METHOD FOR CALIBRATING AN OPTICAL MEASUREMENT SET-UP

Abstract

A method calibrates an optical measurement set-up with a measurement volume seeded with particles and at least two cameras so that the measurement volume can be mapped from different observation angles. The method includes simultaneously mapping the measurement volume by the cameras to produce images; rectifying each camera image in relation to a common reference plane in the measurement volume by using the respective pre-calibrated mapping function; performing two-dimensional correlation for at least one pair of rectified camera images to produce correlation fields that present an elongate correlation maxima band for each correlation field; reducing the correlation maxima band to a straight line representing the band; determining the distance of this representative straight line from the coordinate origin of the correlation field as a correction value, using the determined correction values to correct the mapping functions of those cameras for which rectified camera images were included in the correlations.

Claims

1. A method for calibrating an optical measurement set-up with a measurement volume (V) seeded with particles and with at least two cameras (K1, K2, K3), by means of which the measurement volume (V) can be mapped from different observation angles, in each case with a mapping function known from a pre-calibration, said method comprising the following step: a) simultaneously mapping the measurement volume (V) by means of the cameras (K1, K2, K3) in order to produce a camera image (I.sub.1, I.sub.2, I.sub.3) for each camera (K1, K2, K3). characterized by the further steps: b) rectifying each camera image (I.sub.1, I.sub.2, I.sub.3) in relation to a common reference plane in the measurement volume (V) with use of the associated, pre-calibrated mapping function, c) performing a two-dimensional correlation for at least one pair of rectified camera images (Ir.sub.1, Ir.sub.2, Ir.sub.3) in order to produce a corresponding number of correlation fields (C.sub.12), wherein each correlation field (C.sub.12) presents an elongate correlation maxima band, d) for each correlation field (C.sub.12): d1) reducing the correlation maxima band to a straight line (g.sub.12) representative of this band, d2) determining the distance (d.sub.12) of this representative straight line (g.sub.12) from the coordinate origin of the correlation field (C.sub.12) as a correction value, e) using the determined correction values to correct the mapping functions of those cameras (K1, K2, K3) for which rectified camera images (Ir.sub.1, Ir.sub.2, Ir.sub.3) were included in the correlations in Step c.

2. The method according to claim 1, characterized in that the rectified camera images (Ir.sub.1, Ir.sub.2, Ir.sub.3) before Step c are each divided into a plurality of equally sized and equally positioned interrogation fields, Steps c and d are performed on the interrogation fields and the mapping functions in Step e are corrected in the different spatial regions of the measurement volume (V) with which the different interrogation fields are associated, using the respectively associated, different correction values.

3. The method according to any of the preceding claims, characterized in that the method is performed multiple times, at least from Steps b to e, wherein the camera images (I.sub.1, I.sub.2, I.sub.3) are rectified during each pass in Step b in relation to another common reference plane and wherein the mapping functions in Step e are each corrected using the respectively determined correction values only in the spatial region of the measurement volume (V) with which the respective reference plane is associated.

4. The method according to any of the preceding claims, characterized in that the method is performed from Steps a to c multiple times for multiple points in time, the respectively corresponding correlation fields are summed and then Steps d and e of the method are performed.

5. The method according to any of the preceding claims, wherein the optical measurement set-up has a first camera (K1), a second camera (K2) and a third camera (K3), of whose rectified camera images (Ir.sub.1, Ir.sub.2) only those from the first and second camera (K1, K2) are involved in the correlation and correction of Steps c to e, characterized by the further steps: f) rectification of the camera images (I.sub.1, I.sub.2) from the first and second camera (K1, K2) using the respectively associated mapping function corrected in Step e and of the camera image (I.sub.3) from the third camera (K3) using the associated, pre-calibrated mapping function in relation to a plurality of common parallel reference planes, g) performing, for each reference plane, a two-dimensional correlation between the product of the rectified camera images (Ir.sub.1, Ir.sub.2) from the first and from the second camera (K1, K2) with the rectified camera image (Ir.sub.3) from the third camera (K3) and summing the resulting correlation fields to produce a sum correlation field, h) determining the distance of the correlation maximum in the sum correlation field from the coordinate origin of the sum correlation field as an additional correction value, i) correcting the mapping function of the third camera (K3) using the additional correction value that was determined.

6. The method according to claim 5, characterized in that in Step i the mapping functions of the first and/or of the second camera (K1, K2) corrected in Step e are corrected once again using the additional correction value that was determined.

7. The method according to either of the claims 5 to 6, characterized in that the rectified camera images (Ir.sub.1, Ir.sub.2, Ir.sub.3) before Step g are each divided into a plurality of equally sized and equally positioned interrogation fields, Steps g and h are performed on the interrogation fields and the mapping functions in Step i are corrected in the different spatial regions of the measurement volume (V) associated with the different interrogation fields, using the respectively associated, different correction values.

8. The method according to any of the preceding claims, characterized in that at least one correlation is performed as a cross-correlation of the general form
C.sub.ij(dx,dy)=.sub.x,yIr.sub.i(X,Y)Ir.sub.j(X+dx,Y+dy)

Description

BRIEF DESCRIPTION OF DRAWINGS

[0048] FIG. 1 is a schematic representation of a typical application situation for the method according to the invention, at the same time Step a of the method.

[0049] FIG. 2 is a schematic representation of Steps b, c, d1 and d2 of the method according to the invention, which follow on Step a from FIG. 1.

DETAILED DESCRIPTION

[0050] Identical reference symbols in the figures indicate identical or equivalent elements.

[0051] In a highly schematic representation, FIG. 1 shows a typical measurement situation in which a calibration according to the invention can be applied.

[0052] In the center of the set-up there is a measurement volume V that in the typical application case of a flow measurement contains a flowing fluid that has been seeded with particles. The particles are selected such that they are optically detectable. These can be refractive or fluorescing particles. The lighting and/or detection details required in the specific case are known to one skilled in the art and can be variously applied as is suitable. For the present invention, these details play no role. Moreover, a moving flow is not required either for the calibration method according to the invention.

[0053] Each point in the measurement volume V can be identified based on the spatial coordinates X, Y, Z. This applies in particular to the positions of the particles. A reference plane that has been arbitrarily located at Z=0, for example, appears with a gray background in FIG. 1.

[0054] In the embodiment shown, the measurement volume V is observed by three cameras K1, K2, K3 from different observation angles. The choice of exactly three cameras should be understood as purely an example. The method according to the invention can be performed with any plurality of cameras.

[0055] In Step a (per the nomenclature according to the claims) of the method according to the invention, all three cameras K1, K2, K3 simultaneously take a camera image of the measurement volume. The results are the camera images I.sub.1, I.sub.2 and I.sub.3 shown schematically in FIG. 1. The camera images I.sub.1, I.sub.2 and I.sub.3 show a certain warping that results partially from purely optical characteristics but primarily from their geometric relative positioning to the measurement volume. This is shown in an exaggerated manner in FIG. 1. In the example shown, the camera K1 is positioned exactly perpendicular to the XY plane and oriented toward the center of the measurement volume V. At the same time, it is slightly rotated about its own optical axis. Therefore, the associated camera image I.sub.1 shows merely minor perspectively rotated warping. Conversely, cameras K2 and K3 that are oriented toward the XY plane at a pronounced angle produce camera images I.sub.2 and I.sub.3, which are additionally in perspective geometrically warped, accordingly.

[0056] FIG. 2 shows further steps of the method according to the invention that are computer-based and performed in fully automated fashion. This section of the method according to the invention is typically realized in software.

[0057] Camera images I.sub.1, I.sub.2 and I.sub.3 form the starting point. In Step b (per the nomenclature according to the claims) of the method according to the invention, a rectification of camera images I.sub.1, I.sub.2 and I.sub.3 takes place, which results in the rectified camera images Ir.sub.1, Ir.sub.2 and Ir.sub.3. The rectification must always take place in relation to a defined plane. It is advantageous within the framework of the method according to the invention to use the previously mentioned reference plane Z=0. As one skilled in the art will recognize, the mapping function to be calibrated is incorporated into the method according to the invention via this rectification step.

[0058] In Step c (per the nomenclature according to the claims) of the method according to the invention, a pair-based correlation of the rectified camera images Ir.sub.1, Ir.sub.2 and Ir.sub.3 is performed that results in three correlation fields, of which, for simplicity, only the correlation field C.sub.12 resulting from the correlation of the rectified camera images Ir.sub.1 and Ir.sub.2 is shown. In this regard, a light point refers to a high correlation value; a dark point refers to a correspondingly low correlation value.

[0059] Against the background of an essentially random distribution of correlation peaks across the entire correlation field area, the correlation fields show a longitudinally extended band in which the number of correlation peaks significantly rises.

[0060] Then in Step d, as a subsumption of Steps d1 and d2 (per the nomenclature according to the claims) of the method according to the invention, for each correlation peak band a representative straight line as well as its distance from the coordinate origin of the correlation field are determined. Again, for simplicity, only the correlation field C.sub.12 and the associated line g.sub.12 are shown. The determination of the representative line g.sub.12 can be done with usual image processing algorithms.

[0061] Furthermore, the distance of the representative straight line from the origin of the respective correlation field is calculated. An associated distance vector results in each case, i.e., in the case of the represented correlation field C.sub.12, the distance vector d.sub.12 with its components d.sub.12_x and d.sub.12_y (parallel to the dx and dy coordinate axes, respectively. This vector begins in the respective correlation field origin and is positioned perpendicular to the associated representative straight line.

[0062] In the last step of the method according to the invention (Step e per the nomenclature according to the claim), which is not shown in FIG. 2, the distance vectors determined in this manner are then used to correct the mapping functions M.sub.1, M.sub.2 and M.sub.3. One skilled in the art will understand that when more or fewer cameras are used, correspondingly more or fewer correlations must be performed, although the handling of the individual correlation fields proceeds identically to the above-described example and the correction of the mapping functions proceeds correspondingly.

[0063] In the case of the inline configuration of cameras explained in the general part of the description, the correction according to the invention does result in an improvement of the mapping functions, but not necessarily in their optimization. The above-explained method is therefore only applied to two of the three cameras K1 K2, K3 whose mapping functions are also corrected accordingly.

[0064] Of course, the embodiments discussed in the specific description and shown in the Figures are only illustrative exemplary embodiments of the present invention. The present disclosure gives a person skilled in the art a broad spectrum of possible variations to work with.

LIST OF REFERENCE NUMBERS

[0065] V measurement volume [0066] X, Y, Z volume coordinates in V [0067] K1, K2, K3 cameras [0068] I.sub.1, I.sub.2, I.sub.3 camera images of K1, K2 and K3 [0069] Ir.sub.1, Ir.sub.2, Ir.sub.3 rectified camera images of K1, K2 and K3 [0070] x, y area coordinates in I.sub.1, I.sub.2, I.sub.3 and Ir.sub.1, Ir.sub.2, Ir.sub.3 [0071] C.sub.12 correlation field [0072] dx, dy area coordinates in C.sub.12 [0073] g.sub.12 representative straight line [0074] d.sub.12 distance from g.sub.12 (vectorial)