dlloyd:
My opinion is that this wouldn't work as you are taking far too long to do the conversion just to see if there is something present which most of the time there would not be. Remember the processor also has to control the visible LEDs and the pattern they go in.
I thought the 38 KHz would be the same for all sensors, just one 38 KHz source (constant frequency) and 50% duty cycle. This isn't the same type of sensor that's used for IR communication like TV remotes and garage door openers. The only information it returns is a pulse with varying width, repeating at 50-680 ms.
EDIT: Oops ... you said "visible leds" not IR leds.
MORE:
The processor would only have to track the bit timing of 36 bytes. A method something like this could be used to store the sensor status and time/duration information.
Thanks both for your input. I'll check that method out. I'm being drawn to the Sharp IS471F's after all. That's because, as shown in the video I linked a couple of posts back, it's proven to function for my kind of application, albeit with binary touch only. Given the expense of the components I might opt for only making a corner of the screen interactive such that it could be used as a small controller. This video also uses those components and works really well. As you can see you only need a bit of interaction to play tetris/snake etc.. I would really prefer a fully interactive touch screen but it would cost up to $500 for my display size, which is just crazy (with those components anyway). So I'm now considering using a corner of 3 x 3 pixels for controlling the table. Maybe 9 pixels in each corner for (4 players/persons) but not the entire surface (yet).
In the diagram at the very end of the datasheet (linked above) they use a suitable wavelength IR LED linked to the Sharp IR sensor. The modulation is driven by the sensor and it's also a modulated input so ignores background light. The output is a single bit, I believe. So if I had 9 per corner I need 9 regular IR LEDs, maybe a capacitor, and then a way of collecting the 9 inputs. Firstly, is there any issue with any of that so far? Reaction speed or anything like that...? And secondly, what would be the best way to collect 9 binary outputs, MUXing, shift registers or...?