Line speed, strobing and exposure time

When dealing with online applications, there are some important parameters that have to be considered. Specifically, depending on the object speed and image sharpness that is required for the application, the camera exposure time must be always set to the minimum in order to freeze motion and avoid image blurring. Additionally, black and opaque objects that tend to absorb instead of reflecting light, are particularly critical.

As an example, let’s suppose to inspect an object moving with speed vo using a lens with magnification m and a camera with pixel size p.

The speed of the object on the sensor will be m times vo:

`v_i = m v_o`

Therefore the space travelled by the object xi during the exposure time t is xi = vi t. If this space is greater than the pixel size, the object will appear blurred over a certain number of pixels. Suppose that we can accept a 3 pixels blur: in other words, we require that

`x_i = v_i t = m_vo t < 3 p`

so that the camera exposure time t is required to be

`t < 3 p / (m v_o)`

For example, using p = 5.5 µm, m = 0.66, vo = 300 mm/s (i.e. a line speed of 10,800 samples/hr on a 100 mm FoV) we find a maximum exposure time of t = 83 µs. At such speed, the amount of light emitted by LED illuminator used in continuous mode is hardly ever enough - so that strobing the illuminator for an equivalent amount of time is the best solution.

Another parameter that we can adjust in order to get more light into the system is the lens F/#: by lowering the lens F/# we will gather more light; however, this will lower the depth of field of the system. Moreover, this might also lower the image quality since, in general, a lens performs better in the center and worse towards the edges due to lens aberrations, leading to an overall loss of sharpness. Increasing the camera gain is another way, however this always introduces a certain amount of noise, thus again leading to a degraded image where fewer details can be distinguished.

As a result, it is always a good practice to choose sufficiently bright lighting components, allowing you to correctly reveal the features of interest the inspected of object when used in combination with lenses set at the optimum F/# and without the need to digitally increase the camera gain.

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