Coherent Transfer Function*

Tichenor, Daniel A.; Goodman, Joseph W.

doi:10.1364/josa.62.000293

Cited by 47 publications

(28 citation statements)

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“…Note that in this case, even the diameter of the lens is more than five times' larger than the object, Fourier optics does not hold well. This obeys the conclusions in [14]. Focal plane array imaging is a very hot topic in millimeter wave imaging systems nowadays.…”

Section: Imaging Results Comparisonsupporting

confidence: 87%

“…This is often called "isoplanatic" and it requires a very large distance (infinite theoretically) between object and lens, which matches our discussions of the Fraunhofer diffraction condition above. Tichenor pointed out that this requirement can be loosened and the imaging model can be applied if the size of the object does not exceed one-fourth of the linear dimension of the lens' aperture [14].…”

Section: Imaging Modelmentioning

confidence: 99%

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Limitations of Approximations Towards Fourier Optics for Indoor Active Millimeter Wave Imaging Systems

Feng

Tavakol²,

Schreurs³

et al. 2010

PIER

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Abstract-To simulate imaging systems, Fourier optics has been applied very successfully to optics for decades. However, when simply moving to indoor millimeter wave imaging systems, some assumptions underlying the Fourier optics may break down, which contribute to the errors by applying Fourier optics. During the review of mathematical derivation of the Fourier optics, we point out how the errors are introduced by making the Fresnel approximation and omitting the phase factors. To distinguish from much literature, we discuss the accuracy of Fresnel approximation rather than plane wave. Moreover, we check the simulation results for millimeter wave imaging systems working in both pixel scanning mode and focal plane array mode and compare them to the results predicted by Fourier optics. It is shown that the difference can be 28% for the speckle contrast when the object is with certain roughness. The optical routine is that when the lens is four times' larger than the object, the imaging system can be considered as isoplanatic, thus Fourier optics can hold. Our simulation results imply that it may not be valid in indoor millimeter wave imaging systems. The goal of this paper is to draw some attention to the possibly large errors when modeling or designing the indoor millimeter wave imaging systems by Fourier optics directly. The mathematical discussions of the inaccuracies due to some approximations in Fourier optics can serve to understand and deal with aberrations.

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Section: Imaging Results Comparisonsupporting

confidence: 87%

Section: Imaging Modelmentioning

confidence: 99%

Limitations of Approximations Towards Fourier Optics for Indoor Active Millimeter Wave Imaging Systems

Feng

Tavakol²,

Schreurs³

et al. 2010

PIER

View full text Add to dashboard Cite

show abstract

“…We emphasis that this is only viable when the object to be imaged is very small and lies close to the optical axis. A weaker imaging condition has been obtained by Tichenor and Goodman who showed that non-isoplanatism of a thin lens has a negligeable effect on the intensity distribution of the image if the object diameter is smaller than about a quarter of the lens diameter [4]. In this paper, we investigate the effect of non-isoplanatism on coherent image formation when this condition is not met.…”

Section: Introductionmentioning

confidence: 86%

“…The impulse response function of a thin lens [4,2] is an important concept that has proven to be very useful for the design of optical systems and optical data processing. It turns out that it is given by the same formula as for the pinhole cameraEq.…”

Section: Non-isoplanatism Of a Thin Lensmentioning

confidence: 99%

“…Some spatial phase distortion is unavoidably introduced, which, when combined with a finite resolution, severely modifies the intensity distribution of the image. This was first recognized by Dumontet [3], and later by Tichenor and Goodman [4], who showed that a thin lens can only be considered as an isoplanatic system if both the object and the image lie on spherical surfaces S o and S i , tangent to the geometricaloptics object and image planes O and I respectively, and having their center of curvature in the plane of the lens (see Sec. 3).…”

Section: Introductionmentioning

confidence: 96%

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Coherent imaging of extended objects

Brainis

Muldoon

Brandt

et al. 2009

Optics Communications

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When used with coherent light, optical imaging systems, even diffraction-limited, are inherently unable to reproduce both the amplitude and the phase of a two-dimensional field distribution because their impulse response function varies slowly from point to point (a property known as non-isoplanatism). For sufficiently small objects, this usually results in a phase distortion and has no impact on the measured intensity. Here, we show that the intensity distribution can also be dramatically distorted when objects of large extension or of special shapes are imaged. We illustrate the problem using two simple examples: the pinhole camera and the aberration-free thin lens. The effects predicted by our theorical analysis are also confirmed by experimental observations.

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Characterization of focal field formed by a large numerical aperture paraboloidal mirror and generation of ultra-high intensity (1022 W/cm2)

et al. 2005

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We describe a method to measure the aberrations of a high numerical aperture off-axis paraboloid and correct for the aberrations using adaptive optics. It is then shown that the characterized aberrations can be used to accurately calculate the electromagnetic field at the focus using the Stratton-Chu vector diffraction theory. Using this methodology, an intensity of 7 × 10 21 W/cm 2 was demonstrated by focusing a 45-TW laser beam with an f /0.6, 90 • off-axis paraboloid after correcting the aberrations of the paraboloid and the lowenergy reference beam. The intensity can be further increased to 1 × 10 22 W/cm 2 by including in the correction algorithm the wavefront difference between the reference beam and the high-energy beam.

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Coherent Transfer Function*

Cited by 47 publications

References 0 publications

Limitations of Approximations Towards Fourier Optics for Indoor Active Millimeter Wave Imaging Systems

Limitations of Approximations Towards Fourier Optics for Indoor Active Millimeter Wave Imaging Systems

Coherent imaging of extended objects

Characterization of focal field formed by a large numerical aperture paraboloidal mirror and generation of ultra-high intensity (1022 W/cm2)

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