Measurement of Wavefront Aberration of Human Eye Using Talbot Image of Two-Dimensional Grating

The measurement of human ocular aberration is now frequently performed because of the increase in refractive surgery on the human cornea. The Hartmann-Shack (H-S) wavefront sensor is considered to be the most useful wavefront sensor, and a calculation method for wavefront aberration has been established. New methods of measuring wavefront aberrations of human eyes, using the Talbot image of a two-dimensional grating as a wavefront sensor and local shift of the Talbot image to calculate tilt of the wavefront are shown. The shift of the Talbot image was determined by comparing the phases of fundamental spatial frequency between the grating and the local patch of the Talbot image by Fourier transformation. The actual experiment was performed using a modified commercially available wavefront analyzer. Using these methods, Talbot images were obtained from model eyes and a human eye, and wavefront shapes were successfully reconstructed. Wavefront aberrations can be measured even when the obtained image is degraded by defocusing or scattering.     

泰伯效应的共轭现象

介绍了观察泰伯（Ｔａｌｂｏｔ）像的共轭虚像的实验原理及方法，并给出实验结果及扼要的理论解释，作者首次提出可把泰伯自成像公式的ｍ值扩展的负值。     

Experimental study of the Talbot effect under femtosecond laser illumination

Experimental results of the Talbot effect of an amplitude grating under femtosecond laser illumination are reported. Compared with Talbot image under continuous wave (CW) illumination, Talbot images under femtosecond laser illumination are different due to the wide spectral bandwidth and the Talbot images are more distorted at longer Talbot distances. The spectrums and the pulsewidths of femtosecond laser pulses are measured with the frequency-resolved optical gating (FROG) apparatus. Experimental results are in good agreement with the theoretical analysis.     

Talbot effect under illumination of double femtosecond laser pulses

The Talbot effect under illumination of double femtosecond laser pulses has been reported. Spectrums of double femtosecond laser pulses with phase differences are quite different from that of one single femtosecond laser pulse. Therefore, the Talbot images of the double femtosecond laser pulses with phase differences are different from that of one single femtosecond laser pulse. Specifically, for the phase difference corresponding to π, the Talbot image shows the largest difference from that of one single pulse. Experimental results are in good agreement with the theoretical analysis. The behaviors of Talbot images under double femtosecond laser pulses illumination cannot be obtained under one femtosecond laser pulse, monochromatic or polychromatic light illumination. Therefore, it is a new interesting optical phenomenon for the Talbot effect which should have potential applications.     

Talbot像对谱面的对称性分析及焦距测量

分析了光栅的泰伯（Ｔａｌｂｏｔ）像和透镜焦面的关系，提出了Ｔａｌｂｏｔ像对谱面的对称性原理。并将其用于透镜焦距的测量，方法简单，精度高。     

Application of source encoding to incoherent Talbot imaging and the Lau effect

We demonstrate a technique to generate Talbot images by a spatially incoherent source using a source encoding technique. We further show that a Talbot image can be formed in the optical set-up for the Lau effect following source encoding theory.     

畴腐蚀掺镁铌酸锂可调阵列光分束器的研究

研究了不同畴腐蚀深度的掺镁铌酸锂二维六角可调阵列光分束器的分数Talbot效应.对不同Talbot分数β和不同畴腐蚀深度的阵列光分束器Talbot衍射像进行了数值模拟理论研究.模拟结果表明,Talbot分数β可以改变Talbot衍射像的周期及结构分布,而畴腐蚀深度可有效调制衍射像的光强分布.在理论研究的基础上,设计并制备了具有不同畴腐蚀深度的掺镁铌酸锂二维六角阵列光分束器,对其在不同Talbot分数β条件下的分数Talbot效应进行了通光实验研究,实现了畴腐蚀阵列光分束器对近场Talbot衍射光强分布的调制,实验结果与理论研究结果一致.     

Talbot Images of Two-Dimensional Gaussian Beam Arrays with Amplitude Fluctuation

Talbot images constructed in the Fresnel diffraction region due to two-dimensional Gaussian beam arrays with amplitude fluctuation are statistically investigated using a mathematical model based on the propagation law of a Gaussian beam. The average intensity distribution of Talbot images is analyzed theoretically, and the corresponding simulation is conducted by computer. The relative fluctuation of the peak intensity to the mean with respect to Talbot images is found to be less than that of the source by approximately 1/4. Furthermore, the effect of the finite size of source arrays on the formation of Talbot images is revealed throughout the simulation as well as the effect of the amplitude fluctuation.     

Focal plane tuning in wide-field-of-view microscope with Talbot pattern illumination

We have developed a focal plane tuning technique for use in focus-grid-based wide-field-of-view microscopy (WFM). In WFM, the incidence of a collimated beam on a mask with a two-dimensional grid of aperture produced the Talbot images of the aperture grid. The Talbot pattern functioned as a focus grid and was used to illuminate the sample. By scanning the sample across the focus grid and collecting the transmission, we can generate a microscopy image of the sample. By tuning the wavelength of the laser, we can tune the focal plane of the WFM and acquire images of different depth into the sample. Images of a green algae microscope slide were acquired at different focal planes for demonstration.     

Talbot Images of an Array Source with Correlated Phase Fluctuation Using the Propagation Law of a Gaussian Beam

Talbot images of a two-dimensional array source such as a surface-emitting array laser are investigated with the help of the propagation law of a Gaussian beam. The effect of the phase fluctuation existing between the elements of the source on the formation of Talbot images is revealed by computer simulation. In the study, the correlation extent of the phase fluctuation is taken into consideration together with its magnitude (standard deviation), and Talbot images of good quality are found to be formed when the correlation extent is larger than the extent of the diffraction of a Gaussian beam in the observation plane. It is further shown that the contrast of Talbot images is governed, in a statistical sense, not by the magnitude of the phase itself but by the phase-fluctuation slope in the array source.     

Talbot effect of a high-density grating under femtosecond laser illumination

The Talbot effect of a high-density grating under femtosecond laser illumination is analyzed with rigorous electromagnetic theory which is based on the Fourier decomposition and the rigorous coupled-wave analysis (RCWA). Numerical simulations show that the contrast of the Talbot images steadily decreases as the transmitted femtosecond laser pulses propagate forward and with wider spectrum width of the femtosecond laser pulses. The Talbot images of high-density gratings have much higher sensitivity of the spectrum widths of the incident laser pulses than those of the traditional low-density gratings. In experiments, the spectrums and the pulse widths of the incident pulses are measured with a frequency-resolved optical grating (FROG) apparatus. The Talbot images are detected by using a Talbot scanning near-field optical microscopy (Talbot-SNOM) technique, which are in coincidence with the numerical simulations. This effect should be useful for developing new femtosecond laser techniques and devices.     

Quadric wavefront aberrations in phase-type images of binary amplitude gratings with small opening ratios

We discuss the quadric wavefront aberration of a fractional Talbot imaging ray which distorts the phase-type image of a binary amplitude grating with a small value of the opening ratio. When the opening ratio is equal to 1/2 or 1/3, the imaging rays are shown to have no quadric wavefront aberrations. For the opening ratios of 1/4 and 1/5, two different types of quadric wavefront aberrations are responsible for the three-level phase images. If the opening ratio gets to 1/6, we find that three different types of quadric wavefront aberrations distort the fractional Talbot image. The quadric wavefront aberration formulated here may be used in evaluating the phase-type image of a binary amplitude grating with an arbitrary value of the opening ratio.     

Talbot imaging with increased spatial frequency: a technique for replicating truncated self-imaging objects

The Talbot effect in the presence of a convergent beam of coherent light yields a demagnified image of a self-imaging object. In fact, the object does not even have to fulfill the self-imaging condition; the object with truncated self-imaging feature is sufficient to yield an image that is sufficiently accurate for many practical purposes. We have taken this approach to fabricating circular gratings with a reduced period compared to the period of the mask. Using a simple experimental setup and a concentric circular grating mask, we have created images whose periods are either one-half or one-third of the mask's period. Demagnified Talbot imaging of fully or truncated self-imaging objects provides an attractive approach to photolithographic fabrication of structures whose periods are somewhat greater than the wavelength of the light source.     

Two-Dimensional Talbot Effect with Atomic Density Gratings

We report the experimental observation of two-dimensional Talbot effect when a resonance plane wave interacts with a two-dimensional atomic density grating generated by standing wave manipulation of ultracold Bose gases.Clear self-images of the grating and sub-images with reversed phase or fractal patterns are observed. By calculating the autocorrelation functions of the images, the behavior of periodic Talbot images is studied. The Talbot effect with two-dimensional atomic density grating expands the applications of the Talbot effect in a wide variety of research fields.     

超短脉冲激光照射下光栅Talbot效应的实验研究

理论上研究了超短脉冲激光照射下光栅的Talbot效应,得到了超短脉冲激光照射下光栅Talbot图像的性质.实验上采用严格的实验方法(频率分辨光学开关装置测量超短脉冲激光、反射式扩束系统对超短脉冲进行扩束)很好地验证了理论分析结果.理论分析和实验结果表明,超短脉冲激光照射下光栅的Talbot图像的对比度会显著下降,而且超短脉冲激光的脉宽越短,Talbot距离越大,Talbot图像的对比度会进一步下降.     

Fractional second-harmonic Talbot effect

We demonstrate the fractional second-harmonic (SH) Talbot effect in a hexagonally poled LiTaO3 crystal. We carefully record the SH Talbot images at 1/2, 1/3, and 1/4 Talbot lengths, which are well matched with the simulated images by using the modified Rayleigh-Sommerfeld diffraction formula. A simplified model with a hexagonal array is adopted in the simulations. Also, we use a modified reciprocal vector theory to analytically explain the evolution of the SH array at fractional Talbot lengths. Our results show that the images are sensitive to the duty circle and the background of the array.     

Nonlinear Talbot self-healing in periodically poled LiNbO_3 crystal [Invited]

The nonlinear Talbot effect is a near-field nonlinear diffraction phenomenon in which the self-imaging of periodic objects is formed by the second harmonics of the incident laser beam. We demonstrate the first, to the best of our knowledge, example of nonlinear Talbot self-healing, i.e., the capability of creating defect-free images from faulty nonlinear optical structures. In particular, we employ the tightly focused femtosecond infrared optical pulses to fabricate Li Nb O_3 nonlinear photonic crystals and show that the defects in the form of the missing points of two-dimensional square and hexagonal periodic structures are restored in the second harmonic images at the first nonlinear Talbot plane. The observed nonlinear Talbot self-healing opens up new possibilities for defect-tolerant optical lithography and printing.     

Fractional Talbot effect in a Selfoc gradient-index lens

The fractional Talbot effect is demonstrated inside a standard 0.25-pitch Selfoc gradient-index lens under uniform illumination. Comparisons with theoretical expressions of positions and magnification of fractional Talbot images are given.     

Geometrical condition for observing Talbot effect in plasmonics infinite metallic groove arrays

The plasmonics Talbot effect in metallic layer with infinite periodic grooves is presented in this study. Numerical approach based on the finite element method is employed to verify the derived Talbot carpet on the non-illumination side. The groove depth is less than the metallic layer thickness; however, for specific conditions, surface plasmons polaritons(SPPs)can penetrate through grooves, propagate under the metallic layer, and form Talbot revivals. The geometrical parameters are specified via groove width, gap size, period, and wavelength, and their proper values are determined by introducing two opening ratio parameters. To quantitatively compare different Talbot carpets, we introduce new parameters such as R-square that characterizes the periodicity of Talbot images. The higher the R-square of a carpet, the more coincident with non-paraxial approximation the Talbot distance becomes. We believe that our results can help to understand the nature of SPPs and also contribute to exploring this phenomenon in Talbot-image-based applications, including imaging, optical systems, and measurements.     

Sub-diffraction-limited magnified Talbot imaging in cylindrical metamaterial

We numerically demonstrated the sub-diffraction-limited magnified Talbot imaging in a metamaterial composed of cylindrical stacked metal/dielectric multilayer. It was found that the magnified Talbot imaging could occur without the requirement of the metal/dielectric permittivity matching condition as satisfied in the hyperlens. Specifically, in this work, a practical realization of the magnified Talbot imaging was performed by Ag/Al₂O₃ multilayer stack at the wavelength of 337 nm. Unlike the traditional Talbot effect, the Talbot length in this case is not a constant but a variable and the variable Talbot length can be predicted roughly by ray optics approach. The contrast of the magnified Talbot imaging is decided by both the imaginary part and the real part in permittivity of the metamaterial. In order to obtain a deep sub-wavelength magnified Talbot image at the outer surface of the cylindrical metamaterial, the outer cylindrical radius should be optimized and the imaginary part in the permittivity should be small enough.