For the design of a no-power light detector, I need to boost the output of a small photodiode array (produces 20mV @ 1uA) to 1.5V. Since a short voltage spike would be sufficient and the light source will be oscillating, shouldn't a transformer be able to do the job? I tried this with a 1:50 turn ratio transformer but didn't observe any additional output at the secondary.
You forget the basic principals of transformers. That voltage comes at the cost of current. So for 50 times the voltage, you're getting 1/50th the current, which is 20nA That's hardly a useable amount of power. You could rectify the output signal with a schotky rectifier, and charge a capacitor, but at that charge current it could take some time.
The solar cell from a pocket calculator might be more useful, makes more sense anyways as if your light source is bright enough to detect it will also provide you enough electricity for doing something.