# Laser Brightness Calculator

Created by Luciano Miño
Reviewed by Steven Wooding
Based on research by
Andrew Stockman; Herbert Jägle; Markus Pirzer; Lindsay T. Sharpe The dependence of luminous efficiency on chromatic adaptation Journal of Vision (December 2008)
Last updated: Jun 05, 2023

The laser brightness calculator can help you find the brightness (radiance) and compare two different lasers to see which one is the brightest.

We will briefly explain:

• What a laser is;
• How to obtain its brightness or laser radiance;
• How laser brightness is measured;
• How the human eye perceives brightness according to the luminous efficacy; and
• Many other concepts related to laser brightness.

## How do our eyes perceive color?

As we know, light travels as a wave. One of the properties of a wave is its wavelength or distance between two peaks. Like sunlight, most light sources are not made up of a single wavelength. Instead, they are composed of a range of wavelengths.

Our eyes react to these wavelengths differently to produce the colors inside the brain. In doing so, each wavelength will induce our eyes to see a different color. For example, we will see the color red when a source is emitting light with a ~700 nm wavelength.

The range in which the human eye reacts to these wavelengths to produce an image is the visible spectrum, and it ranges from 400 nm to 700 nm.

🙋 Are you already familiar with these concepts? If so, feel free to start using the laser brightness calculator or jump to the "Laser radiance" section to find how each method used in this tool works.

## What is a laser?

Laser is an acronym for light amplification by the stimulated emission of radiation. A laser has three key differences from any ordinary light source. The light it emits is:

• Monochromatic: Instead of a range of wavelengths or frequencies, laser light is made up of only one frequency;
• Directional: The photons] travel in the same direction within a narrow beam; and
• Coherent: The waves travel in phase with each other (see our phase shift calculator).

## Stimulated emission and lasers

When a ground-level state electron in an atom absorbs a photon, it moves up to a higher energy level within the atom. After a short time (decay time), the electron emits a photon with an energy equal to the difference between the two energy levels $\Delta E$ and falls again back to the original level. Read more about this in our Bohr model calculator.

Sometimes, these electrons can be found in what is called a metastable state, which, in simple words, is a level where the electron takes longer to decay back to the ground state. Again, when doing so, the electron will emit a photon with a $\Delta E$ energy.

If a photon with that same energy (difference between metastable and ground state) were to interact with an electron from a metastable state, it would stimulate the decay of the electron. This process is called stimulated emission.

Why is it important? Because this emitted photon not only has the same energy as the one that stimulated its emission, but it also has the same direction and is in phase with it.

## How does a laser work?

Lasers work by producing stimulated emission of photons with electrons in metastable states. If this effect occurs within a cavity where several electrons are confined, a cascade effect is produced, significantly increasing the number of photons in the closed space. These photons then go through a partially reflective mirror producing the laser beam.

The mirrors are used to further amplify the stimulated emission (turning the cavity into a resonator), and one is partially reflective to allow photons to create the laser beam.

Gaussian beams are lasers with an intensity distribution in the direction perpendicular to beam propagation described by a Gaussian function (as in our normal distribution calculator).

## How is laser brightness measured? Laser radiance definition and formula

There are several definitions for laser brightness, and each is used in different contexts. In this calculator, we use laser radiance.

Radiance ($L$), also called brightness, measures the amount of power emitted by a surface per unit area per solid angle. It tells us how much of the radiation emitted by an object will be received by an optical system looking at it at a specific angle.

For a Gaussian beam with wavelength $\lambda$, we can write radiance as:

$L = \frac{P}{\omega_{0}^{2}\pi^{2} \theta^{2}}$

where:

• $P$ – Laser's power;
• $w_{0}$ – Beam radius or beam waist at the focus point; and
• $\theta$ – Divergence angle.

This equation can be simplified with the relation:

$\theta = \frac{\lambda}{\pi \omega_{0}}$

Resulting in:

$L = \frac{P}{\lambda^{2}}$

This is the formula used in our laser brightness calculator, and, as you can see, it doesn't depend on the distance from the source or solid angle. It characterizes the beam in its entirety.

## How to compare laser brightness

Even though the formula for laser radiance is straightforward, there is a slight inconvenience when trying to compare laser brightness: our eyes see some colors brighter than others.

The luminous efficiency function describes the perceived intensity for each wavelength, and we can use a chart to account for this variation when comparing different lasers (or just use the "compare laser brightness" method within this laser brightness calculator 😉):

Photopic conversion table based on the CIE photopic luminous efficiency function for a short range of wavelengths. Source (full table):

λ(nm)

Photopic conversion (lm/W)

...

...

500

0.348354

505

0.427760

510

0.520497

515

0.620626

520

0.718089

525

0.794645

530

0.857580

535

0.907135

540

0.954468

545

0.981411

550

0.989023

555

0.999461

...

...

If you want to manually compare laser brightness as we do with this laser relative brightness calculator, you need to take two things into account:

• Laser dot brightness; and
• Laser beam brightness, which is produced by Rayleigh scattering.

### Laser dot brightness

Comparing laser dot brightness is pretty straightforward. It's the amount of light in lumens (lm) the laser emits directly in front of its aperture (looking directly into a laser is extremely dangerous, don't do it).

To calculate it, we multiply each laser's power (in watts) by their respective photopic conversion value $ph_{\lambda}$ according to any luminous efficiency function (such as the one used in the table above) and then find the ratio between each result.

$L_{\lambda} = P \cdot ph_{\lambda}$

For example, with two 100 mW laser, with λ=530 and λ=555 respectively:

${\footnotesize L_{530} = 0.1 \cdot 0.85758 = 0.085758\ \text{lm}} \\ {\footnotesize L_{555} = 0.1 \cdot 0.99461 = 0.099461\ \text{lm}}$

Then the ratio becomes:

$\frac{L_{530}}{L_{555}} ≅0.86$

By rearranging this ratio, we find that the 555 nm dot is ∼1.17 times brighter than the 530 nm laser dot.

### Laser beam brightness – How does Rayleigh scattering affect laser brightness?

A visible laser beam is the product of the laser light interacting with the air molecules and being scattered by Rayleigh scattering.

The scattered radiation's intensity is inversely proportional to the fourth power of the wavelength times the initial light's intensity that produces the effect:

$I \propto I_{0} \cdot \frac{1}{\lambda^{4}}$

If we're comparing lasers at exact atmospheric and light conditions and equal models (except maybe in power), we can work around this proportionality by replacing it with a scalar $c$.

Let's call each laser's initial intensity $I_{01}$ and $I_{02}$ respectively. And $I_{1}$ and $I_{2}$ the intensities of the resulting beams.

$I_{1} = I_{01} \cdot \frac{c}{\lambda_{1}^{4}}$
$I_{2} = I_{02} \cdot \frac{c}{\lambda_{2}^{4}}$

Now, if we try to find the ratio between them:

$\frac{I_{1}}{I_{2}} = \frac{I_{01}}{I_{02}} \cdot \frac{c}{c} \cdot \frac{\lambda_{2}^{4}}{\lambda_{1}^{4}} \\$
$\frac{I_{1}}{I_{2}} = \frac{I_{01}}{I_{02}} \cdot \frac{\lambda_{2}^{4}}{\lambda_{1}^{4}}$

As you can see, the proportionality factor is removed entirely (another proof that math is, indeed, witchcraft).

Then, since the intensity is just power transmitted per unit area, and we are dealing with equal laser devices, we can cancel out the areas and leave only each laser's power:

$\frac{P_{1}}{P_{2}} = \frac{P_{01}}{P_{02}} \cdot \frac{\lambda_{2}^{4}}{\lambda_{1}^{4}}$

And if we finally multiply each power by their respective wavelength's photopic conversion value, we can insert the laser dot brightness that we used previously:

$\frac{L_{1}}{L_{2}} = \frac{L_{01}}{L_{02}} \cdot \frac{\lambda_{2}^{4}}{\lambda_{1}^{4}}$

where $L_{01}$ and $L_{02}$ are each laser's dot brightness. This result is the ratio between the beam brightness of two lasers.

## How to use the laser brightness calculator/laser relative brightness calculator

As we said, this calculator functions as a:

• Laser brightness calculator; and as a
• Laser relative brightness calculator.

The calculation is different for each method to take into account different factors such as Rayleigh scattering and brightness definition.

### To use as laser brightness calculator:

1. Select the 'calculate radiance' method.
3. Input the laser's wavelength.
4. The output is your laser's radiance or power transmitted per unit area per solid angle.

### To use as relative brightness calculator or compare laser brightness:

1. Select the 'compare laser brightness' method
2. Input any laser's power and wavelength (between 400-700 nm).
3. Input the other laser's power and wavelength.
4. The output text will describe the ratio between each laser's dot and beam brightness.

If you want to learn more about lasers, check the FAQ ❔ section for some interesting topics.

💡 Congrats! You read through it all, and from now on, you can be called a lasers expert 🥽 (sort of, amongst your friends only). Feel free to use your newly acquired knowledge to experiment with the laser brightness calculator!

## FAQ

### Which is the brightest laser pointer color?

Green lasers at 532 nm are the brightest during most light conditions. During the day, the human eye is more sensitive to 555 nm wavelengths. At night, this sensitiveness shifts towards 507 nm. So 532 nm, the midpoint between the two, provides the most brightness in both scenarios.

### Does a laser go on forever?

Yes, if uninterrupted. However, contrary to popular beliefs, lasers do diverge. The divergence of a laser can't be zero. So by the time the laser has traveled any significant distance, the beam is spread over a wide enough area to be visible.

### How do I calculate laser radiance?

To calculate laser radiance or brightness:

1. Find the laser's power in watts.
2. Write down the laser's wavelength in nanometers and divide by 1,000,000,000. If you don't know the wavelength, use:
• 473 nm for blue lasers;
• 532 nm for green lasers; or
• 650 nm for red lasers.
3. Divide the power by the square of the wavelength. The result is the radiance or brightness of your laser.
Luciano Miño
Method
Power (P)
mW
Wavelength (λ)
nm
W/m²·sr
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