Cirrus pilot reported departing Runway 33 at FNL after another aircraft has reported straight in for landing Runway 15. TCAS warning sounds at 500 AGL and reporter turns right.

Narrative

I was on an IFR flight plan from FNL; and had received my clearance from Denver Departure to depart Runway 33. The ATIS at the time was winds 210@4; Visibility greater than 10 miles; sky clear below 12;000 and altimeter 30.21. My clearance was to depart and turn right to heading of 150; for radar vectors; and climb and maintain 8;000. I monitored the CTAF; and announced my intentions to depart Runway 33; with a downwind departure. At the same time; I heard another plane inbound for a straight in to Runway 15. His last call out was either 5 or 10 miles out. I believed I had sufficient time to clear the runway and pattern area prior to the arrival of the straight in traffic. Accordingly; I once again announced my taking the active Runway 33 and started my takeoff roll. I believed this was the preferred runway for my flight; and had advised ATC of that intention. I had also observed other traffic departing Runway 33 as I taxied to the run-up area. At approximately 500 feet AGL; my TCAS system called traffic above and near my location. I do not remember the exact bearing or distance. I immediately initiated corrective action by turning right to my assigned heading of 150 and cleared the immediate airport vicinity. I do not believe there was a 'near miss' but was concerned that the inbound airplane misjudged his distance from the field; and that contributed to a dangerous situation. Also; the other aircraft's use of a straight in approach my have also contributed; as the problem would have been avoided with a normal pattern entry.