Deep learning based coherent diffraction imaging of dynamic scattering media.

The ptychographic iterative engine (PIE) is a lensless coherent diffraction imaging algorithm known for its simplicity, easy to use, scalability, and fast convergence. However, practical applications often encounter interference in imaging results caused by non-static scattering media, such as dense fog, seawater target detection and medical biology diagnosis. To address this challenge, we propose a novel approach using computational deep learning for dynamic scattering medium image reconstruction, enabling lens-free coherent diffraction imaging through dynamic scattering media. Through extensive analysis, we evaluate the effectiveness of the neural network for PIE image recovery under varying scattering medium concentration conditions. We also test scattering images obtained by hybrid training with different concentrations of scattering medium to assess the generalisation ability of the neural network. The experimental results demonstrate that our proposed method achieve PIE lens-free imaging under non-static scattering media interference. This coherent diffraction imaging method, based on transmission through dynamic scattering media, opens up new possibilities for practical applications of PIE and fosters its development in complex environments. Its significance extends to fields like atmospheric pollution, seawater target detection and medical biology diagnosis, providing valuable references for research in these domains.

Investigation of the effect of chirped factors on the interference enhancement effect of an Airyprime beam propagating in free space.

The first-order and the second-order chirped factors are imposed on the Airyprime beam, and the analytical expression of the chirped Airyprime beam propagating in free space is derived. The phenomenon that the peak light intensity on observation plane other than initial plane is greater than that on initial plane is defined as the interference enhancement effect, which is caused by the coherent superposition of the chirped Airyprime and the chirped Airy-related modes. The effects of the first-order and the second-order chirped factors on the interference enhancement effect are theoretically investigated, respectively. The first-order chirped factor only affects the transverse coordinates where the maximum light intensity appears. The strength of interference enhancement effect of the chirped Airyprime beam with any negative second-order chirped factor must be stronger than that of the conventional Airyprime beam. However, the improvement of the strength of interference enhancement effect caused by the negative second-order chirped factor is realized at the expense of shortening the position where the maximum light intensity appears and the range of interference enhancement effect. The chirped Airyprime beam is also experimentally generated, and the effects of the first-order and the second-order chirped factors on the interference enhancement effect are experimentally confirmed. This study provides a scheme to improve the strength of interference enhancement effect by controlling the second-order chirped factor. Compared with traditional intensity enhancement methods such as using lens focusing, our scheme is flexible and easy to implement. This research is beneficial to the practical applications such as spatial optical communication and laser processing.

Design of autofocusing beams based on accelerating beams.

Autofocusing Airy-like beams have been designed based on the self-accelerating beams along arbitrary polynomial paths. The evolutions of the autofocusing beam in free space and turbulent atmosphere have been studied. Results show that the energy concentration of the autofocusing beam near the focal plane has a close relationship with its accelerating trajectory. The spot size of the autofocusing beam in the focal plane varies with the acceleration trajectory. The influence of turbulence on different autofocusing beams is different and has a relation with the degree of the curvature of the accelerating beam. The autofocusing beam propagating along a small curvature path has better resistance against turbulence.

Quantitative description of the self-healing ability of a beam.

Quantitative description of the self-healing ability of a beam is very important for studying or comparing the self-healing ability of different beams. As describing the similarity by using the angle of two infinite-dimensional complex vectors in Hilbert space, the angle of two intensity profiles is proposed to quantitatively describe the self-healing ability of different beams. As a special case, quantitative description of the self-healing ability of a Bessel-Gaussian beam is studied. Results show that the angle of two intensity profiles can be used to describe the self-healing ability of arbitrary beams as the reconstruction distance for quantitatively describing the self-healing ability of Bessel beam. It offers a new method for studying or comparing the self-healing ability of different beams.

Observation of the asymmetric Bessel beams with arbitrary orientation using a digital micromirror device.

Recently, V. V. Kotlyar et al. [Opt. Lett.39, 2395 (2014)] have theoretically proposed a novel kind of three-parameter diffraction-free beam with a crescent profile, namely, the asymmetric Bessel (aB) beam. The asymmetry degree of such nonparaxial modes was shown to depend on a nonnegative real parameter c. We present a more generalized asymmetric Bessel mode in which the parameter c is a complex constant. This parameter controls not only the asymmetry degree of the mode but also the orientation of the optical crescent, and affects the energy distribution and orbital angular momentum (OAM) of the beam. As a proof of concept, the high-quality generation of asymmetric Bessel-Gauss beams was demonstrated with the super-pixel method using a digital micromirror device (DMD). We investigated the near-field properties as well as the far field features of such beams, and the experimental observations were in good agreement with the theoretical predictions. Additionally, we provided an effective way to control the beam's asymmetry and orientation, which may find potential applications in light-sheet microscopy and optical manipulation.

Beam wander of an Airy beam with a spiral phase.

Beam wander of an Airy beam with a spiral phase in turbulence is investigated. Using the Wigner distribution function, analytical expressions for the second-order moments and second central moments of an Airy beam with a spiral phase in turbulence are derived. A general expression of the beam wander for an Airy beam with a spiral phase is obtained. Based on the derived formula, various factors that impact on the beam wander are illustrated numerically. The results show that increasing the topological charge and the characteristic scale, or decreasing the exponential truncation factor, can be used to decrease the beam wander.

[Theory study on glycine linear oligopeptide vibrational spectrum frequency shift].

By using the density functional theory, glycine linear oligopeptide of different lengths was geometrically optimized on the 6-31G (d) basis set level, their growth processes were simulated, and the average binding energy and vibration frequency were calculated with geometry. The results showed that the average binding energies tend to change in a regular pattern and stabilize with the number of residues increasing; With the oligopeptide chain bond length analysis it was found that the chain to the radial direction there is a opposite trend for chain and radial direction, which is anisotropic. It was found by the IR spectrum analysis that red shifts and blue shifts occur respectively when the same group of peptide bond vibrate, which is anisotropic; These phenomena originate from that quasi one-dimensional nanostructures lead to the anisotropy of the bond length; the induced effects, coupling effects and hydrogen bonding etc. between the same groups lead to the vibration frequency red shifts and blue shifts. The authors conclude that the growth of glycine linear oligopeptide is conducive to stability of the structure, and the authors infer that the oligopeptide has the tendency of self-assembled growth; Through the conformation and spectrum, the authors infer that there is a size effect in physical and chemical properties. The physical and chemical properties of peptide chain end group are extremely stable and unaffected by the impact of the oligopeptide chain length The results are significant to measuring the length and the number of residue of peptide, and to manufacturing the special features oligopeptide chain.

Propagation of a partially coherent hollow vortex Gaussian beam through a paraxial ABCD optical system in turbulent atmosphere.

The propagation of a partially coherent hollow vortex Gaussian beam through a paraxial ABCD optical system in turbulent atmosphere has been investigated. The analytical expressions for the average intensity and the degree of the polarization of a partially coherent hollow vortex Gaussian beam through a paraxial ABCD optical system are derived in turbulent atmosphere, respectively. The average intensity distribution and the degree of the polarization of a partially coherent hollow vortex Gaussian beam in turbulent atmosphere are numerically demonstrated. The influences of the beam parameters, the topological charge, the transverse coherent lengths, and the structure constant of the atmospheric turbulence on the propagation of a partially coherent hollow vortex Gaussian beam in turbulent atmosphere are also examined in detail. This research is beneficial to the practical applications in free-space optical communications and the remote sensing of the dark hollow beams.

Propagation of Airy beams in uniaxial crystals orthogonal to the optical axis.

Analytical propagation expression of an Airy beam in uniaxial crystals orthogonal to the optical axis is derived. The ballistic dynamics of an Airy beam in uniaxial crystals is also investigated. The Airy beam propagating in uniaxial crystals orthogonal to the optical axis mainly depends on the ratio of the extraordinary refractive index to the ordinary refractive index. As an example, the propagation of an Airy beam in the positive uniaxial crystals orthogonal to the optical axis is demonstrated. The acceleration of an Airy beam in the transversal direction along the optical axis is more rapidly than that in the other transversal direction. With increasing the ratio of the extraordinary refractive index to the ordinary refractive index, the acceleration of the Airy beam in the transversal direction along the optical axis speeds up and the acceleration of the Airy beam in the other transversal direction slows down. The Airy beam propagating in uniaxial crystals orthogonal to the optical axis follows a ballistic trajectory. The effective beam size of the Airy beam in the transversal direction along the optical axis is always larger than that in the other transversal direction.

Propagation of an Airy beam with a spiral phase.

The propagation of an Airy beam with a spiral phase is studied. The centroid position and spread of the beam are investigated analytically for different topological charges. Study shows that the centroid position of the Airy beam with a spiral phase keeps moving during propagation. The motion with positive topological charge is in the direction opposite to that with negative topological charge. The speed of the motion of the centroid position is proportional to the topological charge and the normalized distance. From the variation of the second moment of the beam, we can also see that the beam spread is speeded up by the spiral phase during propagation. The speed of the beam spread is proportional to the square of the topological charge.

Evolution of an Airy beam in turbulence.

The evolution of Airy beam intensity distribution in turbulence is examined. Results show that the centroid position and skewness of an Airy beam are independent on turbulence. When the exponential truncation factor is small, an Airy beam has a long tail on the left side. When the exponential truncation factor is larger than 1, an Airy beam can be approximately expressed by an off-axis Gaussian beam. If the effect of turbulence is large enough, the Airy beam converges to a Gaussian distribution. However, the convergence is slower for a small exponential truncation factor than for a large one. That is, an Airy beam with a smaller exponential truncation factor exhibits more resilience against perturbations of turbulence than does a larger one.

Arbitrary moments of elliptical Gaussian-Schell beam in turbulent atmosphere.

Arbitrary moments of elliptical Gaussian-Schell beams in turbulent atmosphere is studied. An analytical formula for arbitrary moments of elliptical Gaussian-Schell beams in turbulent atmosphere is derived. As an example, the kurtosis parameter for elliptical Gaussian-Schell beams in turbulent atmosphere is investigated in detail. The comparison between the variations of the kurtosis parameter for elliptical Gaussian-Schell beams with different parameters is made. Meanwhile, the difference between the kurtosis parameter in vacuum and in turbulent atmosphere is analyzed and discussed.

Propagation of Gaussian-Schell beam in turbulent atmosphere of three-layer altitude model.

We propose a method that is used to derive the moment radius of intensity distribution in a turbulent atmosphere. From this study, we have found that the second moment radius is affected only by the first-order expansion coefficient of the wave structure function. If our attention is directed to a higher moment radius, a higher order approximation of the expansion needs to be used. As an example, the propagation of a Gaussian-Schell beam in a slant path has been studied based on the turbulent atmosphere of a three-layer model. The variation of some beam properties, such as the relative waist width, angular spread, and kurtosis parameter with the initial waist width, wavelength, and zenith angle, has been analyzed and discussed in detail. The study shows that there is little difference between the three-layer model and the Kolmogorov model in studying uplink propagation, and the difference is large for downlink propagation. The intensity profile of the Gaussian beam in turbulence does not keep a Gaussian shape unless the beam spreading due to turbulence is very large or very small.

Average intensity and spreading of a Lorentz-Gauss beam in turbulent atmosphere.

The propagation of a Lorentz-Gauss beam in turbulent atmosphere is investigated. Based on the extended Huygens-Fresnel integral and the Hermite-Gaussian expansion of a Lorentz function, analytical formulae for the average intensity and the effective beam size of a Lorentz-Gauss beam are derived in turbulent atmosphere. The average intensity distribution and the spreading properties of a Lorentz-Gauss beam in turbulent atmosphere are numerically demonstrated. The influences of the beam parameters and the structure constant of the atmospheric turbulence on the propagation of a Lorentz-Gauss beam in turbulent atmosphere are also discussed in detail.

Comparison between quadratic approximation and delta expansion in studying the spreading of multi-Gaussian beams in turbulent atmosphere.

Based on quadratic approximation and delta expansion in the first order, the analytical expressions for multi-Gaussian beams in a turbulent atmosphere have been derived. By comparing the two approaches with numerical calculations, the relative errors of average intensity are investigated. As special cases, the relative errors for Gaussian beams, flattened Gaussian beams, and annular beams are investigated. The investigation shows that the method of delta expansion in the first order agrees well with numerical calculations, no matter what the effect of turbulence. If the effect of turbulence is large enough, the relative error of on-axis intensity trends to a constant. The maximum of relative error is about 2.8%. However, quadratic approximation does not give satisfying results under some circumstance even when the effect of turbulence is small. The relative error of on-axis intensity reaches 9.2% when the effect of turbulence is large enough.

Simultaneous displacement and angular drift measurement based on defocus grating.

We propose and demonstrate a displacement and angular drift simultaneous measurement technique based on a defocus grating. The displacement and angular drift of the incident beam can be detected by monitoring the movements of +/-1 diffraction order spots of the defocus grating. The relationship between drift of the incident beam and movements of +/-1 diffraction order spots is studied in detail. Compared with other methods, this technique eliminates the requirement of two or more detecting systems for measuring displacement and angular drift simultaneously. The proof-of-principle experiment shows that the root-mean-square errors of displacement and angular drift measurements are less than 0.5 microm and 0.84 microrad, respectively.

Propagation of a partially coherent cosine-Gaussian beam through an ABCD optical system in turbulent atmosphere.

The propagation of a partially coherent cosine-Gaussian beam through a paraxial ABCD optical system in turbulent atmosphere is investigated. Analytical expression for the average intensity in the output plane is derived. The presented formula only covers optical systems without inherent apertures, where ABCD are all real-valued. As a special case of the general formula, the analytical formula for the average intensity of a partially coherent cosh-Gaussian beam through an ABCD optical system in turbulent atmosphere is also presented, respectively. The properties of the average intensity of the partially coherent cosine-Gaussian beam are investigated with a numerical example, and the dependence of the average intensity distribution on the spatial correlation length of a partially coherent cosine-Gaussian beam is mainly discussed.

Propagation of a cosh-Gaussian beam through an optical system in turbulent atmosphere.

The propagation of a cosh-Gaussian beam through an arbitrary ABCD optical system in turbulent atmosphere has been investigated. The analytical expressions for the average intensity at any receiver plane are obtained. As an elementary example, the average intensity and its radius at the image plane of a cosh-Gaussian beam through a thin lens are studied. To show the effects of a lens on the average intensity and the intensity radius of the laser beam in turbulent atmosphere, the properties of a collimated cosh-Gaussian beam and a focused cosh-Gaussian beam for direct propagation in turbulent atmosphere are studied and numerically calculated. The average intensity profiles of a cosh-Gaussian beam through a lens can have a shape similar to that of the initial beam for a longer propagation distance than that of a collimated cosh-Gaussian beam for direct propagation. With the increment in the propagation distance, the average intensity radius at the image plane of a cosh-Gaussian beam through a thin lens will be smaller than that at the focal plane of a focused cosh-Gaussian beam for direct propagation. Meanwhile, the intensity distributions at the image plane of a cosh-Gaussian beam through a lens with different w(0) and Omega(0) are also studied.

Power coupling of a two-Cassegrain-telescopes system in turbulent atmosphere in a slant path.

The characteristics of dark hollow beams passing through a two-Cassegrain-telescopes system in turbulent atmosphere in a slant path have been investigated. The distribution of the average intensity at the receiver telescope and the efficiency of power coupling with respect to propagation distance with different parameters are derived and numerically calculated. These studies illuminate that the power of the dark hollow beams is concentrated on a narrow annular aperture at the source plane and its power coupling with a transmitter Cassegrain telescope can remain quite high. For short distance between the two Cassegrain telescopes, the normalized average intensity distribution at receiver plane holds shape similar to that at the source plane, and the two Cassegrain telescopes keep high efficiency of the power coupling. But with the increment in the propagation distance, the power of the dark hollow beams gradually converges to the central and the spot spreads. The central obscuration of the receiver telescope blocks more of the power; meanwhile more of the power moves out beyond the edge of the receiving aperture. Therefore, the efficiency of the power coupling decreases with the increment in the propagation distance. In addition, the relations between the efficiency of power coupling and wavelength of laser beams are also numerically calculated and discussed.

Generating a Bessel-Gaussian beam for the application in optical engineering.

Bessel beam is the important member of the family of non-diffracting beams and has many novel properties which can be used in many areas. However, the source of Bessel beam generated by the existing methods can be used only in a short distance due to its low power. In this paper, based on the coherent combining technology, we have proposed a method which can be used to generate a high-power Bessel beam. Even more, we give an innovative idea to form vortex phase by using discontinuous piston phase. To confirm the validity of this method, the intensity evolution of the combined beam and the Bessel-Gaussian beam at different propagation distance have been studied and compared. Meanwhile, the experimental realization has been discussed from the existing experimental result related to the coherent combining technology.