The Joule Thief mentioned in another answer is an excellent way to harvest the dregs of battery power. However, if surface mount components are not a problem, one can do slightly better.
Look for ultra low power energy harvesting boost converters from Linear Technologies, Texas Instruments and perhaps other manufacturers.
For instance, the TI BQ25504 can harvest energy down to 80 mV supply, as long as an initial 330 mV is available for starting the process. Typical depleted primary cell batteries will provide a higher voltage under no-load than under load, so getting that initial 330 mV at start-up is not difficult.
The standard application circuit from the datasheet is thus:
This is be pretty effective in sucking residual energy out of your depleted batteries down to nearly the last drop.
For something simpler but with less challenging requirements, the SparkFun LiPower boost converter, which uses the TPS61200 boost converter IC, can be easily modified to work down to 0.5 Volt supply power: The original designer of the LiPower board has posted a blog on how to do this modification.
The key advantage these solutions have over the joule thief is the high switching frequency used, courtesy the highly integrated design, and thus the much smaller inductor required. At the end of the day, they are all conceptually similar approaches, with a quantitative difference in execution.
I was thinking of using a 12v to 5v converter and a LT3083 to adjust
the voltage from 5v to 4.2v, this would also mean i could use a 5v
battery bank to power the voltage regulator, do you think this will
work?
Yes, but it isn't the best way. There will be losses with the LDO. Use an adjustable DC-DC converter to go from 12V directly to 4.2V. TI makes lots of parts that are easy to design around.
Because the camera is quite expensive i want to add over voltage
protection and a display that shows the estimated battery life, for
the voltage protection i could use a MCU and a voltage divider to
measure the voltage on the LT3083 output, if the voltage is correct
the MCU can turn on a transistor that goes from the voltage regulator
to the camera,
This will be too slow. By the time the overvoltage is detected, it's likely your camera will be dead. There are several questions about overvoltage protection on here already, do a search.
...and i could use another voltage divider to measure the voltage of
the 12v lead acid to give a estimated battery life.
That is reasonable. I would recommend a high side switch on the voltage divider so you can turn it off when not taking a measurement. Otherwise, it's a constant load on the battery that will slowly drain it.
Best Answer
Don't let this happen to you:
Batteries don't like excessive voltage or current and will destroy themselves and injure others if proper steps are not taken to ensure these conditions do not occur. For these reasons it is very important that the charger you use is suitable to the battery. Remember,
Battery acid can blind or disable you.
Electricity can injure or kill you.
Please do research on battery and electrical safety to ensure these things do not happen to you. If you are determined to do DIY projects like this, follow the instructions exactly and make sure you trust the instructor enough that you can feel confident you won't be injured. In any case of uncertainty, ask before you try!