Laser Doppler Anemometry Experiment

Ux = fD Δx

The optimization of the signal obtained from Avalanche Photo Diode (APD) was done using the low pass filter and the signal modulation depth “η” was determined using the following formula:

η = (Vmax -Vmin) /  (Vmax + Vmin)

Where ”Vmax”  and “Vmin” are the maximum and minimum signal depths.

        

Experimental Apparatus:

        

As shown in figure [1] the following apparatus was used for the experiment:

                        Beam Splitter

Figure [1] Laser Doppler Anemometry experimental setup

• The Helium Neon LASER (λ=0.638 µm)
• Rotatable transmitting optics
• Base plate for transmitting and receiving optics
• Receiving Lens
• Projection Lens
• Observation screen
• Avalanche Photo Diode (APD)
• APD mounting and housing
• Mechanical arrest for APD cable
• A square and a circular glass containers filled with water
• A stand with transparent green sheet for MCV  
• Fastening screws
• Atomiser
• Measuring tape
• Beam Stops
• An Oscilloscope

        

Experimental Procedure:

Two beams were generated from a single laser by means of the Beam Splitter. They were passed through a sending lens. The lens changed the direction of the beams causing them to cross at the point where they were focused. The region where the beams intersected is called the Measurement Control volume. The lab was conducted in five parts. Each part of lab is defined below:

PART 1: Determination of Fringe Spacing (Δx)

In the first part the two laser beams were projected on a surface which was 2.155 meters away from the laser. MCV was measured by adjusting the transparent green sheet (attached to a stand) by placing it at a point where the two beams cross each other. Measurements of “L” and “D” were taken from the observation screen as shown in the figure [2] below:

Figure [2] Experimental setup for calculation of fringe spacing

The same measurements were repeated three times to remove any possible error.

PART 2: Determination of Measurement Control Volume (MCV)

The second part of the experiment was further divided into two sections:

1. In the first part, length of the MCV was determined. Projection lens was positioned just before the crossing point of laser beams and the beam images were observed on the screen. Projection lens was moved away from the laser such that the two spots coincided and fringes started appearing on the screen. That was the starting point of MCV. The position of projection lens was marked. The position lens was further moved in the same direction until the fringes vanish. This position was again recorded. The difference between these two positions was the estimated length of MCV.
2. In this section projection lens was positioned along the MCV so that the fringes were clearly defined. The number of fringes was counted in the 10 mm marked section. The width of the laser beam was measured three times with the measuring tape so as to get the more accurate value for the beam width, from which total numbers of fringes in the MCV were calculated.

The schematic diagram of the experimental setup is shown in figure [3]

Figure [3] Fringe spacing and total number of fringes in the beam

PART 3: Adjustment of the Receiving Optics

Receiving lens was adjusted on the base plate such that the two laser beams were blocked by touching the outer boundaries of its mounts. Now the APD was moved towards the laser until the MCV image became pointed. The APD position was further adjusted with the help of white paper. The distance “L” from MCV to receiving optics and the distance “l” from receiving optics to the APD were measured. Both the distances were put into the Young’s thin lens equation and the given focal length was compared with the experimental values.

PART 4: Optimisation of Signal Detection

In this part of experiment, atomiser was placed on the base plate such that the MCV was inside the atomised air flow as shown in fig [2]. Position of the APD was adjusted so that the oscilloscope was showing a signal of the MCV image. The distance between the MCV and the receiving lens was adjusted to obtain the best modulation depth. Gaussian intensity shape was obtained for the signal and the maximum and minimum modulation depths were measured. From the modulation depths the efficiency of the signal was measured.

Figure [4] Placement of atomiser in the MCV

PART 5: Determination of MCV parameters in Liquids

        

A water filled rectangular tank was placed on the base plate where the laser beams were intersecting each other and the receiving lens was placed at apposition where the laser beam intersection was imaged approximately to the same ratio as it was before the water tank as shown in figure[3]. The beam angle was determined as done in part 1 above. A decrease in beam intersection angle was observed because of the change of refractive index. Elongation of the MCV was observed in water as compared with the measurements taken for air. Rectangular tank was then replaced by a circular tank. Measurements were taken for later calculations to see the difference between the beam angles for circular and rectangular tanks.

Figure [5] Placement of rectangular water container in the MCV

Presentation of Results:

The following measurements and observations were made in different parts of experiment:

PART 1: Determination of Fringe Spacing (Δx)

       

Fringe spacing was determined by taking the distance “L” from MCV to the Observation screen and the distance “D” between the two beam spots on the observation screen. The measurements are shown below:

Table [1] Measurements for the fringe spacing

          

These measurements were used to calculate the angle “θ” in radians according to the following equation:

Angle (θ) = D/2L (Radians)

PART 2: Determination of Measurement Control Volume (MCV)

Table [2] Measurements for the width of MCV

Where “L” is the length of Measurement Control Volume (MCV) and “W” is the width of the beam in mm.

PART 3: Adjustment of the Receiving Optics

According to the Young’s Thin Lens equation, we have:

1/Fel = 1/L + 1/l

Where “Fel = 150 mm” is the focal length of the receiving lens, “L” is the distance from MCV to the receiving lens and “l” is the distance from receiving lens to APD. The calculated focal length using the above equation is shown in the following table:

Table [3] Focal length calculations using Young’s Thin Lens equation

PART 4: Optimisation of Signal Detection

Signal modulation depth or visibility “η” and signal quality “S” were estimated by measuring the width of the signal using the following relations:

η = (Vmax -Vmin) /  (Vmax + Vmin)

S = (Vmax -Vmin) /  Vmax

Where Vmax and Vmin are the signal’s maximum and minimum depths respectively. The modulation depth “η” and quality of the signal “S” using the above formula is given in the following table:

 

Table [4] Signal modulation depth calculations

PART 5: Determination of MCV parameters in Liquids

Table [5] Determination of beam angle in liquid

Theory and Calculations:

“A laser Doppler anemometer measures the velocity at a point in a flow using light beams. An LDA does not disturb the flow being measured (like a Pitot does), it can be used in flows of unknown direction and it can give accurate measurements in unsteady and turbulent flows where the velocity is fluctuating with time” Ref [2].

As described in the experimental procedure section that a beam of Laser light was split into two parallel beams using an optical device called the “beam splitter”. These two beams were brought together at a fixed cross over point by means of front focusing lens. The cross over point was the Measurement Control Volume (MCV). In this forward scattered dual-beam LDA system the flow passing through the MCV was collected by the receiving lens and focused onto the photo detector called the Avalanche Photo Detector (APD).

Part 1: Fringe spacing was determined using the following formulae:

Angle (θ) = D/2L

Fringe spacing (Δx) = λ / 2Sinθ

Where “θ” is the half angle in Radians, L is the distance in mm from MCV to the back screen, D is the distance in mm between the two beam spots on the observation screen, λ = 0.638 µm is the wavelength of Helium-Neon laser. From Table [1] the mean value of “L” and “D” are 2155 mm and 275 mm respectively. Putting these values in the above equations we get,

Angle (θ) = D/2L = 0.0638 Radians

Fringe spacing (Δx) = λ / 2Sinθ = 5.00 µm

 Part 2: Measurement Control volume (MCV) has a Gaussian distribution in three dimensions and is elliptical in shape as shown in figure [6] below:

Figure [6] Measurement Control Volume

“Figure [7] shows schematically the arrangement of the light waves within the two beams. The waves are represented by lines showing where the peaks are. Since laser light is monochromatic (i.e. of one frequency and wavelength) and coherent (all adjacent and successive waves are in phase) all the peaks line up. In the measurement volume the two sets of light waves cross. Where the interfering light waves are in phase (peak aligned with peak) they add up creating a bright fringe. Where the light waves are out of phase (peak aligned with trough) they cancel creating a dark fringe. As can be seen in Figure [7], the bright and dark fringes form in lines parallel to the bisector of the beams.” Ref[2]

Figure [7] MCV showing the formation of fringes Ref [2]

From table [2] the total number of fringes and the width of MCV can be calculated as:

 

Total number of fringes in the control volume Nf = Nfx/10*W

 

= (164.3/10)*6 = 98.4 ≈ 98

Width of MCV = Δx Nf = (5x10-6)*(98)= 0.49 mm

Where “Δx = 5 µm” is the fringe spacing, “Nf” and “Nfx” are the number of fringes and “W” is the width of beam.

Part 3: The distance between the front lens, MCV, receiving lens and APD is a function of the focal length of the two lenses. According to the Young’s thin lens equation:

1/Fel = 1/L + 1/l        =>         Young’s Thin Lens Equation

Where “Fel = 150 mm” is the focal length of the receiving lens, “L” is the distance from MCV to the receiving lens and “l” is the distance from receiving lens to APD. Putting the values from table [3] we have:

1/150 = 1/526 + 1/220 =155 mm

The percentage error can be given by:

%age error = [(155-150)/150]*100 = 3.3%

Table [3] shows the results of “L” and “l” for comparison with the equation.

        

 

Part 4: Now for the optimization of Signal detection Gaussian intensity shape was obtained for the signal. The signal obtained consisted of a low frequency component shown by the Gaussian envelope of the signal amplitude and a high frequency modulation that correspond to a particle crossing the interface fringes. The noise in the signal was suppressed by using a low pass filter. The optimized Doppler signal was determined by the modulation depth or “visibility” by the following relation:

η = (Vmax -Vmin) /  (Vmax + Vmin)

Where “η” is the modulation depth and “Vmax” and “Vmin” are the maximum and minimum values of the signal in mm. An ideal Doppler signal has a modulation depth of unity but practically the signal is not ideal and the value is between zero and one.

From Table [4] the mean value of modulation depth is:

η = (0.48+0.6) /2 = 0.54 = 54 %

The signal quality “S” can be defined as the ratio between the differences of two values divided by the maximum value. From Table [4] we have the mean value of signal quality as:

S = (Vmax -Vmin) /  Vmax = (64+75) / 2 = 0.70 = 70 %

Part 5: By placement of water tank at the crossover point of the laser beams it was observed that the MCV location was changed. It was because of the change in the refractive index because of change in the medium. The beam intersection half angle “θ” was decreased in water as compared to air. This decrease in the beam angle can be obtained from Snell’s law according to which:

n Sin θ = n’ Sin θ

Where “n” and “n’” represents the refractive indices of air and water respectively. For air n=1 and for water n’ =1.33.

Now it can be mathematically proved using the Snell’s law that the fringe spacing “Δx” remains the same due to elongation of all length scales by factor n’, independent of the medium used is air or water. The proof is given below:

From Snell’s Law:

na Sin θa = n’w Sin θw

We have:

Δxw = λw / 2Sinθ and  Δxa = λa / 2Sinθ

Where the subscripts “a” and “w” denote the medium air and water respectively. Using the Snell’s law:

λw = λa / n’

• Δxw = λa / n’2Sinθ

        

• Δxw = (λa / n’) / (2Sinθ/n’)

• Δxw = λa / 2Sinθ = Δxa 

Hence the fringe spacing remains the same in air and water provided that water is not in a curved container with respect to the beams.

   

Discussion of Results:

Throughout the experiment the observations were recorded and measured more than once to have a good approximation of results and to avoid the errors. The other reason was that human eyes behave digitally whereas the beam signal is analogue so different people have different measurements, so to take a good approximation all the values were recorded three times.

In part 2 of the experiment most of the people observed six fringes whereas some people also found seven fringes in 10 mm. This was again due to the same reason as discussed above. In the report number of fringes is taken as six because majority of the people found this figure.

In part three of the experiment the two beams were stopped by using beam stopper to capture the image of particles using APD. The APD was adjusted where the image was sharpest. The purpose of this part was to prove the Young’s Thin Lens equation. The given focal length of the lens was 150 mm and using the formula it came out around 153 mm. The difference is due to the placement of apparatus at the correct position and measurements errors.

In the fourth part of experiment the objective was to receive a good quality signal from the APD. APD used in the experiment can measure 10 µm image. Its position was adjusted to get the best quality signal. It was also observed that the light scattered from the particle was most bright in the direction of beam so the APD was placed exactly opposite to the beam direction as to get the best image. This also proves the Mie scattering theorem for light. The signal received consisted of low frequency component (the Gaussian intensity distribution as shown in figure [8] (Ref [3]) and a high frequency modulation which correspond to a particle crossing the interference fringes.

 

Figure [8] Gaussian Intensity distribution Ref [3]

As the signal contains noise so a low pass filter was used and the signal was optimized by the modulation depth. Ideal modulation depth is one but due to different reason it is less than one. These reasons along with those defined in the beginning include unequal outgoing beam intensities, no proper intersection of beams, larger particle size as compared to fringe spacing, spacing between the lens and detector etc.

In the last part of experiment, a rectangular tank was placed in the MCV to see the effect of change in medium in calculating the velocity. It was observed that the beams were deflected away in water and the crossover point of beams was away as compared with water hence an increase in the MCV as shown in figure [5] and figure [9]. The beam angle was smaller in water as compared to air but the fringe spacing remains the same because of the reason that the wavelength changes with the same ratio as the beam angle as proved in theory and calculation section using Snell’s law.

Now when the rectangular tank was changed with a circular glass container, the MCV was again changed. This time the MCV was shorter than the MCV in rectangular tank. So the beam angle became larger in circular container which can be seen from table [5]. In this case Snell’s law can not be applied because of the curved surface of the container as shown in figure below. The reason is that there is another shift in beam angle due to the change in curvature as shown in figure [9]. Hence the fringe spacing also changes in this situation.

 

Figure [9] Effect of change in refractive indices

Conclusion:

• Liquid and gas flows can be quite accurately measured with Laser Doppler Anemometry.
• Light scattered from the particle is most bright in the direction of beam.
• Focal length of a lens can be quite accurately measured using the laser optical system.
• Results may affect due to change in refractive indices of mediums depending upon the situation.

References:

3. http://www.coseti.org/9101-001.htm