A low cost laser interferometer system for machine tool applications A. Dorsey, R.J. Hocken and M. Horowitz*

A compact low-cost laser interferometer system for measuring linear displace- ments with sub-micrometer resolution is described and first performance evaluations reported. The four-photo-diode detector system can also provide a sensitive, simultaneous indication of straightness in two axes

Keywords: Interferometers, machine-tool control, linear measurement, lasers

It has been argued I that the relatively high capital cost of commercially- available laser interferometer systems has been the major obstacle to their widespread adoption as displacement transducers on a broad spectrum of measuring machines and machine tools. Equally, many laboratories and research establishments would benefit from the availability of a relatively inexpensive accurate digital linear measurement device. In order to address this need, the development of a compact low-cost system was under- taken at the National Bureau of Standards (NBS).

The prototype laser interfero- meter system described here uses a standard HeNe laser as a source for short distance measurements and should cost less than $1000. With a stabilized laser, the same system should be useful over larger distances.

Operation

The system is a variation of the polarizing interferometer first applied by Dyson 2'3 and used, for example, in the 250-mm diffraction grating ruling engine 4 at the National Physical Laboratory, United Kingdom.

The operation of the interfero- meter is straightforward (Fig 1). The horizontal component of the polarized laser beam passes through a beam splitter and is reflected by a moveable corner cube while the vertically polarized component of the beam is reflected by a corner cube physic- ally attached to the beam splitter. The reflected beams recombine at the beam splitter and are sent to the detector. Since the beams have travelled different distances, they wil l be phase-shifted relative to each other; ie, the phase of the

*National Bureau of Standards, Washington, DC 20234, USA tBrand names are used only to provide clarity and in no way constitute an endorse- ment by the National Bureau of Standards

horizontally polarized light is shifted by -2(d n - dv)/X relative to the vertical polarization, where the dis- tances to the moveable and fixed corner cubes are d n and d v, respectively.

The first element in the detector (Fig 2) is a k/4 plate with its extra- ordinary axis 45 ° from vertical which divides the incident light into parallel and perpendicular components. The result is that light polarized parallel to the extraordinary axis is a maximum when the horizontal and vertical polarized states are in phase and the light polarized perpendicular to the extraordinary axis is a minimum when the two beams are in phase. When the horizontally polarized beam is 180 ° out of phase relative to the vertical polarization, the situa- t ion is reversed; ie the light polarized perpendicular to the extraordinary axis is a maximum, and the parallel polarized li.clht is a minimum. The light leaving the ;k/4 wave plate is linearly polarized (to first order) with the direction of the polarization depending on the phase difference; ie difference in path length of the two oppositely polarized beams. In parti- cular, as the phase changes a ful l 360 ° the optical path changes by ;k and the cube corner moves ~/2, the polariza- tion vector rotates through 180 ° .

The light from the X/4 plate passes through a diverging lens and then strikes four photo-diodes mounted on the same header (UDT-PIN SPOT/8D+ t), Polaroidt sheets are placed in front of each photo-diode so that their polarization axes are at 45 ° to each other. When the moveable cube corner changes posi- tion, the polarization vector of the light at the detector rotates producing a sinusoidal current from each of the photo-diodes (Fig 3). A complete cycle occurs each time the distance to the corner cube changes by ;k/2. Since the signals from the detectors with polarization perpendicular to each other are 180 ° out of phase (1 & 3 and 2 & 4 in Fig 4) subtrac- t ion of 3 from 1 and 4 from 2 gives two pure sinewaves 90 ° out of phase.

The two resulting signals have the useful property that, if we let one represent the x and the other the y position of a point on a crt or xy recorder, then as the polarization of the incident light rotates through 180 ° , the point traces out a circle. Thus the detector transforms the distance moved by the corner cube to the position of a point on a circle. As the optical path difference between the reflectors changes by X/2 the position of the spot rotates 360 ° . The direction of rotation is clockwise for increasing

Polorizinq beam splitter

r ~ l = ~ "-'~---- _ ~ Movable corner

" ~ " ~ - cube

45 ° Polarizer Fixed corner cube

. . . . . . Vertical polarized light - - - - - Horizontal polarized light

Fig 1 Optical set-up of the interferometer

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Dorsey, Hocken and Horowitz - Low cost interferometer

distance between the corner cubes, counterclockwise for decreasing distance.

Electronic system The electronic system consists of four sections: the analog interface to the photo-diodes; up/down count genera- tor; up/down counter; and a zero offset corrector. The analog interface uses four low-input current operational amplifiers to perform the current-to- voltage conversion and the channel subtraction. The two resulting signals go to squarers which convert the signals to tt l logic levels. The squarers have hysteresis of about 0.02 V to eliminate oscillations at their outputs, resulting from noise. The output of the squarers then represents the quadrant of the circle that the signal is in (1= 00, 2 = 10,3 = 11 ,4=01) .

This two bit code is the input to the up/down count generator; for higher performance the circuit is synchronous. Two f l ip flops synchro- nize the input code so that it only changes on the rising edge of the clock, while two further f l ip flops store the position of the spot at the last clock pulse. The current position (Ql and Q2) is compared with the point's position in the last clock period (Q3 and Q4). If they are not

the same, the counter is clocked; the direction of the change is also sensed.

The need for a zero offset cor- rection arises from irregularities in the optical system. If the path of the moveable corner cube is not exactly parallel to the laser beam, the position of the beam on the detector changes slightly. This causes the maximum signals from the four detectors to be slightly different, resulting after sub- traction, in a sinewave with a slight offset which affects the performance of the squarers. To prevent this, the analog section can add or subtract an offset to each difference signal. The size of the offset signal required is determined by looking at the average value at the difference signal when the corner cube is moving at a rate greater than a preset rate (about 2 kHz at the detector or 0.7 mm s - ] ). Since this should be zero, the correct offset level can be found. These offset signals come from two d/a converters so they remain constant when the corner cube is moving too slowly for automatic correction.

This offset adjust can also be used to provide a sensitive indication of straightness in two axes.

Evaluation It was clear from the outset that the

resolution and repeatability of the interferometer would be well below the levels required for the vast majority of programs at NBS. Since the intention of this short project was to demonstrate in principle a low-cost system with adequate performance for most machine tool applications, perform- ance evaluation was limited to a simple comparison with a commercial laser interferometer system.

The Hewlett Packard 5500C[t ] interferometer was chosen for com- parison. The test was set up on a 6-m way bed in a room with an environ- ment controlled to approximately +2°C. Both lasers were placed on a platform set at the end of the bed. The two remote interferometers (polarizing beam splitters with corner cube attachments) were mounted f i rmly on the way bed, and the move- able corner cubes were attached side by side to the carriage that rides on the bed. This system provided a relatively smooth and continuous method of moving the corner cubes.

To start the test, the Hewlett Packard (HP) system was set to the •/4 mode, in which the compensation mechanism for wavelength changes is inactive. Since both lasers are o'f the HeNe type, air temperature, pressure, and humidity changes have a negligible

Electronics for photodiodes Detector /

Diverting / / ~ , lens )i" / r~ ~-~

L Polarizers Photodiode (.

t ~ Plate

Ordinary axis 1 fExtraordinary axis

Polarization of -X 4 Plate Diverging lens 4 polaroid sheets incident light (arrows denote

polarization )

4 photodiodes

Fig 2 Detector

o A \~[,'/

" .~ -2i(~-~)1~ / - - A e ' ; '

o A A(I *e-~) I /

Y A~ _,,A ( I,~2-*)___. ~

J, -Ai~ d/I

Fig 3 Effect of X/4 plate on polarization

30 J A N 1983 V O L 5 NO 1

Dorsey, Hocken and Horowitz - Low cost interferometer

effect on the differences of the two readings, and thus no data were taken on these variables.

The carriage was moved in incre- ments 500 000 X/4's (about 79 mm), and readings from both systems were recorded. The yaw of the carriage on the way bed was then measured over the same distance, using the HP angle attachment, and a correction for this systematic angular motion applied to t h e data. (Because of the offset between the two interferometer positions, the yaw caused a difference in the readings due to the Abbe offset.) The corrected differences between the two systems are shown in Fig 5. This graph is the average of the forward and backward measurements of two runs for both yaw and deviations in displacement, thus reducing any time dependent dr i f t in the data. This measurement covered approxi- mately 1.5 m, with a maximum deviation under 0.5/Jm. This distance covers the realm of most applications, although with a collimated beam the device could be used for longer lengths.

Comments The maximum deviation measured (five counts) is rather large, but not unexpectedly so. It is believed that with more rigorous testing, with pre- cautions to eliminate uncertainties from environmental and thermal effects (such as mechanical deforma- tions due to time-dependent tem- perature gradients), the maximum deviation would be substantially reduced.

Mode hopping by the laser was not a serious problem because a Tropelt stabilized laser was used. The cost of less than $1000 did not include the Tropelt laser. In other experiments using a very inexpen- sive HeNe laser over short ranges, mode hopping did occur until the laser had reached operating tempera- ture. After warm-up, mode hopping was not a problem.

I / \ I / - - - " , , I Polor izot ion of the licJht Detector I

Detector ;3 0

De,ector 4 ~ ~ % o

Fig 4 Ohoto4iode output current vs polarization

/<

O >

2

I

- I - -

- 2 I I I 0 2 4 6 8 IO 12

Displacement ,X /8 x I0 a

I I I 14 16 18 2 0

Fig 5 Deviation of the low,cost interferometer from the HP system

References 1. Bai ley W . P . N . Gratings or lasers?

Precision Engineering, 1980, 2(3), 129-132

2. Dyson J. Physic.a, 1958, 24, 532

3. Dye,0n J. Optical Soc. of Am., 1963, 53, 690

4 . Evans C. Design and Construction of a Large Grating Ruling Engine. Precision Engineering, 1981, 3(4), 193-200

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