Lab Report

Worksheet: AIoTs Mie Scattering Experiment in PMT and CCD Modes

Objective: Understand the principles of Mie scattering, perform experiments using PMT and CCD detection modes, and analyze the scattering data using Python and IoT-enabled tools.

Part 1: Setup and Quick Test

1. CCD Mode:

   • Set up the CCD detector and optical path.

   • Perform a quick test with a 650 nm red laser to observe diffraction rings.

   • Capture an image using a webcam and ensure the diffraction pattern is visible.

2. Task:

   • Did you observe clear diffraction rings? (Yes/No)

   • If not, describe the troubleshooting steps you took to correct the setup.

3. PMT Mode:

   • Set up the PMT system and check the diffraction rings using the same 650 nm red laser.

   • Ensure the PMT is correctly calibrated and light intensity measurements can be captured.

4. Task:

   • Record the first test results and describe the setup process.

   • Did the PMT record the expected intensity variation with angle? (Yes/No)

Part 2: Data Acquisition

3. CCD Mode: Image Capture and Analysis

   • Capture an image of the diffraction pattern using the webcam.

   • Open the image in ImageJ and analyze the intensity distribution along the centerline.

4. Task:

   • Using ImageJ, identify the position of the central bright fringe and two adjacent fringes on either side.

   • Record these fringe positions and calculate the angles using trigonometric relationships.

   • How does the distance between the screen and the sample affect the results?

5. PMT Mode: Light Intensity Measurement

   • Upload the Arduino code for PMT mode, run the experiment, and capture the light intensity at various angles (-90° to +90°).

   • Run the Python analysis script to process the data.

6. Task:

   • Document the angular positions where intensity maxima and minima occur.

   • How did the light intensity change with the rotation angle?

Part 3: Analysis and Conclusion

5. CCD Mode: Comparison of Theoretical and Experimental Data

   • Compare your experimental fringe positions with the theoretical values calculated using Mie scattering theory.

6. Task:

   • Record the experimental and theoretical fringe positions and calculate the percentage error.

7. PMT Mode: Particle Size Determination

   • Use the Python analysis tool to estimate the particle size based on the recorded intensity distribution.

8. Task:

   • What is the calculated particle size? How does it compare with the expected value?

   • Discuss the sources of error in your experiment.

Assignment: Data Analysis and Reporting for Mie Scattering Experiment

Due Date: (Insert Date)

Objective: Analyze the data from both PMT and CCD modes, interpret the results, and prepare a detailed report.

Assignment Tasks

1. Experiment Summary:

   • Provide an overview of both the PMT and CCD modes used in the Mie scattering experiment. Explain the setup, principles, and differences between the two detection methods.

2. Deliverable: A concise 300-word description of the experimental methods.

3. Data Analysis:

   • Analyze the data obtained from both PMT and CCD modes.

   • For CCD mode, use ImageJ to calculate the intensity profile and fringe positions. Compare these values with theoretical predictions.

   • For PMT mode, run the Python analysis tool to estimate the particle size and analyze the angular intensity variation.

4. Deliverable:

   • Intensity plots for both PMT and CCD modes.

   • Tables showing experimental vs. theoretical values (angles, fringe positions).

   • Error analysis and particle size estimation.

5. Discussion and Conclusion:

   • Discuss the accuracy and limitations of both detection methods.

   • Compare the results obtained from PMT mode and CCD mode. Which method do you find more accurate or efficient, and why?

6. Deliverable: A 500-word discussion, including error sources and suggestions for improvement.

Problems for the AIoTs Mie Scattering Experiment

Problem Set 1: Basic Mie Scattering Concepts

1. Problem 1: Derive the expression for the Mie scattering cross-section for a spherical particle and explain how it relates to the particle size and wavelength of incident light.

2. Problem 2:

   • A particle has a radius of 1 µm, and the incident light has a wavelength of 650 nm. Use the size parameter x=2πr/λ​ to determine whether the scattering falls in the Rayleigh or Mie scattering regime.

   • Calculate the size parameter xxx.

Problem Set 2: Data Analysis in Mie Scattering

1. Problem 3:

   • In CCD mode, you observe diffraction fringes at distances of 5 mm, 9 mm, and 13 mm from the central bright fringe. If the screen is placed 1 m from the sample, calculate the corresponding angles using the small angle approximation θ=y/L​, where y is the fringe distance, and L is the screen distance.

2. Problem 4:

   • For PMT mode, you recorded intensity maxima at -70°, -35°, 0°, +35°, and +70°. Use Mie scattering theory to calculate the expected particle size based on these angles, assuming the laser wavelength is 650 nm. Compare your results with experimental data.

Problem Set 3: Advanced Analysis Using Python

1. Problem 5:

   • Using Python, simulate the intensity distribution for Mie scattering of a particle with a diameter of 5 µm using a 650 nm laser. Plot the scattering intensity as an angle function and identify the maxima's angular positions.

2. Problem 6:

   • Write a Python function that accepts the particle size and refractive index as input and returns the Mie scattering coefficients. Use this function to compute the scattering coefficients for a 3 µm particle in water (refractive index n=1.33).

1. Worksheet (40%): Completeness and accuracy of theory, calculations, and explanations.

2. Assignment (30%): Detailed report, correct use of formulas, analysis, and discussion of results.

3. Problem Set (30%): Correctness of solutions, step-by-step calculations, and proper explanation.

Each lab group should download the Lab Report Template and fill in the relevant information as you experiment. Each group member should answer the Worksheet, Assignment, and Problem individually. Since each lab group will turn in an electronic copy of the lab report, rename the lab report template file. The naming convention is:

[Short Experiment Number]-[Student ID].PDF

Submit the Lab Report in PDf format