The filtering characteristics of simple grating optical low-pass filters

We studied the characteristics of a two-dimensional grating optical low-pass filter (GOLF) theoretically and experimentally. The modulation transfer function (MTF) of an optical system that consists of a lens and a GOLF is theoretically derived by taking all orders of diffracted beams into consideration. The MTFs of a two-phase chess-board-type GOLF and a three-phase GOLF were calculated for various phase differences and compared with that of a birefringent low-pass filter (BLF). The three-phase GOLF with nine center beams of equal strength removes most moiré fringes, but the resolution degradation is severe compared to the BLF. The two-phase GOLF with a phase difference of 180°, which is similar to the BLF in term of beam distribution, has a medium characteristic somewhere between those of the three-phase GOLF and the BLF. Samples of two GOLFs are made and experimented on by attaching them to a digital camera. The experimental result coincides with the theoretical development. Received: 31 October 2001 / Revised version: 4 March 2002 / Published online: 2 May 2002     

Detection of small phase modulation using two-wave mixing in photorefractive crystals

Two-wave mixing of phase-modulated beams in photorefractive crystals under a dc electric field is studied both theoretically and experimentally. Based on the vectorial theory of light diffraction in crystals of cubic symmetry, we derived an analytical expression that describes the phase demodulation in crystals with an arbitrarily oriented electric field. The phase-demodulation technique was used for estimation of the space-charge field created in photorefractive crystals. It is shown that the space-charge-field grating created in GaP and Bi₁₂TiO₂₀ crystals is much smaller than that predicted from the one-level band-transport model of the photorefractive effect. Received: 12 December 2000 / Revised version: 8 February 2001 / Published online: 27 April 2001     

Three Gaussian beam heterodyne interferometer for surface profiling

A novel three Gaussian beam interferometric technique for profiling optical smooth surfaces is presented. The technique is based on the heterodinization of three Gaussian beams, two of them with the same temporal frequency. The first beam is used as a probe beam after being focused and reflected from the surface under test. The second beam is reflected from a reference surface. The third beam is obtained from the first diffraction order of a Bragg cell and thus, it is shifted in its temporal frequency. The three beams are coherently added at the sensitive plane of a photodetector that integrates the overall intensity of the beams. We show analytically that the electrical signal at the output of the photodetector consists of a temporal carrier whose amplitude is a sinusoidal function of the local topography. We include the measurement of the topography of a sample consisting in a blazed-reflecting grating calibrated by means of an atomic force microscope.     

On the relation between the wave aberration function and the phase transfer function for an incoherent imaging system with circular pupil

The consideration is carried out in its general formulation: the wave aberration function is represented in terms of classical aberrations (the Zernike polynomials), the phase transfer function (argument of the complex optical transfer function) is defined by a chain of transformations originating from the generalized pupil function. Quasi-analytical quadrature formulas are derived that link the optical transfer function and the phase transfer function with the aberration terms. It is shown that the phase transfer function contains information on the odd-order aberrations, which can be retrieved from coefficients to the Taylor expansion of the derived quadrature relation. Received 16 June 2001     

Solving the atmospheric scattering optical transfer function using the multi-coupled single scattering method

The atmospheric scattering optical transfer function （OTF） is solved by applying the multi-coupled single scattering （MCSS） method to the three-dimensional radiative transfer equation （RTE） under the periodic ground condition. This approach is a direct hit to the atmospheric scattering OTF using the same original context of modulation transfer function （MTF） measurement, i.e., images of sinusoidal grating at different spatial frequencies. Both the amplitude and phase shift of the OTF at various zenith and azimuth angles can be obtained at an arbitrary spatial frequency.     

低阶模式校正自适应光学系统的补偿效果分析

引入规格化的相位谱「不一定为科尔莫戈罗夫（Ｋｏｌｍｏｇｏｒｏｖ谱」,推导了大气湍流相位结构函数、低阶模式校正后的残余相位结构函数以及长曝光光学传递函数（ＬＴＦ）。分别给出了在各种不同大气湍流强度ρ０,不同相位谱空间频率的指数下降因子ρ时,大气湍流相位波前低阶模式完全校正后和倾斜部分校正时的长曝光光学传递函数（ＯＴＦ）、长曝光斯特列尔（Ｓｔｒｅｈｌ）比和半高全宽（ＦＷＨＭ）的数值计算结果。     

Relevance of continuously self-imaging gratings for noise robust imagery

We have designed miniaturized, simple, and robust cameras composed of a single diffractive optical element (DOE) that generates a continuously self-imaging (CSI) beam. Two different DOEs are explored: the J₀ Bessel transmittance, characterized by a continuous optical transfer function (OTF) and the CSI grating (CSIG), characterized by a sparse OTF. In this Letter, we will analyze the properties of both DOEs in terms of radiometric performances. We will demonstrate that the noise robustness is enhanced for a CSIG, thanks to the sparsity of its OTF. A camera using this DOE has been made and experimental images are presented to illustrate the noise robustness.     

Femtosecond third-harmonic generation:. self-phase matching through a transient. Kerr grating and the way to ultrafast computing

The third harmonic of 810-nm 100-fs pulses at 130 μJ is generated very efficiently when ultrashort pulses from two noncollinear beams interfere in an optical medium to create an instantaneous transient grating via the optical Kerr effect. The grating couples two pathways for third-harmonic generation, each taking two photons from one beam and one photon from the other beam, respectively. The coupling enables self-phase matching in the complete process, resulting in a conversion efficiency of ≈3%. Scattering an independent beam at the transient grating confirms a lifetime limited by the pulse duration, with a reaction on the order of one optical cycle. Using the second harmonic of a Ti-sapphire laser at 405 nm, it is shown that the generation of the transient Kerr grating is a general feature, requiring less than 20 μJ/pulse. By introducing a third femtosecond beam we are able to emulate various digital logic units with femtosecond response. Received: 16 October 2001 / Published online: 6 June 2002     

Novel Ghost Imaging Method for a Pure Phase Object

We propose a novel ghost imaging scheme which is especially served to a pure phase object. A spatially incoherent beam is mixed with a coherent beam of the same frequency field by a beamsplitter. Then we perform the ghost imaging scheme using the mixed beam. Our theoretical result shows that this approach is capable of reconstructing a pure phase object in joint-intensity measurement. The visibility of the images is also analysed for two pure phase objects, an optical wedge and a phase grating.     

Optical simulation of the quantum Hadamard operator

A possible way to optically simulate quantum algorithms is by making use of the spatial distribution of light in a laser beam. In this approach, the quantum states are represented by the amplitudes of the electromagnetic field in the beam. Temporal evolution is simulated by using optical elements such as lenses and phase shifters. Different elements are required depending on the operation whose implementation is desired. In this paper, we present an optical module to simulate the Hadamard transformation operating on a single qubit. The system is composed by a set of lenses, a phase plate and a phase grating and it could be used as a part of more complex arrangements. As an example, we make use of our Hadamard optical module as a part of the quantum circuit that solves the Deutsch problem. We show the obtained experimental results and we discuss the limitations of the proposal.     

Differentiation and subtraction of amplitude and phase images using a photorefractive novelty filter

In this article, we demonstrate the capability of a two-beam coupling photorefractive optical novelty filter of detecting changes in the amplitude or phase of optical images. These changes may either be continuous or discrete in time. The performance of the two-beam coupling novelty filter is investigated and expressions for the output contrast corresponding to phase and amplitude changes based on a novel, simple interference model of two-beam coupling are derived. These expressions are verified by experimental results on the novelty contrast, revealing that the amplitude contrast is not described correctly by the commonly accepted coupled-wave theory. The novelty filter was applied to the detection of temporally continuous phase changes provided by a gas flow and moving microscopic objects. A novel scheme for image subtraction is also demonstrated, showing the novelty filter’s ability to detect temporally discrete changes. Received: 14 November 1998 / Revised version: 18 January 1999 / Published online: 12 April 1999     

Coherent imaging of extended objects

When used with coherent light, optical imaging systems are inherently unable to reproduce both the amplitude and the phase of a two-dimensional field distribution. This is 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 be dramatically distorted when extended objects are imaged. We illustrate the problem using two simple examples: the pinhole camera and the thin lens. The effects predicted by our theoretical analysis are confirmed by experimental observations.     

Investigation of the dynamic recording process of thick refractive index gratings in photorefractive crystals by the microphotometric method

Diffraction-efficiency measurements are compared with the microphotometric determination of the intensity pattern at the exit face of a LiNbO₃-sample during the holographic recording process. The special advantage of the microphotometric method is the possibility to determine phase shifts of the refractive index grating and of the light intensity pattern simultaneously and independently. Both quantities are very important for an understanding of dynamical effects during the holographic writing process. Furthermore, direct experimental evidence for the change of the modulation degree, i.e. the change of the contrast of the light pattern writing the grating, has been found. This change is caused by a Moiré-like effect which is closely related to the energy transfer between writing beams.     

Effect of partial coherence on four-wave mixing in photorefractive materials via reflection grating approximation

We investigate the effect of beam coherence on four-wave mixing via reflection gratings in photorefractive media. For the case of phase conjugation, the results of our theoretical analysis indicate that partial coherence always leads to a drop of signal gain and phase conjugate reflectivity in non-depleted cases. In general, the mutual coherence of the signal beam and the pump beam can be enhanced due to the process of wave mixing. The mutual coherence of the phase conjugate beam and one of the pump beams depends on the beam intensity ratio as well as the optical path difference. This is distinctly different from the four-wave mixing case with a transmission grating. Received: 15 October 1999 / Revised version: 26 June 2000 / Published online: 7 February 2001     

Simulation of a polarization pupil filter using magneto-optic lens under elliptically polarized illumination

An active lens made of magneto-optic glass element and placed before a linear polarizer is shown to simulate the pupil plane amplitude and phase filter due to thickness dependent Faraday rotation variation in radial direction. Changing the applied magnetic flux density can dynamically change the pupil characteristics. The variation of intensity point spread function (IPSF) and optical transfer function (OTF) with magnetic flux density for elliptically polarized input beam is studied.     

Simultaneous Cartesian coordinate display of defocused optical transfer functions

We show that by using a binary spatial filter and a square-law detector we can display all the defocused optical transfer functions (OTF's) in a given study in a single picture. The resulting unique picture has as its horizontal coordinates the spatial frequency and as its vertical coordinates the amount of defocus. The gray-level variations are proportional to the modulus of the OTF, that is, the modulation transfer function. Numerical simulations are included.     

相干场成像技术接收镜精度对传递函数的影响

根据相干场成像技术(又称傅里叶望远镜)接收镜的特点, 研究了接收镜偏差对相干场成像技术光学传递函数的影响, 推导了光学传递函数与接收光路光程均方差的关系式. 该式表明相干场成像技术的光学传递函数是接收光路光程均方差与频差乘积的平方的负指数函数. 为确定接收系统精度提供了理论依据. 关键词： 相干场成像 傅里叶望远镜 误差 光学传递函数     

Phase-Space Analysis of Wavefront Coding Imaging Systems

We explore the use of the Radon-Wigner transform, which is associated with the fractional Fourier transform of the pupil function, for determining the point spread function （PSF） of an incoherent defocused optical system. Then we introduce these phase-space tools to analyse the wavefront coding imaging system. It is shown that the shape of the PSF for such a system is highly invariant to the defocus-related aberrations except for a lateral shift. The optical transfer function of this system is also investigated briefly from a new understanding of ambiguity function.     

A dispersionless Michelson interferometer for the characterization of attosecond pulses

A novel application of a free-standing transmission grating as a beam splitter in a Michelson-type interferometer is described. The arrangement can operate in the XUV and soft X-ray spectral region and, therefore, it is well suited for the characterization of attosecond pulses. Using ray-tracing codes, we have analyzed three different setups in which spherical mirrors are employed in conjunction with the transmission grating and have investigated in detail their dispersive characteristics. It is shown that such an arrangement can be made to exhibit group-delay dispersion of ∼1 as² while it provides two co-propagating and converging beams. Received: 12 October 2001 / Revised version: 17 December 2001 / Published online: 7 February 2002     

Optical filter with controlled transfer function on the basis of dynamic volume holograms in barium titanate

The feasibility of optical control over the spectral characteristics of an optical filter based on 3D holographic grating recorded in a photorefractive crystal is considered. It is shown experimentally that the transfer function can be configured in real time by introducing phase shifts between the hologram sections.