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Related Concept Videos

Reconstruction of Signal using Interpolation01:10

Reconstruction of Signal using Interpolation

Signal processing techniques are essential for accurately converting continuous signals to digital formats and vice versa. When a continuous signal is sampled with a period T, the resulting sampled signal exhibits replicas of the original spectrum in the frequency domain, spaced at intervals equal to the sampling frequency. To handle this sampled signal, a zero-order hold method can be applied, which creates a piecewise constant signal by retaining each sample's value until the next sampling...
Aliasing01:18

Aliasing

Accurate signal sampling and reconstruction are crucial in various signal-processing applications. A time-domain signal's spectrum can be revealed using its Fourier transform. When this signal is sampled at a specific frequency, it results in multiple scaled replicas of the original spectrum in the frequency domain. The spacing of these replicas is determined by the sampling frequency.
If the sampling frequency is below the Nyquist rate, these replicas overlap, preventing the original signal...
Upsampling01:22

Upsampling

Managing signal sampling rates is essential in digital signal processing to maintain signal integrity. A decimated signal, characterized by a reduced frequency range due to its lower sampling rate, can be upsampled by inserting zeros between each sample. This upsampling process expands the original spectrum and introduces repeated spectral replicas at intervals dictated by the new Nyquist frequency. To refine this zero-inserted sequence, it is passed through a lowpass filter with a cutoff...
Sampling Theorem01:15

Sampling Theorem

In signal processing, the analysis of continuous-time signals, denoted as x(t), often involves sampling techniques to convert these signals into discrete-time signals. This process is essential for digital representation and manipulation. A critical component in sampling is the train of impulses, characterized by the sampling interval and the sampling frequency. The relationship between these parameters and the original signal's properties dictates the success of the sampling process.
Downsampling01:20

Downsampling

When considering a sampled sequence with zero values between sampling instants, one can replace it by taking every N-th value of the sequence. At these integer multiples of N, the original and sampled sequences coincide. This process, known as decimation, involves extracting every N-th sample from a sequence, thereby creating a more efficient sequence.
The Fourier transform of the decimated sequence reveals a combination of scaled and shifted versions of the original spectrum. This...
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.

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Related Experiment Video

Updated: Jun 12, 2026

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
08:39

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

Published on: January 28, 2019

Equal-phase resampling with periodic error suppression in swept-source interferometry under non-ideal I/Q

Hu Peng, Junkang Guo, Yuan Cao

    Optics Express
    |June 11, 2026
    PubMed
    Summary

    We developed Periodic Error Suppressed Resampling (PESR) to correct laser sweep nonlinearity in interferometry. PESR effectively suppresses resampling errors caused by imperfect I/Q demodulation, improving accuracy and repeatability.

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    Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques

    Published on: April 4, 2017

    Area of Science:

    • Optical Metrology
    • Interferometry
    • Signal Processing

    Background:

    • Swept-source interferometry relies on equal-phase resampling to correct laser sweep nonlinearity.
    • Optical I/Q demodulation offers low-latency resampling but suffers from hardware imperfections like amplitude mismatch and quadrature phase deviation.
    • These non-ideal I/Q demodulation effects introduce phase-dependent ripples, distorting the resampling grid and degrading spectral quality.

    Purpose of the Study:

    • To propose and validate a novel equal-phase resampling method, Periodic Error Suppressed Resampling (PESR), robust to significant I/Q imbalance.
    • To theoretically analyze the intrinsic periodic nature of arctangent demodulation errors caused by quadrature deviations.
    • To demonstrate PESR's effectiveness in suppressing resampling errors without compromising accuracy in swept-source interferometry.

    Main Methods:

    • Theoretical analysis proving the π-periodic component of arctangent demodulation error in the phase domain.
    • Development of a "residual-phase-error filtering" strategy to suppress periodic ripples while preserving the resampling scale.
    • Experimental validation on a swept-source interferometric ranging platform under severe quadrature errors.

    Main Results:

    • PESR effectively suppresses the phase-dependent ripple caused by I/Q imbalance.
    • Simulations confirmed the π-periodic characteristic of demodulation errors and highlighted potential biases of simple low-pass filtering.
    • Experimental results showed sidelobe suppression to -25.5 dBc, sub-3-µm RMS accuracy, and 0.09 µm repeatability.

    Conclusions:

    • PESR provides a reliable and efficient solution for correcting sweep nonlinearity in swept-source interferometry, even with significant hardware imperfections.
    • The method relaxes the need for long auxiliary optical path differences common in traditional approaches.
    • PESR enables high-stability metrology with improved accuracy and repeatability.