Abstract

The objectives of this our approach was to study the dimensional assembly problem of a heart rate monitor unit. This unit comprises a frame and a cover lens. Our task was to study how accurately the dimensions and the shape of the frame and of the lens can be measured in order to find out how well these parts will fit together. Two major problems were figured out and solved namely to illuminate the object features properly and to compensate the relief displacement of these object features. When carefully selecting the way to illuminate the object and to controlling the light intensity high sub pixel resolution in the feature detection was achieved. Our method to compensate the relief displacement was verified so that it fully takes account of the relief displacement caused by height differences of the measured objects. The accuracy level we achieved was 7 micrometers (which is the standard deviation measured as differences from the reference shape) for the frame and for the lens. Then using computer simulation the fitting of the lens into the frame can be investigated in order to find proper manufacturing tolerances.

Objective

The objective of this our approach was to study the dimensional assembly problem of a heart rate monitor unit. This unit comprises a frame and a cover lens, see Fig.1. In the assembly line the lens is installed in the frame. The question need to be asked is that how well the lens fits into the frame. The lens and the frame are provided by separate suppliers. Therefore it is important that the faulty units can be rejected as early as possible in the production flow. Thus reliable manufacturing tolerances are needed to control the production flow.

Figure 1. The cover lens and the frame of the heart rate monitoring unit. 

Our task was to study how accurately the overall dimensions and the shape of the frame and the lens can be measured. In the frame there is a hollow where the lens is placed. Then to be more precise our problem was to find out how accurately the innermost corner of the hollow and the outermost location of the curved lens edge can be measured. The location of the hollow corner is measured as a set of corner points in a 2D coordinate system defined in the frame. In the same way the curved lens edge is measured as a set of edge points in a 2D coordinate system defined in the lens. Then using computer simulation the assembly problem can be studied to find out suitable manufacuring tolerances and to control the manufacturing process.

Measurement setup

The measurement setup is shown in Fig. 2. The video camera used was a digital monochrome video camera. The CCD sensor has 1300 x 1030 pixels and the optics is 55 mm telecentric lens. The digital video signal was captured with frame grabber. Lighting system based on red LEDs was developed. Using this lighting system the objects can be illuminated by any combination of direct front, diffuse back and diffuse front lighting. The measurements were performed and results analyzed using Matlab software environment. The laser distance sensor was used for measuring height differences (in this case the height of the hollow corner and the height of the lens edge from the calibration plate). The measurement accuracy of the sensor was better than 30 ?m. 

Figure 2. The measurement setup
 

Measuring procedure

The measuring procedure developed comprises the following steps:
1) Camera calibration, see Machine Vision News Vol. 4, 1999, pages 16-17.
2) Imaging the lens and edge detection of the outermost edge.
3) Imaging the frame and detection of the hollow corner.
4) Solving the object coordinates of the detected corner and edge points including compensation of the relief displacements.
5) Computer simulation to align and to adjust the lens data relative to the frame data in order to find out the proper manufacturing tolerances.
Objective of the lens imaging was to obtain such a high-quality image, that outermost edge of the lens could be reliably detected. Due to the material of the lens (transparent glass) and curved shape of the lens, such a image was difficult to obtain. The main problem was that transparent material did not stand out from the background (measuring table) and only the edge of the black impression (on the base of the lens) could be detected (see Fig. 3). This problem was solved by lifting the lens up and off the measuring table. Desired contrast between lens edge and the background was achieved, when camera system was focused on this new measuring level.

Figure 3. Edge detection of the cover lens: a) image formed with diffuse front lighting, b) image formed with directional lighting c) result of the edge detection (* = coarse precision edge points, ?= sub pixel precision edge points). 

The detection of the lens edges was performed in two steps. Edges were first detected on coarse precision from the image, that was obtained using direct lighting from the horizontal direction. This lighting method produces images with high contrast between the vertical edges and horizontal background, see Fig. 3. Then the obtained edge points were used as initial guess for sub-pixel edge detection, which was performed from the images formed with diffuse front lighting.
Two main questions when imaging the frame were: 1.) how to obtain even and shadow-free lighting to the the bottom corner of the hollow and 2.) how to obtain such a image that subpixel algorithm can be applied. The answer to the first question was diffuse front lighting. The second problem was solved by combining images of the frame illuminated separetely from front and horizontal directions.
Object coordinates of the detected edge and corner points were solved with the calibration parameters obtained from 2D camera calibration and height differences measured from detected edge and corner point levels to the calibration plane. The height differences were needed to determine the amount of the relief displacement of each edge and corner point. A method was developed to compensate the relief displacement and to determine the camera intrinsic parameters (focal length and focus of expansion) needed in relief displacement compensation.
The last step in our procedure was to perform computer simulation to align and to adjust the lens data relative to the frame data. This was done show that the origin and the coordinate axes of the lens were aligned to that of the frame coordinate system. Then the lens coordinates were translated and rotated so that the gap between frame corner and the lens edge is homogeneous around the whole object. Then the maximum and the minimum gap can be determined describing the manufacturing accuracy.

Results
 

Almost 3500 corner and edge points were detected from the hollow and from the lens respectively. Standard deviation of the difference between the reference shape and the detected edge points was 7 ?m. As can be seen in Fig. 5, there are some separate peak values (> 20 ?m), which were probably caused by dust particles on the measured object. 
 

Figure 4. The set of frame and lens points after the adjustment calculations. The leftmost corner of the whole unit is shown on the right hand picture. 

Accuracy of the relief displacement method was verified by following method: calibration plate was placed and imaged on different heigth levels in the depth of field of the camera system. Accurately detected calibration points were projected to the selected base level and relief displacements caused by heigth differences between base and imaging levels were compensated. After compensation distances of the obtained base level coordinates were solved and compared to the distances determined directly from base level images. When evaluating the results no significant variation was observed.
In this particular case the cross-measures, height and width of the lens and the hollow of the frame were measured. With our method the relief displacements order of 200-400 ?m in case of the frame and order of 40-80 ?m in case of the lens were completely compensated.

Figure 5. Differences between detected edge points and the reference shape of the cover lens.

Discussion

The assembly problem of fitting a cover lens of a heart rate monitoring unit into a hollow of the frame was studied. The idea was to measure the location of the corner points of the hollow and the location of the edge points of the lens in terms of 2D co-ordinate values in a co-ordinate system defined in the frame and in the lens respectively. We focused our study to investigate the accuracy level that can be achieved when measuring these real objects. Two major problems were figured out and solved namely the illumination of the proper object feature and the compensation of the relief displacement. When carefully selecting the way to illuminate the object and controlling the illumination intensity high sub-pixel resolution in the feature detection was achieved. If there is a need to increase the resolution of the edge detection then further illumination studies are needed. Our method to compensate the relief displacement was verified so that we can say that the method we developed fully takes account of the relief displacement caused by height differences of the measured objects.
The accuracy level we achieved when measuring the location of the hollow was 7 micrometers (standard deviation) and also the same when measuring the curved lens edge as can be obtained from results shown in Fig. 5. The accuracy level of the measurements can be improved if more attention is paid for the camera calibration algorithm in order to compensate the lens distortions.