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Related Concept Videos

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...
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...
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...
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.

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Compact Lens-less Digital Holographic Microscope for MEMS Inspection and Characterization
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Compact Lens-less Digital Holographic Microscope for MEMS Inspection and Characterization

Published on: July 5, 2016

Undersampled digital holography.

Nazif Demoli1, Hanan Halaq, Kristina Sariri

  • 1Institute of Physics, Bijenicka cesta 46, PO Box 304, 10001 Zagreb, Croatia. demoli@ifs.hr

Optics Express
|September 3, 2009
PubMed
Summary
This summary is machine-generated.

Undersampling in off-axis digital holography allows signal recovery. Increasing beam angles beyond Nyquist limits causes image folding and inversion, but removing the zeroth-order term extends usable intervals.

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Area of Science:

  • Optics and Photonics
  • Digital Imaging
  • Holographic Systems

Background:

  • Off-axis digital holography systems rely on band-pass signals.
  • Hologram reconstruction is limited by photodetector sampling frequency under undersampling conditions.
  • Beam angle is a critical parameter influencing reconstruction fidelity.

Purpose of the Study:

  • To analyze hologram reconstruction from undersampled digital holograms theoretically and experimentally.
  • To define and evaluate the phase point at image fading and non-overlapping intervals for information preservation.
  • To demonstrate extending these intervals by removing the zeroth-order reconstruction term.

Main Methods:

  • Theoretical analysis of undersampled hologram reconstruction.
  • Experimental validation using a typical off-axis digital holography system.
  • Analysis of amplitude distributions using time-averaged holograms of an oscillating membrane.

Main Results:

  • Increasing beam angles beyond Nyquist limits causes repeated folding and inversion of the reconstructed image.
  • The phase point at image fading and non-overlapping intervals were defined and evaluated.
  • Removing the zeroth-order reconstruction term significantly extends the intervals for preserving useful information.

Conclusions:

  • Acceptable signal recovery is achievable in undersampled off-axis digital holography.
  • Understanding the effects of beam angle beyond Nyquist limits is crucial for image reconstruction.
  • Optimizing reconstruction by removing the zeroth-order term enhances data preservation in undersampled holograms.