[Sanjay] P.Photon questions with trouble calc energy of photon and PPFD per joule

[chubba hubba]

Hi Sanjay, et al,

I have read your 'Facts of Light' series and I must say it is excellent! But I do have a few questions for you or anyone who can help me:

1. I am comparing different 'horticultural lamps' via the system wattage (lamp + ballast) and the manufactures SPD curve. But I worry I might be comparing apples to oranges in that the SPD curves were not created with the same environment or equipment (ie. ballast, spectrometer sphere, etc). What kind of error margin should I expect? Is the comparison even valid?
   
   
   I intend to use my uni's spectrometer to get my own SPDs for the bulbs I am testing. I will also test/compare reflectors in terms of their foot-prints and efficiency using a PPFD meter. To do so I want to measure the PPFD one inch from the bulb and then again at 18" (using an avg of many PPFD plots). I will than find the PPFD difference and use that as a comparison for the true reflectance of a reflector. (Does that make sense?) I will use the most effective reflector to test the bulbs. Yet I will not be able to carry out any testing for a few months at least, hence my questions about using the manufacturer's SPD curve.
   
   
   
2. When weighting photosynthetic photons to match the absorption spectrum of my target plant (PUR) I will use the “Inada” curve, formulated with the “Quantum Yield” (QY) of my target plant. Using this method when comparing PPFD (and PAR) of different lamps should be a valid comparison without comparing the SPDs too, correct?
   
   
   
3. Is it valid to use the SPD curve Spectral Irradiance (watt/m^2/nm) to calculate PPFD of each nm if I do not know the lamp distance used when creating the SPD curve? It seems the converted PPFD values would not be of much use because I do not know the lamp testing distance.
   
   
   
4. Is there a standard distance lamp manufacturers use when creating SPD curves?
   
   
   
5. Is the term "Action Spectra of Photosynthesis" (ASP) a valid expression for 400-500 nm U 600-700 nm? (U = union)

MATH QUESTIONS (conversion from watt to photon):

I want to convert all the SPD wavelengths from watt/m^2/sec to PPFD. In order to do so I assume I need to be able to accomplish the following...?

J = joule
h = Plank's constant
nm = nano-meter (wavelength)
E = the energy held in a photon
c = speed of light in meters/second reduced using an exponent of 8
N = the number of photons needed to fill one joule, as in photons per joule

• A.) When I use the equation provided ("Facts of Light: Part I") to find the energy of a single photon at 500 nm I continually get a different solution than Sanjay. I am using a 'TI-83 Plus' Texas Instruments calculator:
  
  Equation: E = hc/nm*10^-9
  
  E = ((6.626*10^-34)(3*10^8))/(500*10^-9)
  
  My solution: E = 3.9756*10^-19 J
  
  Sanjay solution: E = 0.039756*10^-17 J
  
  
  What am I doing wrong?
  
  
  
• B.) I am also having trouble finding the number of photons per joule at 500 nm. I continually get a different solution than Sanjay:
  
  Equation: N = nm/hc
  
  N = 500/((6.626*10^-34)(3*10^8))
  
  My solution: 2.515343596*10^27 photons
  
  Sanjay solution: 25.15*10^17 photons
  
  
  
  What am I doing wrong?

Thanks for your GREAT work!

 

[sanjay]

Hi Sanjay, et al,

I have read your 'Facts of Light' series and I must say it is excellent! But I do have a few questions for you or anyone who can help me:

Thanks. I will try to answer your questions. Good to see someone actually reads my articles :splitspin

1. I am comparing different 'horticultural lamps' via the system wattage (lamp + ballast) and the manufactures SPD curve. But I worry I might be comparing apples to oranges in that the SPD curves were not created with the same environment or equipment (ie. ballast, spectrometer sphere, etc). What kind of error margin should I expect? Is the comparison even valid?

1. 
   
   Most of the manufacturer SPD curves are given in %. So they are scaled with respect to the output at one of the wavelengths. Are they all scaled wrt the same wavelength. ? If so, then yes the comparison can be made. I have no clue about what type of error margin you would expect, without knowing all the details of how the data was taken. I typically see about 5-7% variation in my data when taking multiple readings, and this is when using the same setup. So, with different equipment and different setups you may see more, say 10-15%.
   
   

   I intend to use my uni's spectrometer to get my own SPDs for the bulbs I am testing. I will also test/compare reflectors in terms of their foot-prints and efficiency using a PPFD meter. To do so I want to measure the PPFD one inch from the bulb and then again at 18" (using an avg of many PPFD plots). I will than find the PPFD difference and use that as a comparison for the true reflectance of a reflector. (Does that make sense?) I will use the most effective reflector to test the bulbs. Yet I will not be able to carry out any testing for a few months at least, hence my questions about using the manufacturer's SPD curve.

   
   You cannot measure the true reflectance as you suggest, by taking readings at 1" and then at 18". You will not get the same ratio at different points on area on which the light is falling. Under the center you will get one ratio, and say at 3 inches in x, and y from the center you will get a different ratio.
   
   

   [*] When weighting photosynthetic photons to match the absorption spectrum of my target plant (PUR) I will use the ?Inada? curve, formulated with the ?Quantum Yield? (QY) of my target plant. Using this method when comparing PPFD (and PAR) of different lamps should be a valid comparison without comparing the SPDs too, correct?

   
   No, since the "inada" curve used to calculate PUR will be weighting different photons differently, you will need the SPD curve.
   
   

   [*] Is it valid to use the SPD curve Spectral Irradiance (watt/m^2/nm) to calculate PPFD of each nm if I do not know the lamp distance used when creating the SPD curve? It seems the converted PPFD values would not be of much use because I do not know the lamp testing distance.

   
   You can do what you are suggesting here, by first taking your own readings to get the PPFD value at a known distance. Calculate the PPFD value for the normalized SPD curve from the lamp manufacturer. Then scale the SPD curve by the ratio of (your PPFD measurement/PPFD of normalized SPD), and use that to calculate the photons at each wavelength.
   
   

   [*] Is there a standard distance lamp manufacturers use when creating SPD curves?

   
   It does not matter since most of them give you a normalized SPD curve, with the highest spectral output as being 1.
   
   

   [*] Is the term "Action Spectra of Photosynthesis" (ASP) a valid expression for 400-500 nm U 600-700 nm? (U = union)

If your plant was only absorbing in that wavelength - then yes.

MATH QUESTIONS (conversion from watt to photon):

I want to convert all the SPD wavelengths from watt/m^2/sec to PPFD. In order to do so I assume I need to be able to accomplish the following...?

J = joule
h = Plank's constant
nm = nano-meter (wavelength)
E = the energy held in a photon
c = speed of light in meters/second reduced using an exponent of 8
N = the number of photons needed to fill one joule, as in photons per joule

• A.) When I use the equation provided ("Facts of Light: Part I") to find the energy of a single photon at 500 nm I continually get a different solution than Sanjay. I am using a 'TI-83 Plus' Texas Instruments calculator:
  
  Equation: E = hc/nm*10^-9
  
  E = ((6.626*10^-34)(3*10^8))/(500*10^-9)
  
  My solution: E = 3.9756*10^-19 J
  
  Sanjay solution: E = 0.039756*10^-17 J
  
  
  What am I doing wrong?

• 
  
  Nothing wrong here. Both the numbers are equal. 3.9756*10^-19=.039756*10^17
  
  

  [*] B.) I am also having trouble finding the number of photons per joule at 500 nm. I continually get a different solution than Sanjay:
  
  Equation: N = nm/hc
  
  N = 500/((6.626*10^-34)(3*10^8))
  
  My solution: 2.515343596*10^27 photons
  
  Sanjay solution: 25.15*10^17 photons
  
  What am I doing wrong?

Your units don't match up. you need to convert the 500nm to m. so use 500*10^-9

Thanks for your GREAT work!

[/Quote]

You are welcome.

sanjay.

 

[chubba hubba]

Thanks. I will try to answer your questions. Good to see someone actually reads my articles :splitspin

I can't believe that! Or I at least hope not, they are too good to miss! I have learned SO much from your work, at least I for one am very grateful. Nowhere else can one find the depth of information you presented in a very easily understandable manner, even for this laymen :birthday:

Most of the manufacturer SPD curves are given in %. So they are scaled with respect to the output at one of the wavelengths. Are they all scaled wrt the same wavelength. ? If so, then yes the comparison can be made. I have no clue about what type of error margin you would expect, without knowing all the details of how the data was taken. I typically see about 5-7% variation in my data when taking multiple readings, and this is when using the same setup. So, with different equipment and different setups you may see more, say 10-15%.

I do not fully grasp your answer, sorry. I do not understand this sentence: "Are they all scaled wrt the same wavelength. ?" Do you mean to ask if they all scaled using the same wavelength (ex. 400)? Should I call the manufactures and ask the method they used to scale the SPD curve? And by 'scaled' do you mean the % figures of the Y-axis?

You cannot measure the true reflectance as you suggest, by taking readings at 1" and then at 18". You will not get the same ratio at different points on area on which the light is falling. Under the center you will get one ratio, and say at 3 inches in x, and y from the center you will get a different ratio.

That makes sense. I have been reading your reflector series and I think I may copy most of your methods, thanks for that series too!

When weighting photosynthetic photons to match the absorption spectrum of my target plant (PUR) I will use the “Inada” curve, formulated with the “Quantum Yield” (QY) of my target plant. Using this method when comparing PPFD (and PAR) of different lamps should be a valid comparison without comparing the SPDs too, correct?

No, since the "inada" curve used to calculate PUR will be weighting different photons differently, you will need the SPD curve.

Well what I am doing is 'digitalizing' the SPD curve. I got the idea from someone else who wrote a great spreadsheet to calculate many pieces of info by converting the SPD to numbers. The spreadsheet offers the following and much more: PPFD ranges, PAR, PUR, PYF*, % total input energy which is output as PAR; PUR; PYF; 400-500 nm; 500-600 nm; 600-700 nm; 700-780 nm. Along with LER, PAR/PUR/PYF per kWh, % total PPFD which is 400-500 nm; 500-600 nm; 600-700 nm. Ratio of Red:Blue (600-700:400-500 nm), etc, etc, etc.

This is how I would manually digitalize a SPD curve. I have a spreadsheet which carries out the calculations automatically from grid box number per nm input:

1. I increase the SPDs size to 800%, then I add a grid. (MS Paint works fine for this purpose)
2. I then scale the SPD so 1 grid box = 1 nano-meter (X-axis) and 1 grid box = 1 % number** (Y-axis).
3. Then I find a grid box on the X-axis and note the vertical portion of grid box number (ex. 250) [as X].
4. Next I find the grid box at the very top of each nm and note the vertical portion of the grid box number for each nm (380-780 nm, as most SPD provide that nm range, or 400-700 nm) [as Y].
5. Then I subtract X from all Y to find the grid box height of each nm from 380-780 nm (or 400-700 nm)***
6. The solution is the amount of energy emitted per nm, listed as numbers: a 'digitalized' SPD curve.

I also have a spreadsheet page in which I use 2 nm ranges to make the digitalizing much faster, it gets tedious counting every nm (I do it in groups of 100 nm, then take break, then next 100 nm). There is about a 3-4% margin of error when using 2 nm (as compared to 1 nm).

From the digitalized SPD curve figures all the pieces of info I listed above are derived mathematically. By using the digitalized SPD curve I do not think I need to consult the manufactures SPD curve against my final numerical results when comparing lamps. Does that make sense? Or am I wrong?


* PYF = 380-780 nm using "McCree" curve and absorbance spectra of target plant to weight photons correctly.

** For example: The Y-axis scale is 100% (1-100). So the first single grid box = Y1, the next single grid box = Y2, the next single grid box = Y3, and so on...

*** When using the final figures from the spreadsheet to compare bulbs, among other peices of info, I use PUR (400-700 nm) and PYF (380-780 nm) per system watt (lamp + ballast) to compare bulbs. PUR is a bit more accurate than PYF but by using both I am 'covering my bases'...

Is it valid to use the SPD curve Spectral Irradiance (watt/m^2/nm) to calculate PPFD of each nm if I do not know the lamp distance used when creating the SPD curve? It seems the converted PPFD values would not be of much use because I do not know the lamp testing distance.

You can do what you are suggesting here, by first taking your own readings to get the PPFD value at a known distance. Calculate the PPFD value for the normalized SPD curve from the lamp manufacturer. Then scale the SPD curve by the ratio of (your PPFD measurement/PPFD of normalized SPD), and use that to calculate the photons at each wavelength.

OK. So I would need a lux meter (to calculate PPFD), or a PPFD meter to scale and compare various SPD curves? Hummm. I'd rather not spend $400-500 in the next few weeks. I am buying a quantum line senor (Li-cor) for 3D PPFD and I want a 'portable' PPFD meter from apogee too, but I can not buy either for a few months...

My goal is to compare lamps I do not have access to by evaluating their SPD curves and system wattage. Eventually I will have access to all the lamps I intend to test but not for a few months at least.

If I understand correctly you are saying in order to compare various SPD curves I need to normalize (scale) them via. the same ratio as: my PPFD measurementPFD of normalized SPD? Otherwise I can not use SPD curves to compare lamps of different manufactures?

If I take PPFD readings of a 3x3 foot-print at 18" how many plots within each quadrant (1-4) should I use? I love your method of using the reflector/lamp upside down in the darkened plastic tub, ingenious! I am basically going to copy that method when testing the lamps and reflectors I have.

Is there a standard distance lamp manufacturers use when creating SPD curves?

It does not matter since most of them give you a normalized SPD curve, with the highest spectral output as being 1.

"highest spectral output as being 1.". Would be the same as 100% scale on Y-axis? If so some SPDs I have are not normalized with a Y-axis of 100%. Some are the equivalent of 75% (3/4) on the Y-axis. Could I normalize the 75% SPDs to 100% in regards to Y-axis?

Is the term "Action Spectra of Photosynthesis" (ASP) a valid expression for 400-500 nm U 600-700 nm? (U = union)

If your plant was only absorbing in that wavelength - then yes.

Nah, they use UV-b to 780 nm or so (and maybe IR). I found this term and definition elsewhere and it sounded incorrect to me. I think the person was trying to refer to photosynthetic range of 400-700 nm but was confused.

Nothing wrong here. Both the numbers are equal. 3.9756*10^-19=.039756*10^17

Great! I do not know why I did not see that. What is the preferred format? How would I convert one to the other?

Your units don't match up. you need to convert the 500nm to m. so use 500*10^-9

OK, thanks. I should have seen that as the same conversion was needed in the previous example. Doh!

You are welcome.

sanjay.

Many thanks again!

 

[chubba hubba]

Ooops!

Typo, I should have said grid box number, not "pixel number", in all instances. Sorry.

 

[sanjay]

I do not fully grasp your answer, sorry. I do not understand this sentence: "Are they all scaled wrt the same wavelength. ?" Do you mean to ask if they all scaled using the same wavelength (ex. 400)? Should I call the manufactures and ask the method they used to scale the SPD curve? And by 'scaled' do you mean the % figures of the Y-axis?

When you look a the SPD, is the output at any one wavelength at 100%. If so they are scaled with respect to that wavelength.

Your digitizing approach is fine.

OK. So I would need a lux meter (to calculate PPFD), or a PPFD meter to scale and compare various SPD curves? Hummm. I'd rather not spend $400-500 in the next few weeks. I am buying a quantum line senor (Li-cor) for 3D PPFD and I want a 'portable' PPFD meter from apogee too, but I can not buy either for a few months...

You do not need a Lux meter for anything. All you need is a PAR meter, either the Licor or Apogee will work OK. The Licor is better. You don't need both.

My goal is to compare lamps I do not have access to by evaluating their SPD curves and system wattage. Eventually I will have access to all the lamps I intend to test but not for a few months at least.

Using the system wattage will not help much, since the actual power draw may be different with different ballasts.

If I understand correctly you are saying in order to compare various SPD curves I need to normalize (scale) them via. the same ratio as: my PPFD measurementPFD of normalized SPD? Otherwise I can not use SPD curves to compare lamps of different manufactures?

Right.

If I take PPFD readings of a 3x3 foot-print at 18" how many plots within each quadrant (1-4) should I use? I love your method of using the reflector/lamp upside down in the darkened plastic tub, ingenious! I am basically going to copy that method when testing the lamps and reflectors I have.

That is up to you. I took readings at 3" apart. So on a 3X3 area I had 169 readings.

"highest spectral output as being 1.". Would be the same as 100% scale on Y-axis? If so some SPDs I have are not normalized with a Y-axis of 100%. Some are the equivalent of 75% (3/4) on the Y-axis. Could I normalize the 75% SPDs to 100% in regards to Y-axis?

Yes you can. Its just a mater of scaling.

Great! I do not know why I did not see that. What is the preferred format? How would I convert one to the other?




OK, thanks. I should have seen that as the same conversion was needed in the previous example. Doh!

It does not matter what format you use, as long as the math is correct.

sanjay.

 

[chubba hubba]

Hi Sanjay,

Sorry I have not responeded sooner, I just noticed your post.

When you look a the SPD, is the output at any one wavelength at 100%. If so they are scaled with respect to that wavelength.

Yes and no; some do and some do not. Most SPDs are scaled with respect to different wavelengths, with the exception of a few SPDs. By the wording of your question I assume I will not be able to compare the different SPDs, is that correct?

I guess I could buy a spectrometer, that seems the only way to accomplish my goals. Can you suggest a manufacture/model of quality spectrometers? I assume the price range is around $1,000-5,000?

Using the system wattage will not help much, since the actual power draw may be different with different ballasts.

Yea that occurred to me too. I was thinking of approximating the ballast voltage and current by simply multiplying the lamp wattage by 15% (70-250w), 10% (400w) or 7% (600-1000w). I will add the solution to the lamp wattage for an approximated system wattage. I figure if I use the approximate system wattage it would provide 'ball-park' figures which can be used to get an idea of out/in (PPFD/system wattage) ratios, etc. Is that method sound?



Thanks!

 

[sanjay]

Hi Sanjay,

Sorry I have not responeded sooner, I just noticed your post.



Yes and no; some do and some do not. Most SPDs are scaled with respect to different wavelengths, with the exception of a few SPDs. By the wording of your question I assume I will not be able to compare the different SPDs, is that correct?

I guess I could buy a spectrometer, that seems the only way to accomplish my goals. Can you suggest a manufacture/model of quality spectrometers? I assume the price range is around $1,000-5,000?




Yea that occurred to me too. I was thinking of approximating the ballast voltage and current by simply multiplying the lamp wattage by 15% (70-250w), 10% (400w) or 7% (600-1000w). I will add the solution to the lamp wattage for an approximated system wattage. I figure if I use the approximate system wattage it would provide 'ball-park' figures which can be used to get an idea of out/in (PPFD/system wattage) ratios, etc. Is that method sound?



Thanks!

If you have 2 SPD's on a different scale you should scale of them, so that you bring both to the same scale and then you can compare them.

Ocean optics has a nice small usb spectroradiometer around $1000, called Red Tide.

As for the wattage, it would depend on the ballast. For example, if you look at my data - the 400W HQI lamp could draw as much as 500W for some bulbs, and the electronic ballast may only draw 428W for the same bulb. So as long as you stay within the normal magnetic ballasts 15% may be OK.

Just remember doing all this is going to increase the error in your results.

sanjay.

 

[chubba hubba]

Hi Sanjay,

I hope you are well!

Many of the SPDs I have can not be scaled (different wavelengths) and they were created using different ballasts, reflectors and distances I assume. Making my own SPDs seems wise.

I think I will test lamps with a few different refelctor/ballast (digital and magnetic) combos. I need to review your methods again...

Thanks for the suggestion for the spectrometer. However, I would like to purchase a higher quality/resolution spectrometer. I am looking at Ocean Optics 4000 series, the 6500 series might be a little out of my price range.

I do not want to spend more then about 10-13k, it seems less than 8 or 9k does not provide what I need. If I bought a vanilla 6500 series spectrometer I would spent around 12k. However, I can spend about 9k by purchasing the 'bio-reflectance' kit with the HR-4000 UV/NIS spectrometer. The HR-4000 has a signal-to-noise ratio of 300:1, I understand it would be best if it was below 300, correct?

I will be testing high irradiance HID lamps and I also want to create an action spectra for a few higher plants. I will also be testing in the UV-b range and up, so I am looking at the 'UV' options of the 4000 series along with the UV booster.

I think the 4000 series can do what I need it to, high resolution, accurate qualitative/quantitative testing. But I am not sure exaclty what I need...

I am currently leaning toward the HR-4000 (High Resolution): http://www.oceanoptics.com/products/hr4000.asp

I am interested in the pre-configured model HR-4000-CG (UV-NIR), http://www.oceanoptics.com/products/hr4000cg.asp , mostly because I don't know what components to add to the vanilla HR-4000. I assume the sales person will be able to guide me, a bit of hand holding.

I was reading about the "Bio-reflectance" kit, it seems like it would offer everything I want: SPDs and making action spectra curves. What do you think? I want to see if OO can swap the HR-4000 UV for the USB-4000 UV/VIS in the pre-configured "Bioreflectance" SpectraKit:
http://www.oceanoptics.com/Products/SpectraKit Bio reflectance.pdf

"Bio-reflectance" kit:
Combine UV-VIS spectroscopy with a portable light source and sampling optics to measure reflectance and reflected color of biological samples in the field or at the laboratory, in real time. The BioReflectance SpectraKit has all the tools you?ll need to perform a variety of field reflectance applications, including chlorophyll analysis in crops, UV reflectance of birds and insects, and monitoring of color and reflectance of fruits and vegetables as a function of ripening.

Do you think I will need a 'integrating sphere'?: http://www.oceanoptics.com/products/fois.asp


Thanks!