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00:59Uncertainty: Overview
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01:10Propagation of Uncertainty from Systematic Error
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00:59Propagation of Uncertainty from Random Error
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An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
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01:17Bandpass Sampling
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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....
A bandpass signal has a spectrum with a lower frequency limit, denoted as ω1, and an upper frequency limit, denoted as ω2....
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01:24IR Frequency Region: X–H Stretching
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On space-spectrum uncertainty analysis for spectrally programmable cameras.
Optics Express
|April 1, 2020
Summary
High-resolution spectral programming in cameras is limited by space-spectrum uncertainty. Achieving high spatial resolution compromises spectral resolution due to a fundamental optical trade-off.
Area of Science:
- Optics and Photonics
- Computational Imaging
- Spectroscopy
Background:
- Spectrally programmable cameras offer versatile imaging capabilities.
- Simultaneous high-resolution spatial and spectral information acquisition is a significant challenge in optical systems.
Purpose of the Study:
- To introduce and analyze the concept of space-spectrum uncertainty in spectrally programmable cameras.
- To establish a fundamental limit on the simultaneous acquisition of high-resolution spatial images and spectral information.
Main Methods:
- Theoretical analysis of the Fourier relationship between spectral resolving aperture and spatial diffraction blur.
- Derivation of a lower bound for the product of spatial and spectral uncertainties.
- Experimental validation using a laboratory prototype of a spectrally programmable camera.
Main Results:
- A fundamental trade-off exists between spatial and spectral resolution in spectrally programmable cameras.
- The product of spatial and spectral standard deviations is lower bounded by a physical constant involving wavelength and grating density.
- Experimental results confirm the theoretical predictions of space-spectrum uncertainty.
Conclusions:
- It is impossible to achieve simultaneously high-resolution spatial imaging and high-resolution spectral programming.
- The derived lower bound provides a quantitative measure for the space-spectrum uncertainty.
- Findings have direct implications for the design and optimization of future spectrally programmable imaging systems.