NEW TOOL: Calculate Relative Brightness (of Wavelengths in nm)

rhd said:

That's cool -

I have much more detailed CIE data in there though - so it would be ideal if I could figure out the Rayleigh math to add to the equation, and it would be a pretty darn good comparison tool.

If nobody remembers that thread off hand, I'll re-do the research this weekend, and add it to the tool.

I'm off for the evening.

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That will be awesome, Good Work bud.

We should make a sticky for all these type of programs and have em all in one thread.

rhd said:

Rayleigh Scattering needs to be taken into account.

And if someone could help me figure out where that PHENOMENAL post I read 3 months ago is (the one where the Rayleigh Scattering math was basically stepped through, perhaps for the first time on this forum?), I am anxious to include it in this tool

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I believe this is the thread. But the equations came from wiki I believe.

http://laserpointerforums.com/f44/200mw-red-equivalent-how-much-green-53813.html

Thanks qumefox!

I've added Raleigh functions to the tool now. I actually gave everyone the option of choosing whether to compare the dot, or the beam. Defaults to the beam.

I just added three new features:

• You can enter ? in the mw rating, and the calculator will figure out an equivalent automatically.
• The comparison being made gets dynamically integrated into the page's title.
• The page auto-detects whether it's being queried by the LPF forum software, and uses a shortened titled for auto-naming URL posts to this board.

So for example, normally (for browsers, or google indexing, etc) the titled of the following page is:
"Relative Laser Beam Brightness Calculator: (532nm 75mw) vs. (650nm 300mw)"

But when people paste the URLs here in threads, the calculator will "cut to the chase" and show the LPF forum software a simplified page title to use in naming the URL, as demonstrated now:
Beam: (532nm 75mw) vs. (650nm 300mw)

(and if you were comparing dots not beams, the title would reflect that too)

Neat eh? No need to clutter things up with needless explanation or promotion of the tool's function here on this board. This should make it simpler for people to link directly to comparisons The page just auto-detects when the LPF IP is querying it for the page title

rhd said:

- Do we perceive 2 lumens as twice as bright as 1 lumen?

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No, we don't. Power a 60W lamp (850lm for 120V) and a 100W lamp (1700lm for 120V). The 100W lamp is brighter, but not twice as bright.

You're close - just take the square root of that "X-times brighter" value you have to get a better approximation of perceived brightness. And brightness is brightness, so it should apply for both dot and beam.

Cyparagon: I'm hitting a conceptual roadblock now.

My tool:
Beam: (635nm 200mw) vs. (532nm 23.82mw)
comes to the same conclusion about beam equivalents that they reached here (to the decimal point):
http://laserpointerforums.com/f44/200mw-red-equivalent-how-much-green-53813.html#post758774
And naturally. Not through any manipulation or tweaking on my end.

In the thread, they used values from Chroma as the starting point, and then applied the raleigh factor of x^4.08 to each wavelength, to get a relative weighting, which they applied back to the Chroma response values. So it looked like this for them:

(ChromaResponse(A) x mW(A) x RaleighFactor) / ChromaResponse(B) = mW(B)

My formula is identical, except that instead of Chrome Response values, I have a CIE table, that was probably generated with Chroma (or MatLab) originally anyway.

So I'm left thinking - this doesn't really account for your comment re brightness doubling. IE, my tool (and the formula they agreed on in that thread) would claim that 200mW of 650nm is roughly twice the brightness (with Raleigh considered) of 45mw of 635nm:
Beam: (650nm 200mw) vs. (635nm 45mw)

If we accept that, then we run into a problem when we solve for an unknown (equivalent) power of 635mW:
Beam: (650nm 200mw) vs. (635nm 89.66mw)

We end up with the result of 89.7mW (basically 90mW, or double)

The formula I'm using very well could be flawed - I'm not challenging your point here. But if it is, then the formula in that previous thread is flawed too, and maybe we need to investigate the science here to gain a more precise / grounded understanding of how different mW of power impacts our brightness perception. As far as I can tell, all the formulas so far have considered brightness based on mW rating to be linear.

And brightness is brightness, so it should apply for both dot and beam.

Click to expand...

But the brightness of the beam depends almost entirely on Rayleigh- and maybe Mie-scattering,
whereas the brightness of the dot depends totally on the target material/color.
One should maybe assume a white canvas, for the sake of uniformity.

@rhd:
Are these numbers for photopic or scotopic vision?
I'm guessing photopic ("normal" light conditions)...
Great little tool, by the way.... Once it gets accurate.:eg:

I suppose you've already been here:
http://en.wikipedia.org/wiki/Mie_theory#Comparison_with_Rayleigh_scattering
http://en.wikipedia.org/wiki/Rayleigh_scattering


Basically, I think it's almost impossible to accurately determine the brightness of the BEAM
without considering the size of the particles on the air.
Which will never be the same twice.
So all you can hope for is a good aproximation.

Hey guys,

To date, my tool has been using CIE data tabulated here:
https://spreadsheets.google.com/pub?key=rD0zIkgz3u1N28U9kPpl_hg

But as this tool sees more use (it's been getting a chunk of traffic recently), I've wanted to strengthen its accuracy and provide a better cited justification for the readings.

Specifically:

1) I'm not entirely comfortable having used CIE data from a google spreadsheet, the owner of which I can't verify. I'm sure that I was referred to that spreadsheet by a reputable source, but at this point, I can't remember who that source was, and the spreadsheet itself attributes ownership to "Ben Steigerwald" (unknown to me). So first order of business, I'd like to import a new dataset from a verifiable source.

2) I'd like to add data for scotopic (night) vision as well as the current photopic (day) vision, and give users that ability to choose between the two.

So my primary question - does anyone know of a good source of tabulated data, at fairly small intervals (at least one measurement per nm) for both scotopic and photopic perceived brightness?

rhd said:

And if someone could help me figure out where that PHENOMENAL post I read 3 months ago is (the one where the Rayleigh Scattering math was basically stepped through, perhaps for the first time on this forum?), I am anxious to include it in this tool

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Glad you liked it!

qumefox said:

But the equations came from wiki I believe.

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Heavens, NO! I did make fun of Wikipedia in that post (as well as crazy Google, which at that time was actually ranking wiki pages #1 above legit science sites for many searches, a source of humor & frustration for ppl in my field). The actual reference sources for the revised formula are in my post.

rhd said:

So it looked like this for them:

(ChromaResponse(A) x mW(A) x RaleighFactor) / ChromaResponse(B) = mW(B)

...then we run into a problem when we solve for an unknown (equivalent) power of 635mW:...

The formula I'm using very well could be flawed...

Click to expand...

qumefox's chroma #'s posted in that thread were expressed in relation to a reference wavelength (532nm). So the #'s in my post were expressed in a compatible fashion - the difference in Rayleigh scattering between a given wavelength & the reference wavelength.

Basically, I was using the wavelength-dependent air refractivity corrected formula to calculate the difference in actual beam intensity due to Rayleigh scattering, then incorporating this adjustment into qumefox's chroma values!

So the overall formula I was using was -

Equiv. 532 mW = ChromaAdjust(A,532) * (Rayleigh(A)/Rayleigh(532)) * mW(A)

or, more generally -

Equiv. (B)mW = ChromaAdjust(A,B) * (Rayleigh(A)/Rayleigh(B)) * mW(A)

OK, I think I see a possible problem with your calcs...

rhd said:

and then applied the raleigh factor of x^4.08 to each wavelength

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Remember that the Rayleigh scattering is inversely proportional to the wavelength raised to the 4.08th power, so the Rayleigh value should actually be -

Rayleigh(x) = 1 / (x^4.08)

So, to use your example - solve for equivalent 635nm to 200mw of 650nm, would be -

(Rayleigh(A)/Rayleigh(B)) =

(3.3366719075051241814878134320136e-12 / 3.6701448151112527400749236163961e-12) =

0.90913903281606068532692511225047

(as you can see, due to how close together these two wavelengths are, the Rayleigh scattering difference is not much!)

We don't have a chroma difference between these two wavelengths ATM, but can perhaps extrapolate one from two of the values qumefox already provided...

24.185/49.053 = 0.49303814241738527714920596089944

(which also seems to correspond fairly closely to that table of yours )

Plug this all together, and we get...

0.90913903281606068532692511225047 * 0.49303814241738527714920596089944 * 200 =
89.648043987753767046385272418596

So, 89.65mW of 635nm is equivalent visual beam brightness to 200mW of 650nm!

(Actually, not very far off from the # you came up with!)

Rayleigh scattering has a much greater impact when there is greater difference in wavelengths, and is one of the reasons why a 445 beam looks so much better than a 670nm of the same power, even though the eye's photopic sensitivity is about the same for both!

Note also that the formula was meant to calculate equivalent brightness, i.e. - how many mW of one color laser will look the same brightness as say, 200mW from an LOC. It was NOT meant to compare subjective differences is brightness!

If you start talking about "subjective" values (i.e. - looks twice as bright), you also need to take eye's brightness response curve into account.

So the formula does not say that 200mW of 650nm will look twice as bright as 45mW of 635nm - any more than claiming that 200mW from an LOC should automatically look twice as bright as 100mW! (It does not!)

It can take 4x to 8x increase in actual intensity (depending on conditions) in order to appear twice as bright to the eye - there's some good info on this topic on CPF.

rhd, will answer your latest questions in a follow-up post - as this one is getting somewhat long, and I need to find something for you!

A few months ago I could have posted chroma's 635nm numbers when at work but that will have to wait until I get home.. I've switched this machine at work from windows to ubuntu, and I don't really have time right this second to see if the matlab installer and chroma will work under wine.

I have chroma running on my machine, is it possible to export datasets for both photopic and scotopic brightness from the program?

Nope. That wasn't what chroma was designed to do. Chroma is primarily an application for color mixing. It just also happens to allow you compare relative brightness (of the dot) between different wavelengths as well, I imagine using the photopic curve.

Thanks for the +rep, anselm!

rhd said:

Hey guys,

To date, my tool has been using CIE data tabulated here:
https://spreadsheets.google.com/pub?key=rD0zIkgz3u1N28U9kPpl_hg

But as this tool sees more use (it's been getting a chunk of traffic recently), I've wanted to strengthen its accuracy and provide a better cited justification for the readings.

Specifically:

1) I'm not entirely comfortable having used CIE data from a google spreadsheet, the owner of which I can't verify.

Click to expand...

I took a look at that Google table - those fractional wavelength values have got to be driving you crazy! :banghead:

rhd said:

I'd like to add data for scotopic (night) vision as well as the current photopic (day) vision, and give users that ability to choose between the two.

Click to expand...

On the photopic vs scotopic topic, you may find this graph -



and the following post helpful -

http://laserpointerforums.com/f45/nichia-ship-green-diode-laser-53028.html#post758789

Let's start with photopic. The photopic curve is somewhat of a moving target - there are at least 3 issues that I am aware of that contribute to this...

1) Photopic is actually the combination of 3 separate response curves, one for each of the 3 types of cones in the eye. (To make things even more interesting, the brain also "weighs" the signals from each type differently ).

2) The photopic curve actually CHANGES, depending on what part of the eye you are talking about! The very center of the fovea (0.35 degrees field of view) is completely lacking in "S" cones. As a result, a wide field of view (10 degrees) is more sensitive to blue and violet than a narrow (2 degrees) one.

(The photopic curve in the graph above is for a wide field of view, as this is how I figured a laser beam to be typically viewed by an observer.)

3) As a result of genetics research, at least 10 genetic variants of the "L" and "M: cone photopigments have now been discovered, each with it's own spectral response curve!

So, unless you are going to have an input field for the users to submit their DNA profile... :banghead:

For photopic, as you already have Chroma, what I would suggest doing is this -

1) Play-around with Chroma, and find-out what wavelength it considers to be at the top of the curve (around 555nm, or perhaps around 545nm). Where they place the peak will also tell us how modern the photopic curve they are using is.

2) Assign the peak a value of "1", and then use Chroma to compare that wavelength to others, using the resulting data to build your new table! To make it easy, you can start with 5 or 10nm increments, then fill-in the other values as you have time.

OK, let's look at scotopic - this one's a bit easier, as you only have 1 curve to deal with!

Because the graph above uses log scaling (in order to fit photopic & scotopic on the same graph), the scotopic curve above looks rounded, the curve is actually somewhat steep. For pure scotopic, you may find the following graph more useful -



along with the extra information in the following post (which also covers some of the photopic stuff) -

http://laserpointerforums.com/f45/nichia-ship-green-diode-laser-53028-2.html#post760365

There is one glitch with the scotopic curve where lasers are concerned, however - it is rather unlikely for a person to view a typical laser beam using scotopic vision!

In fact, I can't remember EVER viewing a laser beam with scotopic vision!

Here's a big hint...if you can even vaguely tell what color the laser beam is, then you are not seeing it with scotopic vision!

What you are using when you view a laser beam under subdued or nighttime conditions (but can still tell what color it is), is mixed-mode vision (both rods & cones active).

In this case, the response curve is the combination of both the photopic and scotopic curves! The relative ratio of each will depend on how active each visual system is - the darker it is, the more it will shift away from photopic and towards scotopic.

Also, due to the much greater sensitivity of the rods vs the cones, once it gets dark enough for the rods to start kicking-in, you will see a definite shift in the peak response towards blue, due to the rod sensitivity peaking at ~505nm.

Let me know if you have any questions.

seoguy said:

There is one glitch with the scotopic curve where lasers are concerned, however - it is rather unlikely for a person to view a typical laser beam using scotopic vision!

In fact, I can't remember EVER viewing a laser beam with scotopic vision!

Here's a big hint...if you can even vaguely tell what color the laser beam is, then you are not seeing it with scotopic vision!

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THANK YOU!

I have been defending this same perspective in multiple PMs for the last two months. I've been arguing that this isn't as simple as "day vs night" vision, but everyone has been so set on the notion that both vision types need their own curve in this tool, that I was almost convinced myself.

The reality is that S vs P vision isn't about day or night, it's largely about light intensity. A visible laser beam is going to be high intensity light, even in dark environments.

ok but for this tool it says that a 500mw violet laser would be only as bright as A 0.36 Mw GREEN. is this accurate? i mean i have a 30-50mw violet and its maybe 1/5 as bright as my 5mw green... 500mw blue is only a 16mw green dot..?

jedisaber said:

ok but for this tool it says that a 500mw violet laser would be only as bright as A 0.36 Mw GREEN. is this accurate? i mean i have a 30-50mw violet and its maybe 1/5 as bright as my 5mw green... 500mw blue is only a 16mw green dot..?

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500mW of "blue"......? How very specific of you

In all seriousness, the violet comparison is pretty tough to interpret meaningfully, because 405 is right on the edge of our vision and the visibility figures gets incredibly small.