Your most important decision is which LED.
You want the most photons per watt at the lowest cost.
Comparison of LEDs in the selection process is not as easy as it may appear.
Low power blue LEDs luminous intensity (lm/steradian) ranges from 5 mcd to over 5,000 mcd
View angles range from 15° to 140°
View angle has a huge effect on luminous flux measured in lumens (lm=mcd/steradian).
mcd is the photon intensity within a steradian (sr) cone measured in lm/sr.
The cone has an angle.
If we were to choose a minimum intensity of 100 mcd at 30° that is 0.021 lumens (lm).
Lumens includes every photon exiting the LED at any angle.
If the LED view angle is spec'd at 4x 30° (120°) 100 mcd @ 120° = 0.314 lm about 15x the flux of 0.021 lm @ 30°.
The radiant beam has a maximum distance. The distance of a flashlight beam is the distance where and illuminance is measured at 0.25 lux. 0.25 lux is about the amount of illuminance from a full moon.
Distance the light will travel is a factor.
100 mcd @ 1 meter = 100 lux.
At the given angle and distance the amount of area covered is the luminance (lm/sr/m²).
The intensity of the area (illuminance) measured in lux (lm/m²/s) add the element of time or brightness.
The point being your purpose determines the importance of the view angle (i.e. steradian). And view angle is a very important property in the comparison of LED intensity.
You must understand the various measurement geometries of
- Luminous Flux (lm)
- Luminous Intensity (mcd)
- Luminance (lm/m²)
- Illuminance (lm/m²/s)
How to power the LED depends a lot upon the battery discharge curve. The good thing about a CR2032 is its flat discharge curve. The flat curve is favorable for a cheap current limiting resistor.
Notice the green (internal resistance) curve on the right image changes with capacity and the load remains constant. It is a myth that a CR2032's internal resistance is the same as a current limiting resistor.
For more about internal resistance and CR2932 current see this Texas Instruments app note: Coin cells and peak current draw
The Forward Voltage.
The forward voltage is a function of the current. This means you do not connect an LED to a constant voltage source without current regulation.
3.3 forward voltage blue led.
3.3 Vf is ambiguous. Most important is at what current. Most low power LEDs are spec'd at typical and or max current. The idea here is to get a Vf below the battery voltage.
Below is the Brightek QBLP674-IB
The max Vf of this LED is 3.7V which is reflected in the graph. So it may be safe to say the graph represents the maximum Vf. But the 3.7V is at 100 mA. The LED can be powered at 100 mA with a 10%, 1khz duty cycle.
So if the target minimum luminous intensity at 120° is 10 mcd (10% of minimum 100 mcd). The current can be set between 500 µA and 1 mA. At this current the Vf is about 2.5V.
So given a battery voltage of 2.9V and Vf of 2.5, a current limiting resistor of about 400 Ω would suffice for 10-20 mcd @ 120° or 0.031 - 0.062 lumens.
And alternative would be a Broadcom ALMD-CB1E-VW002 with 5700 mcd @ 15° and 20 mA.
Below 1 mA the Vf is about 2.6V. If the target intensity is 100 mcd (0.306 lm) the current would be about 350 µA (≈850 Ω resistor).
This graph shows the Vf at 20 mA is 3.2V.
This means this is a graph of typical values.
To be safe I would add 0.4V to the minimum.
When calculating the resistor value I would use 2.8V (min)
I would not use this LED unless I sampled a significant number of theses LED and measured the maximum Vf at 1 mA.
To convert from mcd to lumens I used the Rapid Tables online calculator
My Recommendation is the Everlight EAPL2835BA3
Luminous Flux: 2.5 lm to 5.0 lm
View Angle 120°
Test current 50 mA
DigiKey Qty 4000 cost 6.182¢
How does this compare with the 9.360¢ (qty 2K) Brightek QBLP674-IB?
Luminous Flux: 100 mcd (min) to 210 mcd (typ)
View Angle 120°
Test current 20 mA
This means the Everlight is 66% cheaper, and its intensity is about 4x the Brightek.
Both LEDs spec'd a minimum luminous output and the same view angle of 120°.
The minimum intensity of the Bightek LED is 100 mcd.
The minimum flux of the Everlight is 2.5 lm.
2.5 lm converts to 795 mcd @ 120° that is 8x not 4x as I stated above.
When LED output is in flux (lumens) the total light emission is measured.
When LED output is measured in mcd (intensity), it is measured at 50%.
Also we must further reduce the Everlight intensity based on the "test current". The Everlight is spec'd at 60 mA and the Brightek at 20 mA.
View angle intensity is measured in radiometric. So if the wavelengths are not equal then you must do a photometric to radiometric conversion.
A 450 nm blue radiometric is 3.6% of photometric. 1 lux = 0.036 W/m²
A 470 nm blue radiometric is 1.6% of photometric. 1 lux = 0.016 W/m²
When an LED is rated in lumens (flux) and another is rated in mcd (intensity) is is not so easy to compare. Therefore you must look at the spacial distribution (view angle). View angle is measured at 50% relative intensity.
I find the non-polar easier for comparison.