What is Fluence?

The intensity of a light source, such as a laser, can be described in many different ways. Here is a short glossary of commonly used terms, along with their SI units.

Energy

Measured in joules (J) the energy of a laser pulse is, by itself, not typically a very helpful quantity to know, since it is also important to know how the energy is distributed in both time and space. This quantity is typically measured using an energy meter. It is very common for laser manufacturers to quote the total energy per pulse, however keep in mind that this number is not the same as the energy reaching the sample.

Power

The power is the energy of the pulse divided by the duration. Thus, the power tells you how quickly the energy is delivered and usually provides more of an idea as to how much impact the laser pulse will have. The standard unit is called a watt (W). Knowing this is helpful, but it does not explain how the energy is distributed in space. Rather than quoting the power-per-pulse, it is common to quote the average power. The average power will be the total energy of all pulses emitted in 1 second, thus: Average Power = Energy Per Pulse × Pulses Per Second.

When the power is divided by the area on which is it distributed, then we get the irradiance. This is a very useful property to know, since it describes the total energy of the pulse, as well as how it is distributed in both space and time. This can then be used to determine how a certain material responds to the laser light. There is no special unit for irradiance, and we simply use the explicit term: W/m2. Note: for historical reasons it is very rare to find the term irradiance quoted in publications from the Earth Science literature.

Do not confuse “irradiance” with “radiant intensity,” a similar measure but with different units.

Fluence

The fluence is the energy of a laser pulse divided by the area it is illuminating, and for historical reasons is the general term of choice when describing LA-ICP-MS conditions. It is most commonly used in laser applications when the pulse duration is constant and well known, as with an excimer laser which typically produces pulses of 5-20ns in duration, depending on the model and manufacturer. There is no special unit for fluence, and while the SI representation would be J/m2, in the LA-ICP-MS communitity it is much more common to use J/cm2. Note: The energy measurement is performed at the sample, not at the laser.

Some LA-ICP-MS Examples

Starting with energy, consider a laser ablation instrument delivering an on-sample pulse energy of 0.5mJ. The energy can be measured with an energy meter, or is given by the manufacturer or their software. Be cautious, however, as internal energy meters can drift over time or change response due to thermal fluctuations. We believe a regularly-calibrated hand-held energy meter is essential for any LA-ICP-MS laboratory and have always ensured that RESOlution instruments provide easy access for measuring the beam energy.

Power: divide the energy by the duration of the pulse (typically given in the laser specifications). In this example, if we have a 5 ns pulse, then the power of this pulse is: 0.5 × 10-3 / 5 × 10-9 = 0.1 × 106 W, which in friendlier units is 100 KW.

Irradiance: divide the power by the area of the laser spot. The spot size is usually provided by the control software, so for a round spot of 50 µm diameter, the area (πr2) is 7854 µm2 or 7.854 x 10-9 m2. To find the irradiance in this instance we compute: power / area = 0.1 × 106 / 7.854 × 10-9 = 1.3 × 1012 W/m2.

Fluence: divide the energy by the area of the laser spot. If the on-sample spot is a 50 µm round spot with an area of 7.854 x 10-9 m2, we compute: energy / area = 0.5 × 10-3 / 7.854 × 10-9 = 6.4 × 104. A more convenient way to write this is 6.4 J/cm2, which is commonly used in the literature.

For most samples in the Earth Sciences, the on-sample fluence will range from 1 to 8 J/cm2, depending on the sample type. Higher fluence values are of use when ablating highly transparant minerals such as quartz, where values > 20 J/cm2 are recommended. The fluence is typically chosen to match the mineral. In some cases the fluence chosen will not influence the results, while in others excess fluence can lead to pronounced down-hole fractionation. We recommend that the working fluence be set to 1-2 J/cm2 above the ablation threshold for the mineral. For successful LA-ICP-MS the on-sample fluence should be known and also remain stable over the duration of an analytical session.