How the calculation works
While the shutter is open (or the strobe is on), the part moves \(v\,t\). Expressed in object-side pixels of size \(p_o = \text{FOV}/N_\text{px}\), the blur and the maximum exposure are
To image every part of a moving stream with an area camera, a new frame must be taken before the part travels one field of view, less the chosen overlap \(o\):
A line-scan camera builds the image one row at a time. To get square pixels, the line rate must match the time the web takes to move one cross-web pixel:
The light budget
Signal is proportional to irradiance × exposure time. If blur forces a shorter exposure, the lighting must be brighter by the same factor to keep the same image brightness and signal-to-noise ratio. That is why fast lines use high-intensity LED strobes, overdriven for microseconds, rather than continuous lighting. Raising the gain instead amplifies noise along with the signal.
Worked example
Parts move at 500 mm/s under a camera with 2048 pixels across a 60 mm field along the motion:
- \(p_o = 60/2048 = 29.3\) µm per pixel, so for ≤ 1 px of blur the exposure must be ≤ 29.3 µm ÷ 500 mm/s = 58.6 µs.
- A 100 µs exposure smears features over 1.7 pixels. Holding the image brightness at 58.6 µs needs 1.7× more light.
- With 20 % overlap, the camera must capture at least 500/(60 × 0.8) = 10.4 frames per second.
- A 4096-pixel line-scan camera covering 300 mm across the web has 73.2 µm pixels and needs a 6.83 kHz line rate for square pixels at this speed.
Assumptions and limits
- Constant speed and a global-shutter camera. Rolling-shutter sensors read rows at different times, which skews moving parts even with a short exposure. Either fire the strobe only while all rows are integrating (global-reset or global-release mode) or use a global-shutter sensor.
- Motion blur adds to optical blur (defocus, diffraction, aberrations). The total is roughly the root-sum-square of the individual blur widths.
- Speed variation and vibration matter for line-scan cameras. Use an encoder to trigger lines rather than a fixed rate when the speed is not tightly controlled.
References
- B. Jähne, Digital Image Processing, 6th ed., Springer (2005).
- E. Hecht, Optics, 5th ed., Pearson (2017).