Again you're thinking upwards into the well known thermal/saturation limits of efficiency in LEDs, even the links from your lazy google search show that the peak efficiency is at a single forward current point with either too high or too low drive dropping the efficiency (or efficacy):
I apologise if I came across as pompous.
Those graphs are meaningless, without real units, no mention of the type of LED and whether it's got a phosphor or not.If you wish to bring the data into question why can't you provide the data to show its wrong? Phosphors have well known saturation and temperature limitations at the high end, but I can't find any papers discussing non-linear effects towards zero. I'm not sure what you think luminous efficacy is, but its the well defined method of assessing visual brightness:
Show me some real data for a bare LED (no phosphor), with the radiant power output (not luminous efficacy which varies depending on the lighting conditions!) vs power in and I'll take interest.
Yes, it no longer applies in a scotopic vision environment but then you wouldn't be distinguishing colours clearly which is not what the OP is discussing. You raise a lot of questions without backing it up with data or references or even explanations to help people here. Sitting on your high horse and being pompous isn't of much value to the OP when you could be adding information to the discussion rather than trying to discredit it all without alternative facts to back it up.
I agree with you about phosphors but that's not relevant here because the original poster is not using an LED with a phosphor. What I'm referring to is efficiency droop, i.e. there's no point in driving at high current with a low duty cycle. The LED should be run at the current, which gives the highest efficiency. Now I agree, if that's higher, than the OP's power budget then PWM may be a wise choice. In any case, a switch mode supply should be used for optimum efficiency.
Which is the region the OP is considering driving the LEDs at. Mike had already summed it up neatly in his first post:
For maximum visibility, (Cool) white, small size, narrow angle if your viewing angle . match angle to required viewing angle. If you want to stand out from other lights, maybe deep green, as this is at the peak or the eye's sensitivity.The OP was very clear on their operating point:
Where you want "noticeability" for emergency type applications, strobing can help as the eye is more sensitive to movement.
In principle, for a steady brightness, PWMing doesn't give any advantage in terms of perceived brightness, but efficiency at low currents (< about 5% of nominal current) can vary a lot, particularly with white, so if only for consistent appearance, a higher current pulsed at a low duty cycle can be beneficial.
The device is targeted to consume less than 50 uA and it will have four LEDs than can possible be all on. The user can only see two at the time (red and green).Which I'll continue to suggest is usually well below the ideal operating current of an LED if you are trying to extract maximum efficiency from it, so the PWM concept at a peak current within the manufacturers specifications is a much better design.
Is it possible to reach this goal with max 10 uA/LED? Probably the LEDs could be blinked at ~1 Hz with 25-50% on time, which would help saving current at the same visibility.
Is it better to use PWM or a constant current drive for better visibility at the same average current? PWM may be a problem, since the CPU needs to sleep.
Does the size of the LED change the visibility? Is higher lm/W always better? lm/w is given at much higher current typically. Narrow viewing angle would help, but rather wide must be used.
I apologise, you're right. After doing some more reading, I've realised efficiency droop is more of a problem at higher currents, than at extremely low power, where efficiency also deteriorates. LED efficiency does improve at lower currents but this doesn't extend down to the 50µA and this is nothing to do with the phosphor I was so obsessed with. I think Mike was right all along! Sorry I was too pig headed to see that.
Running around 10% of the LED's recommended forward current seems to be the best way to go (unless the datasheet suggests otherwise) and that's quite likely too high for the OP's power budget. For example, assuming a resistor is used to limit the current and the LED's recommended IF
is 10mA, then run it with 1mA pulses at 5% duty cycle to give an average of 50µA. A buck converter, rather than a resistor, could be used to either reduce the current consumption or provide longer pulses, therefore brighter light for less power.