Laser induced damage and irradiation time

[roam]

We want to examine the thermal effects of irradiating a given material with a laser. The material under consideration can either be homogeneous and isotropic or a diffusive turbid material (e.g. biological tissues). Suppose we decrease the power by a certain factor. Will we still get the same amount of thermal damage if we increase the duration of irradiation by the same factor?

So, the energy density incident on the material (also known as the fluence, $\psi$) is the energy per unit area. Since optical power ($W$) is energy per unit time, i.e., $P=E/t \ (J/s)$, therefore, I believe we can write:

$$\psi = \frac{P \ t}{A} \ \text{(typically } J/cm^2) \tag{1}$$

where $A$ is the cross-sectional area of the incident beam.

One reference states that $\psi$ is obtained by integrating the power density $I$ (aka intensity or irradiance, which is the average energy per unit area per unit time, $W/m^2$) over the irradiation period:

$$\psi = \int I \ dt.$$

where at a radial distance $r$, $I$ can be expressed in terms of radiance $L$ (power density per unit solid angle)

$$I (r) = \int_{4 \pi} L(r, \hat{s}) \ d \omega.$$

According to this, for a Gaussian beam at normal incidence, the relavant effective beam area is $A_{\text{eff}}=\pi r^2 /2$ and therefore $I=\frac{2P}{\pi r^{2}}$.

Clearly (1) implies that, for instance, if you let a 2mW laser run for ~28 hours, it is capable of causing the same degree of damage as a 20W laser does in 10 seconds. But is this true?

Is the resulting damage dependant more on the intensity (power density) rather than fluence (energy density)? If so, why? And is it possible to confirm this using equations/analytic expressions?

Any explanation would be greatly appreciated.

 

[mfb]

Will we still get the same amount of thermal damage if we increase the duration of irradiation by the same factor?

Humans can survive years of sunlight without overheating, but will die quickly when exposed to 10 (or 100, or 1000) times the solar radiation.

Using the total energy only makes sense if the time is so short that thermal conduction and other heat transport processes are negligible.

Clearly (1) implies that, for instance, if you let a 2mW laser run for ~28 hours, it is capable of causing the same degree of damage as a 20W laser does in 10 seconds.

I don't see where this claim would come from.

 

[Andy Resnick]

We want to examine the thermal effects of irradiating a given material with a laser. The material under consideration can either be homogeneous and isotropic or a diffusive turbid material (e.g. biological tissues). Suppose we decrease the power by a certain factor. Will we still get the same amount of thermal damage if we increase the duration of irradiation by the same factor?

This is a tricky question to answer in general, because you didn't specify the wavelength or what tissue is being irradiated. One example why this matters is the penetration depth and where the thermal damage occurs- if the energy is deposited in a volume or confined to a nearly 2-D surface.

Also, don't forget that thermal energy diffuses away from the irradiated spot; a low power laser could be depositing energy at a certain rate but that energy also diffuses away from the spot preventing (or mitigating) thermal damage. Irradiating a moving fluid (blood, CSF, etc.) results in the absorbed energy being advected away.

I'm not sure how much relevant information is available- there's lots of data about damage to skin and the retina, but if you are irradiating (say) an explanted organ, it's unlikely that you will find much that is useful. Similarly, information about phototoxicity using cultured cells is out there, but that's primarily in the near UV through near IR band. Most likely, you will have to determine phototoxicity levels yourself.

 

[roam]

Thank you mfb and Andy Resnick for the responses.

This is a tricky question to answer in general, because you didn't specify the wavelength or what tissue is being irradiated. One example why this matters is the penetration depth and where the thermal damage occurs- if the energy is deposited in a volume or confined to a nearly 2-D surface.

Also, don't forget that thermal energy diffuses away from the irradiated spot; a low power laser could be depositing energy at a certain rate but that energy also diffuses away from the spot preventing (or mitigating) thermal damage. Irradiating a moving fluid (blood, CSF, etc.) results in the absorbed energy being advected away.

It was a general question, but we can limit the discussion to turbid material like plant and animal tissue.

Apparently, in these types of media, you will get an exponential attenuation. Incident light intensity diffuses away as it goes deeper (Beer's Law). The rate of attenuation (and therefore penetration depth) depends on the absorption coefficient of the material (for biological samples you often can only have an approximate estimate of this quantity due to the many variables involved).

mfb pointed out that if the time scales are too short, there is not enough time for conduction and convective processes to get rid of the heat, and as a result, we will get overheating and damage. The problem is that (1) only gives the energy/heat deposited in the material over the irradiation period. I wonder if there is a modified version of this equation that takes into account the energy/heat that has left it.

So, given all the parameters (e.g. the wavelength, the absorption coefficient of the media), how do you decide if a given irradiation duration is long enough to cause damage? How do you know when it is appropriate to consider the fluence (energy density) rather than the instantaneous powers?

As a side note, I know that there is an imaging technique called Second Harmonic Generation Microscopy. It uses narrow pulses (a few femtoseconds in duration) with high instantaneous powers $(\lesssim 100 \ \text{mW})$ to cause SHG. But they say it doesn't harm the biological tissue because it has a low total power averaged over pulse period $T$:

$$P_{avg}=\frac{1}{T}\int_{t_{0}}^{t_{0}+T}P\ dt=\frac{E}{T} \tag{2}$$

 

[mfb]

I wonder if there is a modified version of this equation that takes into account the energy/heat that has left it.

That depends on the environment, and in general it will be difficult to find analytical formulas for it. You can simulate it.

 

[Andy Resnick]

So, given all the parameters (e.g. the wavelength, the absorption coefficient of the media), how do you decide if a given irradiation duration is long enough to cause damage? How do you know when it is appropriate to consider the fluence (energy density) rather than the instantaneous powers?

This is a major research project, not a question that can be quickly answered on a discussion board. For example, simply determining the damage threshold for different tissues (or say, a particular species of bacteria) is a project in itself.