I have a stair made of several steps. I want that when I put a foot on a step, the light of the next step is turned on. Each light is placed just under the edge of the step. If I use LEDs as lights, can I build a system with sensors that can be powered with batteries? Since I have to place a sensor on each step, what kind of sensor should I use? Where can I start to build something like this?
I'd avoid retroreflective IR sensors. In my experience they can be fickle, and sensing range depends on the reflectivity of the target (shoe). To make matters worse, you'd need predictable foot placement to meet your objective with just a single retroreflective sensor.
Consider a few opposed pairs of IR LED/sensors, such that the beams cross the full width of the stair tread. You might get it to work with a single pair, located right near the edge. Your circuit would need to detect when the beam was interrupted by a shoe, then illuminate the corresponding step.
The current draw of each IR LED can be as low as a few mA (though it will make it harder to aim/align properly), so battery power is viable. To reduce power consumption, the IR LEDs can be strobed (i.e. on for 10ms every 250ms), though the detector circuit design will become more complex as a result, and you may face latency issues (time from breaking the beam to next stair illumination coming on).
I would be incline to use a sensor something like thisinfrared proximity sensor place in the center of each step and activate the led string whenever something is detected within certain distance using a comparator circuit. Again, I do know what kind of budget you are looking at, but I'm sure there are other similar sensor that might be cheaper if you look in digikey or mouser. Also, since its an infrared sensor sunlight might be an issue but I'm assuming its an indoor application