455-609
AU 233
I11?”?105
Xi
EX
3,134,840
May 26, 1964
3,134,840‘
H. GAMO
OPT‘ICAL masz umsuamc APPARATUS
Filed Aprg 10. 1961
2 Sheets-Sheet 1
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FROM PHASE SHIFTER 237
ENVENTOR
FIG.4
HIDEYA GAHO
..... *1
“24,”, W,
ATTORNE Y 5
United States Patent 0” KB
3,134,840
Patented May '26, 1964
1
2
3,134,840
?ed above. FIGURE 1 shows a simpli?ed block diagram
of this prior art device. Fully or partially coherent quasi
monochromatic light beams 1 and 2 are respectively inci
OPTICAL PHASE MEASURING APPARATUS
Hideya Gamo, Katonah, N.Y., assignor to International
Business Machines Corporation, New York, N.Y., a
corporation of New York
Filed Apr. 10, 1961, Ser. No. 101,750
14 Claims. (CL 88-14)
This invention relates to apparatus for measuring the
dent on the two photodetectors 3 and 4, the output cur
rents of which are proportional to the instantaneous in-
tensity of light 11(1) and Mr) and are directed to the
correlator unit 5. In correlator 5, a multiplier 6 takes the
product of the two currents which is then integrated with
respect to time by integrator 7. The output from the in
polarization characteristics of light, and more particularly, 10 tegrator 7 is a measure of the cross correlation existing
to an intensity interferometer using a coherent light back
between the photon distributions in the light beams 1 and 2.
ground the polarization of which is varied to enable
Photodetectors 3 and 4 may have time constants greater
measurement of polarization characteristics of light falling
than the coherence time of the incident beams, which is
usually on the order of 3><l0-1° seconds. Multiplier 6
Present day interferometry techniques have been 15 can be any one of manywell-known analog multipliers,
strengthened by the development of the so-called intensity
while integrator 7 is shown by Hanbury-Brown and Twiss
interferometer by Hanbury-Brown and Twiss, the theory
to be a motor having a linear relationship between speed
and details of which may be found in the Proceedings of
and input voltage. Of course, any purely electronic in
The Royal Society of London; vol. A242, pages 300-324
tegrating circuit may also be used.
(-1957), and vol. A243, pages 291-319 (1957), herein 20 According to the theory of Hanbury-Brown, Twiss, and
after referred to as Publications A and B. The original
others, the correlation coeflicient between the light beams
Hanbury Brown-Twiss intensity interferometer, as there
is given by the following formula:
described, o?ers experimental proof that the times of emis~
sion of photo-electrons at different points illuminated by
712
coherent beams of light are partially correlated. The 25
authors state that this result forms a basis for the claim
where <A11AI,> is the correlation coe?icient, r, is the co
that the correlation is essentially an interference effect ex
herence time of light, T is the response time of the detector
emplifying the wave, rather than corpuscular, aspect of
(11> and <I3> are the average values of light intensity
light. The intensity interferometer therefore is quite im
at the inputs of the photodetectors 3 and 4, and '11, is the
portant in modern physical optics, since it develops a cor 30 complex degree of coherence or normalized mutual co
relation function for the intensity fluctuations in two 00
herence factor, for the light beams as measured between
herent, or partially coherent, beams of light by sampling
two points A and B, physically spaced d distance apart,
the currents from two photodetectors upon which said
whereat detectors 3 and 4 are located. The <> sur
on said interferometer.
-
.
rounding the values I, and 1, indicate that the integral
The correlation function derived by the original Han 35 with respect to time (usually, the observation time) is
bury Brown-Twiss interferometer is proportional to the
taken of the instantaneous light beam intensities at the
beams impinge.
square of the absolute value of the phase coherence factor
of the two beams. The phase coherence factor itself ,is a
respective photodetectors in order to obtain their time aver
age, r.e.,
'
complex number having a phase as well as an absolute
value. As will subsequently be pointed out, knowledge of 40
this phase is desirable for certain measurements. How
ever, such phase information cannot be conveniently ascer
tained from merely the square of the absolute value of
the phase coherence factor.
Besides knowledge of the phase above mentioned, it is 45
also desirable at times to measure certain polarization
characteristics of light beams. Normally, in order to do
this, polarizing elements must be inserted into the paths
of the beams. However, the present invention provides
The ?uctuations (or AC. values) of the light beam in
tensities are given by AI1=I1—<I,>, and AI,=I,—-<I,>.
AI, and AI, are represented by the output currents from '
photodetectors 3 and 4, respectively, which are propor
polarizing elements only in the coherent background 60 tional thereto. Therefore, after multiplication and inte
gration with respect to time, the output from integrator 7
is <AI,AI,>, which, as de?ned above, is a measure of the
It is therefore an object of the present invention to pro—
source.
,
.
vide an intensity interferometer with a source of coherent
correlation coefficient.
'
,
According-to Principles of Optics, Born and Wolfe,
background so that complete information about the phase
Pergamon Press (1959), page 504 (hereinafter referred to
coherence factor may be determined, including its phase.
as Publication C), the complex degree of coherence 'm
Another object of the present invention is_ to provide
for quasi-monochromatic light is de?ned to be the time
means in the coherent background of an intensity inter-,
average of the product of the wave amplitude of light at
ferometer to measure certain polarization characteristics‘
point A (FIGURE 1) and the complex conjugate of the
of the incident beams.
These and other objects of the invention will become 60 wave amplitude of point B, divided by the product of the
square roots of the intensities at these points. Thus,
apparent during the course of the following description,
when taken in conjunction with the drawings, in which:
FIGURE 1 shows the prior art intensity interferometer;
FIGURE 2 shows a block diagram of the present inven
tion using coherent background and polarizing elements; 65
FIGURE 3 shows the details of FIGURE 2; and
FIGURE 4 shows an electronic synchronous detector for
use in FIGURE 3.
'
In order to fully appreciate the novel concepts of the
present invention, reference will ?rst be made to the in
=<VrV2*>/1?l\/E
where V1(t)=wave amplitude of light at point A,
V,*(t) =complex conjugate of wave amplitude of light at .
point B, and I1 and I3=intensities of light at points A and
B, respectively. [113 is also termed the phase coherence fac
tensity interferometer originally proposed by authors
tor and it is a complex number having both real and im
Hanbury-Brown and Twiss in publications A and B identi
aginary parts. In polar coordinate form, therefore, 7,,
3,134,840
3
-4
.
beam_tallren through its axis of propagation. A resultant
electric/vector B may be derived from the electric vectors‘
may be represented as |712[(cos.¢+i sin o), or l'mle",
D where [713} is the absolute value of '11, and is equal to the
square root of the sum of the squares of the X and Y vec
of the waves making up said beam, whose end point
tors, while ¢ is the phase angle that [712] makes with the X
axis. Physically, the angle may be de?ned geometrically as
moves quite irregularly with ‘respect to time. Such a
beam is considered to be completely unpolarized. This
resultant electric vector may also be resolved into two
electric vectors Ex and By, respectively, vibrating in two
planes X and Y at right angles to each other. These
on page 508 of Publication C, which is herein incorporated,
A ‘and B, |‘Y1zl=1, while for fully incoherent light beams, ‘
I'm =0. Therefore, for partially coherent light beams,
0< 712i<1-
two vectors can be considered as representing two mu
_ _
tualily perpendicular waves. Each 'vector 15,‘ and By
It. is therefore seen that while the original Hanbury
Brown and Twiss interferometer of FIGURE‘ 1 provides
a measure of the absolute value of 7,, (since the corre
varies with time, and each can be considered as having
lation coeflicient observed is proportional to h1g1’), the
a n, and n, with respect to some reference. Thus, the
equations for these electric vectors may take the follow
phase at of the phase coherence factor cannot be con-'
ing form:
veniently ascertained. Also, the shot noise in the opti
cal region of the photodetectors, due to photoelectrons,
E,<o=a=(oe"a<*>-=-m
is predominant over the wave interaction noise, so that
(a)
all noise in the intensity interferometer of FIGURE 1
where T is the'mean frequency, and a1, a2, 0,, and 0y
can be approximated by this shot noise which is given
vary with time. It will be noted that both E; and E,
by <AP>=<I>. Therefore, the signal noise ratio of 20 above are complex quantities.
An unpolarized" beam of light can be applied to a p0
FIGURE 1 is proportional to
llarizing element which may cause either full or partial
s/wuralmF/vm
(3) polarization
of said beam. In a fully polarized beam,
Because l-ml for partially coherent light is less than 1,
the end point of the electric vector E, which is the result
the squaring of 11ml results in a fairly low S/N ?gure.
25 ant of E,' and Ey (de?ned in Equations 5 and 6 above),
Because of the reasons stated previously, the phase of
varies ‘regularly with time. ‘Where certain conditions
the complex degree of coherence yields valuable infor
are present, this regular motion of a fully polarized beam
mation, especially when determining intensity distribu
may take the form of'an ellipse (elliptically polarized), a
tion of a source or the phase of an illuminated object.
circle (circularly polarized), or a straight line (linearly or
An intensity interferometer measuring both phase and 30 plane polarized). In a partially polarized beam, the
amplitude of the factor 71, is the subject of the present
motion of the_end point of the resultant E vector is
invention, which provides a coherent background source
neither completely regular nor completely irregular, with
for the interferometer of Hanbury-Brown and Twiss.
' In the preceding discussion, the polarization character
respect to time.
istics of the incident light beams 1 and 2 were not investi
gated as to their effect upon the correlation coe?icient
- vention, a more general equation is now given for the
'
matrix as de?ned in Publication ~C, page 542. This
<Al1AI,> when measured by the original Hanbury
Brown-Twiss interferometer shown in FIGURE 1. For
the purpose of analyzing these characteristics, whose
measurement may also be performed by the present in
.
The nature of polarized light may be analytically in
ve'stigated and characterized by the use of the coherency
_ matrix takes the following form:
40
J:
where B, and B7 are complex quantities as de?ned in
Equations 5 and 6. Thus, since a complex number
multiplied by its conjugate is equal to the square of its,
absolute value, the coherency matrix (7) may also be rep
45 resented in the following manner:
J__ <a1’>'<maze“°-""'>>
(4)
8
_ <a|aze"°‘-“~>> <a.'>
( )
a For convenience, the elements of the coherency matrix
'
50 may be represented by the following terms: I
where E,(1)_ and 13,") are the complex analytic signals
respectively representing the X and Y components of the
resultant E vector of incident beam 1 in FIGURE ‘2,
15,“) and 15,") are the complex analytic signals respec
tively representing the X and Y components of the result 55
ant E vector of incident beam 2, 71, is the normalized
‘ phase coherence factor previously de?ned, an") is the
measure of correlation between Ex") ‘and By“), an“) is
the measure of correlation between E1") and 15,"), ‘r,,
is the coherence time of light, and T is the time constant 60
of the photodetectors. This equation is applicable for _
all degrees of polarization of incident beams l and 2, as
The total intensity I of any beam is given by the square _
of the absolute value of its resultant E vector as follows:
l=|EP
(13)
But, [Ela may be resolved as
|E|’=lExl’+lEyl’
(14)
Since the square of the absolute value of a complex
,
'
number is equal to the complex number multiplied by
In order to understand and appreciate the signi?cance
of the terms used in Equation 4, reference will ?rst be 65 its conjugate, then Equation 14 becomes
made to some fundamental concepts of light polarization.
According to the electromagnetic wave theory of light,
will later be shown.
each single light wave is considered as a transverse wave
whose electric vibrations B are in a straight line at right
angle to its ‘direction of propagation (see Fundamentals 70
of Optics, ‘Jenkins and White, 2d. edition, pages 486
et seq., hereafter referred to as Publication D). An
ordinary beam of natural light consists of a number of
such waves, each with its own plane of vibration, such
that an electric vector may be found in any plane of the 75
The elements of the coherency matrix may also be em
ployed to represent the degree of correlation ax, between
the components E, and E,.
r
V (11)’
3,134,840
.,
The absolute value In”! is a measure of the degree of
,-
I
6
and ]a'(=)=]w(2J=1/5I,. Substituting these values into
coherence between Ex and E, and its phase (?g-S2,) is
Equation 24, it becomes
a measure of their effective phase 'difference. This phase
gaference may also be represented by the symbol 5, such
I
?=9x—9y’
Equation 25 should be compared with Equation‘l which
(18)
it generally resembles and which is the result found by
When light is fully polarized, lpxyl=l, when nnpolarized
Hanbury-Brown and Twiss with their original intensity
I |,.,,|=o, and when partially polarized o<lPwl<L
interferometer.
For case (B), assume that Ex") and Ex") are present,
As noted previously, light may be either completely
polarized, completely unpolarized, or partially polarized.
while By“) and Eyw) equal 0. Thus |u,,(1)|=|p,y(2)|=1,
The degree of polarization P is de?ned as the ratio of the
lxxm=lb J,,(1>=0, J,,,<=)=1, and J,,<=>=0. Equation
intensity of the polarized portion to the total intensity, and
may be represented by the elements of the coherency
matrix in the following manner:
24 thereby becomes
15
I;__
_4(JxxJn"'JxyJyx)
_
__4[JuJw1_|#11i:]
which should again be‘compared with Equation 1. The
P
1
(J..+ J,,=)
(19)
result follows when By") and B7“) are assumed present,
When P-l, the light is said to be completely polarized.
with Ex") and Exm equal to .
, '
When P=0, it is completely unpolarized. When 0<P<l, 20
the light is partially polarized.
Since Equation 17 gives the relationship between the
factor an and the elements of the coherency matrix,
Equation 19 may also be expressed as follows:
25 Equation 24 then becomes
P'N/I
'
News’)
(2°)
The foregoing discussion has been limited to an analy
sis of the coherency matrix for a single beam of light.
Where the incident beams 1 and 2 are partially polar
In the case where two incident beams 1 and 2 of light 30 ized, then the specific values of the I coherency matrix
are involved, as in the Hanbury-Brown-Twiss intensity
elements do not have the simple relationships shown
interferometer of FIGURE 1, each such beam has its
above for cases (A), (B), and (C).
own coherency matrix consisting of elements In"), In"),
When the incident beams 1 and 2 are a part of a uni
form plane wave whose degree of polarization is the
for beam 2. In addition, a coherency matrix with ele 35 same over the wave‘ front, then 11:13:], and P; (the
ments composed of 13.x and E, values of both beams may
degree of polarization of incident beam 1)=P, (the de
be derived in the following manner. Since
gree of polarization of incident beam 2)=P. In this in
In“), In") for beam 1, and In"), In"), In"), In")
stance, Equation 24 can be reduced to
40
<urnn>=igzlvsrm1+m ‘
(28)
In Equation 28, when the incident beam is completely
unpolarized, then P=0, and Equation ‘28 reduces to Bqua- ’
tion 25 in case (A).
It is thus apparent from the foregoing, especially Equa
45 tion 24, that the correlation measurement of the original
Hanbury Brown-Twiss intensity interferometer yields in
formation only about the absolute value of an") and
paw, but nothing about their respective phases #1 and
Since
Equation 4, given previously, is actually the result of
mathematically manipulating the terms of Equation 23
in a manner not shown herein.
.
In view of the foregoing brief description of light polar
ization, Equation 4 may also now be rewritten using the
I elements of the coherency matrix for each of the inci
dent beams 1 and 2.
[3,. This additional information, however, may be meas
ured according to the principles of the present invention,
by providing this intensity interferometer with a fully
polarized coherent background source such as is shown
in FIGURE 2. In addition, as previously mentioned, the
phase 4: of the phase coherence factor 71, may also be
55 ascertained by this invention.
FIGURE 2 shows a generalized block diagram of the
present invention which will be used when describing the
theory of operation. A beam of light 15 generated from
a coherent source 10 is supplied to both input channels
60 of the original Hanbury Brown-Twiss interferometer as
composed of photodetectors 163, 164, and correlator 165.
Beam 15, which normally emerges from source 10 in a
completely unpolarized state, is ?rst directed through a
linear polarizing element 154. Element 154 transforms
‘+Iu2’lI#2’|(J'.‘.’J§’,’+J‘,?J?’)1 (24) 65 the unpolarized coherent beam 15 into a linearly polar
ized beam 16, whose angle of polarization is a. when
Equation 24 will now be examined for the cases where
measured, for example, with respect to the X axis of inci
incident beams 1 and 2 are both (A) completely unpolar
dent light beam 1. The angle a may be varied according
ized, (B) fully linearly polarized, and (C) fully ellipti
cally or circularly polarized. In all, cases, incident beams 70 to the procedure subsequently to be described. Linearly
l and 2 are considered partially coherent as evidenced by
polarized beam 16 is then equally divided into two sep
: <AI1AI:> =¥lmltJiws+JegJeg
the fact that ]'ym|>0.
,
For case (A), there is no correlation between Ex“)
and E,(1), or ' between EA’) and By“). Therefore
arate beams 155 and 156 by a phase shifter 17 so that a
. phase difference of 6 exists therebetween. The value of
0 may be varied in a manner subsequently to be ex
75 plained. Each beam 155 and 156 should have the same
3,134,340
'
7
.
in Equation 23. To express the correlation coef?cient
<AI1lAI=1> in the form of Equation 23, it is merely nec-. .
cssary to add together the corresponding terms, in their
' unsquared form, of Equations 23 and 35, then square
. intensity 1,. » Beam 155 is then directed through a com
pensator 160 which retards its E, component by a phase
:1, after which said beam 155 (having intensity I0) is
superimposed on incident beam 1 (having intensity 1;) at
photodetector 163. The resultant beam falling on detec
tor 163 therefore has an intensity 11-1-10. In similar fash
each of the resulting terms. This is permissible because
an incident beam and a superposed coherent background
are mutually independent, since they originate from en- .
ion, beam 156 is directed through a compensator 162
which retards its Ey component by a phase eg, after which
said beam 155 is superimposed on incident beam 2 (mak
ing a resultant beam of intensity lz-l-lo) at photodetector 10
164. Phases :1 and e, are also variable. The coherent
light background 10 should preferably be a stable mono
chromatic point source whose intensity is as high or
higher than the incoming beams 1 and 2. In practice
this coherent background may be provided by a mercury 15 In Equation 36, each of the terms Em"), E10“), En") I
(Hg) 198 lamp commercially available having a spec
and En") can be represented as in Equations 31, 32, 33,
trum of approximately 5461A. The best source for this
and 34, respectively, while their complex conjugates are
purpose would actually be a continuous 'wave optical
formed by changing the signs of their exponents. There- '
maser.
fore,
Equation 36 can be written as
The operation of FIGURE 2 will now be described by 20
beginning with an analysis of the effect of the super
<Amm> =TT—‘3H<E‘."E9"> +10 comm’
imposed coherent background beams 155 and 156 on the
incident beams 1 and 2, respectively, as regards the
change in Equation 23. Coherent beam 155 which may
be considered as one half of beam 15, is normally com 25
pletely unpolarized before it is transmitted through linear
polarizer 154, after which the motion of the end point of
Equation 37 may also be put in the following form so
its resultant vector E0") de?nes a straight line making
as to indicate the effect of the terms '11,, an“) and an“)
an- angle a with respect to some reference such as the X
on the correlation measurement.
axis of incident beam 1. This resultant vector Eon) may 30
'
- .
be resolved into component vectors Em") and En")
which also lie on the incident beam 1 X and Y axes, and
which are defined as follows:
35
Ewu)=Eo(r) sin a
(30)
(38)
When the linearly polarized coherent beam 155 is next
passed through compensator 160, its component En")
vector is retarded (delayed) by an amount q with respect 40
to the Em“) vector. Furthermore, since Eolm=lo (the
intensity of coherent beam 155), then E°=V? Thus,
in view of the foregoing, the component vectors Em")
By using the intensity interferometer of FIGURE 2,
and 8,0") which are superposed on incident beam 1, are
it is now desired to measure the phase’ information con‘
de?ned as follows:
.
'
45 tained in '71,, an“), and an“), which may be respectively
-
represented by e, 5,, and #3. This information is not
' measurable with the original Hanbury Brown-Twiss inter- _
ferometer, as may be ascertained by an examination of
In like fashion, the equations for the Em“) and En“)
Equation 24.
'
vectors of coherent beam 156, which are superimposed 50 Step I.—First, set angle a of polarizer 154 equal to
zero, and then vary angle 0 of phase shifter 17 until a
on incident beam 2 at photodetector 164, may be derived
maximum signal <AI;1AI,1> is detected at the output of
as above. However, since coherent beam 156 is out of
correlator 165. In Equation 38, all terms containing sin
phase by avwith coherent beam 155, due to phase shifter
a. will vanish, and the term lo cos2 me“ now equals
17, this variable must be taken into .consideration. There
55
I fore,
foe". Therefore, any change in the correlator output
<£AIJAIQ> is dependent only upon a change in the value
0
'
e
-
>
correlation between only the coherent beams 155 .
and 156, when they respectively arrive at photodetectors 60 which may be conveniently represented by the symbol
163 and 164, may take a form similar to that of Equation
23 which itself considered only .the incident beams 1.
and 2. Thus
-
F,(0).' Since the square of the absolute value of a com
plex number is equal to the product of that number and
its complex conjugate, this function F1(0) can also be ex
pressed as follows:
+|<E;t’Ea">|'+|<EwEs*'>|*
'
.
(35)
where <AIOAI°> is the correlation between the coherent
beams 155 and 156 at photodetectors 163 and 164, each.
70
beam having an intensity la.
The measured correlation at the output of the correla
tor in FIGURE 2, when considering the effect of the
.' superimposed incident and coherent beams at each photo
detector, may be represented by the primed term
<AI1IAIQI> to
it from the term <MIM3> 75
r
-
(39)
In Equation 39,
3,134,840
10
(?g-p1) and (cg-11) cancel out in the square of the
fourth term because they are equal. After squaring the
second and third terms, it is seen that <AI11AIg1> varies
(4°)
Since elite-fees x+i sin 1:, then
only according to
ITEWIU sin 0: cos alts/mint] 008 (9+ 62- 52-45)
(e"m"'+¢"1is) =l'ml’itcos (0'—¢)_+f sin (0-45)]
-
-
5
+[cos (8—¢)—1 8m (Ii-e1}
=2lml 608 (0-4’) or ltmrl'ln (41)
0 has been set equal to e, the above two cosine
where the superscript R
that only the real term 10 Because
expressions reduce to cos '_ (cg-?g) and’ cos (pl-e1).
of the expanded bracketed value need be considered.'
Since e3==?°+eb and ?2=?o+?1, these two cosine expres~
Thus, Equation 39 becomes
sions are seen to be identical, such that the value of
<A111AI21>
(42)
,
15. varies according to the magnitude of cos (q-??. There
fore when e1=?b maximum signal is obtained. 5, can
then be calculated, since it is 30-51. By measuring max
imum and minimum values, the values
From Equation 42 it may be understood ‘that in Step 1,
any variation in the correlator ouput <AI11AI,1> depends
only upon the change in the angle 0, since it can be
assumed that the values lumnlzm, l-yul and I, remain 20
and
‘constant. Therefore, the maximum output signal from
the correlator is obtained when the phase e of phase
l'YnlRvlyyuunu)
coherence factor 71, is cancelled by the phase difference
are
found,
inasmuch
as the values sin a and cos n: are
0 between the two coherent background beams 155 and
known.
156. This is so, because when 0-¢=0, cos (0--¢)=1_ 25
It should further be appreciated from the foregoing
A minimum correlator output is similarly obtained when
discussion
that the squaring of the measured terms
6—¢=1r, or an odd number multiple of r, since cos
r=—l. In the ?rst of these cases, therefore, the term
huh/Juana“)
(Step 1)
ZIOI'yHh/JnUUnW cos (0-¢) is added to the other two 30
lmlww?mu?
(Step 2)
terms in Equation 42, while in the second, this term is
and
negative. By this technique, then, the phase 9': of '11, may
lmlRwum-lyym. l'mlRvlyyw-lu") (Step 3)
be ascertained, since 0 is varied until maximum output is
obtained at which time ¢=0. If the‘minimum output is
together with their summation, results in Equation 24,
subtracted from the maximum output, and the difference 35 which is used to describe the polarization characteristics
divided by two
4
-
of incident beams l and 2.
MAX-MIN
'
FIGURE 3 shows details of a preferred embodiment of
2
then the quantity ['mIVJn<1)Jn(3> can be found when 40
I, is known.
"'
Step 2.—Next, set et=r/2, set e1==eg=O, and vary 0
until maximum signal output is obtained. In this case,
all terms in Equation 38 containing cos a will equal zero,
the invention which mechanizes the functions shown by
FIGURE 2. Corresponding light beams and subcombi
nations are numbered alike in the two ?gures. The com
pletely unpolarized light from coherent source 10 is passed
through any well known ?xed linear polarizer 154 and
emerges with its resultant vector E at right angles to the
sheet,'such as is indicated by the small circles. The angle
45 of polarization is of beam 16 is de?ned to be equal to
zero with respect to the Ex vectors of incident beams 1
and 2. The variable phase shifter 17 is comprised of a
After expanding this quantity in the fashion of Step I,
the only varying quantity therein (as 0 varies) is
50
zlol/nmlrrml'ml cos [0-(Bt—?a)—¢]
A maximum signal <AI1lAI,1> is therefore obtained
half-silvered mirror 200 which receives the linearly polar
ized coherent light beam 16 and divides it into two beams
155 ad 156 having equal intensity. Beam 156 is directed
to another mirror 201' which in turn re?ects said beam to
wards a movable mirror 202. Mirror 202 is movable
by means 203 in either direction A: shown by the arrow,
such that the distance traversed by beam 156, in going
curs for cos 1.
Since the value of 4: was found in Step 1 55 to and returning from, mirror 202, can be changed. Thus,
above, and 0 is known, the value of (pa-3,) can be de
termined. This di?'erence is called 5,. Step 2 also gives
the value of l-mh/lnmlnm by the use of the formula
MAX-MIN
2
.
Step 3.-—Fix now the value 0 equal to o, and ¢=:r/4.
Vary both a; and eg in such a fashion that the difference
13-41, always equals the difference ‘Ba-B1, or so, which
was measured in Step 2. Therefore, the output
<AI1‘AIs‘>
varies only according to the second and third terms
[\/.l,x(1)J”(3)7nR,"I-|-I° sin ct cos M10149]:
and
the phase 0 between beams 155 and 156 can be varied by
moving the mirror 202 a fraction of a wavelength. After
returning from mirror 202, beam 156 emerges from unit
17. Since beams 16 and 156 strike their respective mirror
60 surfaces with their E vectors parallel thereto, there is no
change in the angle of polarization as originally produced
y 154.
,
Beams 155 and 156 are respectively directed to half—
silvered mirrors 204 and 205 which re?ect a portion of
their incident beams up» to strike a photodetector 206.
‘The purpose of mirrors 204, 205, and photodetector 206
will be explained at a later time, since they are included
in FIGURE 3 merely to simplify the problem of measur
1 ing angle 0 in the above-described Step 1 operation.
Beams 155 and 156, which emerge from mirrors 204 and
205, are still equal but diminished in intensity and are
then respectively directed to half-silvered mirrors 207
and 208 in compensators 160 and 162, respectively. In
in Equation as. This is so because the_variables ., and t, ‘
compensator 160, beam 155 is divided into two beams 209 .
do not appear in the ?rst term, and tln phase di?erences 75 and 210 of equal intensity, with beam 210 being directed
8,184,840
11
"
to mirror 211 and thence to a‘ movable mirror 2.12. After _
being re?ected from mirror 212, beam 210 is directed to- ward mirror 213 where a portion is re?ected upwards to
a photodetector 214. Beam 209 is directed to mirror
215 where a portion is also re?ected upwardsto' photo
detector2l4. The purpose of mirrors 213 and 215, to
gether with photodetector 214, is to simplify the proce
dure of Step 3 above, as will be subsequently explained.
In compensator 162, a similar operation occurs in that
beam 156 is divided into two beams 216 and 217, with 10
beam 216 being re?ected from mirror 218 and a movable
mirror 219. However, no mirrors need be included hav
ing a function similar ‘to mirrors 213 and 215 in compen
sator 160, except as a possible way to equalize the in
tensities of beams217 and 216 with those of the emerg 15
ing beams 209 and 210. It will further be noted that
.
'12
-
'
'
-
that beams 210 and 216 are delayed by equal amounts
.f"'(or where any di?erence in delay is a multiple. of the
1' wavelength) with respect to their respective beams 209
and1216, thus insuring the e1=e3. Then, mirror 202 is
moved to vary 0 and consequently obtain maximum, and
minimum values from motor 236.
.
In Step 3, mirror 202 is moved to a position where 0=¢.
Also, shutters 220, 221, 222, and 223 are opened so‘ that
beams 209, 210, 216, and 217 may all pass therethrough,
with equal intensity. This results in a=1|_'/_4_.,__,_Then,
mirrors 212 and 219 are each set relative to‘ each other
such that e3—e;=?q. Then, mirrors 212 and 219‘are
simultaneously moved, still keeping the ?xed relationship
‘between them of ¢,—¢,=p°, so as to obtain maximum
and
outputs from the motor 236.
'
>
Although mirrors 202, 212, and 219 can in theory be
moved and set to any value of 0, c1 and :3, respectively,
the exact measurement of these angles. may be di?icult
due to the extremely small values of A1: and wavelength A
Beams 209 and 210 are next passed through respective
shutters 220 and 221 in compensator 160, while beams 20 of the coherent light. A more practical scheme'for ac
each beam 209, 210, 216, and 211 has the same angle
of polarization.
216 and, 217 are passed through respective shutters 222
i
6.
' and 223 in compensator 162. Shutters 220, 221, 222,
compli'shing the procedure of Steps 1, 2, and 3 is to pro
vide the additional structure for synchronous detection.
As before noted, a portion of each of the beams 155 and
156 is'de?e'cted upwards from respective mirrors 204 .
to pass or block their respective beams. After passing
L through shutter 221, beam 210 is next passed through a 25 and 205 to the photodetector 206. During Steps 1 and 2,
switch 239 is closed to connect photodetector 206 to the
one-half wave plate 224 which rotates its E vector by 90
tuned ampli?er 238, which in turn is connected to the
degrees, as indicated by the vertical lines. In compensa
variable phase shifter 237. ‘ Means 203 may be adapted
tor' 162, beam 216 is likewise passed through a one-half
to slowly move mirror 202 continuously in the same direc
wave plate 225 which rotates its E vector by 90 degrees.
Beam 209 is re?ected from mirror 226 and then mirror 30 tion Ax for the duration of observation during Steps 1
1
' and 223 can each be selectively opened or closed so as
227 where it is, combined with the vertically polarized
and 2. The consequent continuous change in phase of
beam 156, with respect to beam 155, causes an inter
beam 210 to form the ?nal output beam 155'. Beam
ference effect at photodetector 206, which, via tuned am
217 is likewise re?ected by mirrors 228 and 229 to com
pli?er 238, generates a low frequency signal A
bine with vertically polarized beam 216 and form beam
35
156'.
(1+ 608 u!)
In compensator 160, beam 209 may be considered as
where ul=0, and
the 13,0") component of beam 155, while beam 210 is
to = 21%
the Eyoll) component thereof. By moving the mirror 8.
fraction of a wavelength, the Eyom component may be 40 such that angle 0 is modulated with respect to time. Phase
delayed by any phase c; with respect to the component.
‘ shifter 237 varies the phase of this low frequency signal
In like fashion, by moving the mirror 219 in compensator
A (1+ cos wt) by an amount ‘p, such that the output there;
162 by a fraction of a wavelength, the Em") component
from is A[1+ cos (wt-[41)] which is then applied to
(beam 216) is delayed by phase c; with respect to the
motor 236. Inasmuch as the modulated beam 156 is
Em") component (beam 217).
'
’
' _
also applied to photodetector 164, the output from the
Light beam 1 is re?ected by mirrors 230 and 231 to 45 multiplier 234, as expressed in Equation 42, for example,
combine with coherent beam 155 before impinging on
varies according to
photodetector 163. Light beam 2 is likewise re?ected by
mirrors‘ 232 and 233 to combine with beam 156 before
impinging on photodetector 164. The signal generated
since 0=~t. Tuned ampli?er 235 is provided to pass this
by each of the photodetectors, which represents the in 50 component to the other input of two-phase motor 236.
tensity of the total light incident thereon, is then applied
Thus, the term at! in both inputsto motor, 236wwill cancel
to a multiplier 234 in correlator unit165. The product
'sd'that 'the torque therein is proportional "to
@1317)";
therefrom is then applied via a tuned ampli?er 235 to one - where p is the phase angle of 71;. Therefore, by observe"
winding of an integrating circuit, such as a two-phase
ing the maximum degree of motor rotation, which occurs
motor 236. The output of the integrator, as measured 55 when cos (¢—\I/)=1, the angle ¢ can be determined by
by its rpm, is indicative of the value <Il1AI,1> as de
?ned, for example, in Equation 37. The input to the.
other winding of two-phase motor 236 is seen to ‘come
from a variable phase'shifter 237, although this is so
only because of.asxsshsanslsdem?onteahnique.ahich
is used to eliminate problems in measuring very small
noting the value of ill. The advantage of measuring phase
41 instead of 0 is that the former is easily obtained from
any well known calibrated electronic phase shifter. 237
which operates on low frequency signals. In Step 2, the‘
modulation of phase oand changing of phase 1,0 causes the _
output of the multiplier to vary according to
. phase values.
The operation of FIGURE 3 may now be brie?y de
_
608 l¢—(?1-Pa)—¢]
During Step 3, angle 0 is held constant while c1 and e;
' measure the angles 0 etc. Step 1 of the above-described 65 are both varied. Synchronous detection may be employed
during this step also by moving both mirrors 212 and 219
procedure is performed by ?rst closing shutters 221 and
at the same speed in one direction Ax by‘ means 240,
222 such that the coherent beams 155 and 156 are com
posed only of respective beams 209 and 217 each of which
which thereupon modulates q and c3. However, it must
scribed, neglecting the structure speci?cally designed to
has an angle of polarization is equal to zero. Then, mir
be remembered that these mirrors must remain in the
ror 202 is slowly moved, thus changing 0, to obtain maxi 70 same ?xed relationshiup to each other at this time. Switch
239 is set to now connect photodetector 214 to phase
mum and minimum outputs from motor 236. For Step 2
of the procedure, shutters 220 and 223 are closed such
that the angle a of beams 155 and 156 is equal to 1r/2
shifter 237. The beating of beams 209 and 210 at photo
detector 214 causes a signal A (1+ cos wt) to be generated
therefrom, where ‘wt-e1. By varying it: until maximum
because each is respectively composed of only beams 210
and 216. Also, mirrors 212 and 219 are each moved such 75 output is obtained, then {3, can be determined.
3,134,840
14
13
Instead of using the two-phase integrating motor 236,
correlation function between the total light at each of
the same procedure may also be realized by a synchronous
said photodetectors whereby said phase and said phase
detector and integrating neTworkrwhere"tH'e”§ignal'from’
angle can be determined from the values of 0.
2. Apparatus according to claim 1 in which said sec-'
multiplier 234 is detected under the presence of the-signal
from phase shifter 237. Such a_circuit is shown in FIG
URE 4, and may include a quarter square multiplier 250
ond means comprises means for varying the optical path
traveled by one of said coherent portions.
3. Apparatus according to claim 1 in which said sec
such as is shown and described on page 281 of “Electronic
Analog Computers,” Korn' and Korn, McGraw-Hill Pub
lishing Co'. (2d ed.) 1956. This multiplier is responsive
ond means selectively modulates the phase 0, and which
to the outputs from ampli?er 235 and phase shifter 237
in FIGURE 3 to generate a signal proportional to their
product, which in effect is the function also of motor 236.
In order to eliminate higher order harmonics in this out—
put, ampli?er 251 may be provided having an upper cut
of!‘ frequency less than the value to. The output there
from is then applied to some form of integrator 252, such
as the well known capacitor type, for generating the ?nal
output signal over the observing time interval.
In the event that the maximum distance Ax in FIGURE
3 is traversed before signi?cant output results are ob 20.
tained from the intensity interferometer, the direction of
further includes means for generating a signal corre-,
sponding to said modulated phase 8, means for selectively
phase shifting said signal, and synchronous detection
means responsive to both said phase shifted signal and
said correlator output signal.
‘
4. Apparatus according to claim 1 in which said fourth
and ?fth means each selectively modulates the respective
phases 6; and eg at the same frequency, and which further
includes sixth means for generating a signal correspond
ing to one of said modulated phases, seventh means for
selectively phase shifting said signal, and synchronous
detection means responsive to both said phase shifted
' signal and said correlator output signal.
5. Apparatus according to claim 4 in which said sec
ond means selectively modulates the phase 0, and which
phase 11/ of shifter 237 is likewise changed in polarity.
further includes eighth means for generating a signal
Using this procedure, the observation time may be ex
25 corresponding to said modulated phase 8, and means for
tended inde?nitely until a valid measurement is made.‘
selectively connecting one or the other of said sixth and
.It should be appreciated that the detailed operation of
eighth means to said seventh means.
s
FIGURE 3 is slightly different from the general discus
6. Apparatus for the measurement of the phase be?
sion of the invention as illustrated by FIGURE 2. For
tween the‘ vectors and the phase angle of the phase co
example, in FIGURE 2, the linear polarizer has a variable
herence factor of ?rst and second partially coherent
angle a, while in FIGURE 3 the angle of the light vector
beams, comprising in combination: a ?rst photodetector
emerging from the polarizer is ?xed, with shutter means
means upon which said ?rst light beam impinges, a sec
being provided in each compensatorjg vary al‘frorn 0 to
-'motion of mirrors 202, 212-219 may be reversed if the
- r/2 to 1/4. ~ FIGURE 3 therefore providae's'one practical"
way: although not the only way, to avoid any undesirable
change in the angle of linear polarization, which change
could be caused by a beam striking a mirror surface in
such a manner that its resultant vector is not parallel
thereto. Furthermore, it ‘is possible to linearly polarize
at the same angle a by a polarizer in each channel, each
coherent portion after it leaves the coherent background
beam splitting arrangement, instead of linearly polariz
ond photodetector means upon which said second light
beam impinges, a coherent background source of light,
means to linearly polarize said coherent light at any
angle a, ?rst means for dividing said linearly polarized
coherent light into ?rst and second portions each remain
ing linearly polarized at the angle a, second means for
selectively varying the phase relationship 9 between said '
?rst and second coherent portions, third means follow
ing said second means for selectively retarding the phase
q between the E, and E' vectors of the ?rst coherent
.ing_ the coherent .backgroupdprior to their formation,
the latter arrangement being shown in FIGURE 2. How
portion, fourth means following said second means for
ever, again the mirrors must be arranged so as to avoid
selectively retarding the phase e3 between the Ex and E,
any change in angle due to re?ection of the beam there 45 vectors of the second coherent portion, ?fth means for
respectively superimposing the ?rst and second coherent
from. Other arrangements for performing the above
described measuring steps may ‘obviously be provided.
portions on said ?rst and second beams at said ?rst and
Therefore, while a preferred embodiment of the inven
second photodetectors, and correlator means responsive
to the outputs from said photodetectors for producing
tion has been shown and described, modi?cations thereto
may occur to one skilled in the art without departing from 50 an output indicative of the cross correlation function
the spirit of the invention as expressed in the appended
claims.
What is claimed is:
.
,
1. Apparatus for the measurement of the phase be
tween the‘vectors and the phase angl‘e'of-‘the' phase co~
herence factor of ?rst and second partially coherent
' beams, comprising in combination: a ?rst photodetector
means upon which said ?rst light beam impinges, a sec
between the total light at each of said phodetectors where
by said phase and said phase angle can be determined
from the values of 0, a, e; and e: at selected values of said
output.
,
7. Apparatus according to claim 6 inwhich said second
means comprises means for varying the optical path
traveled by one of said coherent portions.
8. Apparatus according to claim 6 in which said sec
ond means selectively modulates the phase 0, and which
ond photodetector means upon which said second light
beam impinges, a coherent background source of light, 60 further includes means for generating a signal corre
sponding to said modulated phase 0, means for selectively
?rst means for dividing said coherent background into
phase shifting said signal, and synchronous detection
?rst and second portions, second means for selectively
means responsive to both said phase shifted signal and
varying the phase relationship 0 between said ?rst and
said correlator output signal.
second coherent portions, third means for linearly polar
izing said ?rst and second coherent portions both at the 65 9. Apparatus according to claim 6 in which said third
and fourth means each selectively modulates the respec
same angle a, means for selectively varying said angle
tive phases q and q at the same frequency, and which
a, fourth means for selectively retarding the phase e1
further includes sixth means for generating a signal cor
between the E,I and E, vectors of the ?rst coherent por
responding to one of said mmodulated phases, seventh
tion, ?fth means for selectively retarding the phase :2
between the E; and E, vectors of the second coherent 70 means for selectively phase shifting said signal, and syn
chronous detection means responsive to both said phase
portion, means for respectively superimposing the ?rst
shifted signal and said correlator output signal.
and second coherent portions on said ?rst and second
10. Apparatus according to claim 9 in which said sec
beams at said ?rst and second photodectors, and corre
lator means responsive to the outputs'from said photm
ond means selectively modulates the phase 0, and which
detectors for producing an output indicative of the cross 75 further includes eighth means for generating a signal
15
corresponding to said modulated phase 0, and means for
photodetector, and correlator means responsive to the A
selectively connecting one or the other of said sixth
11. Apparatus for the measurement of the phase be
outputs from said photodetectors for producing an out
put indicative of the cross correlation function between
the total light at each of said photodetectors whereby said
tween the vectors and the phase angle of the phase "eo- -
phase and said phase angle can be determined from the
herence factor, .of ?rst and second partially coherent
values of 0, a, e1 and e; at selected values of said output.
12. Apparatus according to claim 11 in which said sec
eighth means'to'said seventh means.
.
beams,~ comprising in combination: a ‘?rst photodetector
ond means selectively modulates the phase 0, and which
means upon which said ‘?rst light
impinges, a sec
ond photodetector means upon which said second light
further includes means for generating a signal corre
beam impinges, a coherent background source of light, 10 sponding to said modulated phase 0, means for selectively
phase shifting said signal, and synchronous detection
?rst means to linearly polarize said coherent light at a
means responsive to bothsaid phase shifted signal and
?xed angle a, second means for dividing said linearly
said correlator output signal.
‘
.
'
'
polarized coherent light into ?rst and 'second portions
13. Apparatus‘ according to claim 11 in which said
each remaining linearly polarized at the angle a and for
selectively varying the phase relationship 0 between said 15 third and fourth means each selectively modulates the
?rst and second coherent portions, third means follow
' respective phases e; and e,‘ at the same frequency, and
' ing said second means for operating on said ?rst coherent _ -
portion,_ said third means comprising means to divide
said. ?rst coherent portion into ?rst and second coherent‘
beams and to selectively change the 'phase s; between 20
them, together with means for rotating resultant vector
of said ?rst coherent beam at right angles to the resultant
which further includes sixth means for generating a signal
corresponding to one of said modulated phases, seventh
means for selectively phase shifting said signal, and syn
chronous detection means responsive to both said phase
shifted signal and said correlator output signal.
14. Apparatus according to claim 13 in which said
second means selectively modulates the phase a, and
vector of said second coherent beam and means to se
lectively interrupt either of said ?rst and second coherent ' which-‘further includes eighth means for generating a
beams, fourth means operating on said second coherent 25 signal corresponding to said modulated phase 0, and
means for selectively connecting one or the other of said
portion following said second‘ means and comprised ac
sixth and eighth'means to said seventh means.
cording to said third means forvselectively producing
?rst and second coherent beams therefrom having result
References Cited in the ?le of this patent
ant vectors at right angles to each other with a phase
difference of q, ?fth means for respectively superimpos so. 7 Brown et al.: Interferometry of the Intensity Fluctua
ing the ?rst and second coherent beams from said third
tions in Light III, and IV, Proceedings of the Royal
means on said ?rst beam at said photodetector, and for
superimposing said ?rst and second coherent beams from
' said fourth means on said second beam at said second
Society of London, vol. 248, Sera. A. 1958, pages 199
237.
-
'