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I need to have a low shutter speed to be able to capture a light that is only on for a few milliseconds each frame (light synced with camera fps, but only want it to capture when the light is on). How can I go about doing this?

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Assuming that you are using a Pi Module you have some off-the-box options with the command to capture video (I think about video because you talk about FPS). A combination of exposure settings and metering may give you the desired effects:

raspividd --help

-ex, --exposure : Set exposure mode (see Notes)

-mm, --metering : Set metering mode (see Notes)

Notes

Exposure mode options :

off,auto,night,nightpreview,backlight,spotlight,sports,snow,beach,verylong,fixedfps,antishake,fireworks

Metering Mode options :

average,spot,backlit,matrix

Also, if the light you want to capure is not too short you might use the motion (mmal) https://www.raspberrypi.org/forums/viewtopic.php?f=43&t=44966&p=1116392&hilit=motion+mmal#p1116392

here you have the option to activate the camera when an amount of pixels is modified. And some options to adjust sensitivity.

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This is very easy in python using the picamera library. You can set the shutterspeed in ms, e.g. a value of 10000 is equivalent to 1/100th of a second. A simple script as an example:

import picamera
import time

with picamera.PiCamera() as camera:
    time.sleep(1)
    camera.exposure_mode = 'off'
    camera.shutter_speed = 10000
    camera.start_recording("testvideo.h264", quality = 20)
    camera.wait_recording(60)
    camera.stop_recording()

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