Abstract:
An angular displacement of an object is measured interferometrically by splitting a laser beam into a reference beam and a measuring beam. The reference beam is directed at a stationary reference retroreflector and then a phase shift detector. The measuring beam is directed at a rotatable reflective surface of the object and then a stationary measuring retroreflector and then back to the rotatable reflective surface and then to the phase shift detector such that the phase shift detector measures an angular displacement of the rotatable reflective surface when the length of the path of the measuring beam changes when the rotatable reflective surface is displaced.

Description:
FIELD OF THE INVENTION 
       [0001]    This invention relates generally to interferometers, and more particularly to a rotary interferometer that measure angular displacements of objects. 
       BACKGROUND OF THE INVENTION 
       [0002]    The interferometer was well-known at the end of the 19 th  century, nominally invented by A. A. Michelson in 1881. Michelson&#39;s interferometer design was instrumental in the disproof of the existence of “luminiferous aether,” for which Michelson won the Nobel Prize in physics in 1907. With the invention of the continuous-wave HeNe laser in 1960 by Ali Javan, William Bennet Jr, and Donald Herriot of Bell Labs, the Michelson interferometer has become a principal apparatus and method for accurately measuring displacements of objects over a large range of values. 
       Linear Interferometer 
       [0003]      FIG. 1  shows a conventional linear interferometer based on the Michelson design. A light emitter  100  includes a laser  101  for emitting a coherent laser beam  102 . The beam passes through Faraday isolator  103  to prevent unwanted feedback into the optical oscillator of the laser cavity. 
         [0004]    An emitted light beam  150  is polarized at an angle of 45 degrees from the plane of the Figure. The beam proceeds into a phase detector  200 , passes unaltered through a beamsplitting prism  201 , and emerges from the detector  200  as laser beam  151 . 
         [0005]    Then, the beam enters a phase shifter  300 , where the 45-degree-polarized beam  151  is split into two sub-beams  152  and  153  by a polarizing beamsplitter  301 . A vertically polarized laser beam  152  emerges from the polarizing beamsplitter  301  and is reflected from a stationary reference retroreflector  303 . Concurrently, a horizontally polarized component of the beam emerges from polarizing beamsplitter  301  as a laser beam  153  and proceeds horizontally to be reflected by a linearly displaceable retroreflector  302 . 
         [0006]    Thus, the beam splitting essentially produces two beams. A first beam  152  is used as a reference beam, and a second beam  153  is used as a measuring beam. The relative lengths of the paths traveled by the reference beam and the measuring beams change when the displaceable measuring retroreflector  302  is displaced from an initial orientation as described below to induce a detectable phase shift between the beams. 
         [0007]    It is a property of retroreflectors that any light beam entering the base of the retroreflector exits the retroreflector along a precisely parallel path as the entering beam, but displaced laterally. The exit point, and hence, the amount of lateral displacement of the beam, is at the same radial distance on the circular retroreflector face as the entry point, but rotated by 180 degrees. Effectively the retroreflector takes any incoming light pattern, rotates it circularly 180 degrees, and returns the beam in exactly same the direction as the entering beam. 
         [0008]    After exiting the retroreflector  303 , a vertically polarized beam  154  returns to the polarizing beamsplitter  301  where the beam is reflected again and returns to detector  200  as part of a beam  156 . 
         [0009]    Concurrently, after exiting from the linearly displaceable retroreflector  302 , a horizontally polarized beam  155  proceeds back through the polarizing beamsplitter  301  and recombines with the vertically polarized beam from retroreflector  303  to form a compositely polarized beam  156 . 
         [0010]    Because the retroreflector  302  can be displaced  309  horizontally, the distance that the measuring beam must transverse, with respect to the reference beam, can change. Therefore, the beam  155  returning from retroreflector  302  can have an additional phase delay with respect to the beam  154  from reference reflector  303 . It is this change in the phase delay that enables the distance measurements. 
         [0011]    At the polarizing beamsplitter  301 , the two beams  154 - 155  combine to have the same optical path. Because the beams  154 - 155  have orthogonal polarizations with respect to each other, i.e., vertical versus horizontal, the beams do not interact. The combined beam  156  then passes back into the detector  200  and into the beamsplitter  201  where the beam is reflected to a beamsplitter  202 . The non-reflected beam  117  from beamsplitter  201  is not used. 
         [0012]    The reflected beam  158  from the beamsplitter  202  is reflected fully by a reflective prism  203  as beam  159 , and the reflected beam passes through a 45 degree polarizer  206  to become beam  160 . Because the polarizer collapses the wave function of the traversing beam, the photons of the beam are no longer either vertically or horizontally polarized, but rather all of the photons are now at a 45 degree polarization angle. 
         [0013]    Because the beams now share the same polarization, beam  160  exhibits interference effects, also known as “interference fringes,” manifested as a sinusoidal brightening and dimming of the beam as the retroreflector  302  moves to change the path length. A photodiode  208  converts the energy of the beam  160  into an electrical signal, which can be amplified and measured as a linear displacement. 
         [0014]    The non-reflected beam  161  exiting the beamsplitter  202  passes through a quarter-wave plate  204 . The quarter-wave plate contains an anisotropic optical material such as mica or stressed polystyrene that exhibits a varying index of refraction with varying polarization. In particular, a perfect quarter-wave plate designed for a particular wavelength λ, will have a minimum (ideally zero) phase delay at one polarization rotation of the plate with respect to the beam, and a maximum (ideally, exactly λ/4) phase delay when the beam is polarized perpendicularly to the zero phase delay orientation. 
         [0015]    The quarter-wave plate  204  delays one of the polarizations by λ/4, which is a 90 degree phase shift forming beam  162 . The beam  162  then passes through a 45 degree polarizer  205 , which similar to the polarizer  206 , collapses the polarization of the beam to 45 degrees to form beam  163 . The component parts of beam  163  now share the same polarization, and as such, exhibit interference fringes. These fringes are detected by photodiode  207  to generate a second electrical signal. 
         [0016]    The two electrical signals from photodiodes  207  and  208  are sinusoids with a relative phase angle of 90 degrees, generated by the quarter-wave plate  204 . These two sinusoids can be thresholded at their average values. The resulting pulse trains are used as quadrature signals to a quadrature counter, not shown, to effectively measure the linear displacement  309  when the retroreflector  302  is moved. 
       Rotary Interferometer 
       [0017]      FIGS. 2A-2B  shows a conventional, prior art rotary interferometer that uses rotational displacement rather than linear displacement.  FIG. 2A  is detailed, and  FIG. 2B  summarizes the essential optical features. 
         [0018]    The emitter  100 , detector  200 , and the laser beams  150  through  162  are the same as in  FIG. 1 . 
         [0019]    The phase shifter  300  has a rotatable measuring retroreflector  302  on the rotationally moving linkage  304 . As the linkage  304  rotates through a displacement  305  along an arc  305 , the measuring retroreflector  302  moves with the linkage and produces a phase difference in the laser beam  153  yielding beam  155 , as shown in  FIG. 1 , but now to measure the angular displacement. 
         [0020]    However, this conventional arrangement has several problems. 
       Mass and Angular Inertia 
       [0021]    First, the rotatable measuring retroreflector  302  and the linkage have a significant mass. For lightweight, fast-moving mechanisms, such as laser beam director mirrors mounted on optical galvanometers, the weight of the retroreflector can be greater than the mass of all the other optical components. The additional mass considerably disturbs the dynamics of the system, and also decreases the maximum slewing speed of the laser beam director. 
       Range 
       [0022]    Second, the angular displacement  305  that the system can operate over is limited because the rotatable retroreflector returns the beam on a parallel path with a displaced axis. If the height  317  of the arc  305  is greater than the diameter of the laser beam  156 , then no laser beam is returned to the detector  200 , and measurement of the angular displacement  305  becomes impossible. 
         [0023]    It is desired to reduce the weight and increase the angular range of a rotary interferometer. 
       SUMMARY OF THE INVENTION 
       [0024]    The embodiments of the invention provide a rotary interferometer to measure angular displacements to rotatable objects. 
         [0025]    In contrast with the prior art, this interferometer significantly reduces the weight and angular inertia of the rotary interferometer. 
         [0026]    In addition, the interferometer has a substantially larger range of angular displacements than conventional interferometers. 
         [0027]    Instead of using the rotatable retroreflector and linkage, the embodiments use a polished flat reflective surface on a rotatable object for which the angular displacement needs to be measured. The surface can also be a small planar mirror arranged on a surface of the object, if the object is not reflective. 
         [0028]    A stationary corner reflector is used to produce fringes at a rate proportional to a tangent of an angle of the measured rotatable object. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0029]      FIG. 1  is a schematic of a prior art linear interferometer; 
           [0030]      FIGS. 2A-2B  are schematics of a prior art rotary interferometer; 
           [0031]      FIGS. 3A-3D  are schematics of a rotary interferometer according to embodiments of the invention; 
           [0032]      FIG. 4  is a top view schematic of the interferometer of  FIG. 3D ; and 
           [0033]      FIG. 5  is an isometric view schematic of the interferometer of  FIG. 3D . 
       
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       [0034]      FIGS. 3A-3D  show rotary interferometers according to embodiments of our invention.  FIGS. 3A and 3B  summarize the essential basic details of the interferometers shown in  FIGS. 3C and 3D . The emitter  100  is as shown in  FIGS. 1-2 . 
       Beam Expander 
       [0035]    The phase detector  200  has an optional laser beam expander  210  in  FIG. 3C . The expander increases the diameter of the beam to result in a wider coherent laser beam  163 . By expanding the beam, a range over which angular displacements can be measured is increased, as described below. The beam expander can be a Gallean telescope with one negative lens and one positive lens, or a Keplerian telescope with a pair of positive lenses. 
         [0036]    The expanded beam  163  continues as an expanded beam  151  through the first beamsplitter  201 . 
       Rotatable Reflective Surface 
       [0037]    We do not use the heavyweight rotating measuring retroreflector  302  arranged on the linkage  304 , as in the prior art. Instead, we use a rotatable reflective surface  306  that is inserted in the path of the enlarged beam  153  diverting the enlarged beam  153  as an enlarged beam  165  to a stationary measuring retroreflector  302 . The reflective surface can be a polished surface of the object to which the angular displacement is to be measured. If the surface is not reflective, a mirror can be arranged on the surface. 
         [0038]    As defined herein, a rotatable surface is configured to move an angular displacement  307  along an arc. 
         [0039]    The retroreflector  302  returns the enlarged  165  beam as an enlarged beam  164  to the rotatable reflective surface  306 . The reflective surface  306  reflects the enlarged beam  164  back along the same path as enlarged beam  155 . 
         [0040]    The enlarged beams  154  and  155  merge with crossed polarizations into enlarged beam  156 . The enlarged beam  156  reflects from beamsplitter  201  becoming enlarged beam  166 . 
         [0041]    If the beam expander  210  is used, then the enlarged beam  166  passes through a hole  213  in an optional aperture plate  212  to a reduced diameter beam  157 . The aperture plate reduces the beam to its original diameter before entering the beam expander. The beam  157  propagates through the remainder of the phase detector  200  as described for  FIG. 1  to measure the angular displacement. 
         [0042]    Because the diameter of the beams used for detecting is increased by the beam expander  210 , the reflective surface mirror  306  can rotate through a larger angle before the returned sensing enlarged beam  155 , fails to overlap. As a result, the angle that can be measured is much larger than in the prior art. 
         [0043]    In addition, the reflective surface  306  can be a polished, aluminized, silvered, or otherwise mirrored part of the object to which the angular displacement needs to be measured, and hence, does not increase the overall mass or angular inertia of the object. 
         [0044]    In a preferred implementation, where the invention is used to measure a position of a beam directing optical galvanometer, the mirror  306  is the same mirror as the final beam directing mirror, and so the total mass or angular inertia remains exactly the same as for the beam directing optical galvanometer that does not have the ability to measure rotation interferometrically. 
       Four-Pass Optical Assembly 
       [0045]      FIG. 3D  shows an alternative embodiment of our invention. The emitter  100  and the phase detector  200  are as described above for  FIG. 2 . However, the phase shifter  300  is altered by using a four-pass optical assembly  350 , shown in abbreviated form in  FIG. 4 , and in detail in  FIG. 5 . 
         [0046]    As shown in  FIG. 3D , the beam pattern within the four-pass optical assembly  350  uses the rotatable surface  306 , the stationary retroreflector  302 , and a planar stationary mirror  308  to produce a return beam  155  that does not deviate significantly in position through large angular displacements  307  of the rotatable surface  306   
         [0047]      FIGS. 4 and 5  show the details of the four pass optical assembly  350 .  FIG. 4  shows a top view of the four pass optical assembly  350 .  FIG. 5  shows an isometric view of the four pass optical assembly  350 . The following description applies to  FIG. 4 . 
         [0048]    The beam  153  from polarizing beamsplitter  301  enters the four-phase optical assembly  350  parallel to the plane of the Figure, and is denoted as beam  351 . Beam  351  reflects downward from rotating mirror  306  as beam  352 , shown end-on in  FIG. 4 . 
         [0049]    Beam  352  enters the retroreflector  302 , and is reflected internally as beam  353 , reflecting out of the retroreflector as beam  354 , shown end-on in  FIG. 4 . Note that the displacement of beam  352  with respect to the center of retroreflector  302  causes an equal and opposite displacement of beam  354  from the center of retroreflector  302 . 
         [0050]    The beam  354  emerges from the retroreflector  302 , and reflects from the rotatable surface  306  to form beam  355 . Beam  355  reflects from the stationary planar mirror  307  to form beam  356 . Because of the parallel reflection action of retroreflector  302 , beam  355  is always perpendicular to the stationary planar mirror  307 . The reflected beam  356  is always coaxial with incoming beam  355 , and beam  356  re-traces the route of beam  355  in reverse. 
         [0051]    Beam  356  reflects from the rotatable surface  306  to form beam  357 , again re-tracing the route of beam  354  in reverse. Beam  357  enters the stationary retroreflector  302  and reflects internally, to form beam  358 , again, re-tracing the route of beam  353  in reverse. Beam  353  reflects internally in the retroreflector  302 , and forms beam  359 , again, re-tracing the route of beam  352  in reverse. Beam  359  emerges from the retroreflector  302  and reflects from rotating mirror  306 , yielding beam  360 , and again re-tracing the route of beam  351  in reverse. 
         [0052]    Then, beam  360  emerges from the four pass optical assembly  350  and becomes beam  155  as shown in  FIG. 3D . The beam  155  is combined with a reference beam  154  as shown in  FIG. 3D  to form a combined beam  156  that is then phase-detected by the phase detector  200  as described above for  FIG. 1  to measure the angular displacement. 
         [0053]    With the arrangement as shown in  FIGS. 4 and 5 , the overall beam maintains alignment over a very large angular displacement  307  of the rotatable surface  306 . 
         [0054]    Furthermore, because the beam makes four traverses of a displacement that varies with the position of the rotatable surface  306 , specifically, beam paths  351 ,  355 ,  356 , and  360 , rather than two traverses of path as described above, there specifically beam paths  153  and  155 , the sensitivity of the embodiments as described for  FIGS. 4 and 5  is twice that of the prior art or of the embodiment of  FIG. 3A and 3C . 
         [0055]    Although the invention has been described by way of examples of preferred embodiments, it is to be understood that various other adaptations and modifications can be made within the spirit and scope of the invention. Therefore, it is the object of the appended claims to cover all such variations and modifications as come within the true spirit and scope of the invention.