GB2069169A - Measuring apparatus and method for determining the three- dimensional position of a body - Google Patents

Abstract

An interferometer type measuring system determines the position of a body simultaneously in three co-ordinates. A laser beam is split (at 2) into three parallel beams and each is fed to an interferometer beam splitter (4) forming respective measurement and reference beams. The measurement beams each pass through a respective refracting wedge (8) deflecting the beam a predetermined angle from the axis of the interferometer. The three wedges are oriented at angular intervals about the axis to deflect their beams in different planes. Each measurement beam is reflected back on itself by a triple reflector (9) fixed to the body under test and again reflected back along the complete double path by a plane reflector (11) behind the wedge (8) and fixed relative to the beam splitter (4). The superimposed measurement and reference beams are each monitored by respective photoelectric devices (12) and the output signals of the devices (12) are fed to a processor (13) to calculate the positional changes of the body and reflector (9) in the three reference co- ordinates. The subtractions between the analogue output signals are performed before digitisation. <IMAGE>

Description

SPECIFICATION Measuring apparatus and method for determining the three-dimensional position of a body The invention relates to a measuring apparatus and a method for determining the threedimensional position of a body in a triaxial reference system. The apparatus is especially useful for determining translatory errors in multi-co-ordinate measuring machines or machine tools, and employs an interferometer system.

Length-measuring apparatus having interferometer systems, using lasers as light source, are known to be used inter alia for the determination of translatory errors in multi-co-ordinate machines, for example for determining the errors in measurement machines or machine tools. Interferometer systems are normally however designed only for length measurement in one direction, so that three-dimensional error determination is possible only with three separate measurement arrangements.

The simultaneous measurement of all three translatory errors of multi-co-ordinate machines, especially measuring machines, has hitherto been achieved with sufficient accuracy only in systems for scanning three-dimensional standards (for example rows of balls). These three-dimensional standards are however limited in size and have calibration points with fixed intervals. Thus the measurement is initially limited to a few points predetermined by the constructional design of the standard. The measurement operation becomes relatively complicated if the standard has to be shifted repeately in the working space of the machine.

In one known measuring apparatus of the initially stated kind (F. Ertl, Considerations on the accuracy of three co-ordinate measurement machines, Industrie Anzeiger, 1975, Page 197) for the determination of the three translatory errors of measuring machines, only one single interferometer system is used in which a laser beam, which serves for length measurement in the longitudinal direction of the beam, is used at the same time as an ideal reference straight line (Tooling-laser principle). The two translatory errors which do not coincide with the laser beam direction are ascertained by a photoelectric position detector and by two angle-measuring devices on the laser appliance.This measuring arrangement however in the measurement of straightness has a substantially higher uncertainty of measurement than the conventional measurement methods for ascertaining only a straightness defect (as for example the measurement of the straightness with a mechanical normal of glass or stone and a measuring sensor).

The present invention provides measuring apparatus for determining the three-dimensional position of a body in a triaxial reference system: the apparatus comprising an interferometer system having a source of three parallel monochromatic light beams; interferometer beam splitter means for splitting each beam into a reference beam and a measurement beam; a common triple reflector for attachment to the body, the position of which is to be determined, and a plane reflector fixed with reference to the interferometer splitter means for reflecting back the three measurement beams for superimposition on their respective reference beams; a respective photo-electric receiver for monitoring each superimposed measurement and reference beam; a respective refracting wedge located in the respective path of each measurement beam between the triple reflector and the plane reflector to produce a predetermined angular deflection of the measurement beam, between the wedge and the triple reflector, off the longitudinal measurement axis of the interferometer system; the three wedges being offset relative to one another about said measurement axis so that said measurement beam deflections are in respective predetermined planes containing the measurement axis; and a signal processor receiving the output signals of all three photo-electric receivers and arranged to calculate therefrom changes in the position of the body in the three axes of the triaxial reference system.

With the three measurement beams three length measurements can be made at the same time, each of these measurements being dependent upon the position of the triple reflector in the direction of the corresponding measurement beam. From the three measured lengths it is possible to describe the position of the triple reflector in the reference system using three linear equations, so that the signal processing apparatus can with simple calculation operations determine the position of the body, in the triaxial reference system or, in the particular application mentioned previously, ascertain the three translatory errors of the multi-co-ordinate machine.

Thus the time necessary for the measurement of deviations of position and straightness on measuring machines or machine tools is substantially reduced, since the time taken to measure the three translatory errors using the measuring apparatus of the invention is hardly greater than that for measuring only a single co-ordinate positional change with a conventional measuring apparatus, for example a simple laser interferometer.

Due to the simultaneous measurement of all three translatory errors for each individual measurement point it becomes possible to state the totality of the translatory errors of a machine in three dimensions. The errors measured with former methods on a calibration point on the other hand as a rule do not belong together, since they had to be measured at greater time intervals and by separate approach to the calibration point. This time interval causes an error influence due to a possible temperature drift, while the separate approach to the calibration point causes additional errors due to the machine straying.

The hitherto usual orientation of a laser interferometer for the measurement of the positional deviation took place according to measurement by the eye. For shorter distances this method is inadequate, since the deviation of the direction between laser beam and travelled distance becomes so great that an unacceptably high cosine error occurs. Due to the simultaneous measurement of both the straightness deviation and of the positional deviation in the measuring apparatus according to the invention it is possible for the cosine error to be corrected by calculation in a very simple manner.

Preferably, in the apparatus of the invention, the three wedges are angularly offset about the measurement axis by 1200 in relation to one another.

The invention provides, in another aspect, a method of determining the three-dimensional position of a body in a triaxial reference system, using the apparatus described in the preceding paragraph, wherein the output signals of the three photo-electric receivers are analogue and the changes in path lengths of the three measurement beams (AW1, AW11,AW111) are related to changes in the position coordinates of the body (Ax, Ay, Az) by the expressions: 12 # Cos # #x = #WI + #WII + #WIII # # 4 # Sin&alpha; # #y = - #WI + #WII 12 # Sin&alpha; # #z = - #WI - #WII + 2 # #WIII; the method including digitising directly only the output signal representing #WIII to product AD111, obtaining the difference by analogue means between the analogue output signals #WIII and #WI and between the signals #WIII and #WII, and then digitisign these difference signals to provide #DI = #WIII - #WI and #DII = #WIII - #WII the co-ordinates Ax, Ay and Az then being calculated digitally by the expressions: 12 Cos&alpha; # #x = - #DI - #DII + 3##III VW 4 Since Ay= AD1 - AD,AD 12 Sin&alpha; # #z = #DI = #DII.

An example of the invention will now be described in detail with reference to the accompanying drawings, in which: FIGURE 1 shows a measuring apparatus embodying the invention used for the inspection of a three-co-ordinate measuring machine; FIGURE 2 shows the beam path in the measuring apparatus of FIGURE 1, FIGURE 3 shows a plan view of the wedge plate, and FIGURE 4 shows in a diagrammatic illustration the influence of a shift of the triple reflector upon the optical path of the measurement beam.

A monochromatic light beam of high coherence generated by a laser 1, preferably an He-Ne laser, is divided in a triple beam splitter 2 by means of partially mirror-coated angle prisms 3 into three parallel light beams which are split in a further beam splitter 4 in a known manner, each into a measurement beam and a reference beam. As may be seen from FIGURE 1 a housing 5 containing the beam splitter 4 is arranged on a table 6 of a measuring machine, whereby the reference system for the measurement is fixed.

The reference beam in each case is reflected on a plane reflector 7 while the measurement beam passes in each case through a wedge 8 of a wedge plate 14, where it is deflected, as may be seen from Figure 2. After reflection on a triple prism 9 or triple reflector which is fitted on a spindle 10 of the measurement machine, the measurement beam reflected parallel to itself re-enters the wedge plate 14.

It is reflected into itself on the partially mirror-coated back 11 of the wedge plate 14 and passes back again to the beam splitter 4.

For operating the interferometer system it is possible to use either a two-frequency laser 1,the one part beam of which is polarised in the plane of the drawing (Figure 2) and the other part beam of which is polarised perpendicularly of the plane of the drawing, or a one-frequency laser 1 the light of which is polarised at 450 in relation to the plane of the drawing.

Irrespective of the nature of the laser 1 utilised, the beam splitter 4 generates reference beams which are polarised in the plane of the drawing and measurement beams which are polarised perpendicularly thereto.

The beam splitter 4 contains a V4 plate on each of the wedge plate 14 and the side facing the plane reflector 7, which plates ensure a rotation of the plane of polarisation of the returning measurement and reference beams each by 900, so that after travelling the measurement section the measurement beam is reflected in the beam splitter 4, while the reference beam after travelling the reference section passes unhindered through the beam splitter 4. The reference beam is united with the measurement beam returning from the measurement section. The united or superimposed light beam passes into a photo-electric receiver 12 having a polariser which brings about the interference of the two light beams.A subsequently placed photo-detector arranged in the receiver 12 receives a modulated signal which is a measure for the variation of the optical path length in the measurement section.

In Figure 2 the course of the measurement and reference beams is illustrated for one of the three light beams issuing from the beam splitter 2. This beam path proceeds, for the two other light beams issuing from the beam splitter 2, likewise in the manner as described, the wedges 8 necessary for this purpose being formed on the common wedge plate 14, which is illustrated in plan view in Figure 3. The wedge plate 14 consists of the plane-parallel plate with attached wedges 8, offset each by 1 200 in relation to one another about the measurement axis of the interferometer system. The wedge plate 14 is partially mirror-coated on the side facing the beam splitter 4, in the form of a three-pointed star, the mirror-coated zones lying in each case behind the elongated hatched zones 8.1, 8.2 and 8.3 in Figure 3.

The hatched circles 8.11, 8.22 and 8.33 in Figure 3 indicate the point of emergence where the measurement beams each issue from the wedges 8. In these zones the back of the wedge plate 14 is not mirror-coated.

The elongated hatched zones 8.1, 1.2 and 8.3 indicate the regions where the measurement beam reflected on the triple reflector 9 re-enters the respective wedge 8, before it is reflected on the back 11, mirror-coated in this region, of the wedge plate 14. From the diagrammatic illustration in Figure 4 it is seen that in the case of a lateral shift of the triple reflector 9 this entry point is displaced and that then the optical path length of the measurement beam varies.

The optical axis 1 5 of the interferometer system extends perpendicularly of the partially mirrorcoated back 11 of the wedge plate 14. Each of the three measurement beams is refracted by the associated wedge 8 by an angle a in relation to the axis 1 5. If the triple reflector 9 is displaced by a distance A z transversely of the axis 15, then the optical path of the measurement beam varies by A W = 4 A z sinew. The optical paths of the other two measurement beams then vary likewise, but by half the amount in the opposite direction.If the variations of the optical path lengths of the three measurements beams I, II and III are designated by AW1, AW" and AWtx and the components of a vector describing the displacement of the triple reflector 9 are designated by Ax, by and Az, then: 12 cosa Ax #x = BW, + AW11 + AW111 # 3 # 4 # sine&alpha; # #y = - #WI + #WII 12 # sine&alpha; # #z = - #WI - #WII + 2 #WIII The three interferometric length measuring apparatuses combined into an integrated system are sensitive to the displacement of the triple reflector 9 in the direction of the optical axis 1 5 of the system and also to displacement in each direction perpendicular to the optical axis 1 5.

From the variation of the three optical path lengths, which are detected in the three photo-electric receivers 1 2 and supplied as output signals to the signal processing system 1 3, by evaluation of the above-stated equations therein variation of position of the triple reflector 9 in the direction of the three axes x, y and z is ascertained.

Since the variations of the optical path lengths AW1, #WII and AW", are approximately of the same size, to calculate digitally the difference between two such approximately equal digital values would require a high number of bits, if the digitisation error is to remain small. A high number of bits at the same time would require high counting speeds for the digital counters. These difficulties are avoided if the differences are calculated before digitisation, by analogue means, as described bellow.

In a first stage, by analogue superimposition of the electrical signals, two signals corresponding to the differences #WIII-#WI and #WIII-#WII are formed. Then in a second stage, the analogue signals corresponding to the path lengths #WIII AW111-AW1 and AW111-AW11 are digitised and supplied to digital counters. Now the values: AD, = AW111 - AW1 AD" = #WIII = AW" and #DIII = #WIII are available in digital form at the output of the counters.

The following equations are then used in a digital calculator to ascertain the components Ax, Ay, Az of the vector which describes the displacement of the triple reflector: 12 # cos&alpha; # #x = - #DI - #DII + 3 # #DIII # 3 # 4 # sine&alpha; # #y = #DI - #DII 12 # sine&alpha; # #z = #DI + #DII.

Claims (8)

1. Measuring apparatus for determining the three-dimensional position of a body in a triaxial reference system: the apparatus comprising an interferometer system having a source of three parallel monochromatic light beams; interferometer beam splitter means for splitting each beam into a reference beam and a measurement beam; a common triple reflector for attachment to the body, the position of which is to be determined, and a plane reflector fixed with reference to the interferometer splitters for reflecting back the three measurement beams for superimposition on their respective reference beams; a respective photo-electric receiver for monitoring each superimposed measurement and reference beam; a respective refracting wedge located in the respective path of each measurement beam between the triple reflector and the plane reflector to produce a predetermined angular deflection of the measurement beam, between the wedge and the triple reflector, off the longitudinal measurement axis of the interferometer system; the three wedges being offset relative to one another about said measurement axis so that said measurement beam deflections are in respective predetermined planes containing the measurement axis: and a signal processor receiving the output signals of all three photo-electric receivers and arranged to calculate therefrom changes in the position of the body in the three axes of the triaxial reference system.

2. Measuring apparatus as claimed in claim 1, wherein the three wedges are formed on one common wedge plate.

3. Measuring apparatus as claimed in claim 2, wherein the back surface of the wedge plate remote from the triple reflector is partially mirror-coated and forms the plane reflector.

4. Measuring apparatus as claimed in any preceding claim, wherein the interferometer beam splitter means is formed as a single unit.

5. Measuring apparatus as claimed in any preceding claim, wherein the source of three parallel beams comprises a laser and a unitary triple beam splitter.

6. Measuring apparatus as claimed in any preceding claim, wherein the three wedges are angularly offset about the measurement axis by 1200 in relation to one another.

7. Measuring apparatus substantially as hereinbefore described with reference to and as illustrated in the accompanying drawings.

8. A method for determining the three-dimensional position of a body in a triaxial reference system, using the apparatus described in the preceding paragraph, wherein the output signals of the three photo-electric receivers are analogue and the changes in path lengths of the three measurement beams (AW1 AW11 AW,11) are related to changes in the position co-ordinates of the body (Ax, Ay, Az) by the expressions: 12 Cos Ax= AW, + AW" + AW, # 3 # 4 # Sin&alpha; # #y = - #WI + #WII 12 # Sin&alpha; # #z = - #WI - #WII + 2 # #WIII the method including digitising directly only the output signal representing AW", to produce #DIII, obtaining the difference by analogue means between the analogue output signals AW", and #WI and between the signals #WIII and AW", and then digitising these difference signals to provide #DI = #WIII - #WI and #DII = #WIII - #WII the co-ordinates #x, #y and #z then being calculated digitally by the expressions: 12 Cos&alpha; # #x = - #DI - #DII + 3 # #DIII # # 4 Sin&alpha; # #y = #DI - #DII 12 Sin&alpha; # #z = #DI = #DII.