Adventures in Projection (Part I) - Your Projector(s)
So, you're using projection on a small stage, on a budget, what do you need?
A: The brightest projector possible
Ok, it's more nuanced than that, but it's a simple answer and a good starting point. Use the brightest projector you can find / borrow / afford. 7000 lumens sounds a lot, and it is... until you remember that a single Source Four Jr HPL575 outputs almost 15,000 lumens, over a smaller area.
Stage lighting can easily wash out most projectors, and it's more of a problem in smaller stages as you can't usually get the actors (and therefore light) far away from your projection surface physically.
Resolution doesn't really matter
Some people will vehemently disagree here (or you might be reading it in 2035 when the cheapest projectors you can buy are 4K UHD - although hopefully by then LED wall is cheap!), and that's fine, but the reality is that since the audience are usually a reasonable distance from the upstage wall 1080p or WUXGA (1920x1200) will usually be absolutely fine for this sort of application.
The great thing about this is that older 1080/WUXGA projectors are readily available cheaply as people upgrade to 4K.
Short Throw Projectors
Short Throw or 'Ultra Short' projectors have their problems (typically lower quality than a 'traditional' projector, slight image distortion and inconsitency etc...) but on the small stage they are incredibly useful and the only realistic way to not have your scenery and backdrops projected onto your actors themselves (unless that's what you're going for) with limited depth.
There are now some 4000-5000 lm UST Laser Projectors designed for office home cinema use that are surprisingly good, but still quite expensive (£1800-2300)
I've done a few shows with the much older Epson EH-320UST. This isn't really bright enough (it's claimed 4000 lm, but appears dimmer than a 4000 lm laser projector perhaps due to optical losses, or just the age of the lamp), but the throw ratio of 0.25:1 is fantastic. You can pick these up for a few hundred these days.
Which leads me to the next point...
Use Multiple Projectors
In professional theatre when you see projection it's rarely being driven by one projector, multiple techniques such as 'stacking' and 'edge blending' are used, and you can too.
If you've got two 3000 lumen projectors, overlay them and you've now got a 6000 lumen projector. It's worth noting, however, that we perceive brightness on a logarithmic scale. So a 6000 lumen projector will look around 20-30% brighter than a 3000 lumen projector, to get one that's truly 'twice as bright' would need 12,000 lumens.
Similarly if you have a large wide surface to project onto, consider using multiple short throw projectors closer to the screen rather than one large one further away. Edge blending can help in this scenario, or use a functional vertical design element of your set (for example a pillar, window frame, street light etc) to hide the edge of each projection. This is especially helpful with non-matching projectors.
The image shown below uses two projectors - one 6000 lumen from front of house, and a short throw 4000 lumen lighting the bottom of the projection. This combination allowed the actors to get very close to the projected image (thanks to the short throw) but still allowing us to take advantage of the vivid colour and contrast from the brighter unit out front usually used for film screenings.
(The difference was far less noticeable to the eye than is shown here!)
Feeding Multiple Projectors
You need to think about how you'll control this, just passing the image into an HDMI splitter will never work if you're trying to overlay the projections.
Software like QLab makes it easy to set up projector blending and, if you're only working with 1080 HD (rather than 4k) you can drive four (or even eight!) projectors out the lowest end of macs with hardware that splits the image.
These clever little boxes present to the mac as a single 4K monitor, and then output 4x 1080 feeds to the projectors by splitting the input into four quarters.
The defacto 'industry standard' for this is the Datapath FX4, but it's expensive. There's a variety of extremely cheap and cheerful options marketed as 'video wall controllers' and some are actually pretty good if all you need is a simple 2x2 splitter, I've had success with both of these;
Within QLab you can treat each of the four sections as individual displays, for a fraction of the cost of external graphics cards etc and whilst it might not be suitable for Broadway or the West End, it's certainly more than adequate for most community and small-scale theatres!