Simple LED pulse circuit
I'm going to recommend that you simply not worry about efficiency, right now. You've agreed that it could work to use a flicker frequency that is noticeable. And this means you need to do some experiments first before you can settle on a workable solution. Frankly, I'm not even sure there IS a workable solution for you. But there might be. Before I go there, just a short comment about why operating an LED with PWM, broadly speaking, won't help you at all:



As I wrote in this link, PWM frequency for LED dimming, there's quite a number of studies about human perception of intensity when varying frequency and duty cycle. The Talbot-Plateau says that if a light source blinks fast enough so that it passes beyond the critical flicker fusion frequency (CFF), then the brightness will appear to be the same as if the light source were steadily operated at the time-averaged luminance. The upshot of this is that you won't gain any operating efficiency from operating an LED at a frequency past the CFF. For example, if you use a duty cycle of 50% and a frequency of 200 Hz, and operate the LED at some luminance (current \$I_x\$, for example), then it will appear to have the same luminance as that same LED when operated with DC at half the current, or \$\tfrac{I_x}{2}\$.

In short, no efficiency gains here. In fact, you'd be worsening the efficiency because a semiconductor switch drops some power, itself, as does whatever is operating it.



But there is a possibility trapped between the Broca-Sulzer effect and the Bruecke-Bartley effects, which you might consider exploring for your own purposes. I hadn't discussed these effects much in the above-mentioned link of an answer I gave earlier. So now might be a time to add a few more details to help explain.

The Broca-Sulzer effect found that \$50\:\textrm{ms}\$ flashes appeared to be some 30–40% brighter than \$50\:\textrm{ms}\$ flashes of equal luminance. (This effect was broaded in scope by Ganzfeld's results, which aren't important here.) So, here it seems that the effective brightness begins to rise when the frequency rises from 1 Hz towards 10 Hz.

The Bruecke-Bartley effect covers the other direction, this time lowering the frequency from the CFF. It found that the effective brightness begins to rise when the frequency declines from the CFF and towards 8 Hz to 10 Hz.

The technical details of these two effects would cause a practitioner in these fields to want me to be a lot more precise about what the results say and don't say. But that's a rough summary for the purposes here.

In short, it would seem to be the case that somewhere around the area of 8-10 Hz, you could expect some human perception effects to allow you to use less average power for a similar visual sensation.

This is why I'd suggested you consider this as an option, if you are searching for improved efficiency through PWM. And it would seem, perhaps, that you might be able to expect something like a 30% improvement. That is, if the flicker effect isn't too annoying to use. So you do need to experiment here.



Efficiency isn't ONLY found through PWM. LEDs themselves do exhibit different efficiencies in converting electrical energy into light. And humans are vastly more sensitive to wavelengths near \$550\:\textrm{nm}\$ than to blue or red, for example. But I'm assuming here that things being equal on these points, you want to explore how PWM in the right range might also help out.

But I want to point out that you should have already done the work needed to identify your best LED option before starting down that path. So if you feel you have already got the right LED, then I think you can consider the idea of exploring the boundaries between the Broca-Sulzer effect and the Bruecke-Bartley effect.



For such experiments, I think it would be helpful to have a way to easily vary the frequency from about 1 Hz to close to the CFF. The CFF itself varies a bit when the light source or your eyes cause the light to hit different parts of your retina, over time. So, personally, I'd want the ability to go from 1 Hz to 100 Hz to cover most situations. Plus, I'd want a push button that would immediately over-ride the flicker frequency and go straight to 100 Hz, so that I could quickly make comparisons that way. I'd also want the ability to vary the duty cycle (mostly for fun.) But in your case I think a fixed 50% duty cycle would be good enough for the experimental purposes and you don't actually need a control for that.

Regarding current? If you accept my suggestion for only 50% duty cycle, then you probably just need two control currents -- one at the standard DC current recommended for your LED and one at twice that much, when operating at 50%. I don't think there would be serious harm in allowing you to set it for twice-normal even when operating at 1 Hz (or DC.) The worst that happens is that you damage the LED and those are cheaply replaced.

But you need to figure out what experiments you want to perform. You can read what I wrote here and consider that. Or come up with your own ideas. But either way, this can lead you to a specification that I think you could post here for a useful reply.