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You can't really correct for the chromatic distortion (purple effect) as it is not simply a color correction, the IR light bends differently through the optical elements / lense. (The diffraction coefficient is different for different wavelenghts of light). Thus you have to filter the light out to get rid of the effect.

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I suppose it depends on the bandpass of the filter. I have several older phones which can take (rear) images of IR leds - we used this as a sanity check at work several times. Images of normal things didn't look noticeably worse for having that sensitivity.

Many visible optical filters leak in the infrared, so perhaps a small amount gets through, but not enough to cause a noticeable colour cast in normal photography.

Vegetation in sunlight is a good test target, too. Leaves strongly reflect NIR.

You can correct it (Lightroom, Photoshop, Darktable, etc include tools for this), but it's a waste of processor power if you can fix it in hardware.

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