COMPENSATION OF COMPARATOR ERROR OF AN INTERFEROMETER Ya. M. Kandel'

UDC 531.715.1.088.6

A drawback of longitudinal comparators with a parallel arrangement of the measurement lines is the presence of a comparator error when measuring length. The comparator error A occurs due to nonrectilinearity of the displacement of the carriage along the guides. For small angles of rotation of the carriage A =h~,

(1)

where h is the distance between parallel measuring lines. Satisfaction of the Abb$ principle reduces A to a value of the second order of smallness, but requires an increase in the length of the guides and the carriage, and also worsens the temperature conditions of the measurements. Hence, considerable attention has recently been given to methods of reducing comparators constructed without satisfying the Abbe principle. There are two ways of reducing A when h ~ O: by correction of the position of the carriage, and compensation of the comparator error. Manual correction of the position of the carriage with interference control of its angle of rotation, first used in the universal interference comparator [i, 2], is simple and reliable, but is not suitable for automatic measurements. An advantage of the automatic carriage position correction system [3-5] is the possibility of using it for comparators of any kind. Thus, in interferometers with plane reflectors and interference fringe counters, automatic correction is also used to stabilize the carriage in the plane of the photoreceivers [6]. Automatic correction of the carriage position in a vertical plane using the force of gravity is described in [7]. However, the complexity of automatic correction systems makes them difficult to use. Compensation of A was first achieved in measuring machines in which, using a special optical system, a correction A ' = A was automatically introduced as a result of the measurements. In interferometers an electron-optical instrument is used for this purpose. For example, in a laser interferometer [8], A (which reaches i0 ~) is compensated by an instrument containing a photoelectric autocollimator, a plane reflector, mounted on the carriage, and an electronic circuit. An analog signal from the autocollimator proportional to the angle of rotation of the carriage is applied to the electronic circuit where it is converted into pulsed signals proportional to A. In the computing unit, as a result of the measurement of length, corrections are introduced for the temperature and pressure of the air, the coefficient of linear expansion of the measured object, and A. In interferometers [9, i0] A is compensated in the same way. In an interferometer one can compensate A more simply by introducing a plane-parallel transparent plate into the arrangement [Ii]. Consider the interferometer arrangement shown in Fig. i. Monochromatic light from source I, after collimator 2, falls on beam splitter i0 as a parallel beam. A part of the beam passing through plate i0 falls on fixed reflector 9. Part of the beam reflected from i0 travels towards another mirror 4 through plane-parallel plate 3 to reflector 8. When measuring the length of line standard 5 or some other object microscope 7, 8, and 3 together with carriage 6 are shifted with respect to fixed scale 5. On displacing 6, the light flux of the interference pattern modulates on photoreceivers of the electron counter of the interference fringes ii the electrical signals recorded by this counter. As is well known [12], 3 introduces into one arm of the interferometer a path difference ~ equal to = 2t ( V n ~ - - sin 2 t - - cos i ) ,

Translated from Izmeritel'naya Tekhnika, No. 12, pp. 16-17, December,

(2)

1976.

This material is protected b y copyr~ght regigtered in the name o f Plenurn PUblishing Corporation, 227 West 1 7th Street, N e w York, iV. Y . ~ 10011. N o part ofthispublication may be reproduced, storedin a retrieval system, Or transmitted, in any form or by any means, electronic, [ mechanical, photocopying, microfilming, recording or otherwise, w i t h o u t written permission o f the publisher. A copy o f this article is [ available from the publisher for $ Z 5 0 . I

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-/

i~v

v

"\

v

v

v

v

e

v/I

Fig. i

Pig. 2

where t is the plate thickness, n is the reflective index of the plate material, and i is the angle of incidence of the beam on the plate. Plate 3, attached to the carriage, progressively displaced with the carriage, can be rotated around three mutually perpendicular axes. Rotation around the Oy axis (Fig. 2), parallel to the beam of light incident on the plate does not change the values of ~ and i. When it is rotated about the Ox axis by an angle ~ and about the Oz axis by an angle ~ the value of ~ changes since i = f( ~, ~). The plane P1 (see Fig. 2) is parallel to the Ox axis and inclined to the Oy axis at an angle io. The plane P2 is obtained by rotating the plane PI around the Oz axis by angle ~o; ONI and ON2 are the normals to the planes. By determining the direction cosines of ON1 and ON2 we find cosi-eos~cos%. After

substituting

Eq.

(3)

into

Eq.

(2)

we

(3)

have

6 = 2 t ( g n ~ -- |m cos ~ io cos ~ ~o -- cos io cos *o).

(4)

The additional path difference due to rotation of the plate by angles ~ and ~ will be

d6 = 2 t , I - -

Since dio = ~, when 4o = 0

cos io cos ~o

]/-n 2 - - 1 + cos '~ io cos = ~o

) ,(sin io cos ~o dio -k cos io sin t~o d ~ ) ,

d~o = ~, then when io >> ~o the second term in Eq.

d8

= 2t sin io ( 1

cos io ~ n 2 - - sin2 io / ~"

Hence it follows that when ~o = 0 the additional is independent of small rotations of the plate about mentally by rotating a transparent plate 60-mm thick interferometer. The angles of rotation of the plate

(5)

(5) can be neglected, and

(6)

path difference of the interferometer the Oz axis. This was checked experiintroduced into the photoelectric laser were measured with a graduator.

An inclination of the carriage of the interferometer by an angle simultaneously affects A and the additional path difference d~. To satisfy the compensation condition A ' = --A = d~ it is necessary to have a plate whose thickness, according to Eqs. (i) and (6), is

t=h

/2 s i n i o (I

oo. )"

] , / ~ - - s i n ~io

The accuracy of the compensation depends on the value of A and on the accuracy with which Eq. (7) is satisfied. For example, continuous automatic compensation of A when h = 60 mm can be achieved using a plate of TF-10 glass of thickness of (71.6• mm, and io = --45 ~ i20', and the uncompensated residual error will be less than 0.01 A. The drawbacks of this compensatio n system are the increase in the light losses and the impossibility of using it in interferometers which operate at several wavelengths, since

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n = f(%). However, the simplicity and reliability of this compensator enables it to be used in automatic interferometers. LITERATURE CITED 1 2 3 4 5 6 7 8 9 I0 ii 12

M. L. Brzhezinskii, Soviet patent No. 113,992; Byull. Izobret., No. 6 (1958). M. L. Brzhezinskii, Tr. Inst. Goskomiteta Standartov, No. 78/138 (1965). C. Hoffrogge, Microtechnik, 15, No. 6 (1961). M. L. Brzhezinskii et al., Soviet patent No. 214,093; Byull. Izobret., No. ii (1968). French patent No. 2,088,675 (Jan., 1972). H. D. Cook and L. A. Marsetta, Eng. Instrum., 65, No. 2 (1961). East German patent No. 58,177 (October, 1967). Morokuma Tadashi et al., Byull. Jpn. Soc. Precis. Eng., ~, No. 4 (1970). Japanese patent No. 48-6493 (February, 1973). US patent No. 3,820,902 (June 28, 1974). Ya. M. Kandel, Soviet patent No. 301,520; Byull Izobret., No. 14 (1971). A. N. Zakhat'evskii, Interferometers [in Russian], Oborongiz, Moscow (1952).

APPARATUS FOR DETERMINING GEOMETRICAL PARAMETERS OF SURFACE QUALITY V. O. Aulis and A. S. Ionans

UDC 531.717.82

An increase in the demand for surface quality has created the problem of establishing high accuracy in measurements of surface roughness: roughness, undulations, and deviations in shape. In order to obtain a qualitative picture of the surface it is necessary to measure surface roughness parameters along several paths in different directions, and to connect the paths with repeated measurements [1-3]. To this aim an apparatus was developed which extends the metrological possibilities of the model-201 Kalibr profilograph--profilometer. The apparatus allows the roughness of rotating surfaces to be measured in different directions. The apparatus consists of three basic units: the apparatus itself with the motor drive, the rotating table, and generator supply of the motor drive (see Fig. i). The apparatus in the center. In ied to be centered ing depends on the

consists of a base on which are fastened a front chuck and a rear chuck the front chuck is a shaft whose construction allows the object to be studeither in the jaws of the chuck or on a plane disc. The method of mountshape of the object and the nature of its surface.

The apparatus is positioned on the table of the profilograph--profilometer a rotating table with the help of a directional cotter, springs, and cams,

(PP) or on

The study of surface roughness along the axis of rotation of the object does not differ from the usual operation of the PP: The displacement of the PP transducer along the surface to be studied is carried out by the PP motor drive and the apparatus is only used in the mounting and fastening of the object. In order to remove the profilograms ject a rotating movement of the shaft of by the shaft from the motor drive of the is disconnected during this operation). the surface to be studied depends on the the corresponding reduction gear for the rent power supply for the electric motor.

from the vicinity of the rotating surface of the obthe apparatus is used. The rotation is transmitted apparatus through a pair of gears (the PP motor drive The required magnitude of the angular velocity of diameter of the surface and is obtained by choosing motor drive and adjusting the frequency of the cur-

Translated from Izmeritel'naya Tekhnika, No. 12, pp. 17-18, December,

1976.

This material is protected b y copyright registered in the name o f Plenum Publishing Corporation, 2 2 7 West 1 7th Street, N e w York, N. Y. 10011. N o part o f thispublication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, w i t h o u t written permission o f the publisher. A copy o f this article is available f r o m the publisher f o r $ Z 5 0 .

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