(Lenssurface divided by sourcesurface) x lux @ 1 meter x lensefficiency
Summary: (from posts in this thread )
- Definition of throw: The abillity to enlighten distant objects.. It's as simple as that!
But: Different objects have different levels of reflection when enlightened, so we have a problem. Ok, then lets agree on specify the throw of a torch by stating the distance from the torch at which 1 lux is measured .
- There is a simple ' inverse square law' formula to recalculate distance and lux to go from candlepower to throw-distance and vice versa from Lux-measurement to candlepower.
Rephrased by Walter this comes to: Source intensity (Candlepower) = Intensity (Lux measurement at chosen distance ) / Distance x distance (in meters, of chosen point where the Lux-measurement was or will be).
- Throw is determined only by three things: Lensdiameter (or reflector diameter), surface brightness of the bare source, and the (throw-) efficiency of the lens (or reflector)
Basic formula for calculating throw:
(lenssurface divided by apparant sourcesurface (all in mm2)) x [email protected] meter (bare source) x Throw-efficiency lens (or reflector).
- Surface brightness of the source; measure the candlepower-output of the bare source first, divided by the surface-area of source. The only way to do this without much uncertainty, is to do a lux-measurement on the bare source at one meter (with a calibrated lux-meter) and determain the source size, then divide the lux-measurement by the mm2 surface of the source.
- We're talking about throw: Reflectors and lenses have two types of efficiency: Efficiency for throw and efficiency for lumens output (torchlumens).
Throw-efficiency of lenses is almost always (sometimes much..) higher than of reflectors with the same diameter. (on lumens-efficiency it's mostly the other way around !)
For throw-efficiency: A high quality lens copies the surface brightness of the source, minus the losses caused by surface reflections, absorbtions and stuff like that. So we need to know the effective transmission of the lens: Uncoated, that will be about 90%, when coated with anti-reflective coating this can be 95%.
- F-ratio of the lens (or depth of reflector) does not affect throw, it only affects total lumens output (torchlumens, wideness of the beam and sidespill).
- Within the range of aviable lenses: For all lenses with the same diameter: The focus length does absolutely not affect throw!
- For all lenses with the same diameter: Focus length does affect the amount of lumens, collimated into the beam, affecting the wideness of the beam.
So what is important about focal length: Angle of emittance that is grabbed:
Most sources emit their lumens in a wide area (for most led's about 140 degrees), so the more you cover that area with a lens or reflector, the more lumens you collimate into the main beam. But we're not talking about lumens on this thread, we're talking about throw.
- Lenses more easily give high throw: With led's, which are front-emitting ofcource, lenses are best suited as they grab the light in front of the source. Conventional reflectors are designed mostly for use with side-emitting sources and are less efficient with led's (but still work to certain extend, when you accept the lower efficiency..)
- Throw is not lumens related: A laser pointer throws far but has very poor lumens output !
When putting this to the test: Always use a stable power supply, and the same source (led or bulb). Never use batteries !
When comparing collimators on throw: Always check that the entire surface of the collimator plays along at the test-distance !
It's best to use calibrated equipment (lux-meter).
Theoretical example of calculations:
If a omnidirectional source emits 250 lumens, the lux measurement at 1 meter should give 20 lux (250 divided by 4 times pi) This is called MSCP (Mean Spherical Candle Power)
That also means, that when you know the size of the source, for example led-die 1x1mm, you can calculate the surface brightness: 1x1x20 equals 20 lux/mm2
(Although usually the source will be a unidrectional source like a high power starmounted Led. Then calculate surface brightness from Lux-measurements/mm2).
Then you simply need to know the surface of the collimator in use: For example, 30mm diameter aspherical lens.. 15x15xpi=706.85 mm2
So here we are:
- Source: 20 lux at one meter comming from a 1x1mm source size
- Effective lens surface (always 2-D, seen from a distance..): 706mm2
- Lens efficiency 90% (note that this is the efficiancy for surface brightness, not for lumens output!!)
Source has 1mm2 surface, measures 20 lux at 1 meter: Source + lens will give:
(Lenssurface divided by apparant sourcesurface) x lux @ 1 meter x lensefficiency: (706/1)x20x0.9= 12708 lux at one meter !
So there is your formula...well not quite..with the inverse square law, you now can calculate the throw:
Taking the square root from 12708 (which is the actual CP-output, as this already is at 1 meter) gives 113 meters as the distance at which 1 lux should be the measurement result.
- Another formula for throw: Take a calibrated measurement at any distance from the source, but far enough to be sure that the entire lens- or reflector-surface plays along,
and multiply that measurement with the quadratic of the distance.
- When does one know, he (or she) has enough distance for an accurate measurement:
Double the distance: according to the inverse square law, you should measure 1/4 of the measurement at half the distance.
If this doesn't apply to your results, something is wrong in the way you measure.
Most likely flaw; second measurement too close with the first measurement.
The amount of lux that is received by the object is only determined by the (apparent !!) diameter and surface brightness of the light-source (sun, torch, candle...)
When you focus at infinity, the reflector or lens is not fully lit when you look at it from close by!
This causes the spot not change much in surface brightness, when you increase the projection distance (to prevent more confusion: Here I mean the surface brightness of the projected spot)
That's what I meant when I said one could be too close to the torch for a reliable lux-measurement. That can only be done at a distance at which the entire reflector or lens plays along. And from that point further away, the lux-readings should follow the inverse square law... (note that on very long distances atmospheric conditions play along as well)
Edit 24.06.2010: My thread-starting-post was : I really would like to see a formula that predicts beam intensity and throw, and then calculated back from real life measurements corresponds (for the larger part ) to the assumptions.
I am happy with the results, I think we 've got it pretty much covered ! It sure helped me understanding light and lenses. Now will start experimenting and build me a light !