Figen S. Oktem

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Linear canonical transforms (LCTs) are a family of integral transforms with wide application in optical, acoustical, electromagnetic, and other wave propagation problems. The Fourier and fractional Fourier transforms are special cases of LCTs. We present the exact relation between continuous and discrete LCTs (which generalizes the corresponding relation(More)
Linear canonical transforms (LCTs) form a three-parameter family of integral transforms with wide application in optics. We show that LCT domains correspond to scaled fractional Fourier domains and thus to scaled oblique axes in the space-frequency plane. This allows LCT domains to be labeled and ordered by the corresponding fractional order parameter and(More)
A photon sieve, modification of a Fresnel zone plate, has been recently proposed to achieve higher resolution imaging and spectroscopy at UV and x-ray wavelengths. In this paper, we present Fresnel imaging formulas that relate the output of a photon sieve imaging system to its input, originating from either a coherent or incoherent extended source. By using(More)
Spectroscopy is a fundamental diagnostic technique in physical sciences with widespread application. Multi-order slitless imaging spectroscopy has been recently proposed to overcome the limitations of traditional spectrographs, in particular their small instantaneous field of view. Since an inversion is required to infer the physical parameters of interest(More)
We consider the problem of estimating emission line parameters from the measurements of a multi-order slitless spectrometer. This problem can be viewed as a multi-frame deblurring problem with shift variant Gaussian blur. By using Cramer-Rao lower bound theory, we derive analytical precision limits to this parameter estimation when the measurements are(More)
We study the degrees of freedom of optical systems and signals based on space-frequency (phase-space) analysis. At the heart of this study is the relationship of the linear canonical transform domains to the space-frequency plane. Based on this relationship, we discuss how to explicitly quantify the degrees of freedom of first-order optical systems with(More)
Spectral imaging is a fundamental diagnostic technique in physical sciences with widespread application. Conventionally, spectral imaging techniques rely on a scanning process, which renders them unsuitable for dynamic scenes. Here we study the problem of estimating the physical parameters of interest from the measurements of a non-scanning spectral imager(More)
Photon sieves, modifications of Fresnel zone plates, are a new class of diffractive image forming devices that open up new possibilities for high resolution imaging and spectroscopy, especially at UV and x-ray regime. In this paper, we develop a novel computational photon sieve imaging modality that enables high-resolution spectral imaging. For the(More)
Spectral imaging, the sensing of spatial information as a function of wavelength, is a widely used diagnostic technique in diverse fields such as physics, chemistry, biology, medicine, astronomy, and remote sensing. In this paper, we present a novel computational imaging modality that enables high-resolution spectral imaging by distributing the imaging task(More)
Spectral imaging, the simultaneous imaging and spectroscopy of a radiating scene, is a fundamental diagnostic technique in the physical sciences with widespread application. Due to the intrinsic limitation of two-dimensional (2D) detectors in capturing inherently three-dimensional (3D) data, spectral imaging techniques conventionally rely on a spatial or(More)