Edge enhancement of a phase-conjugate image with a mutually pumped phase conjugator

Usually edge enhancement of optical images is produced by introduction of loss into the low spatial frequency components of the image-bearing beam in the Fourier plane of a lens. We report on edge-enhanced phase-conjugate images from a mutually pumped conjugator accomplished by spatial filtering in the Fraunhofer diffraction region of the input beams. High-resolution (128-160 lines/mm) edge-enhanced images are obtained through traditional spatial filtering in the Fourier plane and in the Fraunhofer regime. Amplification of these edge-enhanced images is observed with some loss of high spatial resolution (50 lines/mm).     

Metasurface Enabled Wide‐Angle Fourier Lens

Fourier optics, the principle of using Fourier transformation to understand the functionalities of optical elements, lies at the heart of modern optics, and it has been widely applied to optical information processing, imaging, holography, etc. While a simple thin lens is capable of resolving Fourier components of an arbitrary optical wavefront, its operation is limited to near normal light incidence, i.e., the paraxial approximation, which puts a severe constraint on the resolvable Fourier domain. As a result, high‐order Fourier components are lost, resulting in extinction of high‐resolution information of an image. Other high numerical aperture Fourier lenses usually suffer from the bulky size and costly designs. Here, a dielectric metasurface consisting of high‐aspect‐ratio silicon waveguide array is demonstrated experimentally, which is capable of performing 1D Fourier transform for a large incident angle range and a broad operating bandwidth. Thus, the device significantly expands the operational Fourier space, benefitting from the large numerical aperture and negligible angular dispersion at large incident angles. The Fourier metasurface will not only facilitate efficient manipulation of spatial spectrum of free‐space optical wavefront, but also be readily integrated into micro‐optical platforms due to its compact size.     

Precise and fast phase wraps reduction in fringe projection profilometry

Phase wraps in a 2D wrapped phase map can be completely eliminated or greatly reduced by frequency shifting. But it usually cannot be optimally reduced using conventional fast Fourier transform (FFT) because the spectrum can be shifted only by a integer number in the frequency domain. In order to achieve a significant phase wrap reduction, we propose a fast and precise two-step method for phase wraps reduction in this paper, which is based on the iterative local discrete Fourier transform (DFT). Firstly, initial estimate of the frequency peak is obtained by FFT. Then sub-pixel spectral peak with high resolution is determined by iteratively upsampling the local DFT around the initial peak location. Finally, frequency shifting algorithm that operates in the spatial domain is used to eliminate phase wraps. Simulations and experiments are conducted to demonstrate the superb computing efficiency and overall performance of the proposed method.     

Fourier transform infrared imaging of human hair with a high spatial resolution without the use of a synchrotron

The cross-section of a human hair has been imaged for the first time using the micro attenuated total reflection (ATR) Fourier transformed infrared (FT-IR) method in combination with a focal plane array (FPA) detector. A rigorous approach was applied to determine the spatial resolution, namely, measuring the distance over which the band absorbance changes from 95 to 5% of the maximum absorbance when passing through a sharp interface. The measured value for IR transmission was approximately 16 microm, while the value obtained using ATR imaging was approximately 5 microm. The enhanced spatial resolution achieved by this method allows the medulla of the hair (approximately 8 microm in diameter) to be imaged clearly without the need for a synchrotron source. The spatial resolution of transmission and ATR imaging is compared, and advantages of ATR imaging are discussed.     

Spatially resolved phase objects using Mach–Zehnder interferometry

Phase characterization with a good spatial resolution is crucial for focused beams in nonlinear media. The phase-shifting interferometry technique, using the least-squares error criterion for several interferograms, is implemented using a reflective spatial light modulator (SLM). The method provides a convenient calibration for any phase-shift steps. The reliability of the proposed method is checked by direct comparison with results obtained by the Fourier transform method as well as using a previously characterized circular phase object.     

Elimination of conjugate image for holograms using a resolution redistribution optical system

A technique to alter the ratio of the horizontal and vertical resolution of a spatial light modulator has been proposed. This technique increases the horizontal resolution by a factor of K and decreases the vertical resolution by a factor of 1/K. The proposed technique increases the horizontal viewing angle by a factor of approximately K, although a conjugate image appeared. In the present study, the resolution redistribution technique is modified to eliminate the conjugate image. The height of a horizontal slit placed on the Fourier plane of a 4 f imaging system used for the resolution redistribution system is reduced by half. The horizontal resolution becomes K times larger, and the vertical resolution becomes 1/2K times smaller. The improved technique generates only the object wave. We demonstrated fourfold enlargement of the horizontal resolution to increase the horizontal viewing angle by approximately four times without generating the conjugate image.     

Infrared atmospheric sounding interferometer correlation interferometry for the retrieval of atmospheric gases: the case of H2O and CO2

Correlation interferometry is a particular application of Fourier transform spectroscopy with partially scanned interferograms. Basically, it is a technique to obtain the difference between the spectra of atmospheric radiance at two diverse spectral resolutions. Although the technique could be exploited to design an appropriate correlation interferometer, in this paper we are concerned with the analytical aspects of the method and its application to high-spectral-resolution infrared observations in order to separate the emission of a given atmospheric gas from a spectral signal dominated by surface emission, such as in the case of satellite spectrometers operated in the nadir looking mode. The tool will be used to address some basic questions concerning the vertical spatial resolution of H2O and to develop an algorithm to retrieve the columnar amount of CO2. An application to complete interferograms from the Infrared Atmospheric Sounding Interferometer will be presented and discussed. For H2O, we have concluded that the vertical spatial resolution in the lower troposphere mostly depends on broad features associated with the spectrum, whereas for CO2, we have derived a technique capable of retrieving a CO2 columnar amount with accuracy of ≈±7 parts per million by volume at the level of each single field of view.     

Enhancement of infrared spectral images for maximizing chemical information by minimizing baseline interferences

The popularity of spectral images in many areas of analysis has greatly increased during the last decade due to the development of charge-coupled device (CCD) and infrared sensitive cameras. Large amounts of spatial information can be obtained in short periods of time. The general goal in analytical chemistry is to convert spectral images into chemical images, which show the spatial locations of various chemical components. Self-modeling multivariate curve resolution methods can be used to extract pure component spectra from the mixture spectra in images and produce chemical images. However, there is a difficulty in processing infrared spectral images due to large pixel-to-pixel baseline variations. Herein, a method for minimizing baseline interferences using fast Fourier transform (FFT) filtering in both the spectral and spatial domains is discussed. The methodology is demonstrated on a microscopic sample of butter contaminated with non-pathogenic E. coli and on a cross-sectional sample of rabbit aorta containing plaque. The processing to reduce baseline effects improved the spatial resolution without compromising the spectral resolution.     

Hybrid method combining orthogonal projection Fourier transform profilometry and laser speckle imaging for 3D visualization of flow profile

This paper reports a straightforward technique for three-dimensional (3D) visualization of a flow profile by a hybrid algorithm combining Fourier transform orthogonal fringe projection and laser speckle imaging techniques. The use of orthogonal projection aims to suppress the zero order allowing surface reconstruction with high spatial resolution and accuracy while analyzing the intensity fluctuations of diffuse backscattered laser light providing 2D flow information. Once both are achieved, 3D flow visualization can be displayed. The method is experimentally validated first with a plastic tube filled with scattering liquid (milk) running at various controlled flow rates and then with the tube embedded under scattering layers (chicken breast) of varying thickness. The system includes a single, common camera, a commercial projector (profilometry channel), a laser light source (flow channel), and a computer station. In addition, orthogonal projection processing was combined with Hilbert transform, increasing the visualization and resolution of the measured flow profile.     

Time-resolved Fourier transform infrared spectroscopic imaging

Fourier transform infrared (FT-IR) imaging allows simultaneous spectral characterization of large spatial areas due to its multichannel detection advantage. The acquisition of large amounts of data in the multichannel configuration results, however, in a poor temporal resolution of sequentially acquired data sets, which limits the examination of dynamic processes to processes that have characteristic time scales of the order of minutes. Here, we introduce the concept and instrumental details of a time-resolved infrared spectroscopic imaging modality that permits the examination of repetitive dynamic processes whose half-lives are of the order of milli-seconds. As an illustration of this implementation of step-scan FT-IR imaging, we examine the molecular responses to external electric-field perturbations of a microscopically heterogeneous polymer-liquid crystal composite. Analysis of the spectroscopic data using conventional univariate and generalized two-dimensional (2D) correlation methods emphasizes an additional capability for accessing of simultaneous spatial and temporal chemical measurements of molecular dynamic processes.     

Attenuated total reflection Fourier transform infrared imaging with variable angles of incidence: a three-dimensional profiling of heterogeneous materials

Depth profiling in Fourier transform infrared (FT-IR) spectroscopic imaging has been demonstrated using a single reflection variable angle attenuated total reflection (ATR) accessory. Chemical information about samples can be obtained in three dimensions by acquiring ATR-FT-IR images at different angles of incidence through the ATR crystal. The image quality and field of view achieved at different angles of incidence has been discussed. A polymer film comprising two layers has been used as an example to demonstrate the principle of the measurement. The demonstrated approach is a promising tool to obtain depth profiles of heterogeneous materials. The extent of the measured depths is limited and ranges from approximately 0.3 to 4 microm, but the spatial resolution in the z-direction is not limited by diffraction. The development of this approach opens up the possibility to study the spatial heterogeneity of thin films including biological tissues, such as hair and skin, with high depth resolution.     

用傅里叶相移特性估计位移

提出了一种从频率域出发,估计出运动物体在空间域位移的算法。利用傅里叶变换的自配准性质和位移特性,用极坐标形式下连续图像相位谱的差直接估计运动目标的位移。与传统的寻找迪拉克峰值的方法相比,本方法无需重新变换回空间域,从而节省了处理时间,具有更好的实时性。实验证明,这种先求出相位谱的差,再用其周期数来估计位移的算法简单明了,其分辨能力不低于一个像素。该理论可以应用于图像跟踪和图像后期处理中。     

基于信号采样的相位相关法亚像素级配准方法研究

为解决小模数齿轮视觉测量中凸显的工业相机高空间分辨率与大视场相互制约的矛盾,对基于相位相关原理的亚像素级配准方法进行了研究。分析相位相关法在应用于具有亚像素位移量的图像时,互功率谱傅里叶逆变换后产生主峰副峰的原因及两者幅值与亚像素位移量的对应关系,将该方法用于小模数齿轮图像配准,实验结果表明:该方法的配准误差小于0.002 pixel;在忽略非相关区域影响的情况下,通过误差分析得出该方法存在的周期为1 pixel的非累积性误差,其中由函数近似引入的误差小于5×10^-8pixel。     

Imaging of trace species distributions by degenerate four-wave mixing: diffraction effects, spatial resolution, and image referencing

We describe the theory of imaging by degenerate four-wave mixing (DFWM) using a standard diffraction theory of imaging by coherent light. We demonstrate that, even with the phase-conjugating geometry, no aberration correction can be achieved by DFWM imaging. We demonstrate the coherent nature of DFWM image formation using spatially modulated signals generated in flame OH in the phase-conjugating geometry. The intensity distribution in the Fourier plane of a telecentric lens system is shown to be the spatial Fourier transform of the object distribution characteristic of coherent imaging. The brightness of the DFWM signals exceeds that of similar laser-induced fluorescence signals that can be discriminated by restricting the aperture of the imaging system while still allowing a spatial resolution of approximately 70 ?m. DFWM imaging with the forward-folded boxcars geometry is demonstrated and used in a simple referencing scheme to compensate for structure on the images imposed by nonuniformity of the laser beams employed. Images formed in NO are used to illustrate that structure on a scale of less than 100 ?m arising from beam inhomogeneity can be removed by this referencing technique.     

Optical resolution and the duality of light

For 15 years, lensless microscopes have been constructed based on the use of holography, a digital CCD detector, and a computer for image reconstruction by use of, e.g., Fourier transformation. Thus, no lens is involved and therefore the conventional resolution limit of half the wavelength no longer applies. Instead of being limited by the wavelength, the resolution is in this case limited by how exact one can measure the phases of the light. It is remarkable that the interference-limited resolution is approximately 0.01 lambda, whereas the diffraction-limited resolution is only of the order of 0.5 lambda. It is my hope that by combining these two techniques it will be possible to increase the magnification in optical systems by at least an order of magnitude. The calculations also indicate that information does not necessarily decrease with distance.     

Modeling of the generic spatial heterodyne spectrometer and comparison with conventional spectrometer

We describe the modeling of the generic spatial heterodyne spectrometer. This instrument resembles a somewhat modified Michelson interferometer, in which the power spectrum of the input source is determined by performing a one-dimensional Fourier transform on the output intensity profile. Code has been developed to analyze the performance of this type of spectrometer by determining the dependence of both spectral resolution and throughput on parameters such as aperture and field of view. An example of a heterodyne spectrometer is developed to illustrate the techniques employed in the modeling and a comparison undertaken between its performance and that of a conventional spectrometer. Unlike the traditional Fourier transform infrared system, the heterodyne spectrometer has the very desirable feature of having no moving components.     

Fourier transform technique with frequency filtering for optical thin-film design

A Fourier analysis of existing and potentially complex refractive index profiles is often useful in the resolution of thin-film design problems. Applications of a frequency-filtering technique, which consists of the suppression of undesired spatial frequencies from the refractive index profiles, are described. A new, extremely simple antireflection coating synthesis method based on this concept is proposed.     

Optimization of multichannel parallel joint transform correlator for accelerated pattern recognition

The multibeam parallel joint transform correlator for optical pattern recognition, which was recently proposed by the authors [Appl. Opt. 37, 5408 (1998)], can increase parallelism without accumulating zero-order background level at the first Fourier transform plane. To evaluate the throughput capability, an experimental trial was made, achieving a 67-ms recognition rate per face per channel, which is limited by the response of the optically addressed liquid-crystal spatial light modulator. A general design theory is developed for dense packing of the optical channels for a given spatial light modulator resolution, considering the bandwidth requirement of the target image. Then the condition for submillisecond throughput with state-of-the-art device technology is discussed.     

Nano-FTIR Absorption Spectroscopy of Molecular Fingerprints at 20 nm Spatial Resolution

We demonstrate Fourier transform infrared nanospectroscopy (nano-FTIR) based on a scattering-type scanning near-field optical microscope (s-SNOM) equipped with a coherent-continuum infrared light source. We show that the method can straightforwardly determine the infrared absorption spectrum of organic samples with a spatial resolution of 20 nm, corresponding to a probed volume as small as 10 zeptoliter (10(-20) L). Corroborated by theory, the nano-FTIR absorption spectra correlate well with conventional FTIR absorption spectra, as experimentally demonstrated with poly(methyl methacrylate) (PMMA) samples. Nano-FTIR can thus make use of standard infrared databases of molecular vibrations to identify organic materials in ultrasmall quantities and at ultrahigh spatial resolution. As an application example we demonstrate the identification of a nanoscale PDMS contamination on a PMMA sample.     

Digital holographic interferometry for measurement of temperature in axisymmetric flames

In this paper, experimental investigations and analysis is presented to measure the temperature and temperature profile of gaseous flames using lensless Fourier transform digital holographic interferometry. The evaluations of the experimental results give the accuracy, sensitivity, spatial resolution, and range of measurements to be well within the experimental limits. Details of the experimental results and analysis are presented.