Analysis of eccentric photorefraction by Fourier optics

Eccentric photorefraction usually is used as early eyesight diagnostic test of infants and small children. Unlike currently approved geometrical optical model of eccentric photorefractometer, the crescent formation and the light-intensity distribution in the pupil image of a myopic eye are analyzed by Fourier optics with the assumption of an isotropic scattering retina. In the case of little circular light source and rectangular slit, the simulation results of different myopic diopters are obtained by geometrical optical theory and Fourier optics respectively. It is found that the simulation results by Fourier optics are similar as those obtained by geometrical optics, and all simulations are almost corresponding to the experimental result. The result demonstrates that the new method presented here is feasible.

Optical Transfer Function Reconstruction in Incoherent Fourier Ptychography

An optical transfer function （OTF） reconstruction model is first embedded into incoherent Fourier ptychography （IFP）. The leading result is a proposed algorithm that can recover both the super-resolution image and the OTF of an imaging system with unknown aberrations simultaneously. This model overcomes the difficult problem of OTF estimation that the previous IFP faces. The effectiveness of this algorithm is demonstrated by numerical simulations, and the superior reconstruction is presented. We believe that the reported algorithm can extend the original IFP for more complex conditions and may provide a solution by using structured light for characterization of optical systems＇ aberrations.

Study on the design and Zernike aberrations of a segmented mirror telescope

The segmented mirror telescope is widely used.The aberrations of segmented mirror systems are different from single mirror systems.This paper uses the Fourier optics theory to analyse the Zernike aberrations of segmented mirror systems.It concludes that the Zernike aberrations of segmented mirror systems obey the linearity theorem.The design of a segmented space telescope and segmented schemes are discussed,and its optical model is constructed. The computer simulation experiment is performed with this optical model to verify the suppositions. The experimental results confirm the correctness of the model.

Nonuniform sampled angular spectrum method by using trigonometric interpolation

The angular spectrum method（ASM） is a popular numerical approach for scalar diffraction calculations. However,traditional ASM has an inherent problem in that nonuniform sampling is precluded. In an attempt to address this limitation,an improved trigonometric interpolation ASM（TIASM） is proposed, in which the fast Fourier transform（FFT） is replaced by a trigonometric interpolation. The results show that TIASM is more suitable to situations in which the source field has a simple and strong frequency contrast, irrespective of whether the original phase distribution is a plane wave or a Fresnel zone plate phase distribution.

Biomedical applications of Jones-matrix tomography to polycrystalline films of biological fuids

Algorithms for reconstruction of linear and circular birefringence-dichroism of optically thin anisotropic biological layers are presented.The technique of Jones matrix tomography of poly-crystalline films of biological fuids of various human organs has been developed and experimentally tested.The coordinate distributions of phase and amplitude anisotropy of bile films and synovial fuid taken from the knee joint are determined and statistically analyzed.Criteria(statistical moments of 3rd and 4th orders)of differential diagnostics of early stages of cholelithiasis and septic arthritis of the knee joint with excellent balanced accuracy were determined.Data on the diagnostic fficiency of the Jones matrix tomography method for polyerystalline plasma(liver disease),urine(albuminuria)and cytological smears(cervical cancer)are presented.

Modified scaling angular spectrum method for numerical simulation in long-distance propagation

The angular method(AS)cannot be used in long-distance propagation because it produces severe numerical errors due to the sampling problem in the transfer function.Two ways can solve this problem in AS for long-distance propagation.One is zero-padding to make sure that the calculation window is wide enough,but it leads to a huge calculation burden.The other is a method called band-limited angular spectrum(BLAS),in which the transfer function is truncated and results in that the calculation accuracy decreases as the propagation distance increases.In this paper,a new method called modified scaling angular spectrum(MSAS)to solve the problem for long-distance propagation is proposed.A scaling factor is introduced in MSAS so that the sampling interval of the input plane can be adjusted arbitrarily unlike AS whose sampling interval is restricted by the detector’s pixel size.The sampling interval of the input plane is larger than the detector’s pixel size so the size of calculation window suitable for long-distance field propagation in the input plane is smaller than the size of the calculation window required by the zero-padding.Therefore,the method reduces the calculation redundancy and improves the calculation speed.The results from simulations and experiments show that MSAS has a good signal-to-noise ratio(SNR),and the calculation accuracy of MSAS is better than BLAS.

Nonlinear Optical Spatial Filtering for Medical Image Processing

The nonlinear properties of Tris(acetylacetonato) Manganese(III) are used to manipulate the spatial frequencies at the Fourier plane using 4f-z scan. The technique is a simple self-adaptive all-optical system, which performs image processing and nonlinear optical measurements at the same time. Preferred spatial frequencies can be selected by shifting the nonlinear sample through the focus. Edge enhancement was demonstrated by filtering of low frequency with the nonlinear material at the Fourier plane.

On-chip photonic Fourier transform with surface plasmon polaritons

The Fourier transform(FT),a cornerstone of optical processing,enables rapid evaluation of fundamental mathematical operations,such as derivatives and integrals.Conventionally,a converging lens performs an optical FT in free space when light passes through it.The speed of the transformation is limited by the thickness and the focal length of the lens.By using the wave nature of surface plasmon polaritons(SPPs),here we demonstrate that the FT can be implemented in a planar configuration with a minimal propagation distance of around 10 mm,resulting in an increase of speed by four to five orders of magnitude.The photonic FT was tested by synthesizing intricate SPP waves with their Fourier components.The reduced dimensionality in the minuscule device allows the future development of an ultrafast on-chip photonic information processing platform for large-scale optical computing.

Studies of beam propagation characteristics on apertured fractional Fourier transforming systems

Based on the principle that a rectangular function can be expanded into a sum of complex Gaussian functions with finite numbers, propagation characteristics of a Gaussian beam or a plane wave passing through apertured fractional Fourier transforming systems are analyzed and corresponding analytical formulae are obtained.Analytical formulae in different fractional orders are numerically simulated and compared with the diffraction integral formulae,the applicable range and exactness of analytical formulae are confirmed. It is shown that the calculating speed of using the obtained approximate analytical formulae,is several hundred times faster than that of using diffraction integral directly.Meanwhile,by using analytical formulae the effect of different aperture sizes on Gaussian beam propagation characteristics is numerically simulated, it is shown that the diffraction effect can be neglected when the aperture size is 5 times larger than the beam waist size.

Optical vortex copier and regenerator in the Fourier domain

The generation and manipulation of optical vortices are of fundamental importance in a variety of promising applications. Here, we develop a nonlinear optical paradigm to implement self-and cross-convolution of optical vortex arrays, demonstrating the features of a vortex copier and regenerator. We use a phase-only spatial light modulator to prepare the 1064 nm invisible fundamental light to carry special optical vortex arrays and use a potassium titanyl phosphate crystal to perform type Ⅱ second-harmonic generation in the Fourier domain to achieve 532 nm visible structured vortices. Based on pure cross-convolution, we succeed in copying arbitrary-order single vortices as well as their superposition states onto a prearranged array of fundamental Gaussian spots. Also, based on the simultaneous effect of self-and cross-convolutions, we can expand the initial vortex lattices to regenerate more vortices carrying various higher topological charges. Our presented method of realizing an optical vortex copier and regenerator could find direct applications in optical manipulation, optical imaging, optical communication, and quantum information processing with structured vortex arrays.

Particle digital in-line holography with spherical wave recording

In this paper, we propose a method of digital in-line holography of particle. A diverging spherical beam is used for illumination in recording hologram, the complex amplitude distribution generated by particle field at a single plane located in the Presnel diffraction region is recorded by CCD, and a plane beam for reconstructing hologram, then, the magnified image can be obtained by numerical reconstruction in computer. This procedure can be interpreted by Fourier optical theory and the theoretical analysis have been done in detail, the experimental results, the air freshener being subject, are also given.

Analysis and simulation of XPM intensity modulation

Based on the split-step Fourier method and small signal analysis, an improved analytical solution which describes the cross-phase modulation (XPM) intensity is derived. It can suppress the spurious XPM intensity modulation efficiently in the whole transmission fiber. Thus it is more coincidence with the practical result. Furthermore, it is convenient, because it is independent of channel separation and the dispersion and nonlinear effects interact through the XPM intensity. A criterion of select the step size is described as the derived XPM intensity modulation being taken into account. It is non-uniform distribution and is the function of average signal power <P(z)> (or z). Compared with the conventional split-step method, the simulation accuracy is improved when the step size is determined by the improved XPM intensity.