Abstract:
A retroreflector has three mutually-orthogonal reflective surfaces arranged around an optical axis. The reflective surfaces stop short of the optical axis to provide a central region of the retroreflector which transmits incident light and a peripheral region of the retroreflector which retroreflects incident light. When the reflector is used in a Jamin-type interferometer with another reflector, this enables the interferometer to be used for measuring displacement between the reflectors.  
     In the interferometer, a projected beam is disposed between a pair of return beams and/or one of the return beams is disposed between a pair of the projected beams. This enables a first contiguous area of a face of a beam splitter to be provided with a phase-shifting coating to produce a phase quadrature relationship between a pair of interferogram beams. This simplifies the masking required when applying the coating.  
     In manufacture of the beam splitting member, a thin-film, beam-splitting, metal coating is applied to the member, and the member and coating are baked so as to modify the phase shift produced by the coating to enable the phase quadrature relationship. During baking a beam of light is projected at the coating with an angle of incidence of substantially π/4 radians so that the beam is split into a transmitted component and a reflected component. The intensities or phases of the transmitted and reflected components are monitored during baking, and the baking is terminated when the monitored intensities or phases have a predetermined relationship. This improves the reliability and/or accuracy of the resulting phase shift.

Description:
BACKGROUND TO THE INVENTION  
         [0001]    1. General Field Of The Invention  
           [0002]    This invention relates to a retroreflectors, to reflector systems, to optical apparatus, to methods of manufacturing reflector systems, to Jamin-type interferometers, to beam splitting blocks and to methods of manufacturing beam splitting blocks.  
           [0003]    2. Particular Fields of the Invention and Description of the Prior Art  
           [0004]    A first aspect of the invention relates to a retroreflector, and more particularly to a retroreflector having three mutually-orthogonal reflective surfaces arranged around an optical axis. Such retroreflectors are well known and have applications in, for example, vehicle rear reflectors and interferometers. In a typical Michelson-type interferometer, a reference beam and a measuring beam derived from a common beam are projected at right angles to each other and are then reflected back by respective reflectors; the reflected beams are superposed to form an interferogram. By contrast, in a typical Jamin-type interferometer (see, e.g., FIGS. 1 and 3 of patent document US-A-4571082 and FIGS. 16 a,b  of patent document US-A-5546184), a reference beam and a measuring beam derived from a common beam are projected parallel to each other, but spaced apart, and then back by a single reflector; again, the reflected beams are superposed to form an interferogram. Retroreflectors can usefully be used in such interferometers so that parallelism of the reflected and projected beams can be assured and so that the reflected beam can be offset from the projected beam. However, the use of a single conventional retroreflector for both the reflected and projected beams in a Jamin-type interferometer limits the applications of the interferometer.  
           [0005]    A second aspect of the invention relates to a reflector system comprising first and second relatively movable reflectors.  
           [0006]    A third aspect of the invention relates to an optical apparatus having an optical axis and a retroreflector.  
           [0007]    Fourth and fifth aspects of the invention relates to a method of manufacturing a reflector or reflector system.  
           [0008]    Sixth, seventh and eighth aspects of the invention relates to Jamin-type interferometers.  
           [0009]    The Michelson-type interferometer mentioned above typically employs polarisation techniques to advantage, but consequently suffers from the disadvantage of the need to align the polarisation directions of the light beam source and polarisation-affecting components in the interferometer. By contrast a Jamin-type interferometer as described above typically does not use polarisation techniques and so does not suffer from the polarisation alignment problem. Indeed, alignment generally of a Jamin-type interferometer is less problematic than a Michelson-type interferometer. A further disadvantage of the typical conventional Jamin-type interferometer is that, because the reference and measuring beams share a common general path and a common reflector, there has been no widespread use of Jamin-type interferometers for displacement measurement— the Jamin-type interferometer of US-A4571082, for example, is limited to use in conjunction with a refractometer to measure refractive index rather than displacement and the Jamin-type interferometers of US-A-5546184 either are for use with a refractometer or employ a complex reflector arrangement to measure displacement.  
           [0010]    The Jamin-type interferometer of the eighth aspect of the invention is concerned with the problem in the type of interferometer shown in FIG. 16 a  of US-A-5546184 that it is necessary to provide two separate phase-shifting means (the phase-shifting films  135 , 137  in US-A-5546184) in order to obtain a pair of interferogram beams in approximate phase quadrature.  
           [0011]    The seventh and eighth aspects of the invention are concerned more particularly with a Jamin-type interferometer wherein: a beam splitter is arranged to split an incident beam of light into first and second generally-parallel, spaced-apart, projected beams; a reflector system is arranged to reflect the first and second projected beams to produce first and second return beams, respectively, which are spaced apart from and generally parallel to each other and the first and second projected beams; and the beam splitter is arranged to enable the first and second return beams to be superposed to produce at least one interferogram.  
           [0012]    The ninth aspect of the invention relates to a method of manufacture of a beam splitting member, comprising the steps of: applying a thin-film, beam-splitting, metal coating to at least part of a surface of the member; and baking the member and coating so as to modify the phase shift produced by the coating.  
           [0013]    Such a method is described in Vyskub VG, et al, 1977,  Pribory i Tekhnika Eksperimenta , (Moscow Engineering Physics Institute), No 4, pp 210-211. That paper explains that members and coatings had been baked to achieve phase shifts of 90±3°.  
         SUMMARY OF THE INVENTION  
         [0014]    An aim of the first aspect of the present invention is to provide a retroreflector which may increase the applications of a Jamin-type interferometer and which may have other uses.  
           [0015]    The retroreflector of the first aspect of the invention is characterised in that the reflective surfaces stop short of the optical axis to provide a central region of the retroreflector which transmits incident light and a peripheral region of the retroreflector which retroreflects incident light. Accordingly, the retroreflector can retroreflect a beam which is incident on the peripheral region (with an offset between the incident beam and the parallel return beam), but can pass a beam which is incident on the central region.  
           [0016]    In a first embodiment of the first aspect of the invention, the retroreflector may comprise a body of optical material which provides the reflective surfaces by internal reflection in the body. In this case, the retroreflector is preferably and conveniently in the form of a solid cube corner having a first transmitting surface for incident light and a second transmitting surface which truncates the cube corner. In this case, the first and second transmitting surfaces may be exactly parallel, but for some applications are preferably generally, but not exactly, parallel, so as to reduce the effects of stray reflections. Alternatively, the retroreflector may be in the form of a solid cube corner having a passageway extending therethrough generally in the direction of the optical axis to provide the central region.  
           [0017]    In a second embodiment of the first aspect of the invention, the retroreflector may comprise three plane mirror elements arranged around the optical axis, each providing a respective one of the reflective surfaces. In this case, the retroreflector is preferably in the form of a hollow truncated cube corner.  
           [0018]    The reflector system of the second aspect of the invention is characterised in that: the first reflector is a retroreflector according to the first aspect of the invention; and the reflectors are arranged so that light which is transmitted through the central region of the first reflector is reflected by the second reflector and transmitted back through the central region of the first reflector. When used as a reflector system for a Jamain-type interferometer, the enables to interferometer to be used to measure relative movement of the reflectors.  
           [0019]    In a first embodiment of the second aspect of the invention, the second reflector is a retroreflector. In this case, the second reflector preferably has three mutually-orthogonal reflective surfaces arranged around a second optical axis, in which case each of the reflective surfaces of the second reflector is preferably arranged parallel to a respective one of the reflective surfaces of the first reflector. The second reflector may comprise a second body of optical material which provides the reflective surfaces by internal reflection in the second body, and in this case the second body may have a transmitting surface for incident light which may be exactly parallel, but for some applications is preferably generally, but not exactly, parallel, to the second transmitting surface of the first reflector, so as to reduce the effects of stray reflections. Alternatively, the second reflector may comprise three plane mirror elements arranged around the second optical axis.  
           [0020]    The first and second reflectors may be joined by a piezo electric material, which can be used to vary the spacing between the reflectors.  
           [0021]    In a second embodiment of the second aspect of the invention, the second reflector comprises a plane mirror, the system further including a lens between the first and second reflectors.  
           [0022]    In a third embodiment of the second aspect of the invention, the second reflector may comprise a polarising beam splitter, quarter-wave plate, plane mirror and second retroreflector arranged such that: light which is transmitted through the central region of the first reflector is transmitted through the beam splitter and quarter-wave retardation plate to the mirror; the light which is thus reflected by the mirror is transmitted through the quarter-wave plate, is reflected by the beam splitter, and is directed to the second retroreflector; the light which is thus reflected by the retroreflector is reflected by the beam splitter and transmitted through the quarter-wave plate to the mirror; and the light which is thus reflected by the mirror is transmitted through the quarter-wave plate, the beam splitter and the central region of the first reflector. Such an arrangement of the second reflector  per se  is known from FIG. 17 of US-A-5546184.  
           [0023]    The apparatus of the third aspect of the invention is characterised in that: the retroreflector is arranged according to the first embodiment of the first aspect of the invention; and the first transmitting surface is generally, but not exactly, orthogonal to the optical axis of the apparatus, so as to reduce the effects of stray reflections.  
           [0024]    The method of the fourth aspect of the invention is characterised by the step of cutting a cube corner retroreflector in a plane generally orthogonal to its optical axis, or forming a passageway through a solid cube corner generally in the direction of the optical axis of the cube corner.  
           [0025]    The method of the fifth aspect of the invention is characterised by the steps of: providing three mirrors each having a pair of mutually orthogonal edges; cutting each mirror along a line intersecting the mutually orthogonal edges to form a first mirror and a second mirror; assembling the first mirrors mutually-orthogonally to form the first reflector.  
           [0026]    The method may also include the step of assembling the second mirrors mutuallyorthogonally to form the second reflector.  
           [0027]    The Jamin-type interferometer of the sixth aspect of the invention is characterised by a reflector system according to the second aspect of the invention. This therefore opens up a new range of applications for the Jamin-type interferometer, including the measurement of displacement of the two reflectors of the reflector system relative to each other, whilst retaining the advantages of the conventional Jamin-type interferometer and avoiding the disadvantages of the conventional Michelson-type interferometer.  
           [0028]    The Jamin-type interferometer of the seventh aspect of the invention is characterised in that the reflector system is in accordance with the second aspect of the invention.  
           [0029]    The Jamin-type interferometer of the eighth aspect of the invention is characterised in that: one of the projected beams is disposed between the return beams and/or one of the return beams is disposed between the projected beams. The enables a single phase-shifting means to be employed to produce a required phase shift in two of the beams.  
           [0030]    Preferably, a first contiguous area of the face of the beam splitter is provided with a phase-shifting coating, one of the projected beams being projected from, and one of the return beams returning to, the first area. The masking which may be required for depositing of the coating is therefore simplified as compared with the case of US-A-5546184 wherein two separate areas of coating need to be applied.  
           [0031]    Preferably, the coating produces a phase shift such that there is a phase difference of substantially π/2 radians between the two interferogram beams, and preferably the coating comprises a thin metal film.  
           [0032]    Preferably, a second contiguous area of the face of the beam splitter is devoid of any coating providing any substantial phase-shift, the other projected beam being projected from, and the other return beam returning to, the second area.  
           [0033]    Preferably, the interferometer employs a reflector system according to the second aspect of the invention.  
           [0034]    The interferometers of the seventh and eighth aspects of the invention may be provided in combination with a dual-chamber gas or liquid refractometer arranged so that the first projected and return beams pass through one chamber of the refractometer and the second projected and return beams pass through the other chamber of the refractometer.  
           [0035]    In the interferometers of the seventh and eighth aspects of the invention, the reflector system may comprise first and second retroreflectors rigidly joined together adjacent each other, the first retroreflector being arranged to retroreflect the first projected beam to produce the first return beam, and the second retroreflector being arranged to retroreflect the second projected beam to produce the second return beam. The interferogram(s) may therefore be used to measure changes in the inclination of the reflector system, so that an auto-collimator function can be provided.  
           [0036]    The interferometers of the seventh and eighth aspects of the invention may further include means for modulating the optical path length of one of the beams, or one of the projected beams and its respective return beam. As will be described in more detail below, such modulation can be used in calibration of the detection of the interferogram beams. In a first embodiment of these aspects of the invention, the modulating means comprises an optically-transmitting, varying-thickness plate disposed in the path of the beam(s) to be modulated, and means for rotating the plate. In a second embodiment of these aspects of the invention, the modulating means comprises a layer of optically-transmitting, flexible material sandwiched between a pair of optically-transmitting plates disposed in the path of the beam(s) to be modulated, and means for modulating the spacing of the plates. In these cases, the modulating means may be disposed adjacent the beam splitter, for example as parts of a head unit of the interferometer.  
           [0037]    In the case where the reflector system is provided by the first embodiment of the second aspect of the invention and the first and second reflectors are joined by a piezo electric material as described above, the modulating means preferably includes means for modulating the thickness of the piezo electric material to modulate the spacing between the reflectors.  
           [0038]    The aim of the ninth aspect of the invention is to improve the reliability and/or accuracy of the resulting phase shift.  
           [0039]    The method of the ninth aspect of the invention is characterised by the steps of: projecting a beam of light at the coating with an angle of incidence of substantially π/4 radians so that the beam is split into a transmitted component and a reflected component; monitoring the intensities or phases of the transmitted and reflected components during the baking step; and terminating the baking step when the monitored intensities or phases have a predetermined relationship.  
           [0040]    It has been discovered that if the intensities of the reflected and transmitted components are equal, the phase shift is such as to produce a phase difference of π/2 radians between the interferogram beams. Therefore, for convenience, preferably it is the intensities which are monitored. The baking step may be terminated when the monitored intensities are generally equal. Alternatively, in the case where the intensity of the transmitted component is monitored after transmission through another surface of the member, the baking step is preferably terminated when the monitored intensity of the transmitted component is substantially equal to a predetermined proportion of the monitored intensity of the reflected component. This can therefore take account of the transmittance at the other surface of the block.  
           [0041]    Preferably, the coating is of aluminium. Preferably, the baking temperature is between 450 and 480° C. Preferably, the intensities of the polarisation components of the projected beam in the perpendicular and parallel directions relative to the plane of the incident light are generally equal to each other.  
           [0042]    In accordance with the tenth aspect of the invention, there is provided a beam splitting block produced by a method of the ninth aspect of the invention.  
           [0043]    In accordance with the eleventh aspect of the invention, there is provided an interferometer of the seventh or eighth aspect of the invention, wherein the beam splitter is provided by a beam splitting block of the tenth aspect of the invention. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0044]    [0044]FIG. 1 is a plan view of an embodiment of interferometer having a head module and a first type of reflector arrangement sectioned as indicated by the section line  1 - 1  in FIG. 2;  
         [0045]    [0045]FIG. 2 is an end view of the reflector arrangement of FIG. 1, as viewed in the direction indicated by the arrow  2  in FIG. 1;  
         [0046]    [0046]FIG. 3 is a block circuit diagram of a signal processing circuit forming part of the interferometer of FIG. 1;  
         [0047]    [0047]FIG. 4 is a sectioned side view of a first type of modulator module for use with the interferometer of FIG. 1;  
         [0048]    [0048]FIG. 5 is a sectioned side view of a second type of modulator module for use with the interferometer of FIG. 1;  
         [0049]    [0049]FIG. 6 is a sectioned side view of a second type of reflector/modulator module and a gas refractometer module for use with the interferometer head of FIG. 1, sectioned on the line  6 - 6  shown in FIG. 7;  
         [0050]    [0050]FIG. 7 is an end view of the second type of reflector/modulator module and refractometer module, as viewed in the direction of the arrow  7  in FIG. 6;  
         [0051]    [0051]FIG. 8 is a side view of a third type of reflector module for use with the head module of FIG. 1, as viewed in the direction of the arrow  8  in FIG. 9;  
         [0052]    [0052]FIG. 9 is an end view of the third type of reflector module, as viewed in the direction of the arrow  9  shown in FIG. 8;  
         [0053]    [0053]FIG. 10 is a side view of a fourth type of reflector module for use with the head module of FIG. 1, sectioned along the line  10 - 10  shown in FIG. 11;  
         [0054]    [0054]FIG. 11 is an end view of part of the fourth type of reflector module, as viewed in the direction of the arrows  11 - 11  shown in FIG. 10;  
         [0055]    [0055]FIG. 12 is a sectioned side view of a fifth type of reflector module for use with the head module of FIG. 1;  
         [0056]    [0056]FIG. 13 is a side view of a sixth type of reflector module for use with the head module of FIG. 1, sectioned along the line  13 - 13  shown in FIG. 14;  
         [0057]    [0057]FIG. 14 is an end view of part of the sixth type of reflector module, as viewed in the direction of the arrows  14 - 14  shown in FIG. 13;  
         [0058]    [0058]FIG. 15 is a schematic plan view of an apparatus for use in manufacture of a beam splitting block used in the head module of FIG. 1;  
         [0059]    FIGS.  16 A-E illustrate a method of construction of the first type of reflector module, FIGS.  16 A,B,D being side views, and FIGS. 16C,E being end views;  
         [0060]    FIGS.  17 A-G illustrate a method of construction of a seventh type of reflector module, FIGS.  17 A-C being face views of a components of the module, FIGS. 17D,F being side views, and FIGS. 17E,G being end views;  
         [0061]    [0061]FIGS. 18, 19 are similar to FIGS. 8 and 9, respectively, but showing a modification to the third type of reflector module;  
         [0062]    [0062]FIG. 20 is a rear view of an eighth type of reflector module; and  
         [0063]    [0063]FIG. 21 is a side view of the reflector module of FIG. 20. 
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0064]    When a Jamin-type beam splitting block (as will be described in detail below) is employed in an interferometer, the projected reference beam and the projected measurement beam of the interferometer are automatically aligned in a common direction with a predetermined spacing between the beams, and the reference reflector and measurement reflector are in a single “arm” of the instrument. This optical configuration has the inherent fundamental advantage of “common-path” measurement characteristics and can provide the fundamental advantage of “zero dead path” measurement characteristics.  
         [0065]    When cube comer type retroreflectors (as will be described in detail below) are employed for reflecting the projected reference and measurement beams, the reflected reference and measurement beams are also automatically aligned in the same common direction, although spaced from the projected beams. The only alignments which the user needs to make for the system to function are therefore to position each retroreflector so that its reflected beam is generally coplanar with both projected beams and so that its reflected beam is appropriately spaced from its projected beam, whereupon the two reflected beams can be superposed to form an interferogram falling on a photodetector. In other words, each retroreflector needs to be aligned so that its reflected beam returns to within a predetermined area on the beam splitting block.  
         [0066]    Optimum interferogram contrast is realised when the two reflected beams are completely superposed by the beam splitting block and fall completely on the photodetector. Typically, photodetectors have an acceptance aperture of 4 to 4½mm and the diameters of the laser beams (if no additional collimating optics are employed) are between 1½mm for a short range system and 3 mm for a one metre range. As will be described in detail below, interferogram contrast can be displayed to the user. In this case, therefore, alignment merely involves coarsely aligning each retroreflector so that its return beam of 1½to 3 mm diameter falls anywhere within a predetermined area of 4 to 4½mm diameter on the beam splitting block, and then finely aligning just one of the retroreflectors so that maximum contrast is indicated on the display.  
         [0067]    When the two cube corner type retroreflectors are pre-aligned (as will be described in detail below with reference to FIGS.  6  to  9 ,  13 ,  14 ,  18  and  19 ), the retroreflectors merely need to be coarsely aligned by the user so that one of the reflected beams returns to within its predetermined area on the beam splitting block (i.e. a 1½to 3 mm diameter beam falling anywhere within a predetermined 4 to 4½mm diameter area in the example just described). The other reflected beam will then automatically return to its predetermined area on the beam splitting block, and moreover the retroreflectors will automatically be finely aligned relative to each other.  
         [0068]    The interferometer system which will now be described in detail utilises a Jamin-type beam splitting block and can meet the requirements of a range of different interferometric metrology applications by employing an appropriate reflector module/arrangement in conjunction with an interferometer head module.  
         [0069]    Referring to FIG. 1, the interferometer  10  has a longitudinal axis  12 , with a head module  14  and a target reflector arrangement  16  both lying on the longitudinal axis  12 . The head module  14  comprises a chassis/housing  18  on which a frequency-stabilised or non-frequency-stabilised helium neon laser  20  is releasably mounted with a V-block assembly (not shown). The laser  20  projects a highly-collimated laser beam A having a nominal wavelength λ= 632 . 8  nm in a direction parallel to the longitudinal axis  12 . Typically, the power of the laser beam A would be 1 to 3 mW and its diameter would be 1 mm. The laser beam A may be unpolarised, but is preferably polarised merely because polarised lasers are generally less noisy than unpolarised lasers. A rectangular beam splitting block  22  of silica or BK 7  glass is mounted on the chassis/housing  18  with its longitudinal axis  24  at 45° to the longitudinal axis  12  of the interferometer  10 . The longitudinal sides of the beam splitting block  22  are substantially perfectly parallel. From the upper apex of the beam splitting block  22 , about 60% (depending upon the spacing of the beams) of the upper longitudinal side of the block  22  is coated with a beam splitting coating  26  (to be described in detail below). The coating  26  causes the transmitted portion and the reflected portion of an incident beam to have generally equal intensities. Half-turn symmetrically, from the lower apex of the beam splitting block  22 , about 60% of the lower longitudinal side of the block  22  is coated with a similar beam splitting coating  28 .  
         [0070]    Referring to FIGS. 1 and 2, the target reflector arrangement  16  comprises a cube corner retroreflector of silica or BK 7  glass which has been cut generally parallel to its equilateral-triangular face  30  so as to form a first, truncated, cube corner retroreflector  32  and a second, smaller cube corner retroreflector  34 . The face  30  of the truncated retroreflector  32  and the cut face  36  of the smaller retroreflector  34  are both arranged generally normally to the longitudinal axis  12  of the interferometer  10 . However, being retroreflectors, the angle is not critical. Although the cut face  38  of the truncated retroreflector  32  is generally parallel to its front face  30 , preferably there is a small inclination between these two faces  30 , 38  in order to prevent interference by stray reflections. Alternatively, the face  38  may be anti-reflection coated. In one application of the interferometer  10 , the truncated retroreflector  32  would be a fixed reference retroreflector, and the smaller retroreflector  34  would be movable. The front faces  30 , 36  of the two reflectors  32 , 34  are anti-reflection coated.  
         [0071]    Referring back to the head module  14 , a signal processing circuit  50  (shown in greater detail in FIG. 3) is included which receives signals from photodetectors  42 , 44 , 46 , 48  and produces a sine output  54 , a cosine output  56  and a laser intensity output  58 . Typically, the photodetectors  42 , 44 , 46 , 48  would have an aperture of 4.5 mm. The circuit  50  also provides a contrast display  52  for example in the form of an LED bargraph to assist in aligning the head module  14  and reflector arrangement  16 .  
         [0072]    The beam A from the laser  20  is projected onto the upper longitudinal side of the beam splitter block  22  near its lower end and is transmitted and refracted so as to diverge downwardly from the longitudinal axis  12  as beam B. Upon reaching the opposite side of the block  22 , the beam B is split into two beams C,K. Beam C is the transmitted beam which is refracted and exits the block  22  and is projected parallel to the longitudinal axis  12  to the target reflector arrangement  16 . The target reflector arrangement  16  is configured so that the beam C falls on a lower portion of the face  30  of the truncated retroreflector  32  and, after three internal reflections, exits from an upper portion of the face  30  of the truncated retroreflector  32  as beam D. Beam D extends in a return direction parallel to the longitudinal axis  12 . Upon return to the head module  18 , the beam D falls onto the lower longitudinal side of the beam splitter block  22  near its upper end where the coating  28  is absent and is transmitted and refracted so as to diverge upwardly from the longitudinal axis  12  as beam E. Beam E upon reaching the opposite, upper side of the block  22 , is split into two beams F,J. Beam F is the internally reflected beam which is reflected downwardly back to a point  40  on the lower side of the block  22  about half way along its length where the coating  28  is present. At point  40 , the beam F is split into two beams G,H. Beam G is the transmitted beam which is refracted and exits the block  22  and is projected orthogonally to the longitudinal axis  12  to a first interferogram photodetector  42  mounted on the chassis/housing  18 . Beam H is the internally reflected beam which is reflected and passes to the uncoated portion of the upper side of the block  22  where it is transmitted and refracted so as to be directed, as Beam I, in a direction parallel to the longitudinal axis  12  to a second interferogram photodetector  44  mounted on the chassis/housing  18 . Beam J mentioned above is the portion of beam E which is transmitted through the coating  26  and is refracted so as to extend in a direction parallel to the longitudinal axis  12  to a DC reference photodetector  46  mounted on the chassis/housing  18 .  
         [0073]    Beam K mentioned above is the internally reflected part of beam B. Beam K travels upwardly to a point about half way along the upper side of the block  22  where the block is coated. Beam K is then split into a transmitted beam O and internally reflected beam L. The beam O is transmitted and refracted so that it extends in a direction orthogonal to the longitudinal axis  12  to a laser intensity photodetector  48 . The beam L returns back across the block  22  to an uncoated point on the lower side of the block  22 , where it is transmitted and refracted so as to form a beam M extending in a direction parallel to the longitudinal axis  12  between the beams C,D and closer to the beam D. The beam M is transmitted straight through the truncated retroreflector  32 , exiting from an upper portion of the cut face  38  of the retroreflector  32  and passing to an upper portion of the cut face  36  of the smaller retroreflector  34 . After three internal reflections, the beam exits from a lower portion of the face  36  of the smaller retroreflector  34  as beam N. Beam N extends in a return direction parallel to the longitudinal axis  12 , entering a lower portion of the cut face  38  of the truncated retroreflector  32  and passing straight through the retroreflector  32 . Due to the geometry of the interferometer  10 , upon return to the head module  18 , the beam N falls onto the lower longitudinal side of the beam splitter block  22  at coated point  40 , where the beam N is split. The part of the beam N which is externally reflected at point  40  is superposed with the part of the beam F which is transmitted at point  40  so as to form the interferogram beam G. On the other hand, the part of the beam N which is transmitted at point  40  is superposed with the part of the beam F which is internally reflected at point  40  so as to form the beam H and thence the interferogram beam I.  
         [0074]    In addition to beams A to O, FIG. 1 also shows a number of stray beams S caused by unwanted reflections at the block  22 . It will be noted that none of the stray beams interferes with the beams A to O or falls on any of the photodetectors  42 , 44 , 46 , 48 . The intensities of the stray beams S can be reduced by suitable anti-reflection coatings and reflection at the ends of the block  22  can be prevented by providing ground surfaces at the ends of the block  22 .  
         [0075]    It should be noted that there are two paths from the laser  20  to the first interferogram photodetector  42 : one which is reflected by the truncated retroreflector  32  (beams A,B,C,D,E,F,G); and the other which is reflected by the smaller retroreflector  34  (beams A,B,K,L,M,N,G). Similarly, there are two paths from the laser  20  to the second interferogram photodetector  44 : one which is reflected by the truncated retroreflector  32  (beams A,B,C,D,E,F,H,I); and the other which is reflected by the smaller retroreflector  34  (beams A,B,K,L,M,N,H,I). It will be appreciated by those skilled in the art of interferometry that the beam G is indeed an interferogram exhibiting successive bright and dark fringes due to constructive and destructive superposition as the smaller retroreflector  34  is moved relative to the truncated retroreflector  32  along the longitudinal axis  12 . One cycle from bright to dark to bright fringe is caused by movement of the smaller retroreflector  34  of λ/2=316.4 nm. Similarly, the beam I is also an interferogram. The intensity of each interferogram beam G,I varies sinusoidally with changes in the path difference.  
         [0076]    If the apparatus described above did not involve any energy loss, then the principles of the conservation of energy impose a phase difference of π radians between the energy in the interferogram beams G,I. However, in order to count the fringes produced by path length differences satisfactorily and unambiguously, ideally this phase difference should be π/2 radians, rather than π radians. Alteration of the phase difference between the two interferogram beams is realised by employing the energy-absorbing coating  28  on the beam splitter block  22 . It will be appreciated by those skilled in interferometry that by employing the beam splitting coating  28  to produce a phase shift of approximately π/2 radians, the interferogram beams G,I will be in approximate phase quadrature.  
         [0077]    In addition to altering the phase difference between the two interferogram beams G,I, in order to realise optimum contrast in the interferograms, the reflected and transmitted intensities produced by the coating  28  on the beam splitter block  22  each time a beam is split should be generally equal. It has been realised that, if the beam splitting coating  28  produces a phase shift of π/2 radians, then this requirement is also met.  
         [0078]    In view of the above, and referring also to FIG. 3, the output signals V 60 ,V 62 ,V 64  from the interferogram photodetectors  42 , 44  and the DC reference photodetector  46  can be written as:  
         V 64  =d; 
         V 60  =(1+e 2 )·[d+a·(1+e 3 )·sin(4πL/λ+e 1 /2 −π4)]; and 
         V 62  =(1+e 4 )·[d+a·(1+e 5 )·cos(4πL/λ−e 1 /2−π/4)], 
         [0079]    where: d is the DC level of the reference signal from the DC reference photodetector  46 ; a is the general AC amplitude of the signals from the interferogram photodetectors  42 , 44 ; L is the position of the movable, smaller retroreflector  34  along the longitudinal axis  12  relative to a convenient datum point, which introduces the common −π/4 term into the equations for V 60 ,V 62 ; e 1  is an error term to take account of the signals V 62 ,V 64  from the interferogram photodetectors  42 , 44  not being exactly in phase quadrature; and e 2  to e 5  are error terms to take account of differences in the AC amplitudes and DC levels of the signals V 62 ,V 64  from the interferogram photodetectors  42 , 44 .  
         [0080]    The photodetector signals V 60 ,V 62 ,V 64  are fed to respective preamplifiers  66 , 68 , 70 . Preamplifier  70  has a gain of p. Preamplifiers  66 , 68  have gains which are set during initial calibration of the apparatus to 1/(1+e 2 ) and 1/(1+e 4 ), respectively. The outputs V 72 ,V 74 ,V 76  from the preamplifiers  70 , 66 , 68  are therefore:  
         V 72  =p.d; 
         V 74  =p.[d+a.(1+e 3 ).sin( 4πL/λ+ e 1 /2 −π4)]; and 
         V 76  =p.[d+a.(1+e 5 ).cos( 4πL/λ− e 1 /2 −π/4)], 
         [0081]    The output V 72  of reference amplifier  70  is subtracted from the outputs V 74 , V 76  of amplifiers  66 , 68  respectively by respective subtractor circuits  78 , 79  having gains which are set during initial calibration of the apparatus to 1/(1+e 3 ) and 1/(1+e 5 ), respectively to produce respective signals V 80 ,V 8   2  such that:  
         V 80  =a.p.sin(4πL/λ+e 1 /2 −π/4) and 
         V 82  =a.p.cos(4πL/λ−e 1 /2 −π/4).  
         [0082]    The signals V 80 ,V 82  are added by an adding circuit  84  and subtracted by a subtracting circuit  86  to produce respective signals V 96 ,V 98 . The circuits  84 , 86  have their gains set during initial calibration of the apparatus as 1/{2.cos(e 1 /2 −π/4)} and 1/{2.sin(e 1 /2 −π/4)}, so that the signals V 96 ,V 98  are:  
         V 96 =a.p.sin(4πL/λ) and  
         V 98 =a.p.cos(4πL/λ).  
         [0083]    It will be noted therefore that the signals V 96 ,V 98  have become independent of the values e 1  to e 5.    
         [0084]    The root of the sum of the squares of the signals V 96 ,V 98  is determined by respective squaring circuits  100 , 102 , adding circuit  104  and square-root circuit  106  to produce a signal V 108  such that:  
         V 108 =a.p. 
         [0085]    The signals V 96 ,V 98  are divided by the signal V 108  by respective divider circuits  110 , 112  to produce sine and cosine output signals V 54 ,V 56  respectively at the sine and cosine outputs  54 , 56  respectively, such that:  
         V 54 =sin(4πL/λ) and 
         V 56 =cos(4πL/λ) 
         [0086]    It will therefore be seen that the output signals V 54 ,V 56:    
         [0087]    are complementary sine and cosine signals (i.e. having a phase difference of π/2) despite the coating  28  not necessarily producing a phase shift of exactly π/2;  
         [0088]    have no DC offset;  
         [0089]    have amplitudes normalised to unity; and  
         [0090]    are dependent merely upon:  
         [0091]    the position L of the movable, smaller retroreflector  34  along the longitudinal axis  12  relative to the datum point; and  
         [0092]    the laser wavelength λ.  
         [0093]    The output signals V 54 ,V 56  therefore provide excellent input signals for conventional interferometer reversible fringe counting apparatus and fringe subdividing apparatus which may be provided as dedicated hardware or as a programmed computer. Merely using phase quadrature fringe counting, the interferometer  10  can be used to measure displacements in the position L to an accuracy of λ/8 ( 80 nm). Furthermore, using known fringe subdivision techniques based on the arctangent of V 54 N 56 , it is possible to measure displacement in L to far greater accuracy. In a prototype of the invention, accuracies of better than 5 nm in linearity in the measured displacement were readily achievable.  
         [0094]    In FIG. 3, the signal V 114  from the laser intensity photodetector  48  represents the intensity i of the laser beam A before travelling to and returning from the reflector arrangement  16  and is supplied to a preamplifier  116  having a gain of p to produce the laser intensity signal V 58 =i.p. This signal V 58  and the output signal V 108 =a.p from the square-root circuit  106  are also supplied to a divider circuit  118  which produces a DC signal V 120 =a/i which is proportional to fringe contrast and which is supplied to the display  52 . The display  52  therefore represents the fringe contrast as a proportion of the laser beam intensity and greatly facilitates the user in aligning the retroreflectors  32 , 34  with the head module  14  when the interferometer  10  is set up so that the components of the interferogram beams G,I are superposed.  
         [0095]    In addition to, or instead of, the normalised sine and cosine outputs  54 , 56 , the signal processing circuit may provide the outputs  96 , 98  from the adder and subtractor circuits  84 , 86  as unnormalised sine and cosine outputs and/or these signal after they have been processed by a square-wave-shaping circuit.  
         [0096]    Although the signal processing has been described above as being implemented by a dedicated circuit  50 , it may alternatively be provided by respective analogue-to-digital converters for each of the photodetectors  42 , 44 , 46 , 48  which supply respective digital signals D 42 ,D 44 ,D 46 ,D 48  to respective input ports of a computer which is programmed to perform calculations corresponding to those set out above, and also to count the fringes where high-speed counting is required, it may be necessary to install a reversible counting card to the computer.  
         [0097]    If the interferometer  10  described above were perfectly calibrated and operated perfectly, the output signals from the sine and cosine outputs  54 , 56  would be of equal amplitude and in exact phase quadrature with zero volt mean DC levels. If these signals were therefore fed as the X and Y signals to an oscilloscope, the oscilloscope trace would be a perfect circle upon movement of the reflectors  32 , 34  relative to each other. If the signals were not perfect so that a non-circular Lissajous figure were produced, compensation may be made, for example using computer software, so that a perfect circle would be obtained, and the compensation parameters could then be applied to the signals from the sine and cosine outputs  54 , 56  during use of the interferometer  10 . In this case, it is expected that an accuracy of better than  1  nm in linearity would be possible where the metrology application merited it. In order to avoid the need to move the reflectors  32 , 34  while calculating the compensation parameters, the optical path length of the projected beam M and/or its return beam N, or of the projected beam C and/or its return beam D, may be modulated, preferably over at least one fringe.  
         [0098]    In order to provide such modulation, a modulator module  120 , as shown in FIG. 4 may be fitted in the interferometer module  14  in the region indicated by the phantom lines  122  in FIG. 1 so as to fall in the paths of the beams M,N to and from the movable retroreflector  34 . The modulator module  120  comprises a pair of parallel silica discs  124 , 126  in between which an annulus  128  of piezo electric material (or an annular piezo electric stack) is sandwiched and cemented. The cavity within the piezo electric annulus  128  and between the disks  124 , 126  is completely filled with silicone rubber  130  which is allowed to cure at room temperature. Upon application of a modulating voltage to the piezo electric annulus  128 , the spacing between the silica discs  124 ,  126  is modulated, and accordingly the thickness of the silicone rubber  130  is modulated so as to modulate the optical path length of the beam M and also the beam N.  
         [0099]    An alternative modulator module  132  is illustrated in FIG. 5 and may be fitted in the interferometer head module  14  in the region indicated by the phantom lines  134  in FIG. 1 so as to fall in the path of the beam C to the reference retroreflector  32 . The modulator module  132  comprises a disc  136  of silica, the thickness of which progressively varies from a maximum at one point on the periphery of the disc  136  to a minimum at a diametrically opposite point on the periphery of the disc  136 . The disc  136  is mounted coaxially on the shaft of an electric motor  138 . When the motor  138  is driven, the disc  136  rotates about its axis, and so the optical path length of the beam C is modulated.  
         [0100]    The interferometer  10  of FIG. 1 may be used in conjunction with a gas or liquid refractometer module  140 , as shown in FIGS. 6 and 7, disposed between the interferometer head module  14  and the reflector arrangement  16 . The refractometer module  140  comprises a pair of coaxial cylinders  142 , 144  sandwiched between and cemented to a pair of circular silica windows  146 , 148  so as to form an inner cylindrical chamber  150  and, coaxially therewith, an outer annular chamber  152 . The beams C,D pass through the outer annular chamber  152 , and the beams M,N pass through the inner cylindrical chamber  150 . The chambers  150 ,  152  can be filled with, and emptied of, any desired gas or liquid via respective valved ports  154 , 156 . For flow-through configurations, the ports  154 , 156  may be provided in pairs. For further description of such a refractometer  per se , reference is directed to FIG. 16 a  of patent document US-A-5546184, and the description thereof, which are incorporated herein by reference.  
         [0101]    Still referring to FIGS. 6 and 7, in order to provide more convenient modulation when the refractometer module  140  is used, a reflector module  16  may be employed which is similar to that described above with reference to FIGS. 1 and 2, except that an annulus  158  of piezo electric material (or an annular piezo electric stack) is sandwiched between and cemented to the larger truncated cube corner reflector  32  and the smaller cube corner reflector  34 . Upon application of a modulating voltage to the piezo electric annulus  158 , the spacing between the reflectors  32 ,  34  is modulated so as to modulate the optical path length of the beam M and also the beam N. In the arrangement of FIGS. 6 and 7, the reflector module  16  may be cemented to the plate  148 , rather than being spaced therefrom.  
         [0102]    A modified form of the signal processing circuit  50  of FIG. 3 may be used when the refractometer module  140  is employed, in which the output signal  72  from the DC retum-intensity amplifier  70  is divided by the output signal  58  from the DC projected-intensity amplifier  116  to provide a measure of the optical absorption of the gas or liquid in the refractometer module  140 , and in which these two output signals  72 , 58  are also used to correct the DC levels of the output signals  74 , 76  from the interferogram amplifiers  60 , 62  to take account of the absorption.  
         [0103]    In the arrangement of FIGS. 1 and 2, the interferometer  10  is used to measure movement of the reflector  34  in the direction of the optical axis  12  relative to the reflector  32  and is substantially insensitive, within limits, to relative movement of the reflectors  32 , 34  in directions orthogonal to the optical axis  12  or tilting of the reflectors  32 , 34 . By contrast, FIGS. 8 and 9 illustrate a reflector module  160  for measuring tilt about an axis  162  orthogonal to the plane containing the beams C,D,M,N and which is substantially insensitive to translational movement of the reflector module  160 . In FIGS. 8 and 9, a pair of identical cube comer retroreflectors  164 , 166  are cemented by their faces to an apertured base plate  168 . It should be noted that, in the case of the reflector module  160 , the beam N is produced by reflection of the beam C by the cube corner reflector  166 , and the beam D is produced by reflection of the beam M by the cube corner reflector  164 . Nevertheless, when used in conjunction with the interferometer head module  14  of FIG. 1 and with appropriate positioning of the reflectors  154 , 166  on the base plate  168 , this arrangement still produces a pair of interferogram beams G, I in phase quadrature. It will be appreciated that, when the base plate  168  is tilted about the axis  162 , a difference in optical path length between the beams C,N, on the one hand, and the beams M,D, on the other hand, is produced which is directly proportional to the amount of tilt.  
         [0104]    [0104]FIGS. 10 and 11 illustrate a further type of reflector arrangement  170 . This arrangement  170  is similar to the reflector arrangement  16  shown in FIGS. I and  2 , except that a convex lens  172  is cemented to the truncated face of the truncated cube comer reflector  32 , and a plane mirror  174  is employed instead of the smaller cube comer reflector  34 . The reflector arrangement  170  is useful for measuring vibration of the plane mirror  174  relative to the reflector  32  and lens  172 . Depending upon the numerical aperture of the lens  172 , a small cosine-error correction is required with this module.  
         [0105]    [0105]FIG. 12 illustrates another type of reflector arrangement  180 , in which the beam C is reflected by a complete cube comer reflector  182  to produce the beam D, and in which the beam M is reflected by a smaller, complete cube comer reflector  184  to produce the beam N, the smaller reflector  184  being nearer the interferometer head module  14  (not shown) than the larger reflector  182 . In this case, a silica block  186  may be cemented to the face of the smaller reflector  184  so that the optical path length through silica is the same for the beams M,N as for the beams C,D. Alternatively, the block  186  may be separate from the reflector  184  and indeed may be mounted in the region  122  in the head module  14 .  
         [0106]    [0106]FIGS. 13 and 14 illustrate yet another type of reflector arrangement  190  employing a truncated cube corner retroreflector  32 . A polarising beam splitting block  192  is cemented to the truncated face of the retroreflector  32 , and a quarter wave retardation plate is cemented to the opposite face of the polarising beam splitting block  192  with its axis at 45° to the plane of the paper. A further, smaller cube corner retroreflector  194  is cemented to one of the side faces of the polarising beam splitting block  192 . A plane mirror  198  is disposed on the optical axis  12 . As in the arrangement of FIG. 1, the beam C is reflected by the truncated retroreflector  32  to produce the return beam D. In the case of the beam M, it is transmitted through the reflector  32  and through the beam splitting block  192  to the mirror  198 . Upon reflection, the beam is reflected by the beam splitting block  192  to the retroreflector  194 . Upon reflection, the beam is reflected by the beam splitting block  192  towards the mirror  198 . Upon reflection, the beam passes through the beam splitting block  192  and the truncated retroreflector  32  to form the return beam N. The beam splitting block  192 , retroreflector  194  and quarter wave plate  196  make the mirror  198  tilt-insensitive, and the sensitivity of the arrangement to movement of the mirror  198  in the direction of the optical axis  12  relative to the other parts of the reflector arrangement is enhanced by the double pass of the mirror  198 . In the case of the reflector arrangement  190 , for complete efficiency and to prevent light being reflected back into the laser cavity, the beam M should be polarised in the plane of the paper.  
         [0107]    As mentioned above, the coating  28  on the block  22  needs to produce particular characteristics regarding phase shift and relative intensities of transmitted and reflected light. Such coatings are known in the context of Michelson interferometers and are described in Raine K W and Downs M J, 1978,  Optica Acta , Vol 25, No 7, pp 549-558 and also Vyskub VG, et al, 1977,  Pribory i Tekhnika Eksperimenta , (Moscow Engineering Physics Institute), No 4, pp 210-211, the contents of which are incorporated herein by reference. For example, the former paper describes a nickel:chromium coating applied by evaporation from an 80:20 nickel:chromium coated tungsten filament and producing a phase shift of about 90°. This paper also describes double-and triple-layer films of aluminium and chromium, aluminium and nickel, gold and chromium, and chromium, gold and chromium, the best results being obtained with a 4 nm base layer of chromium, 16 nm intermediate layer of gold and 5 nm outer layer of chromium. The latter paper describes an oxidised aluminium coating. Aluminium is deposited to a thickness of 16 nm to provide an initial phase shift in transmitted light of 110±3° and then oxidised by heating in air to a maximum temperature of 470° C. and then allowing to cool to provide a phase shift of 90±3°. An improved method of applying this latter type of coating will now be described with reference to FIG. 15.  
         [0108]    In FIG. 15, an oven  200  has a housing  202  with a door  204 , and a heating element  206  with a thermostatic controller which can maintain the oven temperature between 450 and 480° C. A coated beam splitter block  22  can be placed in the housing  202 . The housing has a first window  208  through which a beam of light Q can be projected from a helium neon laser  209  so as to impinge on the coating  28  on one side of the block about half-way along the length of the coating at an angle of incidence of 45°. The light Q is conveniently circularly polarised, or plane polarised at an angle of 45° to the P and S directions of the surface. At the coating  28 , a reflected beam R is produced which passes through a second window  210  to a ‘reflectance’ photodetector  212 . The transmitted refracted beam T is transmitted and refracted at the other side of the block  22  and passes through a third window  214  to a ‘transmittance’ photodetector  216 . The photodetectors  212 , 216  provide signals to respective amplifiers  218 , 220  of generally equal gain, and the outputs of the amplifiers  218 , 220  are connected to a comparator  222 .  
         [0109]    The method of applying the coatings  26 , 28  to the block  22  and treating the coating includes the following steps:  
         [0110]    1. Using a single edged mask, aluminium is deposited on about 60% of one side of the block  22  to a thickness of about 16 nm to form the coating  28 . (After the initial coating, the coating provides a transmittance of between 10 and 12%.)  
         [0111]    2. The block is rotated through half a turn, and, using the same mask, aluminium is deposited on about 60% of the opposite side of the block  22  to a thickness of about 16 nm to form the coating  26 .  
         [0112]    3. The coated block  22  is placed in the oven  200 , the door  204  is closed, and the heating element  206  is switched on to raise the temperature in the oven to between 450 and 480° C.  
         [0113]    4. The beam of light Q is projected at the coating  28  on the block  22  as described above. Initially, the comparator  22  indicates that the intensity of the reflected beam R is greater than the intensity of the transmitted beam T.  
         [0114]    5. As the temperature of the block  22  and coating  28  increases, and with time, the aluminium of the coating  28  oxidises non-homogeneously. The intensity of the reflected beam R decreases, and the intensity of the transmitted beam T increases.  
         [0115]    6. When the comparator  22  indicates that the intensity of the reflected beam R is equal to the intensity of the transmitted beam T, the heating element  206  is switched off, and the door  204  is opened so that the block  22  and coating  28  immediately begin to cool.  
         [0116]    7. The treated, coated block  22  is then removed from the oven  200 .  
         [0117]    It has been discovered that, when the transmittance and reflectance at the coating  28  are equal, the phase shift produced by the coating  28  between the two interferograms G,I when the block is used in the interferometer  10  is π/2 radians.  
         [0118]    In one form of the method described above, the reflectance photodetector  212  and its amplifier  218  have the same gain as the transmittance photodetector  216  and its amplifier  220 . However, it will be noted that the transmitted beam T is refracted at the side of the block  22  opposite the coating  28 , and there is a reflection loss at this surface of typically 3.5%. Therefore in another form of the method, the reflectance photodetector  212  and its amplifier  218  are set to have a gain of 96.5% of the gain of the transmittance photodetector  216  and its amplifier  220 . Also, it will be appreciated that, once the heating element  206  is switched off and the door  204  is opened in step 6 above, the coating  28  may continue to oxidise slightly more while the block  22  and coating  28  cool down. Therefore, in a further form of the method, the gain of the transmittance amplifier  216  may be increased slightly relative to the gain of the reflectance amplifier  218  to take account of this overshoot.  
         [0119]    A method of manufacture of the truncated cube corner reflector  32  and its associated smaller cube comer reflector  34  (as used in the arrangements of FIGS. 1, 2,  6 ,  7 ,  13  and  14 ) will now be described with reference to FIGS.  16 A-E. Starting with a complete solid cube comer reflector  230  as shown in FIG. 16A, the reflector  230  is cut into two using a diamond saw through the plane  232 . The cutting plane  232  is parallel to, or very slightly inclined relative to, the front face  30  of the reflector  230 , and the cutting plane  232  is disposed about two-thirds of the way from the front face of the reflector  230  to its apex  234 . The cut face  38  of the larger cut part, which forms the truncated reflector  32  as shown in FIGS. 16B,C, is polished. The cut face  36  of the smaller cut part, which forms the smaller reflector  34  as shown in FIGS. 16D,E, is polished and treated with an anti-reflection coating as required.  
         [0120]    A method of manufacturing an alternative pair of retroreflectors  240 , 242  which may be used in place of the reflectors  32 , 34  in the arrangements of FIGS. 1, 2,  6 ,  7 ,  13  and  14  will now be described with reference to FIGS.  17 A-G. In this case, the reflectors  240 , 242  are hollow, rather than solid, cube corner reflectors. The reflectors  240 , 242  are made from three mirrors  244 , one of which is shown in FIG. 17A. Each mirror  244  has the shape of an isosceles right-angled triangle, and the shorter two edges  246 , 248  are bevelled outwardly at an angle of 45° away from the reflective surface  250 . Each mirror  244  is cut into two using a diamond saw through the plane  252 . The cutting plane  252  is parallel to the hypotenuse of the mirror  244  and is disposed about two-thirds of the way from the hypotenuse of the mirror  244  to the opposite vertex of the reflective surface  250 . Each mirror  244  therefore produces a larger, truncated triangular mirror  254  as shown in FIG. 17B and a smaller triangular mirror  256  as shown in FIG. 17C. The three larger mirrors  254  are then cemented together with the bevelled edge  246  of each being joined to the bevelled edge  248  of another, so as to form the truncated, hollow, cube corner retroreflector  240  as shown in FIGS. 17D,E. Similarly, the three smaller mirrors  256  are cemented together with the bevelled edge  246  of each being joined to the bevelled edge  248  of another, so as to form the smaller, complete, hollow, cube corner retroreflector  242  as shown in FIGS. 17F,G. Precise alignment of these reflecting surfaces is preferably realised by examining the retroreflector during assembly on a Fizeau interferometer.  
         [0121]    It should be noted that each mirror  244  does not need to be a complete triangle. For example, the portions of the mirror adjacent the vertices at the ends of the hypotenuse may be omitted, and indeed the mirrors  244  may be square. Furthermore, the cut  252  does not need to be straight. The mirror  244  should, however, have the edges  246 , 248  at right angles to each other.  
         [0122]    A modification to the auto-collimation reflector module of FIGS. 8 and 9 will now be described with reference to FIGS. 18 and 19. In FIGS. 18 and 19, the three apices of each reflector  164 , 166  at the corners of its front face have been rounded off, as indicated by reference numeral  167 . Furthermore, the reflector  166  has been rotated through half a turn, as viewed in FIG. 19 compared with FIG. 9.  
         [0123]    A modification of the reflector  32  as shown in FIGS. 1, 2,  6 ,  7 ,  10 ,  11 ,  13  and  14  will now be described with reference to FIGS. 20 and 21. In FIGS. 20 and 21, the three apices of the reflector  32  at the corners of its front face have been rounded off, as indicated by reference numeral  35 . Furthermore, rather than being truncated by cutting off the central apex of the reflector, the reflector  32  of FIGS. 20 and 21 has a hole  33  formed through it coaxial with the optical axis  12 . In use, the beam C is retroreflected by the reflector  32  in the manner described above to produce the beam D. However, the beams M,N pass through the hole  33  unimpeded by the reflector  32 . It should be noted that the hole  33  substantially restricts the aperture of the reflector  32  so as to exclude the areas indicated by horizontal hatching  37  in FIG. 20.  
         [0124]    The reflector  32  of FIGS. 20 and 21 may be manufactured by boring the hole  33  though a solid cube corner reflector and by rounding off the apices as at  35 . If desired, the spikes produced at the rear end of the hole  33  may be removed.  
         [0125]    In another modification of the reflector arrangement  16  shown in FIG. 1, the retroreflectors  32 , 34  are connected by a mechanical linkage which retains the retroreflectors  32 , 34  in alignment on their optical axis but which permits movement of the retroreflectors  32 , 34  towards and away from each other, and a probe is attached to the smaller retroreflector  34  for abutment with a surface whose displacement is to be measured.  
         [0126]    It will be appreciated that a number of improvements to a Jamin-type interferometer  10  have been described above. Additionally, the interferometer  10  is modular, having a head module  14  that can be used with different types of laser, and a range of various reflector modules for displacement, vibration and tilt measurement. Additionally, a refractometer module and a variety of modulator modules may be employed.  
         [0127]    It should be noted that the embodiments of the invention have been described above purely by way of example and that many other modifications and developments may be made thereto within the scope of the present invention.