JP2011058855A - Three-dimensional measuring device - Google Patents

Abstract

PROBLEM TO BE SOLVED: To propose a three-dimensional measuring apparatus for accurately measuring a three-dimensional shape of an object.
A three-dimensional measuring apparatus (100) includes an imaging optical system (10) that images reflected light from the surface of a sample (T), and an imaging that images the surface of the sample via the imaging optical system. The sample (15), the focal position of the imaging optical system, and the position of the sample are relatively changed in the optical axis direction of the imaging optical system, and based on a plurality of images obtained by imaging with the imaging unit A three-dimensional calculation unit (17) for calculating a three-dimensional shape. The imaging optical system satisfies the relationship f * θ <h <f * tanθ.
Where f: focal length of the imaging optical system, h: distance from the optical axis of the imaging optical system to an arbitrary point of the sample, θ: optical axis of the imaging optical system and the imaging optical system to the sample The angle formed with the chief ray.
[Selection] Figure 1

Description

  The present invention relates to a three-dimensional measuring apparatus that measures a three-dimensional shape of an arbitrary object (sample) from a plurality of images having different focal positions.

  Conventionally, various methods have been used for three-dimensional measurement. The ones that require moderate accuracy are those that perform stereo photography using two cameras, or scan the focal position of a moire imaging optical system that projects the stripe pattern and observes its distortion, and the focal position There is a SFF (Shape From Focus) method in which a depth direction (optical axis direction) is measured by searching for a matching portion.

  Among them, since the SFF method can measure the three-dimensional shape of the object (sample) only by scanning the focal position, a measuring machine can be configured relatively easily in combination with an existing optical system. The three-dimensional measuring device disclosed in Patent Document 1 is a measuring device using the SFF method. The three-dimensional measuring apparatus disclosed in Patent Document 1 determines the position based on the contrast of the image when scanning the focal position of the imaging optical system, so that the imaging optical system is required to have excellent imaging performance. The

Japanese Patent No. 2960684

  However, in general, the imaging lens is designed for a specific object point distance, and aberration occurs when the specific object distance is shifted. Strictly speaking, since the Herschel's rule and the abbe's sine rule are not compatible, aberrations in the image plane cannot be corrected at a plurality of object distances. By the way, the aberration includes spherical aberration, coma aberration, astigmatism, curvature of field, distortion, etc., but the three-dimensional measurement by the SFF method is applied to measurement of various objects. In the present embodiment, it is assumed that a relatively large object is measured from a distance. Therefore, the F number on the object T side of the imaging optical system is relatively large. If the F number is limited to a large one, the most important aberrations are field curvature and astigmatism. Spherical aberration is proportional to the cube of NA, and coma is proportional to the square. Therefore, if the NA is small (the F number is large), the aberration is small. On the other hand, since field curvature and astigmatism are proportional to NA, there is a problem that even if NA is small, it cannot be ignored.

  It is an object of the present invention to provide an optical system that provides little change in astigmatism and curvature of field even when the object distance is changed, and to propose a three-dimensional measuring apparatus that accurately measures the three-dimensional shape of an object. To do.

The three-dimensional measuring apparatus according to the first aspect includes an imaging optical system that images reflected light from the surface of the sample, an imaging unit that images the surface of the sample via the imaging optical system, and a focal point of the imaging optical system. A three-dimensional calculation unit that calculates a three-dimensional shape of the sample based on a plurality of images captured by the imaging unit while relatively changing the position and the position of the sample in the optical axis direction of the imaging optical system; Is provided. The imaging optical system satisfies the relationship f * θ <h <f * tanθ.
Where f: focal length of the imaging optical system, h: distance from the optical axis of the imaging optical system to an arbitrary point of the sample, θ: optical axis of the imaging optical system and the imaging optical system to the sample The angle formed with the chief ray.

  The present invention can accurately measure the three-dimensional shape of an object.

2 is a schematic diagram for explaining a configuration of a three-dimensional measuring apparatus 100. FIG. FIG. 6 is a diagram for explaining image correction by an image correction unit 18; 1 is a schematic diagram for explaining an imaging optical system 10. FIG. It is a figure for demonstrating the correction amount of the projection image by the image correction part. It is the figure which showed the structure of the imaging optical system 10 in a specific example. 7 is a graph showing the projection of ftanθ and the ratio of the projection of fθ and h (θ) when the projection of the imaging optical system 10 is h = h (θ). It is a figure which shows the value of MTF at the time of FIG. It is a figure which shows the value of MTF when an object distance is shortened by 54 mm from the state of FIG.

<Configuration of the three-dimensional measuring apparatus 100>
FIG. 1 is a schematic diagram for explaining the configuration of the three-dimensional measuring apparatus 100. A three-dimensional measuring apparatus 100 shown in FIG. 1 includes an imaging optical system 10, an illumination system LX, and an image processing unit 20. In the following description, the direction of the optical axis LK of the imaging optical system 10 is the Z-axis direction, and a plane perpendicular to the Z-axis direction is an XY plane on which the object T is placed.

  In FIG. 1, the imaging optical system 10 includes a plurality of imaging lenses, and moves in the Z-axis direction as indicated by an arrow by a drive motor (not shown). The imaging optical system 10 of the present embodiment is well corrected for aberrations, and the adaptation of the present embodiment suppresses astigmatism and curvature of field even when the focal position is changed. The imaging lens constituting the imaging optical system 10 will be described later with reference to FIG.

  The illumination system LX includes a light source 11, an illumination lens 12, and a half mirror 14. Here, the light source 11 is a normal white filament lamp, halogen lamp, mercury lamp, xenon lamp, or the like. Furthermore, the light source 11 may be an infrared lamp or an ultraviolet lamp, or a laser light source such as a semiconductor laser, an Ar laser, or a He—Ne laser.

  The image processing unit 20 includes an image detection unit 15, a focus position detection unit 16, a maximum focus signal calculation unit 17, an image correction unit 18, and a three-dimensional shape display unit 19. Here, the image detection unit 15 is a one-dimensional or two-dimensional image element such as a MOS or a CCD, and outputs an image signal. The image detection unit 15 outputs an image signal for each measurement surface that is different in the Z-axis direction. The focal position detection unit 16 detects the coordinates of the focal position based on the image signal from the image detection unit 15. The focal position detection unit 16 detects the focal position of the surface of the object T on a plurality of measurement surfaces based on a plurality of image signals different in the Z-axis direction. The maximum focus signal calculation unit 17 connects the focus positions of a plurality of images detected by the focus position detection unit 16.

  The imaging optical system 10 has extremely small field curvature even at a plurality of object distances. The image incident on the image detection unit 15 via the imaging optical system 10 forms an image even in the periphery away from the optical axis of the imaging optical system, and the position in the Z-axis direction can be accurately obtained from good contrast. Can do.

  Thereafter, the image correction unit 18 corrects the distortion generated by the imaging optical system 10. That is, the image correction unit 18 corrects the distortion aberration on the XY plane. Finally, the three-dimensional shape display unit 19 displays the three-dimensional shape of the object T based on the position of the XY plane from the image correction unit 18 and the focal position in the Z-axis direction.

<Measurement operation of the three-dimensional measuring apparatus 100>
Hereinafter, the operation of the three-dimensional measuring apparatus 100 will be described.
The light emitted from the light source 11 irradiates the filter 13 through the illumination lens 12. The light that has passed through the filter 13 is reflected by the half mirror 14 and applied to the object T. A multi-spot image, a lattice pattern, and a random texture are projected onto the object T.

  The reflected light reflected from the surface of the object T passes through the half mirror 14 and passes through the imaging optical system 10. The imaging optical system 10 causes the image detection unit 15 to image the measurement surface z1 of the target T in the Z-axis direction. The reflected light that has passed through the imaging optical system 10 is imaged by the image detection unit 15, and the image detection unit 15 outputs an image signal of the measurement surface z1. Thereafter, the imaging optical system 10 is moved in the Z-axis direction as indicated by an arrow by a drive motor (not shown). Then, the imaging optical system 10 causes the image detection unit 15 to image the measurement surface z2 of the target T in the Z-axis direction. And the image detection part 15 outputs the image signal of the measurement surface z2. Thus, the image detection unit 15 sends a plurality of image signals different in the Z-axis direction to the focus position detection unit 16.

  The maximum focus signal calculation unit 17 detects the Z coordinate that maximizes the contrast in all of the XY planes. Although a detailed discussion is omitted, in order to calculate the maximum contrast value in a short time, generally the detection of the edge of the pattern of the object and the detection of the maximum value of the differential value of the image intensity are performed. Since the contrast of the blurred portion in the object image is lowered, the intensity distribution of the portion becomes gentle, and the value becomes small when the differential component is calculated. On the other hand, when focused, the contrast increases and the differential value of the intensity distribution also increases. The maximum focus signal calculation unit 17 detects a focused portion from the object image based on such calculation.

  In a general imaging optical system, even if no field curvature occurs on the measurement plane z1, if the imaging optical system moves in the Z-axis direction to form an image on the measurement plane z2, field curvature occurs. In particular, it is difficult to detect the focus in the peripheral part away from the optical axis. However, in the imaging optical system 10 of this embodiment, even if the imaging optical system moves in the Z-axis direction, the entire measurement surface z2 can be imaged.

  The imaging optical system 10 of this embodiment does not change astigmatism and curvature of field even when the focal position is changed as will be described later with reference to FIG. Thus, even when the entire lens of the imaging optical system 10 is extended, there is no change in astigmatism and curvature of field, so that a good contrast can always be obtained even if the focal position is changed.

  The imaging optical system 10 of the three-dimensional measuring apparatus 100 is an optical system with little change in field curvature even if the focal position is changed by moving in the Z-axis direction as indicated by an arrow in FIG. Therefore, even if the focal position of the imaging optical system 10 and the position of the object T are relatively changed in the optical axis direction, a good contrast can always be obtained, so that the Z coordinate position accuracy is improved.

<Correction from coordinate value with distortion to coordinate value without distortion>
FIG. 2 is a diagram for explaining that the image correction unit 18 performs image correction. For easy understanding, a 3 × 3 square image signal will be described as an example. For example, when the two-dimensional shape (V11) of the object is a 3 × 3 square, the two-dimensional shape (V11) is deformed into a tall image by the negative distortion of the imaging optical system 10. The image detector 15 captures a tall image and outputs an image signal E15. The image signal E15 detected by the image detector 15 is synthesized via the focus position detection unit 16 and the maximum focus signal calculation unit 17.

  The focus signal (E17) calculated by the maximum focus signal calculation unit 17 still includes negative distortion aberration in both the XY coordinates. The image correction unit 18 corrects the focus signal (E17) input from the maximum focus signal calculation unit 17 so that the negative distortion is eliminated. The corrected signal is sent to the three-dimensional shape display unit 19, and the three-dimensional shape display unit 19 is displayed on the three-dimensional shape display unit 19 as a 3 × 3 square image signal E18 without distortion. The three-dimensional shape display unit 19 displays the shape of the object with excellent accuracy. The correction amount Δh of the image signal on the measurement surface will be described in detail using Equation 18.

<Outline of Imaging Optical System 10>
Hereinafter, the imaging optical system 10 will be described in detail with reference to FIG. FIG. 3 is a schematic diagram for explaining the imaging optical system 10. The imaging optical system 10 is composed of a plurality of lens elements, and has little change in field curvature even if the focal position is changed by moving in the Z-axis direction as indicated by the arrow in FIG. It is. In the imaging optical system 10, this is achieved by forming an image in the range of the formula (1) so as to suppress a change in field curvature.
(1)

Here, h is the distance from the optical axis LK of the imaging optical system 10 to an arbitrary point on the target T, and in the XY coordinates of FIG. 3 or FIG. 4, the relationship is h = √X ² + Y ² . . f is a focal length of the imaging optical system 10, and θ is an angle formed by the principal ray with respect to the optical axis LK on the object T side.

  In addition, by incorporating an optical system that satisfies Equation (1) into the apparatus, even when the imaging optical system 10 is moved to change the focal position, it is possible to always maintain a good field curvature and perform high-precision measurement. . Now, an explanation will be given of how an optical system that satisfies the condition of the formula (1) can maintain good aberrations.

  As described above, it is important to suppress astigmatism and field curvature that occur when the focal position is changed.

Therefore, Petzval sum is important when considering curvature of field. This is because, as is well known, the curvature radius of curvature of field near the optical axis can be calculated from the Petzval sum. By the way, the Petzval sum is determined by the refractive index and the radius of curvature of the lens constituting the optical system. Therefore, the Petzval sum does not change even if the focal position is changed. When the focal position is changed, the sagittal and meridional image planes are curved while astigmatism occurs. Therefore, if it is desired to suppress a change in aberration during focusing, it is only necessary to prevent astigmatism from occurring.
First, the projection relationship of the imaging optical system 10 is expressed by Equation (2).
(2)

Here, g is a function representing the projection relationship.
Differentiating both sides of Equation (2) gives Equation (3).
(3)

Also, the mathematical formula (4) is established from the geometric relationship in FIG.
(4)

  Here, a is the radius of the stop. The fact that the curvature of field does not occur even when the object moves in the optical axis direction means that the movement of the paraxial image point position due to the object movement coincides with the movement of the memorial image point off the axis. More specifically, the object image plane in which the image point 111 for the object point 110 outside the optical axis LK of the object plane 103 is a plane on which the image point 121 for the object point 120 on the optical axis LK of the object plane 103 exists. 104 may be present.

In general, the image plane movement Δz on the optical axis LK is expressed by Equation (5) from Newton's formula.
(5)

On the other hand, assuming that the image point 111 exists on the object image plane 104, the opening angle of the ray on the image plane is α, and the change in image height when the chief ray is inclined by Δθ is Δh. To establish.
(6)

Here, since the meridional image point considers a very thin light beam, when tan α≈sin α and equation (6) is modified, equation (7) is obtained.
(7)

Further, from the relationship corresponding to Helmholtz-Lagrange, more strictly, the Strobel's theorem is applied to the meridional plane, and since there is a relationship of Equation (8), the function g can be obtained.
(8)

First, Equation (9) is obtained from Equation (8).
(9)

Substituting Equation (9) into Equation (7) yields Equation (10).
(10)

Further, when Expression (3) and Expression (5) are substituted into Expression (10), Expression (11) is obtained.
(11)

Substituting Equation (4) into Equation (11) yields Equation (12).
(12)

When Expression (12) is integrated, Expression (13) is obtained.
(13)
Here, F is the first kind elliptic integral.

Furthermore, in order to understand the solution of the equation (13) in an easy-to-understand manner, the equation (15) is obtained by the equation (14) when the approximation equation is applied to the equation (12).
(14)
(15)

  From the above, the function g was obtained as the equation (13), and the result represented approximately by the equation (15) was obtained. That is, if the imaging optical system 10 is designed so as to have a projection relationship obtained by substituting such a function g into the equation (2), an optical system having no curvature of field in any plane on the image side can be obtained. Can be realized.

Next, the specific relationship between the imaging optical system 10 having such a projection relationship will be considered. In a general ftan θ lens, the function g is as shown in Equation (16).
(16)

Further, in a general fθ lens, the function g is as shown in Expression (17).
(17)

  Comparing Expression (15) with Expression (16) and Expression (17), it can be seen that the projection relationship of the imaging optical system 10 is a projection relationship between the projection relationship of the ftan θ lens and the projection relationship of the fθ lens. . Within this range, it is possible to realize the imaging optical system 10 having a very small field curvature in any plane on the image side.

The correction amount (distortion amount) of the projected image will be described with reference to FIG.
FIG. 4 is a diagram for explaining the correction amount of the projected image by the image correction unit 18.
In FIG. 4, for example, a solid square is an example of the image signal E <b> 18 when the image is not distorted by the imaging optical system 10. The dotted-line tall shape is an example of the image signal E17 when the image is distorted by the imaging optical system 10. As shown in FIG. 4, the point B of the image signal E17 distorted by the imaging optical system 10 becomes the point A of the square image signal E18. Here, the distance from the point A of the image signal E18 to the optical axis LK is _{h A,} the distance from the point B of the image signal E17 to the optical axis LK is _{h B.} Therefore, the correction amount Δh of the projected image is (h _A −h _B ).

Further, when the projection method of Equation (16) is used, there is no distortion in the projected image, and distortion up to the projection method of Equation (17) is allowed. For this reason, the extreme value of the correction amount Δh of the projected image is [Formula (17) −Formula (16)], which will be described using mathematical formulas. That is, the range of the correction amount Δh of the projected image is as indicated by the formula (18).
(18)

(Example)
<Configuration of Imaging Optical System 10>
FIG. 5 is a diagram showing the configuration of the imaging optical system 10. Although not depicted in FIG. 5, a two-dimensional light receiving element (see FIG. 1) is arranged on the + Z side. As shown in FIG. 5, the imaging optical system 10 includes eight projection lenses.

  More specifically, the imaging optical system 10 is formed by sequentially joining a biconvex lens L11, a convex lens L12 having a convex surface toward the object T, and a concave meniscus lens L13 having a convex surface toward the object T along the −Z axis direction. A lens L14, a biconvex lens L15, a biconcave lens L16, a cemented lens L19 of a convex meniscus lens L17 having a convex surface directed toward the object T, and a concave meniscus lens L18 having a convex surface directed toward the object T; It is composed of a convex meniscus lens L20 having a convex surface.

  In the specific example, the imaging optical system 10 is an imaging optical system that satisfies the above formula (13) or the formula (15). Even if the imaging optical system 10 is moved, the imaging optical system 10 always has good distortion. Highly accurate measurement is possible while maintaining aberration.

Table 1 shows lens data and specifications in the imaging optical system 10.

here,
R represents the radius of curvature of the lens,
D indicates the distance between the lens surfaces;
nd represents the refractive index of the d-line,
νd represents the Abbe number.

Further, the third surface and the ninth surface are aspherical surfaces, and the aspherical expression is as shown by the equation (19).
... (19)

In Equation (19), z represents the sag amount in the optical axis direction from the apex of the lens surface, h represents the distance from the optical axis, c represents the curvature and represents the reciprocal of the radius of curvature R, and K represents the conic constant. Show. Table 2 shows numerical values of the aspheric coefficients.

  The projection relationship of the optical system in FIG. 5 satisfies the condition of Expression (1). FIG. 6 shows the projection relationship of the optical system of FIG. In FIG. 6, when the projection of the imaging optical system 10 of the specific example is h = h (θ), the ratio of the projection of ftanθ and the projection of h (θ) and the projection of fθ and the projection of h (θ) It is a graph of the ratio. Here, the horizontal axis represents the image height h (θ). The solid line indicates the ratio between the projection of ftanθ and h (θ), and the alternate long and short dash line indicates the ratio between the projection of fθ and h (θ). As can be seen from the graph, h (θ) is smaller than ftanθ and larger than fθ in the range H surrounded by the dotted line. That is, it can be seen that the imaging optical system 10 satisfies the formula (1) near the optical axis.

  After that, the state of aberration when the imaging optical system 10 in FIG. 5 is moved in the optical axis direction to change the distance W from the object T will be described. FIG. 7 shows the MTF value in FIG. 5 (when the object distance W is 191.9 mm), and FIG. 8 shows that the object distance is reduced by 54 mm from the state of FIG. MTF of 137.9 mm) is shown. Looking at both MTFs, there is no astigmatism or curvature of field. It can be seen that the imaging performance is excellent.

  As mentioned above, although the optimal specific example of this invention was demonstrated in detail, as obvious to those skilled in the art, this invention can be implemented by adding various change and deformation | transformation to a specific example within the technical scope.

DESCRIPTION OF SYMBOLS 10 ... Imaging optical system 11 ... Light source 12 ... Irradiation lens 13 ... Filter 14 ... Half mirror 15 ... Image detection part 16 ... Focus position detection part 17 ... Maximum focus signal detection part 18 ... Image correction part 19 ... Three-dimensional shape display part 20 ... Image detection / processing / display unit 100 ... Three-dimensional measuring devices L11 to L20 ... Lens LK ... Optical axis of imaging optical system LX ... Illumination system T ... Object

Claims (5)

An imaging optical system that satisfies the following conditional expression and images reflected light from the surface of the sample;
An imaging unit that images the surface of the sample via the imaging optical system;
Based on a plurality of images obtained by imaging with the imaging unit while relatively changing the focal position of the imaging optical system and the position of the sample in the optical axis direction of the imaging optical system, the tertiary of the sample A three-dimensional calculation unit for calculating an original shape;
A three-dimensional measuring apparatus.
Where f: focal length of the imaging optical system, h: distance from the optical axis of the imaging optical system to an arbitrary point of the sample, θ: optical axis of the imaging optical system and the imaging optical system to the sample The angle formed with the chief ray.   The three-dimensional measurement apparatus according to claim 1, wherein the three-dimensional calculation unit corrects the coordinate value of the sample in a plane orthogonal to the optical axis when calculating the three-dimensional shape of the sample.   The three-dimensional measurement apparatus according to claim 2, wherein the three-dimensional calculation unit corrects the coordinate value according to a distance from a position of the imaging unit corresponding to an optical axis of the imaging optical system. The correction amount Δh for correcting the coordinate value is:
The three-dimensional measuring apparatus according to claim 3, wherein the three-dimensional measuring apparatus is in a range satisfying the conditional expression The imaging optical system is
The three-dimensional measuring apparatus according to any one of claims 1 to 4, which satisfies the conditional expression: