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350-1395
7
SR
15, 1946. ,
W
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nuum
2,409,405
A. F. TUR‘NEZR
RBFLBGTIIG m1 FOR POLARIZED LIGHT,
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Filed Feb. 22‘, 1943
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ARTHUR ‘F. TURNER
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ATTORNEYS‘
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A» F. TURNER
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2,409,401 '
W11” m1’ FOR POLARIZED LIGH!
Fil'odj-‘ob. 22. 1943
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THUR ETURNER
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INVENTOR.
FIG." BY %_M
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ATTORNEYS
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UUU-l \III
2,409,407
UNITED STATES PATENT OFFICE
2,409,407
REFLECTING ELEMENT FOR POLARIZED
LIGHT
Arthur F. Turner, Brighton, N. Y., asslgnor to
Bausch & Lomb Optical Company, Rochester,
N. Y., a corporation of New York
Application February 212, 1943, Serial No. 476,675
4 Claims. (01. 88-65)
1
This invention relates to optical elements and
more particularly to an element for re?ecting
2
and, as understood by the art when referring to
polarized light.
an interference ?lm; I mean a ?lm having a geo
metrical thickness which is of the order of the _
The total internal re?ection of plane polarized
light introduces a phase shift between the electric
vector vibrations in the plane of incidence and
those in the plane perpendicular thereto. Such
magnitude of a wavelength of light.
The phase shift is dependent upon forming the
optical element and the ?lm from materials which
have suitably different indices of refraction and
a phase shift which so alters polarized light is
for a given combination of materials is con
frequently undesirable in many optical systems,
trolled by the thickness of the ?lm as well as the
particularly systems employing analyzing means. 10 wavelength of light and the angle of incidence
Hence, only in special cases and with special pre
caution can a total re?ecting surface be used in
an optical system in which polarized light is
of the same on the re?ecting surface.
There is
no accompanying change of intensity of the light
as a result of the phase shift, that is, the light is
used.
_
completely re?ected. Incidentally, the presence
In its broadest aspect, my invention compre 16 of the ?lm does not change the value of the
hends the modi?cation and/or control of the
critical angle as will be evidenced by the appli
ordinary phase shift created when polarized light
cation of Snell’s law.
'
of any description is re?ected, and an important
feature of the present invention is the ability
The invention is particularly adapted for em
ployment with prisms used in polarized light
through the use of the invention to free re?ected 20 vertical illuminators as well as with prism tele
polarized light from undesired defects which are
scopes and other instruments wherein a roof
present after re?ectance.
prism or a Form system makes the ocular an
A light ray passing from one transparent medi
alyzer of the latter-named instruments partially
um into a contacting medium of lower refractive
inoperative for its intended purpose of reducing
index at any angle other than the normal isbent 25 glare caused by atmospheric polarization or par
away from the normal to the boundary between
tial polarization created by external re?ection.
the two media at its point of incidence with the
It is well known that plane polarized light in
boundary. In accordance with the phenomena
cident on a total re?ecting surface is in general
of total re?ection, if the angle between the in
changed to elliptically polarized light when it is
cident ray and the normal is greater'than the 30 re?ected.
critical angle, the ray will not pass into the sec
The ability of the re?ecting element of the
ond medium but will be completely re?ected in
present invention to alter or modify phase shifts
ternally within the ?rst medium. This condition
is therefore invaluable for varying the phase
can be changed, however, if a third medium of
shift introduced into plane polarized light when
any refractive index is interposed in contact be 35 the same is totally re?ected in order to cause such
tween the ?rst and second mentioned media. If
light to become circularly polarized or to be made
the refractive index of the third medium is great
elliptically polarized to a desired degree. Con
er than Ng sin m, where N; is the index of the
versely, the re?ecting element of the present in- '
?rst medium and a1 is the angle of incidence, the
vention can operate upon elliptically or circularly
e?ect of interposing the third medium between 40 polarized light so as to change the state of the
the two ?rst mentioned media is to shift the
polarization as desired upon its re?ection.‘
occurrence of the total re?ection from within the
In a modi?ed embodiment of the element of
?rst mentioned medium to the boundary between
the present invention, a variable phase shift can
the third and second mentioned media.
be created by forming the interference ?lm so
I have discovered that the phase shift due to 45 that the thickness thereof will vary over the re
re?ection can be selectively modi?ed or controlled
to a marked degree by the presence of an inter
?ecting surface.
_
ference ?lm on the totally re?ecting surface of
Where the ?lm is deposited on only a portion
of the total re?ecting surface, the element can
an optical element which is formed of glass or
be used as a Zernike phase plate for phase con- '
other suitable transparent material and which is 50 trast microscopy. The thickness of the ?lm in
employed for re?ecting polarized light. The ?lm
this application of the present invention is such
forms the third medium just mentioned and is of
as to provide a 90° retardation or acceleration to
an isotropic, homogeneous, ‘transparent and non-'
the zero order of the Abbe diffraction pattern as '
metallic substance. As is well known, ?lms which
required in the theory of the phase contrast
cause interference of light are extremely thin 55 method.
I IUU
,
_
2,409,407
3
4
Other objects and advantages of the present in
vention will appear from the- following descrip
tion taken‘ in connection with the accompanying
drawings in which:
Fig. 1 is a. schematic view of a right angle prism 5
in?nitum until substantially all of the light energy
which embodies my invention and shows the
path of a light ray traced through the prism.
Fig. 2 illustrates graphically the effect on pc
larized light of a thin ?lm placed on a totally
ray components Re through Ra. While, as noted,
the multiple re?ections proceed ad in?nitum and
of the ray L is transmitted out of the prism.
The series of multiple re?ections gives rise to a‘
series of components of the ray L, those occurring
after the ray component R2 being indicated by
hence result in an in?nite number of ray com
ponents, it should be kept in mind that Fig. l
re?ecting surface, this being shown by curves of 10 is for the purpose of diagrammatically illustrat-l
absolute and relative phase displacement for a
ing the general e?ect of the prism and the inter
speci?c ?lm-glass combination.
ference ?lm on light and that only by grossly‘
Fig. 3 is a view similar to Fig. 2 but graphically
exaggerating the thickness of the ?lm 24 is it pos
shows curves of relative phase displacement for
sible to indicate even a few re?ections and result
two different ?lm-glass combinations.
15 ing ray components.
Fig. 4 is a phase shift vector diagram showing
The prism 20 and its ?lm 24 will cause both
the phase shift caused by a particular ?lm-glass
unpolarized and polarized light to be redirected
combination.
in a manner like that just described. However,
Fig. 5 is a schematic view of a vertical illumi
as heretofore noted, a shift in the phase of polar
nator system which employs a right angle prism 20 ized light accompanies its re?ection. In the pres
like that of Fig. 1.
ent invention, the resultant phase shift for a ray
Fig. 6 is a schematic view which shows my in-,
of polarized light will be the vector summation
vention embodied in a special type of deviating
of the phase shifts of its individual re?ected com
prism.
'
ponents which can be vectorially represented by
Fig. 7 is a schematic view showing a modi?ca 25 the components in, m and so on. The total phase
tion of the ‘form of the invention illustrated in
‘ shift for ray L depends on the re?ection of light
Fig. 6.
at the prism-?lm surface, as well as on the total
Fig. 8 is a schematic view of an embodiment
re?ection at the ?lm-air surface and the geo-'
of the invention which employs a rhomb.
metrical thickness of the ?lm. This makes it
Fig. 9 is a schematic view showing a modi?ed 30 possible to selectively alter the phase shift which
form of the element of the present invention.
ordinarily occurs in re?ected polarized light by
Fig. 10 is a schematic view of a microscope
suitably controlling the thickness and index of
in which a still further modi?ed form of the ele
refraction of the interference ?lm which is formed
ment is used.
I
Fig. 11 is a schematic view of an element which
can be substituted for the element of Fig. 10.
One now preferred embodiment of the element
of the present invention is shown by Fig. 1 where
on a totally re?ecting surface.
.
In explanation of the theory underlying the
alteration of phase shift for total re?ection by
means of a thin ?lm, it is to be noted that the
amplitude re?ectance r of a thin ?lm may be
in the reference character 20 represents a simple
expressed in the imaginary form in the following
right angle prism which is formed of glass or other 40 manner, as is customary when ordinary Fresnel
transparent substance of index no. Prism 20,
re?ection as distinguished from total re?ection
as shown, has a hypotenuse surface 2| which
makes an angle of 45° with the side faces 22
and 23. A thin interference ?lm 24 of any suit
able transparent material of index 111' and sub
stantially uniform geometrical thickness d, of the
occurs at each face of the ?lm.
where
“W
(1)
order of a wavelength of light, is carried by the
a is the Fresnel amplitude re?ectance of one
hypotenuse 2|. The prism 20 with its ?lm are
surface of the ?lm;
‘
assumed to be in air. Fig. 1 traces a ray of light
b. is the Fresnel amplitude re?ectance of the
L through the prism 20, the ray L being perpen 50
second surface of the ?lm;
dicular to the face 22, shown as the entrance face,
e is the base of the Naperian logarithms;
and as having an angle of incidence with the I
i is, as usual, the \/—1; and
hypotenuse surface 2| of a1 and an angle of
a, the relative phase displacement between any
refraction in the ?lm 24 of az.
two successive ray components, R1 and R2, R2
When ray L strikes the hypotenuse surface
and Re, etc., which is introduced solely by the
2|, a portion of the ray is re?ected and another
geometrical thickness of the ?lm, and which
portion is transmitted through the prism-?lm
may be given by the following equation:
interface into the ?lm 24 since the total re?ect
ing properties of the prism have been shifted
(2)
from the hypotenuse face to the ?lm-air surface. 60
The re?ected portion of the ray is emitted '
through the exit face 23 and is shown as ray com
it is the geometrical thickness of the ?lm;
a2 is the angle of refraction in the ?lm;
portion of the ray L proceeds through the ?lm 24
to the ?lm-air surface where it is totally re?ected 65 A is the wavelength in vacuum; and
nr is the refractive index of the ?lm.
in a direction substantially parallel to the ray
component R1.
In connection with the sign of a in the fore
At the prism-?lm surface this just-mentioned
going, it is pointed out that a ?nite ?lm thickness
totally re?ected portion of the ray L is partially
introduces a retardation between successive re
re?ected and partially transmitted. The trans 70 ?ected ray components and hence in Equation 1,
mitted portion of the latter forms the ray com
a appears, by convention, with a minus sign.
ponent R: which is substantially parallel to R1.
Contained in the expression for r in Equation 1
At the second re?ection at the prism-?lm surface,
are both the resultant amplitude of re?ectance
the part of the ray so re?ected is directed back
and its resultant phase angle. The latter, herein
into the ?lm 24. This process proceeds ad 75 called u, is the vector summation of the indi
ponent R1. On the other hand, the transmitted
v
2,409,407
6
vidual phase‘ displacements expressed in terms
Where 111 and a: are, as previously noted, the
of angular measure. It is necessary to obtain the
tangent of u and this may be determined through
angles of incidence and refraction, respecg
tively.
the use of a well understood mathematical process
‘
The algebraic signs of a. and 0p are important.
For example, in re?ection at a denser medium
which involves building the quotient of the
imaginary part of Equation 1 with its real part.
This procedures gives rise to the following equa
tion:
there is a phase displacement in the s compo
nent of 180° for all angles of incidence and Equa
tion 7 furnishes a minus sign to express this.
‘ imaginary=
(l-a’) b sin (~11)
(3) 10 For the p component, there is also a 180° phase
tan u
shift up to the Brewster angle. Under custom
real
, a(1+b’)+b(l+a") cos (-a)
ary practice, however, the p component is given
The above equations (1) and (3) are well
a plus sign in this range because the coordinate
known expressions of general character for a
system is so chosen that a plus sign denotes a
thin ?lm. In applying them to the case of an
phase shift. This convention cannot be employed
interference ?lm on a totally re?ecting surface, 15. in the foregoimg calculations and the minus sign
it is necessary to develop these equations into
must be explicit where a, phase shift of 180‘ is
forms where the phase shift caused by total re
involved. As it is written, Equation 8_ for the 1)
?ection at the ?lm-air surface is an explicit fac—
component furnishes the correct sign automati
tor in them. A ray incident on the hypotenuse
cally on both sides of the Brewster angle.
face 2| of prism 20, for example, ?rstsu?ers an 20
Equation 6 requires a valuation of p, the phase
ordinary Fresnel re?ection at the prism-?lm
shift resulting from total re?ection at the ?lm
interface and therefore the symbol a in Equation
air surface at an angle or. This valuation may
1 can be left unaltered. However, the portion of
be acquired by a calculation of the phase shift
this ray which reaches the second surface of the
for the s and p components by the use of the
?lm is totally re?ected and the amplitude re 25 following equations which are based on those,
?ectance of this portion at the second surface for example, set forth by Lord Kelvin in his
may be written as follows:
Baltimore Lectures.
be"’=e“
(4)
Where b is the amplitude re?ectance at the ?lm
air surface and will equal unity where the re
?ection is total; and
s is the phase displacement introduced into each
of the individual ray components R2, R: and.
As indicated by the signs in Equations 9 and
so on by total re?ection at the ?lm-air surface 35 10, the 8 component is advanced in phase while
for light incident on that surface at an angle
the 1) component is retarded, a fact in connection
(12, it being observed that no phase shift due
with polarized light which was ?rst pointed out ‘
by Kelvin.
to total re?ection is added to the ray compo
nent R1 which originates at the prism-?lm
The phase shift occurring in polarized light,
40 when re?ected by an optical element having a
surface.
totally re?ecting surface on which there is an
interference ?lm, may be calculated from Equa
When Equation 4 is incorporated into Equa
tion 1 so as to obtain the factor 5 in .the latter,
it may be shown that the amplitude re?ectance
for a ?lm on a totally re?ecting surface assumes
the value noted below.
tion 6 for given refractive index combinations
of the optical element and the ?lm. In con
45 ducting these calculations, Equations ’7 and 8
are ?rst used to ?nd the Fresnel amplitude re
‘?ectances as and up for a desired angle of in
cidence m. The phase angles 55 and 5;) are then ,
calculated from Equations 9 and 10.
Similarly, where the factor B appearing in 50 In practice, Equation 6 is solved separately for
Equation 4 is introduced into Equation 3, the lat
the s and p components by keeping a and p of that
ter takes on the following form:
equation constant while varying a, the ?lm thick
ness in terms of angular measure, to obtain tan ‘its
tan u=
and up, each as a function of the ?lm thickness.
55 Knowing tan us and up, the angles they represent
The incident or re?ected polarized light may
are readily determined and it is merely a question
be resolved into a component which is vibrating
of adding us to up to obtain the relative phase
in a plane perpendicular to the plane of incidence,
shift produced by the given combination.
herein called the s component, and into a com
Since the phase shifts u are obtained as tan
ponent which is vibratingin a plane parallel to 60 gents, there is an ambiguity as to whether an
the plane of incidence, herein called the p com
ponent. The phase angle u will be different for
the s and p components since both the prism
?lm amplitude reflectance a and the phase shift
angle will fall in'the I or III quadrant if the
. sign is positive or in the II or IV quadrant if the
sign is negative. However, where u is computed
for the complete range of a. from 0° through 360°,
,8, the latter being due to total re?ection, are 65 the correct quadrant will become apparent from
different in the two preferred directions. Re
the continuity of the curve.
“?ectances a. and ap for the s and p components
With the ?lm thickness equal to zero, 1. e. with I
may be obtained from the following Fresnel for
a=0,-Equation 6 should give a value for tan a
mulae:
identical with that obtained in Equations 9 and
70 10 for no ?lm. That such is the case will be ap
_sin (or-a1) ‘
parent when nu instead of ns and (11 instead of a:
are used in the latter equations. It is to be ob
served that the phase shift goes through a com—
=Itan (cg-a1)
tan (ai+a1)
(8)
plete cycle in the thickness range given by ¢=0°
75
to a=360°.
.
:
-
‘
2,409,407
7
8
Fig. 2 graphically plots ?lm thickness 4 against
phase angle 11. for the absolute phase displace
ments uliand up and the relative phase displace
diagrammatically to scale and the phase resultant
given for a ?lm of index 1.72 which is formed on
material of index 1.34 to a thickness or of 210", the
ment A or u. minus up for a particular case in
order to illustrate the phase changes which the
s and p'components undergo. Curves 25 and 26
angle of incidence for the parent ray L being
45°, In Fig. 4, the s and p values for the total
phase shift suffered by each of the ?rst few multi
ple re?ected ray components are disclosed. For
of Fig. 2 are respectively for the u; and up com
ponents while curve 21 gives the values for A.
' example, s and p values for the ray component
R1 are represented, respectively, by the vectors
parent medium of index 1.52 on which there is 10 v1; and mp, for the ray component R2 by the vec
a ?lm of index 1.34, the angle of incidence m be
tors 112s and. ‘172p and so on for the remaining ray
ing equal to 45°, The ?lm thickness parameter a.
components which are disclosed. Lines 12. and 17p
is shown as varying from zero to 360°. For the
represent, respectively, the resultants of the s and
conditions regarding index and angle of incidence
p vectors and connect the point of origin of the
just set forth, curves of the character shown in 15 vector diagram to the s and p vectors for the last
Fig. 2 give phase shifts at each ?lmed totally re
ray component to be re?ected.
The curves are plotted for the case of a trans
fleeting surface of any type of optical element in
cluding of course the right angle prism 20 of Fig.
It will be noted that the angle between the two
strongest vectors, namely, 02. and 172p for the ray
1 as well as the other forms of optical elements
hereinafter described.
component R2 which is re?ected directly from the
20 totally re?ecting surface of the ?lm, is independ
In general of more importance than the phase
angles u. and up taken separately is their di?er
ence A. It is this difference which determines
ent of the thickness of the ?lm. As the ?lm thick
ness varies, vectors v2; and 172p rotate in ?xed rela
tion to each other. It is the addition to them‘ of
the elliptic defect when a totally re?ecting sur
the remaining vectors which alters the phase an
face is used in a system with polarized light. As 25 gle. For this reason, vectors v2; and we are drawn
shown by curve 21 in Fig. 2, A increases in the
?rst in the vector diagram, although so far as
negative direction from a value of 140° at zero
the values of the resultants are concerned, the
?lm thickness to a maximum value of 164°, de-‘
vectors could have been laid out in any desired
creases to a minimum of 134° and rises again to
sequence.
reach the zero thickness value of 140° at the com 30
Moreover, each pair of s and p vectors which
pletion of the cycle or at a value of :1. equal to 360°.
succeed the vectors w; and U2]: will also rotate in
Fig. 3 shows relative phase displacement or A
curves for two other examples. These curves
compare the difference in effect when employing
a ?lm which has a lower refractive index and one 35
having a higher index than the index of the opti
cal element on which each ?lm is deposited.
?xed relation to each other as the ?lm thickness -
changes. However, the rate of rotation is differ
ent for each of the succeeding pair of vectors;
Consequently, there will be large variations in
the phase displacements between the s and p re
sultants as will be apparent from the positions
Curve 28 gives the relative phase displacement A
of the vector ‘Us and up. From three to six of the
for an optical element of refractive index 1.72
?rst succeeding ray components must usually be
with a ?lm of index 1.34 while curve 29 is for an 40 taken into account to obtain an accurate answer
optical element having a refractive index of 1.52
with ?lm index of 2.30. In both curves the angle
of incidence a1 is equal to 45°. The curves 28
and 29 will indicate the e?ect on polarized light
by these graphical methods. In the latter con
nection, it may be necessary to plot more of the 8
values than the p values in preparing the vector
diagram as the s values are more copiously re
caused by right angle prisms which are similar 45 ?ected at the ?lm-prism surface than are the p
in outline to that shown in Fig. 1. Of noteworthy
values and by the same token us is more affected
interest is the opposite trend of the curves 28 and
by the ?lm than up.
29 for like ?lm thicknesses.
To more fully illustrate one useful application
The foregoing will indicate the possibilities of
of the theory heretofore set forth, I have shown
altering the phase shift so as to obtain desired 50 in Fig. 5 the ?lmed right angle prism 20 of Fig.
polarization in re?ected light. With speci?c ref
l embodied in a simple type of vertical illumlnator
erence to the two extreme cases in the three ex
system employed with a microscope. The system
amples set forth in Figs. 2 and 3, it will be evident
shown in Fig. 5 is particularly adaptable for the
that by varying the ?lm thickness it is possible
examination of opaque anisotropic specimens in
to alter the value of the phase shift which occurs 55 polarized light and comprises condenser lenses
at an angle of incidence of 45° between the limits
30 which direct light from a source 3| through a
of 116° to 178° for the index combination which
polarizer 32. Plane polarized light emerging from
curve 28 represents and between the limits of
polarizer 32 is directed by lens 33 into the prism
‘72° and 154° for the index combination of vcurve
20 which is shown with an interference ?lm 24 ’
. 29. Greater divergence of the indices of the ?lm 60 on its hypotenuse. Prism 20 totally re?ects the
and of the substance on which the ?lm is provided
light downwardly through one side of the objec
will widen these limits.
tive lenses 34 onto the specimen 35. Light re
The alteration in phase shift originates in the
?ected from the specimen ascends through the
interference of the ray components broken off
other side of the objective lenses 34 to analyzer
from the parent incident ray L by re?ection at 65 36, from which latter, analyzed light is passed
the two surfaces of the ?lm, as best illustrated
to the eyepiece of the microscope.
in Fig. 1. Since the ray components R1, R2, etc., '
If a right angle prism without a re?ectance
all arise from the parent incident ray L, they are
?lm on its hypotenuse is employed in a system
coherent and their phase displacements will add like that of Fig. 5, it may be demonstrated that
vectorially. The relative phases of the individual 70 the phase displacement A, between the s and p
ray components, as heretofore mentioned, will be
components of plane polarized light which is to
altered both by re?ection at the ?lm surfaces and
tally re?ected by the prism, will equal 139° 45’
also by the retardation due to the thickness of
for a prism having an index of 1.52. When a
the ?lm.
right angle prism without an interference ?lm
Fig. 4 shows this vector addition carried out 75 is used in the semi-aperture type of system of
2,409,407’
Fig. 5, it is necessary to orient the polarizer 32
with extreme precision with regard to the prism
so that the vibration direction of the polarizer
surface 40 at 45°. The end or entrance and exit
surfaces 4| and 42, respectively, of prism 31 are
inclined at 45° to the totally re?ecting surfaces-I
is parallel or perpendicular to a principal section
40 and 39.
of the prism. Otherwise, the ellipticity introduced
by total re?ection would not allow the analyzer
The‘ phase shift normally introduced into po
larized light by material of index 1.52 when the
light is incident to a totally re?ecting surface at
.
to give vextinction. Even if the polarizer be
oriented in this way, oblique rays will become el
45° equals 139° 45' as already noted. Assuming
liptically polarized and only the center of the
prism 31 to have a refractive index of 1.52, the
10 two re?ections at the totally re?ecting and un
?eld can approach good extinction.
If the phase shift A can be made 0° or 180°
?lmed surface 40 will cause phase shifts A1 and
or 360° etc., the elliptic defect will be substan
As, each equal to 139° 45', to be introduced into
tially eliminated when plane polarized light is
polarized light which is traversing the prism.
re?ected. In the case of e?ecting a phase shift
The full phase shift thus caused by re?ection at
of 180° by the employment of a, re?ectance ?lm, 15 the surface 40 will thus equal the sum of A1 and
the totally re?ecting surface acts as a half wave
As or 279° 30'.
-
plate rotating the direction of polarization but
not creating ellipticity. As the curves of Figs. 2
and 3 show, the phase shift A of a right angle
A phase shift also takesv place at the totally
re?ecting surface 39, its value also equaling 139°
45' when 39 is un?lmed. However, if the total
prism of index 1.52 can be varied within the range 20 phase shift desired is 360°, it will be apparent
of 70° to 155° with a ?lm of ‘index 2.3 and with
that the totally re?ecting surface 39 should pro
in a range of 130° to 165° with a ?lm of index
1.34. None of the usable values of A, namely 0°,
180° or 360°, fall within the just-noted ranges.
vide a shift A2 of only 80° '30’ so that A1, A: and‘
As will add to the sum of 360°. Referring now to
Fig. 3, it may be noted that the desired value of
However, a desired value for A of 180° may be 25 80° 30' for A2 may be obtained by providing a, ?lm
reached by changing the glass .or other material
of the prism to that of a higher index.
38 of index 2.3 on the totally re?ecting surface
1.72. This indicates that a prism of still higher
index is needed when using a ?lm of index 1.34
and suggests the use of a prism formed of extra
dense ?int of index 1.75 to give the desired A of
The form of the invention shown in Fig. 6 sug
gests the possibility of ?lming both re?ecting sur
faces of the prism. Such practice is carried out
39 to a thickness on of 75° or a of 160° when the
For example, curve 28 of Fig. 3 shows that a A
prism 31 has an index of 1.52. Obviously, other
of nearly 178° may be obtained when using a ?lm
index combinations for the ?lm 38 and prism
of index 1.34 with a of 210° on a prism of index 30 31 fall within the scope of the invention.
in Fig. 7 which shows a prism 43 of a construc
180°. The foregoing examples, illustrating the 35 tion and design which is substantially similar to
prism 31. The totally re?ecting surfaces of the
effect of ?lm thickness and index, bring out an
prism 43 are denoted by 44 and 45 and its en
important aspect of the invention. This resides
in the ability of the practices herein described to
trance and exit surfaces by 46 and 41. If a
phase shift of 360° is to be obtained, it would be
index combination by the suitable selection of 40 desirable to have a phase shift of 120° at each of
?lm thickness.
the three total re?ections of a ray La shown at
In a system employing a right angle prism,
an angle of incidence of 45°. A1, A1 and A: may,
in this instance, be each given a value of 120° by
such as the prism 20, the use of a phase shift of
placing a suitable ?lm 48 on each totally re?ect
180° as compared to 0° or 360° will reverse the di
rectional sense of rotation given an analyzer, lo 45 ing surface 44 and 45. For a prism of index
1.52, a ?lm 48 having an index of 2.3 and a thick
cated behind the right angle prism, in following a
ness 0: of 20° or 240° will provide the desired
given rotation of the polarizer. A clockwise ro
shift of 120° ~at each re?ection, reference being
tation of the polarizer, as seen by looking towards
again had to the curve 29 of Fig. 3. The inven
the light source, can be followed by rotation of
the analyzer in the same directional sense. The 60 tion also comprehends the use of other index
combinations for the ?lm 48 and the prism 43,
azimuthal rotation sense of the vibration from
the analyzer is reversed by the act of re?ection ’ the foregoing merely being set forth as one illus
trative example to indicate the scope of the in
and also by the half wave or 180° phase shift. In
vention.
the case of the vertical illuminator system shown
in Fig. 5, the re?ection at the surface of the speci 55 In the forms of the invention shown in Figs.
6 and 7, the values of A which are used, occur at
men 35 again reverses the azimuthal rotation
values of a where the curve 29 of Fig. 3 is ascend
sense so that the tube analyzer 36, or a cap
ing or descending. Accordingdy, _a small change
analyzer if used, would have to be rotated coun
in a will change the individual A’s and will destroy
terclockwise to follow a clockwise rotation of
the polarizer 32.
80 the condition that the overall phase shift be ex
actly 360°. It is to be noted that a varies for a .
Use of my invention is not limited solely to a
given geometrical ?lm thickness, not only with the
right angle prism. For example, it may be ap
angle of incidence on the ?lm but also with the
plied to a 90° deviating prism formed of a right
wavelength. Preferred practice hence selects a
angle prism and a rhomb cut from the same piece
of glass or other transparent material. A prism 65 prism-?lm combination having the value of the
desired phase shift A as a maximum or minimum
31 of this character is shown in Fig. 6 and it may
in the curve of A plotted against 0:.
be formed of materials which vary widely in in
Thus in the prism 43 of Fig. 7 it is preferable
dex. The prism 31 of Fig. 6 is shown with a thin
to employ a ?lm of an index such that, the high
?lm 38 on its re?ecting face 39. The other totally
provide a predetermined phase shift in a given
re?ecting face 40 is left un?lmed.
or the low points of the A and 0: curve will fall at
a thickness a corresponding to a A of 120°.
Fig. 6 schematically traces a ray L1 through
Where the curve of A plotted against a ful?lls
the prism 31, the multiple re?ections at the ?lm
this condition, that is to say, when
38 being omitted from the drawingsyfor the pur
pose of clarity. Ray L1 is shown as travelling in
1A
the direction of the arrows and as incident to 76
do:
2,409,407‘
,
equals zero, there will be but slight variation of
A with a. change of 1 caused by change in wave
length or in angle of incidence. Film material
the use of the ?lm 54 on the surfaces 50 and 5|. .1:
In the case of overcoming the elliptic defect
of index'2.0 instead of 2.3 is suggested for de
pressing the A and d curve sufficiently to satisfy
this condition for the 120° phase shift needed in
in plane polarized light, the ?lms 54 should be of
such character as to cause A1 and A: to be each
the prism 43. When the ordinary right angle
equal to 90° thus causing a total phase shift of
180°. A suitable combination for this purpose
prism 20 of Figs. 1 and 5 has an index of about
1.75 and a ?lm of index 1.34 is used to obtain a
phase shift of 180°, the condition that
12
the total re?ection at the two air-glass surfaces.‘
This phase shift will,' of course, be altered by;
is provided by a ?lm of index 2.3 at a thickness
10 on of 60° as will be apparent from a study of the
curve 29 of Fig. 3. However, the preferred con
in
dition that
do:
_
dA
equal zero is perforce satis?ed since a phase
It;
shift of 180° will just barely be reached by this 15
equal zero would not be satis?ed with this ?lm
combination.
While the combination described provides a
index and it would, in general, be advantageous
phase shift of 120° at each totally re?ecting
to select a ?lm material of lower index.
surface of the prism of Fig. 7 so as to cause in
As previously mentioned, my invention compre
cident plane polarized light to be emitted as 20 hends alteration of the phase shift to produce
plane polarized light from the prism, such prac
circularly polarized light. This can be effected
with plane polarized light by the use of the right
tice need not necessarily be followed. The value
angle prism ‘20 of Fig. 1 ?lmed on its hypotenuse
of the phase shift at each total re?ection is im
material so long as the sum of all of the phase
2| to give a value for A of 90°.
shifts caused by the prism of Fig. 7 adds to 360°
if plane polarized light is to emerge therefrom.
bination like that described in connection with
the rhomb of Fig. 8 could be employed for this ’
purpose, the same reservation as to the value of
It will hence be realized that my invention com
prehends the use, on different totally re?ecting
surfaces, of ?lms of different indices and/or
_
(101
thicknesses as well as ?lms of like index and of 30
not equaling zero for this combination being here
noted. Useful applicationof a circularly polariz
ing prism of this nature can be expected in con
nection with a polariscope as well as in other in
the same or different thickness in obtaining a
phase shift of any desired value, including a
phase shift of 360°.
While I am aware that the art has employed a
90° deviating prism of a geometrical shape sub
stantially similar to the prisms of Figs. 6 and '7
for the purpose of eliminating ellipticity, the
prior art effort, as exempli?ed by U. S. Patent
No. 2,128,394, has depended entirely on the
A ?lm-glass com
‘
struments.
-
'
A variable phase shift can be introduced into a
beam of polarized light, referring now to Fig. 9, '
by forming the interference ?lm 55 of variable
thickness on the total re?ecting surface 55 of the
formation of the prism of glass of special refrac 40 prism 51. For example, if a ray such as ray L4
tive index to obtain this effect, namely, an index
be directed so as to be incident on the surface
56 in an in?nite number of cases as by moving
equal to the V3. My invention is distinguish
‘the stop 58 from the position shown in full linesv
able therefrom on the basis that I employ a prism
to the position shown in broken lines, a con
of substantially any index as well as in the use
tinuously varying phase shift will be created in
of an interference ?lm with such a prism. It -‘
the ray L4.
should also be noted that alteration of phase shift
An element such as illustrated in Fig. 9 can
is not limited in my invention to a single value,
at any totally re?ecting surface but that the
be used to compensate and measure an unknown
retardation in a sample introduced in the ray.
alteration may be selected, whereas the phase
shift at each totally re?ecting surface of the just 50
I have found that one embodiment of the ele
ment of the present invention can be used as a
mentioned prior art prism must always be lim
Zerm‘ke phase plate for phase contrast micro
ited to 120°. Furthermore, since one is not lim
ited to a glass of de?nite index, a glass which is
resistant to weathering or staining can be used,
In this embodiment of the present invention,
so that the phase shift produced is permanent
referring now to Fig. 10, an interference ?lm 50 is
and is not altered by the spontaneous formation
deposited on the re?ecting face SI of the prism
62. The ?lm E0 is formed on but a portion of the
of a stain ?lm over long periods of time.
scopy.
Fig. 8 illustrates the invention in use with
‘
,
surface BI and the ?lm should be of such a size
another type of 90° prism, namely, the rhomb
and area as to cover in projection the zero order
49 having the parallel totally re?ecting surfaces
Abbe diffraction pattern in the back focal plane
50 and 5| which are joined by the parallel end
faces 52 and 53, the latter being at an angle of
45° to the two totally re?ecting surfaces. A re
, of the objective of the microscope and should
be of such a thickness as to provide a 90° retarda
tion or acceleration to the zero order as required
?ectance?lm 54 is formed on both of the re
?ecting surfaces 50 and 5|. Passage of a'ray
Le, incident on ?lm 54 at 45°, is traced through
the prism 49.
As heretofore pointed out, glass of index 1.52
will introduce a phase shift of 139° 45’ in polar
ized light which is totally re?ected in such me-v
dium and is at an angle of incidence of 45°. Thus,
if the rhomb 49 were un?lmed and were con
structed of glass of index 1.52, there would be
a total phase shift of 2 X 139" 45' or 279° 30' in
polarized light passing through the prism due to
in the theory of the phase contrast method.
Since the retardation of the ?lm with respect to
the un?lmed remainder of the totally re?ecting
surface 6| will be different for light vibrating in
r the p and s directions, polarized light would prob
ably be preferable for illumination. For a ?lm in
dex of 1.34 on a right angle prism of index 1.52,
Fig. 2 shows that the ?lm thickness should be
that corresponding to a of 85° for the p direction
and a of a value of 120° for the s direction. If the
?lm thickness is one or the other of these two
values, a variation in retardation between these '
“Uni ‘II I I \UU
2,409,401”
13
14
limits would be obtained by rotating‘the polarizer
glass, the re?ectance ?lm may be provided by
,
from one position to the other.
leaching out‘ acid soluble glass forming oxides;
The prism 62 would be inserted in the optical
to leave a layer which is rich in silica on the to»;
system of the microscope as schematically shown‘
tally re?ecting surface of the optical element.
in Fig. 10,-ln which the ocular and objective sys
Films may be formed in many other ways and
tems are indicated at 63 and 64, respectively, and
by the use of many other materials so long as
the specimen at 65. In this use of the element of
the ?lms ful?ll the requirements as to refractive
the present invention, the prism 62 would replace
index and thickness previously mentioned. For
the conventional Zernike phase plate which is
example, a ?lm in the form of a thin layer of
positioned in the back focal plane of the micro 10 glass, which answers theserequisites, falls within
scope objective.
the scope of my invention. Also contemplated
It will be» obvious that an element such as shown
are ?lms formed by the well known process of
in Fig.- 11 could be used in place of the element 62
spraying such substances as titanium tetrachlo
shown in Fig. 10. This element of Fig. 11 com-_
ride, silicon tetrachloride and the like on glass or
prises a prism =66, the re?ecting surface 61 of 15 other transparent material.
which carries, except on a predetermined por
Therefore, while certain preferred embodiments
tion thereof, an interference ?lm 68. In the ele
of the invention have been illustrated and de
ment 68 the un?lmed portion of the re?ecting
scribed herein, it is to be understood that the
surface 61 for the correct indices of the prism
invention is not limited thereby but is suscepti
and ?lm give a variation in phase acceleration 20 ble of changes in form and detail within the
between certain limits by rotating the polarizer
spirit of the invention and the scope of the ap
pended claims.
from one position to the other as in the case of
I claim:
While the foregoing illustrations have ‘all em
‘1. A transparent body having a plurality of
ployed an angle of incidence of 45°, my invention 25 totally re?ecting surfaces from which light en
may be carried into practical effect at other angles
tering the body is successively re?ected, each of
of incidence. Total re?ection at angles other
said surfaces being characterized by introducing
than 45° is often met in practice, for example, in
a shift in the phase of the components of po
roof prisms, where, as in military and other ob
lariz'ed light which is passing through the body‘
servation instruments, atmospheric polarization 30 and which is re?ected by said surfaces; and
the element 62.
_
.
must be considered. The effect of phase shift ,
caused in a. roof prism or a Porro system is to
means on one of said surfaces for selectively
forms an important aspect of my invention.
Besides the single ?lms illustrated in the draw
ings, my invention comprehends the use of mul
tiple ?lms, that is to say, superposed ?lms of dif
metallic interference ?lm, said ?lm being trans
modifying the phase shift between the compo
prevent the full effective use of an ocular analyz
nents normally introduced in polarized light by
er associated with such instruments. Thus, the
re?ection at that surface whereby to selectively
use of ?lms for angles of incidence other than 45° 35 alter the sum of the phase shifts occurring at all
ferent indices.
of the surfaces, said means comprising a non
parent and substantially isotropic and having
an index of refraction different from that of said
In . connection with multiple 40 body and a substantially uniform geometrical
?lms, it may be pointed out that large effects are
to be expected from their use because of the large
values of the vector components to which they
give rise.
As a special case, my invention includes within
its scope the bene?cial effects on phase shift
‘ derived in instances where degenerate total re?ec
tion takes place due to the use of a ?lm of an in
a
thickness which is of the order of magnitude of
a wavelength of light, the refractive index and
thickness of the ?lm being chosen to produce the
selected phase displacement of the polarized light
re?ected by said surfaces.
_
2. An optical element formed of transparent
material and having a surface positioned in a
path of polarized light rays for totally re?ecting
dex which is lower than the index of the ‘optical
the
polarized light rays, means for selectively.
element or prism upon which it is placed.
50
altering the phase displacement between the com
Examples of the invention have been described
ponents which polarized light normally under
in regard to the re?ection of plane polarized light.
goes when it is totally re?ected at said surface,
Obviously, the phase of elliptically or circularly
said means comprising a thin homogeneous, non
polarized light may be altered by the use of a
suitable index combination of the ?lm and the 55 metallic transparent ?lm on said surface, said
?lm having a refractive index which is different
optical element used for total re?ection. Thus,
under suitable conditions, it is possible to alter
elliptically polarized light so that on re?ectionv
it is rendered plane or circularly polarized or is
from that of the element, said‘ ?lm being sub
stantially isotropic and having a substantially
uniform thickness, the refractive index and
elliptically polarized to a desired degree. Sim 60 thickness of the ?lm being chosen so as to pro
duce the selected phase alteration in the polar
ilarly, circular polarized lightv may on re?ection
ized light re?ected by said surface. _
a
be rendered plane or elliptically polarized.
3. An optical element of transparent materi
Re?ectance or interference ?lms employed
having a surface at which total internal re?ec
throughout my invention are of well known types
and their formation is well understood by the art. 65 tion-takes place for use in an optical system em
ploying polarized light of a known wave length
Under one practice, a ?lm suitable for use on a
and which is incident on said surface at a pre
totally re?ecting surface may be formed by de
positing a metallic salt or oxide on such surface
by a high vacuum process. While any suitable
determined angle; and means on said surface for
sorbing as to light, tin oxide and zinc sulphide to
tally re?ected by said surface, said means com
prising a relatively thin non-metallic interfer
selectively controlling the phase displacement be
transparent substance may be used to form an 70 tween the components of polarized light which is
normally introduced ‘when polarized light is to
evaporated ?lm, substances which are non-ab
name two examples, are preferable but notessen- ’
ence ?lm covering said surface, said ?lm being
tial.
Where the optical element to be ?lmed is of 75 substantially isotropic ‘and having an index of
15
2,409,407’
refraction less than that of said element, the
effective optical thickness of said film being less
16
polarized light which normally occurs when pom '
larized light is totally re?ected, said means com?‘
than a wave length 01' said light and varying from’
prising a thin, homogeneous, non-metallic, trans:
a maximum thickness at one side of said surface
parent ?lm, which is substantially isotropic and
to a minimum thickness at the opposite side of
has a refractive index different from that of said
said surface.
body; said ?lm having a, geometrical thickness
4. An optical element for re?ecting polarized
which is of the order of magnitude of a wave a
light comprising a body of transparent material
length of light, the refractive index and thickness
having a surface positioned in a path of'polar
of the ?lm being chosen to produce the selected
ized light rays for totally re?ecting said rays, 10 phase displacement of the components of the
means on the surface for selectively altering the
polarized light re?ected by the surface.
phase displacement between the components of
ARTHUR F: TURNER.
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