Converting from Lux to Irradiance? (halp)
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Re: Converting from Lux to Irradiance? (halp)
I read some of the first page, and skimmed over the last page. Am I right that this thread is about giving a scorpion laser eye beams?

GrehnSkipjack  Maintankadonor
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Re: Converting from Lux to Irradiance? (halp)
GrehnSkipjack wrote:I read some of the first page, and skimmed over the last page. Am I right that this thread is about giving a scorpion laser eye beams?
Shh. The government is listening.
mew wrote:Isotropic.
Yeah, that's a really bad assumption. A point source emitter would be isotropic (meaning that light was emitted equally in all directions). But any real source doesn't do that. If you're far away from the source, and it's very small, it might be close enough and the approximation would be pretty good.
For example, if you took a standard light bulb and put your detector a few cm away from it, it would be a bad approximation. Put your detector 5 meters away and it's probably not bad, 10 meters away and it's a reasonably good approximation.
Your LED has a very small "active region" where the light is being created, right at the center of the clear plastic casing. If the plastic casing were spherical, then it'd be a decent approximation. But as you can see from the diagrams, it's more like a cylinder with a spherical lenslike structure at the end.
There's a reason they design LED cases like that, by the way  it points more of the light in the forward direction, which makes it look brighter. Unfortunately, it also means that the beam dynamics aren't isotropic. It acts more like a Gaussian beam, which is a bit harder to model. It won't be described perfectly by a Gaussian, but I'd still expect the onaxis intensity to decrease in a similar fashion. If you try and model it, try and fit it to:
I = Io / (1+(z/a)^2)
where z is the distance from the LED and a is a free parameter you'll have to fit (it describes the focused spot size for a Gaussian beam, but since your case is a little different you won't be able to easily predict it analytically). Io is the intensity at z=0.
Just for the record, dispersion isn't the word you're looking for, it means something different (variation of index of refraction with wavelength). The way the light behaves after leaving the LED would be called diffraction or propagation.
"Theck, Bringer of Numbers and Pounding Headaches," courtesy of GrehnSkipjack.
MATLAB 5.x, Simcraft 6.x, Call to Arms 6.0, Talent Spec & Glyph Guide 5.x, Blog: Sacred Duty
MATLAB 5.x, Simcraft 6.x, Call to Arms 6.0, Talent Spec & Glyph Guide 5.x, Blog: Sacred Duty

theckhd  Moderator
 Posts: 7801
 Joined: Thu Jul 31, 2008 3:06 pm
 Location: Harrisburg, PA
Re: Converting from Lux to Irradiance? (halp)
So what is variable a? Also, is there any way to take in to account the LED angle that was given to me?theckhd wrote:Your LED has a very small "active region" where the light is being created, right at the center of the clear plastic casing. If the plastic casing were spherical, then it'd be a decent approximation. But as you can see from the diagrams, it's more like a cylinder with a spherical lenslike structure at the end.
There's a reason they design LED cases like that, by the way  it points more of the light in the forward direction, which makes it look brighter. Unfortunately, it also means that the beam dynamics aren't isotropic. It acts more like a Gaussian beam, which is a bit harder to model. It won't be described perfectly by a Gaussian, but I'd still expect the onaxis intensity to decrease in a similar fashion. If you try and model it, try and fit it to:
I = Io / (1+(z/a)^2)
where z is the distance from the LED and a is a free parameter you'll have to fit (it describes the focused spot size for a Gaussian beam, but since your case is a little different you won't be able to easily predict it analytically). Io is the intensity at z=0.

mew  Posts: 1903
 Joined: Sat Sep 27, 2008 5:42 pm
 Location: US
Re: Converting from Lux to Irradiance? (halp)
So what I did was use the power meter in the guy's lab to take measurements of intensity v distance, and then voltage v intensity (at distance=0). I graphed the intensity v distance and it forms a pretty good exponential decay function, so I was just going to use the function excel spit out to me to estimate the intensity at 7V (max) for my 17cm distance. And then use the linear voltage v intensity graph equation (again spit out by excel) to determine the needed voltage for my desired intensity at this 17cm distance.
The power meter readings follow the same pattern as the lux meter readings but the values are really off. For now (I want to get my intensities and start collecting data ASAP) I am not going to worry about comparing the lux meter to the power meter but I will do that in the future.
Edit: Ugggh, problems. So what I am getting is that a 1V change is giving me over a 100 uW/cm^2 change in intensity. This can't be right, can it? I'm going to ignore the actual intensity for now and just go with getting the proper voltages for relative intensities based on the previous intensity for 525nm light I was using in the pilot study.
I think that if I can figure out that equation you posted I can get more accurate actual intensity values.
The power meter readings follow the same pattern as the lux meter readings but the values are really off. For now (I want to get my intensities and start collecting data ASAP) I am not going to worry about comparing the lux meter to the power meter but I will do that in the future.
Edit: Ugggh, problems. So what I am getting is that a 1V change is giving me over a 100 uW/cm^2 change in intensity. This can't be right, can it? I'm going to ignore the actual intensity for now and just go with getting the proper voltages for relative intensities based on the previous intensity for 525nm light I was using in the pilot study.
I think that if I can figure out that equation you posted I can get more accurate actual intensity values.

mew  Posts: 1903
 Joined: Sat Sep 27, 2008 5:42 pm
 Location: US
Re: Converting from Lux to Irradiance? (halp)
mew wrote:So what is variable a? Also, is there any way to take in to account the LED angle that was given to me?
Like I said, "a" is a parameter that describes the "focused size" of the Gaussian beam. You could roughly estimate it based on the divergence angle you were given, but it's not likely to be very accurate since you don't have an actual Gaussian beam. You have something that may look a lot like a Gaussian beam in the far field, but the near field characteristics will be very different. Luckily you don't care about the nearfield stuff so much, but since that's where "a" is defined, it makes it hard to measure "a" directly. Hence why you'd just fit it (for example based on your exponential decay curve  speaking of which, is it actually exponential, or does it fit well to a 1/(1+z^2) or 1/z^2 form?).
mew wrote:So what I did was use the power meter in the guy's lab to take measurements of intensity v distance, and then voltage v intensity (at distance=0). I graphed the intensity v distance and it forms a pretty good exponential decay function, so I was just going to use the function excel spit out to me to estimate the intensity at 7V (max) for my 17cm distance. And then use the linear voltage v intensity graph equation (again spit out by excel) to determine the needed voltage for my desired intensity at this 17cm distance.
This is exactly what I would have done, assuming you're measuring voltage with the lux meter.
mew wrote:The power meter readings follow the same pattern as the lux meter readings but the values are really off. For now (I want to get my intensities and start collecting data ASAP) I am not going to worry about comparing the lux meter to the power meter but I will do that in the future.
What do you mean by "really off?" The lux meter readings should decay exponentially as well, since it's just an intensity measurement at heart. If you could provide the excel spreadsheet or some example data points, maybe I could tell you if the numbers are on the right order of magnitude.
mew wrote:Edit: Ugggh, problems. So what I am getting is that a 1V change is giving me over a 100 uW/cm^2 change in intensity. This can't be right, can it? I'm going to ignore the actual intensity for now and just go with getting the proper voltages for relative intensities based on the previous intensity for 525nm light I was using in the pilot study.
I think that if I can figure out that equation you posted I can get more accurate actual intensity values.
It could definitely be right. Ballpark estimate: Assume the detector has a responsivity of 1 A/W and an active area of 1 cm^2. If it's loaded with a 10k resistor, you'd expect the following voltage output:
Vout = 100 uW/cm^2 * 1 A/W * 10 kOhm * 1 cm^2 = 1 Volt.
10k would be an unusually high terminating impedance, but it depends on how the device is built and how you're reading it out. Plus your detector is likely not Silicon, so the responsivity will probably be a little lower, and your detector is probably not a full square centimeter. But again, it all depends on how the power meter is constructed. If you have a model number or company I can try and look it up.
"Theck, Bringer of Numbers and Pounding Headaches," courtesy of GrehnSkipjack.
MATLAB 5.x, Simcraft 6.x, Call to Arms 6.0, Talent Spec & Glyph Guide 5.x, Blog: Sacred Duty
MATLAB 5.x, Simcraft 6.x, Call to Arms 6.0, Talent Spec & Glyph Guide 5.x, Blog: Sacred Duty

theckhd  Moderator
 Posts: 7801
 Joined: Thu Jul 31, 2008 3:06 pm
 Location: Harrisburg, PA
Re: Converting from Lux to Irradiance? (halp)
I haven't had time to graph the lux meter data yet but I did one to test and it did seem to follow the same exponential decay pattern (I think I converted to uW/cm^2 first). But the converted values were (rough estimate from memory) around 1/5 (if not less) the uW/cm^2 values from the power meter.
I think if I keep messing with the graphs (the distance as well as the voltage relationships) I might be able to find some sort of transformation to use on the lux data to make it in line with the power meter data. But I am going to have to find time to do that.
Here is my data file. I haven't converted the lux values yet but it has some graphs from the power meter.
https://docs.google.com/leaf?id=0B9l7mP ... OGRm&hl=en
I was finding, using the decay equations based on the distance graphs, that the uW/cm^2 at 6.7in away ranged from 6 to 42 (depending on the LED). And then I would have to use the power per voltage equations. I think I may have been doing something mathematically wrong here, but the linear power per voltage equations were (as I mentioned before) coming out to like y=150x (where x=voltage and y=power).
I was trying to plug in the power estimates at 6.7in to figure out what voltage they would be, but now that I think about it that doesn't make any sense (so I think here is where I was doing something wrong). I think what I need to be doing is scaling down the equation and reworking it so that the max intensities are what I calculated using the decay equations; and this should change the slope from the trippledigit values I was getting (this should be simple algebra?).
My brain is kind of frazzled right now So to avoid confusing myself I will probably leave at at that for now (I have quite a bit of stuff to do in the next 2 hours so I don't have much time at this moment).
I think if I keep messing with the graphs (the distance as well as the voltage relationships) I might be able to find some sort of transformation to use on the lux data to make it in line with the power meter data. But I am going to have to find time to do that.
Here is my data file. I haven't converted the lux values yet but it has some graphs from the power meter.
https://docs.google.com/leaf?id=0B9l7mP ... OGRm&hl=en
I was finding, using the decay equations based on the distance graphs, that the uW/cm^2 at 6.7in away ranged from 6 to 42 (depending on the LED). And then I would have to use the power per voltage equations. I think I may have been doing something mathematically wrong here, but the linear power per voltage equations were (as I mentioned before) coming out to like y=150x (where x=voltage and y=power).
I was trying to plug in the power estimates at 6.7in to figure out what voltage they would be, but now that I think about it that doesn't make any sense (so I think here is where I was doing something wrong). I think what I need to be doing is scaling down the equation and reworking it so that the max intensities are what I calculated using the decay equations; and this should change the slope from the trippledigit values I was getting (this should be simple algebra?).
My brain is kind of frazzled right now So to avoid confusing myself I will probably leave at at that for now (I have quite a bit of stuff to do in the next 2 hours so I don't have much time at this moment).

mew  Posts: 1903
 Joined: Sat Sep 27, 2008 5:42 pm
 Location: US
Re: Converting from Lux to Irradiance? (halp)
Ok, a few notes:
1) Looking at the graphs, it's clear I was right about the decay. It's not exponential, it's a distance squared. I.e. rather than y=a*exp(z), you should try fitting it to y=a/z^2. You can't do this easily in excel  the closest you can get is to fit it as a "power" type trendline, which gives you something like y=a*z^(1.9). Alternatively, you could plot P vs 1/(distance^2), which should give you a nice linear relationship. Those trendlines not only looks like a better fit (the R^2 value goes up to around 0.99 for either method, as compared to 0.95 for the exponential fit), but it also fits the theoretical prediction I gave earlier. The beam diameter is expanding almost linearly with distance, so the intensity should drop off as 1/(distance)^2.
2) Looking at the lux data itself, there are some obvious problems with your experiment.
You have multiple "300 lux" entries for each wavelength, which means you're pegging the meter. That makes that data useless, since it could be 300, 400, 500, or eleventy billion. This means that the lux meter is a little too sensitive to give you useful data the way you're using it. Don't worry though, I'll have a suggestion to fix this later on.
The entire data set for 565 nm is junk. The power meter didn't register anything, and the lux meter measurements are very low compared to the rest of the data sets as well. This means that something went wrong  either the LED wasn't pointed at the detectors properly (i.e. misaligned), the detectors malfunctioned simultaneously (unlikely), or something was blocking the beam path. Either way, you'd need to retake that data.
3) I'm not sure what's going on with the rest of the spreadsheet. Columns AE make perfect sense. In column F, you're calculating "uW/cm^2 from lux," but the formula is referencing column D (power meter measurements) rather than E (lux meter measurements). I also don't completely understand what the column header for G means  it says "p(uW/cm^2)@7V," but it's just another scaled version of column D. I'm assuming you meant for this column to be the intensity (uW/cm^2 is an intensity, not a power), since it's taking a mW measurement, multiplying by 1000 (to get uW), and dividing by 0.75 (which I'm assuming is your detector area in cm^2). However, that doesn't explain what the "@7V" means. I'm guessing that you meant for this column to be the one where you took the P & V data from the second worksheet to make the lux>intensity conversion?
In any event, you essentially have 3 different versions of column D, which all tell you the same thing. That's not terribly helpful. Luckily, I think I can tell you exactly what you want to do to simplify this whole process and get the data you want quickly.
Solution: What you really want is a quick way to convert the lux meter data to intensity at each different wavelength. I.e., you want one number that says "at wavelength X, I multiply lux by Y to get intensity."
It's clear that varying the distance isn't the way to do this  the lux meter pegs (or saturates) when it's too close to the LED, so you can't get accurate measurements with it at close range. On the other hand, the power meter starts losing sensitivity at large distances. This is a problem of dynamic range  both meters are designed to operate at slightly different light levels, so there's only a small region of overlap where they both work well.
So here's what you need to do.
NOTE: If the power meter has a "range" setting that you can adjust, you just need to set it to a lower range and you can do this without the ND filter (mentioned below). It's just needed to make the operational ranges of the two detectors overlap. If you can give me the manufacturer and model of the power meter, I can look it up and let you know if the meter's capable of this. I'm assuming for the rest of this post that you're stuck with the current range.
What you'll need:
A way to adjust the power of the LED source directly, like a variable voltage supply. I forget if you mentioned you had this capability or not. If you do, you're all set; if not, it should be relatively easy to obtain  at worst I can tell you how to build a very simple voltage divider circuit.
Something called a neutral density filter or "ND filter." There's a good chance that the person supplying the power meter has one of these (or many of them) in his lab. If not, you can pick them up for under $30 at a local camera store, online (amazon, buy.com, b&h photo), or maybe even at a store like Best Buy (check their digital camera and/or video department, these are commonly used for taking outdoor photo/video).
You want to cut the transmission by at least half, if not more. Anything between 10% and 25% transmission will work for you, which means something between ND8 and ND4. Note that most of these are advertised a little unintuitively. For example, this one says "Neutral density 0.9," which is an ND8. You can see from the Wikipedia article that 0.9 is what's called the optical density. Most will probably be advertised by their optical density rather than by an "NDx" type spec, so you'd ideally want to look for something between 0.6 and 0.9.
Procedure:
1) Set the system up like you did for the power meter measurements, with the meter a few inches away from the LED (probably 3 inches at most). You want to have a substantial reading on the power meter, preferably more than 1 mW. Write down the power (P1), keeping as many significant figures as the meter gives you.
2) Put the ND filter in between the meter and the LED at normal incidence. You can mount this however you like, as long as it's stable. Write down the measured power (P1'). Now you have a transmission coefficient for the ND filter (T=P1'/P1). This should be pretty close to whatever it's specced for, but now you'll know for sure.
3) Now I want you to remove the power meter and put the lux meter in its place. Make sure it's exactly the same distance away from the LED that the power meter was (at least as accurately as you can). The ND filter should still be in  if you have to take it out to measure the distance that's fine, just don't forget to put it back in place. Write down the lux measurement (L1).
4) Use the LED controls to change the intensity of the LED (i.e., change the supply voltage so it's dimmer or brighter). Take another Lux measurement (L2).
5) Replace the lux meter with the power meter (again keeping the distance the same) and take out the ND filter. Take a power measurement (P2).
6) Replace the power meter with the lux meter, and put the ND filter back in.
7) Repeat steps 46 for a bunch of different intensities. Try and cover the whole range of the lux meter if you can, so that you have measurements every 2550 lux between 0 and 300. This will give you a complete mapping of the detector response.
8) Find the active area of the detector. In your spreadsheet, you used 0.75 cm^2 for this. I'm not sure where you got that value  it seems a bit large, but it could be perfectly reasonable. I have no way of knowing without you telling me the make and model of the detector. Either way, write down the area in cm^2 (A).
9) In Excel, plot P*T/A vs L (i.e. [L1, L2, L3, ...] on the xaxis and [P1*T/A, P2*T/A, P3*T/A, ...] on the yaxis). This should hopefully look very linear and have a yintercept that's close to 0 (if it isn't we have to deal with a few more complications which I'll ignore for the moment). Fit this with a linear trendline, and write down the slope (M1). This slope is your conversion from lux to intensity. If you measure 200 lux, then you have 200*M1 mW/cm^2 at the given wavelength (feel free to bake a factor of 1000 into M1 if you want the output in uW/cm^2).
Intermission: You could repeat this whole process for every wavelength of LED you have. That might take a while though, and while it would be more accurate, you would probably find that the detector response curve is essentially the same shape at each wavelength but have a slightly different value of M1. Instead, we're going to assume this is true, and take a shortcut.
10) Back in the lab, replace your LED with one of the other ones. Take a power measurement (without the ND filter in place) and a lux measurement (with the ND filter in place) the same way you did before. Write down the power and lux values (P_lambda and L_lambda). If your original data was perfectly linear, then M_lambda is just P_lambda*T/(A*L_lambda). If it wasn't completely linear, then we'll have to do a little more math, which I can describe later if that's the case.
11) Repeat step 10 for each LED you have. Now you should have a slope M_lambda for each wavelength (i.e. M_395, M_440, etc). So any time you take a measurement with your lux meter, you know that the intensity is I = M_lambda*L.
Note that none of this relies at all on the formal definition of the photometric unit of lux. Why? Well, you're already having problems with the values coming out wrong, which means either you're making a mistake in the math or the detector itself isn't reacting the way it should. But you don't actually care whether the lux meter is calibrated properly or not, you just want the intensity of your light source. So rather than spend a lot of time trying to figure out whether the error is in the lux meter, the conversion math, or who knows what else, you may as well just calibrate the system with the known good detector (the power meter).
It wouldn't even matter if the lux meter had units on it, to be honest. You could do the same thing with a photodiode and a voltmeter, even if you didn't know the responsivity of the photodiode. As long as you know it puts out X volts when the power meter gives you Y mW, you can figure out how to convert Volts to Intensity empirically with the method outlined above.
1) Looking at the graphs, it's clear I was right about the decay. It's not exponential, it's a distance squared. I.e. rather than y=a*exp(z), you should try fitting it to y=a/z^2. You can't do this easily in excel  the closest you can get is to fit it as a "power" type trendline, which gives you something like y=a*z^(1.9). Alternatively, you could plot P vs 1/(distance^2), which should give you a nice linear relationship. Those trendlines not only looks like a better fit (the R^2 value goes up to around 0.99 for either method, as compared to 0.95 for the exponential fit), but it also fits the theoretical prediction I gave earlier. The beam diameter is expanding almost linearly with distance, so the intensity should drop off as 1/(distance)^2.
2) Looking at the lux data itself, there are some obvious problems with your experiment.
You have multiple "300 lux" entries for each wavelength, which means you're pegging the meter. That makes that data useless, since it could be 300, 400, 500, or eleventy billion. This means that the lux meter is a little too sensitive to give you useful data the way you're using it. Don't worry though, I'll have a suggestion to fix this later on.
The entire data set for 565 nm is junk. The power meter didn't register anything, and the lux meter measurements are very low compared to the rest of the data sets as well. This means that something went wrong  either the LED wasn't pointed at the detectors properly (i.e. misaligned), the detectors malfunctioned simultaneously (unlikely), or something was blocking the beam path. Either way, you'd need to retake that data.
3) I'm not sure what's going on with the rest of the spreadsheet. Columns AE make perfect sense. In column F, you're calculating "uW/cm^2 from lux," but the formula is referencing column D (power meter measurements) rather than E (lux meter measurements). I also don't completely understand what the column header for G means  it says "p(uW/cm^2)@7V," but it's just another scaled version of column D. I'm assuming you meant for this column to be the intensity (uW/cm^2 is an intensity, not a power), since it's taking a mW measurement, multiplying by 1000 (to get uW), and dividing by 0.75 (which I'm assuming is your detector area in cm^2). However, that doesn't explain what the "@7V" means. I'm guessing that you meant for this column to be the one where you took the P & V data from the second worksheet to make the lux>intensity conversion?
In any event, you essentially have 3 different versions of column D, which all tell you the same thing. That's not terribly helpful. Luckily, I think I can tell you exactly what you want to do to simplify this whole process and get the data you want quickly.
Solution: What you really want is a quick way to convert the lux meter data to intensity at each different wavelength. I.e., you want one number that says "at wavelength X, I multiply lux by Y to get intensity."
It's clear that varying the distance isn't the way to do this  the lux meter pegs (or saturates) when it's too close to the LED, so you can't get accurate measurements with it at close range. On the other hand, the power meter starts losing sensitivity at large distances. This is a problem of dynamic range  both meters are designed to operate at slightly different light levels, so there's only a small region of overlap where they both work well.
So here's what you need to do.
NOTE: If the power meter has a "range" setting that you can adjust, you just need to set it to a lower range and you can do this without the ND filter (mentioned below). It's just needed to make the operational ranges of the two detectors overlap. If you can give me the manufacturer and model of the power meter, I can look it up and let you know if the meter's capable of this. I'm assuming for the rest of this post that you're stuck with the current range.
What you'll need:
A way to adjust the power of the LED source directly, like a variable voltage supply. I forget if you mentioned you had this capability or not. If you do, you're all set; if not, it should be relatively easy to obtain  at worst I can tell you how to build a very simple voltage divider circuit.
Something called a neutral density filter or "ND filter." There's a good chance that the person supplying the power meter has one of these (or many of them) in his lab. If not, you can pick them up for under $30 at a local camera store, online (amazon, buy.com, b&h photo), or maybe even at a store like Best Buy (check their digital camera and/or video department, these are commonly used for taking outdoor photo/video).
You want to cut the transmission by at least half, if not more. Anything between 10% and 25% transmission will work for you, which means something between ND8 and ND4. Note that most of these are advertised a little unintuitively. For example, this one says "Neutral density 0.9," which is an ND8. You can see from the Wikipedia article that 0.9 is what's called the optical density. Most will probably be advertised by their optical density rather than by an "NDx" type spec, so you'd ideally want to look for something between 0.6 and 0.9.
Procedure:
1) Set the system up like you did for the power meter measurements, with the meter a few inches away from the LED (probably 3 inches at most). You want to have a substantial reading on the power meter, preferably more than 1 mW. Write down the power (P1), keeping as many significant figures as the meter gives you.
2) Put the ND filter in between the meter and the LED at normal incidence. You can mount this however you like, as long as it's stable. Write down the measured power (P1'). Now you have a transmission coefficient for the ND filter (T=P1'/P1). This should be pretty close to whatever it's specced for, but now you'll know for sure.
3) Now I want you to remove the power meter and put the lux meter in its place. Make sure it's exactly the same distance away from the LED that the power meter was (at least as accurately as you can). The ND filter should still be in  if you have to take it out to measure the distance that's fine, just don't forget to put it back in place. Write down the lux measurement (L1).
4) Use the LED controls to change the intensity of the LED (i.e., change the supply voltage so it's dimmer or brighter). Take another Lux measurement (L2).
5) Replace the lux meter with the power meter (again keeping the distance the same) and take out the ND filter. Take a power measurement (P2).
6) Replace the power meter with the lux meter, and put the ND filter back in.
7) Repeat steps 46 for a bunch of different intensities. Try and cover the whole range of the lux meter if you can, so that you have measurements every 2550 lux between 0 and 300. This will give you a complete mapping of the detector response.
8) Find the active area of the detector. In your spreadsheet, you used 0.75 cm^2 for this. I'm not sure where you got that value  it seems a bit large, but it could be perfectly reasonable. I have no way of knowing without you telling me the make and model of the detector. Either way, write down the area in cm^2 (A).
9) In Excel, plot P*T/A vs L (i.e. [L1, L2, L3, ...] on the xaxis and [P1*T/A, P2*T/A, P3*T/A, ...] on the yaxis). This should hopefully look very linear and have a yintercept that's close to 0 (if it isn't we have to deal with a few more complications which I'll ignore for the moment). Fit this with a linear trendline, and write down the slope (M1). This slope is your conversion from lux to intensity. If you measure 200 lux, then you have 200*M1 mW/cm^2 at the given wavelength (feel free to bake a factor of 1000 into M1 if you want the output in uW/cm^2).
Intermission: You could repeat this whole process for every wavelength of LED you have. That might take a while though, and while it would be more accurate, you would probably find that the detector response curve is essentially the same shape at each wavelength but have a slightly different value of M1. Instead, we're going to assume this is true, and take a shortcut.
10) Back in the lab, replace your LED with one of the other ones. Take a power measurement (without the ND filter in place) and a lux measurement (with the ND filter in place) the same way you did before. Write down the power and lux values (P_lambda and L_lambda). If your original data was perfectly linear, then M_lambda is just P_lambda*T/(A*L_lambda). If it wasn't completely linear, then we'll have to do a little more math, which I can describe later if that's the case.
11) Repeat step 10 for each LED you have. Now you should have a slope M_lambda for each wavelength (i.e. M_395, M_440, etc). So any time you take a measurement with your lux meter, you know that the intensity is I = M_lambda*L.
Note that none of this relies at all on the formal definition of the photometric unit of lux. Why? Well, you're already having problems with the values coming out wrong, which means either you're making a mistake in the math or the detector itself isn't reacting the way it should. But you don't actually care whether the lux meter is calibrated properly or not, you just want the intensity of your light source. So rather than spend a lot of time trying to figure out whether the error is in the lux meter, the conversion math, or who knows what else, you may as well just calibrate the system with the known good detector (the power meter).
It wouldn't even matter if the lux meter had units on it, to be honest. You could do the same thing with a photodiode and a voltmeter, even if you didn't know the responsivity of the photodiode. As long as you know it puts out X volts when the power meter gives you Y mW, you can figure out how to convert Volts to Intensity empirically with the method outlined above.
"Theck, Bringer of Numbers and Pounding Headaches," courtesy of GrehnSkipjack.
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Re: Converting from Lux to Irradiance? (halp)
I hope you don't mind if I respond to this in multiple posts (it will keep me from overwhelming myself)theckhd wrote:Ok, a few notes:
1) Looking at the graphs, it's clear I was right about the decay. It's not exponential, it's a distance squared. I.e. rather than y=a*exp(z), you should try fitting it to y=a/z^2. You can't do this easily in excel  the closest you can get is to fit it as a "power" type trendline, which gives you something like y=a*z^(1.9). Alternatively, you could plot P vs 1/(distance^2), which should give you a nice linear relationship. Those trendlines not only looks like a better fit (the R^2 value goes up to around 0.99 for either method, as compared to 0.95 for the exponential fit), but it also fits the theoretical prediction I gave earlier. The beam diameter is expanding almost linearly with distance, so the intensity should drop off as 1/(distance)^2.
2) Looking at the lux data itself, there are some obvious problems with your experiment.
You have multiple "300 lux" entries for each wavelength, which means you're pegging the meter. That makes that data useless, since it could be 300, 400, 500, or eleventy billion. This means that the lux meter is a little too sensitive to give you useful data the way you're using it. Don't worry though, I'll have a suggestion to fix this later on.
The entire data set for 565 nm is junk. The power meter didn't register anything, and the lux meter measurements are very low compared to the rest of the data sets as well. This means that something went wrong  either the LED wasn't pointed at the detectors properly (i.e. misaligned), the detectors malfunctioned simultaneously (unlikely), or something was blocking the beam path. Either way, you'd need to retake that data.
3) I'm not sure what's going on with the rest of the spreadsheet. Columns AE make perfect sense. In column F, you're calculating "uW/cm^2 from lux," but the formula is referencing column D (power meter measurements) rather than E (lux meter measurements). I also don't completely understand what the column header for G means  it says "p(uW/cm^2)@7V," but it's just another scaled version of column D. I'm assuming you meant for this column to be the intensity (uW/cm^2 is an intensity, not a power), since it's taking a mW measurement, multiplying by 1000 (to get uW), and dividing by 0.75 (which I'm assuming is your detector area in cm^2). However, that doesn't explain what the "@7V" means. I'm guessing that you meant for this column to be the one where you took the P & V data from the second worksheet to make the lux>intensity conversion?
3)I'm sorry about that, I was in a hurry to just post it and I didn't clean it up. What I meant by "p" in that column was from the power meter, it was more just my sloppy notation for my own sake. I did not notice that I did the lux to uW/cm^2 conversion using the wrong column though. The @7V is just my note to myself that those measurements were taken at 7Volts (the max voltage) for the LED circuits.
I did try to plug that data in for the 7V in the intensity per voltage tables, but since I took it separately I only used/analyzed the 7V measurements that went along well with the rest of the voltage measurements. I was just being lazy and didn't think to redo the 7V measurements (I think I redid one to test and make sure it was about right and that one was).
2)The 300 lux I just filled in to see what it would look like, it meant that the reading was (as you noticed) >300 lux, so off the chart.
Yeah, it sucks about the 565. I know the power meter readings were poop but I was hoping to be able to salvage the lux meter readings (although it would be a bit pointless since the values would be so low, it probably couldn't even get up to the intensity that I would need from the other LEDs). I just found and ordered a nondiffused version online, so hopefully that one should be detectable by the equipment; basically the problem was that the only 565nm LED I could find was diffused, I ended up (today) having to order a nondiffused one from Japan or something like that (I didn't expect the diffusion would have that much of an impact).
1)Woooooo, that is going to take some time and concentration. Let me go through the rest of this post and I will come back to it.

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Re: Converting from Lux to Irradiance? (halp)
Don't worry too much about the trendlines for the distance data. It's enough to know that a 1/z^2 fit is correct. If you're not going to be changing the distance between LED and scorpion in your experiment, it doesn't matter anyway.
As far as the detailed experimental procedure, it looks like a lot, but the data collection should be rather quick. At most an hour or two, I'd expect. It's mostly just a lot of swapping meters in and out.
As far as the detailed experimental procedure, it looks like a lot, but the data collection should be rather quick. At most an hour or two, I'd expect. It's mostly just a lot of swapping meters in and out.
"Theck, Bringer of Numbers and Pounding Headaches," courtesy of GrehnSkipjack.
MATLAB 5.x, Simcraft 6.x, Call to Arms 6.0, Talent Spec & Glyph Guide 5.x, Blog: Sacred Duty
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theckhd  Moderator
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Re: Converting from Lux to Irradiance? (halp)
I can dial the voltages of my lightstheckhd wrote:Procedure:
1) Set the system up like you did for the power meter measurements, with the meter a few inches away from the LED (probably 3 inches at most). You want to have a substantial reading on the power meter, preferably more than 1 mW. Write down the power (P1), keeping as many significant figures as the meter gives you.
2) Put the ND filter in between the meter and the LED at normal incidence. You can mount this however you like, as long as it's stable. Write down the measured power (P1'). Now you have a transmission coefficient for the ND filter (T=P1'/P1). This should be pretty close to whatever it's specced for, but now you'll know for sure.
3) Now I want you to remove the power meter and put the lux meter in its place. Make sure it's exactly the same distance away from the LED that the power meter was (at least as accurately as you can). The ND filter should still be in  if you have to take it out to measure the distance that's fine, just don't forget to put it back in place. Write down the lux measurement (L1).
4) Use the LED controls to change the intensity of the LED (i.e., change the supply voltage so it's dimmer or brighter). Take another Lux measurement (L2).
5) Replace the lux meter with the power meter (again keeping the distance the same) and take out the ND filter. Take a power measurement (P2).
6) Replace the power meter with the lux meter, and put the ND filter back in.
7) Repeat steps 46 for a bunch of different intensities. Try and cover the whole range of the lux meter if you can, so that you have measurements every 2550 lux between 0 and 300. This will give you a complete mapping of the detector response.
Find the active area of the detector. In your spreadsheet, you used 0.75 cm^2 for this. I'm not sure where you got that value  it seems a bit large, but it could be perfectly reasonable. I have no way of knowing without you telling me the make and model of the detector. Either way, write down the area in cm^2 (A).
9) In Excel, plot P*T/A vs L (i.e. [L1, L2, L3, ...] on the xaxis and [P1*T/A, P2*T/A, P3*T/A, ...] on the yaxis). This should hopefully look very linear and have a yintercept that's close to 0 (if it isn't we have to deal with a few more complications which I'll ignore for the moment). Fit this with a linear trendline, and write down the slope (M1). This slope is your conversion from lux to intensity. If you measure 200 lux, then you have 200*M1 mW/cm^2 at the given wavelength (feel free to bake a factor of 1000 into M1 if you want the output in uW/cm^2).
Intermission: You could repeat this whole process for every wavelength of LED you have. That might take a while though, and while it would be more accurate, you would probably find that the detector response curve is essentially the same shape at each wavelength but have a slightly different value of M1. Instead, we're going to assume this is true, and take a shortcut.
10) Back in the lab, replace your LED with one of the other ones. Take a power measurement (without the ND filter in place) and a lux measurement (with the ND filter in place) the same way you did before. Write down the power and lux values (P_lambda and L_lambda). If your original data was perfectly linear, then M_lambda is just P_lambda*T/(A*L_lambda). If it wasn't completely linear, then we'll have to do a little more math, which I can describe later if that's the case.
11) Repeat step 10 for each LED you have. Now you should have a slope M_lambda for each wavelength (i.e. M_395, M_440, etc). So any time you take a measurement with your lux meter, you know that the intensity is I = M_lambda*L.
Note that none of this relies at all on the formal definition of the photometric unit of lux. Why? Well, you're already having problems with the values coming out wrong, which means either you're making a mistake in the math or the detector itself isn't reacting the way it should. But you don't actually care whether the lux meter is calibrated properly or not, you just want the intensity of your light source. So rather than spend a lot of time trying to figure out whether the error is in the lux meter, the conversion math, or who knows what else, you may as well just calibrate the system with the known good detector (the power meter).
It wouldn't even matter if the lux meter had units on it, to be honest. You could do the same thing with a photodiode and a voltmeter, even if you didn't know the responsivity of the photodiode. As long as you know it puts out X volts when the power meter gives you Y mW, you can figure out how to convert Volts to Intensity empirically with the method outlined above.
The .75cm^2 is the area of the detector of the power meter.
That setup you described is pretty much exactly what I did with the distance measurements in the lab. A slightly confusing part is what the physics guy labeled as 1 inch from the meter might have been more like 0 inches from the meter. So I was messing with calculations using both 1 and 0 as the initial measurements to see which worked better (I think for the most part I was assuming it was 0 inches despite the potential inaccuracy it was still consistent with itself in that I took all the closest measurements from that point).
Another thing is that most of the LEDs didn't even read above 1mW at the closest distance from the power meter's detector.
So are you saying that (I thought this before but was being lazy, I had been in the guy's lab for like 3 hours already) I should focus on that small distance where both the power meter and the lux meter were detecting the light (it wasn't too high on the lux meter nor was it too low on the power meter)? I don't know if anything .04mW or below on the power meter was accurate, in the darkness it was reading between 0 and .03 mW.
I already took power per voltage measurements, I can do lux per voltage for all lights as well. I have the lux meter in my lab available to use at any time, but the power meter needs to be borrowed so I only did those measurements before.
A few weeks ago I took lux per voltage measurements for two of the LEDs to make sure the meter was working linearly and it was, so that's good (just have to repeat it for all lights).

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Re: Converting from Lux to Irradiance? (halp)
mew wrote:I can dial the voltages of my lights
Ok, that makes that part easy.
mew wrote:The .75cm^2 is the area of the detector of the power meter.
Works for me, as long as you're sure it's right. It's probably from the manual, so it's at least "close enough" for your purposes.
mew wrote:That setup you described is pretty much exactly what I did with the distance measurements in the lab. A slightly confusing part is what the physics guy labeled as 1 inch from the meter might have been more like 0 inches from the meter. So I was messing with calculations using both 1 and 0 as the initial measurements to see which worked better (I think for the most part I was assuming it was 0 inches despite the potential inaccuracy it was still consistent with itself in that I took all the closest measurements from that point).
I'm a little confused here. The difference between 0" and 1" is fairly noticeable. As in, 0" would be the LED smacked up against the input port of the detector, whereas 1" would be, well, about an inch away. I could see experimental uncertainty of 1/4" or so at most, even if done by eye. Really though you should have some means of actually measuring the distance between the LED's surface and the detector's input port.
Unless: maybe the detector is housed in such a fashion that there's space between the detector surface and the input port of the housing. Again, this is something that I can't help you with unless I know what model of detector it is. Next time you get a chance to use it, write it down just in case.
mew wrote:Another thing is that most of the LEDs didn't even read above 1mW at the closest distance from the power meter's detector.
So are you saying that (I thought this before but was being lazy, I had been in the guy's lab for like 3 hours already) I should focus on that small distance where both the power meter and the lux meter were detecting the light (it wasn't too high on the lux meter nor was it too low on the power meter)? I don't know if anything .04mW or below on the power meter was accurate, in the darkness it was reading between 0 and .03 mW.
For these measurements, yes. You want to know how the lux meter responds to the intensity of light. If it's linear, it makes everything a lot easier, because you can just use a single scale factor (M_lambda) to do the conversion. If it's highly nonlinear, then you need to know the whole response curve. But to take those measurements, you need both detectors to be giving you accurate values. If the intensity is so weak that one detector is just spitting out noise, or so high that it's pegged, the data won't help you. That's why I suggested the ND filter  it lets you measure higher intensities with the lux meter, because it reduces the amount of light reaching it. However...
mew wrote:I already took power per voltage measurements, I can do lux per voltage for all lights as well. I have the lux meter in my lab available to use at any time, but the power meter needs to be borrowed so I only did those measurements before.
A few weeks ago I took lux per voltage measurements for two of the LEDs to make sure the meter was working linearly and it was, so that's good (just have to repeat it for all lights).
1) If you've already determined that the lux meter is linear in intensity, then you don't need to retake much of the data. If you're sure the LED output is linear in voltage (which it probably should be), then your lux vs. voltage data confirms the lux meter is OK. As long as your data shows that the response curve goes through zero (i.e. the linear fit tells you that at 0 mW of optical power you should get 0 lux), you can probably get away with just taking a single power measurement and a single lux measurement for each wavelength to get your scale factors.
2) The problem with comparing the Power vs. Voltage measurements to newly taken Lux vs. Voltage measurements is that you want to make sure the experimental conditions were identical in both. In other words, if you took the P vs. V data with a 3" separation between LED and power meter, and then took Lux vs. V data with a 4" separation, the conversion factor you come up with will be wrong. To make it right, you'd have to scale appropriately for the extra distance, and since that's at best a rough parameter fit, it might be inaccurate.
That's why I suggested the procedure I did. You want to have data with as many of the other parameters fixed as possible, so that you get a clean comparison of the two things you're interested in. In this case, that means taking power and lux measurements:
with the same LED, in the same circuit
at the same distance for both detectors
in the same transverse spot (i.e. centered on the same optical axis)
in the same lab conditions (room, placement, and even at roughly the same time)
A lot of this may sound unnecessary, but it can actually be important. Taking data in a different room, or even at different times of day in the same room, can make a difference. For example, the room's temperature likely fluctuates with time of day. Which means every resistor in the voltage supply circuit changes slightly, as does the circuitry in each detector, and potentially the emission of the LED itself. Obviously a different room, especially in another building with a different climate control system, suffers the same problems. It's probably a small effect, but you never know  in my current experiment, a change of as much as 12 degrees makes my data essentially meaningless because of thermal expansion of the optical mounts.
For your situation, the more likely thing you'll encounter is pointing error. The LED's output is not the same intensity at all points, it's probably stronger in the center ("onaxis" or "on the optical axis of the system") than it is on the sides ("offaxis" or "displaced in the transverse dimension"). Basically like a flashlight  more light hits the object when you point the flashlight at it than when you point it off to the side. For short distances this might not make a big difference, but even as much as a couple of inches puts you into the regime where it can and will matter. By keeping the rest of the setup stationary and swapping detectors back and forth (and most importantly making sure the detector is centered on the same point every time you do so), you eliminate that as a potential error source.
"Theck, Bringer of Numbers and Pounding Headaches," courtesy of GrehnSkipjack.
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Re: Converting from Lux to Irradiance? (halp)
http://www.cvimellesgriot.com/Products/ ... ystem.aspx
That makes sense, that's pretty much what I did in his lab. I'll have to contact him again to see when I could come in to use his device some more (my lab is a lot warmer than his was).
The detectors are like holes in the devices, I had the LEDs in a clamp so I would scoot the clamp as close as I could to the detector head (the power meter's is what was limiting me on this step so that closest distance is the one I used for both). I didn't stick the LEDs inside the holes but rather directly in front of them (they may have been going inside the holes a little bit but were not pressed up against the detector itself).
I didn't record it exactly but it is somewhere between 0 and .5 inches I'll just have to go back in to his lab and replicate it to find out.
That makes sense, that's pretty much what I did in his lab. I'll have to contact him again to see when I could come in to use his device some more (my lab is a lot warmer than his was).
The detectors are like holes in the devices, I had the LEDs in a clamp so I would scoot the clamp as close as I could to the detector head (the power meter's is what was limiting me on this step so that closest distance is the one I used for both). I didn't stick the LEDs inside the holes but rather directly in front of them (they may have been going inside the holes a little bit but were not pressed up against the detector itself).
I didn't record it exactly but it is somewhere between 0 and .5 inches I'll just have to go back in to his lab and replicate it to find out.

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Re: Converting from Lux to Irradiance? (halp)
OK, that answers a lot of questions I had then. For one thing, I wouldn't trust any measurements below around 0.05 mW. The Noise Equivalent Power, a figure of merit that describes the noise level of the device, is only 10 uW. That's why you were seeing measurements of 0.010.03 mW with the LED off. You might have better luck if you're taking data in the dark, but either way you probably want to work at higher powers just to be safe. This probably means picking up an ND filter somewhere so that your lux meter can handle those measurements.
As far as the setup, I'd reccomend making sure that you have at least ~1 inch of space between the LED and the "face" of the detector. This can be sort of arbitrary as long as you're consistent  i.e. if you want to measure from the tip of the LED to the tip of the detector head, that's fine. They don't have a detailed autocad diagram of the head, but from the picture and the fact that it's a thermopile, it's probably not recessed very much.
As far as the setup, I'd reccomend making sure that you have at least ~1 inch of space between the LED and the "face" of the detector. This can be sort of arbitrary as long as you're consistent  i.e. if you want to measure from the tip of the LED to the tip of the detector head, that's fine. They don't have a detailed autocad diagram of the head, but from the picture and the fact that it's a thermopile, it's probably not recessed very much.
"Theck, Bringer of Numbers and Pounding Headaches," courtesy of GrehnSkipjack.
MATLAB 5.x, Simcraft 6.x, Call to Arms 6.0, Talent Spec & Glyph Guide 5.x, Blog: Sacred Duty
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Re: Converting from Lux to Irradiance? (halp)
So I should be getting the last of those power measurements later this week and that should be pretty easy to do the calculations for.
I am still a bit confused about how to estimate my intensity at __ distance. You said because the points fit the equation as a function of distance squared but how exactly do I get it in to that form?
I am still a bit confused about how to estimate my intensity at __ distance. You said because the points fit the equation as a function of distance squared but how exactly do I get it in to that form?

mew  Posts: 1903
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Re: Converting from Lux to Irradiance? (halp)
If you're limited to excel, the easiest way is this:
1) Take your data of intensity (I) and distance (d) (or use your old data)
2) make a column that's x=1/d^2
3) Plot I vs. x
The formula for the dropoff of Intensity should be something like I = a+b/(d^2) = a+b*x. So fit this with a linear trendline. That will let you predict the intensity dropoff with distance. This formula will work for all of the LEDs, but the parameters will be a little different. If you want a quick and dirty fit that works for all of them, just assume a=0 and let b=I1*d1^2, where I1 and d1 are the intensity and distance values from one of your measurements with that LED.
1) Take your data of intensity (I) and distance (d) (or use your old data)
2) make a column that's x=1/d^2
3) Plot I vs. x
The formula for the dropoff of Intensity should be something like I = a+b/(d^2) = a+b*x. So fit this with a linear trendline. That will let you predict the intensity dropoff with distance. This formula will work for all of the LEDs, but the parameters will be a little different. If you want a quick and dirty fit that works for all of them, just assume a=0 and let b=I1*d1^2, where I1 and d1 are the intensity and distance values from one of your measurements with that LED.
"Theck, Bringer of Numbers and Pounding Headaches," courtesy of GrehnSkipjack.
MATLAB 5.x, Simcraft 6.x, Call to Arms 6.0, Talent Spec & Glyph Guide 5.x, Blog: Sacred Duty
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