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Title:
IMPROVED MEASUREMENT OF ANGULAR MOTION
Document Type and Number:
WIPO Patent Application WO/2011/061514
Kind Code:
A1
Abstract:
The invention relates to an interferometer (1) for measurement of angular motion of a target (40). The interferometer comprises a source of a light beam (10), means for splitting the light beam from the source into at least first and second beams (22a, 22b) directed towards a target location and laterally spaced from one another. First and second retroreflectors (34a, 34b), positioned in the paths of the first and second light beams respectively following reflection from a target in the target location are also provided along with at least one detector for detecting fringes formed by interference of the first and second light beams following reflection from the first and second retroreflectors respectively.

Inventors:
SPEAKE CLIVE CHRISTOPHER (GB)
ASTON STUART MARK (GB)
PENA ARELLANO FABIAN ERASMO (MX)
Application Number:
PCT/GB2010/002157
Publication Date:
May 26, 2011
Filing Date:
November 23, 2010
Export Citation:
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Assignee:
UNIV BIRMINGHAM (GB)
SPEAKE CLIVE CHRISTOPHER (GB)
ASTON STUART MARK (GB)
PENA ARELLANO FABIAN ERASMO (MX)
International Classes:
G01B9/02; G01B11/26
Domestic Patent References:
WO2010030179A12010-03-18
WO2009010750A12009-01-22
WO2009010750A12009-01-22
Foreign References:
US5056921A1991-10-15
US5064289A1991-11-12
US3926523A1975-12-16
Other References:
CLASS. QUANTUM GRAV., vol. 22, 2005, pages 1 - 9
Attorney, Agent or Firm:
WARD, David (Alpha TowerSuffolk Street Queensway, Birmingham B1 1TT, GB)
Download PDF:
Claims:
CLAIMS:

1. An interferometer for measurement of angular motion of a target, comprising: a source of a light beam;

means for splitting the light beam from the source into at least first and second beams directed towards a target location and laterally spaced from one another;

first and second retroreflectors, positioned in the paths of the first and second light beams respectively following reflection from a target in the target location; and

at least one detector for detecting fringes formed by interference of the first and second light beams following reflection from the first and second retroreflectors respectively.

2. The interferometer as claimed in claim 1, wherein the means for splitting the light beam from the source into at least first and second beams comprises a first polarising beam splitter for splitting the light beam from the source into at least first and second beams having orthogonal planes of polarisation.

3. The interferometer as claimed in claim 2, wherein the interferometer is free from non-polarising reflectors in the paths of the first and second light beams between the first polarising beam splitter and the target location.

4. The interferometer as claimed in claim 2 or claim 3, further comprising first and second quarter-wave plates located in the paths of the first and second light beams respectively, so that the plane polarised light leaving the first polarising beam splitter is converted to circularly polarised light before leaving the interferometer.

5. The interferometer as claimed in any one of claims 1 to 4, wherein the

components of the interferometer are arranged such that, following reflection from the first and second retroreflectors respectively, the paths of the first and second light beams are directed towards the target location.

6. The interferometer as claimed in any one of claims 1 to 5, wherein the source of a light beam comprises an optical fibre carrying light into the interferometer.

7. The interferometer as claimed in any one of claims 1 to 6, wherein at least one of the first and second retroreflectors comprises a mirror and an aspheric lens.

8. The interferometer as claimed in any one of claims 1 to 7, wherein at least one of the first and second retroreflectors has a self-conjugate plane perpendicular to the optical axis of the retroreflector, defined such that for an object located on the self- conjugate plane, the retroreflector produces an image on the self-conjugate plane of that object.

9. The interferometer as claimed in any one of claims 1 to 8, comprising at least two detectors for detecting fringes formed by interference of the first and second light beams following reflection from the first and second reflectors respectively.

Description:
IMPROVED MEASUREMENT OF ANGULAR MOTION

The present invention relates to a device suitable for the measurement of angular motion. In many engineering and scientific situations, it is necessary to accurately measure the angular motion of an object. In particular, it is often necessary to measure accurately small amounts of angular motion, requiring high resolution in the measurement device.

At present, angular motion measurement is usually achieved commercially using an autocollimator. These devices measure the angular motion of a mirror (attached to the object) by tracking the reflected image of a light source across a charge-coupled device (CCD). This system has a resolution that is related to the pixel size of the CCD, and hence a linearity limited by the manufacturing precision of the CCD. Autocollimators thus have a limited dynamic range (defined as range divided by resolution). They also require calibration to set the scale parameter relating distance across the CCD to angle, and also to eliminate non-linearities.

It is also known to measure angular motion using an interferometer. Interferometers are devices that measure the interference pattern produced by the superposition of two or more waves, such as those of electromagnetic radiation.

In the standard (Michelson) design of interferometer, a beam of light from a light source is split into two, by means of a beam splitter. One beam of light (the reference beam) is directed towards a reflector (which may be a plane mirror, or a retroreflector such as a cube corner) housed within the interferometer, whilst the other is directed towards a reflector on the target. Following reflection of the two beams from the respective reflectors, the beams of light are recombined, and the resulting interference measured by a detector. Since the reference reflector is held at a fixed position relative to the beamsplitter whilst the target reflector is separate from the interferometer, any movement of the target relative to the interferometer along the light path will change the interference in a predictable manner, allowing changes in the relative distance between the interferometer and target to be calculated. In modern devices, the beam of light frequently has a high degree of coherence, such as a light beam from a laser device. One modern development of a Michelson interferometer is described in Class. Quantum Grav., vol.22 (2005), pages 1 -9. Another such device is sold by Canon, Inc. under the DS-80 model name (http://www.canon.com/optoelectro/6_Micro_Laser/6-l .html).

Where an interferometer is used to measure angular motion, no reference reflector is used. Instead, both beams are directed towards different, parallel and laterally-spaced reflective regions of the target. These different reflective regions may be different reflectors on the target, or different regions of the same reflector. In either case, angular motion of the target changes the relative lengths of the two light beam paths, again producing predictable changes in the resulting interference. Measurement of these changes allows the angular motion of the target to be calculated.

Prior art designs of interferometer require that, in order to function correctly, each target reflective region must be correctly aligned with the axis of the corresponding light beam, which generally means that the normal axis of the reflective region should be coincident with the axis of the incident light beam. Thus, for example, in one embodiment, a misalignment of only 1 mrad of the target reflective region leads to a 2-fold reduction in fringe visibility. Clearly, where the target is rotating, this can cause difficulties, since it would require continual realignment of the target reflector(s) as the target rotates.

It is possible to use retroreflectors as the target reflectors, in which case the tolerance for misalignment of the reflectors is increased. Retroreflectors are optical devices which are able to reflect a beam of light in a direction parallel with the incident beam, even where that incident beam is not axially aligned with the reflector. Common

retroreflectors include half-silvered glass spheres, and corner-cube reflectors. However, it is not always practical to mount retroreflectors on the target. For example, where the target is very low in mass, the additional mass of the retroreflectors may significantly alter the dynamic properties of the target. Where it is desired to measure rotations of a large number of similar or identical components (e.g. on a production line) it may be impractical to apply retroreflectors to each individual component. Furthermore, although the light beam reflected from a retroreflector may be parallel with the incident beam, it will usually (where the incident light beam is not aligned with the optical axis of the retroreflector) be laterally displaced from the incident beam axis, due to translation within the retroreflector. This reduces the degree of overlap and hence the visibility of interference fringes within the interferometer. Furthermore, in order to use target retroreflectors with an interferometer for

measurement of angular motion, it is necessary to use a separate retroreflector for each of the two interferometer light beams. The retroreflectors must be carefully positioned so that each is in the path of the appropriate light beam, with their lateral separation equal to that of the two light beams. This adds additional complexity to the procedure, again, particularly where it is desired to measure rotations on a large number of components.

It is therefore desirable to have a device for measurement of angular rotation which is able to obviate or mitigate one or more of these difficulties.

According to the present invention, there is provided an interferometer for measurement of angular motion of a target, comprising:

a source of a light beam;

means for splitting the light beam from the source into at least first and second beams directed towards a target location and laterally spaced from one another;

first and second retroreflectors, positioned in the paths of the first and second light beams respectively following reflection from a target in the target location; and at least one detector for detecting fringes formed by interference of the first and second light beams following reflection from the first and second retroreflectors respectively. Retroreflectors are known in the art, and are devices capable of reflecting an incident beam of light along a vector parallel to the incident beam, for a range of (non-zero) angles of incidence. Thus, the light beam is reflected substantially back to its source, without requiring a specific alignment of the reflector with the incident light beam. This is in contrast to a simple plane mirror, which is able to reflect an incident light beam back towards its source only where the angle of incidence is zero. Common retroreflectors include corner-cube reflectors and half-silvered spheres.

It will be readily understood by the skilled man that a light source for use in an interferometer must produce light with sufficient coherence to enable the first and second light beams to produce adequately visible fringes. The coherence length I of a light source may be related to the range of wavelengths Δλ produced by the light source according to the e uation:

In certain embodiments of the present invention, the coherence length required is of the order of 50 cm, which is easily achieved using a diode laser as the light source.

It will be understood that the target must be capable of reflecting the first and second light beams substantially in the direction of the interferometer. In some embodiments, in use the target is provided with a reflective surface, such as for example a silvered surface.

In some embodiments, the means for splitting the light beam from the source into at least first and second beams comprises a first polarising beam splitter for splitting the light beam from the source into at least first and second beams having orthogonal planes of polarisation. This allows the first and second beams to be manipulated independently by virtue of their different polarisation states, and later recombined to produce the required interference fringes. In some further embodiments, the interferometer is free from non-polarising reflectors in the paths of the first and second light beams between the first polarising beam splitter and the target location. It will be understood that any reflections required in the paths of the first and second light beams between the first polarising beam splitter and the target location (such as for example to direct the initially orthogonal first and second light beams towards the same target location) will be achieved in such embodiments by means of polarising reflectors, such as for example appropriately oriented polarising beam splitters. In this case, it can be preferable to align the optical components in a non-planar geometry and to utilise two polarising beam splitters at 45 degrees to split the beam into two interfering beams. As used herein, 'polarising reflector' is intended to mean a reflector comprising means to ensure that plane-polarised light reflected by the reflector does not have any significant mixing of the polarisation state. Such means may be inherent in the construction of the reflector, as in the case of most polarising beam splitters, or may be provided separately, such as for example by inclusion of a polarising filter. By contrast, 'non-polarising reflector' is intended to mean a reflector lacking such means. The exclusion of non-polarising reflectors ensures that degradation of the polarisation states of the first and second light beams is minimised, and hence maximises the ability to detect interference fringes in the recombined beam.

In some further embodiments, the interferometer further comprises first and second quarter-wave plates located in the paths of the first and second light beams respectively, so that the plane polarised light leaving the first polarising beam splitter is converted to circularly polarised light before leaving the interferometer. This has the advantage that, on passing through the quarter-wave plates a second time on re-entry to the

interferometer following reflection from the target, the first and second light beams are each returned to plane polarization, but have planes of polarization orthogonal to those originally created. The outgoing and returning light beams can then be processed separately by the same optical components, by virtue of their orthogonal polarizations.

In some embodiments, the components of the interferometer are arranged such that, following reflection from the first and second retroreflectors respectively, the paths of the first and second light beams are directed towards the target location. Thus, the first and second light beams will reflect a second time from the target, and re-enter the interferometer along vectors substantially parallel to their initial paths. In some embodiments, the source of a light beam comprises an optical fibre carrying light into the interferometer. This allows the light generation equipment (such as for example a laser light source) to be located remotely from the interferometer, thereby minimising the size requirements of the interferometer.

In some embodiments, at least one of the first and second retroreflectors comprises a mirror and an aspheric lens. In some embodiments, at least one of the first and second retroreflectors has a self- conjugate plane perpendicular to the optical axis of the retroreflector, defined such that, for an object located on the self-conjugate plane, the retroreflector produces an image on the self-conjugate plane of that object. In some further embodiments, both of the first and second retroreflectors have such self-conjugate planes. In some still further embodiments, the self-conjugate planes of the first and second retroreflectors are coplanar. In some further embodiments, the retroreflector comprises a mirror having a radius of curvature R within 10% of the value iven by the formula:

and a lens having a focal length / within 10% of the value given by the formula:

where are the segments of optical path, each of length / and having refractive index n , between the lens and the mirror, and k are the segments of the intended optical path, each of length l k and having refractive index n k , between the aspheric lens and the target, in use. Such an arrangement is described (in the context of a standard

Michelson-type interferometer having a reference arm and a measurement arm) in publication WO 2009/010750. It will be understood that these formulae relate to a retroreflector defining a self-conjugate plane and consisting of a simple thin lens with a mirror located at the focal plane of the lens, in the paraxial approximation.

Such a design of retroreflector offers the advantage of minimising lateral displacement of the relevant light beam. By contrast, cube corners and half-silvered spheres will always produce some translation of the light beam in addition to reflection (unless the incident light beam is directed along the optical axis, which is unlikely in the case of a beam reflected from a rotating target). If the translation of the light beam is too great, then there is a risk that the reflected light beam will no longer interact with the required optical components. This limits the range at which this type of retroreflector (cube corners and half silvered spheres) can successfully be employed to determine angular rotation. For example, the translation of the light beam may be such that, following an additional reflection from the target, the light beam is no longer directed towards the appropriate region of the interferometer. This is particularly likely where the axis of the target reflector is significantly inclined to the vector of the incident light beam. By minimising translation of the light beam in the retroreflector, and by being able to optimise the working distance, the tolerance of the interferometer to high degrees of rotation of the target is thereby increased. It will also be understood that the interferometer of some embodiments will return an optical path length containing a linear relationship in the angular displacement of the mirror (mirrored surface of the target) and a term proportional to the cube of the rotation (for which a calculation can be made for correction as necessary). Furthermore, the transverse motion of each beam is dependent upon the distance from the optical axis of each beam and the square of the mirror tilt. As the beams track each other, the loss of fringe visibility due to rotation is minimised. It is also desirable to limit optical aberrations by considering the retroreflector as either a focal or an afocal system. In either case, the interferometer can be optimised to give a total wavefront distortion (on the collimated beam reflected from the retroreflector) which is diffraction limited, with the dominant contribution coming from the focal system. Specifically, for this optical design of retroreflector, in the paraxial case with no aberrations, it has been found that the optical path length, L that is introduced by the mirror tilt, 0 is given as

where _?,· is the linear displacement of each mirror (with i=l ,2) from the sweet-plane, which is measured positive along the optic axis. If the mirror is not rotated we have s=0 and the mirror lies in the sweet-plane. In general 5 is given as the product of the transverse distance of each beam from the rotation axis of the target mirror and the mirror tilt. It may therefore be found that

,

where R, is the distance from the optic axis of each beam. Analyser optics can determine the differences between the optical paths of the two beams, and this can be shown to be

L Tolal - A9 2 ).

The interferometer will therefore return an optical path length that contains a linear term in the angular displacement of the mirror but also a term proportional to the cube of the rotation. At an angle of 2.5 degrees this non-linearity amounts to about 1 % but is a calculable correction that can be made if necessary. It may also shown that, for the present retroreflector and interferometer, the transverse motion of each beam, h t ( Θ), returning from the beamsplitter due to mirror tilt Θ, is given as

As the interferometer is mirror symmetric, the rotation of the mirror can be considered to be of opposite sign for each arm of the interferometer as far as tracing the optical paths is concerned. Therefore,

where 6 m is the tilt of the mirror. Given the above, it may therefore be understood that the residual translations due to rotation are equal with

h, * 4R0 2 , assuming R { « R 2 . Advantageously, as the beams track each other the loss of fringe visibility due to rotation is minimised, which is consistent with observations. The simple relationships given in the equations can also advantageously be used to predict non-linearity in the interferometer and its useful angular range. It may be appreciated that although the above analysis is tailored to a particular interferometer, the underlying aspects and optical properties of the retroreflector are applicable to other known interferometers.

It will be further understood that the wavefront distortion on the collimated beam that is reflected from the retroreflector can be minimised. For this purpose the system can be treated as an afocal system with a source at infinity. In order to calculate the position of the sweet-plane the system can be considered to be focusing with sources and images in the sweet-plane. Advantageously, in some embodiments, both focal and afocal systems can be optimised to give a total wavefront distortion which is ultimately diffraction limited, with the dominant contribution coming from the focal system.

It will be understood that, in order for the at least one detector to be able to detect fringes formed by interference of the first and second light beams, the interferometer typically comprises at least one plane polarising filter (such as a polarising beam splitter) having a plane of polarisation inclined (typically at 45°) to the planes of polarisation of the first and second light beams. The or each polarising filter therefore resolves recombined first and second light beams into an analysis beam exhibiting interference fringes. In some embodiments, the interferometer comprises at least two detectors for detecting fringes formed by interference of the first and second light beams following reflection from the first and second reflectors respectively. Typically, the recombined light beam is split into at least first and second parts, each part having substantially the same polarisation state (for idealised beamsplitters), with a respective polarising filter in the path of each part resolving that part into a respective analysis beam exhibiting interference fringes. It will be understood that plane of polarisation of each polarising filter should be inclined to the planes of polarisation of the first and second light beams (typically at 45° to each). In some further embodiments, the interferometer comprises a quarter-wave ( /2) plate in the path of the first part before the first polarising filter, but absent from the path of the second part, the first and second polarising filters having parallel planes of polarisation, so that following resolution the interference pattern of the first analysis beam is a quarter-wave (π/2) out of phase with that of the second analysis beam. It will be understood that this provides greater accuracy in measurement of the fringes, since when the interference pattern of one analysis beam is at a maximum or minimum intensity, with a momentary zero rate of change, the second is at half- height intensity, with a maximum rate of change.

In some further embodiments, the interferometer comprises at least three detectors for detecting fringes formed by interference of the first and second light beams, with at least one of the first and second polarising filters being a polarising beam splitter for directing two orthogonally-polarised analysis beams towards two separate detectors. It will be understood that the polarising beam splitter creates two analysis beam parts having interference patterns which are a half- wave (π) out of phase with one another. In total, therefore, there will be at least three analysis beams, corresponding to the at least three detectors, having interference patterns with relative phases of 0, /2 and π. By comparison of the different intensities, it is possible to normalise the light intensity measurements in a standard manner, improving the utility of the interferometer. The three fringe patterns delivered by the three analysis beams can also be converted into displacement using a field programmable gate array. An embodiment of the invention will now be described by way of example, with reference to the accompanying Figure, which represents a schematic diagram of one embodiment of an interferometer according to the present invention.

Referring to Figure 1, an interferometer 1 is provided with a laser diode 10, such as a monomode VCSEL laser diode operating at 1550.9 nm or a Helium-Neon laser operating at 633 nm and may be a cryogenic laser. The laser light beam 12 produced by the diode 10 then passes through a first polarising beam splitter 14 (5 mm SF2 glass polarising beam splitter cube, 1200-1600 nm, available from Thorlabs Ltd, Ely, UK as part number PBS054). The vertically-polarised component is reflected and lost into a beam dump (not shown), whilst the horizontally-polarised component passes through a non-polarising beam splitter 16 (5 mm BK7 glass non-polarising beam splitter cube, 1 100-1600 nm broadband, available from Thorlabs Ltd, Ely, UK as part number BS009), with a portion emerging as a polarised beam 18. It should be noted that the paths shown for the laser light beams (e.g. 12, 18) are highly stylised and do not represent actual paths of the light beams in space; rather, they are intended simply to be a pictorial representation of the paths of the laser light beams between the components of the interferometer. In addition, neither the components of the interferometer nor the position of the target relative to the interferometer 1 are shown to scale.

The polarised light beam 18 then enters a second polarising beam splitter 20 (PBS054 from Thorlabs Ltd, as above), which is oriented such that the reflective plane is inclined at 45° to that of polarising beam splitter 14. The second polarising beam splitter 20 therefore splits polarised beam 18 into two (equal) component beams 22a and 22b, which are directed to the first 24a and second 24b arms of the interferometer respectively. The first arm component beam 22a is reflected by the second beam splitter 20 via a compensator plate 25 (consisting of a PBS054 beam splitter as above, oriented so as not to deviate the path of the first arm component beam 22a), whilst the second arm component beam 22b is transmitted, arriving at a third polarising beam splitter 26 (PBS054 from Thorlabs Ltd, as above). The third polarising beam splitter 26 is oriented such that the reflective plane is rotated 90° relative to that of the second polarising beam splitter 20 (when viewed along the vector of the polarised beam 18). Thus, the second arm component beam 22b is reflected, rather than transmitted, by the third polarising beam splitter 26. The purpose of the compensator plate 25 is to introduce an increase in optical path length into the path of the first component beam 22a, equivalent to the increase in optical path length caused by the presence of the additional glass of the third polarising beam splitter 26 in the path of the second component beam 22b. It will be appreciated that, although the interferometer is shown figuratively in two dimensions, the relative orientations of the first 14, second 20 and third 26 polarising beam splitters means that the first 24a and second 24b arms of the interferometer should be located below the plane of the paper as drawn. (It will, however, be appreciated that similar constructions could be envisaged in which the arms are located above this plane). Looking along the vector of the polarised light beam 18, the second polarising beam splitter 20 and the first arm 24a should be rotated 45° clockwise from the figurative representation shown, whilst the third polarising beam splitter 26 and second arm 24b should be rotated 45° anticlockwise.

Within each arm 24a, 24b of the interferometer 1, the relevant arm component beams 22a, 22b encounter an arm polarising beam splitter 30a, 30b (10 mm SF2 glass polarising beam splitter cube, 1200-1600 nm, available from Thorlabs Ltd, Ely, UK as part number PBS 104), oriented to reflect the arm component beams 22a, 22b as first and second arm primary incident beams 42a, 42b in the direction of a target 40 via a quarter wave plate 32a, 32b (10 mm diameter custom-manufactured from mica). The primary incident beams 22a, 22b are thus converted from plane polarisation to circular polarisation, before exiting the interferometer 1 in the direction of the target 40. The arm primary incident beams 42a, 42b are each reflected from the target and return towards the interferometer 1 as arm primary reflected beams 44a, 44b. As a result of misalignment of the target 40 relative to the interferometer 1 , the primary reflected beams 44a, 44b are misaligned with the arm primary incident beams 42a, 42b.

Furthermore, as a result of reflection, the primary reflected beams 44a, 44b are circularly polarised in the opposite senses to the corresponding primary incident beams 42a, 42b.

On re-entry to the interferometer 1 , the primary reflected beams 44a, 44b pass a second time through the quarter-wave plates 32a, 32b and are reconverted to plane polarisation, with planes of polarisation which are orthogonal to those of the initial arm component beams 22a, 22b. The primary reflected beams 44a, 44b are therefore transmitted by the arm polarising beam splitters 30a, 30b, reaching retroreflectors 34a, 34b. Each retroreflector is formed from an aspheric lens and convex mirror. The aspheric lens is formed of S-LAH64 and has a diameter of 18 mm, a focal length of 15.0 mm and the aspheric coefficients: R, 240 mm; k, -217.59947; A 2 , 4.0824 x 10 -2 ; A4,

3.1 1 1545 10 "5 ; A 6 , -1.141412 x 10 ~8 ; A 8 , -1.630836 χ 10 "10 ; and Aio,

2.355089 10 "15 (available from Thorlabs Ltd, Ely, UK as part number AL1815-C). The convex mirror is formed from a coated bi-concave lens having a diameter of 9 mm and radii curvature of 8.7 mm (available from Thorlabs Ltd, Ely, UK as part number LD4271), with an aluminium coating on the rearmost concave face for internal reflection, and an antireflection coating on the front convex face. The front of the mirror is located 19.05 mm behind the front of the lens, with the lens itself located 77.85 mm from the ideal target plane (being a plane perpendicular to the axis of the interferometer, in which the target axis of rotation should ideally be located). Each of the primary reflected beams 44a, 44b is reflected by the corresponding retroreflector to give secondary incident beams 46a, 46b, along vectors parallel to, but slightly laterally displaced from, the vectors for the corresponding primary reflected beams 44a, 44b. The secondary incident beams 46a, 46b are again transmitted by the arm polarising reflectors 30a, 30b and pass through the quarter- wave plates 32a, 32b, whereupon they are converted once more to circular polarisation and exit the interferometer 1 towards the target 40. Following a second set of reflections from the target 40, the light beams return towards the interferometer 1 as secondary reflected beams 48a, 48b. Assuming that the target 40 has not moved significantly between the first and second set of reflections therefrom, the secondary reflected beams 48a, 48b will now have vectors parallel to, though laterally offset from, the primary incident light beams 42a, 42b.

The second set of reflections from the target 40 again reverses the sense of polarisation of the light beams. Thus, on passing through the quarter wave plates 32a, 32b, the secondary reflected beams 48a, 48b are again converted to plane polarisation, having the same planes of polarisation as the corresponding primary incident beams 42a, 42b. The secondary reflected beams 48a, 48b are therefore reflected by the arm polarising reflectors 30a, 30b (as were the primary incident beams 42a, 42b), and recombine at the second polarising beam splitter 20.

Upon exiting the second polarising beam splitter 20 as recombined beam 50, the beam 50 is split by the non-polarising beam splitter 16 into a transmitted beam 52 and a reflected beam 54. The transmitted beam 52 passes to the first polarising beam splitter 14, where a portion is reflected. Since the plane of polarisation of the first polarising beam splitter 14 is inclined with respect to the planes of polarisation of the first and second secondary reflected beams 48a, 48b, the light beam portion reflected by the first polarising beam splitter 14 is a superposition of the relevant components from the secondary reflected beams 48a, 48b, creating an interference pattern (due to rotation of the target 40 and hence changes in the path length in the first 24a and second 24b arms of the interferometer) which is detected at a first diode 60 (a 3.0 mm diameter germanium photodiode available from Electo-Optical Systems Inc., of Phoenixville, Pennsylvania as part number G-030). The reflected beam 54 passes through a quarter-wave (π/2) plate 56 (5 mm diameter custom-manufactured from mica) and then enters a fourth polarising beam splitter 58 (PBS054 from Thorlabs Ltd, as above), which is oriented such that the reflective plane is parallel to that of the first polarising beam splitter 14. The reflected beam 54 is therefore split into two orthogonal components, each having interference patterns which are detected at second 62 and third 64 diodes. Thus, the interference patterns at the second 62 and third 64 diodes have phase shifts of ±π/2 respectively relative to that at the first diode 60.

By combining the outputs of the photodiodes appropriately and in the usual way, continuous measurement of the angular displacement of the target 40 can be measured over angles up to at least one degree (and typically more than 2.5 degrees) with a resolution that can be limited by the shot noise in the interference patterns or the quantisation noise in the analogue to digital converters used to read the photodiode outputs. Subtraction of the signals in pairs, in the usual manner, allows compensation for the average voltage measured by the diodes, allowing the difference between light and dark fringes to be more clearly resolved.

Although as described the retroreflectors are formed of an aspheric lens and a convex mirror, it will be appreciated that other types of retroreflector may alternatively be employed. Other optical components are of standard construction as will be readily apparent to the skilled man.




 
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