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use mus-m4

 

DIFFEACTION OF ELECTROMAGNETLC WAVQS

 

AT MICROWAVE FREQUENClfifi.

By

Fr. Jules A. goucher.

if

r‘

A THESIS “ ‘\
Submitted to the College of Science and Arts of
Michigan State University of Agriculture and
Applied Science
in partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE.

Department of Physics.

4.956-

\3\
“\

\
V

\J\

\.,2 ‘

\

RECONNAISSANCE.

Je desire, dés maintenant, exprimer toute mon
appreciation pour l'aide precieuse et les suggestions innombrables que
le Professeur C.D.Hause a bien voulu me fournir tout au long de ce

travail. De mEme, l'intérat des autres membres de la faculté n'a pas

9M4»

o I
ete sans porter encouragement.

TABLES OF CONTENTS.

 

pages

I) ' INTRODUCTION . . . . . . . . . .I

II) OUTLINE OF THEORY . . . . . . . . .3

III) PRODUCTION OF A PLANE WAVE AT MICROWAVE FREQUENCIES.8
A) The generator . . . . . . . . .8
B) The reflector with its feed . . . . .10
C) The detector . . . . . . . . .lh
D) ‘Wave field at 520 and 550 cm. from the reflectonlh
E) wavelength in paraffin and index of refraction 16

IV) DIFFRACTION OF A PLANE WAVE BY.A SLIT
WITH CONDUCTIVE JAWS . . .19

A) The slit aperture . . . . . . . .19
B) In the plane of the slit . . . . . .19
0) Near the slit: at 2.5 and 5.0 wavelengths . .25
V) PHASE SHIFTS INTRODUCED BY PARAFFIN. . . . .33
A) With a slit width of 2 wavelengths . . . .37
B) With a slit width of 3 wavelengths . . . .37

VI) CONCLUSION AND SUGGESTIONS . . . . . . .38

-1-

INTRODUCTION.

The problem of diffraction of electromagnetic waves
has attracted the interest of many investigators of all types, from
the theoretician to the experimentalist. Until recent years, the work
was confined almost entirely to optical frequencies and apertures, and
observation distances large in comparison to the wave length. The
greatest difficulties were then of two kinds:

1) The irreducible gap between the ideal case, which
can be treated theoretically, and the physical situation.

2) The absence of electromagnetic waves of suitable
wavelength. The available waves were either too short or too long to
permit a practical study of all aspects of diffraction.

But now that we can produce microwaves, the second
difficulty disappears. The problem we are left with is the realization
of experiments as close as possible to the ideal case.

Our purpose then is to observe and explain semi-
quantitatively several diffraction patterns of 12. cm. microwaves
produced by slit apertures. The observations are made in the
neighborhood of the apertures, at distances not exceeding several
wavelengths. A qualitative explanation of the observed patterns
is obtained by using Thomas Young's method of interpretation. The
patterns are represented as being formed by the interference of the
direct wave and secondary waves which arise at the edges of the

apertures.

-2-

A more quantitative account is obtained by comparing
our data with that expected from the exact treatement by Sonmerfeld C1)
of the diffraction by an infinite half-plane. Application of this
theory to our problem is only partially valid and discrepancies are

expected.

OUTLINE OF THEORY.

Our interest in this field was excited by an article
in "TheIPhysical Review" Qi),'where C.L. Andrews studies quite
extensively the diffraction of Llcm. microwaves by a circular aperture.
That work presents the patterns in the H—plane as well as in the E-plane,
thus stressing the differences.

Andrews does not extend his observations to the
geometrical shadow, and being three-dimensional, the quantitative
interpretation of his readings is made more complicated and the
qualitative interpretation is not helped. 'We will limit ourselves
to a two-dimensional study, and, at the same time, we will observe only
in the H—plane. However, the high degree of polarization shown by our
apparatus would provide facilities also for good readings in the E-plane.
We will indicate later the small differences due to the absence of a
third dimension. .

Andrews himself, in a later paper (3), does not
hesitate in pointing out that "in the plane of the aperture, ...,

Young's theory yields the experimentally observed positions of maxima
and,ninina".

In this work, we will also attempt to account for

maxima and minima even in the geometrical shadow.

Another investigator, Houston ('4), successfully
detected a "turn up" effect near the edge of a diffracting aperture,

indicating the correctness of the predictions of electromagnetic theory.

-h-

Houston was using a long wavelength (50 cm.), and the patterns are
similar in general to those obtained by Andrews. We are unable to
detect close edge effects in our readings for two reasons:
a) We are using a shorter wavelength. The detector
is relatively large in comparison to the wavelength, approximately 0.DK.
b) The edges of the apertures are not thin and knife-

like, which is the primary condition to get those effects.

The problem of diffraction of a plane wave by a
conducting half-plane has been solved by Sommerfeld. The disturbed

'field takes on three different forms, each having its own equation:

\‘ Sewage,
\. a
‘\
\
\
a -F'an€h
fifdje'
/
/
‘\‘ ’ ‘8
‘\ /

Figure :1

In the region number I, called the reflection region,

|lslel14l~ III

III luall ' II! I I I l { l‘lllcllll‘lllll

-5-

we can represent the disturbed field by the equation:
U150. : CosEKr cod(§°’fo)] "'2 MLKT’ (#0 (T‘ffo)] T' Z

where the first term on the right is the incident plane wave, and
the next term is the reflected plane wave.
In the region number II, called the unshadowed region,

we can represent the disturbed field by the equation:
UEW :. Cos£Kmm(5p~fl)] + Z
In the region number III, called the shadow region,
we can represent the disturbed field by the equation:
a 1

In all these equations, the term 2 is a cylindrical

 

wave arising at the edge, and K is the propagation constant if .

It can be shown that the cylindrical wave arising at the edge undergoes

a phase change of 180°, when the angle 7- 700 goes from 7-%<n' to 7 ITO)“—
And, because of the term :5: in the wave function, we

will have an inflected wave differing from the undisturbed wave by an

angle 77; , when 713le , or a deflected wave differing from the
undisturbed wave by an angle 75!; when 'f”. ("I

In the case we will be dealing with, ('0 is equal to 1/4
and the E-field is parallel to the slit (11' case). In this present case,

(see Fig.2),the above formula for a cylindrical wave, transforms into:

2,. wit—[wow VHS-:7, + 3.17,]

where S is the angle between the radiation and the normal a,

and wherep may be called the distance factor, and “T + ——-T
A. "‘ /a W A

is an angle factor.
It is to be noted that the above formula does not
apply in the neighborhood of 5.: 0 . Here, we are on the edge of the

shadow, and also, the cylindrical wave changes phase.
A

Sovvcc at” infinity

 

 

figurehi

”n

Young's interpretation of diffraction patterns can

be shown from the following:

A

 

\\'J

   
 

 

M

A
i
l
i
i

E
‘e

’fflgufc 3

Consider regions M, N, P.
In M, we have interference of the inflected wave from

A and the deflected wave from B. In N, we have interference of the

-7-

deflected waves from A and B, and the plane wave from the source at
infinity. In P, we have interference of the deflected wave from A and
the inflected wave from B. In the plane of the slit, we have a special
case of N.

It is apparent that Young's interpretation can be made
semi-quantitative by assuming two Sommerfeld half-planes slightly
separated and the edges giving rise to the inflected and deflected
cylindrical‘waves.

we do not expect complete agreement for the following
reasons:

1) The slit is not an "infinite" one.

2) Each half-plane is not infinite.

3) The slit jaws are close enough to each other to
interact with each other.

h) The edges are not knife-like.

5) The"plane wave" is plane in two dimensions only

instead of three as required by Sommerfeld's Theory.

-8-

THE PRODUCTION OF A PLANE WAVE AT MICROWAVE FREQUENCIES.

A) The generator.

We were fortunate enough to be equipped with a
microwave generator fullfilling all the requirements one can ask for:
stability, power, portability, etc. That generating unit is a Microwave
Diathermy Generator, commercially known as "Microtherm" and manufactured
by Raytheon Manufacturing Company, Waltham, Mass. The model used in

this experiment was the CMDbh, Series A-thS.

The "Microtherm" operates at a frequency of 2h50 Mc.,
or a wavelength of 12.2 cm. Its energy is generated in a continuous-
wave magnetron oscillator. The unit has a power output of at least
100‘watts.

A diagram of the main conponents of this unit appears

in Fite 9

-9-

kehvektce u‘ .k

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fa

 

 

 

  

am

 

 

 

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lea as can

 

 

 

 

Lee’s: B m

 

 

 

-10..

B) The reflector and its feed.

The reflector: Since we intended to work in two dimensions only

 

instead of three, we used a parabolic cylinder as a reflector. In so
doing, the reflected wave is a plane wave in the horizontal plane.

The reflector is about one meter wide and one meter
high. The distance from the focus to the directrix of the parabola is
four wavelengths: h8.8 cm. The parabolic cylinder was first made of‘
wood and then coated with aluminum foil. Evidently, this aluminum
surface is far from being perfect but irregularities are less then one
tenth of a wavelength, so that they could be neglected.

In a parabolic cylinder, the focus is a line, so that
we can "feed" it from anywhere on that line.

And, for a reason to be explained later, we thought
better to have the upper portion of the reflector larger than the lower.

The feed was installed in the lower part of the focus.

Its feed: This was of the dipole-disk type, for these reasons:

a) We wanted as much reflection as possible on the
parabolic cylinder and the dipole-disk type shows a good directivity as
can be seen from Fig. 68

b) we wanted to avoid interference between the reflected
wave fro: the reflector and the direct radiation from the feed. This
requirement is fullfilled nicely by the dipole-disk feed.

Now, as can be noticed from Fig. 56 , the E-plane
distribution of intensity is asymmetrical. This is due to the
asymmetry of the dipole. This is the reason why we used an asymmetrical

position for the feed. But this minor inconvenience turned out to be

-11.

 

1.1)

 

an advantage, since we avoid a "shadow" of the feed in our wave field.
Fig. 56 gives an idea of the different dimensions of
the dipole-disk feed. All the different parts of the feed were made of

brass.

41,.

C) The detector:

The detection ensemble here approximates a point
detector. For that reason, as a probe or "antenna" we used the detector
itself: a 1N2} crystal. And furthermore, that crystal proved to be
quite sensitive to polarization. It is interesting to note that, since
we were observing in the H-plane only, the length of the crystal did
not matter at all. i

The crystal was connected by a pair of twisted wires
to an ammeter. The readings of the ammeter were directly proportional

to the intensity of the radiation.

D) The field at 520 and 550 cm. from the reflector.

If everything were perfect, the radiation obtained
should be collimated in the horizontal plane, and also the intensity
should be uniform.

In Fig.‘7 , we have plotted the intensity of the field
at 520 and 550 cm. from the reflector. As can be‘seen from the two
graphs, the field did not vary by more than hfi either side of an average,
over a 60 cm. range.

Those two distances of 520 and 550 cm. were chosen
since they were the positions of the diffracting aperture and field

plane for the majority of measurements.

-15-

‘~'. >9.

0.75

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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—3 see

 

 

-16..

E) Wavelength in paraffin and index of refraction of paraffin.

To deternine the index of refraction of paraffin at
2b50 Mc., a cylindrical lens of paraffin was constructed, its focal
length measured at this frequency and the index deduced.

The cylindrical lens was of the piano-convex type.

5.
:3. g
.- . \o
. V '7’

<FL~———————«--—~a30.1:2.” H—.-H— —»--—-~5;¥

figure 4?

 

The essential dimensions of the lens are indicated in
.Fig. 9 . The radius of curvature of the cylindrical surface is h0.6 cn.
It is known that this type of lens will not have a
Emoint focus, because of aberrations and other physical difficulties.
iiut we are certain that the focal point will be indicated by a naxinun
idltensity. Our task is then reduced to a measurement of that intensity.
Measured on three different occasions, the focal line
'tas deter-ined as being 29.3 cn. from the plane surface, the convex

Surface being turned towards the source, to nininize aberrations.

 

 

-e¢$3dr

 

fiju're 7

-17-
Using thick lens theory, the actual focal length as

measured fron the principal plane is given by:

J.=M-,_.I_.-_L ("-42.1
(1)). ( MR, Ra+mfi,’?g)

where d is the thickness of the lens.

The positions of the principal planes are given by:

 

 

(2 A _ "Rn d __ ‘ R A A
’ ,~ Ham-(w 4 / 1 «mm-w
For 83") 9‘, AI: 0 and A; is not deternined, but:
...—H “‘1 - —- d/M
a R , "
so that: (2a) ’1 " "" #7)

A ..
Rpm

Now, if we call 0 the distance fron the plane surface

to the focus: . r

é———C——>°

 

 

Fig. /0

 

H ”I
using equations (1) and (2a), for file“; we obtain
I? a! -
(3) a? “7" where &= 90'6““
d :- firm
a g :703 M

-18-

Solving for n, the index of refraction at 21.50 Mc.

39:3442’4‘1’01/41_£r=0

and n = 2.28

Kittel (5) lists the index of refraction of paraffin

at 25,000 Me. as 2.26

-19-

DIFFRACTION OF A PLANE WAVE BY A SLIT WITH CONDUCTIVE JAWS.

A) The slit aperture.

The ideal here would be an "infinite slit" or rather,
two infinite conductive half-planes. The best we could dO'was to set
two sheets of thin aluminum alloy in a wooden frame. Each piece was

36 inches high and 6 feet wide. In cases of small widths, this slit

would be considered almost infinite.

B) In the plane of the slit:

In Fig. // , one can see a plot of the intensity
distribution accross the aperture of a 2‘} slit, in the plane of the
slit. The renarkable features of the pattern are: two naxina at one
half of a wavelength from the edge and a nininun in the center. The
.intensity at the maximum reads 1.78 if one takes as unity the intensity
cxf the undisturbed field. At the mini-um point, the intensity reads

0-3? . The amplitude of these two points are 1.33h and 0.836 respective-
ly, unity being again the amplitude of the undisturbed field.

Let us find the anplitude at these two points assuming

'fll’ infinite slit and applying Sonnerfeldis Theory. Let us first take
t11€3 central point. There the distance from the edge is unity (in units
01‘ A ) and the radiation from each of the edges has an amplitude of
J—- " ... .../.... ) .. :in
477' cow/5’" 43.45" " 111'
And since these two radiations are in phase and of

equal amplitude, their sun will be just twice: ”V: .. ...— ,y{
77-

\Mnt~¥.%bV\« 00°09

rem .
Tuwhsakwmfikay . putt-r
Ahab

\\ nmbzfiaux

and)

 

“.3

-21..
And remembering that this amplitude has a phase angle

or.%;f with the radiation Iron the source at infinity,

1.0 m

    

the resultant amplitude is 0.75 (compared with the
measured 0.836). The difference should not be surprising for the reasons
explained in the second section. We feel that the major variation is

caused by the interaction of the two edges.

Following the same method, one can also get an idea of
what the amplitude of the naxina should be. It is to be noticed that
here the intensities contributed from the two edges are not equal on
account of the different distances of the "sources". The phase angle
between these two however remains zero. One can easily figure out
that the amplitude of the contribution of the two edges together is

0.519 + 0.181 = 0.5 and that the phase angle of this amplitude with
regard to the radiation froathe source at infinity, is 77.731101! the

resultant of all three radiations is:

 

 

-22..

which is an anplitude of l.h (compared with the measured 1.33h)

Here, it seens interesting to point out that, in the
corresponding experiment with a circular aperture, (instead of a slit)
Andrews' mininum intensity is practically zero at a point where, with
a slit, it is expected to be around.0}56 . And here again, that is not

surprising since the two apertures are essentially different.

The jaws of the slit can be opened to any desired width.
If the width is three wavelengths, the intensity distribution is that
shown in Fig. F? 'We have three maxina instead of two. In the present
case, let us note that the central maxima is not quite as high as the
two lateral ones.

This is to be expected, fbr, one can go through the same
calculations as before and predict that the three maxina will have

amplitudes of:

l.36-—----~-l.2h-—------l.36

and the two central ninima will have amplitudes of:

0078 $078

 

Our readings for the same cases were:

the maxima: 1.26 1.17-—-----l.2

 

the minima: ‘ 0.82 0.71

 

(Our'pattern lacks symmetry but this should.not disturb

‘3‘11‘ study). Once more, Andrews' ninima go to much lower values because

-2

)
.... CXQLoos .osOOOo

..eE R
V emits. rt 3

«a;

N

 

<2.

2.6

 

m3

-2h..

his aperture is essentially different.
In general then, for a slit width of an integral number
of wavelengths, we should expect an equal number of naxina, the weakest

in the center,.the strongest adjacent to the slit edges.

-25...
C) Diffraction patterns near the slit:

Another series of diffraction patterns can be obtained

close to the slit. p;
i?
L5
. .3.
6—4—9";
/’ :
5117
5 y are l“. Plane of- 055$,”

Here again we will forget about a third dimension, and
the distance we will refer to will be the distance d, the displacenent
along the observing plane.

‘We will study three different patterns: two at a
distance of 2.5 wavelengths and one at a distance of 5.0 wavelengths.
For the first two, the width of the slit is two and three wavelengths.

The interesting feature of these different patterns is
the portion extending into the geonetrical shadow. As a natter of fact,
according to the interpretation we have followed so far, that portion

of’the pattern is contributed to by the two cylindrical waves arising
at the edges only.

 

 

 

.-v‘ ‘

-26—

Evidently, a maximum intensity in that region should show
up at a point where the two cylindrical waves are in phase. ( A small
correction for the distance factor V; is here neglected). One should
not forget that in the shadow region, of the two radiations, one is
deflected and the other is inflected. 'We can say that when the path
difference is a half-integer of a wavelength, the two radiations will
be in phase, accounting for the phase angle between an inflected and
a deflected wave.

In Fig. /3 , we have plotted the intensity distribution
at a distance of 2.5 wavelengths, the width of the slit being 2.0
wavelengths.

The maximal point in the shadow region arises in the
neighborhood of three wavelengths from the central point. As can be
checked easily, the difference between path a and path b at that point

is very close to 1.5 wavelengths.

 

 

 

....t .. 9 a a...” ....
g edaspmemea—t’» 3.0.x-

Fljurc ’7

Following the same method, one can verify that at

1 . S wavelength from the central point, where the difference between

-27-

 

9.12m
w

 

%\ 0....me

2...:

Q‘-

-28-
path a and path b is just about 1.0 wavelength, we get a low point,

in the intensity distribution pattern.

 

 

 

-————.- .—

Iii/aerate»:-

 

Evidently, that low point is not expected to reach
zero, on account of the difference in amplitude between the radiation

from A and the radiation from B, their paths being different.

So far, intentionally, we have neglected the distance
factor V; in the intensity variations. But the influence of that
factor is very low in comparison to the phase angle factor and further;
more, in some cases, it is within the experimental error. We can
mention however that the distance factor might be responsible for the

asymmetry of the secondary maxima about their own maximum points.

The pattern obtained with a 3 k slit at a distance of
2 .S wavelengths, is a little more complicated for the following reasons:
a) The change in path difference being more rapid

than in the previous case, we expect more frequent variations, even in

the unshadowed region.
b) ‘At any point in the unshadowed region we will have

-29-
to account forthree radiations, each having its own intensity, and
phase.

c) ‘we do not know the intensity at points close to

J21)

For all these reasons, we will not attempt to account
for the"shoulders" appearing on the intensity pattern, on Fig. a] .
But the low point of these "shoulders" seems reasonable if one considers
that, for example, at the "shoulder" B,

a) The phase angle between the radiation from the
source at infinity and the radiation from edge B changes very slowly
‘with regard to the displacement.

b) The main factor in the intensity pattern should

be the phase angle between the radiation from.edge A and the plane wave.

A glance at the next diagram and one sees that, at the

low point of the "shoulder", the phase angle is in the neighborhood of 7f.

 

 

 

""‘""‘""' " T...T~‘>“’"‘"""

dISp/Ode new 3"
/:l:7LI71? 43¢)
A similar method shows'that the low point in the

Sluadow'region is again due to the phase angle 1T'between the radiation

-3

axeserm

 

-31-

from A and the one from B. That low point shows up at about 28 cm.

from the central point.

 

 

chap/atom on t

 

We have taken similar readings with a 3} slit at a
distance of 5.0 wavelengths, and the pattern is shown in Fig. 9."
The same method as previously still accounts nicely for the minimum at

23.5 cm. from the central point

V

 

 

figure 3-:

But one should not draw drastic conclusions from this
Pattern, because at this distance, the slit loses its: character of

"infinite slit" , in height as well as in the, size of the half-planes.

-3 2-

 

-33-
PHASE SHIFTS INTRODUCED BY PARAFFIN.

Up to now, we have considered all our diffraction
patterns as interference patterns, the interfering radiations being
from three different sources: a source at infinity and a source at each
of the two edges A and Ba

we have also recognized that the intensity depends upon
different factors among which is the phase angle between the radiations.
Now, if we cause a phase shift in any of the radiations, by introducing
a medium of a different.index of refraction, we should expect changes
in the patterns.

But this may become much more complicated than desired.
In the following, we introduce a first approach to that kind of'work.
And, in so doing, we have tried to make it as simple as possible.

A "slab" of paraffin\was introduced in the path of
two of the radiations. The pattern we should get at a distance of 2.5
‘wavelengths, will depend.upon many different factors:

a) In place of a plane wave coming from.a source at
infinity, a part of our new plane wave will have its phase shifted
by an angle: at: 2317(44-0‘:
where X is the wavelength

n is the index of refraction of paraffin for this frequency.
t is the thickness of the "slab"
[:1 ]

"‘""‘"L_.__--

- - .5. g.-
L a" w. —v o;

- - ..‘b an! —-I.n.‘w-'l
* —-.-— .N-

i:lgitl7’€1 3b5' I

 

-3L-
b) The radiation from A is also shifted by an angle:
CXC:: f§512e1-5)£?1e44; tr
where S‘is the angle between the radiation and the
normal .

A

C—"'f\ “I

 

figu re 26

-----

1‘

c) The intensity of those two radiations will be
somewhat diminished because of the reflection at the two surfaces of
the paraffin "slab" (change of index of refraction).

d) Furthermore, there will be a third cylindrical
were arising at the edge of the "slab" of paraffin. And, as up to now,

we must admit that there is not much we can say about this last radiation.

However, the problem is simplified if;
t) we stay away for the moment from.the critical point p,

'where there is a phase change.

 

L

 

 

’
I
/5gure 37 I
P

b) the reflection at the two surfaces of the "slab"of

paraffin is neglected.

c) the third cylindrical wave arising at the edge of

-35-

the "slab" is certainly very weak, in the same way and order as the
reflected wave and is neglected.
Besides these small corrections then, the new problem

looks the same as before except for the phase shifts.

 

 

 

In the new pattern, there is one feature we can predict
at once: the central maximum that we observed in almost all patterns will be
shifted. Indeed, most of the time, in the unshadowed region, a maximum
point will show up where the two cylindrical radiations are in phase.
Since one of these radiations is now shifted in phase, most of the time
one should expect to find a maximum point shifted.from.the center.

However, one should not try to predict accurately the
place of the maximum unless we are certain of:

l) the index of refraction of the introduced medium.

2) the intensity of the transmitted.radiation, through
that medium.

3) the 8 factor of the intensity of the radiation.

h) the exact thickness of the introduced medium.

-36-

5) and something more about the cylindrical wave

arising at the edge of the "slab" of paraffin.
In Fig.3/ , we have plotted the intensity distribution

for two different situations: with and without the "slab" of paraffin.

Fig.3’a is for the case cf a 2X slit:

 

 

42=e———~—-1).—————-Ea>
\

L

figure )7

Fig. 3H>is for the case of a 3/\ slit:

 

 

_ 6 3A 3

 

#‘

l I

figure 30

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
  
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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.. .... a, . ... ... .... ... . ... . .. .. .... ... .. . . .... ... ....io. . ... ... . . ... ... .... .5... 49>.-
.. .... .. .. . .... .. . . . .. ... . .... ... .... ...- ... t... . . .. .. . . . . .. .. . .. ....t..e.
.. .. . ... . . ... .... A... . . ... .. .... .. . ... .... .. .. .4.. o. .. . . . ... . .. . .. .. ... .o.. a...
. .... - . . ... .. . ., . ... ... .. .. ..A .A. .... .. .. . . .A.. ... . . . - .... .. .... .. - ...-A.... . .. ....
. .... .. A. . i. . . . ... . .. ._ i .. . .. ...i.... .... . .A. ... .... o.v0 «... .5. . . -. .- . .... 0.. .... .... .... .... ... win.
., . .. .. . .... .... A . ... . . ... . . . . . A ... .. o t... ... .. . .. . ... . . . .. .. a . .. .... .... .... I... .eoni
.
. .. _ . . . . .. . .. i. . . . .. , . . ... .. .4 .... .. . _ . . .. .oo. . .#. a.». .c.. ..a ....lo.¢.
.. .. . . . . .. . . .. - . ... . . .. ..A e. i.... ... ‘ . ... .. : .... s... I. . .... .... .. . Anetta
. . .. . .. . . . . A . ... .... . .. . . . . ... . . . . .. .... ... .... .... .... .... .... .... .... .fiobl
. . , .. . .0. . . ... . . . . . .... . .. ..4 .. .... ... .... e... .... ....i,... .... .... ...vv.94v.ll.viioeda
. a 1
. ._ . . .... ... o . . . . . ... . .. . .......... ...-.... . . ...- .... i.........-..
. . - .. . _. .A. .. . . .. . .... .. .... .. . . .... . . .. c i. . l .. .... ... . .A ..A o. . .... .... .v.. l..cl .
.. . . . A . . . . _ ... .... ... , .N ... . .. . .. ... ... .... ... . . . . . .. . .. .--. .... . .. .... V.-- 4‘t0i
.. .... .. . . _ . . . ...- ... .. .—. .. .... . . . .. . . ... .. . v... .... ....¥ ...w v . .It. A. . .. . .... ..Q‘ -19. «bale

~38-

GONCLUSION AND SUGGESTIONS .

An appreciable improvement would show up in the
quantitative readings if the slit were wider: 5) or 8)‘ or so. The
interaction between the edges would then be considerably reduced. But
at the same time, the slit would lose some of its "infinity" in height.
A good idea would be to use a shorter wavelength, so that the dimension

of the instruments will not become prohibitive.

There is still a lot of work to do in the region of
6:0 . In fact, we know that the intensity is not infinite at that
point. In our interpretation we assumed a sudden change of phase for
the plane wave from the source at infinity: which should give a
discontinuity in the intensity distribution at that point unless there
is another sudden change of phase of another radiation‘oi‘ equal inten-

city, which can only be the cylindrical wave from the edge.

#13078 33‘

 

    

‘”-—.

Another point of interest would be the study of the

different radiations independently. One could then make use of the

-39..

very strong polarization of the system and study independently the 77"

and 0" cases.

A rapid check in the course of our experiment showed
that one can use the polarization of the system and "separate" the dif-
ferent radiations. The detector used as a probe, ean take three orien-
tations: three perpendicular axes. Each orientation will eliminate

any radiation propagating along that axis.

(1)

(2)

(5)

(4)

(5)
(6)

-ho-

REFERENCES.

Wolfsohn G. "Strenge theorie der Interferenz und Beugung."
Handbuch der Physik. Vol. XX.
C.L. Andrews: "Diffraction pattern of a Circular Aperture at
Short Distances" in "The Physical Review" Vol. 71
June 1, 19h7, p. 777
C.L. Andrews: "Correction to the treatment of Fresnel Diffraction"
in "The American Journal of Physics" Vol. 19,
May 1951, p. 280
Robert E. Houston Jr.: "The radiation pattern of circular apertures".
A thesis for the degree of “.3. at Michigan State College.
Charles Kittel: Introduction to Solid State Physics, p. 110
S. Silver "Microwave Antenna Theory and Design" Radiatidn‘Laboratory

L

Series. (19h9). s5

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