DE102019132219B4 - Method for calibrating a system, system, flow cell arrangement and storage medium - Google Patents

Abstract

Method for calibrating a system (4) with a first camera (10) and a second camera (20), - wherein the system (4) the degrees of freedom first rotation of the first camera (10) about its optical axis (14), second rotation of the second camera (20) around its optical axis (24), zoom difference between first camera (10) and second camera (20), and height difference between first camera (10) and second camera (20), - with over a respective number first rotations, a number of second rotations and a number of zoom differences are iterated, - a number of corresponding reference image pairs being generated for each combination of first rotation, second rotation and zoom difference and a respective height difference being calculated therefrom, with each reference image pair having a respective first reference image and has a respective second reference image, a number of reference objects (1, 2, 3) being imaged in each case in the first reference image and the second reference image et ist. - each height difference is calculated using a respective kernel density estimator as follows: - definition of an initial kernel density function of the kernel density estimator, the definition range of which comprises the set of all possible height differences in a first coordinate and whose value range represents the frequency of the respective height difference in a second coordinate - Recognition of the reference objects (1, 2, 3), - Calculation of a respective length for each reference object (1, 2, 3), - Formation of respective reference object pairs from a first reference object (1, 2, 3) of the first reference image and one second reference object (1, 2, 3) of the second reference image of a respective reference image pair, so that each reference object (1, 2, 3) of the first reference image forms exactly one reference object pair with each reference object (1, 2, 3) of the second reference image, Update the kernel density function for each reference object pair or at least part of the ref erence object pairs with a core function from the domain of definition of the core density function, the core function depending on an offset between the first reference object (1, 2, 3) and the second reference object (1, 2, 3), - definition of the respective height difference as that value of the first Coordinate at which the kernel density function has its maximum value, determining at which combination of first rotation, second rotation and zoom difference the height difference with the greatest value of the kernel density function was determined.

Description

The invention relates to a method for calibrating a system with a first camera and a second camera, an associated system, an associated flow cell arrangement and an associated storage medium.

Flow measuring cells are used, for example, to monitor crystallization processes. In particular, they can be used to carry out a continuous measurement of a crystal size distribution. Image-based methods have proven to be advantageous in this context, as they contain information about the crystal size as well as the crystal shape and the individual crystal faces. In particular, online microscopes, which are fed with a suspension to be measured via a bypass, offer the advantage of being able to record a statistically significant amount of objects in a short time and with high image quality in terms of particle sharpness and few particle overlaps. In particular, in comparison to the observation of crystallization processes in large vessels, particles can be viewed in focus and a better image quality can be achieved. Online microscopes that have been commercially available to date use flow measuring cells for this purpose, in which the crystals flowing past are recorded from one direction via a viewing window by means of a light source and a camera.

For example, systems with a first camera and a second camera can be used to improve the observation, but these are difficult to calibrate.

The document U.S. 5,905,568 A discloses a system and method for measuring three-dimensional velocities at a plurality of points in a fluid using at least two cameras which are arranged approximately at right angles to one another.

It is therefore an object of the invention to provide a method for calibrating a system with a first camera and a second camera, which method is designed as an alternative or better than known designs. It is also an object of the invention to provide an associated system, an associated flow measuring cell arrangement and an associated storage medium.

According to the invention, this is achieved by a method, a system, a flow measuring cell arrangement and a storage medium according to the respective main claims. Advantageous refinements can be found in the respective subclaims, for example. The content of the claims is made part of the description by express reference.

The invention relates to a method for calibrating a system with a first camera and a second camera. The system has the degrees of freedom of first rotation of the first camera about its optical axis, second rotation of the second camera about its optical axis, zoom difference between first camera and second camera and height difference between first camera and second camera.

In the context of the method, iterates over a respective number of first rotations, a respective number of second rotations and a number of zoom differences.

For each combination of first rotation, second rotation and zoom difference, a number of corresponding reference image pairs is generated, and a respective height difference is calculated therefrom. Each reference image pair has a respective first reference image and a respective second reference image. A number of reference objects are depicted in each case in the respective first reference image and in the respective second reference image. One reference image pair can be used for each combination, or several reference image pairs can be used.

• - Festlegung einer anfänglichen Kerndichtefunktion des Kerndichteschätzers, deren Definitionsbereich in einer ersten Koordinate die Menge aller möglichen Höhendifferenzen umfasst, und deren Wertebereich in einer zweiten Koordinate die Häufigkeit der jeweiligen Höhendifferenz repräsentiert,
• - Erkennen der Referenzobjekte,
• - Berechnen einer jeweiligen Länge für jedes Referenzobjekt,
• - Bilden jeweiliger Referenzobjektpaare aus je einem ersten Referenzobjekt des ersten Referenzbilds und einem zweiten Referenzobjekt des zweiten Referenzbilds eines jeweiligen Referenzbildpaars, so dass jedes Referenzobjekt des ersten Referenzbilds mit jedem Referenzobjekt des zweiten Referenzbilds je genau ein Referenzobjektpaar bildet,
• - Aktualisieren der Kerndichtefunktion für jedes Referenzobjektpaar oder zumindest einen Teil der Referenzobjektpaare mit einer Kernfunktion aus dem Definitionsbereich der Kerndichtefunktion, wobei die Kernfunktion von einem Versatz zwischen dem ersten Referenzobjekt und dem zweiten Referenzobjekt abhängt,
• - Festlegen der jeweiligen Höhendifferenz als denjenigen Wert der ersten Koordinate, an welchem die Kerndichtefunktion ihren maximalen Wert hat.

Each height difference is calculated using a respective kernel density estimator as follows:

• - Establishing an initial kernel density function of the kernel density estimator, the definition range of which includes the set of all possible height differences in a first coordinate and the value range of which represents the frequency of the respective height difference in a second coordinate,
• - Recognition of the reference objects,
• - Calculating a respective length for each reference object,
• Formation of respective reference object pairs from a first reference object of the first reference image and a second reference object of the second reference image of a respective reference image pair, so that each reference object of the first reference image forms exactly one reference object pair with each reference object of the second reference image,
• - Updating the kernel density function for each reference object pair or at least some of the reference object pairs with a kernel function from the domain of definition of the kernel density function, the kernel function being dependent on an offset depends between the first reference object and the second reference object,
• - Establishing the respective height difference as that value of the first coordinate at which the kernel density function has its maximum value.

Finally, it is determined for which combination of first rotation, second rotation and zoom difference the height difference with the greatest value of the kernel density function was determined.

By means of such a method, a system comprising a first camera and a second camera can be calibrated in a particularly advantageous manner, so that the known degrees of freedom can be taken into account. In this way, it can be avoided in particular that small adjustment errors, which are often unavoidable in experimental setups, lead to errors in measurement results or evaluations. The values obtained can be used, for example, to electronically correct recorded images or to readjust the structure so that, for example, measurements can be carried out without deviations of the rotations from specified initial values and / or without height difference and / or without zoom difference.

In particular, the initial kernel density function can be set such that all values in the second coordinate are zero.

The length can in particular be understood to mean a length of the reference objects in the direction of a height offset of the cameras and / or along a vertical direction in the system and / or along an axis along which the respective camera can be vertically adjusted. This can typically easily be taken into account in the image evaluation.

It should be understood that reference object pairs are typically only formed between reference images of a respective reference image pair. If more than one reference image pair is used for a combination of first rotation, second rotation and zoom difference, all reference image pairs can be evaluated separately, with typically only one kernel density estimator with a kernel density function being used for all such reference image pairs that belong to a combination is updated across all reference image pairs.

With each calculation of a height difference, a difference between the length of the first reference object and the length of the second reference object can preferably be calculated for each reference object pair. The core function also preferably depends on the difference. As a result, the difference can be taken into account, wherein, for example, the core function can have a greater maximum value or a greater integral value, the smaller the difference. It can thus be taken into account that small differences in the lengths of the reference objects indicate that there is a high degree of probability that the same object is involved.

According to one embodiment, each reference image pair is obtained by converting a respective output reference image pair with a first output reference image and a second output reference image. A first intermediate reference image can be obtained from the first output reference image by rotating with the first rotation. A second intermediate reference image can be obtained from the second output reference image by rotating with the second rotation. The rotation can take place in the direction indicated by the respective rotation, or also in the opposite direction. The first intermediate reference image and / or the second intermediate reference image can be scaled as a function of the zoom difference. The first intermediate reference image can then be used as the first reference image and the second intermediate reference image can be used as the second reference image. As a result, the reference images can be calculated from output reference images without the need to manually set the rotation or zoom difference.

The output reference images of each output reference image pair can in particular be recorded or have been recorded at the same time, and / or they can be or have been extracted from a video stream at the same recording time. This allows the output reference images to be generated easily.

The reference objects can be recognized in particular by means of color recognition and / or by means of gray level recognition. This has proven to be advantageous for typical situations. However, other methods can also be used for this purpose, for example other methods of image recognition.

According to one embodiment, it can be provided that the kernel density function is updated only if a difference between the length of the first reference object and the length of the second reference object is less than a predefined threshold value. It can also be provided that a respective offset is only calculated if a difference between the length of the first reference object and the length of the second reference object is less than a predefined threshold value. It can thereby be taken into account that typically only in the case of differences in the lengths below the threshold value can it be assumed that, with an ideal configuration of the Camera degrees of freedom, the same object was actually viewed with sufficient probability. Conversely, it can thus be achieved that even if the same object was observed in both cameras, the kernel density function remains unaffected, since in this case the configuration of the camera degrees of freedom is insufficient. If the difference between the lengths is greater, it can be assumed that different objects were considered and therefore no further calculations are required. In particular, it is then possible to refrain from updating the kernel density function, since this would not lead to an improvement in the result when considering different physical objects.

The core function can in particular be a Gaussian function. This has proven to be advantageous for typical applications, since blurring is taken into account. However, other functions can also be used, for example a function can be used which only has a value in the value range at a discrete value of the definition range.

The core function can in particular have a maximum and / or an axis of symmetry for the offset. It can also have a maximum value or an integral value which becomes smaller as the difference between the length of the first reference object and the length of the second reference object increases. As a result, the kernel function can be ideally adapted in such a way that it updates the kernel density function in such a way that the height difference is calculated in the best possible way.

When the kernel density function is updated, the respective kernel function can be added to the previous kernel density function. This is a simple procedure that produces good results. However, other ways of updating are also possible.

The respective core function can in particular be determined by scaling an output core function with a factor that is dependent on a respective difference between the length of the first reference object and the length of the second reference object. This makes it possible to take into account that the smaller the difference, the higher the probability that it is the same physical object. Accordingly, the smaller the difference, the higher the factor.

The length and / or offset and / or difference between the length of the first reference object and the length of the second reference object can in particular be determined along the same direction. This corresponds to a suitable approach. In particular, the same direction with reference to a coordinate system can also be used for all reference images.

The first rotation, the second rotation and the zoom difference, for which the height difference is or has been determined with the largest value of the kernel density function, as well as this height difference can in particular be used as calibration values or calibration values can be generated therefrom. Calibration values can thus be provided for calibrating the system.

The first camera and the second camera can in particular record a flow measuring cell or a measuring cell, which is not a flow measuring cell, for example, or also another object from different directions. The method described has proven particularly useful for such a use with a flow measuring cell. However, objects other than a flow cell can also be recorded and the system can still be calibrated as described.

The zoom difference can in particular correspond to a difference between the respective focal lengths of the first camera and the second camera. Such focal lengths are typically used to characterize a zoom of a respective camera. The height difference can in particular correspond to a vertical distance between the optical axis of the first camera and the optical axis of the second camera. This corresponds to a typical degree of freedom which, if two cameras are set up on an optical table or another surface, without special calibration, cannot be set so precisely that it would be identically zero or at least negligible. The height difference can thus be determined in an advantageous manner by means of the method described herein in order to then compensate for it.

The first rotation can in particular be iterated between a lower limit and an upper limit at equal or variable intervals. The second rotation can in particular be iterated between a lower limit and an upper limit at equal or variable intervals. The zoom difference can also be iterated between a lower limit and an upper limit at equal or variable intervals. The respective lower limits and upper limits can be set individually. In particular, they can also be the same for the first rotation or the second rotation. Overall, a respective number of values, which are iterated with respect to the respective degree of freedom, can be specified in the manner described or also in other ways. These are then taken into account one after the other.

The kernel density estimator can in particular be a histogram. This has proven to be advantageous for typical applications. The kernel density function can in particular be specified in discrete values of the first coordinate and / or the second coordinate. This has been found to be practical for typical numerical calculations. However, it is also possible to specify functions that are represented by a formula.

The method described herein can in particular be carried out on an electronic device, for example a computer or an electronic control device.

The invention also relates to a system with a first camera and a second camera. The first camera is rotatably mounted about a first rotation. The second camera is rotatably mounted about a second rotation. The first camera and / or the second camera have a variable focal length for producing a zoom difference. The first camera and / or the second camera are attached in a height-adjustable manner in order to set a height difference between the cameras. The first camera and the second camera are directed at an optically transparent object from different directions, so that the respective recording volumes of the cameras at least partially overlap.

The system also has a control device which is configured to carry out a method according to the invention. With regard to the method, all embodiments and variants described herein can be used.

The advantages already described above can be achieved by means of the system according to the invention. In particular, the system can be calibrated in a particularly simple manner by means of the method.

The invention further relates to a flow measuring cell arrangement with a flow measuring cell and a system according to the invention. The flow measuring cell represents the object. In other words, the system can also be referred to as a flow measuring cell arrangement. With regard to the system, all of the embodiments and variants described herein can be used.

The disclosure further relates to the use of a system according to the invention or a flow measuring cell arrangement according to the invention for displaying 3D crystals or crystallization processes. It has been shown that flow measuring cells are particularly suitable for displaying such 3D crystals or crystallization processes, in particular if they can be observed by two cameras at the same time. For such a system with two cameras, the method according to the invention for calibration has again proven to be particularly suitable. With regard to the system or the flow cell arrangement, all of the designs and variants described herein can be used.

The invention further relates to a non-volatile computer-readable storage medium, on which a program code is stored, which, when executed, a processor carries out a method according to the invention. With regard to the method, all embodiments and variants described herein can be used.

The method can be used in particular in connection with a flow measuring cell described below as an independent aspect of the invention. It can also be used in particular in a system or a flow measuring cell arrangement which has the flow measuring cell described below.

According to a further, independent aspect, the invention relates to a flow measuring cell. The flow measuring cell has a housing in which at least a first viewing window, a first connection and a second connection are formed. The flow measuring cell has a channel element which has a first opening and a second opening as well as a channel for at least one fluid that is continuous between these openings. The flow measuring cell also has a holder.

The channel element is divided along the channel into a first end section, a middle section and a second end section. The middle section has a rectangular outer cross section and is designed to be optically transparent. The first end section and the second end section each have a round outer cross section.

The first opening is formed in the first end portion and connected to the first connector. The second opening is formed in the second end portion and connected to the second terminal. This can in particular be a respective fluidic connection.

The holder is connected to the housing and to the channel element in order to fasten the channel element to the housing in such a way that the housing surrounds the channel element and a first outer surface of the central section is aligned parallel to the first viewing window.

The design makes it possible to use a channel element which provides both a rectangular outer cross-section through which a visual inspection can take place in a particularly advantageous manner, as well as a transition to round end sections which are advantageously connected to hoses such as supply and discharge lines which have a round cross-section. It has been shown that a particularly well-functioning flow measuring cell can be produced in this way, which can be easily connected and offers ideal optical conditions for optical measurements or observations through viewing windows.

The channel element can in particular be spaced apart from the housing on all sides, wherein such a spacing can be predetermined in particular by the holder.

In particular, observation by means of a camera or another optical device can take place through the viewing window. Other types of measurements are also possible through the viewing window. Targeted lighting is also possible via this viewing window or via another viewing window.

The channel is preferably designed such that fluid can flow between the first opening and the second opening in such a way that it does not escape from the channel. A fluid can in particular be a liquid or a gas. In this liquid or in this gas, for example, particles such as intermediate or end products of crystallization processes can be present, which in this way can be guided through the channel and thus measured.

The holder is provided in particular to hold the channel element in the housing in a specific position.

The rectangular outer cross-section of the middle section enables a particularly good possibility for performing optical observations or measurements in the middle section. The rectangular outer cross-section prevents undesired deflection of light rays. The rectangular outer cross-section can in particular also be square.

In contrast, the round external cross-sections of the two end sections serve to ensure an advantageous connection to round lines. This enables simple use and avoids the need for additional adapters, which complicate the structure and can lead to undesirable effects or tension.

The alignment of the first outer surface of the middle section parallel to the first viewing window also ensures that a completely or largely unimpeded and unchanged beam path through the first viewing window and the outer surface into the channel and out again is possible. This also avoids unwanted distractions or other disturbances during an optical measurement or observation.

Briefly summarized, it can be said that the channel element with its different external cross-sections is ideally adapted to a measurement (in the middle) and for fluidic connections (at the ends).

According to a preferred embodiment, a second viewing window is also formed in the housing, a second outer surface of the middle section being aligned parallel to the second viewing window. This enables measurement or observation from two directions, the optical advantages already mentioned above also being fully effective with regard to the second viewing window. In particular, a largely or completely unhindered and distraction-free optical measurement or observation through the second viewing window into the channel is possible.

The first viewing window and the second viewing window can in particular be aligned at right angles to one another. In particular, this makes it possible to observe the fluid in the channel from two directions at right angles to one another. However, other designs are also possible, for example an arrangement of the viewing windows opposite to one another or at other angles to one another can be provided.

The first viewing window and the second viewing window can, in particular, be arranged so as to overlap when viewed along the channel. For example, you can expose the same section or at least overlapping sections of the duct to view as seen along the duct. This makes it possible for a single volume within the channel to be observed and / or illuminated from two different directions. However, it should be understood that other arrangements of the viewing windows are also possible. The same applies if there are more than two viewing windows.

According to a preferred embodiment, the flow measuring cell has a first line and / or a second line. The first opening is preferably connected to the first connection by means of the first line. The second opening is preferably connected to the second connection by means of the second line. Through the lines will A connection between the openings and the respective connection is established inside the housing, so that a connection of the flow measuring cell with connection lines, which can supply and discharge fluid, is possible from outside the housing. In order to change connection lines, no changes have to be made within the housing. Due to the round outer cross-sections of the end sections of the channel element, the openings can be connected to the connections through the lines in a particularly simple manner, since round lines can also be used here.

The first line can in particular be a flexible line. A flexible line can be designed, for example, as a silicone hose, made of polymer, rubber and / or Teflon. Likewise, the second line can in particular be a flexible line. By using flexible lines, any component tolerances in the production of the flow measuring cell can be compensated for easily and without disadvantages, whereby, for example, it is possible to react in a simple manner to the fact that the channel element may not be completely straight geometrically. For example, an angle of a few degrees, for example less than one degree, less than two degrees, less than five degrees or less than 10 degrees, can be present in the channel element between the first end section and the middle section and / or between the middle section and the second end section, which for example, may be inevitable due to production. In the case of a direct connection of the openings to the connections without an interposed flexible element, an exact adaptation of fixed elements would have to take place or tension would have to be accepted. By using flexible lines, on the other hand, such an adaptation to the specific channel element, which is afflicted with production-related inaccuracies, is carried out in a particularly simple manner.

The first line can in particular be fastened to the first end section and / or slipped onto the first end section. Likewise, the second line can be attached to the second end section and / or slipped onto the second end section. A secure and permanent connection is achieved by such an attachment. A pull-up is a particularly simple implementation of a connection of a line to a respective end section.

The viewing windows can in particular be designed to be planar. The outer surfaces of the middle section can in particular be designed to be planar. Such a planar design enables a particularly advantageous beam path.

The housing can in particular be designed to be fluid-tight. In particular, it can form a chamber surrounding the channel element. Such a fluid-tight design or the design of a chamber surrounding the channel element makes it possible to provide temperature control for the channel in the housing. For example, the housing can have an inlet and an outlet for the passage of temperature-regulating fluid through the chamber. As a result, temperature-regulating fluid can be introduced into the chamber and also discharged again. This fluid can, for example, be brought to a desired temperature beforehand, so that the channel can also be brought to a desired temperature.

The channel can in particular be designed in a straight line. This enables a particularly advantageous and undisturbed flow of fluid. A straight design can preferably also be used when the manufacturing tolerances already mentioned above lead to slight deviations from a strictly straight shape.

Furthermore, it should be understood that a design of the channel other than a straight design is also possible. For example, bends or other elements can be provided.

The middle section can in particular have a rectangular internal cross-section. This enables a particularly advantageous, for example distortion-free or low-distortion beam path to be made possible.

The first end section and / or the second end section can each have a round internal cross section. This enables a particularly advantageous connection to round connection elements, for example the lines already mentioned above.

A transition between round or angular inner and / or outer cross-sections can be realized by the channel element, which has proven to be a simple and reliable construction.

The channel element can in particular be designed in one piece. For example, it can be composed of elements which each form one of the sections and which can be connected to one another by a form-fitting connection, for example by fusing. For example, it can be made of glass. In particular, it can be designed to be completely optically transparent, so that a single material can be used for the channel element and the optical transparency desired in particular in the central section is provided.

Preferably, the holder on the channel element only makes contact with the middle section. This has proven to be advantageous because the channel element is thereby held in a defined manner at precisely the section in which particularly exact positioning with respect to the viewing windows is advantageous. Even if the manufacturing tolerances already described above occur in the channel element, no stresses are generated within the channel element which could occur if the channel element were also fastened outside the central section.

The holder can in particular have a first holder element and a second holder element, which are spaced apart from one another along the channel. As a result, the channel element can be held in two places, which stabilizes its position in space in a particularly advantageous manner. The holder can in particular only have the two holder elements, but can also have further holder elements or further components.

The first holding element and the second holding element can in particular each be designed in a planar manner transversely to the channel. As a result, a simple design that advantageously fixes the channel element is achieved.

The first holding element and the second holding element can in particular each be designed in the manner of a grid. This allows a light and stable design.

The first holding element and the second holding element can in particular have a respective groove. The respective groove can, in particular, receive the central section in a three-sided manner in a contacting manner. Such a design achieves two-dimensional contact with the middle section, as a result of which it can be held in position particularly precisely.

The first holding element and the second holding element can in particular have a respective bar which covers the groove, so that the middle section is received in a contacting manner on all sides. An even better fixation of the channel element can thereby be achieved. The bar can be designed to be removable from the rest of the respective holding element, which allows the channel element to be changed.

It should be understood that the holder can also be designed differently than described here, for example with more than two holder elements or with differently designed holder elements.

It should be understood that in addition to the first and second viewing windows already mentioned, further viewing windows can also be present. For example, a third viewing window can be formed opposite the first viewing window, and a fourth viewing window can be formed, for example, opposite the second viewing window. These opposing viewing windows can in particular be aligned parallel to one another. The respective outer surfaces of the middle section can also be aligned parallel to a respective viewing window. As a result, it can be achieved, for example, that a straight beam path is possible between the first and third viewing window, and that a straight beam path is also possible between the second and fourth viewing window. As a result, for example, a volume in the channel can be illuminated through the third viewing window and viewed from the first viewing window, and the volume can likewise be illuminated through the fourth viewing window and viewed from the second viewing window.

The already mentioned viewing windows can in particular be made of quartz glass. The channel element can also be formed from quartz glass.

The objects carried along in the fluid can in particular be measured using a high-speed camera or two high-speed cameras and associated light sources, for example LED light sources, at the level of the viewing windows, for example with variable resolution and / or frequency. For example, both cameras can be controlled together with their light sources in such a way that the corresponding images record the same objects at exactly the same point in time. This typically requires precise positioning of the cameras in space and axially to the viewing windows and the channel element. To ensure this, a mounting system can be used, for example, which has a planar base plate and height-adjustable guide rails on which the cameras are mounted. The flow measuring cell can also be mounted in a matching holder on the base plate, which ensures that the cameras can be adjusted to the cell. A separate calibration block, which can be placed at the position of a cell holder, can also be used to calibrate the recorded image pixels to spatial coordinates using a microscale. It should be mentioned that a high-speed camera can record, for example, more than 40 images per second or, for example, 50 images per second. However, it is not absolutely necessary to use a high-speed camera. For example, a release time or an exposure time of a camera used can be a value between 10 and 20 μs, which enables an advantageous synchronization with light sources and / or can lead to the fact that at typical movement speeds of particles, blurring is reduced to a few pixels or only one pixel at most.

For the quantitative evaluation of the image or video sets obtained by the two cameras, it is advantageous to recognize photographed crystals and to identify the detected images of the individual crystals in relation to the image data of the two cameras.

A camera system with two cameras aligned at right angles makes it possible in particular to observe crystals from two perspectives oriented at right angles to one another, which in turn makes it possible to reliably reconstruct a three-dimensional crystal shape from the image data obtained. This can be used, for example, in software to automatically determine the three-dimensional geometric shapes of the crystals. This makes it possible, for example, to describe the crystal population through a multivariate crystal shape and size distribution, with which the properties and dynamics of the crystallization process can be quantified and predicted much more precisely.

• Christian Borchert, Erik Temmel, Holger Eisenschmidt, Heike Lorenz, Andreas Seidel-Morgenstern, Kai Sundmacher, „Image-Based in Situ Identification of Face Specific Crystal Growth Rates from Crystal Populations“, Crystal Growth & Design 14(3):952-971, 2014 .

To evaluate the images obtained with regard to a crystal size distribution or the shape of the crystals flowing through, it is possible to fall back on mechanisms which are already known. In this regard, reference is made in particular to the following publication:

• Christian Borchert, Erik Temmel, Holger Eisenschmidt, Heike Lorenz, Andreas Seidel-Morgenstern, Kai Sundmacher, "Image-Based in Situ Identification of Face Specific Crystal Growth Rates from Crystal Populations", Crystal Growth & Design 14 (3): 952-971 , 2014 .

• Christian Borchert, Erik Temmel, Holger Eisenschmidt, Heike Lorenz, Andreas Seidel-Morgenstern, Kai Sundmacher, „Experimental Investigation of Crystal Size and Shape Dynamics“, 4th European Conference on Crystal Growth, 19.06.2012 .

In addition, a suitable procedure was published for the following lecture:

• Christian Borchert, Erik Temmel, Holger Eisenschmidt, Heike Lorenz, Andreas Seidel-Morgenstern, Kai Sundmacher, "Experimental Investigation of Crystal Size and Shape Dynamics", 4th European Conference on Crystal Growth, June 19, 2012 .

• 1: ein System,
• 2: einen Teil einer Durchflussmesszelle,
• 3: einen Teil einer Durchflussmesszelle in einer Schnittansicht,
• 4: eine Durchflussmesszelle,
• 5: eine Durchflussmesszelle in einer anderen Ansicht,
• 6: ein Ablaufdiagramm,
• 7 bis 16: eine Vorgehensweise bei einer Bestimmung einer Höhendifferenz,
• 17: einen Verlauf eines Gewichtungsfaktors,
• 18: einen Kerndichteschätzer,
• 19: einen weiteren Kerndichteschätzer, und
• 20: ein weiteres Ablaufdiagramm.

The person skilled in the art will learn further features and advantages from the exemplary embodiments described below with reference to the accompanying drawings. Show:

• 1 : a system,
• 2 : part of a flow cell,
• 3 : a part of a flow cell in a sectional view,
• 4th : a flow cell,
• 5 : a flow cell in a different view,
• 6th : a flow chart,
• 7th until 16 : a procedure for determining a height difference,
• 17th : a course of a weighting factor,
• 18th : a kernel density estimator,
• 19th : another kernel density estimator, and
• 20th : another flow chart.

1 shows a system 4th , which can be used, for example, to monitor crystallization processes. The individual components are described in more detail below. The system 4th can also be referred to as a flow cell arrangement.

The system 4th has an optical table 5 on which other components described below are mounted. It should be mentioned that it is at the table 5 is a typical design for such an optical system, but other types of tables or other surfaces can also be used.

The system 4th has a first camera 10 and a second camera 20th on. The first camera 10 is via a first fastener 12th on the table 5 assembled. About the first fastener 12th is the first camera 10 height adjustable. The second camera 20th is via a second fastener 22nd on the table 5 assembled. Via the second fastening element 22nd is the second camera 20th also height adjustable.

The first camera 10 has a first optical axis 14th on. This also defines a longitudinal direction of the first camera 10 . The second camera points accordingly 20th a second optical axis 24 on. This also defines a longitudinal direction of the second camera 20th . The first camera 10 is around the first optical axis 14th rotatable, which is called the first rotation. The second camera 20th is about the second optical axis 24 rotatable, which is called the second rotation.

The first camera 10 and the second camera 20th each have a zoom setting, by means of which a focal length of the respective camera 10 , 20th can be changed. Thus, there can be a zoom difference between the first camera 10 and the second camera 20th as the degree of freedom of the system 4th can be set.

The system 4th further comprises a first light source 30th and a second light source 40 on. These are also at the table 5 assembled.

The system 4th also has a flow cell 100 on. The flow cell 100 is also on the table 5 mounted and is explained below with reference to the 2 until 5 are described in more detail.

Through the flow cell 100 In particular, a fluid can be conducted, which by means of the two cameras 10 , 20th should be observed. There are viewing windows in the flow cell for this purpose 100 provided below with reference to the 2 until 5 are described in more detail. The cameras 10 , 20th are like in 1 to see arranged so that their optical axes 14th , 24 stand at right angles to each other. Both cameras 10 , 20th consider part of the flow through the flow cell 100 flowing fluids thus from two mutually perpendicular directions.

The first light source 30th is related to the flow cell 100 opposite to the first camera 10 arranged. So is the second light source 40 regarding the flow cell 100 opposite to the second camera 20th arranged. Thus, the cameras can 30th , 40 respective parts of the through the flow cell 100 flowing fluids illuminate which of the opposite camera 10 , 20th to be observed. In particular, the cameras 10 , 20th observe the same volume of fluid.

The system 4th also has an electronic control device shown only schematically 6th which is configured to carry out a method as described below, for example.

2 shows part of the flow cell 100 in a perspective view. This includes all components of the flow cell 100 with the exception of a lid, which is only in the 4th is shown.

The flow cell 100 has a housing 105 on. In the case 105 are a first connection 110 and a second port 120 arranged. The first connection 110 and the second port 120 are arranged opposite one another along a longitudinal direction as shown. The connections 110 , 120 serve for the inlet or outlet of fluid.

In the case 105 is a channel element 200 arranged. The channel element 200 is formed in one piece from a transparent material, in the present case glass. The channel element 200 divides into a first end section 210 , a second end portion 220 and a middle section therebetween 230 . In the channel element 200 is a channel 205 arranged, which as an elongated cavity between a first opening 215 and a second opening 225 is trained. The channel 205 goes through the channel element 200 completely along its longitudinal direction and thus offers a possibility of a fluid through the channel 205 pass through. The first opening 215 is in the first end section 210 formed and the second opening 225 is in the second end section 225 educated.

As shown, the first end portion 210 and the second end portion 220 a respective round outer cross-section. Their inner cross-sections are also round. The middle section 230 in contrast, has a rectangular outer cross-section, with an inner cross-section of the middle section as well 230 is rectangular. The cross-sections of the middle section are shown here 230 not just rectangular, but square, which corresponds to a preferred embodiment. In other words, the middle section has 230 of the channel element 200 in the present case, a square inner cross-section and a square outer cross-section.

Due to the rectangular design of the outer cross-section of the middle section 230 this has a total of four outer surfaces which are aligned at right angles to one another. Reference is made to the external surfaces 3 will be discussed in more detail.

The channel element 200 is by means of a bracket 300 on the housing 105 attached. The bracket 300 is divided into a first mounting element 310 and a second support member 320 which along the canal 205 are spaced from each other. Both the first support element 310 as well as the second mounting element 320 only contact the middle section 230 of the channel element 200 .

Both the first support element 310 as well as the second mounting element 320 are latticed as shown.

The first support element 310 has a first groove 312 on showing the middle section 230 of the channel element 200 receives three-sided contact. The first support element 310 also has a first bar 314 on which the first groove 312 covers so that the middle section 230 with its rectangular outer cross-section on all sides is recorded contacting. A game between the middle section 230 and the first support element 310 is therefore not provided.

The second support element 320 has a second groove 322 on showing the middle section 230 of the channel element 200 receives three-sided contact. The second support element 320 also has a second bar 324 on which the second groove 322 covers so that the middle section 230 is received with its rectangular outer cross-section contacting on all sides. A game between the middle section 230 and the second support member 320 is therefore not provided.

The bars 314 , 324 are in the present case removably attached, which means replacing the channel element 200 enables.

Through the formation of the first mounting element 310 and the second support member 320 the bracket 300 is achieved that the channel element 200 only at its middle section 230 held and there with respect to its spatial orientation relative to the housing 105 is fixed. This allows a very precise alignment of the middle section 230 to in 2 viewing windows that cannot be seen, which are in the housing 105 and a cover to be described and which will be discussed in more detail below. This allows for the middle section 230 of the channel element 200 particularly good optical properties can also be achieved in connection with the viewing windows.

The first end section 210 and the second end portion 220 can, due to production, have small angles of their respective longitudinal directions relative to a longitudinal direction of the central section 230 on the middle section 230 be arranged. The channel 205 is not exactly straight in this case, but points at the transitions between the first end section 210 and the middle section 230 and / or between the middle section 230 and the second end portion 220 slight bends of, for example, a few degrees each.

In order to accommodate such production-related variations, the first end section is 210 with the first connection 110 via a first flexible line 115 connected, and accordingly is the second end portion 220 with the second connection 120 via a second flexible line 125 tied together. The flexible lines 115 , 125 are in each case over the respective end section 210 , 220 slipped over.

As already mentioned, the described embodiment determines the position of the channel element 200 in the housing 105 set in a particularly advantageous manner so that the optical properties in the middle section 230 are ideal, and at the same time the channel element ensures 200 that there is a transition to round connections. A conversion of a round inner or outer cross-section, which is typically at the connections 110 , 120 is used for connection to external connection lines, in a rectangular inner or outer cross-section is thus outside of the duct element 200 not necessary anymore. Through the flexible lines 115 , 125 can at the same time the production-related variations already mentioned, which may lead to a possibly not completely straight course of the canal 205 can lead to be taken into account without tensioning the channel element 200 There would be a risk of a particularly exact positioning of the connections 110 , 120 would be required. The combination described has proven to be particularly advantageous because it can be implemented very easily with the best possible optical properties.

Surrounding around the channel element 200 is in the flow cell 100 a chamber 130 formed into which temperature-regulating fluid can be introduced. This allows an immediate temperature control of the channel element 200 and with it one through the canal 205 fluids flowing through.

Overall, therefore, through the channel 205 a fluid can be passed, which for example through the first connection 110 initiated and through the second port 120 can be diverted again, or vice versa. By means of the already referring to 1 described cameras 10 , 20th and the light sources 30th , 40 It is thus possible to observe crystallization processes, or other evaluations are also possible, which are carried out by means of the system shown 4th can be carried out.

3 shows part of the flow cell 100 in a sectional view. The first holding element is in particular here 310 the bracket 300 can be seen particularly well, whereby it can also be clearly seen that the middle section 230 with its present square outer cross-section without play in the first groove 312 of the first support element 310 is taken up and also free of play from the first bar 314 of the support element 310 is contacted from above. Thus is the channel element 200 in the first support element 310 kept free of play. This allows a particularly exact positioning. It should be mentioned that the second mounting element 320 which is in 3 is not shown, is constructed accordingly and acts.

Furthermore, in 3 also see three viewing windows, namely a second viewing window 142 , a third viewing window 143 and a fourth viewing window 144 . These are in the housing 105 and each have a planar shape. In the flow cell 100 is also a first viewing window 141 trained, which, however, in 3 is not visible and only in the 4th and 5 is shown.

As in 3 can also be seen, the middle section 230 of the channel element 200 a first outer surface 231 , a second outer surface 232 , a third outer surface 233 and a fourth outer surface 234 on. These are each flat, as the middle section 230 of the channel element 200 as already mentioned has a rectangular outer cross-section. The first outside surface 231 is parallel to the first viewing window in the assembled state 141 aligned. The second outer surface 232 is parallel to the second viewing window 142 aligned. The third outer surface 233 is parallel to the third viewing window 143 aligned. The fourth outer surface 234 is parallel to the fourth viewing window 144 aligned. The parallel alignment of the outer surface and the respective viewing window creates a particularly advantageous, undisturbed beam path through the viewing window 141 , 142 , 143 , 144 and the middle section 230 of the channel element 200 achieved. Deflections of light rays are not to be feared due to the parallel alignments. It has been shown that it is precisely this parallel alignment due to the shown design of the holder 300 can be implemented in a particularly advantageous manner.

4th shows the complete flow cell 100 in a perspective view. It can be seen that the housing 105 with a lid 106 is locked. Thus is the chamber 130 fluid-tight. The lid 106 can be used as part of the housing 105 be understood.

In the lid 106 is the already mentioned first viewing window 141 educated. In the arrangement shown in 1 is shown is the first viewing window 141 the first camera 10 facing, and the second viewing window 142 is the second camera 20th facing.

In the lid 106 are also an influx 132 and a sequence 134 educated. In this way, as already mentioned, temperature-regulating fluid can enter the chamber 130 initiated and also diverted again. This enables reliable temperature control of the channel element 200 and thus also through the canal 205 flowing fluids.

The lid 106 can be removed in the present case for maintenance work inside the flow cell 100 to be able to make.

5 shows the flow cell 100 from 4th in another view. Only the perspective has changed, so that the third viewing window 143 is visible.

6th shows schematically a calibration sequence. Before describing the figure in more detail, however, general aspects relating to the calibration of the system should be considered 4th explained.

It is particularly desirable for the in 1 illustrated system 4th , with both cameras 10 , 20th an identical volume of the canal 205 to be photographed simultaneously and automatically. The simultaneous and preferably also automated triggering of both cameras can be used here 10 , 20th can be ensured via the hardware used. It is advantageous if both cameras 10 , 20th mechanically precisely aligned with one another to ensure that the duct is the same volume 205 is photographed. As already mentioned above, the two cameras 10 , 20th differ in their zoom and the rotation of the image plane and also in terms of their height. For example, if the zoom of the second camera 20th relative to the zoom of the first camera 10 determined, a total of four degrees of freedom result, the values of which are to be determined experimentally. As soon as these values are known, for example either the images can be converted so that they actually have the same volume of the duct 205 picture, or the cameras 10 , 20th can be readjusted manually so that they observe the same volume. The latter variant saves a computational effort to convert the images.

In order to determine appropriate parameters, videos can, for example, first be recorded, including test particles through the channel 205 be directed. For example, an equidistant grid can be generated in which values for the parameters of the relative zoom (in this case second camera 20th relative to the first camera 10 ) and scanned for both rotations. The grid points can, for example, be traversed systematically in three nested for loops. With each run, i.e. for each constellation of three varied parameters, the individual images can be converted according to the current camera configuration. In detail, the images can, for example, be rotated against the currently examined angle of rotation and the images from the second camera 20th can be compressed or stretched according to the currently examined zoom value. Furthermore, an estimated value for the height difference of the cameras can be calculated in order to determine the optimal camera configuration, for example via the best estimated value of the height difference.

In an ideal configuration, the two have cameras 10 , 20th the same zoom and no height difference to one another, and the angle of rotation of the image planes is zero. In this case, the objects that can be seen in the respective image sets have identical maximum and minimum coordinates in the vertical direction, which is also referred to below as the z-direction. In the event that the cameras have a height offset, but an identical zoom and rotation angle of 0 °, the maximum and minimum coordinates of identical objects have a constant offset, which corresponds to the height difference of the cameras. In this case, identical particles can be identified on the basis of their identical length in the z-direction, i.e. the height direction.

The properties of the second case are used to determine a height difference. It is possible to search for objects that have an identical or at least very similar length in the z-direction in both images. If this is the case, the height offset of the object is stored in a histogram in both images. The more pairs of objects have an identical height offset, the more likely it is that this height offset is the true offset, i.e. the height difference of the cameras 10 , 20th acts.

The generation of a histogram, which can also be referred to as a kernel density estimator, is described below with reference to the 7th until 16 are described in more detail. In the configuration shown with three objects, an exemplary procedure is illustrated, with an identical zoom, camera rotations of 0 ° and a height difference of 100 Pixels is assumed. Every possible object combination, i.e. three by three combinations, is checked here. In the case in which both checked objects have an identical or similar length in the z-direction, a weighted Gaussian distribution is added to the existing histogram. In the present case, this distribution has a fixed standard deviation of ten pixels and a mean value which corresponds to that of the height offset of the pair of objects. It should be understood that other values are also possible here.

The illustrated procedure can be repeated for each combination of objects, and the histogram can be expanded successively. When all object combinations have been processed, the maximum of the histogram is searched for. The position of the maximum then gives the estimated value for the height difference to which of the currently examined parameter combinations (relative zoom, both camera rotations) is assigned. The larger the maximum value, the more object pairs with identical length in the z-direction and identical height offset were identified, and the better the estimated value of the height difference.

In the context of three for loops for varying the zoom and the camera rotations, the combination of parameters can be searched for which has the greatest maximum value in the respective histograms. This combination of parameters, together with the value of the height difference belonging to the maximum, then results in the estimated values for the camera parameters.

A determination of maximum and minimum z-coordinates of the individual objects, which form the basis for the entire calibration procedure, can be subject to inaccuracies. Such inaccuracies can originate, for example, from image recording and image processing and typically range from a few pixels. The presence of such inaccuracies can influence the creation of the histogram in two main ways. On the one hand, a height offset between the objects in both images can only be determined up to a certain degree of accuracy. In addition, the values determined for the length of the objects in the z-direction are also subject to errors.

An iterative update of the histogram in the sense of H (dz) = H (dz) +1 is, if there are measurement inaccuracies, only conditionally effective in numerous situations, since it is not possible to completely differentiate between height differences that are close together. For example, a height difference of 100 Pixels cannot be significantly differentiated from a height difference of 104 pixels on the basis of an object pair. For this reason, instead of a point estimator, a Gaussian distribution can advantageously be added to the existing histogram in order to take possible measurement errors into account in the evaluation.

As part of the histogram update, a distinction can also be made between object pairs whose length difference is too great, which is an indication that they are not identical objects, or are sufficiently small, which is an indication that they are the same Object acts. Typically, this distinction cannot be made completely absolutely if there are measurement errors. For this reason, a weighting factor can advantageously be introduced which preferably weights small differences in length, but also allows larger differences in length, but with a lower weighting factor. A possible course of a weighting factor is exemplified in 17th shown. Furthermore, in 18th a an exemplary histogram is shown, which was obtained with an optimal combination of camera parameters, and in 19th an exemplary histogram is shown which was obtained with an incorrect combination of camera parameters. It should be mentioned again that the term kernel density estimator can also be used instead of the term histogram.

The following is the procedure corresponding to a possible process sequence with reference to 6th described. It should be understood that this is only an exemplary implementation and that other implementations are accordingly also possible.

In step 10 the process is started first. In step 12th the test videos already mentioned above are loaded. Reference image pairs are also generated, each reference image pair having a first reference image and a second reference image. There are respective reference objects in each reference image. The first reference images come from the first camera 10 , the second reference images come from the second camera 20th . In step 14th grids are specified for camera rotations and camera zooms.

In diamond 20th first begins an iteration over each camera rotation to be used. In step 22nd all reference images of the first camera are thereby 10 as well as the second camera 20th rotates according to the current rotation. In step 24 become respective frames for all reference objects in all reference images of the second camera 20th calculated. In step 26th these frames are saved.

In diamond 30th an iteration begins over each zoom difference, which is present in the form of a variable zoom of the first camera 10 is realized. In step 32 becomes the resolution or scaling of the images of the first camera rotated with the current camera rotation 10 adjusted according to the current zoom difference. In step 34 become frames of all objects in the rotated and scaled reference images of the first camera 10 calculated. In step 36 these frames are saved.

In diamond 38 the iteration over the camera zoom ends, and in diamond 28 the iteration over the camera rotation ends.

In diamond 40 begins an iteration over the second rotation of the second camera 20th and in diamond 50 begins an iteration over the first rotation of the first camera 10 . In diamond 60 Furthermore, an iteration over reference image pairs begins.

In step 62 become maximum and minimum z-coordinates of all objects in the rotated second reference images of the second camera 20th certainly. In step 64 a kernel density estimator is defined as an empty kernel density estimator which is subsequently used.

In diamond 70 starts an iteration over all camera zooms. In step 72 become all minimum and maximum z-coordinates of all objects in the currently rotated and zoomed reference image of the first camera 10 certainly.

In diamond 80 an iteration begins over each reference object in the second reference image of the second camera 20th . In step 82 the differences from the minimum and maximum z coordinates of the current reference object in the current reference image of the second camera 20th with all minimum and maximum z-coordinates in the current reference image of the first camera 10 calculated. In diamond 90 an iteration begins again over all reference objects in the current reference image of the first camera 10 .

In step 92 are deviations from differences in the minimum and maximum z coordinates between current reference objects in the reference images of the first camera 10 and the second camera 20th calculated. In step 94 a scaling factor is assigned for the object configuration currently under consideration. In step 96 a Gaussian distribution is defined which has the mean z-deviation as the mean value. In step 97 the Gaussian distribution is multiplied by the scaling factor and is then added to the kernel density function.

In diamond 98 the iteration over the reference objects ends in the first reference image of the first camera 10 . In diamond 88 the iteration over reference objects ends in the second reference image of the second camera 20th . In diamond 78 the iteration over camera zooms ends.

In step 100 the maximum value of the kernel density function is determined. In the diamond displayed below, it is first determined whether this value F is greater than the previously largest measured value Fmax. If this is not the case ("0"), there is a diamond 125 the iteration over the reference object pairs is ended. In diamond 130 becomes the iteration over the first rotation of the first camera 10 finished and in step 140 becomes the iteration over the second rotation of the second camera 20th completed. In step 150 the determined best camera configuration is saved and in step 160 the process is ended.

Is after step at the above decision diamond 100 However, if the maximum value is greater than the largest value measured so far ("1"), the largest measured maximum value Fmax is set as the maximum value just measured, in step 110 the current camera orientations or camera rotations are saved and in step 120 become the best camera zoom and the optimal difference in z-coordinates between the two cameras 10 , 20th identified. Then the process continues as just described with a diamond 125 away.

In the 7th until 16 is described in more detail below, using two reference images of a reference image pair, that is, a first reference image shown in the respective figure a) and a second reference image shown in the respective figure b), based on three reference objects contained therein 1 , 2 , 3 a kernel density estimator can be updated several times in order to determine an altitude difference. The reference objects 1 , 2 , 3 are also referred to below as objects for the sake of simplicity. In 7a) and 7b) the reference objects are shown with respective frames drawn in dashed lines, which can be used to determine the respective extent of the respective object in the z-direction also drawn. In the present case, this is a simulated image set with three objects each, the data set in the present case with an identical camera zoom, rotations of the two cameras 10 , 20th of 0 ° each and with a height offset of 100 Pixels is simulated.

Both 8th until 16 is still in the respective c ) specifies the generated kernel density estimator, which can also be referred to as a histogram, for example.

at 8th becomes the object 1 of the first reference image with the object 1 of the second reference image compared. The former has a length of 226 Pixels, the latter has a length of 277 Pixels. Both objects therefore have a significantly different length, which is why they cannot be the same object if the camera configuration is correct. Thus, the kernel density estimator is not updated.

at 9 becomes object 1 of the first reference image with the object 2 of the second reference image compared. Both objects have a length of each 226 Pixels up. This is identical, so it is very likely that it is the same object. The offset, which is also drawn in, which is denoted by v in this and the following figures, is +100 pixels. Accordingly, the kernel density estimator is updated with a Gaussian function, which has a maximum at 100 Has pixels.

at 10 becomes the object 1 of the first reference image with the object 3 of the second reference image compared. The former has a length of 226 Pixels, the latter has a length of 230 Pixels up. They are therefore of a similar length and have an offset of +498 pixels. The four-pixel difference in length could also be due to inaccurate image processing. The kernel density estimator is thus updated with a weighted Gaussian distribution, the maximum of which is at 498 Pixels and which is weighted with a factor of 0.841 in order to take into account the poorer fit of the lengths.

at 11 becomes object 2 of the first reference image with the object 1 of the second reference image compared. The former has a length of 230 Pixels, the latter has a length of 277 Pixels up. Both objects therefore have a significantly different length, which is why they cannot be the same object if the camera configuration is correct. The kernel density estimator is therefore not updated.

at 12th becomes object 2 of the first reference image with the object 2 of the second reference image compared. Both objects are of similar length with an offset of -298 pixels. The four-pixel length difference could also have been due to inaccurate image processing. The kernel density estimator is thus updated with a weighted Gaussian distribution, the maximum of which is -298 pixels, and which was multiplied by a weighting factor of 0.841 in order to take account of the poorer fit of the lengths.

at 13th becomes object 2 of the first reference image with the object 3 of the second reference image compared. Both objects have an identical length of 230 Pixels up. The offset is +100 pixels. The kernel density estimator is thus updated with a Gaussian function, the maximum of which is +100 pixels and which has not been multiplied by a weighting factor.

at 14th becomes object 3 of the first reference image with the object 1 of the second reference image compared. Both objects have an identical length of 277 Pixels, where the offset is +100 pixels. The kernel density estimator is thus updated with a Gaussian function, which is not scaled and has a maximum of +100 pixels.

at 15th becomes object 3 of the first reference image with the object 2 of the second reference image compared. The former has a length of 277 Pixels, the latter has a length of 226 Pixels up. Both objects therefore have a significantly different length, which is why they cannot be the same object if the camera configuration is correct. The kernel density estimator is therefore not updated.

at 16 becomes object 3 of the first reference image with the object 3 of the second reference image compared. The former has a length of 277 Pixels, the latter has a length of 230 Pixels up. Both objects therefore have a significantly different length, which is why they cannot be the same object if the camera configuration is correct. The kernel density estimator is therefore not updated.

How out 16c ) clearly shows, the largest value in the kernel density estimator is +100 pixels. For the camera configuration mentioned at the beginning of a zoom difference of 0 and respective rotations of 0 °, a height difference of +100 pixels was thus correctly determined, as also from 16c ) can be seen with a maximum value of the kernel density function of 0.12.

A sensible procedure for determining the actual height difference, rotations and zoom difference between the two cameras 10 , 20th of the system 4th which is in 1 is shown, can in particular take the form that iterated over respective predetermined values of the first rotation, second rotation and zoom difference and in each case as with reference to the 7th until 16 described an associated altitude difference is determined. One reference image pair can be used in each case, or several reference image pairs can also be used in each case. That height difference which was determined with the greatest value of the kernel density estimator is then assumed to be the actually existing height difference, and the associated values of the first rotation, second rotation and zoom difference are also used as the respective actual values of the system 4th accepted. This has proven to be a sensible and reliable approach for typical configurations. For example, a manual adjustment to correct rotations, zoom difference and height difference can then take place, so that both cameras 10 , 20th actually see the same volume, or it can be measured with the determined values without changing the physical structure and the determined values can be used as a calibration, which is taken into account in a subsequent computational evaluation. For example, images can be rotated according to the determined rotations and scaled according to the determined zoom difference. The height difference can also be taken into account by shifting the respective image in the z-direction.

The procedure described in 20th shown schematically, which will be described in more detail below.

17th shows, as already mentioned above, a function of a weighting factor p as a function of a length difference Δz of the two objects. This was, for example, in the case of the 7th until 16 described procedure is used. It can be seen that the weighting factor is higher, the smaller the length difference Δz of the objects. The greater the difference in length, the smaller the weighting factor and the less the correspondingly generated Gaussian function will contribute to the overall result.

18th shows an example of a kernel density estimator with a combination of values, i.e. rotations and zoom differences, which lead to a clearly recognizable height difference. In view of the clear maximum, it can be assumed that the values used are good or even ideal. 19th in contrast, shows an example of a kernel density estimator for poorly fitting values, with no pronounced maximum being discernible. The values should therefore not be used.

20th shows a typical procedure for calibration according to a compared to FIG 6th modified embodiment.

In diamond 10 starts an iteration over specified values of the first rotation. In diamond 20th starts an iteration over specified values of the second rotation. In diamond 30th starts an iteration over specified values of the zoom difference. The iterations can each run, for example, from a predetermined minimum value to a predetermined maximum value, specifically with a predetermined distance between respectively adjacent values. However, other designs are also possible here.

In step 40 a number of one or more reference image pairs is generated for each current combination of first rotation, second rotation and zoom difference, each reference image pair having a respective first reference image and a respective second reference image. For all reference image pairs, step 42 a procedure similar to that described with reference to the 7th until 16 has been explained. It should be mentioned here that the kernel density estimator can in principle be updated over several reference image pairs, and that the procedure described can be adapted for any number of respective objects.

In step 44 the maximum of the kernel density estimator is then determined, and the associated value on the horizontal axis is determined as the height difference which belongs to the combination of first rotation, second rotation and zoom difference.

In the diamonds 38 , 28 and 18th the respective iterations end. When all iterations have been carried out, step 50 determines which of the height differences was determined with the greatest absolute value of the kernel density estimator. The associated combination of first rotation, second rotation, zoom difference and height difference thus forms a calibration of the system. This procedure has proven to be very reliable for typical configurations, ie it determines the correct values for first rotation, second rotation, zoom difference and height difference in almost all conceivable constellations.

It should be understood that the procedure shown here can also be modified, and that in particular variations in the actual implementation of the method management are possible, which do not lead out of the scope of protection of the claims. This is especially true if the same effect or the same result is achieved.

Mentioned steps of the method according to the invention can be carried out in the order given. However, they can also be carried out in a different order if this is technically sensible. The method according to the invention can be carried out in one of its embodiments, for example with a specific combination of steps, in such a way that no further steps are carried out. In principle, however, further steps can also be carried out, including those which are not mentioned.

It should be pointed out that features can be described in combination in the claims and in the description, for example to facilitate understanding, although these can also be used separately from one another. The person skilled in the art recognizes that such features can also be combined with other features or combinations of features independently of one another.

References back in subclaims can identify preferred combinations of the respective features, but do not exclude other combinations of features.

Claims (19)

Method for calibrating a system (4) with a first camera (10) and a second camera (20), - wherein the system (4) the degrees of freedom first rotation of the first camera (10) around its optical axis (14), second rotation of the second camera (20) around its optical axis (24), zoom difference between the first camera (10) and the second Camera (20) and height difference between first camera (10) and second camera (20), - with iterating over a respective number of first rotations, a number of second rotations and a number of zoom differences, - For each combination of first rotation, second rotation and zoom difference, a number of corresponding reference image pairs is generated and a respective height difference is calculated therefrom, each reference image pair having a respective first reference image and a respective second reference image, with the first reference image and the second Reference image each a number of reference objects (1, 2, 3) is mapped. - where each height difference is calculated using a respective kernel density estimator as follows: - Establishing an initial kernel density function of the kernel density estimator, the definition range of which includes the set of all possible height differences in a first coordinate and the value range of which represents the frequency of the respective height difference in a second coordinate, - Recognition of the reference objects (1, 2, 3), - Calculating a respective length for each reference object (1, 2, 3), - Formation of respective reference object pairs from a first reference object (1, 2, 3) of the first reference image and a second reference object (1, 2, 3) of the second reference image of a respective reference image pair, so that each reference object (1, 2, 3) of the first Reference image forms exactly one reference object pair with each reference object (1, 2, 3) of the second reference image, - Updating the kernel density function for each reference object pair or at least some of the reference object pairs with a kernel function from the definition range of the kernel density function, the kernel function being dependent on an offset between the first reference object (1, 2, 3) and the second reference object (1, 2, 3) depends, - Defining the respective height difference as that value of the first coordinate at which the kernel density function has its maximum value, Determination of the combination of first rotation, second rotation and zoom difference for which the height difference with the greatest value of the kernel density function was determined. Procedure according to Claim 1 - Whenever a height difference is calculated, a difference between the length of the first reference object (1, 2, 3) and the length of the second reference object (1, 2, 3) is calculated for each reference object pair, - the core function also being based on the difference depends. Method according to one of the preceding claims, - wherein each reference image pair is included by converting a respective output reference image pair a first output reference image and a second output reference image is obtained, - a first intermediate reference image is obtained from the first output reference image by rotating with the first rotation, - a second intermediate reference image is obtained from the second output reference image by rotating with the second rotation, - the first The intermediate reference image and / or the second intermediate reference image is scaled as a function of the zoom difference, and then the first intermediate reference image is used as the first reference image and the second intermediate reference image is used as the second reference image. Procedure according to Claim 3 The output reference images of each output reference image pair are recorded simultaneously and / or extracted from a video stream at the same recording time. Method according to one of the preceding claims, - the reference objects (1, 2, 3) being recognized by means of color recognition and / or gray level recognition. Method according to one of the preceding claims, - the updating of the core density function and / or a calculation of a respective offset only takes place if a difference between the length of the first reference object (1, 2, 3) and the length of the second reference object (1, 2, 3) is less than a predetermined threshold. Method according to one of the preceding claims, - where the core function is a Gaussian function. Method according to one of the preceding claims, - wherein the core function has a maximum and / or an axis of symmetry at the offset, and / or - wherein the core function has a maximum value or an integral value which becomes smaller as the difference between the length of the first reference object (1, 2, 3) and the length of the second reference object (1, 2, 3) increases. Method according to one of the preceding claims, - wherein when the kernel density function is updated, the respective kernel function is added to the previous kernel density function. Method according to one of the preceding claims, - The respective core function is determined by scaling an output core function with a factor dependent on a respective difference between the length of the first reference object (1, 2, 3) and the length of the second reference object (1, 2, 3). Method according to one of the preceding claims, - the length and / or offset and / or difference between the length of the first reference object (1, 2, 3) and the length of the second reference object (1, 2, 3) being determined along the same direction. Method according to one of the preceding claims, the first rotation, the second rotation and the zoom difference, for which the height difference is determined with the largest value of the kernel density function, and this height difference are used as calibration values or calibration values are generated therefrom. Method according to one of the preceding claims, - wherein the first camera (10) and the second camera (20) record a flow measuring cell (100) or a measuring cell from different directions. Method according to one of the preceding claims, - wherein the zoom difference corresponds to a difference between the respective focal lengths of the first camera (10) and the second camera (20), and / or - wherein the height difference corresponds to a vertical distance between the optical axis (14) of the first camera (10) and the optical axis (24) of the second camera (20). Method according to one of the preceding claims, the first rotation being iterated between a lower limit and an upper limit at equal or variable intervals, and / or the second rotation being iterated between a lower limit and an upper limit at equal or variable intervals, and / or the zoom difference between a lower limit and an upper limit being iterated at equal or variable intervals. Method according to one of the preceding claims, - wherein the kernel density estimator is a histogram, and / or - the kernel density function being specified in discrete values of the first coordinate and / or the second coordinate. System (4) with a first camera (10) and a second camera (20) - wherein the first camera (10) is rotatably mounted about a first rotation, - wherein the second camera (20) is rotatably mounted about a second rotation - wherein the first camera (10) and / or the second camera (20) has a variable focal length for producing a zoom difference, - wherein the first camera (10) and / or the second camera (20) is mounted adjustable in height to a Set height difference between the cameras (10, 20), - wherein the first camera (10) and the second camera (20) are directed from different directions onto an optically transparent object, so that the respective recording volumes of the cameras (10, 20) are at least partially overlap, and - wherein the system (4) further comprises a control device (6) which is configured to carry out a method according to one of the preceding claims. Flow cell arrangement, with a flow cell (100) and a system (4) according to Claim 17 - wherein the flow cell (100) represents the object. Non-transitory computer-readable storage medium on which a program code is stored, when executed, a processor executes a method according to one of the Claims 1 until 16 executes.

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