. patent application No. 10/857,792, entitled “Polarization-Maintaining Retroreflector Apparatus,” and U.S. patent application No. 10/856,204, entitled “Systems Using Polarization-Manipulating Retroreflectors,” which are concurrently filed, commonly assigned, and incorporated herein by reference. 
     DESCRIPTION OF RELATED ART 
     In differential interferometers, such as those described by U.S. Pat. Nos. 4,930,894 (“Baldwin”) and 4,693,605, cyclic nonlinearities arise from polarization leakage of the reference beam into the measurement path and vice versa. Sources of polarization degradation (i.e., undesired polarization changes), hence leakage, in these interferometers include imperfect polarizing coatings, imperfect retardation plates, and polarization transformation by silver coated cube corner retroreflectors. 
     In one interferometer described by Baldwin and reproduced in  FIG. 1 , a significant source of ⅛ wave nonlinearity arises in the “differential adapter,” which consists of a turning mirror  150 , a quarter-wave plate  14 , and a silver coated cube corner retroreflector  13 . Quarter-wave plate  14  is oriented to convert incident linearly polarized light into circularly polarized light on its way to silver coated cube corner  13 . By its construction, silver coated cube corner  13  degrades the circular polarization and outputs elliptically polarized light with its major axis rotated such that when the light is returned for a second pass through quarter-wave plate  14 , the output light is not perfectly linearly polarized. The light now has a linearly polarized component orthogonal to the desired polarization state. This component is polarization leakage that results in cyclic nonlinearity error. 
     Thus, what are needed are an apparatus and a method for addressing the polarization leakage in differential interferometer systems, and specifically polarization leakage caused by a quarter-wave plate in the path to a silver coated cube corner. 
     SUMMARY 
     In one embodiment of the invention, an interferometer system includes a plane mirror interferometer, a turning mirror, a retardation plate assembly having a retardation plate that can be adjusted and then fixed, and a retroreflector. A light beam travels in a path comprising the plane mirror interferometer, the turning mirror, the retardation plate assembly, and the retroreflector. In one embodiment, the retardation plate assembly includes a plurality of bearings, a ring riding on the bearings, the retardation plate mounted to the ring, and a plunger pushing the ring against the bearings. In one embodiment, the retardation plate is fixed by adhesive after determining an orientation that produces little polarization leakage in the system. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  illustrates a conventional differential interferometer system. 
         FIGS. 2 and 3  illustrate a differential interferometer system in one embodiment of the invention. 
         FIGS. 4 ,  5 , and  6  illustrate a retardation plate assembly that allows for precise, in situ adjustment of the retardation plate in the interferometer system of  FIGS. 2 and 3  in one embodiment of the invention. 
         FIG. 7  is a flowchart of a method for adjusting the retardation plate assembly in a differential interferometer system to reduce polarization leakage in one embodiment of the invention. 
         FIG. 8  illustrates a differential interferometer system in another embodiment of the invention. 
       Use of the same reference numbers in different figures indicates similar or identical elements. 
     
    
    
     DETAILED DESCRIPTION 
       FIGS. 2 and 3  illustrate a differential interferometer system  200  in one embodiment of the invention. A laser head  202  generates a coherent, collimated light beam consisting of two orthogonally polarized frequency components. One frequency component f A  (e.g., a measurement beam having a P-polarization) enters the system&#39;s measurement path while the other frequency component f B  (e.g., a reference beam having an S-polarization) enters the system&#39;s reference path. 
     In the measurement path, a polarizing beam-splitter  204  transmits frequency component f A  to a measurement plane mirror  206  mounted to a moving stage. Since frequency component f A  passes through a quarter-wave plate  208 , the returning polarization is rotated 90 degrees and the newly S-polarized frequency component f A  is reflected by polarizing beam-splitter  204  to a cube corner retroreflector  210 . Cube corner  210  directs frequency component f A  again to polarizing beam-splitter  204 , which again reflects frequency component f A  to measurement plane mirror  206 . Again, since frequency component f A  passes through quarter-wave plate  208 , the returning polarization is rotated 90 degrees and the newly P-polarized frequency component f A  is transmitted through polarizing beam-splitter  204  to a turning mirror  212 . 
     Turning mirror  212  directs frequency component f A  through a retardation plate assembly  216  (shown in more detail in  FIGS. 4 ,  5 , and  6 ) onto a silver coated cube corner retroreflector  214 , which returns frequency component f A  back to mirror  212 . Since frequency component f A  passes through a quarter-wave plate in assembly  216 , the returning polarization is ideally (but not actually) rotated 90 degrees. Mirror  212  then returns the newly S-polarized frequency component f A  to polarizing beam-splitter  204 , which reflects frequency component f A  to a cube corner retroreflector  218 . Cube corner  218  returns frequency component f A  to polarizing beam-splitter  204 , which reflects frequency component f A  to a receiver  220 . Note that turning mirror  212  is used to make system  200  more compact. If a larger system  200  is constructed, turning mirror  212  may be eliminated and cube corner  214  placed directly behind polarizing beam-splitter  204  with assembly  216  in between. 
     In a conventional setup, the fast (or slow) axis of the quarter-wave plate in assembly  216  would be oriented 45° to the polarization vector in order to convert the incident linearly polarized light into circularly polarized light. Unfortunately, in such a setup, the silver coated cube corner  214  would transform the circularly polarized light in the input beam so that the light in the output beam is elliptically polarized. When this elliptically polarized light is returned for a second pass through the quarter-wave plate in assembly  216 , the output would not be in the desired linear polarization state, i.e., perfectly linear polarization along the direction orthogonal to the polarization of the input beam. Instead, the output would have a linearly polarized component orthogonal to the desired linear polarization state. 
     Thus, the ideal alignment for the fast axis of the quarter-wave plate for converting linear polarization to circular polarization (i.e., 45° to the polarization vector) is not ideal when the circularly polarized light subsequently passes through a silver coated cube corner. With a silver coated cube corner in the path, there exists a rotational “sweet spot” for the fast axis that takes advantage of the polarization-transforming effect of the silver coated cube corner. This sweet spot does not produce perfectly circularly polarized light out of the first pass through the quarter-wave plate. However, this sweet spot causes the silver coated cube corner to output an elliptical polarization state that, after returning through the quarter-wave plate, has a smaller, linearly polarized component orthogonal to the desired linear polarization state. The result is that after the return pass through the quarter-wave plate, the original linear polarization state is substantially preserved but, of course, rotated 90°. This in turn produces less polarization leakage and hence smaller cyclic nonlinearity in the interferometric measurements. 
     In general, in the differential interferometer system  200 , a retardation plate can be chosen according to the properties of the silver coating on the cube corner so that the combination of this retardation plate, oriented at its “sweet spot,” and the silver coated cube corner retroreflector gives an even smaller linearly polarized component orthogonal to the desired linear polarization state than the one obtained from the combination of the quarter-wave plate and the silver coated cube corner. For example, a linear retardation plate with a retardation angle of 90.189° gives a smaller unwanted linear component than the quarter-wave plate (retardation angle=90°) when it is combined with a silver-coated cube corner. Similarly, a retardation plate can be chosen for a cube corner with another type of coating so that the combination of this retardation plate and the cube corner minimizes the linearly polarized component orthogonal to the desired linear polarization state. 
       FIGS. 4 ,  5 , and  6  illustrate a retardation plate assembly  216  that allows for precise, in situ rotational alignment of the quarter-wave plate in one embodiment of the invention. A quarter-wave plate  302  is fixed to a ring  304  with adhesive. In one embodiment, quarter-wave plate  302  is made of quartz and ring  304  is made of brass. Ring  304  is kinematically supported by two bearing pins  306  that form a “V block bearing”. In one embodiment, bearing pins  306  are made of Delrin AF. Ring  304  is forced into the V block bearing by two spring loaded plungers  308  mounted to a housing  310  within the V block contact lines. In one embodiment, plungers  308  are made of Delrin AF. 
     A housing  310  includes a face  322  that defines a circular recess  324  for receiving ring  304 . Along the circumference of circular recess  324  are slots  323  ( FIG. 6 ) for receiving bearing pins  306 . Silver coated cube corner  214  can be mounted to housing  310  on face  322 . Turning mirror  212  can be mounted to housing  310  on a face  328  oriented 45° to face  322 . Bores  325  and  326  are defined between faces  322  and  328  to provide the offset paths between turning mirror  212  and cube corner  210 . 
     A plane mirror interferometer  230  (consisting of beam-splitter  204 , cube corners  210  and  218 , and quarter-wave plate  208 ) can be mounted to housing  310  on a face  330 , which is oriented orthogonal to face  322 . Bores are defined between faces  328  and  330  to provide the offset paths between turning mirror  212  and plane mirror interferometer  230 . Glue holes  332  leading to circular recess  324  are provided on the faces of housing  310 . 
     Fine rotational position control of ring  304  (and quarter-wave plate  302 ) is achieved with a dual ball lever  312 . A small ball  314  (on top of a large ball  318 ) engages one of the radial holes  316  in ring  304 . Large ball  318  engages a fulcrum hole  320  and acts as the fulcrum for a first class lever. Fulcrum hole  320  and plunger mounting holes  334  ( FIG. 6 ) are located on face  321  of housing  310  and are connected to circular recess  324 . 
     The combination of high leverage and low friction between ring  304  and bearing pins  306  allows precise alignment of the sweet spot for the quarter-wave plate fast axis to the polarization vector. The spring loaded plungers  308  hold the position of quarter-wave plate  304  once lever  312  is removed. Adhesive is then injected through glue holes  332  to fix the position of ring  304 . 
     Referring back to  FIGS. 2 and 3 , in the reference path, polarizing beam-splitter  204  reflects frequency component f B  to a cube corner  218 . Cube corner  218  returns frequency component f B  to polarizing beam-splitter  204 , which reflects frequency component f B  to mirror  212 . Mirror  212  directs frequency component f B  to silver coated cube corner  214 , which returns frequency component f B  back to mirror  212 . Since frequency component f B  passes through quarter-wave plate  216 , the returning polarization is rotated 90 degrees. 
     Mirror  212  directs the newly P-polarized frequency component f B  to polarizing beam-splitter  204 , which transmitted frequency component f B  to a reference mirror  222  that may move. Since frequency component f B  passes through quarter-wave plate  208 , the returning polarization is rotated 90 degrees and the newly S-polarized frequency component f B  is reflected by polarizing beam-splitter  204  to cube corner  210 . Cube corner  210  returns frequency component f B  to polarizing beam-splitter  204 , which again reflects frequency component f B  to reference mirror  222 . Again, since frequency component f B  passes through quarter-wave plate  208 , the returning polarization is rotated 90 degrees and the P-polarized frequency component f B  is transmitted through polarizing beam-splitter  204  onto receiver  220 . 
       FIG. 7  is a flowchart of a method  700  for searching the sweet spot for the quarter-wave plate fast axis in interferometer system  200  in one embodiment of the invention. 
     In step  702 , the measurement and reference beams are both turned on to propagate through the measurement and reference paths in an assembled interferometer system  200 . 
     In step  704 , the amplitude (hereafter “first amplitude”) of the beat signal from the recombined measurement and reference beams is measured. 
     In step  706 , one of the beams (measurement or reference) is interrupted (e.g., blocked). Theoretically, if there is no polarization leakage, then the beat signal would cease. However, if there is polarization leakage, a detectable beat signal would remain (at the original beat frequency). 
     In step  708 , the amplitude (hereafter “second amplitude”) of the beat signal at the original beat frequency is measured again. 
     In step  710 , it is determined if the polarization leakage is below a threshold, which signifies that the sweet spot for the fast axis of quarter-wave plate  302  in assembly  216  has been found. In one embodiment, the polarization leakage is defined as the ratio of the second amplitude to the first amplitude. If the polarization leakage is not less than the threshold, then step  710  is followed by step  712 . Otherwise step  710  is followed by step  714 . 
     In step  712 , the fast axis of quarter-wave plate  302  in assembly  216  is adjusted. As described above in reference to  FIGS. 4 ,  5 , and  6 , the fast axis of quarter-wave plate  302  is adjusted by using lever  312 . Step  712  is followed by step  708  and the process is repeated until the sweet spot for the fast axis of quarter-wave plate  302  is found. 
     In step  714 , the fast axis of quarter-wave plate  302  is fixed. As described above in reference to  FIGS. 4 ,  5 , and  6 , adhesive is injected through glue holes  332  of housing  310  to fix the orientation of ring  304  and quarter-wave plate  302 . 
       FIG. 8  illustrates a differential interferometer system  800  in one embodiment of invention. System  800  is similar to system  200  except that retardation plate assembly  216  is replaced by an input half-wave plate assembly  816 A in the input path and an output half-wave plate assembly  816 B in the output path, and silver coated cube corner  214  is replaced with an uncoated, TIR (total internal reflection) cube corner retroreflector  814 . It has been determined that a properly oriented TIR cube corner  814  preserves orthogonal linear (horizontal/vertical) polarizations in transit if they are rotated by 13.7° counterclockwise at the input (looking into the cube corner). The output polarizations remain linear but rotated by 13.7° in the opposite direction looking into the cube corner. The 13.7° rotation angle depends on the properties of the cube corner material. For the common optical glass BK-7, the rotation angle is close to 13.7°. 
     Input half-wave plate assembly  816 A is adjusted in situ to rotate the linearly polarized input to TIR cube corner  814  by 13.7°. Output half-wave plate assembly  816 B is adjusted in situ to rotate the resultant linearly polarized output by 13.7°+/−90° so that for each of the frequency components f A  and f B , the returning beam is linearly polarized along the direction orthogonal to the polarization direction of the input beam. System  800  eliminates the undesirable polarization transformation caused by silver coated cube corners altogether. Furthermore, it improves retroreflection efficiency and polarization conversion of vertically polarized light to horizontally polarized light and vice versa. In one embodiment, assemblies  816 A and  816 B are constructed like assembly  216  in  FIGS. 4 ,  5 , and  6  with a half-wave plate instead of a quarter-wave plate. 
     Method  700  described above can be modified to reduce the polarization leakage of system  800 . Instead of adjusting a single quarter-wave plate in step  712 , two half-wave plates are adjusted to search for a sweet spot where the polarization leakage is below a threshold. 
     Various other adaptations and combinations of features of the embodiments disclosed are within the scope of the invention. While the illustrated embodiments utilize plane mirrors and cube corner retroreflectors, other reflective, refractive, diffractive, and holographic components may be substituted. Furthermore, a single spring-loaded plunger  308  centered between the contact lines of bearing pins  306  can be used in place of two spring-loaded plungers  308 . In addition, instead of silver coated cube corner  214 , cube corners coated with other material may be used. The mechanical bearings described in these embodiments are of stable, kinematic design using anti-friction materials. Clearly, less stable, inefficient bearings may be substituted, such as a simple journal bearing comprised of ring  304  running in circular recess  324 . Furthermore, a true kinematic design may be used, such as three bearing balls that support ring  304 . Numerous embodiments are encompassed by the following claims.