# Intensity of Near-Infrared Spectroscopy Laser

• creative_wind
In summary, the light beam after it penetrates through 3.5 cm of tissue is in the range of 1.92-2.4 mW.
creative_wind

## Homework Statement

Light in the near-infrared (close to visible red) can penetrate surprisingly far through human tissue, a fact that is being used to "illuminate" the interior of the brain in a noninvasve technique known as near-infrared spectroscopy (NIRS). In this procedure an optical fiber carrying a beam of infrared laser light with a power of 1.5 mW and a cross-sectional diameter of 1.4 mm is placed against the skull. Some of the light enters the brain, where it scatters from hemoglobin in the blood. The scattered light is picked up by a detector and analyzed by a computer.

(a) According to the Beer-Lambert law, the intensity of light, I, decreases with penedtration distance, d, as I=I0e-µd, where I0 is the initial intensity of the beam and µ = 4.7 cm-1 for a typical case. Find the intensity of the laser beam after it penetrates through 3.5 cm of tissue.

(b) Find the electric field of the initial light beam.

## Homework Equations

I0=P/A
I=I0e-µd
I=c$$\epsilon$$0E2 (I think this is the equation I need to answer b)
$$\epsilon$$0=8.85*10-12

## The Attempt at a Solution

a)
Step 1) Solve for I0 (I'm assuming the cross-sectional area refers to a circle)
I0=P/A = 1.5mW/(pi*(1.4*10-4m/2)2 = 9.744*105mW/m2

Step 2) Solve for I
I=I0e-µd = (9.744*105mW/m2)*e(-0.047m-1*0.035m) = 9.728*105mW/m2

This answer gets me "Your answer differs from the correct answer by orders of magnitude." Since the e term is about 0.998, my I0 must be incorrect. The math is correct (as far as me quadruple-checking can affirm ) so is there a different equation I should be using to determine I0?

creative_wind said:

## Homework Statement

Light in the near-infrared (close to visible red) can penetrate surprisingly far through human tissue, a fact that is being used to "illuminate" the interior of the brain in a noninvasve technique known as near-infrared spectroscopy (NIRS). In this procedure an optical fiber carrying a beam of infrared laser light with a power of 1.5 mW and a cross-sectional diameter of 1.4 mm is placed against the skull. Some of the light enters the brain, where it scatters from hemoglobin in the blood. The scattered light is picked up by a detector and analyzed by a computer.

(a) According to the Beer-Lambert law, the intensity of light, I, decreases with penedtration distance, d, as I=I0e-µd, where I0 is the initial intensity of the beam and µ = 4.7 cm-1 for a typical case. Find the intensity of the laser beam after it penetrates through 3.5 cm of tissue.

(b) Find the electric field of the initial light beam.

## Homework Equations

I0=P/A
I=I0e-µd
I=c$$\epsilon$$0E2 (I think this is the equation I need to answer b)
$$\epsilon$$0=8.85*10-12

## The Attempt at a Solution

a)
Step 1) Solve for I0 (I'm assuming the cross-sectional area refers to a circle)
I0=P/A = 1.5mW/(pi*(1.4*10-4m/2)2 = 9.744*105mW/m2

Step 2) Solve for I
I=I0e-µd = (9.744*105mW/m2)*e(-0.047m-1*0.035m) = 9.728*105mW/m2

This answer gets me "Your answer differs from the correct answer by orders of magnitude." Since the e term is about 0.998, my I0 must be incorrect. The math is correct (as far as me quadruple-checking can affirm ) so is there a different equation I should be using to determine I0?

You made two mistakes, one small, one big:

First, you have been given the diameter of a circle, not the radius. That's a factor of 4 you miss.

Second, 1cm^-1 is certainly not equal to 0.01m^-1: this is where you're orders of magnitude off.

The 1.4e-4 was a typing error on my part, it should have been -3, which still yields the initial value for I that I wrote. I did completely err on the m^-1 though. Thank you so much for that!

As for part b, I solved for E using the correct I value of 9.744e11 W/m^2.
E=(I/c*constant)^1/2
E=(9.744e11/3e8*8.85e-12)^1/2=1.92e7 V/m=1.92e4 kV/m which is off by orders of magnitude again. BAH! Your help is greatly appreciated.

Where are you getting 9.744e11 from? Your intensity is orders of magnitude off, which is the problem here.

It's from my calculation in the first post for I0. It's in megawatts, I converted it to watts for the second step so I wouldn't have unit problems.

(9.744*105mW/m2)*(1*106/1mW)=9.744*1011.

I used this number to calculate the answer for a) which was correct. Please tell me how it's orders of magnitude off for part b).

"mW" is milliwatts. Megawatts would be "MW".

Forgive my lack of shift-usage. Can you help me answer the problem at all?

It's supposed to be milliwatts (mW), as written originally. Nobody is going to shoot a megawatt laser through somebody's head in a noninvasive technique, since a megawatt would be quite invasive, to put it mildly.

Just do the conversion from mW to W.

## 1. What is the purpose of using near-infrared spectroscopy laser intensity in scientific research?

The intensity of near-infrared spectroscopy (NIRS) laser is used to measure the levels of light absorption and scattering in a sample. This information can then be used to determine the concentration of various compounds in the sample, making NIRS a useful tool for analyzing biological, chemical, and physical properties of a wide range of materials.

## 2. How is the intensity of a near-infrared spectroscopy laser measured?

The intensity of a near-infrared spectroscopy laser is typically measured using detectors such as photodiodes or photomultiplier tubes. These devices are able to convert the light energy from the laser into an electrical signal, which can then be analyzed and quantified.

## 3. Can the intensity of a near-infrared spectroscopy laser be adjusted?

Yes, the intensity of a near-infrared spectroscopy laser can be adjusted by changing the power output of the laser or by using neutral density filters. This allows researchers to control the amount of light energy being emitted and optimize the intensity for their specific experiments.

## 4. How does the intensity of a near-infrared spectroscopy laser affect the accuracy of the results?

The intensity of the laser can have a significant impact on the accuracy of NIRS measurements. Too low of an intensity may result in weak or unreliable signals, while too high of an intensity can cause saturation and distort the measurements. It is important for researchers to carefully calibrate and optimize the laser intensity for each experiment.

## 5. Are there any safety considerations when working with a near-infrared spectroscopy laser?

Yes, like any laser, near-infrared spectroscopy lasers can be potentially harmful if not handled properly. It is important to follow safety protocols and wear appropriate protective equipment when working with these lasers. Additionally, the intensity of the laser should always be kept at a safe level to avoid any potential hazards.

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