Mold for optical element and a method of molding optical element

A method of molding an optical element numerically analyzes the thermal stress produced on a molded optical element product within a mold in a visco-elastic temperature range or elastic temperature range of an optical element material in a cooling step of the molding process is on the basis of a visco-elastic characteristic of the optical element material. A correction for the molding face of the mold is made on the basis of the value obtained by the numerical analysis so that any error between the optical functional face of optical element molded by the mold at room temperature and the optical functional face set on design may fall within a tolerance, thereby determining the molding face adapted to the shape of the optical functional face set on design.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates to a method for molding an optical element in 
which the optical element having a complex face shape such as an 
aspherical lens is press-molded at high precision. 
2. Related Background Art 
Recently, as optical instruments become smaller and lighter, it is desired 
to reduce the number of glass lenses for use in the optical system. One 
means for realizing this includes using an aspherical lens capable of 
correcting aberration even if the number of lenses is reduced. A method of 
producing such a lens having an aspherical shape is well known, in which 
glass material is sandwiched between the mold members having a 
predetermined surface precision and then is press molded. 
A conventional method for molding an optical element by press molding has 
been disclosed in Japanese Patent Publication No. 61-32263. This method is 
such that glass material is sandwiched between a pair of mold members 
having a molding face finished to a face shape precisely corresponding to 
an ideal form of a completed shape of an optical element, and is 
press-molded in a range of temperatures at which the viscosity of glass 
material is from 10.sup.8 to 5.times.10.sup.10 poise. Thereafter, the 
cooling is effected so that the temperature difference of the glass 
material and the mold members may not exceed at least 20.degree. C., and a 
molded optical element is taken out from the mold members in a range of 
temperatures at which the viscosity of glass material is less than 
10.sup.12 poise. With such a method, it is possible to produce high 
precision optical elements. 
In the above conventional example, however, when producing an optical 
element of a shape whose surface accuracy is hardly obtained, such as a 
concave lens having a large radius of curvature of the surface or a 
meniscus lens, it often occurs that required surface accuracy (e.g., a 
high accuracy value such as less than one-fourth (1/4) line of Newton 
ring) can not be satisfied even though various molding conditions are set 
to be optimum. 
In order to improve the surface accuracy of a completed optical element 
even in a minor way, the pressing force is necessary to be strictly 
controlled in the cooling step after molding, for example, but it is quite 
difficult to control the pressing pressure strictly. Also, any slight 
change in the other molding conditions will decrease the surface accuracy. 
Furthermore, to improve the surface accuracy of an optical element, an 
auxiliary device may be often needed, so that there arises a problem that 
the cost of a processing apparatus is increased, thus giving rise to the 
higher cost of the optical element itself. 
SUMMARY OF THE INVENTION 
Accordingly, the present invention has been achieved in the view of the 
aforementioned problem, and its object is to provide a method for molding 
an 10 optical element, capable of producing the optical element having a 
high surface accuracy without strictly controlling the molding conditions 
and preparing for any auxiliary device. 
In order to solve the aforementioned problem and accomplish the above 
object, there is provided a molding method for an optical element, 
according to the present invention, in which a glass material rendered in 
a softened state by heating is pressed using a pair of mold members, and 
an optical functional face to which surface shape of a molding face on the 
mold members is transferred, is formed on the surface of the glass 
material, comprising, in molding a plurality of optical elements, a first 
step of setting the molding condition such that a certain contour map of 
the surface can be stably formed on the optical functional face of each 
optical element, and a second step of molding the optical elements using 
the mold members worked into such a shape that the surface shape of the 
molding face cancels the certain contour map of the surface. 
Also, the molding method for an optical element according to this invention 
is characterized in that the molding conditions are defined by the 
temperature difference of the one pair of mold members, the cooling rate, 
the pressure applied to the glass material in the cooling step, and the 
releasing temperature. 
Also, there is provided a molding method for an optical element, according 
to the pre sent invention, in which a glass material rendered in a 
softened state by heating is pressed using a pair of mold members, and an 
optical functional face to which surface shape of a molding face on the 
mold members is transferred, is formed on the surface of the glass 
material, comprising a first molding step of molding the glass material 
using primary mold members having a molding face shape corresponding to 
the surface shape of an optical element of a predetermined shape, based on 
the molding conditions such as predetermined heating temperature, mold 
member temperature, pressing force, pressing time and cooling rate, a 
measurement process of measuring the surface shape of optical element 
molded in the first molding step, a calculation step of calculating the 
error between measurement data obtained in the measurement process and 
final desired shape data of the optical element, a correction working step 
of working secondary mold members by correcting the molding face of the 
primary mold members based on a result obtained in the calculation 
process, and a second molding step of press molding the glass material 
under the same molding conditions as in the first molding step. 
Also, the molding method for an optical element according to this invention 
is characterized in that the difference between measurement data obtained 
in the measurement process and the final desired shape data is at least 
equal to or less than 0.2 line of Newton ring. 
Also, the molding method for an optical element according to this invention 
is characterized in that among the molding conditions, the temperature 
difference of the one pair of mold members is 0.degree..+-.2.5.degree. C., 
the cooling rate is 20.degree..+-.5.degree. C./min, and the pressure in 
cooling is set at 5.+-.1.5 kN. 
Also, the molding method for an optical element according to this invention 
is characterized in that the optical element is an aspherical lens. 
It is a second object of the present invention to produce a mold in 
consideration of the visco-elastic characteristic of glass material. 
A thermal stress is produced in the cooling step due to a difference 
between thermal expansion coefficient of glass material within the mold 
and that of the mold, and may cause a deformation in the molded optical 
element after opening of the mold. In particular, when the optical element 
to be molded is a concave lens on both faces or a concave meniscus lens, 
the molding face of the mold can not be transferred to the glass material 
precisely, giving rise to a contour map of the surface on the optical 
functional face. The bad effect is remarkable when the ratio of lens 
central thickness to lens outer peripheral thickness is large. 
The present invention has been achieved in the light of the above problem, 
and aims to provide a mold and a producing method thereof, wherein taking 
into consideration that in a cooling step regarding from press molding 
temperature to releasing temperature, the glass material exhibits 
remarkable visco-elastic characteristic in a range of temperatures at 
which the viscosity of glass material lies from 10.sup.12 to 10.sup.15 
poise, exerting great effect on the thermal stress, numerical analysis is 
conducted, and the molding face is determined on the basis of numerical 
analysis so that the optical functional face of a molded optical element 
may be adapted to an optical functional face set on design. 
Therefore, in the mold and the producing method thereof according to the 
present invention, when press molding the optical element material using 
the mold, the thermal stress produced in an optical element molded product 
within the mold in a visco-elastic temperature range or elastic 
temperature range of the optical element material in the cooling step of 
the molding process to be performed is numerically analyzed based on a 
visco-elastic characteristic of the optical element material. The molding 
face of the mold is corrected based on the value obtained by the numerical 
analysis so that any error between an optical functional face of the 
optical element molded by the mold at room temperature and an optical 
functional face set on a design may fall within a tolerance level, thereby 
determining the molding face to be adapted to a shape of the optical 
functional face set on design. 
In this case, for the numerical analysis of the thermal stress, the history 
of temperature and/or pressing force upon the thermal stress being 
produced, may be added to the calculation basis. Also, it is preferable 
for the molding face to have its correction value determined based on the 
value obtained by the numerical analysis by means of computer simulation 
over several order. Also, the molding face may be determined in such a 
manner as to mold an optical element molded product, using practically a 
mold having the molding face corrected on the value obtained by the 
numerical analysis, and to correct it repeatedly over several order until 
the error between the optical functional face of the optical element 
molded product at room temperature and the optical functional face set on 
the design falls within a tolerance level.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
A preferred embodiment of the present invention will be described below 
with reference to the accompanying drawings. 
FIG. 1 illustrates the construction of a mold 12 to which a molding method 
of an optical element in one embodiment is applied. FIG. 1 also 
illustrates the construction of the mold 12 for molding a concave lens in 
a state in which the pressing operation of glass material 4 has been 
completed by an upper mold member 16 and a lower mold member 18, so that a 
glass lens has been substantially molded. 
In FIG. 1, a shell mold 14 constituting the outer shell portion of the mold 
12 is laid on a molding device body 10 of an optical element through 
support substrate 20. The shell mold 14 is formed like a prism of a 
substantial square shape as viewed from the above, with through holes 14a, 
14b formed on its central axis, penetrating the shell mold 14 from top to 
bottom. Among these through holes, an upper through hole 14a has an upper 
mold member 16 which is formed like a column fitted thereinto to be 
slidable vertically. At the upper end of the upper mold member 16, a 
disk-like flange portion 16a is formed, whereby the upper mold member 16 
is prevented from moving further downward by the lower face of the flange 
portion 16a which comes into direct contact with the upper face 14c of the 
shell mold 14 from upward, whereby, the press stroke of the upper mold 
member 16 downward is defined. Also, on the lower face of the upper mold 
member 16 is formed a molding face 16b for forming the optical element 
face by pressing glass material 40 and transferring a desired shape to its 
surface. 
Above the upper mold member 16, an air cylinder 22 for producing a pressing 
force on to the glass material 40 is disposed, supported by a support 
member (not shown). Below the air cylinder 22, a piston rod 22a extends 
along a vertical direction, with the lower end of the piston rod 22a 
connected to the upper end face of the upper mold 16. Accordingly, when 
the air cylinder 22 is activated to push the piston rod 22a downward, a 
pressing force P1 is applied to the glass material 40. 
A lower mold member 18 formed to be column-like similar to the upper mold 
member 16 is fitted through hole 14a so as to be slidable vertically. At 
the lower end of the lower mold member 18, a disk-like flange portion 18a 
is formed. The lower face 18c of the flange portion 18a is in direct 
contact with the upper face of the support substrate 20 on which the shell 
mold 14 is laid. The pressing force P1 is applied downward from the upper 
mold member 16 through the glass material 40 onto the lower mold member 18 
laid on the support substrate 20. On the upper end face of the lower mold 
member 18 is formed a molding face 18b for forming the optical functional 
face by transferring a desired shape to the lower face of the glass 
material 40. 
Accordingly, the glass material 40 includes, on its upper plane, an optical 
functional face 40a to which the surface shape of the molding face 16b of 
the upper mold member 16 is transferred, and on its lower plane, an 
optical functional face 40b to which the surface shape of the molding face 
18b of the lower mold member 18 is transferred. 
The thickness of a molded concave lens (glass material 40) is defined by 
the lower plane of the flange portion 16a of the upper mold member 16 
coming into direct contact with the upper plane 14c of the shell mold 14 
as described above so that the thickness of the concave lens (40) may not 
change for each working. 
An air cylinder 24 is secured to the lower plane of the molding apparatus 
body 10. A piston rod 24a of the air cylinder 24 is connected to the lower 
plane 18c of the lower mold member 18 sequentially through a through hole 
10a formed in the molding apparatus body 10 and a through hole 20a formed 
in the support substrate 20. This air cylinder 24 acts to apply a pressure 
P2 on the concave lens (40) by pushing the lower mold member 18 upward, to 
prevent the concave lens (40) from collapsing in shape during cooling step 
after molding operation of the concave lens (glass material 40). 
On the side plane of the shell mold 14 is formed an opening hole 14d, 
through which the glass material 40 is supplied into the inside of the 
mold 12. The concave lens (40) molded is taken out from the inside of the 
mold 12. 
Heaters 26 are disposed within the shell mold 14 to heat the shell mold 14, 
the upper mold member 16 and the lower mold member 18, as well as heat the 
glass material 40 via the shell mold 14, the upper mold member 16 and the 
lower mold member 18. The heaters 26 are positioned at the four corners. 
A procedure for molding the concave lens by the mold 12 thus constructed 
will be described below. 
First, the piston rod 22a of the air cylinder 22 is retracted, whereby the 
upper mold member 16 is slid upward with respect to the shell mold 14, as 
shown in FIG. 2, to move away from the lower mold member 18. In this 
state, the glass material 40 heated to a predetermined high temperature is 
supplied onto the molding face 18b of the lower mold member 18 through the 
opening hole 14d of the shell mold 14 by means of an autohand or the like. 
The glass material 40 supplied at this time has been formed in a disk-like 
shape or in a substantially completed shape of the concave lens, when the 
concave lens is molded. Also, the shell mold 14, the upper mold member 16 
and the lower mold member 18 have been heated up to temperatures 
corresponding to predetermined molding conditions. 
After the glass material 40 is supplied onto the molding face 18b of the 
lower mold member 18, the piston rod 22a of the air cylinder 22 is 
extruded, so that the molding face 16b of the upper mold member 16 comes 
into direct contact with the upper plane of the glass material 40, and a 
pressing force P1 is applied on to the glass substrate 40. When the upper 
mold member 16 is moved downward gradually with this pressing force P1 
applied, the glass material 40 is squashed down, finally resulting in a 
state as shown in FIG. 1. In this state, on the upper and lower planes of 
the glass material 40 are formed optical functional faces 40a , 40b to 
which the shapes of the molding face 16b of the upper mold member 16 and 
the molding face 18b of the lower mold member 18 are transferred 
respectively. The thickness of the glass material 40 is molded into a 
desired thickness. 
Thereafter, the molded concave lens (glass material 40) is gradually 
cooled. In this cooling step, the air cylinder 24 is activated to push the 
lower mold member 18 upward so that the shape of the molded concave lens 
(40) may not collapse, whereby a pressing force P2 is applied on the 
concave lens (40). When the temperature falls down to a predetermined 
temperature, the air cylinder 22 is retracted again to move the upper mold 
member 16 upward, so that the concave lens is taken outside through the 
opening hole 14d of the shell mold 14 by means of an autohand or the like. 
In a series of operations as described above, the concave lens (40) is 
molded, whereas the molding conditions by which the surface accuracy of 
the optical functional faces 40a, 40b of the concave lens (40) is possibly 
affected in the course of this molding process, include (1) pressing force 
P2 in the cooling step, (2) temperature difference of the upper and lower 
mold members 16, 18 during the cooling, and (3) cooling rate. 
Herein, FIG. 3 shows the results in which the shapes of the optical 
functional faces of the concave lens (40) were investigated using a 
Fizeau's interferometer. The glass material 40 of a dense barium crown 
glass (SK12) was molded into the lens shape as shown in this embodiment by 
changing the pressing force P2 in cooling from ON to 10 kN. 
According to the results of FIG. 3, release failure (failure of releasing 
from mold) takes place at the pressing forces below a point at which the 
pressing force P2 in the cooling is 2.0 kN. On the other hand, the concave 
lens has poorer surface accuracy with increasing the pressing force P2. 
Accordingly, it can be said that the optimal pressing force at which the 
occurrence of the release failures can be prevented to the minimum, and 
the surface accuracy of the concave lens is not degraded is 2.0 kN. But it 
is very difficult to control the pressing force at 2.0 kN precisely. Also, 
even if the pressing force P2 is controlled at 2.0 kN precisely, it is not 
possible to ensure that no release failure occurs at all and the shape 
precision is made better. Accordingly, even if the pressing force P2 in 
the cooling is set at 2.0 kN, all disadvantages can not be resolved. 
It has been found that regarding a temperature difference of the upper and 
lower mold members 16, 18 during the cooling, the surface accuracy of an 
optical functional face is not decreased so much by the temperature 
difference of about .+-.5.degree. C., and that regarding cooling rate, the 
surface accuracy is hardly affected by the difference of cooling rate of 
about 1.degree. C./min. to about 20.degree. C./min. 
In this embodiment as described above, the pressing force P2 is selected so 
as to prevent the occurrence of release failures securely even though the 
surface accuracy may decrease to some extent, but not to look for the best 
point to take balance of releasing ability and surface accuracy. However, 
it is important that the optical functional face is finished with good 
reproducibility and in the shape having the same contour map of the 
surface at all times, when molding a plurality of lenses, even though the 
surface accuracy may decrease to some extent. Accordingly, if the lens is 
worked in the shape having the same contour map of the surface at every 
time of molding, the shapes of the molding faces for the mold members 16, 
18 can be determined to cancel this contour map of the surface, so that 
the lens having theoretically no contour map of the surface can be 
produced when molding under the same conditions. 
To this end, in this embodiment, in order to provide an invariable contour 
map of the surface on the lens to be molded for every time of molding, the 
temperature difference of the upper and lower mold members in cooling and 
the cooling rate are roughly controlled to be 0.degree..+-.2.5.degree. C. 
and 20.degree..+-.5.degree. C./min, respectively, and the pressing force 
P2 in the cooling is set at a high value of 5.+-.1.5 kN. The setting of 
the cooling pressing force at such a high value can securely prevent 
release failures from occurring, even though the surface accuracy of an 
optical functional face decreases slightly, resulting in good 
reproducibility of the shape of an optical functional face. 
FIG. 4 illustrates the results of examining the molding face shapes of the 
upper and lower mold members in molding a concave lens and the shapes of 
optical functional faces of molded concave lens under the above molding 
conditions by means of a Fizeau's interferometer. In this case, the shapes 
of the molding faces of the mold members are not made to cancel the 
contour map of the surface. 
A left-hand view of FIG. 5 illustrates the results of reading the contour 
map of the surface of the optical functional face for the concave lens 
from the results of FIG. 4 and examining the mold members, by means of a 
Fizeau's interferometer, having the molding faces worked into the shapes 
of cancelling the contour map of the surface. A right-hand view of FIG. 5 
illustrates the shapes of the optical functional faces of the concave lens 
when molding using such mold members under the above molding conditions. 
As will be clear from the results of FIG. 5, it can be found that the 
concave lens molded with the method of this embodiment has the astigmatism 
and the contour map of the surface which are both less than one-fourth 
line (1/4) of Newton ring, resulting in quite excellent surface accuracy. 
As a result of molding the concave lens continuously using the mold 
members of the shape with the contour map of the surface cancelled, all of 
the lenses had both the astigmatism and the contour map of the surface 
less than one-fourth line (1/4) of Newton ring. 
It should be noted that the contour map of the surface for the optical 
functional faces of the lens is read from the number of Newton ring lines 
as described above, and then the molding faces of the mold members 16, 18 
can be manually worked into the shapes so as to cancel this contour map of 
the surface. However, such a manual operation for working the mold is 
quite troublesome, but in practice, the working of the mold is subjected 
to automatic process using an NC machine tool, as hereinafter described. 
FIG. 6 is a flowchart showing the procedure for correction-working the mold 
members into the shapes so as to cancel the contour map of the surface for 
the optical functional faces of the concave lens. 
First, at step S2, the molding conditions are set such that the contour map 
of the surface for the lens to be molded become constant for every 
molding. In this embodiment, the glass material 40 is a dense barium crown 
glass (SK12) as previously described, the temperature difference of the 
upper and lower mold members 16, 18 in the cooling is 
0.degree..+-.2.5.degree. C., the cooling rate is 20.degree..+-.5.degree. 
C./min, and the pressing force P2 in the cooling is 5.+-.1.5 kN. 
At step S4, the lens is molded under the above molding conditions by the 
same method as conventionally used. In this case, by setting the molding 
conditions as above shown, any shape error which is not axial symmetrical 
around the optical axis of the concave lens (40) can be completely 
prevented. 
At step S6, the shapes of the optical functional faces 40a, 40b are 
measured along the straight line passing through the optical axis, with a 
tracer 28 of a well known tracer-type shape measuring device (tally-surf) 
placed on the optical functional face 40a, 40b of the concave lens (40) 
molded at step S4, as shown in FIG. 7. Since the shapes of the optical 
functional faces of the concave lens (40) molded are in axial symmetry, 
measurement with the tally-surf is necessary to be made along only one 
line. 
At step S8, the deviation of the measured value at step S6 from the design 
value of the optical functional faces 40a, 40b of the concave lens (40) is 
calculated. Since the measured values are distributed symmetrically around 
the entire periphery with respect to the optical axis as described above, 
if the deviation in the Y direction is calculated at a certain position in 
the X direction from the optical axis as shown in FIG. 8, this value can 
be applied around the entire periphery of the concave lens (40). 
At step S10, the deviation calculated at step S8 as shown in FIG. 9 is 
input into an NC grinding machine 30 commercially available, in the form 
of (X=distance from the optical axis, Y=deviation from the design value), 
so that the molding faces 16b, 18b of the upper and lower mold members 16, 
18 are correction-worked. In this way, with such correction-working of the 
molding faces 16b, 18b of the molding members 16, 18, the molding faces 
16b, 18b are worked into the shapes so as to cancel the shape error of the 
concave lens. 
Next, at step S12, the molding faces 16b, 18b ground by the NC grinding 
machine are subjected to finish-working. The working data X, Y as already 
calculated are converted to a cylindrical coordinates system, that is, 
consisting of the angle .theta. from the optical axis and the deviation r 
of optical functional face at its angle from the design value, as shown in 
FIG. 10, whereby the molding faces are finish-worked by an apparatus and 
method as disclosed in U.S. Pat. No. 4,956,944. 
At step S14, the concave lens is molded using the corrected mold members 
produced in the steps from S2 to S12 as mentioned above under the molding 
conditions set at step S2. 
As a result of molding the concave lens according to the above procedures, 
the concave lens could be molded at a accuracy in which the deviation of 
the optical functional face from the design value is 0.33 .mu.m or less. 
Other Embodiments 
FIG. 11 illustrates another embodiment, where a meniscus lens is molded. In 
this other embodiment, the glass material 40' is a flint glass (FS). 
In this other embodiment, since the shape of the lens to be molded is 
different from the one embodiment as previously described, the temperature 
difference of the upper and lower mold members during cooling may exert 
greater influence on the surface accuracy of the optical functional face 
of lens than the pressing force P2 upon cooling. Therefore, the molding 
conditions are roughly controlled so that the pressing load P2 in cooling 
is 3.0.+-.1.5 kN and the cooling rate is 20.degree..+-.5.degree. C./min. 
Also in order to stabilize the surface accuracy of the optical functional 
face at each molding, the temperature of the upper mold member 16 is set 
at 7.5.degree..+-.2.5.degree. C. above the temperature of the lower mold 
member 18. 
FIG. 12 illustrates the results of examining the shapes of molding faces of 
the upper and lower mold members when the meniscus lens is molded under 
the above molding conditions and the shapes of optical functional faces of 
a molded optical element by means of a Fizeau's interferometer. 
A left-hand view of FIG. 13 illustrates the results of reading the contour 
map of the surface for the optical functional face for the meniscus lens 
from the results of FIG. 12 and examining the mold members having the 
molding faces worked into the shapes so as to cancel the contour map of 
the surface by means of a Fizeau's interferometer. A right-hand view of 
FIG. 13 illustrates the shapes of the optical functional faces of the 
meniscus lens when molded using such mold under 10 the above molding 
conditions. As will be clear from the results of FIG. 13, it can be found 
that the meniscus lens molded with the method of this embodiment has the 
astigmatism and the contour map of the surface below one-fourth line (1/4) 
of Newton ring, resulting in quite excellent surface accuracy. As a result 
of molding the meniscus lens continuously using the mold members having 
the shape of the cancelled contour map of the surface, all of the lenses 
had the astigmatism and the contour map of the surface below the 
one-fourth line (1/4) of Newton ring. 
It should be noted that in this other embodiment the correction-working of 
the mold members can be made in the exactly same way as the one embodiment 
according to the flowchart of FIG. 6. Thus, according to the molding 
method for an optical element in the above embodiment, it is possible to 
mold the optical element into the shape as conventionally difficult with 
high accuracy, using a quite basic apparatus similar to that as 
conventionally used, and the need of controlling the highly precise 
molding conditions. 
The present invention is also applicable to the modifications or variations 
of the above embodiment in the range without departing from the spirit of 
the invention. 
For example, the above embodiment is related to the molding of the concave 
lens and the meniscus lens, whereas the present invention is also 
applicable to the molding of other shapes of optical elements, e.g., a 
convex lens or a plane-like optical element. 
As described above, according to the molding method for an optical element 
of the present invention, the molding conditions are set so that the 
contour map of the surface appearing on the completed optical element may 
be constant at all times, and the molding faces of the mold members are 
worked into the shapes so as to cancel the constant contour map of the 
surface, whereby it is possible to work an optical element having high 
surface accuracy. The molding conditions such that the contour map of the 
surface always becomes constant are not required to be controlled as 
strictly as the molding conditions necessary to always finish the optical 
element with high surface accuracy. Therefore, it is possible to produce 
easily high accurate optical elements. 
Next, a mold and a producing method thereof according to the second 
embodiment of the invention will be specifically described below by way of 
example in connection with the drawings. 
First, a molding process using the mold will be outlined herein. The 
molding process is shown, in which a lens concave on both faces (e.g., 
diameter: 15 mm.phi., central wall thickness: 0.8 mm, radius of curvature 
on the optical functional face: R=30 mm) is molded from the spherical 
glass blank. The glass blank as used herein is a glass material 1 of dense 
barium crown glass SK12, which is prepared in, for example, a shape 
concave on both faces having a diameter of 15 mm.phi., a central wall 
thickness of 1.2 mm, and a radius of curvature on the optical functional 
face of R=31 mm. A mold as shown in FIGS. 14A to 14C is made of, for 
example, W-C alloy, and is accommodated within a casing (not shown). The 
casing contains nitrogen gas introduced therein after the pressure 
reduction to, for example, 1.times.10.sup.-2 Torr. An upper mold member 
102 and a lower mold member 103 constituting the mold are heated near 
620.degree. C. (with glass viscosity of 10.sup.9.7) by a heater (not 
shown) provided on a shell mold 104 surrounding them. When the mold 
members 102, 103 are heated up to the above-mentioned temperature, the 
glass material 1 preheated (e.g., 620.degree. C.) within the same casing 
is sucked by using a suction hand 109, and is laid on a molding face 103a 
of the lower mold member 103 through an access port opened in the shell 
mold 104 (see FIG. 14A). The shell mold 104 is installed on a base 105. 
The upper mold member 102 is lowered through manipulating means 106 such as 
a ram to enable the press molding. A glass material 100 is preheated up to 
620.degree. C. (with glass viscosity of 10.sup.9.7 poise) in advance as 
described above, and is loaded between the mold members 102,103, but it 
will be appreciated that the glass material may be heated to the 
temperature after loading. The upper mold member 102 is continuously 
lowered until a stopper portion provided at the upper edge of the mold 
member 2 comes into contact with an upper plane 104a of the shell mold 
104, while the temperature is maintained to heat uniformly the glass 
material. In the course of the lapse of a predetermined time, each molding 
face 102a, 103a of the mold members 102,103 is transferred onto each 
surface of the glass material 1, so that the glass material 1 is molded 
into a predetermined molded product 107 (FIG. 14B). The pressing load in 
this case is as large as 320 kgf, and the thickness of the molded product 
7 is determined to the level at which the stopper portion abuts on the 
upper plane 4a of the shell mold 4. 
Thereafter, the heater is deenergized, and the cooling is conducted by 
passing nitrogen gas, for example, through cooling passages (not shown) 
provided on the respective mold members 102,103. The mold is then opened 
at the time when the temperature of the molded product (optical element) 
107 falls below a glass transition point, e.g., 480.degree. C. (with mold 
pressure being zero), and the molded product is taken out (FIG. 14C). The 
cooling rate is 20.degree. C./min, for example, so that non-uniform 
temperature distribution may not occur in the molded product within the 
mold during the cooling. 
Next, the situation of the thermal stress occurring due to a difference 
between thermal expansion coefficients of the mold and the glass material 
in the cooling step of such a molding process will be considered below. 
Table 1 as listed herein indicates the thermal characteristic temperatures 
of the glass material, and Table 2 indicates the mechanical properties of 
the glass material and the mold in the cooling step of the molding 
process. 
TABLE 1 
______________________________________ 
Softening 
Yield Transition Slow cooling 
Strain 
point point point point point 
______________________________________ 
672.degree. C. 
588.degree. C. 
550.degree. C. 
534.degree. C. 
503.degree. C. 
______________________________________ 
TABLE 2 
______________________________________ 
Young's Poisson's Thermal expansion 
modulus ratio coefficient 
______________________________________ 
Glass Visco-elastic 0.25 Function of 
characteristic temperature 
(see FIG. 25) 
Mold 5.80 .times. 10.sup.4 kgf/mm.sup.2 
0.2 Function of 
temperature 
(see FIG. 25) 
______________________________________ 
FIG. 25 illustrates how the thermal expansion coefficients of the glass 
material and the mold change for every 10.degree. C. in the cooling step 
of the molding process. The thermal expansion coefficient of the glass 
material is greater than that of the mold, particularly exhibiting great 
change in the region of high temperatures. 
The visco-elastic characteristic of the glass material in the cooling step 
is the molding process of remarkable in the range of temperature 
corresponding to a range in which the glass viscosity is from 10.sup.12 to 
10.sup.15 poise, which temperatures lie between the molding temperature 
(620.degree. C.) and the releasing temperature (480.degree. C.). 
Typically, the material having the visco-elastic characteristic is 
involved in two specific phenomena in the analysis of the stress 
condition, one of them being a creep phenomenon in which deformation is 
sustained if a fixed force is loaded on the visco-elastic material, and 
the other being a stress relaxation phenomenon in which if the 
visco-elastic material having a stress is held at a constant temperature, 
the stress decreases. 
We have determined that upon molding the optical element, the matters to be 
considered concerning the thermal stress are the creep phenomenon and the 
stress relaxation phenomenon, and have verified these. First of all, the 
glass sample in the visco-elastic temperature range is subjected to a 
bending test of continuously applying a fixed load thereto in three-point 
bent state, while being held at constant temperature in order to measure 
deflection of the sample, whereby the creep compliance indicating the 
easiness of creep deformation is obtained. 
EQU D.sub.c (t,T)=4bd.sup.3 /1.sup.3 .times.v(t)/WO 
Where D.sub.c (t,T) is a creep compliance after loading t seconds at a 
temperature T.degree. C., b is a width of a specimen, d is a length of the 
specimen, 1 is a span distance, v(t) is deflection on the loading point 
after loading t seconds, and WO is a load. 
FIG. 16 shows the creep compliance at each temperature of the glass in the 
above embodiment of the present invention. The glass in the region of 
visco-elastic temperatures has a simple property of thermal rheology, so 
that the creep compliance curves can be integrated into one creep 
compliance curve (represented as a master curve in FIG. 17) by moving each 
creep compliance curve of each temperature in parallel horizontally. 
In this way, a master curve of creep compliance is obtained by moving in 
parallel the creep compliance curve of each temperature by the amount 
corresponding to a certain time, and the relation between temperature and 
time can be represented by a time/temperature shift factor (FIG. 19). The 
time/temperature shift factor of the glass as shown herein can be 
approximated by two straight lines (Arrhenius' equation), the temperature 
at the point of intersection being slightly lower than the transition 
point temperature of the glass. 
The relaxation elastic modulus corresponding to the elastic modulus of 
normal elastic material in the visco-elastic material can be adopted as 
the function of temperature and time due to the influence of stress 
relaxation phenomenon, but because the glass as an object has the simple 
property of thermal rheology, the same master curve of creep compliance as 
mentioned above (typically, the master curve of relaxation elastic modulus 
can be approximated by the inverse of the creep compliance master curve of 
FIG. 17) can be obtained (FIG. 18 ). 
That is, in the case of the visco-elastic material having the simple 
property of thermal rheology as described above, by calculating the 
relaxation elastic modulus E.sub.r (t,T) at a certain temperature 
T.degree. C. from the master curve of relaxation elastic modulus of FIG. 
18 and the time/temperature shift factor of FIG. 19, it is possible to 
represent the relation between stress .sigma. and strain .epsilon., that 
is, the construction equation by an expression of history integration 
(shown below) in the linear visco-elastic theory. 
##EQU1## 
That is, if the numerical analysis is made with the finite element method 
using this construction equation, the thermal stress can be calculated in 
consideration of the stress relaxation phenomenon of visco-elastic 
material. 
Thus, to introduce the visco-elastic characteristic into the numerical 
analysis, the numerical expression involving the master curve of 
relaxation elastic modulus and the time/temperature shift factor is 
needed. The time/temperature shift factor is approximated by Arrhenius' 
equation as described above. The master curve of relaxation elastic 
modulus is approximated by Prony expansion. 
In this way, the master curve of relaxation elastic modulus and the 
time/temperature shift factor can be obtained by measuring the creep 
compliances of the glass in the region of visco-elastic temperatures, so 
that the stress relaxation phenomenon of visco-elastic material can be 
numerically analyzed, and the thermal stress occurring in the optical 
element during the cooling can be analyzed by taking into consideration 
the stress relaxation due to visco-elasticity. 
The correction for the molding faces of the mold in such molding process is 
performed as follows. That is, when the optical element material is 
press-molded by using the mold in accordance with the process as 
schematically shown in FIG. 14D, the thermal stress produced on an optical 
element molded product within the mold in a visco-elastic temperature 
range or elastic temperature range of the optical element material in the 
cooling step of the molding process to be performed is numerically 
analyzed based on a visco-elastic characteristic of the optical element 
material. Then the correction for the molding faces of the mold is made 
based on the value obtained by the numerical analysis so that the error 
between the optical functional face of an optical element molded by the 
mold at room temperature and optical functional face set on a design may 
fall within an acceptable tolerance level, thereby determining the molding 
face adapted to a shape of optical functional face set on the design. 
This calculation procedure is specifically described in connection with the 
embodiment. In the numerical analysis of the thermal stress, the 
temperature history and/or pressing force history when this thermal stress 
occurs, is applied to the calculation basis. First of all, supposing that 
the optical element molded product is in a viscous state while the optical 
element molded product is cooled from a press molding temperature 
(620.degree. C.) to 560.degree. C., the thermal stress produced for that 
period is relaxed instantaneously as already described, whereby it is 
possible to assume that no stress remains within the molded optical 
element product. 
Then, supposing that the molded optical element product is in a 
visco-elastic state while the optical element molded product is cooled 
from 560.degree. C. to 500.degree. C., the thermal stress produced for 
that period can be numerically analyzed by taking into consideration the 
stress relaxation phenomenon due to visco-elasticity. The numerical 
analysis is accomplished by the finite element method. That is, by 
incorporating the master curve of relaxation elastic modulus of FIG. 5 
obtained from the creep test of material and the value of time/temperature 
shift factor of FIG. 19 into a structural analysis program of finite 
element method, the thermal stress produced within the optical element 
molded product during the cooling is numerically analyzed in consideration 
of the stress relaxation phenomenon due to visco-elasticity. In this case, 
in order to take into consideration the visco-elastic characteristic of 
material and the non-linearity of thermal expansion coefficient as shown 
in FIG. 25, the numerical calculation of thermal stress in this 
temperature range is performed at every 60 steps. 
Finally, supposing that the molded optical element product is in an elastic 
state while the molded optical element product is cooled from 500.degree. 
C. to room temperature, the stress produced for the period can be 
numerically analyzed by the finite element method. That is, in this 
embodiment, it is considered that the optical functional face of the 
molded optical element product and the molding face of the mold are placed 
in a close contact state to each other during the period from the press 
molding to the releasing and are cooled, therefore, the thermal stress 
increasingly produced within the molded optical element product during 
cooling from 500.degree. C. to 480.degree. C., is numerically analyzed. If 
it is released from the mold at 480.degree. C., the constraint by the mold 
members is released in the molded optical element product so that the 
product is deformed by residual thermal stress. The shape variation of the 
molded optical element product is analyzed by elasticity calculation of 
the finite element method, and further the shape variation of the molded 
optical element product upon cooling down to room temperature is likewise 
numerically analyzed by the finite element method. In this case, in order 
to take into consideration the non-linearity of thermal expansion 
coefficient of material as shown in FIG. 25, the numerical calculation of 
the thermal stress in this temperature range is performed at every 40 
steps. In this embodiment, for the calculation of thermal stress, it is 
presumed that there is no non-uniform temperature distribution in the 
molded optical element product within the mold during the cooling as well 
as the mold. 
The specific flow of the numerical calculation process is shown in FIGS. 46 
to 49. A flowchart of FIG. 46 shows collectively the total process of 
numerical calculation. At step S51, first of all, numerical data 
concerning the ideal shapes as a target for the optical functional faces 
of an optical element are picked up as the initial setting values of the 
molding faces of the mold members. Next, at step S52, the shapes of 
optical functional faces of a molded product to be expected upon 
completion, are calculated under the given conditions by the finite 
element method. For this purpose, various data necessary for the numerical 
calculation must be prepared. Accordingly, for this step S52, Young's 
modulus, Poisson's ratio, thermal expansion coefficient, specific heat, 
heat conductivity, heat transfer rate of the mold members and the glass 
material are measured in another measurement process P1, and stored in a 
calculation memory as data DA. Also, the creep compliance of the glass in 
the visco-elastic region is measured in a measurement process P2, and 
further the master curve of the creep compliance, the shift factor and the 
master curve of relaxation elastic coefficient are obtained in the 
processes P3, P4 and P5, respectively. The results are stored in the 
calculation memory as data DB. Besides, the cooling temperature and the 
pressing force during the cooling are set as further conditions. 
At step S52, the thermal stress of the mold members and the glass molded 
product in the visco-elastic region is calculated, the thermal stress of 
the mold members and the glass molded product in the elastic region until 
released from the mold is calculated, and the deformation (spring back) of 
the glass molded product due to releasing from the mold is calculated. 
Further, the numerical value concerning the shape of the glass molded 
product when cooled down to room temperature is calculated. The final 
value is compared with the initial shape value at step S53, as will be 
described later, to obtain the contour map of the surface. At step S54, a 
determination is made whether or not the calculated value of an the shape 
of a optical functional face of glass molded product is within a range of 
design tolerance. If it is out of the tolerance, numerical data for the 
initial shape of the mold member is corrected at step S55, and the 
procedure feeds back to step S52. If it is within the tolerance, the value 
is picked up as the design value concerning the shape of molding face of 
the mold member at step S56, and adopted as data for an NC control 
grinding machine and a molding face polishing machine. 
A specific detailed flow chart for the step S52 is shown in FIGS. 47 and 
48. That is, at step S101 in FIG. 47, data concerning the shape of the 
mold member at room temperature is input, and the shape of the mold member 
at 560.degree. C. is calculated at step S102 (herein, deformation due to 
thermal expansion of the mold is obtained from the Young's modulus, 
Poisson's ratio, and thermal expansion coefficient of data DA by the 
elastic thermal stress analysis based on the finite element method). Then, 
at step S103, data for the shape of the molded product is input in such a 
state that a glass molded product is contained within the mold members at 
560.degree. C. (herein, the mold members and the glass molded product are 
unstressed). 
At step S104, a temperature decreasing amount (1.degree. C.) per 1 step is 
determined (temperature decreasing amount .DELTA.T=(560-500)/60=1). Next, 
at step S105, the temperature T.sub.o (control point) of the mold member 
is decreased by one step. That is, T.sub.o =T.sub.o .DELTA.T is executed 
(the initial value is 560.degree. C.). At step S106, temperature 
distribution of the mold member and the molded glass product when 
temperature decreases by one step, is calculated from the specific heat, 
the heat conductivity, the heat transfer rate and the cooling rate. 
(Herein, the thermal analysis is executed by the finite element method to 
calculate the temperature distribution T.sub.(r,z). The initial condition 
of the finite element method is that initial value T.sub.(r,z) 
=560.degree. C.). At step S107, increment .DELTA..delta. of thermal stress 
produced at temperature distribution under temperature decreasing of one 
step is obtained from the conditions concerning Young's modulus, Poisson's 
ratio, thermal expansion coefficient, visco-elastic characteristic 
(relaxation elastic modulus, shift factor) of data DA, DB, cooling rate, 
and pressing force during the cooling. The stress distribution 
.sigma..sub.(r,z) at this time is obtained. (Herein, the visco-elastic 
thermal stress analysis is made by the finite element method, to obtain 
.DELTA..sigma..sub.(r,z) and to calculate the stress distribution by 
.sigma..sub.(r,z) =.sigma..sub.(r,z) +.DELTA..sigma..sub.(r,z). The 
initial condition of the finite element method is that initial value 
.sigma..sub.(r,z) =0). Note that r and z in the above expressions 
T.sub.(r,z) and .sigma..sub. (r,z) indicate the stress coordinate system 
in the radial direction of molded glass product and that in the pressing 
direction of mold member. At step S108, a determination is made whether or 
not T.sub.o =500.degree. C. is reached, and the feedback to step S104 is 
continuously performed until this is reached. In this way, the stress 
distribution in the visco-elastic region from 560.degree. C. to 
500.degree. C. is obtained for each temperature decreasing step. Finally, 
the value of stress distribution .sigma..sub.(r,z) at 500.degree. C. can 
be obtained at step S109. 
Subsequently, a flowchart as shown in FIG. 48 is executed. Herein, like 
previous steps S104 to S108, the stress distribution in the elastic region 
from 500.degree. C. to 480.degree. C. (mold releasing temperature) is 
obtained for each temperature decreasing step at steps S201 to S205. (This 
will be fully understood by referring to the drawings, thus its detailed 
explanation of the flow is omitted.) At step S206, numerical calculation 
concerning the shape of the molded glass product after released from mold, 
is performed (in the practical molding, if released from mold at 
480.degree. C. the glass molded product is released from the constraint 
within the mold members, and under these conditions, the elastic analysis 
is conducted by the finite element method. That is, the molded product 
undergoes elastic deformation (spring back phenomenon) to such a shape 
that the potential energy of residual thermal stress is minimum, for which 
the calculation is performed.) 
Like previous steps S104 to S108, the stress distribution in the elastic 
region from 480.degree. C. (mold releasing temperature) to 20.degree. C. 
(room temperature) is obtained for each temperature decreasing step at 
steps S207 to S211. (This can be fully understood by referring to the 
drawings, thus its detailed explanation is omitted.) As a result, the 
shape of an optical functional face of an molded product at room 
temperature can be correctly obtained by the above simulation (step S212). 
When the molding face of a mold is formed using a corrected value by the 
numerical analysis as above shown, a Fizeau's laser interferometer is used 
to verify the situation of an optical functional face of an optical 
element molded by the mold at steps S3 and S4. It is effective to verify 
visually an image such as a photograph of interference fringes. 
FIGS. 49 and 50 show the specific processes at steps S53 and S54, 
respectively. In FIG. 49, at step S301, the shape of the optical 
functional face of molded glass product at room temperature obtained at 
step S212 as previously described (coordinate value Z(r) obtained by 
thermal stress analysis in consideration of the visco-elasticity of glass) 
is compared with the design value Z.sub.s (r) initially provided to 
thereby obtain the deviation .DELTA.Z(r)=Z(r)-Z.sub.s (r). At step S302, 
the deviation is represented by interference fringes of Newton ring (i.e., 
in black when .DELTA.Z(r)=(.lambda./2)n, and in white when 
.DELTA.Z(r).noteq.(.lambda./2)n. Herein, .lambda.=632.8 nm). The results 
are judged as to whether or not the form of interference fringes is easy 
to see visually on the monitor. If the judgment is good, the operation 
exits from this routine, while if the judgment is bad, the form of 
interference fringes is changed by changing the tilt angle of the optical 
functional face on the design with respect to the optical functional face 
of the glass molded product at step S304. The deviation 
.DELTA.Zt(r)=Z(r)-Z.sub.tS (r) from the design value in tilt state is 
calculated at step S305, and the operation returns to step S301 again. In 
this way, the contour map of the surface (deviation from the design value) 
of the glass molded product appears on the monitor in the form of 
interference fringes, whereby it is easy to determine whether or not the 
contour map of the surface is within the design tolerance. 
Also, in FIG. 50, at step S401, the set value of the optical functional 
face of molded glass product and the initial design value are compared to 
obtain the deviation .DELTA.Z(r), which is added as a correction value to 
the initial design value of the molding face of the mold member (or the 
value of previously corrected value if correction is the second time or 
after) at step S402 (Z.sub.K (r)=Z.sub.K (r)+.DELTA.Z(r)). Thus, the ideal 
design value of the mold member can be obtained. 
FIG. 21 illustrates a specific example of an optical functional face based 
on the numerical analysis as described above, with the mold uncorrected. 
An image as shown herein involves interference fringes when a He--Ne laser 
is used, one line of interference fringe corresponding to a deviation from 
a spherical surface as large as 0.3164 .mu.m. This calculated result 
(improper by judgment) indicates that the optical element molded product 
has the contour map of the surface amounting to three lines of Newton ring 
(a deviation of about 1 .mu.m from a desired spherical surface), wherein 
the optical element with such accuracy of an optical functional face can 
not be used for a high accuracy optical part such as a lens of a focal 
plane shutter camera (single lens reflex camera). 
FIG. 22 illustrates interference fringes of a photographed optical 
functional face of an optical element molded using the mold, with a laser 
interferometer. It can be understood that the result is analogous to image 
interference fringes of FIG. 21, and has the contour map of the surface 
amounting to three lines of Newton ring. In other words, the shape of an 
optical functional face relying on the above numerical analysis is 
realistic, thus it indicates a high predictability for the practical 
optical functional face. 
In this way, it has been confirmed that the above numerical analysis is 
applicable to correction for the molding face of mold on the basis of the 
fact that the shape of the optical functional face by numerical analysis 
is coincident with the shape of the practical optical functional face. 
Therefore, in the case of making a correction by such numerical analysis, 
the result of molding the optical functional face of optical element 
molded product using the mold is predicted as follows. 
First, as the first time, the shape of the molding face of mold is 
corrected based on the numerical analysis as mentioned above. The 
correction amount at this time is indicated by the difference between the 
shape of an optical functional face of a molded product in using an 
uncorrected mold previously calculated and the ideal shape of a desired 
optical functional face. A mold thus corrected in the shape of a molding 
face is used, into consideration while the visco-elastic characteristic is 
taken into consideration as previous time, the thermal stress produced 
within the molded optical element product in the cooling step is 
numerically analyzed to obtain the shape of an optical functional face for 
the molded optical element product at room temperature. As a result, it 
has been found that the optical element molded by the mold corrected at 
the first time (primary) has a contour map of the surface amounting to one 
line of Newton ring. 
Thus, at the second time, the shape of a molding face for the mold is 
corrected based on the numerical analysis performed on the optical 
functional face of an optical element product molded by corrected mold on 
the basis of the first time correction. That is, the correction amount at 
this time is indicated by the difference between the shape of the optical 
functional face of an optical element product molded by the corrected mold 
made at the first time correction and that of the ideal optical functional 
face. As a result of repeating such mold correction, the optical 
functional face of an optical element product molded by the mold corrected 
at the fourth time has a contour map of the surface as many as 0.1 line or 
less, whereby an excellent high accurate optical functional face can be 
indicated by calculation results as shown in FIG. 10. 
The optical element molded by this corrected mold has a spherical optical 
functional face. The mold is corrected into an aspherical shape, the 
maximum deviation (between spherical shape and aspherical shape) being 
about 0.8 .mu.m. 
According to the present invention, the molding face of the mold in 
practice can be finally determined in such a way that the optical 
functional face (virtual optical functional face) at room temperature of 
an optical element molded by the mold (virtual mold) having molding face 
(virtual molding face) corrected in accordance with the correction value 
obtained by the numerical analysis is calculated by computer simulation. 
The numerical analysis and the correction for the molding face based on 
this analysis are repeated over several order (one or more times) until 
the error between this virtual optical functional face and the set optical 
functional face falls within tolerance. As a result, it is possible to 
obtain the optical element having its optical functional face analogous 
precisely to a desired optical functional face and to produce such mold. 
The determination of a molding face as described above may be made by 
repeating the numerical analysis of the thermal stress based on the 
visco-elastic characteristic of an optical element molded product within 
the mold and the correction for the molding face of a practical mold based 
on this analysis over several order. 
In this embodiment, the verification is made supposing that there is no 
difference between the temperature of the mold being cooled and that of 
the inside of the optical element molded product. In practice, in order to 
prevent the molded product from adhering to the molding face of an upper 
mold member and leaving away from the molding face of a lower mold member 
upon releasing from mold, the temperature control is provided with a 
slight temperature difference of the upper and lower mold members. Thus, 
if the molding is conducted by providing such a temperature difference of 
the upper and lower mold members of the mold in this way, general 
verification will be performed as follows. 
The shape of an optical element provided herein is concave on both faces, 
as shown in FIG. 26, wherein the diameter is 15 mm.phi., the central wall 
thickness is 1.7 mm, and the radius of curvature on the optical functional 
face is R=30 mm (both faces). The material of the optical element and the 
quality of mold material are the same as in the previous embodiment. The 
blank as the molding material is premolded into a shape (diameter: 15 
mm.phi., central wall thickness: 1.8 mm, radius of curvature on the 
optical functional face: R=31 mm) approximate to the shape of the optical 
element. This blank is first loaded between the upper and lower mold 
members, and the upper mold member and the lower mold member are heated 
upon to 605.degree. C. and 630.degree. C., respectively, and is 
pressurized continuously until the central wall thickness of a molded 
product reaches 1.7 mm. In this way, pressurization is finished after 
molding the optical element. Then the cooling step is entered. In this 
cooling step, a temperature difference of 25.degree. C. is held between 
the upper and lower mold members. Finally, when the temperature of the 
upper mold member reaches 455.degree. C. and the temperature of the lower 
mold member reaches 480.degree. C., the molded product is released from 
the mold, taken out therefrom, and cooled down to room temperature. The 
cooling rate is 20.degree. C. per minute for both the upper and lower mold 
members. 
The shape of the optical functional face of optical element provided in 
such a molding process can be obtained as the above-described embodiment 
by the numerical analysis in consideration of the visco-elastic 
characteristic of the material of optical element. There is a need of the 
numerical analysis in consideration of the internal temperature 
distribution of molded the product. 
First, where an optical element is molded using a mold with an uncorrected 
shape of an optical functional face obtained by the calculation at this 
time (by computer simulation), the shape (image) of the optical functional 
face on the upper side is shown in FIG. 28, and the shape (image) of the 
optical functional face on the lower side is shown in FIG. 29. The upper 
and lower molding faces of the mold have the same radius of curvature, but 
owing to a constant temperature difference of the upper and lower molding 
faces in the cooling step, each of the upper and lower optical functional 
faces of the optical element contains a difference, the contour map of the 
surface amounting to three lines of Newton ring missing for the upper 
face, and five lines of Newton ring ridging for the lower face. As the 
evaluation, it is impossible to utilize an optical element having such 
contour map of the surface for the high precision optical device. 
On the other hand, interference fringes appearing on the optical element 
examined at this time which is molded in practice using a mold with the 
shape of a molding face corresponding to the optical functional face 
uncorrected, are illustrated in FIG. 30 (upper mold) and FIG. 31 (lower 
mode). It has been found that the results have the same contour map of the 
surface as the above-described image. That is, it has been confirmed that 
supposing a certain temperature distribution having a temperature gradient 
within the molding material, the shape of the optical element can be 
predicted precisely. 
In this embodiment, it has been found by simulation that the results of 
calculating the shape of an optical functional face of optical element 
molded by the mold corrected at the fifth order have interference fringes 
as illustrated in FIG. 32 (upper mold) and FIG. 33 (lower mold). The 
contour map of the surface for this optical element molded product has 0.2 
line or less of Newton ring, and an excellent high accuracy optical 
functional face can be obtained. 
On the other hand, it has been found by simulation that the results of 
measuring the shape of an optical functional face of an optical element 
molded by the mold corrected at the fifth order have interference fringes 
as illustrated in FIG. 34 (upper mold) and FIG. 35 (lower mold). The 
contour map of the surface for the molded product is 0.2 line or less of 
Newton ring, and the excellent high accuracy optical functional face can 
be obtained. The optical element molded by the mold corrected at this time 
has a spherical optical functional face, with the mold being corrected an 
aspherical shape. The maximum deviation (between spherical and aspherical 
shapes) is about 1 .mu.m for the upper mold and about 2 .mu.m for the 
lower mold. 
Next, the production of an aspherical lens having a high precision optical 
functional face which may be required in cameras or video cameras, using 
the mold of the present invention, will be described below. A concave 
meniscus lens aspherical on both faces as shown in FIG. 36 will be 
examined. The lens specifications on design are such as the diameter: 16 
mm.phi., the central wall thickness: 1.0 mm, R=51 mm, the maximum 
deviation: 12 .mu.m, aspherical for the convex face, and R=9 mm, the 
maximum deviation: 8 .mu.m, aspherical for the concave face. The material 
of the optical element is the same as in the first embodiment, and 
particularly in this embodiment, the optical element material is coated 
with a CH film on the surface thereof to make better the separation 
between mold and molded product. Also, the mold is coated with a TiN film 
to improve the durability of the molding face, although the mold material 
is the same as previously described. For the optical element material, the 
blank is premolded into a shape (a concave meniscus shape with a diameter 
of 16 mm.phi., R=48 mm and R=10 mm) approximate to the shape of the 
optical element. 
This optical element material is put into a prepared mold, press molded 
with a predetermined temperature difference of the upper and lower mold 
members, and then cooled, as in the previous embodiment. When the molded 
product is released from the mold at a higher temperature than the glass 
transition point temperature, the glass will be deformed due to viscosity, 
making worse the shape of the optical functional face, against which a 
second pressing force of 210 kgf is applied to the molded product while 
the lower mold member is cooled from 600.degree. C. to 480.degree. C. When 
the upper mold member reaches 455.degree. C. and the lower mold member 
reaches 480.degree. C., the molded product is taken out of the mold, and 
cooled down to room temperature. The cooling rate in this cooling step is 
20.degree. C. per minute. 
The optical element produced under such molding conditions has internal 
residual stress, leaving behind optical strain and causing the 
birefringence. Also, because the optical material is heated above the 
glass transition point temperature and is cooled at a rate of 20.degree. 
C./min., its refractive index will change. Accordingly, in order to use 
the molded product as the high precision optical part, it is necessary 
that the molded product is subjected to optical anneal for purposes of the 
removal of optical strain and the adjustment of refractive index. In this 
embodiment, under the temperature condition of 49.degree. C. the annealing 
was performed for seventeen hours, while the temperature dropped at a rate 
of 5.degree. C./hour, so that the molded product was cooled down to 
430.degree. C. 
The shape of the optical element product molded under such molding and 
annealing conditions is obtained by numerical analysis, as in the above 
embodiment. Since the annealing temperature is within a visco-elastic 
temperature range of the molded product material, the residual stress 
arising in that range will be relaxed. 
Thus, in this embodiment, the shape of optical functional face in the 
cooling step to room temperature after the annealing will be calculated in 
consideration of the relaxation of residual stress during the annealing. 
First, it is supposed that an optical element product is molded using the 
mold with an uncorrected shape of optical functional face obtained by this 
calculation. 
Under the condition that the optical element product is subjected to an 
annealing process, the upper and lower optical functional faces at room 
temperature are illustrated in FIG. 38 (upper face) and FIG. 39 (lower 
face), respectively. The results molded by the mold in practice under 
these conditions are illustrated in FIGS. 40 and 41, respectively. A 
comparison between the result of computer simulation and the practical 
result has revealed that the shape of the optical functional face after 
optical annealing can be predicted at good precision. From this result, it 
can be predicted that by making correction for the molding face of the 
mold over several order, as the previous embodiment, the optical 
functional face of optical element product molded by this corrected mold 
has high accuracy. 
In this embodiment, as a result of molding the optical element by the mold 
corrected at the fifth order, the optical functional face has interference 
fringes as illustrated in FIG. 42 (upper face) and FIG. 43 (lower face). 
The contour map of the surface for the molded product is 0.2 line or less 
of Newton ring, resulting in excellent high accuracy of optical functional 
face being exhibited. In practice, interference fringes of optical 
functional face of optical element product molded by the mold corrected at 
the fifth order are illustrated in FIG. 44 (upper face) and FIG. 45 (lower 
face). In this case, the contour map of the surface for the molded product 
is 0.2 line or less of Newton ring, resulting in excellent high accuracy 
of optical functional face being exhibited. 
From the above description, it can be concluded that in molding a lens 
concave on both faces, as in this embodiment, even if optical annealing 
may be conducted after molding wherein a second pressing force is applied 
to the molded product in the cooling step in order to prevent the molded 
product from being released from a mold at high temperatures, there is no 
trouble in the correction for the optical functional face according to the 
present invention. 
According to the present invention as above detailed, by premolding an 
optical element using a mold with the shape of a molding face 
corresponding to that of an optical functional face corrected, it is 
possible to produce with high accuracy a lens having the shape of which 
the optical functional face is conventionally difficult to transfer at 
desired precision by the molding, for example, an aspherical concave lens, 
whereby the production costs can be reduced.