Patent Publication Number: US-2007109552-A1

Title: Optical interferometer

Description:
BACKGROUND  
      Optical interferometers are useful in exacting precise measurements. For example, optical interferometers are used to determine movement of optical elements used in photolithographic processing of semiconductor wafers, where precision on the order of nanometers (10 −9  m) and greater is desired.  
      Optical interferometers include two (or more) optical beams. One optical beam is ideally directed along a fixed optical path length, known as the reference path. This beam is known as the reference beam. Another optical beam is directed along a path to a measurement reflector that is connected to an element that may move. This beam is known as the measurement beam, and the path it traverses is known as the measurement path.  
      In many known optical interferometers, the reference beam and the measurement beam have linear polarization states that are orthogonal to one another (orthonormal direction vectors). Moreover, the frequency of the orthogonal polarization states is purposefully different. The orthogonality of the polarization states allows for the separation of the light from a light source (e.g., a laser head) into the measurement and reference beams, which traverse different optical paths. The orthogonality of the linear polarization states also allows for the recombining of the reference and measurement beams after traversal of their respective light paths.  
      Once recombined, any differential in phase is measured, normally as a beat frequency. The purposeful differential in the frequency of the beams from the light source provides a baseline beat frequency or differential. Using known signal processing techniques, it is possible to ascertain differentials in measured and reference paths (OPLs) and measure the change in the position of the measurement reflector.  
      As is known, the OPL is dependent on the index of refraction of the medium through which light travels. In order to provide precise displacement measurements in an interferometer measuring system, the entire path of the measurement and reference beams must exist in a medium (e.g., air) that has a substantially stable index of refraction. Because the index of refraction of a medium may vary with temperature, pressure, humidity and the content of the medium, providing a medium having a substantially stable index of refraction can be difficult.  
      There is a need for an interferometer that overcomes at least the shortcomings described above.  
      Defined Terminology  
      As used herein, the term ‘monolithic’ means comprised of more than two parts, which are fastened together to form a single component; or comprised of a unitary part. For example, a monolithic element may have a plurality of parts fastened together; or may be molded from a material(s) with or without elements embedded in the material(s). 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
      The example embodiments are best understood from the following detailed description when read with the accompanying drawing figures. It is emphasized that the various features are not necessarily drawn to scale. In fact, the dimensions may be arbitrarily increased or decreased for clarity of discussion. Wherever applicable and practical, like reference numerals refer to like elements.  
       FIG. 1  is a side view of an interferometer in accordance with an example embodiment.  
       FIG. 2A  is a perspective view of an interferometer in accordance with an example embodiment.  
       FIG. 2B  is another perspective view of the interferometer in accordance with the example embodiment of  FIG. 2A .  
       FIG. 2C  is another perspective view of the interferometer in accordance with the example embodiment of  FIG. 2A .  
       FIG. 2D  is a side view of the interferometer of  FIG. 2B .  
       FIG. 3A  is a perspective view of an interferometer in accordance with an example embodiment.  
       FIG. 3B  is a side view of the interferometer of  FIG. 3A   
       FIG. 4  is a perspective view of an interferometer in accordance with an example embodiment.  
       FIG. 5  is a perspective view of an interferometer in accordance with an example embodiment.  
       FIG. 6  is a perspective view of an interferometer in accordance with an example embodiment.  
       FIG. 7  is a perspective view of an interferometer in accordance with an example embodiment.  
       FIG. 8A  is a perspective view of an interferometer in accordance with an example embodiment.  
       FIG. 8B  is a side view of the interferometer of  FIG. 8A .  
       FIG. 9A  is a perspective view of an interferometer in accordance with an example embodiment.  
       FIG. 9B  is a side view of the interferometer of  FIG. 9A .  
       FIG. 10A  is a perspective view of an interferometer in accordance with an example embodiment.  
       FIG. 10B  is a side view of the interferometer of  FIG. 10A .  
       FIG. 11A  is a perspective view of an interferometer in accordance with an example embodiment.  
       FIG. 11B  is a side view of the interferometer of  FIG. 11A .  
       FIG. 12A  is a perspective view of an interferometer in accordance with an example embodiment.  
       FIG. 12B  is an end view of the interferometer of  FIG. 12A .  
       FIG. 12C  is a side view of the interferometer of  FIG. 12A .  
       FIG. 13  is a perspective view of an interferometer in accordance with an example embodiment.  
       FIG. 14  is a perspective view of an interferometer in accordance with an example embodiment.  
       FIG. 15  is a perspective view of an interferometer in accordance with an example embodiment.  
       FIG. 16  is a perspective view of an interferometer in accordance with an example embodiment.  
       FIG. 17A  is a perspective view of an interferometer in accordance with an example embodiment.  
       FIG. 17B  is a side view of the interferometer of  FIG. 17A . 
    
    
     DETAILED DESCRIPTION  
      In the following detailed description, for purposes of explanation and not limitation, example embodiments disclosing specific details are set forth in order to provide a thorough understanding of embodiments according to the present teachings. However, it will be apparent to one having ordinary skill in the art having had the benefit of the present disclosure that other embodiments according to the present teachings that depart from the specific details disclosed herein remain within the scope of the appended claims. Moreover, descriptions of well-known apparati and methods may be omitted so as to not obscure the description of the example embodiments. Such methods and apparati are clearly within the scope of the present teachings.  
       FIG. 1  is a side view of a measurement system  100  in accordance with an example embodiment. An input beam  101  from a laser (not shown) is incident on an optical element  102  adapted to substantially transmit the beam  101  with minimal reflection. Usefully, the optical element  102  has an antireflective (AR) coating to reduce reflection of the incident light. The input beam  101  is reflected from a surface  103  and is rotated by approximately 90° and in a manner similar to a periscope in order to avoid an obstruction  104  that may be a structural element of the measurement system  100 .  
      The input beam  101  is incident on an interferometer  105 . A portion of the light  101  is output as a measurement beam  106  and is incident on a measurement reflector  107  that is connected to a structure (not shown). As described in detail herein, the light  106  is useful in exacting a measure of any displacement of the structure from a nominal position.  
      In the region  108  between the interferometer  105  and the measurement mirror  107 , the medium is controlled to provide a substantially stable index of refraction. This control of the medium between the interferometer  105  and the measurement substantially eliminates variance in the index of refraction in the region  108 . As can be appreciated, this is useful in preventing variance in the OPL due to factors other than movement of the structure. However, and as noted previously, it can be difficult to control the index of refraction of the medium completely. For example, in the regions near the structure  104  it is difficult to stabilize the index of refraction of the medium. In known measurement systems, this instability can result in measurement errors due to variations in the OPL of the light. By contrast, the interferometer  105  of the example embodiments substantially reduces, if not eliminates the variation in OPL due to variation in the index of refraction of the medium through which the measuring light beams in the region near the structure travel.  
      The function of the measurement system relies on known electronics (not shown) including, but not limited to a laser head, a tuning circuit, photodetectors and optical elements for routing signals into and out of the measurement system. The measurement and reference light beams are then combined and based on the beat frequency of the combined light beam; a measurement of displacement of the structure is made.  
      As described in detail herein, the interferometers of the example embodiments allow all light beams outside the interferometer to exist in a volume that has a substantially stable index of refraction.  
       FIG. 2A  is a perspective view of the interferometer  105  according to an example embodiment. The interferometer  105  includes a monolithic optical element  201  that receives an input light beam  202  from a laser head (not shown). The input light beam  202  traverses an optical element  203  that includes an anti-reflection coating, and is reflected from a first reflective surface  210 . The angle of incidence of light  202  with respect to the surface  210  is illustratively approximately 45°, so that the light  202  is substantially internally reflected and the reflected light is substantially orthogonal to the light  202 . In addition, the reflective surface  210  may include a known coating or layer to improve reflection.  
      The interferometer  105  also includes a polarization beamsplitter (PBS)  204  and a retroreflector  205 . The PBS  204  is substantially parallel to the first reflective surface  210 . Light traversing the monolithic optical element  201  is incident on a second reflective surface  211  oriented so that the light is incident at approximately 45°. With this arrangement, the light incident in the surface  211  is substantially totally internally reflected as light  207 , which is substantially orthogonal to the light incident on the surface  211 . It is contemplated that the orientation of the first and second reflective surfaces  210 ,  211  is other than 45°. However, in specific embodiments the first and second reflective surfaces  210 ,  211  are substantially parallel.  
      The light  207  traverses a retarder  206  that is a quarterwave retarder adapted to retard light  207  having a wavelength in vacuum of λ by nλ+λ/4 (n=integer) upon passing through the retarder  206 . Beneficially, the retarder includes AR coatings on opposite sides so that light incident thereon is substantially transmitted. The light  207  is reflected by the measurement reflector  107  and traverses the retarder  206  a second time and undergoes a relative phase shift of λ/2. Thus, the light  207  undergoes a halfwave (λ/2) polarization transformation. As such, light that emerges from the monolithic optical element  201  linearly polarized along one axis will reenter the element  201  polarized along a second perpendicular axis.  
      Light  208  also traverses the element  206 , is reflected by the measurement reflector  107 , and traverses the element  206  again. Thereby, the light  208  enters the monolithic optical element  201  having a polarization state that is rotated by π/2.  
      The interferometer  105  includes another retarder  209  disposed over the monolithic optical element  201  and specifically above the PBS  204 . Like retarder  206 , retarder  209  a quarterwave retarder is adapted to retard light that traverses its width by (nλ+λ/4). However, unlike the retarder  206 , retarder  209  has a reflective top surface so the light traverses the retarder  209 , is reflected by the top surface and traverses the retarder  209  a second time. Thereby, the light enters the monolithic optical element  201  having a polarization state that is orthogonal to its polarization state upon exiting the monolithic optical element  201 .  
      In accordance with an example embodiment, the monolithic optical element  201  is a rhomboid and may be fabricated in using materials disclosed in and in accordance with the teachings of commonly assigned U.S. Pat. No. 6,542,247 to Bockman. The disclosure of this patent is specifically incorporated herein by reference.  
      In a specific embodiment, the retarders  206 ,  209  are multi-layer dielectric stack retarders or birefringent elements such as quartz, mica or an organic polymer having an OPL that provide a retardance of nλ+λ/4 so a halfwave relative phase shift is realized by a double pass through the retarders. In a specific embodiment, the retarders  206 , 209  are optically contacted to the monolithic optical element; and the retroreflector  205  and the element  203  are secured to the monolithic optical element  201  are adhered using an index matching adhesive material. Accordingly, an optical interface is provided between the retarders  206 ,  209 , the retroreflector  205 , the optical element  203 , and the monolithic optical element  201 . Notably, many optical components in subsequently described example embodiments are optically coupled to the monolithic optical element  201  similarly.  
       FIG. 2B  is a perspective view of the interferometer  105  of an example embodiment. The interferometer  105  is substantially the same as that shown in  FIG. 2A , however with the monolithic optical element  201  faintly drawn to show the function of the various components and the light path.  
      Light  202  is incident on the first surface  210  and is reflected in an orthogonal direction as shown. The light  202  includes two orthogonal linearly polarized light components, each having a specific frequency. Notably, the light components have a frequency difference in the range of approximately 2.0 MHz to approximately 6.0 MHz and an average wavelength of approximately 633 nm. The light  202  may be from a He—Ne laser having a magnetic field applied axially to the laser cavity, which causes Zeeman splitting. Illustratively, the laser may be a component of a laser head such as the 5517 family of laser heads available from Agilent Technologies, Inc., Palo Alto, Calif. USA.  
      Upon reflection from the first surface, the light  202  is incident on the PBS  204 , which transmits light  213  of a first linear polarization state (e.g., p-polarized) and reflects light  214  of a second linear polarization state (e.g., s-polarized). The transmitted light  213  is incident on the second surface  211 , which reflects the light through the retarder  206 . The light  213  emerges as circularly polarized light  207  and is reflected back through the element  206  by the measurement reflector  107 . Thus, the light  213  is transformed into light  213 ′ having an orthogonal polarization state (e.g., s-polarized) to that of light  213 . The light  213 ′ is reflected from the second surface  211  and is incident on the PBS  204 , where it is reflected as light  215  to the retroreflector  205 . The retroreflector  205  reflects and displaces the light  215 . Upon reflection from the retroreflector, light  215  is incident on the PBS  204 , where it is reflected in an orthogonal direction. This light  215  is incident on the second reflective surface  211  and traverses the retarder  206  twice after being reflected by the measurement reflector  107 . Because of the polarization transformation caused by the double pass through the element  206 , the light  215 ′ has a polarization state that is rotated by π/2 compared to light  215 . As such, light  215 ′ has a polarization state (p-polarized following the example) that is transmitted through the PBS  204 . This component of output light  212  is referred to as the measurement path light because it has traversed the (variable) measurement light path.  
      Light  214  is reflected from the PBS  204  and traverses the retarder  209  twice upon reflection. The polarization state of light  214  is rotated by π/2 upon traversing the element  209  twice emerging as light  214 ′. Consistent with the convention of the example, light  214 ′ is now p-polarized and thus traverses the PBS  204 , where it is reflected and displaced by the retroreflector  205 . Light  214 ′ then traverses the PBS  204  and the retarder  209  twice. Upon re-entry into the monolithic optical element  201 , light  214 ′ is transformed to an orthogonal polarization state (e.g., s-polarized). This orthogonally polarized light is reflected by the PBS  204  as light  214  as shown. Because of the polarization transformation provided by the retarder  209 , the light  216  traverses the PBS and is combined with light  215 ′ to form output light  212 . The path of the light  216 ,  214 ′ is substantially constant and is referred to as the reference path.  
       FIG. 2C  is another perspective view of the interferometer  105 . The interferometer is substantially the same as the interferometer shown in  FIGS. 2A and 2B , however oriented in an inverted manner. Common details are not provided so as to avoid obscuring the presently described example embodiment.  
      The interferometer  105  includes the reflective element  205 , which is illustratively a retroreflective element. Characteristically, the light that is incident on the retroreflective element at an angle of incidence (with respect to a normal to the retroreflective element) is reflected from the element at substantially the same angle relative to the normal. In a specific embodiment, the reflective element is a cube corner described in detail in commonly assigned U.S. Pat. No. 6,736,518 to Belt, et al. The disclosure of this patent is specifically incorporated herein by reference. The cube corner not only reflects light at an angle substantially equal to the angle of incidence, but also displaces the light by a finite distance. Accordingly, light  214 ′,  215  are incident at a particular angle (illustratively 0°) and is reflected at substantially the same angle, but is displaced as shown after reflections within the cube corner. It is emphasized that the use of a cube corner is merely illustrative and that other optical components known to those skilled in the art may be used to realize the same result.  
      As defined above, the monolithic optical element  201  may be comprised of more than two parts, which are fastened together to form a single component; or comprised of an indivisible part. The monolithic optical element  201  may be two substantially identical rhomboids having approximately 45° end-faces. As noted, the rhomboids may be fabricated with and according to the teachings of U.S. Pat. No. 6,542,247. The PBS  204  may be a separate component fastened between two of the end faces with an index matching/anti-reflective adhesive; or may be a coating or plurality of known coatings on an end-face of one of the rhomboids. In the latter embodiment, after the coating(s) is applied, the endfaces are bonded using the index matching/anti-reflective adhesive referenced previously. In yet another embodiment, the monolithic optical element  201  is molded with the PBS  204  embedded in the molded piece.  
       FIG. 2D  is a side-view of the interferometer  105  shown in  FIGS. 2A and 2B . Common details are not provided so as to avoid obscuring the present description. The interferometer  105  provides a measurement path and a reference path. The measurement path includes the OPL from the PBS  204  up to the measurement reflector  107 . Thus, the measurement path includes the OPL from the PBS  204  and through a second portion  217  of the element  201 . Additionally, the measurement path includes the OPL from the second surface  211  through the retarder  206 , and the OPL through the medium between the retarder  206  and the measurement reflector  107 . Finally, the measurement path includes the traversal through the reflective element  205 . Notably, each ‘leg’ of the measurement path is traversed four (4) times.  
      The reference path includes the OPL from the PBS  204  through the monolithic optical element  201  and through the retarder  209 . Thus, the reference path also includes the OPL through a first portion  217  to the reflective element  205  and the OPL through the reflective element  205 . Notably, each ‘leg’ of the reference path is also traversed four (4) times.  
      As is known, the measurement path and the reference path are the same or a known multiple/difference of one another within accepted limits of accuracy. Any difference in the reference and measurement paths results in a change in the beat frequency of the output beam  212  comprised of light components  216 ,  215 ′. As such, movement of the measurement reflector  107  indicates movement of the structure to which the reflector  107  of the measurement system  100  is attached. The magnitude of the movement is directly proportional to the difference in the beat frequency and can be quantified by relatively straight-forward calculations using a microprocessor (not shown) of the system  100 .  
      As noted previously, if there is significant variation in the indices of refraction of the various components through which the measurement beam, or the reference beam, or both, travel a variation in the OPL of the measurement path, or the reference path, or both will occur. Ultimately, this reduces the accuracy of the measurements exacted by the interferometer. However, the index of refraction of the monolithic optical element  201  of the example embodiments is substantially immune to variations due to ambient factors, rendering the index of refraction of the monolithic optical element substantially stable. Thus, inaccuracies in measurements from changes in the index of refraction due to an uncontrolled medium are substantially avoided. It is noted that rather slight variations in the OPL of the measurement and reference paths of the interferometer  105  may result from temperature variations. These variations can be used to compensate for other thermally induced measurement errors in the measurement system.  
       FIG. 3A  is a perspective view of an interferometer  301  in accordance with an example embodiment. The interferometer  301  includes many features described in connection with the embodiments of  FIGS. 1A-2D  and may be used in the measurement system  100 . Accordingly, common features are not described in detail to avoid obscuring the presently described embodiments.  
      The interferometer  301  includes the monolithic optical element  201  having the PBS  204  described previously. Light  202  is incident on the first surface  210  and is reflected toward the PBS  204 . The PBS  204  reflects light of one linear polarization state and transmits light of the orthogonal polarization state. Reflected light  302  traverses the retarder  209  and is reflected by the measurement reflector  107 . The light reflected from the measurement reflector  107  traverses the retarder  209  a second time and emerges therefrom as light  302 ′ having an orthogonal linear polarization state to light  302 . Because of the polarization transformation, the light  302 ′ traverses the PBS  204  and is incident on the reflective element  205 . The reflective element  205  reflects the light  302 ′ in a manner described previously, and the light  302 ′ emerges displaced. The light  302 ′ then traverses the PBS  204  and the retarder  206  twice after reflection from the measurement reflector  107 . Upon entering the monolithic optical element  301  from the retarder  206 , the polarization of light  302 ′ is again rotated and emerges as light  305  having a linear state of polarization that is orthogonal to that of light  302 ′. Accordingly, the light  302  is reflected by the PBS  204  and comprises one component of the output light  212 . Thus, the measurement path includes the OPL just described.  
      The component of the light  202  having a linear polarization state that is orthogonal to that of light  302  is transmitted by the PBS  204  and emerges as light  303 . Light  303  is reflected by the second surface  211  and traverses the retarder  206  twice, having been reflected by a reflective element (e.g., a highly reflective (HR) coating) on the top surface of the retarder  206 . As such, the polarization of light  303 ′ is orthogonal to that of light  303 . Light  303 ′ is then reflected by the PBS  204  to the reflective element  205 , where it undergoes reflections and a translation as described. The light  303 ′ is again reflected by the PBS  204  and is incident on the second surface  211  where it is reflected to the retarder  206 . Upon traversing the retarder  206  twice, the linear polarization vector is again rotated by π/2 (or nπ/2) and is reflected by the second surface  211  as light  305 . Light  303  is transmitted by the PBS  204  and comprises the second component of the output light  212 . As described previously, any movement of the measurement reflector is indicated by a change in the beat frequency of the components  304 ,  305 .  
       FIG. 3B  is a side view of the interferometer  301 . The measurement path and the reference path are essentially the same as the reference path and measurement path, respectively, described in connection with  FIG. 2D . Accordingly, the description is not repeated in the interest of clarity. However, it is noted that like the interferometer  105  described previously, the interferometer  301  is substantially not susceptible to variations in OPL of either the measurement path or the reference path caused by variations in the index of refraction due to unconditioned air.  
       FIG. 4  is a perspective view of an interferometer  401  in accordance with an example embodiment. The interferometer  401  has many common features with the interferometer described in connection with the example embodiments of  FIGS. 2A-2D . Accordingly, such details are not repeated so as to avoid obscuring the presently described embodiment. The interferometer  401  receives input light  202  comprising two frequency components having orthogonal states of linearly polarized light; and emits output light  212  comprising two frequency components having orthogonal states of linearly polarized light. As noted previously, variations in the beat frequency are used to exact a measure of the displacement of a measurement reflector.  
      In the example embodiment, the measurement reflector comprises a first retroreflective element  402 , and a second retroreflective element  403 . The retroreflective elements  402 , 403  are adapted to receive light at a particular angle of incidence and reflect the light at substantially the same angle of incidence with substantially no on-axis translation. The first and second retroreflective elements  402 ,  403  thus comprise the measurement reflector  107  of the interferometer.  
       FIG. 5  is a perspective view of an interferometer  501  in accordance with an example embodiment. The interferometer  501  has many common features with the interferometer described in connection with the example embodiments of  FIGS. 2A-2D  and  4 . Accordingly, such details are not repeated so as to avoid obscuring the presently described embodiment. The interferometer  501  receives input light  202  comprising two frequency components having orthogonal states of linearly polarized light; and emits output light  212  comprising two frequency components having orthogonal states of linearly polarized light. As noted previously, variations in the beat frequency are used to exact a measure of the displacement of a measurement reflector.  
      In the example embodiment, the measurement reflector comprises a retroreflective element  502 . The retroreflective element  502  is adapted to receive light at a particular angle of incidence and reflect the light at substantially the same angle of incidence with a set translation. The retroreflective elements  502  thus comprise the measurement reflector  107  of the interferometer.  
       FIG. 6  is a perspective view of a differential interferometer  601  in accordance with an example embodiment. Notably, by separating the reference reflective element(s) from the monolithic optical element  201  of the example embodiments, the interferometer is made into a differential interferometer.  
      The interferometer  601  has many common features with the interferometers described in connection with the example embodiments of  FIGS. 2A-2D ,  4  and  5 . Accordingly, such details are not repeated so as to avoid obscuring the presently described embodiment. The interferometer  601  receives input light  202  comprising two frequency components having orthogonal states of linearly polarized light; and emits output light  212  comprising two frequency components having orthogonal states of linearly polarized light. As noted previously, variations in the beat frequency are used to exact a measure of the displacement of a measurement reflector.  
      In the example embodiment, the measurement reflector comprises the first retroreflective element  402 , and the second retroreflective element  403 . The retroreflective elements are adapted to receive light at a particular angle of incident and reflect the light at substantially the same angle of incidence. The first and second retroreflective elements  402 ,  403  thus comprise the measurement reflector  107  of the interferometer.  
      The interferometer  601  also comprises a third retroreflective element  602  and a fourth retroreflective element  603 . As can be appreciated, in a differential interferometer, the difference in OPLs of two defined paths is measured. One OPL can be the reference path and the other the measurement. Of course, because a relative measure is provided, it is not necessary that either of OPL be fixed. To this end, the retroreflective elements  402 , 403  and  602 ,  603  may be attached to objects that are subject to displacement. Thus, both OPLs are measurement paths. In the interest of consistency of terminology, in the differential interferometers described herein, one path is considered the measurement path and the other is the reference path, even though the reference path is not necessarily fixed. In a specific embodiment, the retroreflective elements  602 ,  603  are in the reference path and are substantially the same as the first and second retroreflective elements  402 , 403 . In another specific embodiment, the first and second retroreflective elements  402 ,  403  are in the reference path and the third and fourth retroreflective elements  602 , 603  are in the measurement path of the interferometer.  
       FIG. 7  shows a differential interferometer  701  in accordance with an example embodiment. The interferometer  701  has many common features with the interferometer described in connection with the example embodiments of  FIGS. 2A-2D ,  5  and  6 . Accordingly, such details are not repeated so as to avoid obscuring the presently described embodiment. The interferometer  701  receives input light  202  comprising two frequency components having orthogonal states of linearly polarized light; and emits output light  212  comprising two frequency components having orthogonal states of linearly polarized light. As noted previously, variations in the beat frequency are used to exact a measure of the displacement of a measurement reflector.  
      In the example embodiment, the measurement reflector comprises the retroreflective element  502 . The retroreflective element  502  is adapted to receive light at a particular angle of incident and reflect the light at substantially the same angle of incidence. The retroreflective element  502  thus comprises the measurement reflector  107  of the interferometer.  
      The interferometer  701  also comprises another retroreflective element  702 . In a specific embodiment, the retroreflective element  702  is in the reference path and is substantially the same as the retroreflective element  502 . In another specific embodiment, the retroreflective element  502  is in the reference path and the retroreflective element  702  is in the measurement path of the interferometer.  
       FIG. 8A  is a perspective view of an interferometer  801  in accordance with an example embodiment. The interferometer  801  has many common features with the interferometer described in connection with the example embodiments of  FIGS. 2A-2D . Accordingly, such details are not repeated so as to avoid obscuring the presently described embodiment. The interferometer  801  receives input light  202  comprising two frequency components having orthogonal states of linearly polarized light; and emits output light  212  comprising two frequency components having orthogonal states of linearly polarized light. As noted previously, variations in the beat frequency are used to exact a measure of the displacement of a measurement reflector.  
      The interferometer  801  includes a monolithic optical element  802  having the reflective surface  211 . The monolithic optical element  802  includes a rhomboid with the PBS  204  oriented as described previously. The monolithic optical element  802  also includes a prism  803  that is optically contacted to or adhered to the PBS  204 . Thus, the monolithic optical element  802  includes a rhomboid and a prism. The monolithic optical element  802  is illustrative of the diversity of the applications of the interferometers of the example embodiments. In particular, it may not be necessary for the monolithic optical element to extend as far in certain applications as in others. As such, the interferometer  801  may be implemented with a smaller monolithic optical element.  
       FIG. 8B  is a side view of the interferometer  801 . The measurement path length includes the OPL from the PBS  204  to the measurement reflector  107 , including the OPL through the retroreflector  205 . Notably, in the present embodiment, the polarization component of the input light beam  202  that is reflected by the PBS  204  (e.g., s-polarized light) is reflected into the measurement path. The reference path includes the OPL from the PBS  204  to the reflecting retarder  209 , including the OPL through the retroreflector  205 . In the present embodiment, the polarization component of the input light beam  202  that is transmitted by the PBS  204  (e.g., p-polarized light) is transmitted into the reference path.  
       FIG. 9A  is a perspective view of an interferometer  901  in accordance with an example embodiment. The interferometer  901  has many common features with the interferometer described in connection with the example embodiments of  FIGS. 2A-2D  and  8 A- 8 B. Accordingly, such details are not repeated so as to avoid obscuring the presently described embodiment. The interferometer  901  receives input light  202  comprising two frequency components having orthogonal states of linearly polarized light; and emits output light  212  comprising two frequency components having orthogonal states of linearly polarized light. As noted previously, variations in the beat frequency are used to exact a measure of the displacement of a measurement reflector.  
      The interferometer includes the monolithic optical element  802  described previously. The monolithic optical element  802  is illustrative of the diversity of the applications of the interferometers of the example embodiments. In particular, it may not be necessary for the monolithic optical element to extend as far in certain applications as in others. As such, the interferometer may be implemented with a smaller monolithic optical element.  
       FIG. 9B  is a side view of the interferometer  801 . The measurement path includes the OPL from the PBS  204  to the measurement reflector  107  and the OPL through the retroreflector  205 . Notably, in the present embodiment, the polarization component of the input light beam  202  that is reflected by the PBS  204  (e.g., s-polarized light) is reflected into the reference path. The reference path includes the OPL from the PBS  204  to the reflecting retarder  209 , and the OPL through the retroreflector  205 . In the present embodiment, the polarization component of the input light beam  202  that is transmitted by the PBS  204  (e.g., p-polarized light) is transmitted into the measurement path.  
      Finally, in specific embodiments, many of the retroreflective elements described in connection with  FIGS. 4-7  may be included as the reflective elements (e.g., the measurement reflector  107 ) in the example embodiments of  FIGS. 8   a - 9 B.  
       FIG. 10A  is a perspective view of a differential interferometer  1001  in accordance with an example embodiment. The interferometer  1001  has many common features with the interferometer described in connection with the example embodiments of  FIGS. 2A-2D  and  8 A- 9 B. Accordingly, such details are not repeated so as to avoid obscuring the presently described embodiment. The interferometer  1001  receives input light  202  comprising two frequency components having orthogonal states of linearly polarized light; and emits output light  212  comprising two frequency components having orthogonal states of linearly polarized light. As noted previously, variations in the beat frequency are used to exact a measure of the displacement of a measurement reflector.  
      The interferometer  1001  includes side plates  1002  and a reflective element  1003  that are adhered to the monolithic optical element  802 . As such, a monolithic optical element is comprised of all components of the interferometer  1001  with exception of a reflective element  1004  and reflective element  107 . The reflective element  1003  is oriented substantially parallel to the first reflective surface  210  so that the light reflected to and from the measurement reflector  107  is substantially reflected. The side plates  1002  may be made of a material having a coefficient of thermal expansion (CFE) on the order of approximately 0.0. Thus, the plates  1002  do not appreciably expand during ambient temperature increases or contract during ambient temperature decreases. Accordingly, the interferometer  1001  is substantially immune to changes in the OPL of either the measurement path or the reference path due to ambient temperature changes.  
      As shown in  FIG. 10B , the measurement path includes the OPL from the PBS  204  to the measurement reflective element  107  and the OPL through the retroreflective element  205 . The reference path includes the OPL from the PBS  204  to the reference reflective element  1004  and the OPL through the retroreflective element  205 .  
       FIG. 11A  is a perspective view of a differential interferometer  1101  in accordance with an example embodiment. The interferometer  1000  has many common features with the interferometer described in connection with the example embodiments of  FIGS. 2A-2D  and  8 A- 10 B. Accordingly, such details are not repeated so as to avoid obscuring the presently described embodiment. The interferometer  1101  receives input light  202  comprising two frequency components having orthogonal states of linearly polarized light; and emits output light  212  comprising two frequency components having orthogonal states of linearly polarized light. As noted previously, variations in the beat frequency are used to exact a measure of the displacement of a measurement reflector.  
      As shown in  FIG. 11B , the measurement path includes the OPL from the PBS  204  to the measurement reflective element  107  and the OPL through the retroreflective element  205 . The reference path includes the OPL from the PBS  204  to the reference reflective element  1004  and the OPL through the retroreflective element  205 .  
       FIGS. 12A, 12B  and  12 C are a perspective view, an end view and a side view, respectively, of a multi-axis interferometer  1201  in accordance with an example embodiment. The description of the present embodiment is best understood through a concurrent review of  FIGS. 12A-12C .  
      The multi-axis interferometer  1201  receives input light  1202  comprising two frequency components having orthogonal states of linearly polarized light. The light  1202  is incident on a monolithic optical element comprising a rhomboid  1203  and a prism  1204 . The light  1202  is incident on a reflective surface  1205  of the rhomboid  1203  and approximately 50% of the light  1202  is reflected and approximately 50% of the light  1202  is transmitted at the interface. A reflected portion  1206  of the light is substantially totally internally reflected at surface  1207  and is reflected into the monolithic optical element  1208 . The monolithic optical element  1208  is similar to certain monolithic optical elements described previously. The light  1206  is substantially totally internally reflected at surface  1209  and is incident on a PBS  1210 . The PBS  1210  reflects one of the polarization components (p-polarized light), which is light  1211 . Light  1211  is incident on the retarder  209 . Light  1211  is in the reference path as previously described, is reflected by the retarder  209  and is incident again on the PBS  1210  in an orthogonal polarization state. This light is incident on the retroreflective element  205  and is translated. As described previously, this light is combined with light from the measurement path, which is emitted as output light  1218 . The other polarization component of light  1206  is transmitted by the PBS  1210  as light  1212 . Light  1212  is incident on a surface  1213  and is substantially totally internally reflected to the retarder  206 . This light is then is reflected by the measurement reflective element  1214  back through the retarder  206  and emerges as light  1216 . Light  1216  is reflected at the surface  1213  to the PBS  1210 , where it is reflected to the retroreflector  205  and is translated. The light  1216  from the measurement path is combined with the light  1211  from the reference path as noted above.  
      Light  1217  is transmitted at the surface of the rhomboid  1203  and is reflected at surface  1209 . Light  1217  also includes orthogonal linear states of polarization. The light  1217  forms the input light and provides the reference light and measurement light in the same manner described above in connection with light  1203 . The measurement and reference light beams are combined and emerge as light  1215 .  
      The multi-axis interferometer  1201  is useful in determining any angular displacement of a measured structure. For example, if the measurement reflective element  1214  were a single element attached to a structure under measure and the reflective element  1214  were to rotate (e.g., rotate in the plane of  FIG. 12B ), the measurement path length for light  1206  would be different than the measurement path length for light  1217 . This differential can readily be computed and an angular rotation determined.  
       FIG. 13  is a perspective view of a differential interferometer  1301  in accordance with an example embodiment. The interferometer  1301  has many common features with the interferometers described in connection with the example embodiments of  FIGS. 2A-2D  and  8 A- 9 B. Accordingly, such details are not repeated so as to avoid obscuring the presently described embodiment. The interferometer  1301  receives input light  1302  and input light  1303 , each comprising two frequency components having orthogonal states of linearly polarized light. The interferometer  1301  emits output light  212  comprising two frequency components having orthogonal states of linearly polarized light. As noted previously, variations in the beat frequency are used to exact a measure of the displacement of a measurement reflector.  
      The interferometer  1301  differs from certain embodiments described previously as a single path is provided for each input light beam. In particular, light  1302  is incident on the first reflective surface  210  and is reflected to the PBS  204 . The light  1302  is separated into orthogonal linear polarization states  1304 ,  1305 . Light  1304  is reflected into a retroreflective element  1306  and is reflected back onto the PBS with substantially no angular deviation from the angle of incidence on the element  1306 . The light  1305  of the orthogonal linear polarization state is transmitted at the PBS  204  and is reflected by the second reflective surface  211  to another retroreflective element  1307 . The light  1305  is reflected at element  1307  at substantially the same angle of incidence and is transmitted through the PBS  204 . The components  1304  and  1305  are combined to provide a differential in the path lengths traversed.  
      Light  1303  is similarly separated into orthogonal linear states of polarization by the PBS  204 . The details are not repeated so as to avoid obscuring the description of the embodiment.  
      The differential in OPLs traveled by the states of polarization (e.g., light  1304 ,  1305 ) provides a measure of displacement of objects to which retroreflective elements  1306  and  1307  are attached.  
       FIG. 14  is a perspective view of an interferometer  1401  in accordance with an example embodiment. The interferometer of the present embodiment is substantially the same as that of the example embodiment of  FIG. 13 . However, the retroreflective element  1306  is disposed over the monolithic optical element  201  as shown. The light paths to the element  1306  form the reference paths and the light paths to the element  1307  form the measurement paths.  
       FIGS. 15 and 16  are perspective views of a differential interferometer  1501  and an interferometer  1601 , respectively, in accordance with an example embodiment. Light  1502  having orthogonal polarization states is incident on the monolithic optical element  201  as shown. The light  1502  is separated into linear polarization components at the PBS  204 , with light  1503  being reflected and light  1504  being transmitted. The light  1503  traverses the retarder  209  and is reflected by a retroreflective element  1505 . After traversing the retarder  209  the polarization state of light  1507  is orthogonal to that of light  1503 , and light  1507  is transmitted by the PBS  204 . Light  1504  is reflected at surface  211 , traverses the retarder  209  and is reflected by a retroreflective element  1506 . Light  1509  emerges from the retarder  209  and is reflected by the PBS  204 . Light  1509  is combined with light  1507  to form output light  1510  which is used to exact measurements of the difference in the OPL of each component.  
      The interferometer  1601  is substantially the same as the interferometer  1501 . However, the retroreflective element  1505  is disposed over the monolithic optical element  201  as shown. The light path to the element  1505  forms the reference path and the light path to the element  1506  forms the measurement path.  
       FIGS. 17A and 17B  are perspective and side views, respectively, of an interferometer  1701  in accordance with an example embodiment. The interferometer  1701  has many common features with the interferometers described in connection with the example embodiments of  FIGS. 2A-2D  and  8 A- 8 B. Accordingly, such details are not repeated so as to avoid obscuring the presently described embodiment. The interferometer  1701  receives input light  1702  comprising two frequency components having orthogonal states of linearly polarized light; and emits output light  1711  comprising two frequency components having orthogonal states of linearly polarized light. As noted previously, variations in the beat frequency are used to exact a measure of the displacement of a measurement reflector.  
      Light  1702  is separated into orthogonal linear polarization states by the PBS  204  disposed between rhomboid  1703  and a prism  1704 . The light  1705  is reflected and traverses the retarder  209 , and is reflected by a retroreflector  1706 . After traversing the retarder again, light  1707  is transmitted by the PBS  204 . Light  1708  is transmitted by the PBS  204  and traverses the retarder  206  and is reflected by a retroreflector  1709 . Light  1710  emerges from the retarder  209  and is reflected by the PBS  204 . Light  1707  and light  1710  are combined to form an output beam  1711 . As can be appreciated, the measurement path includes the OPL of light  1705  and light  1707 ; and the reference path includes the OPL of light  1708  and light  1710 .  
      In accordance with illustrative embodiments described, an interferometer is useful in measurement systems. One of ordinary skill in the art appreciates that many variations that are in accordance with the present teachings are possible and remain within the scope of the appended claims. These and other variations would become clear to one of ordinary skill in the art after inspection of the specification, drawings and claims herein. The invention therefore is not to be restricted except within the spirit and scope of the appended claims.