Ep 12 — Michelson Interferometer: The Heart of FTIR

Series: Encyclopedia of Infrared Spectroscopy: From Principles to Practice
Chapter: Part 2 · Beginner Level — Entering the Lab
Audience: Undergraduate and graduate students, new laboratory technicians
Prerequisite: Ep 11 (Dispersive IR vs FTIR)
Reading time: Approx. 32 minutes

Prologue: A "Failed" Experiment That Changed Physics

In 1887, American physicist Albert A. Michelson and chemist Edward Morley conducted an experiment in Cleveland to detect Earth's motion relative to the "luminiferous ether." The result was astonishing — they measured nothing [1][2].

This "failed experiment" disproved the existence of the ether, paving the way for Einstein's 1905 special theory of relativity. Michelson was awarded the 1907 Nobel Prize in Physics, becoming the first American to win a Nobel Prize in science [1][2].

But the interferometer invented by Michelson was not buried along with the ether. Quite the opposite: that ingenious instrument — the Michelson interferometer — a century later became the "heart" of modern infrared spectrometers [3][4].

Today, every one of the hundreds of thousands of FTIR instruments worldwide contains a Michelson interferometer. In this episode, we will delve into this "heart" and understand how it transforms a beam of ordinary infrared light into the "code" of molecular spectra.

1. Structure of the Michelson Interferometer

1.1 Four Key Components

The Michelson interferometer in FTIR consists of four key components [3][5][6]:

                          Fixed Mirror
                              ↕
   IR Source → [Beamsplitter] ←——————→ Moving Mirror
                ↓
            [Detector]

Table 1: Core components of the Michelson interferometer (Data sources: LibreTexts [5]; Newport [3])

1.2 Optical Path Details

The optical path proceeds as follows [3][5][6]:

1. Infrared source emits broadband radiation
2. The beam reaches the beamsplitter and is split into two beams:
   • Transmitted beam → goes to the fixed mirror → reflects back to the beamsplitter
   • Reflected beam → goes to the moving mirror → reflects back to the beamsplitter
3. The two beams recombine at the beamsplitter
4. Half of the combined beam goes to the detector, the other half returns to the source
5. The detector records the light intensity as a function of the moving mirror position — this is the interferogram

1.3 Zero Path Difference (ZPD)

Newport's technical literature points out a key concept [3]:

"FT-IR has a natural reference point when the moving and fixed mirrors are at the same distance from the beam splitter. This condition is called the zero path difference or ZPD."

When the moving mirror and fixed mirror are equidistant from the beamsplitter, the optical path difference between the two beams is zero, called zero path difference (ZPD). At this point, all wavelengths undergo constructive interference, producing the centerburst of the interferogram — the most prominent feature of the interferogram [3][6].

The relationship between optical path difference (OPD) and the physical displacement Δ of the moving mirror is [3]:

$$\text{OPD} = 2\Delta$$

(Because the beam travels round trip, the optical path difference is twice the physical displacement. In air, refractive index n≈1)

2. Principle of Interferogram Generation

2.1 Constructive and Destructive Interference

The essence of interference is the superposition of two light waves [6][7]:

Constructive Interference: When the optical path difference between the two beams is an integer multiple of the wavelength:

$$2x = n\lambda \quad (n = 0, 1, 2, \ldots)$$

The two beams are in phase, and the light intensity is maximum [6][7].

Destructive Interference: When the optical path difference is an odd multiple of half-wavelengths:

$$2x = \left(n + \frac{1}{2}\right)\lambda$$

The two beams are out of phase, and the light intensity is minimum [6][7].

2.2 Interferogram of Monochromatic Light

For a monochromatic light source of wavelength λ, the intensity received by the detector varies cosinusoidally with mirror displacement x [6][7][8]:

$$I(x) = \frac{1}{2}P(\lambda)\left[1 + \cos\left(\frac{2\pi x}{\lambda}\right)\right]$$

where P(λ) is the original light intensity at that wavelength.

Shimadzu's technical newsletter explains this process [7]:

"When the moving mirror moves back and forth, the optical path difference with the fixed mirror changes, and the phase difference varies with time. The two beams recombine in the Michelson interferometer to produce interference light."

Interferogram of monochromatic light:

  I(x)
   ↑
   │  ╱╲    ╱╲    ╱╲    ╱╲
   │ ╱  ╲  ╱  ╲  ╱  ╲  ╱  ╲     ← Perfect cosine wave
   │╱    ╲╱    ╲╱    ╲╱    ╲
   └──────────────────────────→ x (mirror displacement)
         λ/2    λ/2    λ/2

Professor Frank Rioux from CSB|SJU provided a full quantum derivation, yielding the detector intensity for a monochromatic source [8]:

$$I_D(\delta) = \frac{1}{2}\left[\cos\left(\frac{2\pi\delta}{\lambda}\right) + 1\right]$$

2.3 Interferogram of a Broadband Source — Centerburst

For a broadband source (e.g., a Globar for infrared radiation), all wavelengths are in phase at ZPD, producing a sharp centerburst [3][6]:

Interferogram of a broadband source:

  I(δ)
   ↑
   │       │
   │       ║        ← Centerburst
   │      ║║║
   │    ║║   ║║
   │  ║║       ║║     ← Rapid decay away from ZPD
   │║             ║║
   └─────────────────→ δ (optical path difference)
       ↑
      ZPD (δ=0)

As one moves away from ZPD, different wavelengths reach their respective constructive/destructive conditions at different positions, and the interferogram gradually decays into a complex oscillatory signal [3][6].

Key insight: The centerburst of the interferogram contains all the spectral information of the broadband source — but this information is "encoded" in the oscillation pattern of the interferogram and needs to be "decoded" via Fourier transformation [6][7].

📷 Figure 1: Interferogram of a broadband source and the centerburst
Source: Newport FTIR technical literature [3]
https://www.newport.com.cn/n/…

3. Fourier Transform: From Interferogram to Spectrum

3.1 Mathematical Relationship

The interferogram I(δ) and the spectrum B(σ̃) form a Fourier transform pair [6][7][9]:

From spectrum to interferogram (forward transform):

$$I(\delta) = \int_0^\infty B(\tilde{\nu}) \cos(2\pi\tilde{\nu}\delta)\, d\tilde{\nu}$$

From interferogram to spectrum (inverse transform):

$$B(\tilde{\nu}) = \int_{-\infty}^{\infty} I(\delta) \cos(2\pi\tilde{\nu}\delta)\, d\delta$$

where [6][9]:

• δ is optical path difference (cm)
• σ̃ is wavenumber (cm⁻¹)
• B(σ̃) is the spectrum we are familiar with—the light intensity at each wavenumber

3.2 Physical Meaning

LibreTexts explains [9]:

"The Fourier transform describes a function ƒ(t) in terms of basic complex exponentials of various frequencies."

Physical meaning: The Fourier transform decomposes the interferogram signal in the "spatial domain" (optical path difference δ) into frequency components (wavenumber σ̃), yielding the spectrum in the "wavenumber domain" [6][9].

Interferogram (spatial domain)     Fourier Transform     Spectrum (wavenumber domain)

  I(δ)                                              B(σ̃)
  │  center burst                                    │ peak
  │   /\                                             │   /\
  │  /  \    ~~~~    ~~~~                           │  /  \    /\
  │ /    \~~    \~~    \~~                          │ /    \~~  \~~
  └────────────────────────→ δ       →      └────────────────────→ σ̃
  (Optical path difference cm)                     (Wavenumber cm⁻¹)

📷 Figure 2: Comparison of interferogram and Fourier-transformed spectrum
Source: Shimadzu FTIR Talk Letter vol.15 [7]
https://www.shimadzu.com/an/s…

3.3 FFT Algorithm—Making the Transformation a Reality

As described in Ep 11, the FFT algorithm published by Cooley & Tukey in 1965 reduced the computational complexity of the Fourier transform from O(N²) to O(N log N), making real-time computation possible [10].

In modern FTIR instruments, the FFT completes a transformation in 0.1–0.2 seconds [7][10].

🔗 Further reading: See Ep 11 for the history of the FFT algorithm.

4. Resolution and Moving Mirror Travel

4.1 Core Formula

The spectral resolution of FTIR is determined by the maximum travel of the moving mirror [11][12]:

$$\Delta\tilde{\nu} = \frac{1}{2L}$$

where:

• Δσ̃ is spectral resolution (cm⁻¹)
• L is the one-way travel of the moving mirror (cm)

Equivalent expression: maximum optical path difference = 1 / resolution [11][12].

Since the beam travels back and forth, the optical path difference is twice the physical mirror travel [11].

4.2 Resolution vs. Travel Table

Thermo Fisher's technical data provides a clear table [11]:

Table 2: Correspondence between resolution and mirror travel (data from Thermo Fisher [11])

Examples:

• Routine analysis (4 cm⁻¹): mirror only needs to travel 1.25 mm
• High-resolution gas analysis (0.1 cm⁻¹): mirror needs to travel 5 cm
• Ultra-high resolution (0.01 cm⁻¹): mirror needs to travel 25 cm (e.g., Bruker 125HR and similar high-resolution instruments)

Newport material points out [12]:

"FT-IRs are capable of high resolution because the resolution limit is simply an inverse of the achievable optical path difference."

Thermo Fisher also explains the difference between single-sided and double-sided interferograms [11]:

"In a Thermo Fisher Scientific FTIR system, this general rule holds true for the resolutions of 0.5 cm⁻¹ and higher because the instrument collects a single-sided interferogram. For resolutions of 1 cm⁻¹ and lower, the instrument will collect a double-sided interferogram."

4.3 Practical Implications

This formula tells us an important practical implication: higher resolution requires longer mirror travel [11][12].

• Conventional FTIR mirror travel is typically 0.5–1 cm (corresponding to 1–2 cm⁻¹ resolution)
• High-resolution research-grade instruments can achieve 10–100 cm travel (corresponding to 0.005–0.05 cm⁻¹)
• Longer travel demands higher precision in guide rails and mirror alignment

💡 Practical tip: In routine analysis, 4 cm⁻¹ resolution is sufficient to distinguish functional groups of most organic compounds. High resolution below 0.1 cm⁻¹ is only needed for gas small molecules or lattice vibration studies.

5. Beamsplitter Materials

Beamsplitter materials must be selected according to the spectral range to ensure good transmittance and appropriate refractive index in that range [13][14].

5.1 Beamsplitters for Different Spectral Regions

Table 3: Beamsplitter materials for different spectral regions (data from Tydex [13]; HKUST [14])

Tydex provides a complete mapping of beamsplitter materials to wavelength ranges [13]:

| Visible-IR Fused Silica | 0.4–1.1 μm or 0.65–3.0 μm |
| CaF₂ | 0.65–8.5 μm |
| BaF₂ | 0.65–12 μm |
| ZnSe | 2–14 μm |
| HRFZ-Si | 50–1000 μm |

5.2 Precautions for KBr Beam Splitter

KBr is the most commonly used beam splitter substrate for mid-infrared, but it has a fatal weakness—extremely hygroscopic [13][14].

After KBr absorbs moisture [14]:

• The surface becomes cloudy, reducing transmittance
• Beam splitter efficiency changes, affecting spectral quality
• Replacement may be required in severe cases

Therefore, FTIR instruments using KBr beam splitters require [14]:

• Continuous purging with dry air or nitrogen
• Keeping the instrument interior dry (desiccant)
• Sealed storage when not in use for extended periods

💡 Practical Tip: If your laboratory environment has high humidity, consider using a ZnSe beam splitter (non-hygroscopic), which is more expensive but easier to maintain.

6. He-Ne Laser Reference: The "Ruler" of FTIR

6.1 Why is a Laser Reference Needed?

The wavenumber axis (x-axis) of FTIR requires precise calibration. In dispersive instruments, wavelength calibration relies on external calibration standards and the mechanical uniformity of grating movement [3][15].

In FTIR, an internal He-Ne laser (wavelength 632.8 nm) provides absolute calibration [3][15]:

• He-Ne laser wavelength is extremely stable (stability better than 10⁻⁸)
• The laser beam passes through the interferometer parallel to the infrared beam
• The laser produces a sinusoidal reference signal on a separate detector

6.2 Sampling Trigger Mechanism

Key relationship: For each complete laser interference fringe (one full cycle), the moving mirror travels [3][15]:

$$\Delta x = \frac{\lambda_{\text{HeNe}}}{2} = \frac{632.8\text{ nm}}{2} \approx 316.4\text{ nm}$$

This is due to the round trip of the beam—physical movement of λ/2 corresponds to an optical path difference change of λ [3].

Hackaday's engineering documentation describes this elegantly [15]:

"Since the HeNe wavelength λ_HeNe = 632.8nm is stable and known to extreme precision, every single fringe (cycle) corresponds to a mirror movement of exactly λ_HeNe/2 ≈ 316.4 nm. This stability is why the HeNe has been the Grandfather of FTIR; it converts a noisy, unpredictable motor movement into a perfectly known, equidistant sampling grid."

Sampling process [3][15]:

1. The He-Ne laser interference fringes are received by the reference detector
2. High-precision electronics output voltage pulses at the zero crossings of the sinusoidal signal
3. Each pulse triggers the A/D converter to sample the main (infrared) interferogram once
4. Therefore, interferogram data points are equally spaced on the optical path difference axis with a spacing of 316.4 nm

Newport documentation adds [3]:

"By use of only positive zero crossings, the circuitry can output one pulse per cycle of the reference interferogram, or use all zero crossings for two pulses per cycle (oversampling)."

6.3 Wavelength Calculation

For the infrared light being measured, its wavelength is determined by the reference laser wavelength and the frequency ratio [3]:

$$\lambda_i = \lambda_r \times \frac{f_r}{f_i}$$

where subscript r denotes the He-Ne reference laser and i denotes the infrared light being measured [3].

Since λ_r is known with extreme precision, the wavenumber calibration of the infrared light is directly determined by the laser wavelength—this is the physical basis of the Connes advantage (Ep 11) [3][15].

"These instruments are self-calibrating and never require user calibration."
—— Thermo Fisher [16]

7. Nyquist Sampling Theorem

7.1 Theorem Statement

Nyquist-Shannon sampling theorem: To faithfully reconstruct a continuous signal from its discrete samples, the sampling frequency f_s must be at least twice the highest frequency f_max present in the signal [3][17]:

$$f_s \geq 2 \cdot f_{\max}$$

The Nyquist frequency f_N = f_s / 2 [3][17].

7.2 Application in FTIR

The interferogram is sampled at the zero crossings of the He-Ne laser. Newport documentation derives the maximum measurable wavenumber determined by this [3]:

Since the minimum value of (f_r/f_i) is 2, the corresponding minimum measurable wavelength is [3]:

$$\lambda_{\min} = 633\text{ nm} \times 2 = 1.266\text{ μm}$$

Corresponding to a wavenumber of approximately 7,902 cm⁻¹ [3].

If oversampling is used (using all zero crossings, effectively halving the laser wavelength) [3]:

$$\lambda_{\min} = \frac{633\text{ nm}}{2} \times 2 = 633\text{ nm}$$

Corresponding to 15,800 cm⁻¹ [17].

Bruker documentation (Herres & Gronholz) confirms [17]:

"nHeNe = 15800 cm⁻¹, i.e. the maximum bandwidth which can be measured without overlap has a width of 15800 cm⁻¹. A larger range can be covered, if the laser frequency is electronically doubled (frequency multiplication)."

7.3 Aliasing

If the Nyquist condition is violated—i.e., the signal contains components above the Nyquist frequency—aliasing occurs: high-frequency components are "folded" into the low-frequency region, causing spectral distortion [3][17].

Normal sampling (satisfies Nyquist condition):
  Original signal frequency f < f_N → Correct reconstruction

Undersampling (violates Nyquist condition):
  Original signal frequency f > f_N → Mistaken as (f_s - f) → Spectral distortion!

Practical impact: Standard He-Ne sampling (15,800 cm⁻¹ Nyquist frequency) is sufficient to cover the mid-infrared (4000–400 cm⁻¹) without aliasing. However, if measuring near-infrared (up to 10,000 cm⁻¹), ensure the sampling frequency is high enough [3][17].

8. Apodization

8.1 Why is Apodization Needed?

The moving mirror travel is finite; the interferogram is truncated at ±L. Mathematically, this is equivalent to multiplying the interferogram by a rectangular function (boxcar) [7][17].

The Fourier transform of a rectangular function is a sinc function, whose first sidelobe amplitude is -21.7% of the main lobe [7][17]. These sidelobes (called "feet") can mask weak signals near the main peak.

The term "apodization" comes from Latin, meaning "cutting off the feet" [7].

8.2 Common Apodization Functions

Shimadzu's technical note provides a detailed comparison of several common apodization functions [7]:

| Happ-Genzel (HG) | 0.54+0.46·cos(πx/L) | Medium | Good | Bruker default |
| Norton-Beer | Polynomial weighting | Medium | Best compromise | High-precision quantitation |

Table 4: Comparison of common apodization functions (data sources: Shimadzu [7]; Naylor & Tahic [18])

Shimadzu explains the cost of apodization [7]:

"Applying some type of function to Fourier transform integration to reduce the ripples... is called 'apodization'... reducing the ripples... the central peak is also lower and somewhat wider. This appears as reduced resolution."

Apodization effect comparison:

  Rectangle (no apodization):      Triangle (apodized):

  │   ╱╲                    │   ╱╲
  │  ╱  ╲  ╱╲              │  ╱    ╲
  │ ╱    ╲╱  ╲  ╱╲        │ ╱      ╲
  │╱         ╲╱  ╲         │╱        ╲
  └──────────────→ σ̃       └──────────────→ σ̃

  High resolution, large sidelobes     Slightly lower resolution, small sidelobes

📷 Figure 3: Instrument functions (sinc function vs. triangular function) for different apodization functions
Source: Shimadzu FTIR Talk Letter vol.15 [7]
https://www.shimadzu.com/an/s…

8.3 Practical Choice

The Chinese textbook "Fourier Transform Infrared Spectroscopy Analysis" (Weng Shifu) states [19]:

"After using the apodization function, the 'feet' are removed, but the spectral resolution is reduced... In most cases, regardless of the apodization function used, the obtained spectra are quite similar."

Practical recommendations:

• Routine analysis: Use the instrument's default apodization function (usually Happ-Genzel or Norton-Beer medium)
• High-resolution gas analysis: Boxcar may be required for maximum resolution
• Quantitative analysis: Norton-Beer offers the best photometric accuracy

IX. Phase Correction

9.1 Why is phase correction necessary?

An ideal interferogram is symmetric about ZPD, and a cosine transform yields the correct spectrum. However, actual interferograms have phase errors φ(σ̃) due to the following reasons [9][20]:

1. Electronic filter delay — the signal processing circuit introduces a phase shift
2. Optical dispersion — the refractive index of the beamsplitter and windows varies with wavelength
3. Imprecise ZPD sampling — data sampling points may not exactly coincide with ZPD

Phase errors cause asymmetry in the interferogram, leading to peak position shifts and spectral distortions [9][20].

9.2 Common Methods

Table 5: Comparison of phase correction methods

9.3 Detailed Mertz Method

The Mertz method is the standard phase correction method in most commercial FTIR instruments [9][20]:

1. Take a short double-sided interferogram near ZPD (e.g., ±64 data points)
2. Perform FFT on this double-sided interferogram to obtain a low-resolution phase spectrum φ(σ̃)
3. Interpolate the phase spectrum to the full interferogram length
4. Use the phase spectrum to correct the complex spectrum of the full interferogram
5. Take the real part as the final spectrum

Deng Jinglan et al. (2021) from the Hefei Institutes of Physical Science, Chinese Academy of Sciences, proposed an improved Mertz method using odd-order polynomial weighting, which increased the average signal-to-noise ratio by 1.2% and 2.3% in the 900–1100 cm⁻¹ and 2500–2600 cm⁻¹ bands, respectively [22].

X. Zero-Filling

10.1 What is zero-filling?

Zero-filling is the addition of zeros at the end of the interferogram to increase the number of data points before performing the FFT [17][23].

Original interferogram (N data points):
[████████████████████]

After zero-filling (2N data points):
[████████████████████ 00000000000000000000]
                       ↑ zeros added

10.2 Effects

1. Spectral interpolation: More FFT points yield a denser spectral data grid, smoother spectral lines, and easier peak determination [17][23]
2. Power-of-two requirement: FFT algorithms require the number of data points to be a power of two; zero-filling can bring the data length to 2^n [23]
3. No increase in true resolution: Zero-filling only interpolates existing data; it does not add new spectral information [17]

Bruker documentation (Herres & Gronholz) provides a rule of thumb [17]:

"One should always at least double the original interferogram size for practical measurements by zero filling it, i.e. one should choose a zero filling factor (ZFF) of two. In those cases, however, where the expected line width is similar to the spectral sample spacing (as e.g. in case of gas-phase spectra), a ZFF of four or higher may be required."

10.3 Important Distinction

Zero-filling increases digital resolution (data point density), not optical resolution [17].

• Optical resolution = 1/(2L), determined by the moving mirror travel
• Digital resolution = spectral range / number of data points, can be altered by zero-filling

For example: 4000–400 cm⁻¹ range, 4 cm⁻¹ optical resolution, original data point spacing 4 cm⁻¹ (about 900 points). After one zero-filling, the data point spacing becomes 2 cm⁻¹, the spectral lines are smoother, but the minimum resolvable peak separation is still 4 cm⁻¹ [17].

XI. Evolution of Interferometer Design

11.1 Classical Michelson Interferometer

The classical design uses a plane fixed mirror and a plane moving mirror [15][24]. The structure is simple, but it is extremely sensitive to tilting of the moving mirror — any angular error α causes the returning beam to deviate by 2α [15].

Hackaday's engineering documentation gives an example [15]:

At an optical path length of 1 meter, a tilt of 0.1° would cause a beam offset of 3.4 mm — catastrophic for precision interferometry.

11.2 Corner Cube Retroreflector

To address tilt sensitivity, modern FTIR instruments widely use corner cube retroreflectors [15][24]:

• Three mutually perpendicular reflecting surfaces

• After three reflections, the beam returns strictly parallel to the incoming direction

• Key advantage: Insensitive to tilt—even if the entire prism is tilted, the triple-reflection correction cancels the initial tilt [15][24]

Hackaday JASPER project comparison [15]:

"The moving mirror must maintain perfect parallelism... A plane mirror would require impossible mechanical precision... The retro-reflector, however, can handle the minute mechanical imperfections of the moving stage, automatically correcting the beam's path."

Note: Solid corner cube prisms (e.g., BK7 glass) absorb infrared light, so FTIR uses hollow retroreflectors—corner cubes made of three plane mirrors [15][24].

11.3 Dynamic Alignment

High-end instruments such as Bruker use dynamic alignment [24]:

• Uses an auxiliary laser to monitor the moving mirror's attitude in real time
• Active correction via piezoelectric actuators
• Maintains alignment over long travel (high resolution)

11.4 Other Designs

Table 6: Comparison of interferometer designs

12. Michelson's Historical Legacy

12.1 Michelson-Morley Experiment

Albert A. Michelson (1852–1931), German-American physicist [1][2]:

• 1881: Invented the Michelson interferometer at the Helmholtz Laboratory in Berlin, Germany, to detect the "ether wind"
• 1887: Conducted the famous Michelson-Morley experiment with Edward Morley
• Result: Negative—no expected interference fringe shift was observed [1][2]

Britannica encyclopedia records [2]:

"Those results were still negative; there were no interference fringes and apparently no motion of the earth relative to the ether."

This "failed experiment" is considered "the theoretical starting point of the second scientific revolution," paving the way for Einstein's special theory of relativity (1905) [1][2].

12.2 Nobel Prize

1907, Michelson won the Nobel Prize in Physics, with citation [1]:

"...for his optical precision instruments and the research which he has carried out with their help in the fields of precision metrology and spectroscopy."

He became the first American to win a Nobel Prize in science [1].

12.3 Michelson's Contributions to Spectroscopy

Michelson not only did the ether drift experiment, but also [1][2]:

• Invented the "echelon grating"
• Measured stellar diameters (Betelgeuse) using an interferometer
• First observed fine structure of spectral lines (later explained as isotope effects and hyperfine structure)
• Nobel lecture titled "Recent Advances in Spectroscopy" (December 12, 1907) [1]

12.4 Legacy Continues—LIGO

The legacy of the Michelson-Morley experiment continues: LIGO gravitational wave detector (first detected gravitational waves in 2015) is essentially a giant Michelson interferometer with 4 km arms [1].

From the "failed experiment" of 1887 to the gravitational wave detection in 2015, to the precise interferometer in every FTIR today—the story of the Michelson interferometer is one of the most moving chapters in the history of science.

📷 Figure 4: Michelson interferometer principle and portrait of Michelson
Source: Nobel Prize official website [1]
https://www.nobelprize.org/pr…

🔗 Extension: The interferometer determines wavenumber accuracy; when performing daily wavenumber verification using polystyrene film, the aromatic ring-related peaks can be referenced at ftir.fun aromatic page (see Ep 50 for details).

Summary of This Episode

Table 7: Quick reference of core knowledge points in this episode

Review Questions

1. Why does the interferogram have a sharp "center burst" at ZPD? What would the detector see if the moving mirror stops at ZPD?

2. To achieve a resolution of 0.5 cm⁻¹, how far must the moving mirror travel? What about 0.01 cm⁻¹?

3. The He-Ne laser wavelength is 632.8 nm. What is the optical path difference between two adjacent sampling points? Why?

4. What phenomenon appears in the spectrum if the Nyquist sampling theorem is violated? How to avoid it?

5. What is the "cost" of the apodization function? Why can't we simply not use apodization?

6. Can zero-filling improve the optical resolution of the spectrum? Why? What can it improve?

7. Why is the KBr beamsplitter prone to moisture absorption? How should you maintain it if your FTIR uses a KBr beamsplitter? What are alternatives?

8. Why is the plane moving mirror in a classic Michelson interferometer extremely sensitive to tilt? How does a corner-cube retroreflector solve this problem?

References

[1] Nobel Prize. "Albert A. Michelson – Nobel Lecture: Recent Advances in Spectroscopy." 1907.
https://www.nobelprize.org/pr…

[2] Britannica. "A.A. Michelson." Encyclopaedia Britannica.
https://www.britannica.com/bi…

[3] Newport. "Introduction to FTIR Spectroscopy." Technical Note.
https://www.newport.com.cn/n/…

[4] LibreTexts. "FTIR: Hardware." Analytical Chemistry Supplemental Modules.
https://chem.libretexts.org/B…

[5] JASCO. "What is an FTIR Spectrometer?" Learning Center.
https://jascoinc.com/learning…

[6] LibreTexts. "3.08: Fourier Transform IR Spectroscopy." CHE 205 - Heffern, UC Davis.
https://chem.libretexts.org/C…

[7] Shimadzu. "Fourier Transform and Apodization." FTIR Talk Letter, vol.15.
https://www.shimadzu.com/an/s…

[8] Rioux, F. "The Michelson Interferometer and Fourier Transform Spectroscopy." CSB|SJU.
http://www.users.csbsju.edu/~…

[9] LibreTexts. "FTIR: Computational." Analytical Chemistry Supplemental Modules.
https://chem.libretexts.org/@…

[10] Rockmore, D. "The FFT: An Algorithm the Whole Family Can Use." Stanford CS339 Lecture Notes.
https://web.stanford.edu/clas…

[11] Thermo Fisher Scientific. "FTIR Moving Mirror Travel Distance Calculation." Knowledge Base.
https://knowledge1.thermofish…

[12] Newport. "Introduction to FTIR Spectroscopy." (Resolution section)
https://www.newport.com.cn/n/…

[13] Tydex Optics. "FTIR Beam Splitter Substrates."
https://www.tydexoptics.com/p…

[14] HKUST MCPF. "Fourier Transform Infra-Red Spectroscopy (FTIR)." Materials Preparation and Characterization Facility.
http://www.mcpf.hkust.edu.hk/…

[15] Hackaday. "JASPER FTIR Project Logs." (He-Ne laser sampling, retroreflector comparison)
https://hackaday.io/project/2…
https://hackaday.io/project/2…

[16] Thermo Fisher Scientific. "Introduction to FTIR." Brochure BR50555.
https://documents.thermofishe…

[17] Herres, W. & Gronholz, J. "Understanding FT-IR Data Processing." Bruker/Caltech Document.
https://mmrc.caltech.edu/FTIR…

[18] Naylor, D.A. & Tahic, M.K. "Apodizing Functions for Fourier Transform Spectroscopy." J. Opt. Soc. Am. A, 2007, 24(11).
https://www.researchgate.net/…

[19] Weng, S. "Fourier Transform Infrared Spectroscopy Analysis (Third Edition)."
https://read.qq.com/read/1025…

[20] Zhang, M., et al. "Research on Phase Correction Method for Fourier Transform Spectrometer." Spectroscopy and Spectral Analysis, 2012, 32(5):1203-1208.
https://www.gpxygpfx.com/EN/1…

[21] Furstenberg, R. & White, J. "Phase Correction of Interferograms Using Digital All-Pass Filters." Applied Spectroscopy, 2005.
https://www.researchgate.net/…

[22] Deng Jinglan et al. "Improved Mertz Phase Correction Method." Chinese Journal of Quantum Electronics, 2021.
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Next episode preview: Ep 13 — Introduction to Sampling Techniques: Transmission Method (KBr pellet, liquid cell, thin film)
After understanding the "heart" of FTIR, in the next episode we turn to sample preparation. From the classic KBr pellet method to liquid cell and thin film methods, learn how to prepare samples of different forms for infrared transmission measurements.

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