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N
4T?1e following areas have beery worked on during the period
starting February 26, 1965.
Target fabrication. As a first go around a target
confirguraticn as shown in'rig. 1 was adopted. The
ratio between the sttgcesej
largest target is 1 1in.e4x.
targets is
10
10. The
The range from I 1000
11.nes/mm then falls naturally-into three series:
l - !0 lines/mm, 10.-1 - l eis/mm, and 100 1000
lines/mm. Lach ser-ies ie:- & er down into the following
steps.
Step ` ../t factor
l I4oO
2 $'= s 2.59.
2 ,'512
3;`163
982
9 6 , 313.
MQVINOP'Al
;98
0400
I.`
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The first series was f',&a *i -ted in the following`"-Y.
First one step wa..+s drawn on a large scale. Then this
was photographed. From this photograph all the steps
of the first series were printed by varying the enlarge-
ment for each step. Then this series was rephotographed
and the first series was' obtained in negative f-orm.
This then was printed 'as a direct contact print
The second series was conipJished by taking the
negative of the first s+ rise arn-d photographing it with
a 10 to 1 reduction. The optics usedaas a_ gild "YVAP"
lens,, f' 13ttrtrx , f l :.
By photographing the pi,t of the first series in the
same manner, -we ended up with a negative of the second
series.
As a third steps An
idea of the difficulties
involved, we took a neg,ati:vE of the second series and
reduced it ten times with the setup used to make the
second series. The in-berest:i part here was that we
could resolve 500 11 sl iwithbut any trouble.
The targets fabricated this way are very encouraging.
For our purpose
they are fine up to 500 lines/mm.
feel, however, that they a uld be improved so as to
make the phase meastu:=possible. Therefore, the
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. 3 -
a) Experiments are being made to determine various
methods of dave1op hg the film. These methods
were discussed by Dick, a representative of the
customer, and Haroldkof, our organization.
b) The contact print necessary to get a- series one
positive is being el hated, The contact print,
will be made at the large stage where a loss of
detail is much less c.*itieal. Furthermore, parallel
illumination xill,brt.u aCl in the printing process.
In order to hold precise reduction factors and
locate the three serifs precisely on one piece
of film', a more-accurate setup is being constructed.
Ei) With more precise prose sing combined with a better
lens, it will be attempted to go up to 1000 lines/mm.
2. During this period an ex iwental setup was fabricated
to give us an idea of they precision obtainable in.this
method measuring the !4kn ir function of the lens and
also to find the best val~'of the contrast in the filters
and the necessary _ frequency ?.range in the filters.
After the equipment was.- fiskished, the first measurements
show that a contrast of 2% .in the filters is too small.
We therefore are now. waiting for more filters with dif-
ferent contrasts.
After working with the instrument our overall impression
is that it will be easy to use when all parameters are
adjusted.
OUP I
tPr~ }'ray".rl ^:"'('Clt
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3. Mathematical discussion of the attainable precision.
Introduction
Let us first, for the sake of simplicity, assume that the
light distribution in the target is sinusoidal. We shall
write for the .intensity-in the object plane:
in which V stands for the -visibility of the target and W
,l
is proportinal to its line frequency.
In the image plane this leads to an intensity distribution
I = i o 1 V cos w x
(2)
in which "Z is the mothrlus ref the transfer function of the
lens under test, and its ph$se shift,
The underlying idea of the ethod is to use a compensation
method in determining the val s of z- and 4` . There are
two funcementally differentWayS of doing this. The first
method consists of projecting the image (2) onto a filter
with a periodic transmission. The principle of this method
is to arrange things such that the emerging light distribution
is uniform when the proper.seting-s are made, We shall call
this method the multiplicative method.
The second method consists of adding to the image given-by (2)
a second light distribution* auch that the resultant sum again
shows ng modulation. This mat we shall call the additive
method.
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a. The Multiplicative Method
An absorpition filter the4 transforms a sinusoidal
intensity distribution exactly into a uniform intensity
distribution must have a.periodic transmission according
to
- V cos c/x (3)
.he fir?;t thin; to note is.that this function is not
s1 nUsoida 1 . In fact we have:
'I' can not exceed unity, hence C must not exceed 1 - V.
So the c:verape tr?ansmisS,jon cannot exceed
1. - V
V
Equation (4) in itself is not great importance because
a;e cannot expect to produce filters that are f cii thf ul iv
represented by it. It is, how v , indicative of some of
the problems associated wit1 the multiplicative method.
In multiplying two periodic functions the harmonics get
"mixed." The simplest case is the generation of a second
harmonic by multiplying two sinusoidal functions-. A much
more dangerous effect is-the Qottribution to the first
harmonic in the final image by the second harmonic in the
obiect.
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0 - 6 - 0 0
For the monent we shall leave these matters aside.
We now consider a target image
,' 1 - tV 1 os (w x + f)
Fo T
and feed it through a filter with transmission
C I + V cos (&-x +'f ) (5)
0
We assume that the product TV V can be neglected, and
so find tor the light distribution to be observed -
I,. z Cl r
0
-- tV 606C W x + 4) -t- V Cos (c;, x + '7)
T o
= CI' 1 + (V cos"r - Z- V Cris T ) Cos G rx
U O _ T
(V s"-Dv sintp) sinwx (6)
i
o T
A uniform light distribution-will be observed when
V V
p T
The phase adjustment can be made by either vary ink? f a
(moving the target) or varying:. (moving the filter).
The contrast adjustment must be made by varying the contrast
of the target V ; it does not seem feasible to vary the
filter contrast.
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P.ssuminp that the limiting visibility the eve can perceive
is Equation (b) leads to:
2 2
(V cos'h' cos 9') + (V si.n'y' - 'VV s n !gyp) < - , (9 )
This Equation can be solved geometrically in a polar
coorainate diagram. The result is that we can expect the
following measuring accuracies:
(10)
A( r- P) = =--. (11)
V
O
From Equation (1-0) we can find the accuracy ;n
F Z
It follows that the relative accuracy in 'C is constant.
We observe, however, that as V T can not exceed unity, the
lcwest value o -r that can be measured is eaua] to V .
t . The Fciditi ve Method
c ac;d to The image of the target
I ' - I ' F I - 'V V cos (W X + C )
a second light distribution;
I" = I' r1+Vcos(x+'')I
a
The addition does not produce any higher harmonic
problems. The intensity distribution to he observed is:
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0 ! 0 ?
I' 1 TV Cos( te x
= _yo )
T-
I + V Cos( (4)' x + T
1 0
(I' + I1) + I I I Vocos' - I I TV Cos f
I' ZV Gin tp X
c> 7
sin uox (14)
A uniform light distribution is observed when
11 V I' Dv
0 T
In this case we have two choices to make the contrast
adjustmEent. we can vary either the reference beam contrast V0 ,
1) We -sha11 first assume that VT is varis c~. Making the
same assumption about the eye as in the previous section
we have:
or the target contrast V,T *
Q(I' 'CV ) +
a ,{
d~ - I' + I'
0 1 2"
T'
1
Oa4Up I
V
a
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0 9 OP
A ( {P - 'Y/ )
e f ;:nd-:
'.
I' + T I
o..
It
I
It
The lowest that can be measured i s l v'
0
We see that the accuracies are worse than for the r^u i. t a_ f>i
cation "m"ethod. (Writing VrL for
''h s show!; that it is profitabb"le to make the tarp et
bean bri phhter than the reference hear, and at the same
t r;e c noose V a quite high. The best we war, do is to
Tin ake v e?ua to unity. Then
AT
r'cr the phase accuracy we find in this case:
A (C' -' ') + (23)
ir. this optimum case the. difference between the
acidditive and the multiplicative method is only a
f a !.' r + 7 , a rather minor' u1.f terence.
113 lV 1`'~wj i {1F71 ~1i3 `b. .a 3y l`la=w?x.
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For the phase error
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2) Sc far we as-sumed that the target contrast was
varied. anal that the reference bean, contrast was
con