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I've done a lot of research regarding filters as I'm about to do a modification on my DSLR for astrophotography. I've settled on removing the existing IR filter and replacing it with one the will still allow H-alpha (656 nm) and S-II (672 nm) plus the visible spectrum below that.
My question is..if the eye can see red to approximately 700nm (before it reaches near-IR), why do most stock IR filters cut off below 650 nm ?

With few exceptions, data for infrared filters are not published for the region from 700 to 900nm. This is because most infrared filters are offshoots of the Wratten gelatin filters recipe. These were made by dissolving dye in gelatin and then floating the liquid gelatin on the surface of water. The gelatin was then allowed to gel and then lifted from underneath via a wire frame. The dried gelatin filter was then over-coated with lacquer. Often these gelatin filters were sandwiched between two sheets of optically flat glass.

Anyway, infrared radiation is strongly absorbed by matter. Most gelatin filters begin to absorb infrared beginning at about 2000nm and fully absorb at about 3000nm. Most glass infrared filters fare worse. The typical absorption curve is generally published for the region 750nm to 3000nm

To pass the frequencies you need, the filter would likely need to be made of quartz. I think none are available at affordable prices. Perhaps you can find such a filter under “specialized filters for science”. I don’t think you will find them in the general photographic community.

Camera imaging sensors are much more sensitive to longer wavelengths than human vision. The normalized response of the "red" sensitive cone cells drops off rapidly above 640nm. A camera without ir filters will be much more sensitive to red light that contains material percentages of photons with longer wavelengths. Cameras often have such filters built-in just to prevent overly strong response to flames and red hot embers. Add-on IR filters are most useful for cameras that have weak or no IR filtering.

However, these filters are a problem when trying to capture longer wavelengths in astro-photography and replacing these with filters that pass specifically desired, longer wavelengths allows better capture of this light.