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# How to solve questions of the form "Is (*)mW at (*)nm brighter than (*)mW at (*)nm?"

#### imallett

##### New member
How to solve questions of the form "Is (*)mW at (*)nm brighter than (*)mW at (*)nm?"

Hi,

I've seen a lot of questions of the form: "Is (*)mW at (*)nm brighter than (*)mW at (*)nm?" (ex 1, 2, 3, 4, 5, 6, etc.).

The first thing to know about is the luminosity function, which basically says how bright a given wavelength looks. Unfortunately, I couldn't find a nice chart built off of it, so I made one myself:

The curved lines are the luminosity function. Each curved line represents a laser shining with the same power, and the height represents the relative brightness at each wavelength. Note the logarithmic scale, which is necessary for clarity in the short and long wavelengths.

This allows you to compare brightnesses at different wavelengths. For example, say I want to see how much brighter a common 532nm @ 5mW (green) laser is versus a somewhat-rarer 638nm @ 5mW (orange-red) laser. The power of the second laser is the same as the first, so we select the "power ⨯1" line for both (since they're in a 1:1 ratio). Then we compare the heights (relative brightnesses) of that line at the appropriate wavelengths (≈9∙10⁻¹ versus ≈2∙10⁻¹). Thus we conclude that the green laser appears 4.5⨯ brighter ( 9∙10⁻¹ / 2∙10⁻¹ = 4.5 ).

For a more complicated example, let's try a 473nm @ 20mW (cyan) laser versus a 445nm @ 5mW (blue-violet) laser. We select the power ⨯4 line (right below the ⨯5 line) for the cyan laser and the ⨯1 line for the blue-violet laser because the cyan laser is 4⨯ more powerful ( 20mW / 5mW = 4 ). We again compare the heights (relative brightnesses) (≈4∙10⁻¹ for the cyan and ≈3∙10⁻² for the blue-violet). Thus we conclude that the cyan laser appears 13⅓⨯ brighter ( 4∙10⁻¹ / 3∙10⁻² = 13⅓ ).

This chart is most-valid for lasers viewed under normal lighting (outdoor / lit indoor) conditions. If it's very dark, the curves are similar, but shifted to the left. The colors in the background are rendered assuming an sRGB monitor, with out-of-gamut colors (err, all of them; computer display technology sucks) clamped to valid colors. There are other approaches, but personally I feel like the chromaticity is best-preserved this way.

(first post here; wheeeeee)

#### lasersbee

##### Well-known member
Re: How to solve questions of the form "Is (*)mW at (*)nm brighter than (*)mW at (*)n

Your pic is 2.5 times the width of the
default 600 X 800 Pixels per screen.
If you resize your pic everyone can
see all of it and all your Text on one
screen without needing to scroll right
and left for each line of text. :beer:

Jerry

Last edited:

#### GSS

##### Well-known member
Re: How to solve questions of the form "Is (*)mW at (*)nm brighter than (*)mW at (*)n

Am I reading or not following you and the graph wrong?
Its basicly showing a red at 650nm is the same as blue at 470nm...

Last edited:

#### CurtisOliver

##### Well-known member
LPF Site Supporter
Re: How to solve questions of the form "Is (*)mW at (*)nm brighter than (*)mW at (*)n

I very much admire your effort. But luminous efficacy data looks more like this.
It is a basic plot on excel that I made.

In either scotopic or photopic conditions a 470nm and 650nm won't be of equal brightness. Either the red will overpower the blue, or vice versa depending on what condition you are basing upon.
Something looks wrong with the graph IMO.
Your peak is at 555nm so you are basing upon photopic data, yet the drop off curve is nearly identical on the blue side as it is on the red. This is inaccurate, as blue is dimmer under photopic conditions.

#### Steppenwolf

##### Banned
Re: How to solve questions of the form "Is (*)mW at (*)nm brighter than (*)mW at (*)n

Your pic is 2.5 times the width of the
default 600 X 800 Pixels per screen.
If you resize your pic everyone can
see all of it and all your Text on one
screen without needing to scroll right
and left for each line of text. :beer:

Jerry
How's this?

#### paul1598419

##### Well-known member
Re: How to solve questions of the form "Is (*)mW at (*)nm brighter than (*)mW at (*)n

I Noticed this graph is not accurate when comparing several lasers I have at known powers and their visibility in light and dark conditions.

#### steve001

##### Well-known member
Re: How to solve questions of the form "Is (*)mW at (*)nm brighter than (*)mW at (*)n

Hi,

I've seen a lot of questions of the form: "Is (*)mW at (*)nm brighter than (*)mW at (*)nm?" (ex 1, 2, 3, 4, 5, 6, etc.).

The first thing to know about is the luminosity function, which basically says how bright a given wavelength looks. Unfortunately, I couldn't find a nice chart built off of it, so I made one myself:

The curved lines are the luminosity function. Each curved line represents a laser shining with the same power, and the height represents the relative brightness at each wavelength. Note the logarithmic scale, which is necessary for clarity in the short and long wavelengths.

This allows you to compare brightnesses at different wavelengths. For example, say I want to see how much brighter a common 532nm @ 5mW (green) laser is versus a somewhat-rarer 638nm @ 5mW (orange-red) laser. The power of the second laser is the same as the first, so we select the "power ⨯1" line for both (since they're in a 1:1 ratio). Then we compare the heights (relative brightnesses) of that line at the appropriate wavelengths (≈9∙10⁻¹ versus ≈2∙10⁻¹). Thus we conclude that the green laser appears 4.5⨯ brighter ( 9∙10⁻¹ / 2∙10⁻¹ = 4.5 ).

For a more complicated example, let's try a 473nm @ 20mW (cyan) laser versus a 445nm @ 5mW (blue-violet) laser. We select the power ⨯4 line (right below the ⨯5 line) for the cyan laser and the ⨯1 line for the blue-violet laser because the cyan laser is 4⨯ more powerful ( 20mW / 5mW = 4 ). We again compare the heights (relative brightnesses) (≈4∙10⁻¹ for the cyan and ≈3∙10⁻² for the blue-violet). Thus we conclude that the cyan laser appears 13⅓⨯ brighter ( 4∙10⁻¹ / 3∙10⁻² = 13⅓ ).

This chart is most-valid for lasers viewed under normal lighting (outdoor / lit indoor) conditions. If it's very dark, the curves are similar, but shifted to the left. The colors in the background are rendered assuming an sRGB monitor, with out-of-gamut colors (err, all of them; computer display technology sucks) clamped to valid colors. There are other approaches, but personally I feel like the chromaticity is best-preserved this way.

(first post here; wheeeeee)

Are you familiar with Sam's Laser FAQ?
See this chart. https://www.repairfaq.org/sam/laserioi.htm#ioilvs

#### imallett

##### New member
Re: How to solve questions of the form "Is (*)mW at (*)nm brighter than (*)mW at (*)n

Are you familiar with Sam's Laser FAQ?
See this chart. https://www.repairfaq.org/sam/laserioi.htm#ioilvs
I've definitely encountered Sam's laser pages, though not this chart in-particular.

In either scotopic or photopic conditions a 470nm and 650nm won't be of equal brightness. Either the red will overpower the blue, or vice versa depending on what condition you are basing upon.

[...]

Your peak is at 555nm so you are basing upon photopic data, yet the drop off curve is nearly identical on the blue side as it is on the red. This is inaccurate, as blue is dimmer under photopic conditions.
I don't think this is correct; in photopic conditions e.g. 473nm and 650nm have almost exactly the same response—see e.g. the chart in Sam's laser page (0.104 vs. 0.107). The chart may look qualitatively different because of the log scale, but the numbers are actually very similar.

As I mentioned, this is based on photopic lighting conditions. (Actually, it's based on the CIE standard observer functions, not the luminosity function, though one gets the same thing.) That said, you're absolutely right that the chart isn't valid under mesopic or scotopic conditions.

I found a few variants of the scotopic function, but I don't know which is best (and I found none for mesopic). If you could please point me to these datasets, I'll make graphs for mesopic and scotopic as well!

Your pic is 2.5 times the width of the
default 600 X 800 Pixels per screen.
If you resize your pic everyone can
see all of it and all your Text on one
screen without needing to scroll right
and left for each line of text. :beer:
I made it wide so it would have a lot of detail. Should . . . should I resize it?

#### Benm

##### Well-known member
Re: How to solve questions of the form "Is (*)mW at (*)nm brighter than (*)mW at (*)n

Something seems off on that chart: Looking at it something of equal power at 450 nm should be as bright as 670 nm or around there according to the chart.

I'd practically find that say 10 mW of 450 nm looks a lot brighter than 10 mW of 670 nm. This may vary between people, but i think most people would agree when looking at two actual lasers (or their projected dots on a white surface).

This might not be your fault though, but just an error in the luminosity function that is not very accurate towards the ends of the visible spectrum.

Another issue with the dot is that the shorter wavelengths will make many targets fluoresce so appear far brighter - something like that is certainly true for near-invisible light like 405 nm that can produce a surprisingly bright dot onto a piece of paper. This has nothing to do with the luminosity function being wrong as such, but people will notice it in practical use.

#### paul1598419

##### Well-known member
Re: How to solve questions of the form "Is (*)mW at (*)nm brighter than (*)mW at (*)n

As far as 405nm goes, it depends on whether or not the paper has fluorescent material in it. I know laundry detergents use fluorescence to make otherwise stained clothing "look" cleaner. It isn't really cleaner, but does look whiter and brighter to our eyes.