Advice for building a laser receiver grid

I want to build a grid 20cm x 20cm (8in x 8in) that detects laser hits from one of these. It appears to be a simple IR/red laser.

I'd like the grid to be able to indicate where the hit was (row and column), if possible. Mainly I want to use it for timing. The receivers Laser Lyte sells for use with the emitters indicate a hit, but not how long it took (and the receivers appear to be pretty small as well).

My first thought was to create a 2D array of phototransistors, but I'd probably need to space them every 5mm or so, which would mean 1600 transistors, which would be nearly 1000USD.

Is there a better way to build this?

Alternatively, I suppose, I could buy their receiver and tap into the signals that indicate start and a hit, amplify them, and feed them to the arduino to calculate and display the time.

Use a camera, there is a project:
http://coolarduino.wordpress.com/2011/12/07/arduino-laser-3d-tracking-range-finder/
and
http://coolarduino.wordpress.com/2012/07/28/visual-navigator-making-it-mobile/

resolution 500x 800 , but vision field of camera has to be adjusted to target size by lens or accurate close installation. Speed 1/60 sec, so 100 msec flash should be reliable registered in 5-6 consecutive frames.

So...what is this "time it took" you intend to measure? I hope you're not trying to measure time-of-flight of a laser pulse with an Arduino.

macegr:
So...what is this "time it took" you intend to measure? I hope you're not trying to measure time-of-flight of a laser pulse with an Arduino.

Sorry, I guess that part was a bit vague. I want to light an LED or buzz a buzzer, then start the timer. I'll stop the timer when the laser hits the target. I'm trying to measure (and improve) the time it takes to draw from a holster, acquire a target, and fire. And lasers are a lot cheaper than live ammo these days.

I remember seeing a "live" firearms trainer at a trade show, where the shock and light of the firing of a blank round triggered a laser fitted in the pistol's barrel.
The "players" (law enforcement) wore vests woven with a broad mesh of notched optical fibre, forming the optical equivalent of a leaky feeder.
Photodiodes were attached only at the ends of a run of fibre, giving the controller an x-y position of a hit.
I don't imagine getting the notches right was easy though.

Could you use a plate of plexiglass, with X and Y photodiodes at the edges?

TanHadron:
Could you use a plate of plexiglass, with X and Y photodiodes at the edges?

Phototransistors, but yeah I was wondering the same thing. The signal might not be variable enough across the face of the plexiglass to get a good distance measurement but maybe you could cut grooves into the face to improve that. Worth experimenting with, anyway.

I'm going to try Magician's advice: point a camera at the target (I didn't realize I can get an arduino-able camera for $30), buzz & start the timer, poll the camera until I see a big red spot, stop the timer, and display the time and image on a TFT display.