Method and apparatus for measuring eccentricity of aspherical lens having an aspherical surface on only one lens face

In a method and an apparatus for measuring eccentricity of an aspherical lens, a detected lens as the aspherical lens is supported by a holding device and is rotated by a driving device around a rotating axis approximately conforming to an optical axis of the detected lens. Light is irradiated from a light source to the detected lens through a beam splitter and an optical system. Light reflected on the detected lens is reversely transmitted through the optical system and is focused and formed as a spot image. A pressing face of an alignment adjusting device is arranged in a position separated from the optical axis by a radius of the detected lens. The pressing face pushes an outer circumferential edge of the detected lens deflected outward by rotating the detected lens. Thus, the pressing face moves the detected lens and coarsely adjusts a position of the detected lens by approximately conforming the optical and rotating axes to each other. Thus, the spot image of the reflected light can be formed on an image forming face. Another method and another apparatus for measuring eccentricity of an aspherical lens are also shown.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates to a method and an apparatus for measuring 
eccentricity of an aspherical lens having an aspherical surface on only 
one lens face. More particularly, the present invention relates to a 
method and an apparatus for measuring an angle between an optical axis of 
the aspherical lens having an aspherical surface on only one lens face and 
an axis of the aspherical surface. 
2. Description of the Related Art 
When an aspherical lens is constructed by a spherical surface on one lens 
face and an aspherical surface on another lens face, an optical axis of 
the aspherical lens is a connecting line between a center of curvature of 
the spherical surface and a center of curvature of a reference spherical 
surface as a base of the aspherical surface. An axis of the aspherical 
surface is a connecting line between the center of curvature of the 
reference spherical surface and an vertex of the aspherical surface. If 
the aspherical lens is manufactured as designed, the optical axis of the 
aspherical lens is completely in conformity with the axis of the 
aspherical surface. 
However, such a lens cannot be really manufactured. In reality, a shift 
called eccentricity is slightly caused between the lens optical axis and 
the aspherical surface axis. Accordingly, when the aspherical lens is 
manufactured, it is necessary to measure eccentricity of this aspherical 
lens. 
Some apparatuses for measuring eccentricity of the aspherical lens are 
generally proposed on the basis of such requirements. 
In a measuring apparatus shown in Japanese Patent Application Laying Open 
(KOKAI) No. 3-37544, a detected lens as an aspherical lens is attached to 
a lens holder. A laser beam is irradiated onto the detected lens in a 
rotating axis direction thereof by approximately rotating the detected 
lens around an optical axis thereof. Thus, while a reflected spot image 
from the detected lens is monitored, the detected lens is moved in a 
direction perpendicular to the rotating axis thereof. A setting shift of 
the detected lens is corrected such that the rotating and optical axes of 
the detected lens are in conformity with each other. Thereafter, 
eccentricity of the detected lens is measured. 
In addition to this measuring apparatus, various kinds of eccentricity 
measuring apparatuses are also proposed. However, in each of these 
eccentricity measuring apparatuses, the setting shift must be corrected 
such that the rotating and optical axes of the detected lens are in 
conformity with each other. Further, a high accuracy of about 1 .mu.m is 
required in this correction to secure a measuring accuracy in 
eccentricity. 
Accordingly, skill is required for an operation for correcting the setting 
shift of the detected lens and it takes much time to perform this 
correcting operation. 
SUMMARY OF THE INVENTION 
It is therefore a first object of the present invention to provide a method 
and an apparatus for easily performing a setting operation including a 
coarse adjustment of a detected lens when eccentricity between the optical 
axis of an aspherical lens and the axis of an aspherical surface is 
measured. 
A second object of the present invention is to provide a method and an 
apparatus for easily measuring eccentricity of an aspherical lens for a 
short time without performing any difficult operation for correcting a 
setting shift of this lens. 
In accordance with a first construction of the present invention, the above 
first object can be achieved by a method for measuring eccentricity of an 
aspherical lens and having a process in which a detected lens having an 
aspherical surface on only one lens face is rotated around a rotating axis 
approximately conforming to an optical axis of the detected lens; 
light is irradiated onto the detected lens in a direction of the rotating 
axis and reflected light from the detected lens is focused and formed as a 
spot image on an image forming face of an optical system; and 
a shift between the optical axis and the rotating axis of the detected lens 
and a direction of this shift are detected by the size of a circle drawn 
by the spot image when the detected lens is rotated; 
the eccentricity measuring method measuring eccentricity between an axis of 
the aspherical surface and the optical axis and comprising the steps of: 
forming a pressing face for pushing and moving the detected lens in a 
direction approximately perpendicular to the optical axis in a state in 
which the pressing face comes in contact with an outer circumferential 
edge of the detected lens; 
arranging the pressing face in a position separated from the optical axis 
by a radius of the detected lens before the spot image is focused and 
formed on the image forming face; and 
coarsely adjusting a position of the detected lens. 
In accordance with a second construction of the present invention, the 
above first object can be also achieved by a method for measuring 
eccentricity of an aspherical lens and having a process in which a 
detected lens having an aspherical surface on only one lens face is 
rotated around a rotating axis approximately conforming to an optical axis 
of the detected lens; 
light is irradiated from a light source onto the detected lens in a 
direction of the rotating axis and reflected light from the detected lens 
is focused and formed as a spot image on an image forming face of an 
optical system; and 
a shift between the optical axis and the rotating axis of the detected lens 
and a direction of this shift are detected by the size of a circle drawn 
by the spot image when the detected lens is rotated; 
the eccentricity measuring method measuring eccentricity between an axis of 
the aspherical surface and the optical axis and comprising the steps of: 
fixing the light source, the optical system and the image forming face onto 
the same stage; and 
forming the spot image on the image forming face by moving the stage 
forward and backward in a direction of the optical axis. 
In accordance with a third construction of the present invention, the above 
first object can be also achieved by a method for measuring eccentricity 
of an aspherical lens and having a process in which a detected lens having 
an aspherical surface on only one lens face is rotated around a rotating 
axis approximately conforming to an optical axis of the detected lens; 
light is irradiated from a light source onto the detected lens in a 
direction of the rotating axis and reflected light from the detected lens 
is focused and formed as a spot image on an image forming face of an 
optical system; and 
a shift between the optical axis and the rotating axis of the detected lens 
and a direction of this shift are detected by the size of a circle drawn 
by the spot image when the detected lens is rotated; 
the eccentricity measuring method measuring eccentricity between an axis of 
the aspherical surface and the optical axis and comprising the steps of: 
detecting the shift between the optical axis and the rotating axis and the 
shifting direction by arithmetic means; and 
correcting the shift by the arithmetic means by moving the detected lens in 
a direction perpendicular to the optical axis on the basis of shape data 
of the detected lens inputted to the arithmetic means in advance. 
In accordance with a fourth construction of the present invention, the 
above first object can be also achieved by an apparatus for measuring 
eccentricity of an aspherical lens, comprising: 
means for holding a detected lens having an aspherical surface on only one 
lens face; 
driving means for rotating the holding means around a rotating axis 
approximately overlapping an optical axis of the detected lens; 
an angle sensor for detecting a rotating angle of the detected lens; 
a light source for irradiating light onto the detected lens in a direction 
of the rotating axis; 
an optical axis for focusing and forming a spot image of reflected light 
from the detected lens; 
means for detecting a position of the spot image and arranged on an image 
forming face of the optical system; 
displacement measuring means for really measuring a deflection of a 
detected face of the detected lens in a direction of the optical axis; and 
a pressing face for moving the detected lens in a direction perpendicular 
to the optical axis in a state in which the pressing face comes in contact 
with an outer circumferential edge of the detected lens; 
the pressing face being arranged in a position separated from the optical 
axis by a radius of the detected lens. 
In accordance with a fifth construction of the present invention, the above 
first object can be also achieved by an apparatus for measuring 
eccentricity of an aspherical lens, comprising: 
means for holding a detected lens having an aspherical surface on only one 
lens face; 
driving means for rotating the holding means around a rotating axis 
approximately overlapping an optical axis of the detected lens; 
an angle sensor for detecting a rotating angle of the detected lens; 
a light source for irradiating light onto the detected lens in a direction 
of the rotating axis; 
an optical axis for focusing and forming a spot image of reflected light 
from the detected lens; 
means for detecting a position of the spot image and arranged on an image 
forming face of the optical system; 
displacement measuring means for really measuring a deflection of a 
detected face of the detected lens in a direction of the optical axis; and 
driving means for fixing the light source, the optical system and the spot 
position detecting means onto the same stage and moving the stage forward 
and backward along the optical axis of the detected lens. 
In accordance with a sixth construction of the present invention, the 
measuring apparatus further comprises stage position detecting means for 
detecting a position of the stage on the optical axis; and arithmetic 
means for controlling an operation of the driving means of the stage. The 
arithmetic means performs feedback control of the moving means based on 
shape data of the detected lens, data of the optical system and stage 
position data from the stage position detecting means. 
In the above constructions, the detected lens is rotated around a rotating 
axis approximately conforming to the optical axis. At this time, if the 
rotating and optical axes are shifted from each other, an outer 
circumferential edge of the detected lens is also deflected or displaced 
in a direction perpendicular to the optical axis in accordance with the 
rotation of the detected lens. Therefore, a pressing face of an alignment 
adjusting means is formed in a position separated from the optical axis by 
a radius of the detected lens. The pressing face presses the detected lens 
and prevents the outer circumferential edge from being displaced in 
accordance with the rotation of the detected lens so that the detected 
lens is moved toward the optical axis as a center. As the detected lens is 
rotated, the position of the detected lens is coarsely adjusted. Thus, the 
shift between the rotating axis and the optical axis is reduced so that 
the spot image can be focused and formed on the image forming face. 
Light is first irradiated onto a rotating aspherical surface in the optical 
axis direction to form the spot image on the image forming face. The stage 
is then moved forward and backward in the optical axis direction to 
determine a position of the stage such that the irradiated light is 
converged by the optical system to a paraxial curvature center of the 
aspherical surface. If the position of the stage is determined, the spot 
image can be formed on the image forming face at any time since the 
optical system, the light source and the image forming face are fixed to 
the stage and are held in a constant relation in position. 
At this time, the optical system can be automatically positioned by 
calculating a moving distance of the stage by an arithmetic unit from 
shape data of the detected lens and data of the optical system. 
When the spot image is formed on the image forming face and the detected 
lens is rotated, the spot image draws a circle as mentioned above if the 
rotating and optical axes are not in conformity with each other. However, 
when the aspherical surface is a convex or concave face, a shifting 
direction of the spot image and an eccentric direction of the detected 
lens are in conformity with each other, or are different from each other 
by 180.degree.. Therefore, an outermost projecting position of the outer 
circumferential edge of the detected lens is calculated from a shift in 
the spot image in consideration of convex or concave data of the 
aspherical surface. This projecting portion is pressed by the alignment 
adjusting means in accordance with a shifting amount of the spot image so 
that the rotating and optical axes can be in conformity with each other. 
In accordance with an eighth construction of the present invention, the 
above second object can be achieved by a method for measuring eccentricity 
of an aspherical lens, comprising the steps of: 
rotating a detected lens having an aspherical surface on only one lens face 
around a rotating axis approximately conforming to an optical axis of the 
detected lens; 
irradiating light onto the detected lens in a direction of the rotating 
axis; 
focusing and forming reflected light from the detected lens as a spot image 
on an image forming face of an optical system; 
detecting a shift between the optical axis and the rotating axis by the 
size of a circle drawn by the spot image when the detected lens is 
rotated; 
setting a reference position in an outer circumference of the detected 
lens; 
calculating a direction of the shift from an angle formed between a line 
connecting the reference position and a rotating center of the detected 
lens to each other and a line connecting the spot image and the rotating 
center of the detected lens to each other; 
really measuring a deflection of the aspherical surface caused by rotating 
the detected lens in an optical axis direction; 
calculating a correction value of the deflection from the size of the 
circle and the shifting direction; and 
calculating eccentricity between the optical axis and an aspherical surface 
axis by subtracting the correction value from the deflection really 
measured. 
In accordance with a ninth construction of the present invention, the 
measuring method further comprises the steps of: 
displacing the detected lens in a direction approximately perpendicular to 
the optical axis of the detected lens; 
calculating the deflection of the aspherical surface caused by this 
displacement in the optical axis direction; 
calculating a changing amount of the shift between the optical and rotating 
axes of the detected lens; and 
calculating the correction value by using a ratio of the changing amount of 
the shift and an amount of the deflection. 
In accordance with a tenth construction of the present invention, the 
eccentricity of the aspherical surface is corrected by calculating the 
deflection of the aspherical surface in the optical axis direction from a 
shape parameter of the detected lens when an angle between the optical and 
rotating axes of the detected lens is changed by .phi.. 
In accordance with an eleventh construction of the present invention, the 
above second object can be also achieved by an apparatus for measuring 
eccentricity of an aspherical lens, comprising: 
means for holding a detected lens having an aspherical surface on only one 
lens face; 
driving means for rotating the holding means around a rotating axis 
approximately conforming to an optical axis of the detected lens; 
an angle sensor for detecting a rotating angle of the detected lens; 
a light source for irradiating light to the detected lens in a rotating 
axis direction; 
an optical system for focusing and forming reflected light from the 
detected lens as a spot image; 
means for detecting a position of the spot image and arranged in an image 
forming position of the optical system; 
displacement measuring means for really measuring the deflection of a 
detected face of the detected lens in an optical axis direction; and 
arithmetic means for calculating a correction value with respect to a 
deflecting value really measured by the displacement measuring means from 
a shift between the rotating axis and the optical axis of the detected 
lens and a direction of this shift detected by the spot position detecting 
means and the angle sensor. 
In accordance with a twelfth construction of the present invention, the 
measuring apparatus further comprises an actuator for moving the detected 
lens forward and backward in a direction approximately perpendicular to 
the optical axis of the detected lens. 
In accordance with a thirteenth construction of the present invention, the 
actuator displaces the detected lens by the correction value calculated by 
the arithmetic means in the direction approximately perpendicular to the 
optical axis in cooperation with the arithmetic means, the displacement 
measuring means and the actuator. 
The holding means for holding the detected lens rotates the detected lens 
around a rotating axis approximately conforming to the optical axis of the 
detected lens. Light is irradiated onto the detected lens in a direction 
of the rotating axis. Light reflected on a surface of the detected lens is 
focused and formed as a spot image by the optical system on an image 
forming face thereof. If no optical and rotating axes of the detected lens 
are in conformity with each other, the spot image draws a circle by 
rotating the detected lens. A theoretical deflection of an aspherical 
surface in an optical axis direction caused by rotating the detected lens 
can be calculated from a radius R of this circle and an angle .beta. 
formed between a reference position and the spot image at a center of 
rotation of the detected lens. A real value of this deflection is measured 
by the displacement measuring means. A deflection caused by eccentricity 
is calculated by subtracting the theoretical deflection from the really 
measured deflection value. Eccentricity of the aspherical lens can be 
calculated from this calculated deflection by a well-known method. 
Accordingly, the eccentricity of the aspherical lens can be easily 
measured for a short time without correcting a setting operation of the 
detected lens. 
The detected lens may be displaced by a correction value calculated by the 
arithmetic means in a direction approximately perpendicular to the optical 
axis in cooperation with the arithmetic means, the displacement measuring 
means and the actuator. In this case, a setting shift of the detected lens 
can be automatically corrected and eccentricity of the detected lens can 
be simply measured without requiring skill. 
Further objects and advantages of the present invention will be apparent 
from the following description of the preferred embodiments of the present 
invention as illustrated in the accompanying drawings.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
The preferred embodiments of a method and an apparatus for measuring 
eccentricity of an aspherical lens in the present invention will next be 
described in detail with reference to the accompanying drawings. 
FIG. 1 is a view showing the construction of an apparatus for measuring 
eccentricity of an aspherical lens as a detected lens in accordance with 
one embodiment of the present invention (proposed in Japanese Patent 
Application No. 5-2481 of the same applicant as this patent application). 
In FIG. 1, one face 1a of a detected lens 1 is set to a spherical surface, 
The other face 1b of the detected lens 1 is set to an aspherical surface. 
A holding means 2 of the detected lens 1 supports the detected lens 1 by 
adsorbing the spherical surface la by a cylindrical edge portion of this 
holding means 2. A driving means 3 is constructed by a stepping motor to 
accurately control a rotating angle of the detected lens 1. A rotating 
angle sensor 4 detects the position of a rotating origin and can detect a 
rotating amount of the detected lens 1 from this origin. Reference 
numerals 5, 6 and 7 respectively designate a light source, a beam splitter 
and an optical system. The optical system 7 is constructed by two lenses 
7a and 7b. The lens 7b on a light source side of the optical system 7 
changes incident light to a parallel light beam. The lens 7a on a side of 
the detected lens 1 converges this parallel light beam onto a detected 
face. A spot position detecting means 8 is arranged on an image forming 
face of the optical system 7 and is constructed by a charge coupled device 
(CCD) camera. A displacement measuring means 9 is constructed by an 
electronic indicator. The displacement measuring means 9 comes in contact 
with the aspherical surface 1b of the detected lens 1. The displacement 
measuring means 9 measures a displacement of the detected lens in the 
direction of an optical axis caused by rotating the detected lens 1. A 
computer 10 constitutes an arithmetic means. 
The detected lens 1 is supported and held by the holding means 2 on the 
spherical surface 1a. The detected lens 1 is rotated by the driving means 
5 around a rotating axis of the detected lens 1 approximately conforming 
to the optical axis thereof. A light beam emitted from the light source 5 
is transmitted by the optical system 7 such that this light beam is 
converged to a paraxial curvature center of the aspherical surface 1b. The 
light beam is irradiated and incident to a surface of the detected lens 1 
in a direction perpendicular to this lens surface. This light beam is then 
reflected on this lens surface and reversely passes through the optical 
system 7. The light beam is formed as a light spot image on the spot 
position detecting means 8. A position of this spot image shows the 
optical axis of the detected lens 1. Accordingly, when the detected lens 1 
is rotated, the spot image draws a circle on an image forming face in 
accordance with the rotation of the detected lens 1 if the rotating and 
optical axes of the detected lens are not in conformity with each other. 
The position of the spot image formed on the spot position detecting means 
8 is detected as a coordinate of a center of gravity of the spot image. 
The angle sensor 4 calculates an angle between the spot image and the 
position of a rotating origin of the detected lens 1. Further, a shifting 
amount of the spot image from a radius of the circle is calculated. 
Measured data of the displacement measuring means 9 are corrected from 
these data of the coordinate of the center of gravity, the above angle, 
the shifting amount, etc. In this case, it is not necessary to correct a 
setting shift of the detected lens 1 with high accuracy. 
However, in the above measuring method, a size of the image forming face of 
the spot position detecting means 8 is limited. Accordingly, as shown in 
FIG. 2, when the detected lens 1 is eccentrically held by the holding 
means 2, going and returning optical paths are different from each other 
as shown by arrows so that no spot image can be formed on the spot 
position detecting means 8. Therefore, it is necessary to focus and form 
the spot image on the spot position detecting means 8 by coarsely 
adjusting the position of the detected lens 1 in advance. However, 
considerable skill is required for only this coarse adjustment and it 
takes much time to make this coarse adjustment. 
It is necessary to move the optical system 7 forward and backward in the 
optical axis direction and adjust and set this optical system 7 to a 
focusing state so as to focus and form the spot image. In accordance with 
this movement, it is also necessary to move the light source 5 and the 
spot position detecting means 8 as the image forming face on the optical 
axis. This focusing operation is also a very difficult work. 
Further, when the rotating and optical axes of the detected lens 1 are 
automatically set to be in conformity with each other after the coarse 
adjustment, a shifting direction of the spot image and an eccentric 
direction of the detected lens are conformed to each other or are opposed 
to each other when the aspherical surface is set to a convex or concave 
face. Therefore, when an adjustment similar to that in the case of a 
convex detected face is made with respect to a concave detected face, 
eccentricity of the detected lens is not corrected, but is further 
increased. 
FIG. 3 is a view showing the construction of an apparatus for measuring 
eccentricity of an aspherical lens in accordance with another embodiment 
of the present invention. A main construction of this measuring apparatus 
is similar to that explained with reference to FIG. 1. Therefore, the 
differences between FIGS. 1 and 3 are mainly explained in the following 
description. In FIG. 3, an alignment adjusting means 11 is opposed and 
fixed to an outer circumferential edge of a detected lens 1. The alignment 
adjusting means 11 is constructed by a stepping motor 11a and a cam 
follower 11b operated by this stepping motor 11a. A pressing face 11c of 
the cam follower 11b at a front end thereof comes in contact with the 
outer circumferential edge of the detected lens 1. 
A vertical displacement measuring means 12 comes in contact with the outer 
circumferential edge of the detected lens 1 to measure an eccentric amount 
of the detected lens in a direction perpendicular to an optical axis of 
the detected lens 1. Namely, the vertical displacement measuring means 12 
measures a displacement of the detected lens 1 in this direction. Similar 
to a displacement measuring means 9, this vertical displacement measuring 
means 12 is constructed by an electronic indicator. 
A coarse adjustment of eccentricity of the detected lens 1 will next be 
explained. In FIG. 
the pressing face 11c is set such that a distance between the pressing face 
11c and the optical axis is equal to a radius of the detected lens 1. In 
this state, the detected lens 1 is held by the holding means 2. Similar to 
the explanation using FIG. 1, the detected lens 1 is rotated in this 
state. When a rotating axis of the detected lens 1 is shifted from the 
optical axis thereof, an eccentric portion of the detected lens at its 
outer circumferential edge is pressed by the pressing face 11c. The 
detected lens 1 is adsorbed by the holding means 2 on a spherical surface 
side thereof. When the eccentric portion is pressed by the pressing face 
11c, the detected lens 1 is slid and moved on the holding means 2. Thus, 
when the detected lens 1 is rotated one time, a coarse adjustment of 
eccentricity of the detected lens 1 can be made and a light spot image can 
be focused and formed on the spot position detecting means 8. Normally, no 
optical axis of the detected lens 1 is accurately in conformity with a 
center of the detected lens 1. Therefore, possibility of complete 
conformity between the rotating axis and the optical axis of a detected 
face is small. However, it is possible to make a coarse adjustment in 
which the spot image is focused and formed on the spot position detecting 
means 8. 
The holding means 2 adsorbs and supports the detected lens 1 on its 
spherical surface la at a cylindrical end edge of this holding means. 
Accordingly, a center of curvature of the spherical surface la is located 
in a constant position at any time even when the detected lens 1 is slid 
and moved on the holding means 2 as mentioned above. 
FIG. 4 is a view showing the construction of an apparatus for measuring 
eccentricity of an aspherical lens in accordance with another embodiment 
of the present invention. In this embodiment, a light source 5, a beam 
splitter 6, an optical system 7 and a spot position detecting means 8 as 
shown in FIG. 3 are collected and fixedly arranged on one stage 13. The 
stage 13 can be moved forward and backward in the direction of an optical 
axis by a stage driving means 14 constructed by a stepping motor, a ball 
screw, a nut, etc. 
A position of the stage 13 is detected by a stage position detecting means 
15 constructed by a linear scale, etc. The stage position detecting means 
15 detects the position of the stage 13 as a position of a stage face 13a 
on a side of the holding means 2. In this case, the position of the stage 
15 is set to zero when the stage face 13a is in conformity with a 
receiving face 2a of the holding means 2. 
FIG. 5 is a partially enlarged view of the detected lens 1 and a converging 
lens 7a. Parameters c, d, R1, R2, h, e, f and g are set as follows when 
each of a spherical surface 1a and an aspherical surface 1b of the 
detected lens 1 is set to a convex face. The parameter c is set to a 
distance from the receiving face 2a to the stage face 13a. The parameter d 
is set to a distance from the stage face 13a to a principal plane 7c of 
the converging lens 7a a on a side opposed to the detected lens 1. The 
parameter R1 is set to a radius of curvature of the spherical surface 1a 
of the detected lens 1 on a holding side thereof. The parameter R2 is set 
to a paraxial curvature radius of the aspherical surface 1b. The parameter 
h is set to a radius of the receiving face 2a. The parameter e is set to a 
thickness of the detected lens 1. The parameter f is set to a focal length 
of the converging lens 7a. The parameter g is set to a distance from the 
receiving face 2a to a vertex of the spherical surface 1a. In this case, 
the distance g is provided by the following formula (1). 
EQU g=1-R1 cos {sin.sup.-1 (h/R1)} (1) 
The distance c is provided by the following formula (2). 
EQU c=f-d-{R2-(e-g)} (2) 
Light reflected on the aspherical surface 1b as a detected face is focused 
and formed as an image in a position of the stage 13 providing this 
distance c. 
Similarly, when the spherical surface 1a of the detected lens 1 as a 
holding face is a concave face and the detected face 1b is a convex face, 
light reflected on the detected face 1b is focused and formed as an image 
in a position of the stage 13 providing the following distance c. 
EQU c=f-d-{R2-(e+g)} (3) 
When the holding face 1a of the detected lens 1 is a concave face and the 
detected face 1b is a convex face, light reflected on the detected face 1b 
is focused and formed as an image in a position of the stage 13 providing 
the following distance c. 
When both the surfaces of the detected lens 1 are concave faces, light 
reflected on the detected face 1b is focused and formed as an image in a 
position of the stage 13 providing the following distance c. 
EQU c=f-d+{R2+(e+g)} (5) 
In the above formulas (1) to (5), the values f, d, R2 and e are known and 
it is also known that both the surfaces of the detected lens are convex or 
concave faces. Further, the value g can be calculated. Accordingly, an 
arithmetic means can select any one of the formulas (2) to (5) by 
inputting the respective values and conditions to the arithmetic means 
before measurement. Otherwise, each of the surfaces of the detected lens 1 
may be judged as a concave or convex face by a radius of curvature of the 
detected lens or a sign of the paraxial curvature radius as known shape 
data. 
When the present position of the stage 13 is set to x and a moving amount 
of the stage 13 from the present position is set to .DELTA.x, the 
following formula (6) is formed. 
EQU .DELTA.x=c-x (6) 
The stage 13 is moved by providing this moving amount .DELTA.x to the stage 
driving means 14. At this time, the stage 13 can be automatically 
positioned by detecting the position of the stage 13 by the stage position 
detecting means 15 and performing a feedback operation of this stage 
position. The light source 5, the beam splitter 6 and the spot position 
detecting means 8 are fixed together to the stage 13. The light source 5, 
the beam splitter 6 and the spot position detecting means 8 can be 
simultaneously positioned by positioning the optical system 7 so that the 
positioning operation can be easily performed. 
The next explanation relates to an automatic adjustment of a setting shift 
of the detected lens using a stepping motor 11a and a vertical 
displacement measuring means 12. 
A light spot image is focused and formed on the spot position detecting 
means 8 by the above-mentioned coarse adjustment. When the detected lens 1 
is rotated, the spot image draws a circle as mentioned above if the 
optical axis and the rotating axis of the detected lens 1 are not in 
conformity with each other. The vertical displacement measuring means 12 
also measures a displacement (deflection) of an outer circumferential edge 
of the detected lens 1 in a direction perpendicular to the optical axis. A 
size of the circle drawn by a center of gravity of the spot image detected 
by the spot position detecting means 8 is inputted to an arithmetic unit 
10. Data of an angle between a rotating origin detected by the angle 
sensor 4 and the center of gravity of the spot image are also inputted to 
the arithmetic unit 10. Further, the displacement of the detected lens 1 
measured by the vertical displacement measuring means 12 is inputted to 
the arithmetic unit 10. 
Each of FIGS. 6a and 6b is a view for explaining a state in which an 
eccentric direction of the detected lens and a shifting direction of the 
spot image are changed in accordance with a shape of the detected lens. 
FIG. 6a shows a case in which the detected lens 1 is constructed by a 
biconvex lens and is eccentrically supported by the holding means 2 below 
the optical axis. A light beam from the light source 5 is transmitted as 
shown by an arrow and is reflected on a detected face. Since the detected 
lens is eccentric, a spot image is focused and formed above an optical 
axis of the spot position detecting means 8. In this case, eccentricity of 
the detected lens 1 is corrected by pushing the detected lens 1 from below 
to above as shown by an arrow in FIG. 6a. 
FIG. 6b shows a case in which the detected lens is constructed by a lens 
having a concave face on one side and having a convex face on the other 
side. Similar to the case of FIG. 6a, the detected lens 1 is eccentrically 
supported below the optical axis. In this case, since a detected face is 
set to a concave face, a spot image is focused and formed below the 
optical axis. A focusing position of the spot image is opposite to that 
shown in FIG. 6a. 
As mentioned above, the arithmetic unit 10 can calculate an eccentric 
amount of a certain constructional portion of the detected lens 1 on an 
outer or inner circumferential side thereof in consideration of a shape of 
the detected lens 1 to be measured if this shape of the detected lens is 
inputted to the arithmetic unit 10 in advance. Therefore, an outermost 
eccentric portion of the detected lens 1 is moved to the position of a 
pressing face 11c of the alignment adjusting means 11 by giving commands 
to the driving means 3. Next, the detected lens 1 is pushed by the 
pressing face 11c by giving commands to the stepping motor 11a so as to 
correct a displacing amount of the detected lens 1. At this time, the 
vertical displacement measuring means 12 measures a moving distance of the 
detected lens 1 and this measured moving distance is fed back to the 
stepping motor 11a. When the displacing amount of the detected lens 1 is 
minus or negative, the detected lens 1 is rotated 180.degree. and is 
pressed from an opposite side. 
When the detected lens 1 is rotated one time, the rotating and optical axes 
of the detected lens 1 should be in conformity with each other. However, 
it is confirmed by further rotating the detected lens 1 whether the spot 
image draws a circle or not. If the circle is still drawn, the above 
procedures are continuously repeated until no spot image is moved. 
When the rotating and optical axes of the detected lens are completely in 
conformity with each other, the displacement (deflection) of a detected 
face in the optical axis direction is measured by the displacement 
measuring means 9 by again rotating the detected lens 1. A total 
deflection width is divided by a displacement-angle conversion coefficient 
calculated in advance so that an eccentric amount of an aspherical surface 
of the detected lens 1 with respect to the optical axis can be calculated. 
A detailed method for calculating this eccentric amount is described in 
the above-mentioned Japanese patent application relative to FIG. 1. 
As mentioned above, the measuring apparatus in the present invention has a 
pressing face coming in contact with an outer circumferential edge of the 
detected lens and pushing and moving the detected lens in a direction 
approximately perpendicular to an optical axis of the detected lens. The 
pressing face is arranged in a position separated from the optical axis by 
a radius of the detected lens. Accordingly, it is possible to very simply 
make a coarse adjustment of the detected lens in which a spot image is 
focused and formed on a limited image forming face. 
A light source, an optical system and the image forming face are fixed onto 
the same stage. The spot image is focused and formed on the image forming 
face by moving the stage forward and backward in an optical axis 
direction. Accordingly, the spot image can be easily formed and no skill 
for such an adjustment is required. 
Shape data of the detected lens are inputted to an arithmetic unit in 
advance. The arithmetic unit gives commands to an alignment adjusting 
means in accordance with a shape of the detected lens. Accordingly, the 
detected lens can be positioned irrespective of concaveness and convexness 
of a detected face. 
In this case, the optical system can be automatically positioned by 
inputting face shape data, etc. to the arithmetic unit. 
An apparatus for measuring eccentricity of an aspherical lens in accordance 
with another embodiment of the present invention will next be described 
with reference to FIG. 1 explained above. 
In FIG. 1, one face 1a of a detected lens 1 is set to a spherical surface. 
The other face 1b of the detected lens 1 is set to an aspherical surface. 
A holding means 2 holds the detected lens 1 on a side of the spherical 
surface 1a and is constructed by a spindle. A driving means 3 for rotating 
the spindle is constructed by a stepping motor to accurately control a 
rotating angle of the spindle. An angle sensor 4 detects a rotating angle 
of the stepping motor 5. Reference numerals 5, 6 and 7 respectively 
designate a light source, a beam splitter and an optical system. The 
optical system 7 is constructed by two lenses 7a and 7b. A spot position 
detecting means 8 is arranged on an image forming face of the optical 
system 7 and is constructed by a charge coupled device (CCD) camera. A 
displacement measuring means 9 is constructed by an electronic indicator. 
The displacement measuring means 9 comes in contact with the aspherical 
surface 1b of the detected lens 1. The displacement measuring means 9 
measures a displacement of the detected lens in the direction of an 
optical axis caused by rotating the detected lens 1. A computer 10 
constitutes an arithmetic means. 
Light emitted from the light source 5 is reflected on the beam splitter 6 
and is converged onto the aspherical surface 1b by the optical system 7. 
Light reflected on the detected lens 1 is transmitted in a direction 
reverse to the above optical path. This light is then transmitted through 
the beam splitter 6 and is converged to the spot position detecting means 
8 located on an image forming face of the optical system 7. Thus, a spot 
image is focused and formed on the spot position detecting means 8. 
The detected lens 1 is held by the spindle 2. A shaft of the spindle 2 is 
rotated as a rotating axis by the driving means 3 to which the angle 
sensor 4 for detecting the above rotating angle is attached. The 
displacement measuring means 9 measures a deflection or displacement of 
the aspherical surface 1b caused by rotating the detected lens 1 in the 
optical axis direction. A measured value of this displacement is inputted 
to the arithmetic means 10. The angle sensor 4 sequentially measures a 
rotating angle of the detected lens 1 rotated by the driving means The 
measured rotating angle is inputted to the arithmetic means 10. 
Accordingly, the arithmetic means 10 provides the deflection of the 
aspherical surface 1b in the optical axis direction at an arbitrary 
rotating angle. 
FIG. 7a is a conceptional view showing the relation between the detected 
lens 1, an image forming face 8a of the spot position detecting means 8, 
an optical axis 11 of the detected lens, a rotating axis 12 of the spindle 
and an aspherical surface axis 13 when no lenses 7a and 7b are considered. 
In FIG. 7a, reference numeral 0 is set to an intersecting point between the 
rotating axis 12 and the image forming face 8a. Reference numeral P is set 
to an intersecting point between the optical axis 11 and the image forming 
face 8a. Reference numeral Q is set to an intersecting point between the 
aspherical surface axis 13 and the image forming face 8a. Further, x and y 
axes perpendicular to each other are set on the image forming face 8a as 
shown in FIG. 7a. 
An angle .alpha. between the optical axis 11 and the rotating axis 12 of 
the spindle shows an error amount caused by a setting shift. An angle 
.beta. between a line segment OP and the x-axis shows a direction of this 
error. When the optical axis 11 is rotated in conformity with the rotating 
axis 12, an angle .theta. between the optical axis 11 and the aspherical 
surface axis 13 shows a net eccentric amount. An angle .gamma. between a 
line segment PQ and the x-axis shows an eccentric direction. 
FIG. 7b is a view showing the relation between the detected lens 1 and the 
image forming face 8a when two lenses 7a and 7b are considered. A point 
O.sub.1 shows a center of curvature of a curved surface 1a of the detected 
lens 1. A point O.sub.2 shows a center of curvature of the aspherical 
surface 1b near the optical axis. Accordingly, a line connecting the 
points O.sub.1 and O.sub.2 to each other is set to the optical axis 11 of 
the detected lens. The holding means 2 holds a spherical surface side of 
the detected lens 1. The curvature center O.sub.1 on the side of the 
spherical surface 1a is located on the rotating axis 12 at any time 
irrespective of a value of the setting shift .alpha.. The other point 
O.sub.2 is shifted from the rotating axis 12 as shown in FIG. 7b since the 
setting shift .alpha. is caused with respect to the detected lens 1. 
Light is emitted from the light source 5 such that this light is converged 
to the point O.sub.2 by the lens 7a. However, since the setting shift 
.alpha. is caused, the light is transmitted such that this light is 
converged to a point O.sub.2 ' near the point O.sub.2. Light reflected on 
a detected face 1b is approximately returned to an original optical path 
so that this light is transmitted through the lenses 7a and 7b and is 
focused and formed as a spot image at a point P on the image forming face 
8a. 
When the spindle 2 is rotated, the spot image at the point P is rotated on 
the image forming face 8a around the point O as a center. The optical axis 
11 and the above light reflected on the detected lens 1 formed as an image 
by the spot position detecting means 8 has a relation shown in FIG. 7b and 
represented by the following formulas. 
EQU R=f.sub.2 tan .delta. 
EQU (f.sub.1 tan .delta.)/2=T sin .alpha.=e 
Here, 
f.sub.1 is set to a focal length of the lens 7a. 
f.sub.2 is set to a focal length of the lens 7b. 
.delta. is set to an angle between the reflected light and the rotating 
axis. 
.alpha. is set to an angle between the optical axis 11 of the detected lens 
and the rotating axis 12. 
Value e is set to a distance between the point O.sub.2 and the rotating 
axis 12. 
A coordinate of the spot image at an arbitrary rotating angle can be read 
with respect to a circle drawn by rotating the spot image. 
Therefore, for example, the coordinate of a center of gravity of this spot 
image can be taken out as an electric signal by using a charge coupled 
device (CCD) camera as the spot position detecting means 8. This electric 
signal is inputted to the arithmetic means 10. Thus, a radius R of the 
circle drawn by the spot image can be calculated and the angle .alpha. 
between the optical axis 11 and the rotating axis 12 can be calculated. 
The reflected spot image and the optical axis 11 as shown in FIGS. 7a and 
7b pass through the same point O.sub.1 and the same rotating axis 12. 
Therefore, the reflected spot image and the optical axis 11 are considered 
to be located on the same plane. Accordingly, the angle .beta. can be 
calculated if the detected lens 1 is rotated and a rotating angle of the 
detected lens is read from the angle sensor 4 when the reflected spot 
image passes through the position of a rotating origin. 
In accordance with rotation of the spindle 2, the displacement measuring 
means 9 constructed by an electronic indicator measures a displacement 
Do(i) of the aspherical surface in the optical axis direction in each of 
positions in which circumference 2.pi. is equally divided into i-parts. 
Data of the measured displacement are inputted to the arithmetic means 10. 
This detected displacement Do(i) includes an error caused by the setting 
shift .alpha.. 
The real deflection D(i) as a corrected displacement can be calculated from 
the obtained measured value Do(i) by the following formula. 
EQU D(i)=Do(i)-A .alpha.cos [{2 .pi.(i-1)/n}+.beta.] (.mu.m) 
In this formula, values i, n and A are respectively set to a counting 
number, a sampling number and a conversion coefficient (.mu.m/min). Values 
.alpha. and .beta. are respectively set to a setting shift and a setting 
shift direction. 
FIG. 8 shows one example of a sine wave curve drawn by i-corrected 
displacements calculated from the above formula. A net eccentric amount 
can be calculated from a total width T shown in FIG. 8 by a method 
described in Japanese patent application No. 4-29995, etc. An initial 
phase shows an eccentric direction .gamma.. 
Each of FIGS. 9 and 10 is a view for explaining one calculating example of 
the conversion coefficient A in the above formula. FIG. 9a shows a state 
in which optical and rotating axes of the detected lens 1 are in 
conformity with each other. Reflected light from the detected lens 1 is 
focused and formed as an image at a center of the spot position detecting 
means 8. 
As shown in FIG. 9b, the detected lens 1 located in this position is 
slightly shifted by applying an external force to this detected lens in an 
arrow direction. In this case, a spot image is focused and formed in a 
position shifted from the center of the spot position detecting means 8. A 
displacement measuring means 9 detects a deflecting amount S (.mu.m) of a 
detected face of the detected lens in an optical axis direction. The spot 
position detecting means 8 detects a shifting amount .lambda. (pixel) from 
a point O.sub.2. The conversion coefficient can be calculated as 
A=(SB)/.lambda.(.mu.m/pixel). In this case, B is set to a moving amount of 
a reflected light spot moved on the position detecting means when the 
reflected light spot is inclined one minute. This value B is simply 
provided by an experiment. 
In FIG. 9a, the optical axis and the rotating axis are first set to be in 
conformity with each other. However, the conversion coefficient can be 
calculated by the same calculating method since the shifting amount is 
normally small even when the optical axis and the rotating axis are not in 
conformity with each other. 
In FIG. 10, an axis of abscissa shows the moving amount .lambda. (pixel) of 
the light spot and an axis of ordinate shows the deflecting amount S 
(.mu.m) of the detected face in the optical axis direction. The detected 
lens 1 is slightly moved arbitrary times in a direction perpendicular to 
the optical axis as shown in FIGS. 9a and 9b. Measured results of each of 
these movements are plotted in FIG. 10. The conversion coefficient A can 
be calculated when a regression straight line is drawn along these plotted 
points and an inclination of this regression straight line is calculated. 
The conversion coefficient A can be more accurately calculated if a range 
of the displacement S of the detected lens is set to be wide and the 
measuring operation is performed many times. 
FIG. 11 is a view for explaining another method for calculating the 
conversion coefficient. A center O.sub.1 of curvature of a spherical 
surface of the detected lens 1 is set to an origin. A rotating axis 12 of 
the spindle is set to an x-axis. A line segment perpendicular to the 
x-axis at the origin O.sub.1 is set to a y-axis. When the detected lens 1 
is pushed in a direction perpendicular to the optical axis, the detected 
lens 1 is rotated around the origin O.sub.1 as a center. A rotating angle 
of the detected lens is set to .phi. (minute). At this time, the 
displacement measuring means 9 measures a deflecting amount S of a 
detected face in an x-axis direction. 
A value of this deflecting amount S can be calculated from a shape 
parameter of the detected lens 1. Accordingly, the deflection of the 
detected face in the optical axis direction can be calculated by S/.phi. 
when a reflected light spot is inclined a unit angle (one minute). 
FIG. 12 shows the construction of an apparatus for measuring eccentricity 
of an aspherical lens in accordance with another embodiment of the present 
invention. In this embodiment, in addition to the measuring apparatus 
shown in FIG. 1, the eccentricity measuring apparatus has an actuator 14 
for applying an external force to a detected lens 1 held by a holding 
means in a direction approximately perpendicular to an optical axis of the 
detected lens. The actuator 14 is constructed by a stepping motor 14a and 
a cam follower 14b operated by this stepping motor. A vertical 
displacement measuring means 15 is arranged on a side of the detected lens 
1 opposed to the actuator 14. The vertical displacement measuring means 15 
measures a displacing amount of the detected lens 1 displaced in a 
direction perpendicular to the optical axis. The vertical displacement 
measuring means 15 is constructed by an electronic indicator similar to 
that of the displacement measuring means 9. 
As explained with reference to FIG. 1, a setting shift .alpha. (minute) and 
a setting direction .beta. (degree) of the detected lens 1 can be 
calculated by an angle sensor 4 and a spot position detecting means 8. 
Accordingly, an arithmetic means 10 calculates a setting shift in a 
direction perpendicular to the optical axis from a value of the setting 
shift .alpha.. The arithmetic means 10 gives commands to a driving means S 
in accordance with such calculated values so as to rotate the detected 
lens 1 until a rotating angle of the detected lens is set to be equal to 
.beta. by the angle sensor 4. Next, the detected lens 1 is moved by a 
designated amount from a position indicative of this rotating angle in a 
direction perpendicular to the optical axis by a feedback system 
constructed by the actuator 14 and the vertical displacement measuring 
means 15. 
When a moving amount of the detected lens is negative, the detected lens 1 
is rotated 180.degree. and is pushed by the actuator 14 from an opposite 
side to correct the position of the detected lens. 
As mentioned above, in accordance with the present invention, true 
eccentricity of an aspherical lens as the detected lens can be calculated 
by correction in an eccentric measurement thereof without correcting a 
setting shift of the detected lens. Accordingly, a setting operation of 
the detected lens requiring skill can be omitted and eccentricity of the 
detected lens can be precisely measured for a short time. 
Further, a setting shift of the detected lens can be automatically 
corrected if the detected lens is displaced by a correction value 
calculated by the arithmetic means in a direction approximately 
perpendicular to the optical axis in cooperation with the arithmetic 
means, the displacement measuring means and the actuator. 
Many widely different embodiments of the present invention may be 
constructed without departing from the spirit and scope of the present 
invention. It should be understood that the present invention is not 
limited to the specific embodiments described in the specification, except 
as defined in the appended claims.