Cubic sinusoidal phase mask: Another choice to extend the depth of field of incoherent imaging system

Wave-front coding is a well known technique used to extend the depth of field of incoherent imaging system. The core of this technique lies in the design of suitable phase masks, among which the most important one is the cubic phase mask suggested by Dowski and Cathey (1995) [1]. In this paper, we propose a new type called cubic sinusoidal phase mask which is generated by combing the cubic one and another component having the sinusoidal form. Numerical evaluations and real experimental results demonstrate that the composite phase mask is superior to the original cubic phase mask with parameters optimized and provides another choice to achieve the goal of depth extension.     

An apodized cubic phase mask used in a wavefront coding system to extend the depth of field

The point spread function (PSF) caused by a wavefront coding system with a cubic phase mask has big side-lobes which leads to bad image restoration. This paper proposes a novel apodized cubic phase mask to suppress the side-lobes of the PSF. Simulated annealing algorithm is used to optimize the cubic and the truncation parameter of the phase mask. The system with the novel phase mask has better performance in the modulation transfer function (MTF) especially in low-and-medium spatial frequency region. The simulation results show that the restored images with the novel phase mask are superior to the one with the classic cubic phase mask in contrast and ringing effect. The experimental results show that the side-lobes of the PSF are suppressed by using the apodized cubic phase mask.     

Analytical and experimental demonstration of depth of field extension for incoherent imaging system with a standard sinusoidal phase mask

The wavefront coding technique is used to enlarge the depth of field（DOF）of incoherent imaging systems. The key to wavefront coding lies in the design of suitable phase masks.To date,numerous kinds of phase masks are proposed.However,further understanding is needed regarding phase mask with its phase function being in a standard sinusoidal form.Therefore,the characteristics of such a phase mask are studied in this letter.Deriving the defocused optical transfer function（OTF）analytically proves that the standard sinusoidal phase mask is effective in extending the DOF,and actual experiments confirm the numerical results.At the same time,with the Fisher information as a criterion,the standard sinusoidal phase mask shows a higher tolerance to focus errors（especially severe focus errors）than the classical cubic phase mask.     

Optimized annular phase masks to extend depth of field

A radially symmetric phase mask composed of several annular zones with equal area (called APM) was designed based on the incoherent imaging theory from Fourier Optics. The phase of any ring equals minus of the phase function caused by certain defocus. Another circularly symmetric phase mask similar to the APM (called MQPM) was proposed, except for the different phase function deriving from the quartic phase mask (QPM). For MQPM, there are two differences from an existing phase mask: the selection of the phase parameters and the method to divide the phase mask. An optimization model was developed to obtain optimized parameters of the phase masks. Numerical evaluations show that both APM and MQPM are less insensitive to defocus than QPM, and the defocused optical transfer functions with two phase masks are symmetric about the in-focus plane in the axial direction.     

Optimized free-form phase mask for extension of depth of field in wavefront-coded imaging

To achieve a further extension of the depth of field in wavefront-coded imaging by reducing the impact of focus error in the optical transfer function, we propose the use of a free-form phase mask (FPM) instead of a conventional cubic phase mask (CPM). We optimized the shape of the FPM using the simulated annealing algorithm and confirmed that the optimized FPM provides a much larger focal tolerance and better final images than the CPM in the noise-free case.     

Pupil design based on Fisher information optimization to extend field depth in practical optical system

<正>Wavefront coding(WFC) is used to extend the field depth of an incoherent optical system by employing a phase mask on the pupil.We uses a Fisher information(FI) metric based optimization method to design a phase mask by taking the modulation transfer function(MTF) of the practical optical system into consideration. This method can modulate the wavefront so that the point spread function and optical transfer function are insensitive to the object distance.The simulation results show that the optimized phase mask based on the proposed method can further improve the defocusing image quality while maintaining the focusing image quality.     

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     

Effects of relative phase in an open ladder system without incoherent pumping

We studied effects of the relative phase between the probe and driving fields on the absorption and dispersion properties in an open three-level ladder system with spontaneously generated coherence but without incoherent pumping. It is shown that by the phase controlling, switching from absorption to lasing without inversion (LWI) and enhancing remarkablely LWI gain can be realized; large index of refraction with zero absorption and the electromagnetically induced transparency can be obtained. We also find that varying the atomic injection and exit rates has a considerable influence on the phase dependent-absorption property of the probe field, existent of the atomic injection and exit rates gives the necessary condition of the realization of LWI, getting LWI is impossible in the corresponding closed system without incoherent pumping.     

非相干成像双目视觉系统的误差分析

影响双目视觉系统测量精度的因素很多,目前系统结构参数对测量精度的影响主要有光轴与基线的夹角、基线距离、水平视角、物距以及透镜焦距等。由于孔径尺寸直接影响成像分辨率,是决定双目视觉测量精度的核心因素,因此依据非相干成像理论,对双目成像过程进行仿真和实验,采用加速鲁棒特征算法对所成的图像对进行特征提取与匹配,获取其视差值,并且计算其视差均方根误差来表征系统误差。研究结果表明,系统误差随着透镜孔径大小的增大而减小,并且趋于饱和。该研究可以为双目系统设计过程中系统参数和孔径尺寸的选取提供理论和实验依据。     

Analyzing wavelength behavior of a cubic phase mask imaging system based on modulation transfer function

The wavefront coding technology is an effectively method for extending the depth of field. However, the phase delayed by the phase mask changes with light wavelength, and the chromatic aberration is caused by chromatic dispersion of the optical elements. The modulation transfer function (MTF) of the cubic phase mask (CPM) system is derived with considering the axial chromatic aberration and optical path difference variation with wavelength, and the wavelength behavior of CPM system is analyzed in details. We yield that the MTF is approximately wavelength invariant within a certain frequency bandwidth, and the bandwidth is nearly inverse proportional to wavelength and varies with axial chromatic aberration. The effect induced by dispersion of the CPM material is very weak. If the CPM system is illuminated by wideband spectral light and the ACA exists, then the frequency bandwidth may become narrower than the monochromatic case, and the position of image sensor can be relocated to balance frequency bandwidth among all wavelengths.