DE4317744C1 - Method for microscopically measuring the surface structure of an object - Google Patents

Abstract

This method is used for microscopically measuring the surface structure of an object with the aid of at least one lens. In this case, surface points Pi of the object which are of interest are sharply and successively imaged, while keeping the image distance constant, from two different lines R, R' of sight, and the respective viewpoint coordinates xi, yi and x'i, y'i, respectively, are measured. The object space coordinates ui, vi, wi of the surface points Pi are then determined from the associated image point coordinates by using a transformation matrix T. The latter can be determined with the aid of three reference points of known position in the object space and of their image point coordinates obtained from the same two lines R, R' of sight. <IMAGE>

Description

The invention relates to a method for microscopic measurement the surface structure of an object.

The measurement methods customary in photogrammetry for the purpose of Reconstruction of three-dimensional object or terrain surfaces that relying on the central perspective can mi microscopic surface structures are not used. This is due to the fact that with the op systems with a large aperture and correspondingly reduced warping Deep depth perspective shots are not possible.

Although K.B. Atkinson (Ed.): Developments in Close Range Photogram metry-1, Applied Science Publishers Ltd., London, 1980, chapters 1 and 2, already a method for microscopic measurement of the surfaces structure of an object is known, but cannot be removed there, meh More interesting surface points while keeping the image constant successive sharp image. Above all, there is the togetherness slope between pixel and object space coordinates is not linear, and the essential determination of the object for the invention described below spatial coordinates the image coordinates in the sense of a parallel projection with incl Drawing scale is also not addressed there.

The invention has for its object a method specify which the surveying and reconstruction microscopic, three-dimensional object surfaces on simple Enables way and with little equipment.

This object is achieved according to the invention by the Features specified claim 1 solved.

Accordingly, as in photogrammetry, two are initially distinguished direction of the object, i.e. two different optical Axes selected. However, in photogrammetry, apart from Image overlaps in the marginal areas of the object or the respective only one shot from each line of sight is made, it is proposed in the present case, from each of the make a series of shots in both directions, the one in interesting or for the characterization of the surface structure striking surface points are gradually depicted sharply. This The procedure takes into account that the depth of field of the microscope object tives will generally be much smaller than the spatial Aus expansion of the object surface in the direction of the optical axis of the Sy stems. If the entire object surface is to be captured, then each that of the two viewing directions is a sequence of shots  men made where the relative distance between the object and lens the steps corresponding to the depth of field are changed. As a result, the object surface is sharply "layered" so to speak forms. For object surfaces with a particularly simple structure Chen, whose structure, for example, by flat surfaces, straight edges, Cornerstones and regularly designed trenches or depressions are determined it suffices, only the striking ones that determine the overall structure "Approach" surface points and depict them sharply.

In the three-dimensional object space, for example, the object is kar assigned to the tesian coordinate system u, v, w. The recordings from the both viewing directions are kept constant while maintaining the image distance, i.e. of the distance between the lens and the image plane. The image level of the op table system is a two-dimensional, for example Cartesian Coordinate system assigned. A surface point P (u, v, w) of the Ob objects in the object space are therefore from the two when the image is sharp Viewing directions R and R ′ two pixel coordinate pairs x, y and x ′, assigned to y ′. For the successive sharp illustration of waiters of interest The surface points of the object become that in each of the two viewing directions Lens in object space, i.e. relative to the object, along its optical Axis shifted. Not only the image spacing remains, but also the object distance, i.e. the distance to the center of the depth of field object plane located in the area from a reference plane in the lens, constant. The object level gradually moves through the Ob, so to speak yes. Because of these conditions, they can be following pictures each sharply depicted surface areas of the Object in the sense of a parallel projection to a single total put together. Except for the ver caused by the lens The two represent enlargement and the reversal of the page that takes place two-dimensional imaging sequences of the object actually two den parallel projections of this object assigned to both viewing directions represents.

The invention is based on the knowledge that it is based on the above described facts is possible with the help of the two un  different viewing directions, each two-dimensional Image coordinates through linear transformation to the three-dimensional nals object space coordinates of the mapped surface point close. The transformation matrix T to be used here can by Measurement of three reference points with a known position in the object space the same two perspectives can be gained. This results in as explained in more detail below, nine linear determination equations conditions for the maximum of nine matrix elements of the transformation matrix.  

The two admission sequences from the two selected viewing directions can with a single lens. According to one he Most variant, the lens can be fixed and the slide can pivots and shifted in the direction of the optical axis of the lens become. According to a second variant, the slide can be pivoted and the lens can be moved axially. According to a third variant finally the slide can be fixed and the lens both be pivotally and axially displaceable. of course is the invention can also be carried out with an arrangement which has two or more rere lenses, which from different perspectives on the Object directed and are axially displaceable. Such an arrangement This enables two or more image sequences to be recorded simultaneously take, but is more expensive in terms of equipment.

The recording and evaluation of the two sequences of images can largely run automatically, but generally the intervention of a human observer may be required when selecting in interesting pixels. First of all, the two sequences of images by changing the relative distance between the lens and the object steps corresponding to the depth of field without human intervention fen as well as the pixel-wise electronic Storage of the respective images, with a CCD camera for use dung can come. The saved images can then be viewed called and on a screen or parallel screens from one Person for the purpose of selecting interested and corresponding Pixels are considered. The corresponding image coordinates  can then be selected, for example using the mouse, and added to another Memory read in and then for automated further off evaluation.

In the interest of high measurement accuracy, it is generally from Vor be part of choosing the two viewing directions so that they are vertical stand on each other.

Advantageous embodiments of the invention are set out in the subclaims remove.

In the following, the invention is described in an exemplary embodiment on the basis of Illustrations explained in more detail. In a schematic representation:

Fig. 1, the illustration of two points of an object in the object space by means of parallel projection in two different directions of view in perspective,

Fig. 2, the measurement of three reference points view of the object in Seitenan,

Fig. 3, the definition of an object point using image coordinates dinaten.

In Fig. 1, an object in the form of an irregular polyhedron in the object space, defined by the three-dimensional Cartesian coordinate system u, v, w, is shown. Two different viewing directions R, R 'are selected to measure the object. The corresponding optical axes are designated A or A '. They intersect at the origin 0 of the coordinate system. From the viewing direction R, the two surface points P₁ and P₂ are sharply depicted in two correspondingly different positions of the lens, schematically identified by M₁ and M₂, on the respective image planes E₁ and E₂. This results in the two pixels B₁ and B₂. Since both the image and the object distance remain constant when the lens is moved from the position M 1 to M 2, the same imaging scale is available in both cases. The two picture planes E 1 and E 2 can thus be shifted into a common, fictional superposition plane S and brought to cover there. The two-dimensional coordinate system there x, y is identical to the coordinate systems assigned to the two image planes E 1 and E 2. The individual pixels B₁ and B₂ corresponding points in the superposition plane S are denoted by S₁ and S₂. In the event that the distance between the two lens positions M₁ and M₂ is equal to the depth of field of the lens, the surface areas of the object in the superposition plane S that are sharply formed in the two image planes are directly adjacent to one another. Analogous relationships are shown with respect to the second viewing direction R ', with lens positions M₁' and M₂ ', image planes E₁' and E₂ ', pixels B₁' and B₂ ', a superposition plane S' with corresponding pixels S₁ 'and S₂' and a two-dimensional rectangular coordinate system x ′, y ′ occur.

Fig. 1 is a schematic diagram in which no Abbilidungsstrahl lengänge are shown, but only the principle of parallel projection is shown. The connection of the imaging beam paths with the parallel projection can be seen in FIG. 2.

The superposition plane S of FIG. 1 is purely fictional and is only shown for the sake of explaining the principle. The two image planes shown, e.g. B. E₁ and E₂, in the specific case are of course identical with the only one, the lens optically subordinate Bildebe ne identical. Shown are two different positions of this image plane in the object space after moving the lens on the optical axis, for. BA

The relationship between the image coordinates x _i , y _i and x _i ′, y _i ′ and the object space coordinates u _i , v _i , w _i is conveyed via the transformation matrix T by the following equation:

where the index i identifies the respective object or pixel, for the variable t _i either t _i ≡ x _i ′ or t ≡ x _i ′ applies and the transformation matrix T has the following form:

The nine matrix elements a _mn (m, n = 1, 2, 3) naturally depend on the special selection of the two viewing directions R and R ', can in principle be determined using purely geometric considerations, but are simpler in practice using the can be determined in the following described calibration operation.

A maximum of nine independent equations are required to determine the matrix elements a _mn . These can be obtained if the object spatial coordinates of three points, which are not all in one plane, are known. For these three reference points P _rk (k = 1, 2, 3), given the constellation of the two selected viewing directions R and R ', the respective pixel coordinates x _rk , y _rk and x _rk ' and y _rk 'are to be determined. From this, the following system of equations, consisting of nine individual equations, can be set up:

where: t _rk ≡ x _rk ′ or t _rk ≡ y _rk ′.

In the system of equations, both of the image coordinates x _rk , y _rk assigned to a viewing direction R are also used here, but only one of the two image coordinates which are assigned to the viewing direction R ', namely either x _rk ' or y _rk '. This is sufficient to determine the system of equations. It corresponds geometrically to the fact that a point in space is sufficiently defined by the intersection of a straight line with a plane, see FIG. 3, the straight line being given by the axially parallel projection of the one image point and the plane containing the straight line which is formed by the Axially parallel projection of the pixel assigned to the other viewing direction is given.

Fig. 2 shows in side view a schematic representation of the parallel projection of three reference points P _rk (3 k = 1, 2,) in the object space. The two viewing directions R and R 'running in the direction of the optical axes A and A' intersect at the origin 0 of the object space coordinate system. The relative orientation of the two viewing directions corresponds to the generally best case of a 90 ° swivel. Three different lens positions M _k and M _k 'are shown schematically with the respectively assigned image planes E _k and E _k ' arranged at a constant image distance. Also indicated are the three imaging beam _{paths assigned} to the reference points P _rk with the resulting pixels B _rk and B _rk '. These can each be shifted into common fictitious superposition levels S or S 'into the positions S _rk or S _rk '. The figure also makes it clear that the pixels can be back-projected from these positions by pure parallel projection, resulting in intersections _rk , which exactly represent the constellation of the reference points P _rk , taking into account the scale of the image as well as the page traffic resulting from the image.

Fig. 3 shows schematically how an object point P by the intersection of a straight line G with a plane E _t is defined, wherein the straight line G where the pa rallel extending to the optical axis A (viewing direction R) projection of the one viewing direction R associated pixel B is and the plane E _{t contains} a straight line G ', which corresponds to the axis-parallel projection (axis A', viewing direction R ') of the other viewing direction R' assigned pixel B '. The plane E _{t is} appropriately chosen so that it runs parallel to the one coordinate axis se, in this case y ', the associated image plane E', so that to define this plane E _t only one of the two image point coordinates , in this case t ≡ x ′, is required, as has already been expressed in the system of equations above.

As mentioned above, it is advantageous to look at the two directions to be arranged so that they are perpendicular to each other. Of course the general point of view is to be considered that all if possible surface points of interest also from both perspectives are visible. Therefore, the vertical constellation of the directions of view are deviated. It can also happen that none there are two directions of view, from which all interested waiters area points can be measured. Then there will be two or more groups give pen of surface points, which each have different con positions of two gaze directions with different trans formation matrices are assigned. Each of these constellations then a separate calibration operation of the type described above, from which the respective transformation matrix results.

Claims (6)

1. A method for microscopically measuring the surface structure of an object, in which

• - Surface points of interest (P _i ) of the object that are of interest in a sequence of successive recordings, each with a central perspective along two predetermined optical axes (A, A ′), are sharply depicted while keeping the image distance constant, and
• - The respective coordinates (x _i , y _i ; x _i ′, y _i ′) of the image points (B _i ) in associated image coordinate systems (x, y; x ′, y ′) are measured and from them along the lines in the sense of a parallel projection optical axes (A, A ′), including the image scale, the coordinates (u _i , v _i , w _i ) of the surface points (P _i ) are determined in an object space coordinate system (u, v, w),
• - The relationship between image and object space coordinates is given linearly by a transformation matrix (T), the elements (a _mn ) for the given optical axes (A, A ') based on three reference points (P _rk ; k = 1, 2, 3 ) with known object space coordinates (u _rk , v _rk , w _rk ) and the associated image coordinates (x _rk , y _rk ; x _rk ′, y _rk ′) can be determined.

2. The method according to claim 1, characterized in that the at the optical axes (A, A ') are perpendicular to each other. 3. The method according to claim 1 or 2, characterized in that the successive exposures by axially shifting a lens in the Object space can be obtained in steps corresponding to the depth of field. 4. The method according to any one of the preceding claims, characterized in that in the formation of the transformation matrix (T) of the one of the two optical axes (A ') associated image coordinates (x _i ', y _i ') each only one (x _i ) or the other (y _i ′) is used. 5. The method according to claim 4, characterized in that the object space coordinates (u _i , v _i , w _i ) are determined from the image coordinates (x _i , y _i ; x _i ', y _i ') according to the following equation: with t _i ≡ x _i ′ or t _i ≡ y _i ′ and the transformation matrix 6. The method according to claim 5, characterized in that the Ma trix elements a _{mn of} the transformation matrix T are determined by solving the following system of equations: with k = 1, 2, 3 and t _rk ≡ x _rk ′ or t _rk ≡ y _rk ′, where the u _rk , v _rk , w _{rk are} the object space coordinates of the three known reference points P _rk and x _rk , y _rk as well x _rk ′, y _rk ′ mean the associated image coordinates with respect to the two optical axes (A, A ′).