A LENS C O M P E N S A T O R FOR T E S T I N G A U T O C O L L I M A T O R S

V. D. L i z u n o v , N. F . S e k u s h e n k o ,

M. S. Z i l ' b e r m a n , a n d V. V. K o p y t o v

UDC 535.885.5.089.6

Theodoli tes of the TO5 and T1 types or opt ica l wedges are frequently used in order to de termine the errors

of autocol l imators [1].

The mean square error commit ted in measuring angles with the TO5 theodol i te may be as much as • 1" [21. The accuracy of testing the autocol l imator is considerably affected by the mutual disposition of the theodol i te and

the autocol l imator .

Opt ical wedges are compl ica ted to make and inconvenient to use. The scale of an autocol l imator may only be tested at discrete points with the aid of these devices. Thus for testing a s ix-minute range at intervals of 1' a set of six wedges is required.

In this paper we shall consider the possibili ty of using a device with a var iable wedge (an opt ica l lens com-

pensator) for testing autocoll imators; the lens compensator is i l lustrated in Fig. 1.

The lens compensator constitutes an achromat ic system comprising two lenses (a movable posit ive lens 3 and a stat ionary negat ive lens 2) of the same opt ica l power and opposite signs. These form an afocal opt ica l system. The focal length of each lens is equal to 6413 mm.

The compensator is p laced in the path of a para l le l beam of rays arising from the col l imator 1. If the opt ica l axes of the lenses coincide, the beam of rays passing through the col l imator will not alter its direct ion. If the lens 3

is displaced in a di rect ion perpendicular to the path of the rays through a distance a , the beam will change its d i r ec - tion by an angle c~. The following approximate equation will then hold

1

where f is the focal length of the lens.

\ f

7

5

Fig. 1

Translated from Izmer i t e l ' naya Tekhnika, No. 6, pp. 23-24, June, 1975.

�9 1975 Plenum Publishing Corporation, 227 West 17th Street, New York, N. Y. 10011. No part o f this publication may be repro- duced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, micro- filming, recording or otherwise, without written permission o f the publisher. A copy o f this article is available from the publisher for $15.00.

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R _~ --L

Y z~ , . - ,

i

Fig. 2

TABLE 1

Readings of the compensator scale

0 58"

1 '11" 1'17,2" 1 '43" 1 ' 5 9 , 5 " 5 '03" 6 ' 04"

Angular devia t ion determined with mi - crometer eyepiece of the te lescope

0 58 ,01 1 ' 1 0 . 9 4 " 1 ' 1 7 , 5 0 " 1 ' 4 3 , 3 0 " 1 ' 5 9 , 9 " 5 ' 0 3 , 3 " 6 " 0 4 , 1 "

The degree of approximation provided by this equation is quite

high: the error is of the third order of smallness. The value of a is

determined from the scale 4, which is r igidly fixed on the framework of the movable lens. When the lens of the compensator moves, the lines on the scale move in the field of view of the reading microscope 5. In order to ensure smooth motion of the lens a guide screw is pro- vided in the housing of the compensator; i t has a smooth cyl indr ica l guide and a threaded surface; a nut moves along this guide together with a movable frame. A guiding groove in the body of the compen- sator l imits the rotat ion of the unit around the screw.

Our experiments with the lens compensator were concerned with

the quali ty of the image, t h e existence of focusing properties, and the error in the def lec t ion angle.

The quali ty of the compensator image was est imated by reference to the diffraction image of a point in an

apparatus consisting of a co l l imator with a focal length of 1200 mm and a microscope with a magnif icat ion ors0 x.

The focusing characterist ics of the compensator were determined in an apparatus containing a co l l imator (a

cross-wire being placed in the focal plane of its object ive) and a telescope with a micrometer eyepiece , Using a rack and pinion the te lescope was focused on the image of the col l imator cross-wire; using a scale with a vernier, readings were taken before and after placing the compensator under test between the col l imator and the telescope. The difference in the readings was 0.9 mm.

The focusing property of the compensator was determined from Newton's equation

x x ' = I f ' ,

where x' is the d isplacement of the rack and pinion of the telescope, f ' is the focal length of the te lescope ob jec -

tive, and f is the focal length of the co l l imator objec t ive . For f = 3000 mm and x' =0.9 we have x= 10 kin.

This focusing property of the compensator introduces a systematic error commit ted in measuring an angular

def lect ion with the compensator. The horizontal and ver t ica l lines of the micrometer eyep iece of the telescope were made to coincide with the image of the col l imator cross-wires. The compensator was placed between the co l - l imator and the telescope in such a way that for a zero reading of the compensator scale the image of the c o l l i m a - tor cross-wire did not move re la t ive to its original position. We set a specific value of the angle along the c o m -

pensator scale, and using the micrometer eyep iece of the telescope determined the transverse d isp lacement of the image of the ver t ica l l ine of the col l imator .

The angular d isplacement was determined from the equation

h ~ - f ' , (1 )

where h is the d isp lacement of the image determined by reference to the micrometer eyepiece , f ' is the foca l l eng th of the telescope object ive .

The accuracy of measuring the def lec t ion angle depends [as may readi ly be seen from Eq. (1)] onthe error c o m - mi t ted in reading Ah with the micrometer eyep iece and the error commit ted in determining the focal length A f ' .

830

Thus

(2)

For f ' -- 3000 mm, A f ' is no greater than 0.003-0.005 mm.

The focal length of the telescope objec t ive was determined in an Abb6 focimeter by a method based on m e a - suring the magnif icat ion of the test objec t ive for several positions of the object . An analysis of the results of m e a -

surements carried out by three operators showed that f a v = 2997.88 ~ 1.18 ram.

Taking the error in the readings of the mic romete r eyepiece as 0.005 mm and the error in measuring the

focal length of the microscope as 1.18 ram, we may ca lcu la te the error commit ted in checking the s ix-minute range of the lens compensator

r' J +_0.47,,

The accuracy of checking the lens compensator may be increased by increasing the measuring accuracy h.

The total error of the compensator is influenced by errors arising from the noniineari ty of the motion of the

lens, the nonperpendicular nature of the motion of the co l l ima tor re la t ive to the op t ica l axis of the system, and the lens aberrations. A de ta i led anaiysis carried out in [3] shows that these errors are no greater than 0.01" and may be

neglected.

Table 1 shows the results of some measurements of angular deflections for various readings of the compensator

scale. The maximum angutar deviat ion is no greater than 0.4".

The compensator may be used for determining the error of an autocol l imator by either of the two procedures i l lustrated in Fig. 2a, b, where 1 represents the autocol l imator under test, 2 the lens compensator, 3 the telescope, and 4 a mirror.

When working with the arrangement of Fig. 2b the scale divisions of the lens compensator are reduced by a factor of two.

Lens compensators have a much smal ler error than theodoli tes and opt ica l wedges (Ac~ < 0.8"), compactness

of construction, and s impl ic i ty in use. The apparatus may be widely used for determining the error in the readings of AK-0.25, AK-0.5, and AK-1 autocoll imators .

1,

2.

3.

LITERATURE C I T E D

All -Union State Standard 18806-70. Autocoll imators. Methods and Means of Testing [in Russian].

Al l -Union State Standard 10620-70. Theodolites. Types. Basic Parameters and Technical Requirements [in Russian]. E. I. Finkel 'shtein, Opt.-Mekh. Prom., No. 6 (1973).

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