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In this workshop, we will construct a Michelson Interferometer using the UC2 modular microscope toolbox. The Michelson Interferometer is a device that measures the interference properties of light and has been fundamental in advancing our understanding of the nature of light and space-time. We will treat light as a wave with very high frequency and use it to perform fascinating experiments that demonstrate wave optics principles.
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### Materials Needed
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8. Screen for visual alignment and pattern observation
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9. Computer with MVS camera software installed
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**Mechanical Components: (optional)**
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**Mechanical Components:**
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10. UC2 Modular Microscope Toolbox including:
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- 8+ optical cubes with threaded inserts
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**TODO**: Specify exact part numbers and suppliers for all optical components, add vibration isolation requirements for optimal performance
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### Diagram
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The Michelson Interferometer operates as a two-beam interference device where coherent light is divided into reference and sample arms. The beam splitter acts as both a divider and combiner, sending half the light to each arm and then recombining the reflected beams. The interference pattern depends on the optical path difference between the two arms, making it extremely sensitive to small distance changes.
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In ray optics, light is represented as a bundle of rays (arrows), which entails a simplification pf the physical properties of light. The arrow indicates the direction of the beam direction/light. The beam splitter divides the light in to two different directions in t terms of magnitude. Here i is important how the beam splitter is built into the cube.
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if we extend the beam splitter by to mirrors the split light is reflected back to them. the consequence that the two parts of the light unite again and form a new wave. This is called Interference.
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----
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### Theoretical Background
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Interference is a phenomenon that occurs when two or more waves overlap in space and combine their amplitudes. When waves are in-phase (their crests and troughs align), they constructively interfere, resulting in a larger amplitude. When they are out of phase (their crests and troughs are misaligned), they destructively interfere, resulting in a smaller or zero amplitude. Interference is a fundamental concept in wave physics and plays a crucial role in understanding the behavior of light.
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**Wave Superposition and Path Difference**
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The fundamental principle underlying interferometry is the superposition of electromagnetic waves. When two coherent light beams recombine, the resulting intensity follows:
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Where $$\Delta\varphi = \frac{2\pi}{\lambda}\Delta L$$ is the phase difference corresponding to path difference $$\Delta L$$.
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**Coherence Requirements**
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For stable interference patterns, the light source must exhibit both spatial and temporal coherence:
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-**Temporal coherence**: The wave trains must maintain phase relationships over time scales relevant to the path difference
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-**Spatial coherence**: The wavefronts must be sufficiently uniform across the beam cross-section
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-**Coherence length**: Lc = λ²/Δλ, where Δλ is the spectral width of the source
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**Historical Context and Significance**
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The Michelson Interferometer was invented by Albert Michelson in 1881 and played a crucial role in:
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-**Michelson-Morley experiment (1887)**: Disproved the existence of luminiferous aether, paving the way for Einstein's special relativity
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-**Precision measurement of the speed of light**: Earning Michelson the 1907 Nobel Prize in Physics
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-**Definition of the meter**: Originally defined in terms of wavelengths of krypton-86 radiation using interferometric measurements
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**Modern Applications and Technology**
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Contemporary applications demonstrate the continued relevance of Michelson interferometry:
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-**LIGO gravitational wave detectors**: Use arm lengths of 4 km to detect strain sensitivities of 10⁻²¹
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-**Optical coherence tomography (OCT)**: Medical imaging with micrometer resolution
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-**Fourier transform infrared spectroscopy (FTIR)**: Chemical analysis and identification
-**Fiber optic sensors**: Distributed sensing in civil engineering and geophysics
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**TODO**: Add specific technical specifications for optimal laser coherence length and power requirements for educational setups
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**Sensitivity and Measurement Principles**
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The key principle behind the Michelson Interferometer is wave superposition. When two coherent light waves with the same frequency but different phases combine, the resulting intensity depends on their phase relationship:
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- Constructive interference (bright fringes): Path difference $$= n\lambda$$ (where n is an integer)
The Michelson Interferometer, invented by Albert A. Michelson in the late 19th century, is a classic optical device that exploits the principles of interference to measure various optical properties, including the speed of light. Michelson used this interferometer in the famous Michelson-Morley experiment (1887) to test the existence of the luminiferous aether, leading to fundamental insights that contributed to Einstein's theory of special relativity.
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**Coherence Requirements**
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For stable interference patterns, the light source must exhibit both spatial and temporal coherence:
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-**Temporal coherence**: The wave trains must maintain phase relationships over time scales relevant to the path difference
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-**Spatial coherence**: The wavefronts must be sufficiently uniform across the beam cross-section
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-**Coherence length**: Lc = λ²/Δλ, where Δλ is the spectral width of the source
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**Speed of Light Measurement**
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---
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In the Michelson Interferometer setup, a light beam is split into two equal parts using a beam splitter. One part is directed towards a stationary mirror (the reference mirror) while the other part is directed towards a movable mirror (the sample mirror). The two beams are then reflected back towards the beam splitter, and they recombine. Depending on the path difference between the two beams, they may interfere constructively or destructively.
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### Historical Context and Significance
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By moving the sample mirror, the path difference between the two beams changes. When the path difference corresponds to an integral number of wavelengths (constructive interference), the interference pattern exhibits bright fringes. Conversely, when the path difference corresponds to a half-integral number of wavelengths (destructive interference), the pattern exhibits dark fringes.
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The Michelson Interferometer was invented by Albert Michelson in 1881 and played a crucial role in:
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-**Michelson-Morley experiment (1887)**: Disproved the existence of luminiferous aether, paving the way for Einstein's special relativity
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-**Precision measurement of the speed of light**: Earning Michelson the 1907 Nobel Prize in Physics
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-**Definition of the meter**: Originally defined in terms of wavelengths of krypton-86 radiation using interferometric measurements
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The key to measuring the speed of light with the Michelson Interferometer lies in precisely measuring the movement of the sample mirror. As the mirror is displaced, the fringe pattern shifts, and by measuring this shift, we can determine the change in path difference and, consequently, the speed of light.
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**Modern Applications**
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There is a newer version of the alignment procedure after this one.
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*Image of all the components needed for the Michelson Interferometer setup*
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### Step 1: Assemble the Optical Components
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This guide will walk you through the assembly step by step. You can follow the process according to the functional modules or refer to the diagram above for orientation.
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**⚠️ ATTENTION!**
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NEVER LOOK DIRECTLY INTO THE LASER! EYE WILL BE DAMAGED DIRECTLY
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NEVER SWITCH ON THE LASER WITHOUT INTENDED USE
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BEAM HAS TO GO AWAY FROM ONESELF - ALWAYS!
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#### 1.1: Build a Four Base Plate Configuration
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Build a four base plate as shown. This will be used to connect the laser diode, pinhole, the beamsplitter, and an empty cube. Add the base plates to fix them.
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*Note: At this point the laser diode should be turned off the whole time. Don't look at the laser directly. Always use screens to look for the laser light.*
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#### 1.2: Place the Pinhole
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Place the pinhole such that it is as far as possible from the laser diode.
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#### 1.3: Close the Diaphragm
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Close the diaphragm as much as possible to end up with a small hole for spatial filtering.
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#### 1.4: Place the Screen and Align the Laser
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Place the screen after the pinhole and turn the laser on. The alignment is most likely off. To align the laser you should use the screwdriver and adjust the laser mount screws so that the beam is centered on the pinhole. Turn the laser off.
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#### 1.5: Replace the Pinhole with a Kinematic Mirror
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Without touching the screws of the laser, remove the pinhole from the group of cubes and add a kinematic mirror instead.
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#### 1.6: Align the Beam with the Pinhole
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Using the top and bottom base plates, place the pinhole after the beamsplitter connecting the pinhole and the kinematic mirror in a straight line. Place the screen after the pinhole, turn the laser on and align the beam to the center of the pinhole as shown. Turn the laser off.
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#### 1.7: Set the Michelson Interferometer Arms
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Remove the pinhole and set other base plates as shown. These are the variable and reference arms of the Michelson interferometer. Place the reference and movable mirrors as shown. Place the pinhole in the detection spot. Fix everything with base plates.
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### Step 2: Aligning the Michelson Interferometer
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#### 2.1: Align and Observe the Interference
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#### 1: Align and Observe the Interference
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Place the screen after the pinhole, turn the laser on. You will see two beam spots, one from each mirror. Adjust the movable mirror angles with the screwdriver so that you can see an improvement in brightness of one of the spots and look for the maximum.
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After the complete Assembly, remove the lens and turn the laser on. You will now see two beam spots, one from each mirror. Adjust the movable mirror angles with the screwdriver so that the two beamspots overlap as much as possible.
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#### 2.2: Adjust the Reference Mirror
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Adjust the screws of the reference mirror so that the two beams overlap as much as possible.
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#### 2. Observe the Interference Pattern
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Reinsert the lens. You will see two extended beams. Adjust the reference mirror screws to overlap the beams perfectly. You will see the interference pattern emerging. Then try to center the pattern on the screen. Turn the laser off.
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For problems look at the **troubleshooting guide** on the end of this page.
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#### 2.3: Observe the Interference Pattern
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Remove the pinhole and place the screen only. You will see two extended beams. Adjust the reference mirror screws to overlap the beams perfectly. You will see the interference pattern emerging. Then try to center the pattern on the screen. Turn the laser off.
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#### 2.4: Set up the Camera
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Place the camera and fix it with the base plates. Connect it to the computer and open the MV Software. To check the MVS tutorial click [here](Camera_Software_tutorial.md).
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### Optional Tutorial: Camera setup
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#### 1. Set up the Camera
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remove the screen and place the camera behind the beam splitter and fix it with the base plates. Connect it to the computer and open the MV Software. To check the MVS tutorial click [here](https://openuc2.github.io/docs/Electronics/HIKCamera/SoftwareTutorial).
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*Picture of older setup with camera*
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#### 2.5: Adjust the Camera Exposure
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#### 2 Adjust the Camera Exposure
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Adjust the exposure time of the camera. You should see a fringe pattern. Try to adjust the reference mirror screws finely to bring the center of the interference pattern to the center of the camera.
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*Fully assembled UC2 interferometer with green laser diode, camera, beamsplitter, kinematic mirror and translatable mirror*
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*Picture of older setup with camera - Fully assembled UC2 interferometer with green laser diode, camera, beamsplitter, kinematic mirror and translatable mirror*
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### 1.2: Record the Pattern
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Using the camera, capture images of the interference pattern. Note the bright and dark fringes and their spacing.
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*Newton rings interference pattern showing circular fringes from two overlapping spherical wavefronts*
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*Picture of older setup with camera - Newton rings interference pattern showing circular fringes from two overlapping spherical wavefronts*
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