Doing a little math, I think this might actually work. Assumeing we want 1 hour of light for each hour of charge.
Best case, if you work with single crystal solar cells, which are the most efficent (using the numbers from a Siemans SM55) and you are content with the brightness of an infinity, the collector would need an area of (13*50.9/55)*(.055*1.5)= need .993 square inches.
Worst case, amorphous solar cells which are the cheapest and lowest efficiency, and you want Arc-AAA brightness, the collector would be (29*54/64)*(.25*1.5)= need 9.2 square inches.
So this flashlight would need a face somewhere in the range between .5x2 and 3x3.
I suppose the collector could fold, but that would probably make the light less rugged
Assuming approximately 4 hours of charge (which is nominally my area, some places get 6) you would want a storage capacity between .33 watt-hours and 1.5 watt hours. What do these lithium AAAs you have in mind hold?
I've seen NiMh cells that are 1.8x.65x3 and hold 800 maH, or about 1.02 watt-hours, so if the lithiums are a little better, we're in the ballpark for storage in one cell.
Now all of this makes some big assumptions about charging efficiency, which is really more like 70%, so the collectors would have to be about 40% larger. On the other hand, a DC boost might extend the charging day a bit by taking solar output that is less than charging voltage and turning it into pulses that will charge. Such a circuit could actually be more efficient than your standard blocking diode that stops discharge thru the solar panel.
I'd avoid the strip on the side that shows charge. If it works like the ones Duracell has, it will burn a lot of power each time you check. Since you already have in mind a PIC controller, it could count charge pulses from the charge DC-DC converter (or if it is part of that converter, it could just keep track) and it could count discharge pulses sent to the LED and estimate remaining charge. It might measure battery voltage and either confim its count or just use that to estimate state of charge. The PIC could report state of charge by flashing the LED once for each estimated 1/4 hour of light left, 0-15 pulses in a system designed for 4 hours capacity. The PIC could also prevent overcharge and deep discharge.
You can certainly improve a lot on the pocket solar flashlight I bought about 20 years ago. It had about 2 square inches of amorphous collector, a 50 maH Ni-cad button cell, and a penlight bulb.
It didn't work very well. I think most of the improvement would be in charge and discharge control, DC-DC converters and bright LEDs, I mean that penlight bulb was murder on that tiny button cell, which was always overloaded and in deep-discharge.
Of course you could spend a lifetime trying different ways to optimise it.
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