Method of making a hologram

This specification discloses a method of making a hologram imaged substantially without aberrations during the use when the wavelength of a light during the making differs from the wavelength of a light during the use and having high diffraction efficiency. In order to eliminate any aberration occuring when the hologram is used in a light beam of a different wavelength and to obtain high diffraction efficiency, a making light beam is caused to enter a predetermined coaxial optical system from outside the axis thereof to impart a suitable aberration, and a hologram is formed on a hologram sensitive material by the making light beam.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
This invention relates to a method of making a hologram, and in particular 
to a method of making a hologram imaged substantially without aberrations 
during use when the wavelength of light in making the hologram differs 
from the wavelength of light during the use and having high diffraction 
efficiency. 
2. Description of the Prior Art 
A hologram lens can be obtained by making a hologram of a point source of 
light by the use of the holography technique. The hologram lens is of 
planar shape and has advantages that it is a thin film lens having a 
thickness of the order of several microns and that a number of lenses can 
be mass-produced on the same flat plate by the step-and-repeat method. 
Therefore, the utilization of the hologram lens as an optical element in 
an optical system utilizing a laser light, such as the condensing lens of 
the optical head of an optical disc device or a collimation lens for 
converting the divergent light beam from a semiconductor laser into a 
parallel light beam, has been proposed. 
The optical system of the optical head portion of the optical disc device 
is such that a condensing hologram lens is disposed on the front surface 
side of a disc substrate so as to read through the disc substrate a signal 
recorded on the back surface of a plastic plate usually of a thickness of 
the order of 1.1 mm which is the disc substrate. The hologram lens is 
disposed with an air space of the order of 1 mm with respect to the disc 
substrate so that no collision is caused by vibration of the disc, and a 
cover glass or protective layer of a suitable thickness is interposed 
therebetween to prevent adherence of dust or the like to the hologram 
lens. 
An example of the optical system for making the hologram lens used in such 
an optical system is shown in FIG. 1 of the accompanying drawings. In FIG. 
1, part of a monochromatic light 2 emitted from a laser light source 1 is 
transmitted through a half-mirror 3, is reflected by a reflecting mirror 4 
and is condensed in a pin-hole 16 by a microscope objective lens 15, and 
the light transmitted through the pin-hole 16 is transmitted through a 
collimation lens 17 and becomes a parallel light beam 18, which is 
transmitted through a parallel flat plate 9 and enters a hologram 
sensitive material 11 applied to a hologram substrate 10. This is a 
reference light. On the other hand, the light beam reflected by the 
half-mirror 3 is reflected by a reflecting mirror and is condensed in a 
pin-hole 8 by a microscope objective lens 7, and the light transmitted 
through the pin-hole 8 becomes a divergent light beam 12, which is 
transmitted through the parallel flat plate 9 and enters the hologram 
sensitive material 11. This is an object light. The object light beam 12 
is made into a divergent light beam having spherical aberration by the 
parallel flat plate 9, and this light beam and the reference light beam 
form interference fringes at the position of the hologram sensitive 
material 11, and these interference fringes are recorded on the hologram 
sensitive material 11. By developing this, there is obtained a hologram 
lens. 
Where the hologram lens thus made is used, a laser light of the same 
wavelength as that of the laser light used during the forming of the 
hologram lens is made into a parallel light beam at the same angle as the 
parallel light beam 18 but in the reverse direction and is caused to enter 
the hologram 11. The light diffracted by the hologram 11 becomes a 
convergent light beam having the spherical aberration imparted to the 
object light during the making and, after this has been transmitted 
through the cover glass and the disc substrate, a light spot is produced 
at a position corresponding to the pin-hole 8 during the making of the 
hologram. 
Thus, by using light of the same wavelength during the making and during 
the use, complete wave surface reproduction can be accomplished by the 
hologram lens substantially without aberrations. 
Particularly, where a volume type phase hologram is made with bichromate 
gelatine or the like used as the hologram sensitive material 11, the 
diffraction efficiency of the hologram can be improved up to approximately 
100% and the utilization efficiency of light becomes sufficient. 
Presently, it is preferable that a compact, light-weight semiconductor 
laser requiring no special modulator be used as the light source in an 
optical system using a hologram. The oscillation wavelength range of such 
a semiconductor laser is usually from the near-infrared range to the 
infrared range (0.78 .mu.m or more). Accordingly, where the making of the 
hologram lens as described above and the image reproduction using the same 
are to be effected by the use of such semiconductor laser, it is necessary 
to use a hologram sensitive material having effective sensitivity at 0.78 
.mu.m or more. As a hologram sensitive material having sensitivity in this 
wavelength range, there is a silver salt sensitive material sensitized by 
infrared light. However, the hologram made by the use of this sensitive 
material is an absorption type hologram and therefore has the disadvantage 
that its diffraction efficiency is as low as several %. By means of 
bleaching, the diffraction efficiency may be improved to a certain degree, 
but there is a limit to this. 
Accordingly, to improve the diffraction efficiency, it is necessary to 
adopt a volume type phase hologram, and the aforementioned bichromate 
gelatine is typical as a sensitive material used for making of such a 
hologram, but in this sensitive material, the effective sensitivity area 
is up to green light having a maximum wavelength of 0.55 .mu.m, and it is 
merely possible to endow such sensitive material with the sensitivity up 
to red light of 0.6 .mu.m even if special pigment sensitization is 
effected thereon. Further, a volume type hologram sensitive material 
having effective sensitivity in the near-infrared range and the infrared 
range is not yet known. 
Therefore, no semiconductor laser can be used during the making of a volume 
type phase hologram, but a laser of a shorter wavelength is used. When the 
hologram made in this manner is used in an optical system using a 
semiconductor laser, the wavelength of light differs during the making and 
during the use and therefore, it is not imaged without aberrations and 
thus, in some cases, aberration correction becomes necessary. 
Further, in the hologram making optical system as shown in FIG. 1, the 
parallel flat plate 9 is disposed immediately forwardly of the hologram 
sensitive material 11, and this results in creation of harmful ghost 
images. That is, a light beam 13 resulting from part of the object wave 
light beam 12 being reflected by a second surface and then a first surface 
of the parallel flat plate 9 or a light beam 13' resulting from part of 
the object wave light beam 12 being reflected by the surface of the 
hologram sensitive material 11 and then the second surface of the parallel 
flat plate 9 enters the hologram sensitive material 11, whereby harmful 
ghost images are recorded. These ghost images are reproduced during the 
use of the hologram lens and may thus result in creation of unnecessary 
ghost light and reduction in diffraction efficiency. 
For the reasons set forth above, it has been difficult in the conventional 
making method to make a hologram used in a light of a wavelength different 
from the wavelength of the light during the making. However, there is a 
method in which, as shown, for example, in Japanese Laid-open Patent 
Application No. 74708/1982, a suitable aberration is pre-imparted to a 
hologram making light beam and a hologram is made so that there is no 
aberration when it is used in a different wavelength, but in this case, 
the optical system for imparting a suitable aberration is not coaxial and 
use has been made of such means as inclining the optical element. 
Accordingly, the designing of such optical system for making a hologram 
has been very cumbersome and has required much labor and, when it is to be 
actually disposed, strict positional accuracy has been required and 
therefore, the setting thereof has also required much labor. 
SUMMARY OF THE INVENTION 
In view of the above-described prior art, it is an object of the present 
invention to provide a hologram making method which is capable of imaging 
a light substantially without aberrations during the use and making a 
hologram having high diffraction efficiency when the wavelength of a light 
during the making of the hologram differs from the wavelength of a light 
during the use of the hologram and which enables an apparatus for making 
the hologram to be easily obtained and readily permits the setting of the 
apparatus. 
The present invention achieves the above object by causing a making light 
beam to enter from outside the axis of a coaxial optical system, imparting 
a suitable aberration to said making light beam in advance by said coaxial 
optical system, and making a hologram so as to produce a predetermined 
diffracted light at each point of the hologram during the use and to 
substantially satisfy the Bragg condition at said each point. 
Said coaxial optical system comprises an optical element such as a 
conventional spherical lens, a non-spherical lens or a cylindrical lens 
and constitutes rotation-symmetrical optical system or a 
rotation-symmetrical optical system. Accordingly, where said coaxial 
optical system is to be designed in order to impart a suitable aberration 
such as coma or astigmatism to said making light beam, the designing can 
be accomplished as simply as the conventional optical designing and the 
setting of the optical element is also easy. 
Also, where two light beams, i.e., the object wave light beam and the 
reference wave light beam, are used as said making light beam, a hologram 
can be ideally made by substantially equalizing the intensities of the 
object wave light beam and the reference wave light beam in the hologram 
sensitive material.

DESCRIPTION OF THE PREFERRED EMBODIMENT 
In order to describe the present invention in detail, the Bragg condition 
in a volume type hologram will hereinafter be described by reference to 
Tosihiro Kubota, "A Study on the Characteristic and Applications of Lipman 
Hologram" (Tokyo University Production Technology Institute Report Vol. 
30, No. 2, February 1982). 
FIG. 2 shows the manner in which an incident light ray is diffracted by a 
volume type hologram. When the coordinate system is plotted as shown and 
the unit vectors in the directions of the incident light 18 and the 
diffracted light 19 are X.sub.c (l.sub.c, m.sub.c, n.sub.c) and X.sub.i 
(l.sub.i, m.sub.i, n.sub.i), respectively, and the pitch of the 
interference fringes in the hologram 17 at the point of incidence 20 (y,z) 
of the incident light 18 onto the hologram 17 is P.sub.x, P.sub.y, P.sub.z 
and the wavelengths of the incident light 18 and the diffracted light 19 
are .lambda..sub.c and the refractive index of the hologram 17 is N.sub.c, 
the incident light 18 and the diffracted light 19 satisfy the following 
grating equations: 
EQU P.sub.y (m.sub.c -m.sub.i)=.lambda..sub.c /N.sub.c (1.1) 
EQU P.sub.z (n.sub.c -n.sub.i)=.lambda..sub.c /N.sub.c (1.2) 
##EQU1## 
When l.sub.i is of the same sign as l.sub.c, it shows the transmission 
type, and when l.sub.i is of the sign different from l.sub.c, it shows the 
reflection type. 
The diffraction efficiency of the diffracted light 19 decreases as the 
amount of deviation from the Bragg condition becomes greater. When the 
wave number vectors of the incident light 18 and the diffracted light 19 
are .rho. and .omega., respectively, and the wave number thereof is 
k.sub.c and the inverted grating vector of the hologram 17 is K.sub.c, 
there is established the following relation between these amounts: 
EQU .omega.=.rho.-K.sub.c -.DELTA.k (2.1) 
where .DELTA.k is a vector having only an x component, and this is an 
amount representative of the measure of the deviation from the Bragg 
condition. The condition expressed by equation (2.1) when .DELTA.k=0 is 
called the Bragg condition. These amounts can be expressed as follows: 
EQU .omega.=k.sub.c X.sub.i (2.2) 
EQU .rho.=k.sub.c X.sub.c (2.3) 
EQU 1/P.sub.c.sup.2 =1/P.sub.x.sup.2 +1/P.sub.y.sup.2 +1/P.sub.z.sup.2 (2.4) 
EQU K.sub.c .tbd..vertline.K.sub.c .vertline.=2x/P.sub.c (2.5) 
EQU .DELTA.k=k.sub.c (l.sub.c -l.sub.i)-k.sub.e (l.sub.r -l.sub.o)/M.sub.x ( 
2.6) 
EQU k.sub.c =2.pi.N.sub.c /.lambda..sub.c (2.7) 
EQU k.sub.e =2.pi.N.sub.e /.lambda..sub.e (2.8) 
where k.sub.e, .lambda..sub.e and N.sub.e are the wave number and 
wavelength of the light and the refractive index of the hologram sensitive 
material, respectively, during the making of the hologram, P.sub.c is the 
pitch of the interference fringes at the point of incidence 20, 
.vertline.K.sub.c .vertline. is the norm of K.sub.c, and l.sub.r and 
l.sub.o are the x component of the unit vectors X.sub.r (l.sub.r, m.sub.r, 
n.sub.r) and X (l.sub.o, m.sub.o, n.sub.o) in the directions of the 
reference light and the object light at points (y,z) during the use of the 
hologram. M.sub.x is the rate of variation in dimensions in x direction 
caused by the developing process or the like of the hologram. Likewise, 
the rates of variation in dimensions in y direction and z direction are 
represented by M.sub.y and M.sub.z, respectively, and these are called the 
shrinkage. .DELTA.k is the measure of the deviation from the Bragg 
condition, and the amplitude intensity of the diffracted light is maximum 
when .DELTA.k is zero. 
From what has been described above, it will be seen that to obtain a formed 
image substantially free of aberrations and high diffraction efficiency 
during the use, a hologram making light beam may be made so that the 
diffracted light ray by the diffraction at each point of the hologram 
determined by equations (1.1)-(1.3) is imaged without aberrations and 
further the Bragg condition is satisfied at each point of the hologram. 
Accordingly, consideration will hereinafter be given to a light beam which 
satisfies equation (2.1) under the condition of .DELTA.k=0. If .DELTA.k=0 
is given in equation (2.1), 
EQU .omega.=.rho.-K.sub.c (2.1.1). 
Since equations relating to the y component and the z component of equation 
(2.1.1) are equations (1.1) and (1.2), the inverted grating vector which 
satisfies grating equations (1.1)-(1.3) at each point of the hologram so 
as to image substantially without aberrations during the use and satisfies 
the Bragg condition equation (2.1.1) is nothing but K.sub.c which 
satisfies equation (2.1.1). Accordingly, the making light beam may be 
determined so as to satisfy equation (2.1.1) at each point of the 
hologram. The determination of the making light beam will hereinafter be 
described by reference to FIG. 3. In FIG. 3, reference numerals 22 and 23 
designate the wave number vectors R and O, respectively, of the reference 
light and the object light. Reference numeral 21 denotes the inverted 
grating vector K.sub.e of the interference fringes formed by R and O. When 
the pitch of the interference fringes during the making of the hologram is 
P.sub.e and K.sub.e is the norm of k.sub.e, and V.sub.e is the unit vector 
of k.sub.e , the following equation are established: 
EQU K.sub.e .tbd..vertline.k.sub.e .vertline.=2.pi.P.sub.e (3.1) 
EQU 1/P.sub.e.sup.2 =1/P.sub.xe.sup.2 +1/P.sub.ye.sup.2 +1/P.sub.ze.sup.2 (3.2) 
where P.sub.xe, P.sub.ye, and P.sub.ze are the grating pitch during the 
making. If the unit vector of k.sub.c is V.sub.c, V.sub.c is as follows: 
##EQU2## 
Next, with the shrinkage taken into account, V.sub.e (l.sub.ve, m.sub.ve, 
n.sub.ve) may be found from V.sub.c (l.sub.vc, m.sub.vc, n.sub.vc) as 
follows: 
EQU m.sub.ve =Sign(m.sub.ve).multidot.[1+(l.sub.vc M.sub.y /m.sub.vc 
M.sub.x).sup.2 +(n.sub.vc My/m.sub.vc M.sub.z).sup.2 ].sup.-1/2 
EQU n.sub.ve =Sign(n.sub.vc).multidot.[1+(l.sub.vc M.sub.z /n.sub.vc 
M.sub.x).sup.2 +(m.sub.vc M.sub.z /n.sub.vc M.sub.y).sup.2 ].sup.-1/2 
##EQU3## 
Here, it is to be understood that l.sub.ve is of the same sign as l.sub.vc 
in the case of the transmission type and l.sub.ye is of the sign different 
from that of l.sub.vc in the case of the reflection type. 
R and O for preparing this V.sub.e can be calculated by the use of the 
following equations: 
EQU V.sub.e1 =(R.times.O)/.vertline.R.times.O.vertline. (3.6.1) 
EQU V.sub.e2 =(R+O)/.vertline.R+O.vertline. (3.6.2) 
EQU V.sub.e =(V.sub.e1 .times.V.sub.e2)/.vertline.V.sub.e1 +V.sub.e2 
.vertline.(3.6.3) 
If equation (3.6.3) is arranged by substituting thereinto equations (3.6.1) 
and (3.6.2), the following equation is obtained: 
EQU V.sub.e =(O-R)/.vertline.O-R.vertline. (3.6.4) 
On the other hand, the pitch P.sub.e of the interference fringes during the 
making is determined by the following equation: 
EQU P.sub.e =(l.sub.vc /l.sub.ve).multidot.(1/M.sub.x).multidot.P.sub.c (3.6.5) 
By the use of equations (3.6.4) and (3.6.5), the inverted grating vector 
K.sub.e is found as follows: 
##EQU4## 
The relative relation between R and O is determined by equation (3.6.4). 
This state is shown in FIG. 3. The cone 24 of FIG. 3 is determined by 
equation (3.6.4), but has a degree of freedom of rotation relative to 
V.sub.e axis 21. The reference light 22 and the object light 23 must be in 
the same plane 25. Also, at this time, the inverted grating vector is in 
the same plane 25. 
There are various methods of continuously determining the directions of the 
localized reference light 22 and object light 23 in the hologram over the 
whole surface of the hologram, and as seen, for example, from FIG. 3, the 
plane 25 containing the inverted grating vector K.sub.e may be determined 
primarily and over the whole surface of the hologram. For that purpose, a 
continuous vector field may be found over the whole surface of the 
hologram passing through the origin 20 of K.sub.e, and for example, a unit 
vector field in the direction of the x-axis or a divergent vector field 
having a source on the surface of the hologram is a good example of it. 
FIG. 4 shows an optical system in a case where a hologram lens is used in 
the optical head portion of an optical disc device. In FIG. 4, a parallel 
light beam 26 of wavelength .lambda..sub.c enters a hologram substrate 28, 
is diffracted by about 100% by a hologram 29, passes through a cover glass 
or protective film 30 into the air, becomes a converged light beam 27 and 
is condensed on the back 31' of a disc 31. 
FIG. 5 shows an optical system for making the hologram used in the optical 
system of FIG. 4. In FIG. 5, a reference wave light beam 33 of wavelength 
.lambda..sub.e and an object wave light beam 34 are caused to enter a 
hologram sensitive material 32. The reference wave light beam 33 and the 
object wave light beam 34 are the reference light R and the object light O 
having the same azimuth angle as the inverted grating vector K.sub.e at 
each point of the hologram as described above. As a method of making such 
light beams, there is a method using a conventional lens system. 
Description will hereinafter be made of the method using a conventional 
lens system. 
The method of making the reference wave light beam and the method of making 
the object wave light beam are identical to each other and therefore, only 
the method of making the object wave light beam will be described herein 
and making an intended wave surface by controlling the off-axis aberration 
of a spherical or non-spherical lens will be considered. In FIG. 6, a 
reference plane 36 is set in a portion of the object wave light beam 
(including also the other skew light rays than the meridional plane) 34 in 
which no caustic line is produced, and this is defined as the image side 
principal plane of the lens system. The object side principal plane 37 is 
set at a suitable position, and the angle formed between the normal 35 to 
the two principal planes and the central light ray 34' of the object wave 
light beam 34 to be made is .omega..sub.1. Thus, the object wave light 
beam 34 is formed as a wave surface having the off-axis aberration of a 
parallel light beam 38 which has entered this optical system at an angle 
of view .omega..sub.2. However, it is to be understood that the image side 
principal plane 36 is coincident with the exit pupil position and the 
object side principal plane 37 is coincident with the entrance pupil 
position. The third-order and fifth-order aberration coefficients are 
found from the amount of lateral aberration (.DELTA..sup.y1, 
.DELTA..sup.z1) on the image plane 36' and the pupil coordinates (.xi., 
.rho.), and the arrangement of the optical system is determined. Thereby, 
such a lens arrangement which could not be realized by the actual lens 
system is excluded before the system is designed. The direction of the 
optic axis of the lens system is the x.sup.1 -axis, and the coordinate 
axis in the meridional plane is the y.sup.1 -axis. Thereafter, an optical 
system for creating the object wave light beam 34 having a predetermined 
aberration may be designed by the use of the conventional lens designing 
technique. At this time, a realizable lens is designed with the reference 
plane 36 being regarded as the exit pupil. 
Examples of the numerical values of the pupil coordinates (.xi., .rho.) and 
the amount of lateral aberration (.DELTA..sup.y1, .DELTA..sup.z1) will be 
shown in Tables below. Table 1 below shows the values regarding the object 
wave light beam, and Table 2 below shows the values regarding the 
reference wave light beam. Also, the meridional plane and the sagittal 
plane refer to those on the surface of the hologram. The wavelength of the 
light during the making was 0.488 .mu.m. 
TABLE 1 
__________________________________________________________________________ 
Meridional 
.epsilon. 
21.744 
12.959 
0 -12.640 
-20.637 
plane .DELTA.y.sup.1 
0.3044 
0.1083 
0 0.1181 
0.340 
Sagittal 
.epsilon. 
1.4759 
0.5570 
0.0634 
plane .eta. 
21.359 
12.93 4.327 
.DELTA.y.sup.1 
0.1246 
0.0471 
0.00535 
.DELTA.z.sup.1 
-0.0484 
-0.0194 
-0.00501 
Focal length 44.5 
Angle of view 5.degree. 
F.degree. No. 1.1 
__________________________________________________________________________ 
TABLE 2 
__________________________________________________________________________ 
Meridional 
.epsilon. 
21.736 
14.462 
0 -17.937 
-31.182 
plane .DELTA.y.sup.1 
2.291 
1.6417 
0 -2.3170 
-4.270 
Sagittal 
.epsilon. 
-2.5855 
-1.0358 
-0.1218 
plane .eta. 
-14.454 
-9.2368 
-3.1841 
.DELTA.y.sup.1 
-0.4122 
-0.1651 
-0.01942 
.DELTA.z.sup.1 
-0.6039 
-0.4523 
-0.1675 
Focal length 110.0 
Angle of view 15.degree. 
F.degree. No. 2.1 
__________________________________________________________________________ 
FIG. 7 shows a specific example of the hologram making optical system 
designed in the manner as described above. A parallel light beam 40 having 
entered a lens system for reference wave at an angle of view of 
.omega..sub.r is converted into a reference wave light beam 33. On the 
other hand, a parallel light beam 42 having entered a lens system 41 for 
object wave at an angle of view of .omega..sub.o is converted into an 
object wave light beam 34. The 10 reference wave light beam 33 and the 
object wave light beam 34 enter a hologram sensitive material 32, and the 
interference fringes formed there are recorded. By developing this 
sensitive material, there is obtained a hologram. It is desirable to 
render the object wave light beam 34 and the reference wave light beam 33 
into substantially the same intensity in the hologram sensitive material 
32, and for this purpose, suitable means for adjusting the quantity of 
light can be disposed in the optical system. 
In the above-described embodiment, only a hologram lens has been shown as 
the hologram, but the present invention can also be utilized in making 
other popular holograms. 
In the hologram making method according to the present invention, the 
procedure as described previously is used to select the used wavelength 
during the use of the hologram and the making wavelength during the making 
of the hologram, and by taking into account the required specification and 
performance of the hologram and the aberration occurring when the hologram 
is made at said making wavelength and used at said used wavelength, an 
aberration for correcting said aberration is imparted to the hologram 
making light beam by a predetermined coaxial optical system, and a 
hologram is made by said light beam, whereby there can be obtained a 
hologram having a desired performance. 
Accordingly, the present invention is not restricted to the above-described 
embodiment, but various applications thereof based on the concept of the 
present invention are conceivable.