MATLAB Code Implementation for Simulating Interferogram Data

In optical measurement and spectral analysis, interferograms are common data forms typically generated by interferometers. Simulating interferogram data using MATLAB, along with apodization processing and spectral analysis, helps us better understand interference phenomena and their data processing methods.

### 1. Simulating Interferogram Data Interferograms usually consist of interference signals from light sources, which can be simulated as cosine waves or Gaussian envelope modulated signals. Assuming the interference signal comes from an ideal monochromatic light source, we can construct an interferogram containing optical path difference and wavenumber information. By setting the wavenumber range and sampling points, a symmetric interference signal can be generated to simulate actual interferometer output data. Code Implementation Approach: - Use linspace() to create optical path difference arrays - Implement cosine functions with phase terms to simulate interference patterns - Apply Gaussian modulation using exp() functions for realistic signal envelopes - Generate symmetric signals using array manipulation techniques

### 2. Apodization Processing Due to finite sampling ranges in actual interferometer measurements, direct Fourier transformation of interferograms causes sidelobe effects that affect spectral resolution. Apodization reduces sidelobes and improves spectral quality by applying window functions (such as Hanning, Hamming, etc.). Common apodization methods include: Rectangular window (no apodization): Uses raw data directly with high sidelobes Hanning window: Provides smooth transition, reduces sidelobes, but slightly decreases spectral resolution Gaussian window: Offers further smoothing, suitable for high-precision spectral analysis Key MATLAB Functions: - window() function for various window types - Element-wise multiplication (.*) to apply windows to interferogram data - Parameter tuning for window width and shape optimization

### 3. Spectral Calculation Performing Fourier transform (FFT) on apodized interferograms yields the light source's spectral distribution. Since interferograms are real signals, single-sided FFT is typically used to obtain the positive frequency portion of the spectrum. The final spectral data requires normalization processing and wavenumber calibration to obtain spectral curves that match experimental expectations. Algorithm Implementation: - Use fft() for Fourier transformation with proper scaling - Implement fftshift() for frequency domain rearrangement - Apply absolute value operations and normalization factors - Include wavenumber calibration using interpolation functions

Simulating interferogram data with MATLAB and performing apodization processing can effectively validate the reliability of spectral analysis algorithms, providing theoretical support for actual experimental data processing.