WO2010058165A1

WO2010058165A1 - Interferometric system for profiling surfaces with application in the field of manufacturing radioastronomic antennas and corresponding method

Info

Publication number: WO2010058165A1
Application number: PCT/GB2009/002699
Authority: WO
Inventors: John Benjamin Mitchell; Paul Howard Morantz
Original assignee: Cranfield University
Priority date: 2008-11-18
Filing date: 2009-11-18
Publication date: 2010-05-27
Also published as: GB0821015D0

Abstract

Apparatus for determining displacement relative to a reference beam of radiation, comprising an emitting arrangement serving to emit the beam, wherein the determining is by an interferometer detecting movement perpendicular to the beam of a received end of the beam. In this way, pointing instability of the reference beam of radiation may be determined with an interferometer. Such determination enables a surface of an object to be measured highly accurately without a mechanical straightness reference artefact. Rather, the straightness of propagation of the reference beam of radiation is used as an absolute reference.

Description

INTERFEROMETRIC SYSTEM FOR PROFILING SURFACES WITH APPLICATION IN THE FIELD OF MANUFACTURING RADIOASTRONOMIC ANTENNAS AND

CORRESPONDING METHOD

The present invention relates to a method and apparatus for interferometric self-referencing of a measuring device. In one particular application, the invention relates to a self-referencing, interferometric, long- trace, height-measuring profiler.

There exists a requirement for a means of independently verifying the full aperture (whole area) interferometric testing of large optical elements. Such elements are typified by the segmented primary mirrors of the next generation of extremely large telescopes (ELTs). A typical ELT segment would be 1.5m width and be highly aspheric with a very long radius of curvature (approximately 84m for a planned European ELT). The long radius of curvature makes it impractical for a full aperture measurement to be made from the centre of curvature as this would require the construction of a tower at least 84m high. As a result, the test set-up would be shortened by auxiliary folding, focussing and corrective optical elements. Misalignments of these elements can introduce unwanted aberrations into the tested wavefront (ideally of the same profile as the surface being tested), leading to errors in the determination of the test element surface profile. It is for this reason that it is important to be able to verify the full aperture test by an independent measurement to characterise and/or eliminate any unwanted errors.

Profilers, whether contact or non-contact, are commonly used to characterise high spatial frequency surface features over short length scales. For these applications, the accuracy of motion of a scanning head of. the profiler over the object under test and for low spatial frequencies is not critical. However, for long-trace profiling, to determine the overall surface figure, the errors in mechanical motion of the scanning head cannot be ignored.

One approach to this problem is to reference the position of the scanning head to a calibrated straight edge artefact, normally a mechanical straight edge which can be an extremely heavy structural element. This straight edge needs to be at least as long as the longest scan length required. It is also necessary to be confident that the profile of the straight edge should remain constant over periods between calibration and over environmental variations such as temperature during a measurement cycle. A second approach is to measure surface slope and numerically integrate this over the scan length to obtain a surface profile. This is the principle used by the Long Trace Profiler (LTP) first developed by Takacs et al. (US-A-4884697) and commonly used in various developments for the profiling of X-Ray optic mirrors. A problem with this method is the possible accumulation of errors from integration over the scan length. Another problem is the range of slopes that can be accommodated while maintaining high accuracy (dynamic range). X-ray optics, typically, are very flat even when compared to the long radius optics for ELTs and slope variations are thus very small. It is known to detect the position of a beam centroid; this is a geometric approach which determines the centre of a cross-section of a beam of radiation.

It is known that interferometric detection of motion of a beam of radiation perpendicular to itself requires that the perpendicular motion impart a phase (or path length) change on the detection (normally measurement) beam relative to a reference beam that is not influenced by that motion. This would appear not to be possible using reflective or refractive optics as a consequence of Fermat's Principle, which states that the optical path length must be constant, i.e. any change in path length due to a perpendicular motion in one direction is exactly cancelled by an opposite change elsewhere. It is, however, possible to impart a phase change in a beam by perpendicular translation of a diffraction grating. The effect is well known in the use of acousto-optic modulators (moving phase gratings) to impart a frequency shift (continuous phase shift) to a beam of radiation. The frequency shift is given by:

¥ ^J = - d .

where n = diffraction order, v = perpendicular velocity, d = grating period.

For discrete motions of the diffraction grating this is equivalent to introducing a phase shift: 2π.n.s

Aφ = - d

where s is the perpendicular translation.

US-A-2006/0077396 discloses interferometer systems for measuring displacement including a displacement interferometer. The displacement interferometer includes a displacement converter responsive to a measuring beam of light. The displacement converter is configured to transform movement thereof in a direction orthogonal to the measuring beam of light into a change in path length between a reflective surface of the displacement converter and the measuring beam of light. The displacement converter may include a transmission grating and a displacement mirror or a reflecting grating.

According to one aspect of the present invention, there is provided apparatus for determining displacement relative to a reference beam of radiation, comprising an emitting arrangement serving to emit said beam, wherein said determining is by an interferometer detecting movement perpendicular to said beam of a received end of said beam.

Owing to this aspect, pointing instability of the beam of radiation may be determined with an interferometer. This determination enables a surface profile of an object to be measured highly accurately without a mechanical straightness reference artefact. Rather, the straightness of propagation of the reference beam of radiation is used as an absolute reference.

Compared with detection of the position of a beam centroid, an absolute interferometric measurement traceable to the wavelength of radiation would be particularly advantageous in surface profiling. Preferably, the beam of radiation is a beam of light, i.e. visible radiation, for example a laser beam, and the beam could be emitted as a pencil beam, as a scanning pencil beam moving in a plane, or as a planar beam.

According to a second aspect of the present invention, there is provided a method comprising emitting a beam of radiation to form a positional reference, using said positional reference while using said beam for determining positional displacement of said beam and, in using said positional reference, compensating for said displacement of said beam. Owing to this aspect, the accuracy of determination of positional displacement by using a beam of radiation as a positional reference can be greatly improved. The method is particularly useful in compensating for instabilities in the pointing direction of a reference straightness beam of a surface profiler.

Preferably, there is also an optical device movable by roll motion about an axis, the optical device being arranged in a plane oblique to the axis, a roll motion-detecting beam of radiation impinging upon the optical device at a radius from the axis, and a determining arrangement serving to determine the roll motion from a change in the optical path length of the roll motion-detecting beam. Thus, the determining of roll motion of the optical device, in particular of a means carrying the optical device, can be greatly simplified.

Advantageously, there are two substantially parallel roll motion-detecting beams of radiation spaced apart from each other and impinging upon the optical device because two such beams will produce at least one change in optical path length irrespective of a moving axis of roll motion. The optical device is preferably a diffraction grating associated with an interferometer. Thus, roll motion of the optical device can be determined and compensated for in a high- accuracy measuring system, such as a surface profiler. In order to reference the height of a surface being measured to the straightness of a light beam, the direction of propagation of that light beam should have a mathematical component substantially parallel to the surface of the object being scanned at all points along the profile scan section. For simplicity, it is to be assumed that the reference beam is nominally parallel to the best-fit straight line through that section. For a measuring instrument connected to a scanning head to be sensitive to surface height, there should be a component of a measurement beam perpendicular to the surface. That measurement beam may be locally generated or derived from the straightness reference beam. Alternatively, the surface height may be measured by a mechanical contact probe. The height of the surface may then be measured with reference to the position of the scanning head. A problem that occurs is then to compensate for errors in that measured height due to non-straight motion of the scanning head over the surface. This problem is alleviated by detecting motion of the scanning head perpendicular to the direction of the straightness reference beam.

In order that the present invention may be clearly and completely disclosed, reference will now be made, by way of example, to the accompanying drawings, in which:-

Figure 1 shows two per se known interferometer configurations sensitive to perpendicular motion,

Figure 2 shows a diagrammatic elevational view of a first version of a surface profiling system using perpendicular interferometers and constituting a first embodiment of the present invention,

Figure 3 shows a similar view to Figure 2, but of a second version of the surface profiling system and constituting a second embodiment of the present invention,

Figure 4 shows a similar view to Figures 2 and 3, but of a third version of the surface profiling system and constituting a third embodiment of the present invention,

Figure 5 is a diagrammatic representation of components of an interferometer sensitive to roll motion and constituting a further embodiment of the present invention, and Figure 6 shows a similar view to Figure 4, but of a fourth version of the surface profiling system incorporating similar components to that of Figure 5 and constituting a yet further embodiment of the present invention.

Figure 1 shows interferometer component configurations sensitive to perpendicular motion which can be interpreted as a geometrical change in the path length of the beam. The acronym OPD in the Figures is for Optical Path Difference.

The uppermost diagram in Figure 1 shows a diffraction grating 102 in the Littrow configuration where the diffraction angle equals the incident angle of a beam 104 which can be displaced by distance D owing to beam pointing instability, and the beam 104 is returned along its incident path. In this configuration, the grating groove profile is usually manufactured or blazed so that the efficiency is greatest for a given wavelength and blaze angle. The lowermost diagram of Figure 1 shows the geometry for a reflection grating 102a with the diffracted beam 104a retro-reflected by a mirror 106. The same geometry would also apply to a transmission grating.

In each configuration shown in Figure 1 , the sensitivity of an interferometer of which the shown configurations are a part, increases with the diffraction angle and thus with increasing groove density and/or diffraction order.

Figure 2 shows a diagrammatic layout of a long-trace profiler 200 which comprises a laser source 206 for supplying a laser beam for transmission by an optical fibre 208. Supports S indicate where components are mechanically coupled into a constant spatial relationship.

The reference of the profiler 200 is derived from a single-mode, fibre- delivered, laser beam collimated by a lens 210. The collimated beam has superior beam pointing stability because it is isolated from the thermal environment of the laser. The collimated beam is split by way of a beam- splitting and -steering optical arrangement 211 into two parallel beams 212a and 212b. The beam 212a goes to the first perpendicular interferometer 202 (Z- axis interferometer) connected to a scanning head 214. A diffraction grating 216 in the first interferometer 202 is coupled to a height measuring probe 218 which may be a contact (stylus) or non-contact (optical) probe, a contact probe being shown. The grating 216 and an interferometer beam splitter 220 are also coupled so that the output from the first interferometer 202 to a detector 222 is sensitive to movements in the z-axis direction (shown in Figure 2). The first interferometer 202 can be compensated for variations in the incident position of the laser beam due to pointing instability because of the presence of a second interferometer 204 (pointing interferometer), included to monitor this type of motion through receiving the beam 212b. The first and second interferometers 202 and 204 are referenced to the straightness of the laser beam 212b, with compensation for reference beam pointing instability. The second interferometer 204 is coupled to a surface 224 being measured and so does not move in the z- axis direction and is sensitive only to beam pointing variations. The output from the second (pointing) interferometer 204 to a second detector 230 varies with movement of the beam 212b perpendicular to itself. Errors in the probe z-axis motion due to beam pointing instability may be compensated for given a knowledge of the probe x-axis position. The probe x- axis position is measured by using a conventional displacement measuring interferometer (DMI) 226 and a mirror 228 mounted on the probe 218, the output of the interferometer in this respect going to a third detector 232. The DMI 226 may also be utilised to measure angular pitch errors in the motion of the scanning head 214 to compensate for cosine errors, the output of the interferometer in this respect going to a fourth detector 234. The DMI 226 can be optically connected to the first or second interferometers 202 or 204 by way of a beam splitter 227 (in Figure 2, the DMI 226 is optically connected to the first, z-axis interferometer 202). The DMI 226, the mirror 228 and the third and fourth detectors 232 and 234 are optional, the same data being obtainable by independent measurement.

In order that the pointing instabilities measured by the second pointing interferometer 204 are the same as those affecting the first z-interferometer

202, it is important that no extra instabilities are introduced by components that are not common to both beam paths. It is thus desirable that the beam-splitting and -steering optics 211 following the collimator lens 210 and the interferometers 202 and 204 themselves be of monolithic construction. Residual non-common pointing instabilities due to index gradients in air refractive index should be minimised by careful environmental control of currents and temperature. For example, the beam paths to the first and second perpendicular interferometers 202 and 204 might be enclosed in a common bellows arrangement and flushed with helium. Issues relating to temperature are not relevant if non-expansive materials such as "INVAR" (Registered Trade

Mark) are used.

An alternative embodiment of the profiler is shown in Figure 3 where like features of Figure 2 are shown with like reference numerals with the prefix '3'. In this arrangement, the beam splitter 311 (instead of the beam-splitting and - steering optics 211 of Figure 2) is mounted on the scanning head 314 of the profiler 300 and serves to direct the beam of light 312 to the first, z-axis interferometer 302 and to the second, pointing interferometer 304. A possible disadvantage with mounting this beam splitter 311 on the scanning head 314 is that it may introduce beam deviations due to scan motion errors that would cause an error in the output signal from the second pointing interferometer 304 to the detector 330. In this arrangement, the positions of the grating 316 and a mirror 317 in the first perpendicular interferometer 302 may be interchanged. Again, as with Figure 2, supports S indicate where components are mechanically coupled into a constant spatial relationship. In this embodiment, as with the Figure 2 embodiment, the DMI 326 is optically connected to the first, z-axis interferometer 302.

In a further version of the profiler, particularly where the z-axis range to be measured is relatively large, it may be desirable to measure probe z-axis motion separately to scanning head z-axis motion in order, for example, to minimise possible errors from grating non-uniformity. Such a system is shown in

Figure 4 in which the range of motion of the probe 418 in the z-axis direction is not limited by the size of the diffraction grating 416, as is the case with the versions of the profiler shown in Figures 2 and 3. Again, like features of Figure 2 are shown with like reference numerals with the prefix '4'. The profiler 400 comprises a separate probe 418 and scanning head 414 for z-axis measurement and a further displacement measuring interferometer (DMI) 450, for example a Zygo. differential plane mirror interferometer. The further DMI 450 receives a beam of radiation split from the beam 412a by way of a beam splitter 452, and a probe z-position detector 454 measures the position of the probe

418 in the z-axis. In this embodiment, the DMI 426 is optically connected to the second, pointing interferometer 404. The probe 418 comprises a mirror 456 mounted at its upper end for the purpose of optically communicating with the

DMI 450. Yet again, supports S indicate where components are mechanically coupled into a constant spatial relationship.

Cosine errors due to roll motions may also be compensated for by employing a roll-sensitive development of the perpendicular interferometer. A configuration of an interferometer using a diffraction grating that is sensitive to roll motion (rotation about the optical axis) is shown in Figure 5. The upper diagram in Figure 5 shows a plan view from above of components of an interferometer sensitive to roll motion and the lower diagram shows a side elevation of those components.

An incident beam of radiation 500 is split, by way of a. beam splitter 506, into two spaced-apart parallel beams of radiation 502 and 504 separated by a distance L. The spaced-apart beams 502 and 504 impinge upon a diffraction grating 508 (shown in the Littrow configuration) and are returned along their incident paths to a detector 510. When a roll motion of the grating 508 occurs about an axis parallel to the x-axis, one of the spaced-apart beams 502 or 504 gets longer while the other gets shorter, thereby imparting the necessary phase shift for the interferometer to measure that roll motion as detected by the detector 510. The change in path length for a small roll angle, α is given by:

OPD = 2Z. sin a. tan Θ

An embodiment of the profiler, similar to that shown in Figure 4 and incorporating similar components to those shown in Figure 5, is shown in Figure 6. Again, like reference numerals are shown with a prefix '6'. The profiler 600 is sensitive to roll motion about an axis parallel to the x-axis. In this arrangement, a reflecting diffraction grating 608 (in the Littrow configuration) is connected to the scanning head 614. The spaced apart beams 658 and 660 are returned along their incident paths to a 3-axis interferometer 626. The 3-axis interferometer 626 has three outputs to three detectors; a detector 632 for detecting linear displacement of the scanning head 614; another detector 634 for detecting angular pitch in the scanning head 614; and a further detector 662 for detecting the roll motion about the aforementioned axis. The 3-axis interferometer 626 is optically connected to the pointing interferometer 604 by way of a beam splitter 627. In a similar way to Figure 5, when a roll motion of the grating 608 occurs about the axis parallel to the x-axis, one of the spaced- apart beams 658 or 660 gets longer while the other gets shorter, thereby imparting the necessary phase shift for the relevant part of the 3-axis interferometer 626 to measure that roll motion as detected by the detector 662.

In each of the versions shown in Figures 2 to 4 and Figure 6, the support S on the right-hand side of the profiler system 200, 300, 400 or 600 could be omitted and be replaced by a mirror fixed relative to the surface 224, 324, 424 or 624 being measured, the mirror optically communicating with the second, pointing interferometer 202, 302, 402 or 602.

Such a profiling system 200, 300 or 400 can thus be utilised to perform very high accuracy measurements and be self-compensating for not only beam pointing instabilities, but also for errors in the mechanical motion of the scanning head 214, 314 or 414 across the surface 224, 324 or 424.

Although the description above has concentrated on applications to profiling, other applications, where measurements are to be made relative to a straight reference, will be apparent. Such applications may include three- dimensional co-ordinate measuring machines (CMM), and on-machine metrology for precision machining and precision motion control.

Claims

1. Apparatus for determining displacement relative to a reference beam of radiation, comprising an emitting arrangement serving to emit said beam, wherein said determining is by an interferometer detecting movement perpendicular to said beam of a received end of said beam.

2. Apparatus according to claim 1, wherein said interferometer is a component of a surface profiling system.

3. Apparatus according to claim 1, wherein said interferometer is a component of a co-ordinate measuring machine.

4. Apparatus according to any preceding claim, wherein said emitting arrangement serves to emit another beam of radiation, and wherein said determining is by another interferometer arranged to receive the other beam and for detecting movement perpendicular to said reference beam of the other interferometer.

5. Apparatus according to claim 4, wherein the other beam is emitted substantially parallelly to said reference beam.

6. Apparatus according to any preceding claim, and further comprising a height measuring probe for measuring a surface.

7. Apparatus according to claim 6, and further comprising a scanning head arranged to scan across said surface to be measured and having said probe connected thereto.

8. Apparatus according to claim 7, wherein said height measuring probe is rigidly fixed to said scanning head.

9. Apparatus according to claim 7, _t wherein there is an optical connection between said scanning head and said height measuring probe.

10. Apparatus according to claim 9, wherein said optical connection comprises a further interferometer effective between said scanning head and said height measuring probe.

11. Apparatus according to any one of claims 7 to 10, wherein said scanning head includes an optical device movable by roll motion about an axis, said optical device being arranged in a plane oblique to said axis, said emitting arrangement serving to emit a roll-motion-detecting beam of radiation impinging upon said optical device at a radius from said axis, and a determining arrangement serving to determine said roll motion from a change in the optical path length of the roll-motion-detecting beam.

12. A method comprising emitting a reference beam of radiation to form a positional reference, using said positional reference while using said beam for determining positional displacement of said beam and, in using said positional reference, compensating for said displacement of said beam.

13. A method according to claim 12, wherein said determining is interferometrically determining.

14. A method according to claim 12 or 13 and further comprising emitting another beam of radiation for further determining positional displacement relative to said positional reference.

15. A method according to claim 14, wherein the other beam is emitted substantially parallelly to said reference beam.

16. A method according to claim 14 or 15, wherein said further determining is interferometrically determining.

17. A method according to any one of claims 12 to 16 , wherein said reference beam is a positional reference straightness beam of a system for profiling a surface.

18. A method according to claim 17, and further comprising measuring a height of said surface substantially perpendicularly to said reference beam.

19. A method according to claim 18, wherein said measuring of said height is performed using a further beam.

20. A method according to any one of claims 12 to 19, and additionally determining roll motion about an axis comprising causing a roll-motion- detecting beam of radiation to impinge upon an optical device at a radius from the axis, and determining roll motion from a change of the optical path length of said roll-motion-detecting beam.