JPH0444201B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to a three-dimensional position measuring method and apparatus for detecting three-dimensional position coordinates of an object point in a non-contact manner.

[Conventional technology]

Conventionally, to measure the three-dimensional position of an object, the point of contact between the probe and the object is detected using a combination of a probe that detects contact with the object and an XYZ stage, or the surface of the object is traced with the tip of a stylus. The coordinate values of each point on the object were determined by moving the object.

[Problem that the invention seeks to solve]

However, in all of these conventional three-dimensional position measurement methods, measurement is performed by touching the object, so if the object is flexible or cannot be touched, the three-dimensional position of the object cannot be measured, and the former In the latter case, mechanical movement of the XYZ stage is required, so there is a risk of measurement errors due to mechanical precision.In the latter case, the tip of the stylus is spherical, so it is difficult to understand the fine structure of the object. Not only is measurement impossible, but it is also extremely difficult to increase the measurement speed.

An object of the present invention is to provide a three-dimensional position measuring method and apparatus that can solve these conventional problems.

[Means for solving problems]

Therefore, in the first invention, the three-dimensional position measuring method and device according to the present invention include: a first optical system having a first optical axis; telecentric second and third optical systems having the same focal length and second and third optical axes parallel to The three-dimensional position of the object point is determined from the coordinates from the origin of each of the image points of the first, second, first, and third optical systems of the object point to be measured, which are arranged to match the front focal plane of the system. It calculates coordinates.

Further, a second invention is an apparatus for carrying out the first invention, which comprises: a first optical system having a first optical axis; second and third optical systems having parallel second and third optical axes and having the same focal length and whose front focal plane coincides with the rear focal plane of the first optical system; , provided around the front focal point of the third optical system,
second and third apertures that make the second and third optical systems telecentric; second and third photoelectric conversion sensors provided near the rear focal points of the second and third optical systems; The device is provided with calculation means for processing output signals from these second and third photoelectric conversion sensors.

Furthermore, the third invention, in addition to the second invention,
It is equipped with a scanner that scans a light spot that illuminates the object to be measured.

Here, the focal plane means a plane that includes the focal point and is perpendicular to the optical axis.

[Effect]

The three-dimensional position measuring device configured as described above reads the positions of the image points on the second and third photoelectric conversion sensors as coordinate values from their respective origins, and inputs these values into a predetermined calculation formula. The three-dimensional position of the object point can be determined by processing the information using the calculation means.

Furthermore, by scanning a light spot that illuminates a measurement point on an object with a scanner, the three-dimensional coordinates of the object can be sampled at high speed.

〔Example〕

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, a measuring method and an apparatus thereof according to the present invention will be specifically explained with reference to the accompanying drawings, but prior to explaining the present invention, a general method of displaying points in a three-dimensional space will be briefly explained.

A point P (xyz) in a three-dimensional space having coordinates x, y, and z from the origin is expressed using a four-dimensional quantity P (XYZH).

Here, x=X/H, y=Y/H, z=Z/H, and when H=0, it represents a point ∞. For example, P(2341) and P(4682) represent the same point P(234), and P(1000) represents the point at x=∞.

To simplify the explanation, the optical system described below is a lens system whose thickness is extremely thin compared to the radius of curvature, and its front principal point and rear principal point are both aligned with the center of the lens, that is, the optical center. Assume that the front focal length is equal to the back focal length.

Generally, when a point P (0yz1) in a three-dimensional space at the origin O is imaged in the image space at the origin O' by an optical system 1 with a focal length f as shown in Fig. 4, the image point is
If P′(0y′z′h′), then in the meridional plane, between the points P(0yz1) and P′(0y′z′h′), (0y′z′h′)=(0yz1) T T = 0 0 0 0 0 f 00 0 0 0 −f ² 0 0 1 0 (a) The following relationship holds true.

Also, the transformation of the general point P (xyz1) is expressed as Ψ=RTR ^-1 (b).

However, R represents a rotation matrix, R=cosθ −sinθ 0 0 sinθ cosθ 0 0 0 0 1 0 0 0 0 0 (c) R ^-1 = cosθ sinθ 0 0 −sinθ cosθ 0 0 0 0 1 0 0 0 0 1 (d) Here, θ=π/2−tan ^-1 y/x (a), (c), (d) Substituting equations into (b), Ψ=fsin ² θ fsinθcosθ 0 0 fsinθcosθ fcos ² θ 0 0 0 0 0 −f ² 0 0 1 0 (e) From this, the transformation of the general point P (xyz1) becomes (x′y′z′h′) = (xyz1)Ψ (e′) .

Here, when considering the position of the image point when out of focus in a general optical system using Fig. 5, the image point P' when in focus is image A in the rear focus state, and image A in the front focus state. B, spreads to the image plane, and changes the position of its chief ray, that is, the center P', P of images A and B.
It can be seen that the x′ and y′ coordinates of are also changed.

On the other hand, in a telecentric optical system, as shown in Figure 6, the chief ray on the image side is parallel to the optical axis of the optical system, so if the focus shift is ignored, the image
The barycentric coordinates (x′y′) of P′ can be considered as an orthogonal projection onto the x′y′ plane.

In this case, even if z′ information is lost, x′ and y′ information are not lost.

There are several ways to make the optical system telecentric, but the simplest and most commonly used method is to make the front focal point F of the optical system 1 telecentric, as shown in Figure 7.
This can be achieved by narrowing down the diaphragm 4 to the position as much as possible.

If we consider the case where the point P (xyz1) is orthogonally projected onto the point P' on the z=n plane, as in the case of projection by such a telecentric optical system, then P (xyz1) → P' (xyn1), so that The transformation matrix S is expressed as S=1 0 0 0 0 1 0 0 0 0 0 n 0 0 0 1 (f).

Therefore, the projection of a point P in three-dimensional space onto the focal plane by a telecentric optical system can be expressed as a combination of the transformation Ψ shown in equation (e) and the transformation S shown in equation (f). , if the focal plane is z'=0, ΨS=fsin ² θ fsinθcos 0 0 fsinθcosθ fcos ² θ 0 0 0 0 0 −f ² 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 to ΨS=fs ² fsc 0 0 fsc fc ² 0 0 0 0 0 0 0 0 1 0 (1) However, S=sinθ, c=cosθ, θ=π/2−tan ^-1 y/x This (1) From the equation, it can be known to what point on the focal plane the three-dimensional object point P is converted.

Conversely, if a point on the focal plane is given, the object point 3
Think about how to find dimensional positions.

As shown in FIG. 8, a telecentric second optical system 2 having a second optical axis O ₂ at a distance f ₂ and a third telecentric optical system 2 parallel to the second optical axis O ₂ separated by a distance 2B. A telecentric third optical system 3 with a focal length f ₃ having an optical axis is provided, and the front focal points F ₂ and F ₃ of the second and third optical systems 2 and 3 are located on the second and third optical axes.
These front focal points are perpendicular to O ₂ and O ₃ .
The Z coordinates of F ₂ and F ₃ are made to match, and the origin O of the three-dimensional space on the object point side is set at the midpoint of the line F ₂ F ₃ connecting the focal points F ₂ and F ₃ .

In addition, second and third planes Σ 2 and Σ 3 are provided at the rear focal positions of the second and third optical systems ₂ and ₃ orthogonally to the optical axes O ₂ and O ₃ , and points in the three-dimensional space are provided. the second of P(xyz),
Projection coordinates x _{2 ′} , y _{2 ′} , θ ₂ and
Expanding x ₃ ′, y ³ ′, θ ₃ using equation (1), we get becomes.

If we convert this into the form of an equation for the unknowns x, y, and z, we get (f ₂ s ₂ )・x+(f ₂ s ₂ c ₂ )・y−(x ₂ ′)・z
=−Bf ₂ s ₂ ² (f ₂ s ₂ )・x+(f ₂ s ₂ c ₂ )・y−(x ₂ ′)・z
=−Bf ₂ s ₂ ² (f ₂ s ₂ c ₂ )・x+(f ₂ c ₂ ² )・y−(y ₂ ′)・z=−Bf ₂
s ₂ c ₂ (f ₂ s ₂ )・x+(f ₂ s ₂ c ₂ )・y−(x ₂ ′)・z
=−Bf ₂ s ₂ ² (f ₂ s ₂ c ₂ )・x+(f ₂ c ₂ ² )・y−(y ₂ ′)・z=−Bf ₂
s ₂ c ₂ (f ₃ S ₃ ² )・x+(f ₃ s ₃ c ₃ )・y−(x ₃ ′)・z=Bf ₃ s ₃
² (f ₂ s ₂ )・x+(f ₂ s ₂ c ₂ )・y−(x ₂ ′)・z
=−Bf ₂ s ₂ ² (f ₂ s ₂ c ₂ )・x+(f ₂ c ₂ ² )・y−(y ₂ ′)・z=−Bf ₂
s ₂ c ₂ (f ₃ S ₃ ² )・x+(f ₃ s ₃ c ₃ )・y−(x ₃ ′)・z=Bf ₃ s ₃
² (f ₃ s ₃ c ₃ )・x+(f ₃ c ₃ ² )・y−(y ³ ′)・z=Bf ₃ s ₃
c ₃ (3) However, is obtained.

That is, when the image points (x ₂ ′y ₂ ′) and (x ₃ ′y ₃ ′) are given, s ₂ , c ₂ , s ₃ , and c ₃ are found by equation (4),
From these values and the known values f ₂ , f ₃ , B, equation (3)
The three-dimensional coordinates x, y, z of point P (xyz1) can be found using

At this time, since there are 4 sets of equations for 3 unknowns, optimal fitting is performed to calculate the position coordinates xyz of point P.
It is necessary to ask for

Next, in equation (2), if we examine the change in the coordinates of the image point when we keep the xy coordinates of the object point constant and change only the z coordinate, we find that ∂x ₂ ′/∂z=−1/z ² {(x+B)f ₂ sin ² θ ₂ +yf ₂ sinθ ₂ cosθ ₂ }(5) ∂y ₂ ′/∂z=−1/z ² {(x+B)f ₂ sinθ ₂ cosθ ₂ +yf ₂ cos ² θ ₂ }(6) In equations (5) and (6), the numbers inside { } are constants determined by x, y, and B, so these can be expressed as K ₂ (x, y,
B) and K ₃ (x, y, B), Δx ₂ ′=−K ₂ /z ²・Δz (7) Δy ₂ ′=−K ₃ /z ²・Δz (8) Here, x=y Considering the case where K ₂ =Bf ₂ , K ₃ =0, Δx ₂ ′=−Bf ₂ /z ²・Δz (9) |Δz|=z ² /Bf ₂・|Δx ₂ ′ | (10) If the resolution of image sensors such as CCDs and PSDs, which are photoelectric conversion sensors placed on the second and third planes Σ ₂ and Σ ₃ , is ε, the measurement error |Δz| is |Δz|=z ² / Bf ₂ ·ε (11) It is found that the accuracy 1/|Δz| is inversely proportional to the square of z.

In this way, it is undesirable that the position measurement accuracy changes depending on the position of the object point P to be measured.

In order to avoid the above drawbacks, as shown in FIG.
are the same, the front focal planes of both optical systems are matched, and the first optical system has a rear focal point at the midpoint O between the front focal points F ₂ and F ₃ of the second and third optical systems 2 and 3. The system 1 may be arranged to sandwich the first optical axis O ₁ so that the second and third optical axes O ₂ and O ₃ are symmetrical within the same plane.

In FIG. 9 with such a configuration, the first
Let the focal length of the optical system 1 be f ₁ , and the image of the point P(z) on the first optical axis O ₁ by this first optical system 1 is the image point.
If P ₁ ′(z′), then from Newton's formula for lenses, z′=−f ₁ ² /z (12) Furthermore, from equation (11), the detection accuracy at image point P ₁ ′ is |Δz′| =z′ ² /Bf ₂ ·ε (13) is obtained.

Differentiating equation (12) and substituting equation (13) into it, we get |Δz|=f ₁ ² /Bf ₂・ε (14) As can be seen from equation (14), the measurement accuracy with such an optical system is are the first, second, and third optical systems 1, 2,
3. Characteristics and arrangement and image sensor resolution ε
, and is independent of the position of the object point P to be measured.

Furthermore, for the x and y directions, it is clear that the measurement error from the imaging characteristics does not depend on the position of the object point.

In the optical system shown in FIG. 9, as shown in FIG. 1, second and third apertures 4 and 5 are provided at the front focal positions of the second and third optical systems 2 and 3 to limit the passing light flux. Then, the
PSD (Position Sensitive Device)
An image of an object point P illuminated by a laser beam or the like is projected onto image sensors 6 and 7 such as a CCD (Charge Coupled Device) or the like in the form of a light distribution centered on the chief ray.

Here, if the image sensors 6 and 7 are PSD, the center of gravity of the light distribution is automatically detected, but
In this case, the center can be determined via an arithmetic circuit.

Therefore, in order to measure the three-dimensional coordinates P (xyz) of the object 10 to be measured using the optical system shown in _FIG .
Find the coordinates x ₂ ′, y ₂ ′, x ₃ ′, y ₃ ′ of P ₃ ′, and write the equation (A
)
Solve to find the point P ₁ ′(x′, y′z′).

(f ₂ s ₂ )x′+P( ₂ s ₂ C ₂ )y′−(x ₂ ′)z′
= −Bf ₂ s ₂ ² (f ₂ s ₂ ) x′ + P ( ₂ s ₂ C ₂ ) y′ − (x ₂ ′) z′
= −Bf ₂ s ₂ ² (f ₂ s ₂ C ₂ )x′+(f ₂ C ₂ ² )y′−(y ₂ ′)z′=−Bf ₂ s ₂ C
_{2 ( f 2 s 3} ² _{) _ _} ^_ _{_ _} ^_ _{_ _} C ₃ )y′−(x ₃ ′)z′=Bf ₂ s ₃ ³ (f ₂ s ₃ C ₃ )x′+(f ₂ C ₃ ² )y′−(y ₃ ′)z′=Bf ₂ s ₃ C ₃ (
A) However, s ₂ = sin (π/2−tan ^-1 y ₂ ′/x ₂ ′) c ₂ = cos (π/2− tan ⁻¹ y ₂ ′/x ₂ ′) s ₃ = sin (π /2−tan ^-1 y ₃ ′/x ₃ ′) c ₃ = cos (π/2−tan ⁻¹ y ₃ ′/x ₃ ′) Next, P ₁ ′(x′y′z′) is expressed as equation ( B) and the object point P
Finding the three-dimensional position coordinates of However, S′=sinθ=sin(π/2−tan ⁻¹ y′/x′) c′=cosθ=cos(π/2−tan ⁻¹ y′/x′).

Equation (A) is derived from equation (3), and equation (B) is derived by expanding equation (e′).

That is, the second and third image sensors 6 and 7
Coordinates of upper image points P ₂ ′, P ₃ ′ (x ₂ ′, y ₂ ′), (x ₃ ′, y ₃
′)
, and solve equation (A) to find the coordinates (x', y', z') of the image point P ₁ ', and substitute those values into equation (B), then the point P in three-dimensional space can be found. You can know the coordinates (xyz) of

In this case, the measurement accuracy Δ is the image sensor 6, 7
If the resolution of is ε, then Δ=f ₁ ² /Bf ₂ ·ε.

In actual measurement, a part of the object is irradiated with a laser beam to form a light spot, and this light spot is manually moved to a desired position on the object to obtain three-dimensional position information at that point. Alternatively, the optical spot is scanned with a scanner to obtain a data file {(x ₂ ′, y ₂ ′), (x ₃ ′, y ₃ ′)}i, which is
A wide variety of application examples are possible, such as a method of converting to a dimensional file {(xyz)}i to obtain shape information of a three-dimensional object.

Here, some embodiments of the three-dimensional position measuring device according to the present invention will be shown.

FIG. 2 shows an embodiment in which the present invention is applied to, for example, a digital stereoscopic microscope device.
an objective lens 1, which is an optical system, and an imaging lens 2, which is a second and third optical system, each having the same focal length and having parallel optical axes that maintain symmetrical positions on the same plane, sandwiching the optical axis of the objective lens 1. , 3 are arranged so that the rear focal plane of the objective lens 1 coincides with the front focal plane of the imaging lenses 2 and 3.

Apertures 4 and 5 with small apertures are provided around the front focal points of the imaging lenses 2 and 3, respectively.
3 is a telecentric optical system, and second and third image sensors 6 and 7 consisting of CCDs are installed near the rear focal points of these imaging lenses 2 and 3, respectively, from the respective imaging lenses 2 and 3. The distance is perpendicular to the optical axis.

Furthermore, the output signals from the image sensors 6 and 7 are displayed on a cathode ray tube 11 for observation, and
The input is input to a control device 12 equipped with a CPU to perform predetermined arithmetic processing, and the control device 12 is connected to the cathode ray tube 1.
1 and the control panel 13.

According to the microscope device configured in this way, by specifying a desired point of a figure on the cathode ray tube 11 with the cursor 14, the three-dimensional coordinates of that point can be easily measured, and the product and standard workpiece can be easily measured. It is also possible to perform a three-dimensional comparison.

Note that a point on the cathode ray tube 11 may be designated with a light pen.

Next, FIG. 3 shows another embodiment in which the present invention is applied to a three-dimensional digitizer, in which visible light is cut behind the first optical system 1 and only laser light such as infrared light is reflected. Mirrors 15a, 15b, 16
a, 16b and direct the reflected light beam to the first optical axis.
They are introduced into second and third optical systems 2 and 3 having the same focal length and having second _and third optical axes O ₂ and O ₃ that are parallel to each other and maintain symmetrical positions in the same plane with O 1 in between. The rear focal plane of the first optical system 1 is arranged to coincide with the front focal planes of the second and third optical systems 2 and 3 so that the optical system 1 has a rear focal plane.

Then, apertures 4 and 5 are arranged around the front focal points of the second and third optical systems 2 and 3, and these optical systems 2,
3 is a telecentric optical system, and second and third image sensors 6 and 7 consisting of PSD are installed near the rear focal point and are perpendicular to the optical axes O ₂ and O ₃ respectively. It is provided at a position equidistant from the optical systems 2 and 3.

Further, a light projecting lens 17 is provided on the same optical axis O ₁ behind the first optical system 1, a half mirror 18 is provided obliquely behind the light projecting lens 17, and a CCD for monitoring is provided behind the projecting lens 17. An image sensor 19 is provided.

Further, an angle-variable scanner mirror 20 constituting a scanner for scanning a light spot is provided corresponding to the half mirror 18, and a condensing lens 21 and a laser diode 22 are arranged behind it. The light is focused by the condensing lens 21, reflected by the scanner mirror 20 and the half mirror 18, and then reflected by the light projecting lens 17 and the first
The point P of the object 10 is reached through the optical system 1 of .

The laser beam reflected at point P passes through the first optical system 1, the projection lens 17, and the half mirror 18, forms an image on the image sensor 19, and can be monitored on a cathode ray tube (not shown).

At the same time, the laser beam that has passed through the first optical system 1 travels on second and third optical paths O ₂ and O ₃ by mirrors 15a, 15b and 16a, 16b, and the aperture 4,
5, image points P ₂ ′,
P ₃ ', and from the points x ₂ , y ₂ and x ₃ , y _3, calculate the three-dimensional coordinates x, y, z of the object point P using equations (A) and (B).
can be found.

At this time, if the angle of the scanner mirror 20 is continuously changed automatically or manually, it becomes possible to sample the three-dimensional coordinates of the object 10 at high speed.

〔Effect of the invention〕

As described above, in the first and second inventions, the three-dimensional position measuring method and device according to the present invention include a first optical system having a first optical axis;
telecentric second and third optical systems each having the same focal length and having second and third optical axes symmetrically parallel to each other in the same plane, sandwiching the optical axis of the first optical system; The rear focal plane is arranged to match the front focal planes of the second and third optical systems, and the image points of the object point to be measured by the first, second, and third optical systems are arranged from their respective origins. Since the three-dimensional positional coordinates of the object point are calculated from the coordinates, the three-dimensional position of the object point can be measured with high precision by a non-contact and extremely simple operation.

Furthermore, if necessary, it is not necessary to provide a mechanically operating part in the measuring device, and errors in measurement accuracy due to mechanical errors in the operating part can be completely eliminated.

Furthermore, according to a third invention, in addition to the second invention, a scanner for scanning a light spot is provided,
It becomes possible to sample the three-dimensional position coordinates of an object at high speed.

[Brief explanation of drawings]

Figure 1 is a configuration diagram showing the optical system of this invention, Figure 2 is a configuration diagram showing the optical system of this invention.
The figure is a block diagram of one embodiment of the three-dimensional position measuring device according to the present invention, FIG. 3 is a block diagram of another embodiment, and FIG.
The figure is an explanatory diagram showing the relationship between a point in a three-dimensional space and an image point in a general optical system, Figure 5 is an optical path diagram showing an out-of-focus state in a general optical system, and Figure 6 is an image of a telecentric optical system. FIG. 7 is an optical path diagram showing the effect of the aperture to make the optical system telecentric. FIG. 8 is a configuration diagram showing only the latter half of the optical system of this invention. FIG. 9 is a diagram showing the configuration of the optical system of this invention. FIG. 2 is an explanatory diagram showing the principle of a measuring method. 1...First optical system, 2...Second optical system, 3...Third optical system, 4...Second aperture, 5...Third aperture,
6... Second image sensor, 7... Third easy sensor, 10... Object, 11... Braun tube, 12... Control device, 13... Tablet, 14... Cursor, 1
5a, 15b, 16a, 16b...Mirror that cuts visible light, 17...Light projection lens, 18...Half mirror, 19...Image sensor, 20...Scanning mirror, 21...Condensing lens, 22...Laser diode, _f1 ... Focal length of the first optical system, f ₂ ... Focal length of the second and third optical systems, O ₁ ... First optical axis, O ₂ ...
Second optical axis, O ₃ ...Third optical axis, 2B...Distance between the second and third optical axes, P...Object point, _P1 '...Image point by the first optical system, P2 _' ...image point on the second image sensor, P ₃ '...image point on the third image sensor.

Claims (1)

[Claims] 1. A first optical system having a first optical axis;
telecentric second and third optical systems having the same focal length and having second and third optical axes that are symmetrically parallel to each other in the same plane, sandwiching the optical axis of the first optical system; The rear focal plane is arranged so as to coincide with the front focal plane of the second and third optical systems, and the image point of the object point to be measured is determined by the first, second and first and third optical systems. From the coordinates from each origin,
A three-dimensional position measuring method characterized by calculating three-dimensional position coordinates of the object point. 2 a first optical system having a first optical axis;
have second and third optical axes that are symmetrically parallel to each other in the same plane with the optical axis of second and third optical systems for telecentricity, and second and third optical systems that are provided around the front focal points of the second and third optical systems and that make the second and third optical systems telecentric. aperture, second and third photoelectric conversion sensors provided near the rear focal points of the second and third optical systems, and arithmetic processing of output signals from the second and third photoelectric conversion sensors. A three-dimensional position measuring device, characterized in that it is provided with a calculation means. 3 a first optical system having a first optical axis;
have second and third optical axes that are symmetrically parallel to each other in the same plane with the optical axis of second and third optical systems for telecentricity, and second and third optical systems that are provided around the front focal points of the second and third optical systems and that make the second and third optical systems telecentric. aperture, second and third photoelectric conversion sensors provided near the rear focal points of the second and third optical systems, and arithmetic processing of output signals from the second and third photoelectric conversion sensors. A three-dimensional position measuring device comprising a calculation means and a scanner that scans a light spot that illuminates an object to be measured.