Optical axis displacement sensor

A first convex lens, having a focal length f1 and a second convex lens, having a focal length f2, are arranged at an interval d (=f1+f2). A mirror is provided, on the optical axis, to reflect the laser beam from a laser thereby emitting parallel beams, through the first lens, onto the surface to be measured. The interval between the first lens and the surface is f1+z1. The interval between the second lens and the image point, at which the image of the surface is formed, is f2+z2. A position detector of this point, comprises a slit plate, a third convex lens, having a focal length f3, and a CCD line sensor. The interval between the slit plate and the sensor is l.sub.0. The second and third lenses are so arranged that the focal points coincide. The slit plate is provided perpendicular to the optical axis, immediately before the third lens, and a pin hole is opened at an interval d.sub.0 on either side of the optical axis. The line sensor is positioned in parallel with the slit plate. The position z2 of the image point is obtained from the interval x of the incident positions of the beams incident onto the sensor, through the two pin holes. EQU x={(f3.sup.2 +f3z2-l.sub.0 z2)d.sub.0 }/f3(f3+z2) The position z1 of the surface is obtained from the position z2 of the image point, per the formula: EQU z1=z2/(f2/f1).sup.2.

BACKGROUND OF THE INVENTION 
This invention relates an optical axis displacement sensor. 
Recently, position-sensing apparatuses for measuring the displacement of a 
surface have been developed for loading numerical data representing a 
three-dimensional free-form surface having a complicated shape. These 
apparatuses can be classified into two types. The first type measures the 
distance to a surface by use of the principle of triangulation. The second 
type has a photoelectric converter and can be moved by a servo mechanism. 
The photoelectric converter detects the displacement of an image of a 
surface which has resulted from the displacement the surface with respect 
to a reference point. The apparatus is then moved by a servo mechanism 
until the displacement of the image is compensated, and finds the position 
of the surface from the distance it has been moved. 
FIG. 6 shows a conventional apparatus of the first type. The apparatus has 
angle detector 12. Detector 12 comprises calibrating disk 11, and has a 
telescope, a slit plate and a photoelectric converter, all attached to 
disk 11. A laser beam emitted from a laser (not shown) is reflected at 
point P on surface S, and is incident onto angle detector 12. When surface 
S is shifted for distance .DELTA.z along the laser beam emitted from the 
laser, the angle of reflection of the beam varies. The angular variation 
.DELTA..theta. detected by detector 12 is given as: 
EQU .DELTA..theta.=.DELTA.z.multidot.sin .phi./R (1) 
where .phi. represents the angle of an incident laser beam with respect to 
a line joining point P, before displacement, with the center of disk 11, 
and R represents the distance between point P, before displacement, and 
the center of disk 11. 
When variation .DELTA..theta. is obtained by detector 12, displacement 
.DELTA.z of surface S can be calculated by way of the above equation (1). 
FIG. 7 shows a knife-edge type positioning sensor of the second 
conventional apparatus. Positioning sensor 14 has micro-mirror 3 for 
reflecting a slightly diverged laser beam onto the optical axis of convex 
lens 2, knife-edge shielding plate 15 having a knife edge perpendicularly 
crossing the optical axis, at an image point Q of a point P, and 
photodetecting diodes 16a, 16b positioned symmetrically with respect to a 
plane defined by the optical axis and the knife edge. Sensor 14 is moved 
by a servo mechanism (not shown), the distance travelled being detected. 
The apparatus is so adjusted that, when surface S is inclined in a plane 
including point P (i.e., when the image point is located at point Q), a 
differential output Ea-Eb of diodes 16a and 16b becomes zero. When surface 
S moves from the plane including point P, whereby the image point is 
shifted from point Q, part of the light incident on either one of diodes 
16a and 16b is shielded by plate 15, so that the output Ea-Eb does not 
become zero. The servo mechanism moves sensor 14 such that the 
differential output becomes zero, and the degree of displacement from the 
plane including point P of surface S can be known by measuring the 
distance moved by sensor 14. 
As can be understood from equation (1), in the apparatus of FIG. 6, 
.DELTA..theta. reaches its maximum when .phi. is .pi./2, provided .DELTA.z 
remains unchanged. Therefore, detector 12 should be so positioned that its 
detection face is perpendicular to the laser beam. In this case, however, 
a so-called "shadow effect" may occur wherein the light reflected from 
surface S is shielded by a projection protruding from detector 12 when 
surface S is shifted greatly as is shown in FIG. 8. Thus, a dead angle 
occurs, and the displacement of surface S cannot be correctly measured. 
The knife-edge type sensor shown in FIG. 7 has the following drawbacks with 
regard to its incorporation in an optical system and the signal 
processing. 
Plate 15 must be positioned at image point Q of point P in the optical 
system. To this end, the position of point Q must first be defined. As is 
apparent from the principle of reversibility, micro-mirror 3 must be 
designed and adjusted so as to reflect the beam applied from the light 
source and convert the beam to divergent light flux L represented by 
broken lines jointing point Q with some points on the surface of mirror 3. 
In other words, since the position of point Q (and hence point P) depends 
upon the optical system of the light source, the design, assembling and 
adjustment become complicated. Therefore, not only does the cost of the 
device increase, but it is also difficult to operate. 
To eliminate such drawbacks, it is considered that point P depends upon the 
sole optical constant. For example, when parallel light beams are incident 
from a light source onto mirror 3, point P becomes the focal point of lens 
2, and does not accordingly depend upon other optical constants. However, 
in this case, a new problem that image point Q (and hence the position of 
shielding plate 15) becomes infinitely remote. 
As the rules of geometrical optics show, in the system of FIG. 7, no 
linearity exists between the positional changes of surface S and the that 
of image point Q. It is therefore difficult for a photoelectric converter 
to generate an output which quantitatively corresponds to the displacement 
of surface S. Since the light beams incident onto surface S are not 
parallel, the light-receiving area varies as surface S is displaced from 
the plane including point P, with the result that the size of the image 
alters, thereby giving rise to the drawback wherein the precise 
measurement of the displacement in a wide range is disabled. 
Since the position of surface S where the differential output of diodes 16a 
and 16b becomes zero is located at point P, the absolute amount of light 
incident onto the diodes does not necessarily pose a problem with regard 
to signal processing. Hence, as long as the apparatus is used as a 
reference-pointing sensor, neither a variation in the incident energy of 
the diodes, generated by variations in the reflectivity of surface S and 
in the luminous intensity of the light source, nor an external disturbance 
such as an optical noise becomes a significant problem. In this sense, 
this apparatus is preferable, but another disadvantage of this apparatus 
resides in its employment of the servo mechanism. If the displacement of 
surface S is measured only with the apparatus in FIG. 7, without servo 
mechanism, the relationship between the displacement of surface S and the 
displacement of the image point becomes complicated. Since the measured 
result depends upon the difference of luminous quantities incident to 
diodes 16a and 16b, this apparatus has such disadvantages that the 
measured result cannot be obtained with reproducibility due to the 
difference in the reflectivity of surface S and the external disturbance. 
Further, the other drawback of the apparatus in FIG. 7 is that, if surface 
S is not perpendicular to the optical axis, the apparatus does not 
correctly function. Since shielding plate 15 and diodes 16a, 16b correctly 
operate on the basis that the intensity distribution of lights incident 
from lens 2 to knife edge is symmetrical with respect to the optical axis, 
if surface S is inclined with respect to the optical axis, the intensity 
distribution of the reflected light does not become axis-symmetrical. 
SUMMARY OF THE INVENTION 
An object of this invention is to provide an optical axis displacement 
sensor of a noncontacting type capable of accurately measuring the 
displacement of a surface to be measured having a complicated 
three-dimensional free form in a wide range without shadow effect. 
According to this invention, there is provided an optical axis displacement 
sensor comprising: 
an optical system having a first convex lens including an aperture on an 
optical axis and a second convex lens positioned on the optical axis of 
the first lens, 
light source means for emitting parallel light beams through the aperture 
of the first lens onto a surface to be measured, 
means for detecting the position of an image point at which an image of the 
surface to be measured is formed by said optical system, and 
calculating means for calculating the position of the surface according to 
the output of said position detecting means.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
An embodiment of an optical axis displacement sensor according to this 
invention will be described in detail with reference to the accompanying 
drawings. 
A principle will be first described. When first and second convex lenses 
having focal distances f1 and f2, respectively are arranged so as to have 
a distance d and the optical axes thereof are coincide with each other, an 
object (a surface to be measured) is positioned at a point on the optical 
axis separated by f1+z1 from the first lens, and the image of the object 
is formed at a point on the optical axis separated by f2+z2 from the 
second lens, the following relations can be obtained from optogeometrical 
imaging conditions: 
EQU (f1.sup.2 /z1)-(f2.sup.2 /z2)=d-(f1+f2) (2) 
EQU where 
EQU -f1&lt;z1&lt;f1.sup.2 /f2 (3) 
The relationship between z1 and z2 of equation (2) is complicated, but if 
the following equation (4) is assumed, 
EQU d=f1+f2 (4) 
the equation (2) can be simply expressed as below. 
EQU z2=(f2/f1).sup.2 z1 (5) 
The above equation (5) exhibits that the optical system which employs this 
lens system (d=f1+f2) has the following features: 
1. There is a simple proportional relation between position z1 of the 
surface to be measured and position z2 of the image point. Therefore, when 
position z2 of the image point is measured, position z1 of the surface to 
be measured can be obtained. 
2. The proportional relationship between z1 and z2 can be arbitrarily 
varied by the ratio of f1 of f2. Therefore, the wide range of displacement 
of z1 from micrometers to a few hundred millimeters can be measured with 
the constant displacement of z2. 
3. When position z1 of the surface to be measured is zero, position z2 of 
the image point also becomes zero. More specifically, when the surface to 
be measured is positioned at a focal point F1 of the first lens, the image 
point becomes focal point F2 of the second lens. Therefore, when focal 
point F1 is used as a reference (fixed point) of the position of the 
surface to be measured, focal point F2 becomes a reference position of the 
image point. Thus, the reference position depends only upon a sole optical 
constant (which is focal point F1 of the first lens in this case) 
irrespective of the arrangement of the component of the apparatus. 
Therefore, the construction and the adjustment of the apparatus can be 
simplified. 
FIG. 1 shows the construction of a first embodiment. First convex lens 2 
having focal length f1 (40 mm) and second convex lens 4 (each lenses 2 and 
4 is fixed in a cylinder) having focal length f2 (40 mm) are positioned at 
distance d=(f1+f2) of 80 mm and the optical axes thereof coincide with 
each other. An aperture of about 3 mm in diameter is formed in parallel 
with the optical axis at the center of lens 2. The output light of an 
He-Ne gas laser 8 is reflected by mirror 9 toward the optical axis of the 
lens system composed of first and second lenses 2 and 4. The center of 
micro mirror 3 is positioned on the optical axes between first and second 
lenses 2 and 4, the micro mirror 3 reflects a laser beam incident from 
mirror 9 in parallel with the optical axes so as to irradiate surface S to 
be measured with the parallel laser beams through the central aperture of 
lens 2. The distance between lens 2 and surface S to be measured is 
denoted as f1+z1. 
The reflected light of surface S to be measured is focused at an image 
point W through lenses 2 and 4. The distance between lens 4 and image 
point W is denoted as f2+z2. Position detector 1 of the image point has a 
light shielding plate 5, third convex lens 6 having a focal length f3 (30 
mm) and a CCD line sensor 7 (having 2592 elements). Lens 6 is positioned 
so that the optical axis thereof coincides with those of first and second 
lenses 2 and 4. 
Second and third lenses 4 and 6 are so positioned that the focal points 
thereof coincide with each other. Plate 5 is positioned immediately before 
lens 6 perpendicularly to the optical axis and has a pin hole or slit at 
an interval d.sub.O (20 mm) on either side of the optical axis. Sensor 7 
is arranged in parallel with plate 5. The output of sensor 7 is inputted 
to calculating circuit 100 to measure the position of surface S to be 
measured. 
The laser beam reflected on mirror 3 is incident onto surface S through the 
central aperture of lens 2 and is reflected at point U on the optical 
axis. The reflected beam is focused at image point W through lenses 2 and 
4 and partly passed through the pin holes of plate 5, converged by lens 6, 
and incident onto sensor 7. When the interval of the incident positions of 
the beams incident onto sensor 7 through two pin holes of plate 5 is 
represented by x, the output voltage of sensor 7 has two peaks separate at 
a distance corresponding to x as shown in FIG. 3. Thus, x can be obtained 
by attaining the CCD element numbers corresponding to the peaks and the 
difference therebetween. When x is obtained, since there is the following 
relationship between x and position z2 of the image point, the position z2 
of the image point is obtained by the calculation circuit 100 x, and 
position z1 of the surface to be measured can be obtained from the 
equation (5). 
EQU x={(f3.sup.2 +f3z2-l.sub.O z2)d.sub.O {/f3(f3+z2) (6) 
where l.sub.O is the interval between plate 5 and sensor 7. 
According to the embodiment, the lens system is constructed so that the 
position of surface S to be measured with respect to the focal point of 
objective lens 2 and the position of image point W with respect to the 
position of the image point of surface S which is positioned at the focal 
point are proportional. Therefore, the measuring range and the resolution 
can be altered by the combination of the lenses of the lens system without 
necessity of particular correction in the measurement. 
The measuring range of the embodiment is 20 mm (-3.5 mm to +16.5 mm with 
the focal point of first lens 2 as a reference). The resolution is about 
10 microns. 
According to the embodiment, mirror 3 is arranged between first and second 
lenses 2 and 4, an aperture is formed (on the optical axis) at the center 
of first lens 2, and parallel light beams are incident onto surface S to 
be measured through mirror 3 and the aperture. Therefore, an area 
irradiated with the laser beam of surface S to be measured becomes 
constant irrespective of the position of surface S. Thus, the measurement 
of the position of surface S in a wide range can be performed. Since the 
beam is emitted on the optical axis of the measuring system and the 
reflected beam is measured on the optical axis or in the vicinity of the 
axis, there is no dead angle. 
Further, information regarding the image point is obtained from the address 
of the CCD element of sensor 7 to which the light is incident. More 
particularly, since the information can be obtained by the CCD element 
number at which the output voltage becomes maximum, the good 
reproducibility of the measured result can be obtained without depending 
upon the intensity of the incident light to the line sensor or the 
variation in the beam quantity nor the influences of the reflectivity, 
roughness, curvature and inclination of the surface to be measured, and an 
external disturbance signal as the conventional apparatus which employs an 
analog type photoelectric converter (photodetecting diode). The detection 
of the image point by detector 1 is performed not on the basis of the 
symmetry of the light beam intensity distribution to the optical axis of 
the lens as in the conventional technique. Therefore, even if the surface 
to be measured is not perpendicular to the optical axis and the light beam 
intensity distribution is resultantly asymmetrical to the optical axis, 
the measured result is not affected. 
Since the measurement is conducted without contact, the apparatus can be 
also used for the measurement of the displacement of an article such as an 
elastic body, a soft body or an article in a high temperature vessel. 
A second embodiment will be described. The second embodiment is the same as 
the first embodiment except the construction of position detector 1 of 
image point W. FIG. 4 is a view showing the construction of position 
detector 1 according to the second embodiment of the invention, and FIG. 5 
shows the output signal of CCD line sensor 7 of FIG. 4. 
In the first embodiment, sensor 7 is positioned in a direction 
perpendicular to the optical axes of first and second lenses 2 and 4. 
However, in the second embodiment, sensor 7 is positioned on the optical 
axes of first and second convex lenses 2 and 4. When surface S to be 
measured is positioned at the focal point of lens 2, the reflected beam is 
incident onto the center of line sensor 7, as shown by a broken line of 
FIG. 4. At this time, the output of sensor 7 has a peak value 
corresponding to the center of sensor 7. When the position of surface S is 
changed, the trace of the reflected beam is changed as shown by the solid 
line of FIG. 4 and the output of sensor 7 has a peak value corresponding 
to the element distanced from the center of sensor 7 by z2. In other 
words, the image point is shifted by z2 due to the displacement of surface 
to be measured. Distance z2 can be obtained by detecting the shift of the 
peak of the output of sensor 7. Z1 is obtained by z2 by equation (5). 
According to the invention as described above, the optical system is 
constructed so that the position of the surface to be measured with the 
focal point of an objective lens as a reference and the position of the 
image point corresponding to the reference position of the surface to be 
measured as a reference are proportional. Therefore, the measuring range 
and the resolution can be varied by the combination of the lenses of the 
optical system without necessity of the particular correction in the 
measurement. Since the CCD line sensor is used as position detecting 
means, the influence of the reflectivity, roughness, curvature and 
inclination of the surface to be measured is alleviated. Since the 
parallel beams are emitted on the optical axis of the optical system and 
the reflected light is picked up near the optical axis, no dead angle 
occurs in the measurement. Since the measurement is conducted without 
contact, the apparatus can be used for the measurement of the displacement 
of the article such as an elastic body, a soft body or an article in a 
high temperature vessel which is detrimental in the contact measurement. 
This invention is not limited to the particular embodiments described 
above. Various other changes and modifications may be made within the 
spirit and scope of the present invention. For example, interval d between 
first and second lenses 2 and 4 is not always the sum of focal lengths f1 
and f2. Further, the position of mirror 3 is not disposed between first 
and second lenses 2 and 4, but may be arranged between lens 2 and surface 
S to be measured. In summary, it is sufficient to irradiate surface S with 
parallel beams. In the embodiments described above, only the apparatus for 
detecting the displacement of the surface to be measured in the direction 
of z-axis along the emitted beam has been described. However, when the 
apparatus is arranged on a table movable in X- and Y-axes directions and 
displacement .DELTA.z of the surface to be measured is obtained in x- and 
y-axes coordinate values, three-dimensional data of the surface to be 
measured may be provided.