Dimensional Measurement using Vision Systems - NPL Publications ...

More documents

Recommendations

Info

<strong>Measurement</strong> Good Practice Guide No. 39 Figure 21: Lens relative aperture. 4.1.2 Thin lens formulae Equations 6 to 10 are based on the assumption that the dimensions of the lens, does not affect the formation of an image. Figure 22 shows the image formed by a thin lens. In this case the lens is actually producing an image that is smaller than the object. Figure 22: Image formation by a thin lens. The lens magnification (M) is given by the ratio of the image height (b) to object height (a). It can be seen from Fig 22 that the magnification can also be expressed as the ratio of the image distance (v) to object distance (u): 35
<strong>Measurement</strong> Good Practice Guide No. 39 M = b/a and M = v/u …..(6) The thin lens imaging equation is: 1/f = 1/u + 1/v …..(7) Where; f = focal length By rearranging equation 7 the image distance v, can be expressed in terms of the object distance u and the focal length f: v = uf / (u-f) …..(8) If equations 6 and 8 are combined the image size can be expressed in terms of the object size, focal length and object distance as follows: b = a f/(u-f) …..(9) Two optical properties of this simple imaging system may be deduced from equations 8 and 9. Firstly, for a given object size and distance, increasing the focal length increases the size of the image. Secondly, for a given object size and focal length, moving the lens closer to the object increases the size of the image. In both cases the image distance also increases. Hence in a vision system, employing a camera at the image plane, changing to a longer focal length lens, or moving the lens closer to the object to increase the magnification will also require that the lens is moved further away from the camera in order to keep the image in focus. In practice, this is normally achieved by simply rotating the lens tube. Two of the most important criteria when selecting the correct lens for a vision system, are the field of view and the angle of view. The size of the object to be measured is a key factor, as the whole object must fall within the field of view in order that it may be measured. Rearranging equation 9 gives an expression that can be used to calculate the maximum object size (a) that can be seen by the camera: a = b(u-f)/f …..(10) Where; b = image height, determined by the size of the CCD sensor 36
Page 2 and 3: Measurement Good Practice Guide No.
Page 4 and 5: Dimensional Measurement using Visio
Page 6 and 7: 7 MAKING MEASUREMENTS..............
Page 8: MEASUREMENT GOOD PRACTICE There are
Page 43: Measurement Good Practice Guide No.
Page 75: Measurement Good Practice Guide No.

Dimensional Measurement using Vision Systems - NPL Publications ...

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?