Related Experiment Video
Updated: Jun 12, 2026

06:48
A Multimodal Wide-Field Fourier-Transform Raman Microscope
Published on: December 30, 2025
Incoherent bandpass spatial filtering with longitudinal periodicity
Applied Optics
|June 23, 2010
Summary
This study demonstrates bandpass filtering with longitudinal periodicity in incoherent systems. A two-pupil system using Fresnel zone plates enables this spatial filtering effect.
Area of Science:
- Optics and Photonics
- Wave Phenomena
Background:
- Incoherent optical systems typically lack longitudinal periodicity in their filtering characteristics.
- Achieving controlled spatial filtering in the longitudinal dimension is a challenge.
Purpose of the Study:
- To investigate the feasibility of bandpass filtering with longitudinal periodicity in incoherent systems.
- To derive the conditions necessary for achieving longitudinally periodic spatial filtering.
Main Methods:
- Theoretical derivation of the necessary conditions for longitudinally periodic spatial filtering.
- Analysis of a two-pupil system employing Fresnel zone plates.
Main Results:
- A necessary condition for achieving longitudinally periodic spatial filtering was successfully derived.
- The study confirmed that bandpass filtering with longitudinal periodicity is achievable.
- This effect was demonstrated in a specific two-pupil configuration using Fresnel zone plates with a small opening ratio.
Conclusions:
- Bandpass filtering with longitudinal periodicity is possible in incoherent optical systems.
- The proposed two-pupil system with specific Fresnel zone plates offers a practical method for realizing this phenomenon.
Related Concept Videos
Bandpass Sampling
In signal processing, bandpass sampling is an effective technique for sampling signals that have most of their energy concentrated within a narrow frequency band. This type of signal is known as a bandpass signal. The key principle of bandpass sampling involves sampling the signal at a rate that is greater than twice the signal's bandwidth to prevent aliasing.
A bandpass signal has a spectrum with a lower frequency limit, denoted as ω1, and an upper frequency limit, denoted as ω2. The spectrum...
A bandpass signal has a spectrum with a lower frequency limit, denoted as ω1, and an upper frequency limit, denoted as ω2. The spectrum...
Passive Filters
Passive filters are utilized to shape the frequency spectrum of signals across a diverse array of applications. These filters, using only passive elements like resistors (R), inductors (L), and capacitors (C), are capable of selectively allowing or blocking certain frequency ranges without the need for external power sources.
Low-Pass Filters
Low-pass filters are designed to transmit signals with frequencies lower than the cutoff frequency, ωc, and attenuate those above it. The cutoff frequency...
Low-Pass Filters
Low-pass filters are designed to transmit signals with frequencies lower than the cutoff frequency, ωc, and attenuate those above it. The cutoff frequency...
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...
Parallel Resonance
The parallel RLC circuit is an arrangement where the resistor (R), inductor (L), and capacitor (C) are all connected to the same nodes and, as a result, share the same voltage across them. The parallel RLC circuit is analyzed in terms of admittance (Y), which reflects the ease with which current can flow. The admittance is given by:
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.
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.
Active Filters
Active filters are electronic circuits that use operational amplifiers (op-amps), resistors, and capacitors to filter out unwanted frequency components from a signal. A first-order low-pass active filter is designed to pass signals with a frequency lower than a certain cutoff frequency and attenuate frequencies higher than that cutoff frequency. The transfer function for a first-order low-pass active filter is:
