Fourier Methods in Imaging

Easton, Roger L.

doi:10.1002/9780470660102

Cited by 66 publications

(42 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Truncation causes non-zero amplitudes belonging to the lower frequencies located at the higher frequencies after we perform the IFT. 16 To reduce the effects of signal truncation we can multiply the measured interferogram by an apodization function that slowly decays to zero at the endpoints. We perform apodization with the Hamming window, as in the SHIMCAD system.…”

Section: Apodizationmentioning

confidence: 99%

“…This causes an induced phase error we need to correct by taking the magnitude of the spectrum after the IFT to maintain the spectrum power. 16 We also need to scale the IFT to account for the instrument optics and resolution such that the raw recovered spectral radiance is:…”

Section: Inverse Fourier Transformmentioning

confidence: 99%

“…By the Nyquist theorem, we must sample at at least two times the number of fringes per centimeter to recover a non-aliased signal. 16 The interferogram as a function of position, x, along the detector is given by:…”

Section: Spatial Heterodyne Spectroscopymentioning

confidence: 99%

See 2 more Smart Citations

Spatial heterodyne spectrometer: modeling and interferogram processing for calibrated spectral radiance measurements

2013

View full text Add to dashboard Cite

This work presents a radiometric model of a spatial heterodyne spectrometer (SHS) and a corresponding interferogram-processing algorithm for the calculation of calibrated spectral radiance measurements. The SHS relies on Fourier Transform Spectroscopy (FTS) principles, and shares design similarities with the Michelson Interferometer. The advantages of the SHS design, including the lack of moving parts, high throughput, and instantaneous spectral measurements, make it suitable as a field-deployable instrument. Operating in the long-wave infrared (LWIR), the imaging SHS design example included provides the capability of performing chemical detection based on reflectance and emissivity properties of surfaces of organic compounds. This LWIR SHS model outputs realistic, interferometric data and serves as a tool to find optimal SHS design parameters for desired performance requirements and system application. It also assists in the data analysis and system characterization. The interferogram-processing algorithm performs flat-fielding and phase corrections as well as apodization before recovering the measured spectral radiance from the recorded interferogram via the Inverse Fourier Transform (IFT). The model and processing algorithm demonstrate results comparable to those in the literature with a noise-equivalent change in temperature of 0.35K. Additional experiments show the algorithm's real-time processing capability, indicating the LWIR SHS system presented is feasible.

show abstract

Section: Apodizationmentioning

confidence: 99%

Section: Inverse Fourier Transformmentioning

confidence: 99%

See 1 more Smart Citation

Spatial heterodyne spectrometer: modeling and interferogram processing for calibrated spectral radiance measurements

2013

View full text Add to dashboard Cite

show abstract

“…If we assume that the optical system behaves as a linear shift-invariant system, then we can model the spatial modifications by understanding the effects on a single point of light, resulting in a point spread function (PSF). [4][5][6] The resulting spatial modification to the spectral radiance in the imaging plane, L image ðx; y; λÞ, can then be modeled by simply convolving the PSF for the system, PSF system , with scene spectral radiance, i.e.,…”

Section: Image Formationmentioning

confidence: 99%

Modeling the optical transfer function in the imaging chain

Fiete

Paul

2014

Opt. Eng.

View full text Add to dashboard Cite

Modeling the imaging chain has become a critical design tool to understand the relationship between design trades and image quality in camera systems. The mathematical models for the fundamental components of an imaging chain are well understood and have been validated using working camera systems. However, the complexity of camera designs continues to grow as the technology advances to drive higher performance using different approaches. The fundamental imaging chain models do not always meet the needs of the new imaging system designs, thus requiring the models to advance in complexity as well. Of particular interest to the optical designers is the development of mathematical models that enable more complex modeling of the wavefront errors for the optical transfer functions (OTF) in the image chain models. A tutorial on the imaging chain is given followed by an innovative approach using an η matrix for modeling the OTF in the imaging chain.

show abstract

“…The convolution of a finite impulse train and a sinc function is a periodic sinc function or Dirichlet kernel, 7,17 written as E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 1 7 ; 6 3 ; 3 5 1…”

Section: Periodic Sinc (Dirichlet Kernel)mentioning

confidence: 99%