The Michelson Interferometer, a clever optical device, allows us to split a beam of light and then recombine it, creating interference patterns that reveal a wealth of information about the light itself. It's the heart of many scientific instruments, and it's especially crucial in Fourier Transform Spectroscopy (FTS).

How a Michelson Interferometer Works

Imagine a beam of light hitting a "beam splitter"—a special mirror that transmits half the light and reflects the other half. This creates two separate beams.

• Beam 1: Travels to a fixed mirror, reflects back to the beam splitter.
• Beam 2: Travels to a movable mirror, reflects back to the beam splitter.

The two beams then recombine at the beam splitter and are directed towards a detector. The path length difference between the two beams determines whether they interfere constructively (bright) or destructively (dark).

The Interferogram: A Dance of Light and Dark

• Monochromatic Light (Single Color):
• If you use a laser, which emits a single wavelength (monochromatic light), you'll see a simple sinusoidal (wave-like) pattern as you move the movable mirror. This pattern, called an "interferogram," represents the intensity of the combined light as a function of the path length difference.
• When the path lengths are identical, the waves align perfectly (constructive interference), creating a bright spot. As you move the mirror, the path difference changes, and the waves start to cancel each other out (destructive interference), creating a dark spot. This oscillation between bright and dark creates the sine wave like interferogram.

• Broadband Light (Multiple Colors):
  • Now, let's use white light, which contains a spectrum of many wavelengths (broadband light). Each wavelength will produce its own sinusoidal interferogram.
  • When the movable mirror is at zero path difference (both paths are equal), all wavelengths interfere constructively, resulting in a strong central peak in the interferogram.
  • As you move the mirror, the different wavelengths start to interfere differently. Shorter wavelengths oscillate faster than longer wavelengths. This causes the interferogram to become a complex pattern, where the central peak rapidly decreases in amplitude as the mirror moves.
  • The interferogram for broadband light looks like a central peak that rapidly decreases in intensity with distance from the zero path difference.
  • The broadband Inteferogram image from Wikipedia 

From Interferogram to Spectrum: Fourier Transform Magic

The key to Fourier Transform Spectroscopy lies in the fact that the interferogram contains all the information about the wavelengths present in the light. To extract this information, we use a mathematical tool called the Fourier Transform.

• The Fourier Transform takes the interferogram (intensity versus path length difference) and converts it into a spectrum (intensity versus wavelength or frequency).
• Essentially, it breaks down the complex interferogram into its individual sinusoidal components, revealing the intensity of each wavelength present in the light.
• This is the same math that is used to decompose a sound wave into its constituent frequencies.
• Because the Fourier Transform is a mathematical process, it can be done very quickly with computers. This is one of the reasons that Fourier Transform Spectrometers are so powerful.

Why Use a Fourier Transform Interferometer?

• High Throughput: FTS instruments collect all wavelengths simultaneously, making them much faster than traditional spectrometers that scan through wavelengths one by one.
• High Accuracy: The precise measurement of path length difference in the interferometer allows for very accurate wavelength determination.
• High Signal-to-Noise Ratio: FTS instruments can achieve high signal-to-noise ratios, allowing for the detection of weak signals.

Next Steps

The Michelson Interferometer, when combined with the power of the Fourier Transform, provides a powerful tool for analyzing light. By measuring the interferogram and applying the Fourier Transform, we can unlock the secrets of the light's spectral composition, revealing the presence and intensity of different wavelengths. Stay tuned for more in-depth explorations of the Michelson Interferometer and detailed interferogram analysis