Biomedical subjects

Yangjian Cai

Publications and source records attributed to Yangjian Cai.

At least 19 recordsLinked to original sources

PubMed2007

Lensless imaging with partially coherent light.

Based on the fourth-order correlation of light, lensless imaging with incoherent or partially coherent light is investigated theoretically by use of classical optical coherence theory. A novel lensless optical system for implementing imaging is proposed. The visibility and quality of the image are influenced by the coherence and transverse size of the light source. The results suggest useful imaging applications in x-ray, gamma-ray, or other wavelengths where no effective lens is available, and they have potential applications in optical metrology and holography.

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PubMed2006

Propagation of a decentered elliptical Gaussian beam through apertured aligned and misaligned paraxial optical systems.

By expanding the hard aperture function into a finite sum of complex Gaussian functions, approximate analytical formulas for a decentered Gaussian beam (DEGB) passing through apertured aligned and misaligned paraxial apertured paraxial optical systems are derived in terms of a tensor method. The results obtained by using the approximate analytical expression are in good agreement with those obtained by using the numerical integral calculation. Furthermore, approximate analytical formulas for a decentered elliptical Hermite-Gaussian beam (DEHGB) through apertured paraxial optical systems are derived. As an application example, approximate analytical formulas for a decentered elliptical flattened Gaussian beam through apertured paraxial optical systems are derived. Our results provide a convenient way for studying the propagation and transformation of a DEGB and a DEHGB through apertured paraxial optical systems.

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PubMed2006

Lensless optical implementation of the coincidence fractional Fourier transform.

A lensless optical system for implementing the coincidence fractional Fourier transform (FRT) is proposed. The conditions for the lensless optical system to implement the coincidence FRT with incoherent light and entangled photon pairs are discussed. The results offer a novel scheme for FRTs and thus suggest useful applications.

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PubMed2006

Propagation of partially coherent twisted anisotropic Gaussian Schell-model beams through an apertured astigmatic optical system.

By expanding the hard-aperture function into a finite sum of complex Gaussian functions, we derived an approximate analytical formula for a partially coherent twisted anisotropic Gaussian Schell-model (AGSM) beam propagating through an apertured paraxial general astigmatic (GA) optical system by use of a tensor method. The results obtained by using the approximate analytical formula are in good agreement with those obtained by using the numerical integral calculation. Our formulas avoid time-consuming numerical integration and provide a convenient and effective way for studying the propagation and transformation of a partially coherent twisted AGSM beam through an apertured paraxial GA optical system.

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PubMed2006

Average intensity and spreading of an elliptical gaussian beam propagating in a turbulent atmosphere.

An analytical formula for the average intensity of an elliptical Gaussian beam (EGB) propagating in a turbulent atmosphere is derived. The spreading properties of an EGB in a turbulent atmosphere are studied. It is found that an EGB will eventually become a circular Gaussian beam in a turbulent atmosphere. This interesting phenomenon is quite different from the propagation of an EGB in free space. The evolution properties are closely related to the parameters of the beam and the turbulent atmosphere.

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PubMed2006

Coincidence subwavelength fractional Fourier transform.

The coincidence subwavelength fractional Fourier transforms (FRTs) with entangled photon pairs and incoherent light radiation are introduced as an extension of the recently introduced coincidence FRT. Optical systems for implementing the coincidence subwavelength FRTs are designed. The width of the coincidence subwavelength FRT pattern is two times narrower than the width of the coincidence FRT. The coincidence subwavelength FRT with partially coherent light radiation is also studied numerically. Differences between the coincidence subwavelength FRT with entangled photon pairs and that with incoherent light radiation are discussed.

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PubMed2006

Propagation of hollow Gaussian beams through apertured paraxial optical systems.

On the basis of the generalized Collins formula and the expansion of the hard-aperture function into a finite sum of complex Gaussian functions, an approximate analytical formula for a hollow Gaussian beam propagating through an apertured paraxial stigmatic (ST) ABCD optical system is derived. Some numerical examples are given. Furthermore, by using a tensor method, we derive approximate analytical formulas for a hollow elliptical Gaussian beam propagating through an apertured paraxial general astigmatic ABCD optical system and an apertured paraxial misaligned ST ABCD optical system. Our results provide a convenient way for studying the propagation and transformation of a hollow Gaussian beam and a hollow elliptical Gaussian beam through an apertured general optical system.

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PubMed2006

Partially coherent flattened Gaussian beam and its paraxial propagation properties.

A simple model called partially coherent flattened Gaussian beam (FGB) is proposed to describe a partially coherent beam with a flat-topped spatial profile. An explicit and analytical formula is derived for the cross-spectral density of a partially coherent FGB propagating through a paraxial ABCD optical system. The propagation factor and propagation properties of a partially coherent FGB in free space are studied in detail and found to be closely related to its coherence and beam order.

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PubMed2005

Ghost imaging with incoherent and partially coherent light radiation.

We theoretically study ghost imaging with incoherent and partially coherent light radiation by using classical optical coherence theory. A Gaussian thin lens equation is derived for the ghost image. The equation depends on both paths. The quality and visibility of the ghost image are influenced by the source's transverse size, coherence width, and object characteristics. The differences between ghost imaging formed with incoherent light radiation and with entangled photon pairs are discussed.

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PubMed2005

Second-order fractional Fourier transform with incoherent radiation.

Based on the coherent optical theory, we extend the fractional Fourier transform of first-order correlation to a fractional Fourier transform of second-order correlation. An optical system for implementing a second-order fractional Fourier transform was designed. As a numerical example, we investigate the second-order fractional Fourier transform for a single slit.

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PubMed2005

Coincidence fractional Fourier transform implemented with partially coherent light radiation.

We introduce the coincidence fractional Fourier transform (FRT) implemented with incoherent and partially coherent light radiation. Optical systems for implementing the coincidence FRT are designed. The results show that the visibility and quality of the coincidence FRT of an object are closely related to the light source's transverse size, coherence, and spectral width. As an example, we numerically study the coincidence FRT of a single slit.

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PubMed2004

Ghost interference with partially coherent radiation.

Ghost interference with partially coherent radiation sources is studied using optical coherence theory. The visibility of the ghost interference fringes is strongly influenced by the transverse size and transverse coherence width of the source. An increase of the transverse source size leads to a decrease of the fringes' visibility. An increase of the transverse coherence results in an increase of the visibility. The difference between ghost interference formed with entangled photon pairs and with partially coherent light is discussed.

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PubMed2004

Partially coherent flat-topped beam and its propagation.

A partially coherent beam with flat-topped profile is proposed. The cross-spectral density of this beam can be expressed as a finite series of the cross-spectral density of partially coherent Gaussian-Schell-model beams with different parameters. Analytical propagation formulas for partially coherent flat-topped beams are derived through aligned and misaligned optical systems. The propagation property of partially coherent flat-topped beams in free space is illustrated numerically. The fractional Fourier transform of partially coherent fiat-topped beams is also studied. Our method provides a convenient way to describe partially coherent flat-topped beams and treat their propagation and transformation.

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PubMed2004

Hollow elliptical Gaussian beam and its propagation through aligned and misaligned paraxial optical systems.

A new mathematical model called hollow elliptical Gaussian beam (HEGB) is proposed to describe a dark-hollow laser beam with noncircular symmetry in terms of a tensor method. The HEGB can be expressed as a superposition of a series of elliptical Hermite-Gaussian modes. By using the generalized diffraction integral formulas for light passing through paraxial optical systems, analytical propagation formulas for HEGBs passing through paraxial aligned and misaligned optical systems are obtained through vector integration. As examples of applications, evolution properties of the intensity distribution of HEGBs in free-space propagation were studied. Propagation properties of HEGBs through a misaligned thin lens were also studied. The HEGB provides a convenient way to describe elliptical dark-hollow laser beams and can be used conveniently to study the motion of atoms in a dark-hollow laser beam.

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PubMed2003

Hollow Gaussian beams and their propagation properties.

A new mathematical model, described as hollow Gaussian beams (HGBs), is proposed to describe a dark hollow laser beam (DHB). The area of the dark region across the HGBs can easily be controlled by proper choice of the beam parameters. Based on the Collins integral, an analytical propagation formula for the HGBs through a paraxial optical system is derived. The HGBs also can be expressed as a superposition of a series of Lagurerre-Gaussian modes by use of a polynomial expansion. As a numerical example, the propagation properties of a DHB in free space are illustrated graphically. The HGBs provide a convenient and powerful way to describe and treat the propagation of DHBs and can be used conveniently to analyze atoms manipulated with a DHB.

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PubMed2003

Decentered elliptical Hermite-Gaussian beam.

A new kind of laser beam called the decentered elliptical Hermite-Gaussian beam (DEHGB) is defined by use of a tensor method. The propagation formula of the DEHGB passing through a nonsymmetrical paraxial optical system is derived through vector integration. The derived formula can be easily reduced to the propagation formula of an aligned elliptical Hermite-Gaussian beam and that of a decentered elliptical Gaussian beam under certain conditions. By use of this formula, the propagation characteristics of the DEHGB through free space are presented graphically. As application examples, we construct a generalized laser array using the DEHGB as the fundamental mode. We also obtain the decentered elliptical flattened Gaussian beam by expressing it as superposition of a series of DEHGBs by using polynomial expansion.

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PubMed2003

Transformation and spectrum properties of partially coherent beams in the fractional Fourier transform plane.

An analytical and concise formula is derived for the fractional Fourier transform (FRT) of partially coherent beams that is based on the tensorial propagation formula of the cross-spectral density of partially coherent twisted anisotropic Gaussian-Schell-model (GSM) beams. The corresponding tensor ABCD law performing the FRT is obtained. The connections between the FRT formula and the generalized diffraction integral formulas for partially coherent beams passing through aligned optical systems and misaligned optical systems are discussed. With use of the derived formula, the transformation and spectrum properties of partially coherent GSM beams in the FRT plane are studied in detail. The results show that the fractional order of the FRT has strong effects on the transformation properties and the spectrum properties of partially coherent GSM beams. Our method provides a simple and convenient way to study the FRT of twisted anisotropic GSM beams.

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PubMed2002

Decentered elliptical Gaussian beam.

A new kind of laser beam, called a decentered elliptical Gaussian beam (DEGB), is defined by a tensor method. The propagation formula for a DEGB passing through an axially nonsymmetrical paraxial optical system is derived through vector integration. The derived formula can be reduced to the formula for a fundamental elliptical Gaussian beam and a decentered Gaussian beam under certain conditions. As an example application of the derived formula, the propagation characteristics of a DEGB in free space are calculated and discussed. As another example we study the properties of a generalized laser beam array constructed by use of a DEGB as the fundamental mode.

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