Use of some statistical techniques in optical metrology

Use of some statistical techniques in optical metrology

Citation for published version (APA):

Telli, S. (1968). Use of some statistical techniques in optical metrology. (TH Eindhoven. Afd.

Werktuigbouwkunde, Laboratorium voor mechanische technologie en werkplaatstechniek : WT rapporten; Vol. WT0201). Technische Hogeschool Eindhoven.

Document status and date: Published: 01/01/1968

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techrii'sche hogeschooi eindhoven -, t; . , . .

·Jaboratorium voormo~hani5che techno/ogie

en

werkplaatstechniek ," , rapport von de sedie: "

Werkplaatstechniek.

OF. SOME. :STATISTICAL TECHNiQuEs

,'~IN

' ( , ' , " ~.,

, . , ' i i '

.", '~samenvattin~J~l' :;. _,

\t'%~;'~:'7/::

)/'tJ

l .

;~~:;;)

(1.

Dete".uomw.' .... n ... i""n~g. accuracy<;>i

::;a,.thelPdol1te and a coU::Lmator.introducing a

_. . / I . -to', ,.}.J.,

lA:·

~ J.,~;~. c~~

:1~;}

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f;:.::'~:':_. :-;.'--, .

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blz.~n

van ?

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rapport nr. . codering: datum:

29/5/1968

aontal biz. ?"

bijl. 1/4.

geschikt vO\)r ,,~:: publicatl. In: . ' -.".' .

RaEEort nr .. 0201 .

,..'

" . R £ P

b

R T

o

N T H E SE CON DP', R A e T I C A L P E R . I ·0 . D Sub j e c, t Metrology

Place : Eindhoven Technical University Mentor Partioipaat ,Period' , . Nr.ofpages :

6

Nr.of appendices :

4-" Nr.of copies required by men to! : .1.

Nr. of. copies required by participant' : 2

"

; '.~

-

.

", 1 ..;

I N

'1'

RO'D U C '1"I 0 N

Rapport. nr .0201

, . 'Metrology 'laborator1 ,18 EINDBOVEN·TECC'B1UCAL 'UNIVERSITY wllere ,I studied

"~

..

~" , ,

durillg ~ eecoild, practictil periollt~s one :of ,t.he practice laboratories' for the

.'

...

.

mqob.a:ldcal eng~eeriag. studients. ,1'here 8.l"e maJlY'ldndof measurement appliances

for various ld.ild of purposes.

I.espe~iall3' interested in the optical ones.Therefo~e I made a ~omplete

expertmeutw1th the ,a~to,:",coli:imator and thEfdol1te using a machine to~l tUrn

table' to determine its accuracy ..

l

This experiment has ~ee~ peing used inpr~c.tice too.Before explaining.

,

~

, the

e~eriJnent which Ib4ve done,I fihould like to gi'Ye some tnformation, about

. j ~ . i _,

.

; , auto-collimators

on17

0 i

./ j

I '

This apparatus,. is ,tised for checking the alignement' or straight~fU!UlJ' or

,~bmina11Y

fiat surfaces 'and,DY

~

a'xteu"tlon 'of the

~ethod'

the areas of

l~'ge

, ' /f"

. , ' " .

. . , . .

. '

.. "

' :

" ,

i'f~at surfaces.Norni.al17~the e1'1St~ument is used for measuring the straighm..es8

i

f

~/~. ~ ~ ..

l,of long and rel,atirelJ,'ilarrowsurfa.ces such as the beds of long latlies~d

pIa.-I ' ~ •

. :; . 1 ' '. , , ' .

{'}niiigmaChines.Itsoudhere be polntedout thatth~auto"':collimator is used, as

.) .

~

r::

y

, ;a paral].e1beams'o.fligJit' S011rce f9r this exper1~ent which I' have done,,~

"

The princ~ple of ·the instrument is' iilustrateditl " App:' 1, F~~,:

,3 ".

: Referr1Ds. to 'that ~igur~~grati.eule 'G' isstuated in the princ~pal. focE!l. plane

" . "

,.. 2,-' Rapport nr.0201

!

tb.ia plate .0 f 'clear glaijs R " Light'rays from the 'centre _, It of the graticule'i

lying on the a.rlS 'ot l~ns'

,

_,

"

a:O.lhIr this beam, is intereepted by a tdrror)'1 whoaereflecting : surface is

square to the telesoopearls,theil the ,light raY's are re'flected

'back

upon' their

, ,

orig:i.na1paths,~d re';'entel"ingthetelescope,f~rm ~ image of. It coincident

, 'I

with the point' It itself. A propo'rtion

of

this reflected light is transmitted

. ,

by the plate R arid ent~rs the, ,eye of the observer,who sees one image only ,

of the point· K .If the, mirror is inclined at 'an angle' W to the axxis,however,

"'i-the incident light rays are renee't,ed baCk at an angle, 2W with their, original'

\

direetioll,an re-entering ,the telelScope the7:form _{. , . . .} an image of It at It' . , .., where ,

renected back bY. the components of telescope, and ',an image at K' formed

.7,

the light reflected by the mirror M ~By, 'tilting the mirror un~U 'K' coincides

nth K, i t is, se't accUratel.,. square to the telescope

arls.Con:ve~~eli,'tiif

the"

r . _ t I

mirror is known to be square to thfsax:is,then the point K can be set _{. ,} ~pon the

axis by'adjusting the graticul~ until It and its refiectedimage oo1!ncide •

. ~ • • 1

Moreovet₉provided that the mirror is f'lat,fot' K' andK' to be sharPly focuSed

in 'the same plane, they must both be in princj.p~ focal plane .of theobjeftiyeJ

th1s provides a ready me,ansof'

adjust~~g

the telescope for infirdtYfOCUS;\that. is

, \ .

.

.

of setting'the grat:1cu1e in the focal plane ..

,

" .

By'the provision or a suitable sc8.le on the,graticulethe actuait1lt of the mirror can be measured,since 'the refiected ray is i'riclined to its ioriginal

, I ·

, i '

.

d:irectiOD. by an'angle ,equal to twice that, through which the mirror ',is tUtefi_{t .}

Ra ppor,t nr. 02.01 " '

ai:1dcollimator of the sameo'p.ti;caJ.., performance • Since for !1. tilt W of. tbe ,mi:J:'ror

the late,ral ,denectioll in the fo~ai plaD~ of,the ,o~jectiv~ isfo.tn.g·Z\f $ this

corresponds

to

0.006, U.per. minute ,for 'an object glass of 10 ill. foc~ length ..

Any pro~lell ill .bich the ,tilt of

a

carriage' is ,to, be observed,s~ch as in ,tile

exa-m1nation of a m~chine bed or surface plate for stra.i:ghtness,can be ,dealt with

'!!Sing an autocoll.imator bysecurelymounting a mirror on the ,c~riag.e!,Asin the.

case .oftelescope, and collimator ,the accuracy of such ,measurements;is independent

_.

,

,

of the distance between instrument and mIrror,proVtded thet atmospheri~ conditio~

do not impair visibiiity.For a given range of meaSurement,however,the maXimum

. "" , . .

operati,'re distance' is limitedtthis limitation beilig set by the maximum angle.

, . , ' .

. ,

i t 'is required to meas_Ul18 and the diameter of the obje,ctive.For tilt to be

measu-rable tile reflected ligldl raysml18t ~e-enter the objective ,and it is appare~t

that the farther'away the mirror~is from the object glass the smaller is the per ...

, mi.ssible tUtfor thill condition

to

be, satisfiedo

As I have l'l1en,tioned bef<U"e')the autocollimator is used cDJ.y' for

aux-" ~ I . , ' . '

ialary purpose in my experiment • That is to say it was only a fix target for' the,

theodal:i.te measurement. (See appn,Fig:2)

EXPERIMENT

. A - P r o b 1 em:

To estimate the 18et~1:t14rerror"of the turn-table and introduce' a

.c'or-. recting curve.c'or-.

B - S e't t i n g (See: Fig: 1 )

- 4- ...

Rapport nr.0201 ;

Every

6

revolutions of the handwheel corresponds to 20gons

=.18

degrees

~:

of the tur,n table.

:T.

I have taken the theodolite readings for each 20 gons i~ two revolution of the turn-table .. Results are _.. ta~ulated b(;app:2) .. Inevery settilig of the table

' , - . " . "

two readingaare made /jilst changing the·thedolite sett1.ngo

C - S o l u t.i 0 ~

•

Heasuring error of the turn-·table ·is

7.,71

second of arc for· each setting of the handwheel.

- Correction curve ip draW1l'in( app:

4 ) ..

P -

Mot i v a t i o n

Through the columns

nr:4

and

8 :

'.Q ·m 8.88ll gons, is· cal.cUlatedoApart irem thatvaltte :

St = t.~ c

0,887

.~

O,OOll :: 0,00098

goDS. =

3,11

second of arc"

This is the theodolite read:ing error.

, ( .App :

.3 ).

has been showing the range ,chart of reading angles.~here:

L.C .L. :: 0,04 • O,Oon

=

0,000044 rv·O

gon.

Since .all .the values are within the statistical; ·control limits.,there is no systematic difference between the range

.

values. I

,

~

.

.->~

9

th

The COlU1l111 nr: 10 is showing the differences between · t h _'5 and

columns. Through this. column. :, , . . ,

,Rapport nr 40201

are calcUlated. Where,:

1:1 Measuring errPr: of the whole system and comp()seci of two errors : " ,

Where ,

_St

&::: 'rhedol:i.te readi.lig, erro~, -

0,00C?9S

~gons ,

Thus ':

=

O,002}8" goDs

"

.

D - C 0 ,n c 1 u '~ i o n ': 'I

Thi.s :Ls the me~uring error, of the turn-table wh±ch I wanted

,

-. to find aut.

NOT: Therei.$ no ,sy~tematic difference bettween the values in the'

column nr: lO, 0 Beacouse 'Hn>' : t '"

a

=

0,

a _

SdlFn., :'

0,,001.42,. V

-

0,0035

21.

.

=

1,86

"

'1,86,

<.

t_{1_-}

,~

( 2 0 ) , ,fa

2~t

086

, "

Tht.s t hypo t'hesis is accepteti" . '1', .

'~.,"

,',

, ' .

(. App:

4 )

'is showing the ,cumulative correction curve thi-ough'the . va.1~es .in 'c·olumn·· Dr : "12 •. Ca1cuia.tio~ o·r. th:ls column vaiue's is" rna'de as fo11ow':

.... 6 ;,;

Rapport.nr.0201 " . F~st.valu.e : •• i

100,8846

+1.001

879

1 ' - .'(,

80,8~45

....

80_J

8773 )

.m: 20 i OO10 2 Secolld. vaiue : _{.. t} . ,,".'" and so on~· ••. " . E - Con c 1 u s 1 0 n : II

Giving this curve to the operator who uses this

turn-table,acorreo-..

tive action can be taken Jl1stregul.a~1ng the hait~whee1 in order to eleminate the existing error.

, .

Rapport nr.0201

.APPfNDix,

Nr:"'/

",j Theo~oli/e

..

Collimator ...

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I

S£T- UP

,

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of

h!Jht

_Col/ima/or

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PRiNCiPAL

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---. '---. _.f /

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Rapport

nr.0201 _APP[ND/~

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tarn:.;'

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Rapport nr.0201

IiPPE NDIX

Nr:3