Abstract:
According to one aspect, a part has two reflective surfaces, one being a conic surface portion having an axis with a focus thereon, and the other being part of a spherical surface with a centerpoint at the focus. According to a different aspect, a method includes fabricating a part with first and second reflective surfaces, the first being a conic surface portion with an axis and a focus on the axis, and the second being a spherical surface portion with a centerpoint at the focus. The second surface is used to position the part so that the focus coincides with the centerpoint of a spherical wave from an interferometer. Then, a reflective further spherical surface portion on a member is used with the interferometer to position a centerpoint of the further surface at the focus. The interferometer then evaluates the first surface for accuracy.

Description:
FIELD OF THE INVENTION 
   This invention relates in general to techniques for testing optical surfaces and, more particularly, to techniques for testing conic optical surfaces. 
   BACKGROUND 
   In the optical arts, it is often necessary to fabricate an optical component with a reflective optical surface. For example, a workpiece of optical material is mounted in a machine tool, and the tool is then used to carry out a diamond point turning operation that forms an optical surface on the workpiece. For some applications, the reflective optical surface is a conic surface, such as an ellipsoid, or paraboloid of revolution. 
   After the optical surface has been created, it is usually tested for accuracy, for example by using an interferometer. For test purposes, the optical surface needs to be mechanically aligned very accurately with respect to the interferometer. This is usually achieved by making a very precise test jig or fixture that mates with some mechanical feature on the workpiece. However, these test jigs or fixtures are relatively expensive, and can suffer from a build up of tolerances. Consequently, although pre-existing testing techniques and devices have been generally adequate for their intended purposes, they have not been satisfactory in all respects. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     A better understanding of the present invention will be realized from the detailed description that follows, taken in conjunction with the accompanying drawings, in which: 
       FIG. 1  is diagrammatic sectional side view of an apparatus that is an optical workpiece, and that embodies aspects of the present invention. 
       FIG. 2  is a diagrammatic side view of a test apparatus that has the workpiece of  FIG. 1  removably mounted thereon, and that includes an interferometer,  FIG. 2  showing a first operation in an operational sequence for positioning and testing the workpiece, and showing the workpiece in section for clarity. 
       FIG. 3  is a diagrammatic view similar to  FIG. 2 , but showing the next operation in the sequence. 
       FIG. 4  is a diagrammatic view similar to  FIGS. 2 and 3 , but also showing additional structure of the test apparatus, and the next operation in the sequence. 
       FIG. 5  is a diagrammatic view similar to  FIG. 4 , but showing two remaining operations of the sequence. 
       FIG. 6  is a diagrammatic sectional side view of a workpiece that is an alternative embodiment of the workpiece of  FIG. 1 . 
       FIG. 7  is a diagrammatic side view similar to  FIG. 2 , except that the test apparatus supports the workpiece of  FIG. 6  rather than the workpiece of  FIG. 1 , and  FIG. 7  shows a first operation in an operational sequence for positioning and testing the illustrated workpiece, the workpiece being shown in section for clarity. 
       FIG. 8  is a diagrammatic view similar to  FIG. 7 , but showing the next operation in the sequence. 
       FIG. 9  is a diagrammatic view similar to  FIGS. 7 and 8 , but also showing the additional structure of the test apparatus, and showing the next operation in the sequence. 
       FIG. 10  is a diagrammatic view similar to  FIG. 9 , but showing the next operation in the sequence. 
       FIG. 11  is a diagrammatic sectional side view of a workpiece that is a further alternative embodiment of the workpieces shown in  FIGS. 1 and 6 . 
   

   DETAILED DESCRIPTION 
     FIG. 1  is diagrammatic sectional side view of an apparatus that is an optical workpiece  10 , and that embodies aspects of the present invention. In the disclosed embodiment, the workpiece  10  is a block of aluminum, but it could alternatively be made of any other suitable material. The workpiece  10  has a reflective optical surface  12  formed thereon. The surface  12  is a conic surface and, in the disclosed embodiment, is a paraboloid of revolution. In other words, the surface  12  has a shape that is swept out in space when a parabola is rotated about an axis  14 , where the parabola has a focus  16  and a vertex  17  that both lie on the axis  14 . 
   The workpiece  10  also has a further reflective optical surface  21  formed thereon. The surface  21  is annular, encircles the surface  12 , and is a portion of a spherical surface that has its centerpoint coincident with the focus  16  of the surface  12 . The surface  21  is used as a reference surface, in a manner explained later. 
   The workpiece  10  has a further reflective optical surface  26  formed thereon. The surface  26  is annular, encircles the surfaces  12  and  21 , and is a portion of a planar surface that extends perpendicular to the axis  14 . The surface  26  is used as a reference surface, in a manner explained later. The workpiece  10  has a radially outwardly facing cylindrical side surface  31 . 
   In order to fabricate the illustrated workpiece  10 , the workpiece  10  would typically be mounted in a not-illustrated machine tool such as lathe. The surface  31  can be used for accurate mechanical positioning of the workpiece  10  within the machine tool. Then, the machine tool would be used to machine all of the reflective optical surfaces  12 ,  21  and  26  on the workpiece  10 , while the workpiece remained securely mounted in the lathe. In the disclosed embodiment, the optical surfaces  12 ,  21  and  26  are all formed by diamond point turning, but it would alternatively be possible to form them in any other suitable manner. Moreover, although it is contemplated that a lathe or other machine tool would be used to form these optical surfaces, it would alternatively be possible to form them in any other suitable manner. 
   After the optical surfaces  12 ,  21  and  26  have been formed on the workpiece  10 , it is desirable to test the accuracy of the conic optical surface  12 . In this regard,  FIG. 2  is a diagrammatic side view of a test apparatus  41  having the workpiece  10  removably mounted thereon, the workpiece  10  being shown in section for clarity. The test apparatus  41  includes a base  46 , and a interferometer  48  that is stationarily supported on the base  46 . The interferometer  48  is a conventional type of device that is very well known to persons skilled in the art, and is therefore not shown and described in detail here. For the purpose of this discussion, it is sufficient to point out that the interferometer has an axis  49 , and can selectively output either a flat wave that travels parallel to the axis  49 , or a spherical wave that converges to a centerpoint located on the axis  49 . If reflections from either type of wave arrive back at the interferometer  48 , the interferometer  48  can analyze those reflections in a known manner. 
   The test apparatus  41  has a stage that includes both a member  51 , and a 5-axis support mechanism  53  that supports the member  51  for movement with respect to the base  46 . More specifically, the mechanism  53  supports the member  51  for linear movement parallel to any of three orthogonal axes of a Cartesian coordinate system, for rotational movement about a roughly vertical axis, and for tilting movement about a roughly horizontal axis. The workpiece  10  is fixedly and removably mounted on the member  51 , with the optical surfaces  12 ,  21  and  26  facing toward the interferometer  48 . 
   In order to test the optical surface  12  with the interferometer  48 , the workpiece  10  first needs to be accurately positioned with respect to the interferometer  48 . This positioning is achieved with a sequence of operations that is discussed below. First, with reference to  FIG. 2 , the interferometer  48  is set to output a flat wave in a direction parallel to its axis  49 , as indicated diagrammatically by broken-line arrows  61  and  62  in  FIG. 2 . The annular planar reference surface  26  on the workpiece  10  reflects a portion of this flat wave back toward the interferometer  48 , and the interferometer analyzes the reflection in a known manner in order to determine information such as the orientation of the surface that reflected the wave. While monitoring the results of the analysis being performed by the interferometer, the mechanism  53  is used to adjust the workpiece  10  in relation to the interferometer  48 , until the interferometer indicates that the reflections from surface  26  are traveling perpendicular to the axis  49  of the interferometer  48 . At this point, the axis  14  of the workpiece  10  will be parallel to the axis  49  of the interferometer  48 . This does not necessarily mean that the axis  14  is coaxial with the axis  49 , as there may possibly be some radial offset between these two parallel axes. 
     FIG. 3  is a diagrammatic view similar to  FIG. 2 , but showing the next operation in the positioning sequence. In this operation, the interferometer  48  is set to generate a spherical wave rather than a flat wave, as indicated diagrammatically by broken-line arrows  71  and  72  in  FIG. 3 . The annular spherical reference surface  21  reflects a portion of this spherical wave. The interferometer  48  is used to monitor the reflections from the reference surface  21 . While monitoring the results of the analysis being performed by the interferometer, the mechanism  53  is used to adjust the workpiece  10  in relation to the interferometer  48 , in directions parallel to one or more of the axes of the Cartesian coordinate system, until each ray of radiation arriving at the surface  21  is reflected back along exactly the same path of travel by which it arrived at the surface  21 . When this state is achieved, the centerpoint of the spherical wave (where the arrows  71  and  72  intersect) will be exactly coincident with the centerpoint  16  of the spherical reference surface  21 , which as discussed above is also the focus of the parabolic surface  12 . 
     FIG. 4  is a diagrammatic view similar to  FIGS. 2 and 3 , but also showing an additional structural component of the test apparatus  41 . In particular, the test apparatus  41  has a stage that includes both a member  81 , and a 3-axis support mechanism  82  that supports the member  81  for movement relative to the member  51 . The mechanism  82  supports the member  81  for linear movement parallel to any of three axes of a Cartesian coordinate system. A reflective spherical ball  84  is fixedly mounted to the member  81 , at an outer end of the member remote from the support mechanism  82 . The reflective spherical ball  84  is commonly called a “retro” ball. 
   With reference to  FIG. 4 , in the next operation of the test sequence, the mechanism  53  maintains the workpiece  10  in the position that was obtained during the operation discussed above in association with  FIG. 3 . The interferometer  48  still generates the spherical wave, as represented diagrammatically by the broken-line arrows  71  and  72 . The mechanism  82  is used to move the retro ball  84  until every ray of the interferometer&#39;s spherical wave impinges on the outer surface of the retro ball  84  exactly perpendicular to that surface. Consequently, in that position of the retro ball, every ray of the spherical wave impinging on the surface of the retro ball be reflected back along exactly the same path of travel by which it arrived at the retro ball  84 . When the interferometer  48  detects that this condition has been achieved, the centerpoint of the retro ball  84  will be precisely coincident with the centerpoint of the spherical wave and with the focus  16  of the parabolic surface  12 . 
     FIG. 5  is a diagrammatic view similar to  FIG. 4 , but showing two remaining operations of the test sequence. In  FIG. 5 , the interferometer  48  is again set to produce a flat wave, as indicated diagrammatically by the broken-line arrows  61 ,  62 ,  91 ,  92 ,  93  and  94 . Initially, the interferometer  48  is used to monitor portions of this flat wave that are reflected by the annular planar reference surface  26  on the workpiece  10 , in essentially the same manner discussed above in association with  FIG. 2 . It may be found that the planar reference surface  26  is still perpendicular to the axis  49  of the interferometer  48 . But if not, the mechanism  53  is used to tilt the workpiece  10  as well as the retro ball  84  until the planar surface  26  is again perpendicular to the axis  49 . The mechanism  82  keeps the retro ball  84  stationary in relation to the workpiece  10 , or in other words keeps the centerpoint of the retro ball at the focus  16  of the surface  12 . 
   As the workpiece  10  is tilted to cause the planar reference surface  26  to become perpendicular to the axis  49 , the focus  16  may move radially away from the axis  49  of the interferometer  48 . However, since the interferometer  48  is generating a flat wave at this point, it is not necessary that the axis  49  extend through the focus  16 . It is only necessary that the axis  14  of the workpiece  10  be parallel to, but not necessarily coaxial with, the axis  49  of the interferometer  48 . 
   Then, when it is clear that the axes  14  and  49  are parallel, the attention of the interferometer  48  is shifted from portions  61  and  62  of the flat wave that are being reflected by the planar reference surface  26  to other portions  91 - 94  of the flat wave that are being reflected by the parabolic surface  12 . By definition, when a ray of radiation is traveling parallel to the axis of a parabolic surface, and is reflected by any point on the parabolic surface, the radiation will then travel directly toward the focus of that parabolic surface. Consequently, if the parabolic surface  12  has been accurately machined, each of the rays  91 - 94  will be reflected by the surface  12  and will travel directly toward the focus  16 . Consequently, each ray will then impinge on the surface of the retro ball  84  exactly perpendicular thereto, and will be reflected to travel back to the interferometer  48  along exactly the same path of travel by which it arrived at the interferometer  48 . 
   If the interferometer  48  finds that each of the rays  91 - 94  is returning to exactly the same point from which it originated, then it can be concluded that the surface  12  has been accurately machined. On the other hand, if the interferometer  48  determines that some rays are arriving back at points different from where they originated, then it means that the surface  12  was not accurately machined, and has an aberration. The error measured by the interferometer will, of course, be twice the actual error, because the radiation from the interferometer will have been reflected twice by the surface region having the aberration. In particular, the surface region with the aberration will reflect the radiation once as the radiation travels from the interferometer  48  to the retro ball  84 , and will then reflect it again as the radiation travels from the retro ball back to the interferometer). 
     FIG. 6  is a diagrammatic sectional side view of a workpiece  110  that is an alternative embodiment of the workpiece  10  of  FIG. 1 . The workpiece  110  has a reflective optical surface  112  that, like the surface  12 , is a conic surface. However, the surface  112  is an ellipsoid, rather than a paraboloid of revolution. In other words, the surface  112  has a shape that is defined in space when an ellipse is rotated about its major axis  14 . By definition, an ellipse has two spaced foci that each lie on the major axis. In  FIG. 6 , one focus is shown at  116 , and the other at  118 . 
   The workpiece  110  has an annular reflective optical surface  121  that encircles the surface  112 , and that serves as a reference surface in a manner explained later. The surface  121  is a portion of a spherical surface having its centerpoint coincident with the focus  116  of the surface  112 . The workpiece  10  also has a further annular reflective optical surface  123  that encircles the surfaces  112  and  121 , and that serves as a reference surface, in a manner explained later. The surface  123  is a portion of a spherical surface having its centerpoint coincident with the focus  118  of the surface  112 . 
   The workpiece  110  has an annular reflective planar surface  126  that encircles the surfaces  112 ,  121  and  123 , that is normal to the axis  14 , and that serves as a reference surface in a manner explained later. The workpiece  110  also has a radially outwardly facing cylindrical side surface  131 . 
   In the disclosed embodiment, the workpiece  110  is made from a block of aluminum, and the surfaces  112 ,  121 ,  123  and  126  are machined thereon by diamond point turning while the workpiece  110  remains mounted in a machine tool. Alternatively, however, the workpiece  110  can be made of any other suitable material, and could be fabricated in any other suitable manner. After the workpiece  110  has been fabricated, it is desirable to test the ellipsoid surface  112  for accuracy. In the disclosed embodiment, this is carried out by a sequence of operations that is described below. 
     FIG. 7  is a diagrammatic view that is similar to  FIG. 2 , except that the test apparatus  41  supports the workpiece  110  rather than the workpiece  10 .  FIG. 7  shows the first operation of the test sequence, in which the interferometer  48  generates a flat wave represented by broken-line arrows  61  and  62 . The portions of this flat wave reflected by the annular planar reference surface  126  on the workpiece are monitored by the interferometer, and the mechanism  53  is used to adjust the orientation of the workpiece  110  relative to the interferometer  48  until the axis  14  of the workpiece  110  is parallel to the axis  49  of the interferometer  48 . As discussed above, this does not necessarily mean that the parallel axes  14  and  49  are also necessarily coaxial. 
     FIG. 8  is a diagrammatic view similar to  FIG. 7 , but showing the next operation in the test sequence. In  FIG. 8 , the interferometer  48  is set to produce a spherical wave rather than a flat wave, as indicated diagrammatically by the broke-line arrows  71  and  72 , The interferometer  48  monitors reflections from the spherical surface  121 , and the mechanism  53  is used to adjust the position of the workpiece  110  until the centerpoint of the spherical wave (where arrows  71  and  72  intersect) is coincident with the centerpoint of the spherical surface  121 , this centerpoint also being the focus  116  of the ellipsoid surface  112 . 
     FIG. 9  is a diagrammatic view similar to  FIGS. 7 and 8 , but showing the additional structure of the test apparatus  41 , including the retro ball  84 , member  81  and support mechanism  82 . In  FIG. 9 , the interferometer  48  continues to generate a spherical wave, represented by the arrows  71  and  72 . While the mechanism  53  holds the workpiece  110  stationary with respect to the interferometer  48 , the mechanism  82  is used to adjust the position of the retro ball  84  until its centerpoint is coincident with the focus  116 , in a manner similar to that discussed above in association with  FIG. 4 . 
     FIG. 10  is a diagrammatic view similar to  FIG. 9 , but showing the next operation in the test sequence. More specifically, the interferometer  48  continues to generate a spherical wave, as indicated diagrammatically by arrows  71  and  72 . The mechanism  82  keeps the retro ball  84  from moving relative to the workpiece  110 , so that the centerpoint of the retro ball  84  remains positioned at the focus  116  of the ellipsoid surface  112 . The interferometer  48  monitors reflections from the spherical reference surface  123  on the workpiece  110 . The distance between the foci  116  and  117  of the surface  112  is known, and the mechanism  53  therefore moves the workpiece  110  approximately linearly by this distance in a rightward direction in  FIG. 10 , parallel to the axis  49  of the interferometer  48 . The mechanism  53  then adjusts the position of the workpiece  110  along with retro ball  84  as necessary (without moving the retro ball relative to the workpiece), until the focus  117  is coincident with the centerpoint of the spherical wave  71  and  72 . 
   The interferometer  48  then shifts its attention from portions  71 - 72  of the spherical wave that are being reflected by spherical surface  123  to other portions  191  and  192  of the same spherical wave that are being reflected by the ellipsoid surface  112 . As is well known, if a ray of radiation passes through either focus of an ellipsoid surface and then is reflected by the ellipsoid surface, the ray will then travel directly toward the other focus of the surface. Thus, assuming that the surface  112  was accurately machined, rays such as those at  191  and  192  will each pass through the focus  117 , will be reflected by the surface  112 , and will then travel directly toward the other focus  116 , impinging on the surface of retro ball  84  exactly perpendicular to that surface. Each ray will then be reflected by the retro ball  84  to travel back along precisely the same path of travel by which it arrived at the retro ball  84 . In particular, each ray will be reflected by the surface  112 , pass through focus  117 , and then arrive back at the interferometer  48  at exactly the same point from which it originated. 
   If the interferometer  48  determines that all rays associated with the surface  112  are arriving back at exactly the same points from which they originated, then the interferometer will know that the surface  112  was accurately machined. On the other hand, if some of the rays are arriving back at points that are different from the points where those rays originated, the interferometer  48  will know that the surface  112  has an aberration and is not accurate. As discussed earlier, the error measured by the interferometer will be twice the actual error, because the radiation will be reflected twice by the surface region with the aberration. 
   Referring again to  FIG. 6 , the workpiece  110  has a cylindrical central portion  201  with the ellipsoid surface  112  thereon, and the central portion  201  is surrounded by an annular portion  202  that has the reference surfaces  121 ,  123  and  126  thereon. After the accuracy of the ellipsoid surface  112  has been tested and verified in the manner discussed above in association with  FIGS. 7-10 , the portion  202  of the workpiece  110  that carries the reference surfaces can optionally be removed, for example by cutting or machining, or in some other suitable manner, leaving only the cylindrical central portion  201  with the ellipsoid surface  112  thereon. 
     FIG. 11  is a diagrammatic sectional side view of a workpiece  210  that is an alternative embodiment of the workpiece  110  of  FIG. 6 . The workpiece  210  includes a cylindrical central portion  228  that has the ellipsoid surface  112  thereon, and includes an annular outer portion  229  that encircles the central portion  228 , and that has the reference surfaces  121 ,  123  and  126  thereon. A rigid plate  234  is disposed against the rear surface of each of the portions  228  and  229 , and is fixedly and removably secured to each of the portions  228  and  229  by several bolts  235 . After the portions  228  and  229  are bolted to the plate  234 , the workpiece  210  is mounted in a machine tool, and then the optical surfaces  112 ,  121 ,  123  and  126  are machined thereon. The optical surface  112  is then tested in the manner described above in association with  FIGS. 7-10 . When this testing is complete, and the accuracy of the ellipsoid surface  112  has been verified, the bolts  235  can optionally be removed, so that the portion  228  with the surface  112  thereon can be easily separated from the portion  229  with the reference surfaces  121 ,  123  and  126  thereon. 
   In the foregoing discussion, it has been assumed for simplicity that the spherical reference surfaces  21 ,  121  and  123  are all accurate. As a practical matter, however, the interferometer  48  can optionally be used in a conventional manner to verify the accuracy and the radius of each of the spherical reference surfaces  21 ,  121  and  123 . 
   Although selected embodiments have been illustrated and described in detail, it should be understood that a variety of substitutions and alterations are possible without departing from the spirit and scope of the present invention, as defined by the claims that follow.