Related Experiment Video
Updated: Jun 15, 2026
06:48
A Multimodal Wide-Field Fourier-Transform Raman Microscope
Published on: December 30, 2025
Qualitative and semiquantitative Fourier transformation using a noncoherent system
Applied Optics
|March 10, 2010
Summary
This study demonstrates a zone plate system capable of generating both sine and cosine Fourier transforms of inputs. Artifacts were observed in transforms due to moire patterns, impacting off-axis accuracy.
Area of Science:
- Optics
- Fourier Optics
- Diffractive Optics
Background:
- Zone plate systems are known to display Fourier transforms of inputs.
- Typically, these systems produce cosine transforms with positive-only intensity variations.
Purpose of the Study:
- To investigate the generation of sine and cosine Fourier transforms using zone plate systems.
- To analyze the performance and limitations of such systems, including artifact formation.
Main Methods:
- Utilized a zone plate system with a diffuse source, transparent input, lens, and focusing screen.
- Employed phase-shifting of a zone plate to obtain the sine transform.
- Analyzed the sine and cosine transforms of a small circular aperture.
Main Results:
- Successfully generated both sine and cosine Fourier transforms.
- The sine transform of a circular aperture resulted in a uniform gray output.
- Observed unwanted artifacts beyond 0.1 rad off-axis in both transforms.
- Identified circularly symmetrical moire patterns between zone plates as the cause of artifacts.
Conclusions:
- Zone plate systems can be adapted to produce sine and cosine Fourier transforms.
- System limitations, such as moire patterns, introduce artifacts affecting transform accuracy at larger angles.
- Further system redesign may be necessary to mitigate these artifacts for improved performance.
Related Concept Videos
01:21Properties of Fourier Transform I
The application of Fourier Transform properties in radio broadcasting is multifaceted, enabling significant advancements in the way signals are transmitted and received. Key areas where these properties are utilized include simultaneous multi-channel transmission, audio clip speed adjustments, live broadcast delays for different time zones, audio frequency adjustments, and signal demodulation.
In radio broadcasting, multiple audio signals often need to be transmitted simultaneously. The Fourier...
In radio broadcasting, multiple audio signals often need to be transmitted simultaneously. The Fourier...
01:15Discrete Fourier Transform
The Discrete Fourier Transform (DFT) is a fundamental tool in signal processing, extending the discrete-time Fourier transform by evaluating discrete signals at uniformly spaced frequency intervals. This transformation converts a finite sequence of time-domain samples into frequency components, each representing complex sinusoids ordered by frequency. The DFT translates these sequences into the frequency domain, effectively indicating the magnitude and phase of each frequency component present...
01:24Properties of Fourier Transform II
The Fourier Transform (FT) is an essential mathematical tool in signal processing, transforming a time-domain signal into its frequency-domain representation. This transformation elucidates the relationship between time and frequency domains through several properties, each revealing unique aspects of signal behavior.
The Frequency Shifting property of Fourier Transforms highlights that a shift in the frequency domain corresponds to a phase shift in the time domain. Mathematically, if x(t) has...
The Frequency Shifting property of Fourier Transforms highlights that a shift in the frequency domain corresponds to a phase shift in the time domain. Mathematically, if x(t) has...
01:11Continuous -time Fourier Transform
The Fourier series is instrumental in representing periodic functions, offering a powerful method to decompose such functions into a sum of sinusoids. This technique, however, necessitates modification when applied to nonperiodic functions. Consider a pulse-train waveform consisting of a series of rectangular pulses. When these pulses have a finite period, they can be accurately represented by a Fourier series. Yet, as the period approaches infinity, resulting in a single, isolated pulse, the...
01:07Basic signals of Fourier Transform
The Fourier Transform is a pivotal mathematical tool in signal processing, enabling the transformation of time-domain signals into their frequency-domain representations. Among the numerous elements within this domain, certain functions like the sinc function, delta function, and exponential signals hold significant importance due to their unique properties and implications.
The sinc function, defined as sinc(x) = sin(πx)/(πx), is particularly notable for its symmetry and behavior at zero. It...
The sinc function, defined as sinc(x) = sin(πx)/(πx), is particularly notable for its symmetry and behavior at zero. It...
01:26Discrete-time Fourier transform
The Discrete-Time Fourier Transform (DTFT) is an essential mathematical tool for analyzing discrete-time signals, converting them from the time domain to the frequency domain. This transformation allows for examining the frequency components of discrete signals, providing insights into their spectral characteristics. In the DTFT, the continuous integral used in the continuous-time Fourier transform is replaced by a summation to accommodate the discrete nature of the signal.
One of the notable...
One of the notable...