Design of lenses with curved Petzval image surfaces

Abstract

Design strategies have been devoted to simplify and miniaturize optical systems. In this paper, by constraining image surface to coincide with the Petzval surface, we achieve a compact f/2.8 lens system design with a curved Petzval image surface. Arc distortion is proposed to accurately measure the distortion relative to a curved image surface. The optical performance of our curved image surface lens is analysed and compared. Results show that modulation transfer function (MTF) of our curved Petzval design over 69% at 100 cycles/mm for entire fields is achievable with 100-mm effective focal length, 40º full field of view, >92.4% edge relative illumination, <0.5% arc distortion. Comparisons with a traditional lens with a planar image plane demonstrate that a curved Petzval image surface is an excellent strategy to simplify and miniaturize optical systems, compensate field curvature and benefit astigmatism correction, increase off-axis illumination and improve MTF. Furthermore, the lens with a curved Petzval image surface has a more uniform optical power distribution and greater degree of lens symmetry.     

计量型紫外显微镜实时焦点及倾角测量算法的研究

计量型紫外光学显微镜采用248 nm深紫外光源和高数值孔径物镜系统,工作距离和景深均很小,为实现清晰的成像,需要进行自动聚焦。因此研究了一种焦点及倾角测量算法,采用基于图像处理的自动聚焦方法,选择Tenengrad函数作为图像清晰度判据,进行清晰度评价。针对在扫描测量时标准样板倾斜与镜片可能会出现相撞的问题,提出了样板倾角测量方法来判断样板的倾斜方向和角度,从而确定物镜执行器的移动方向,实现物镜扫描成像过程中的动态对焦。     

Optimum lens aperture in phase-shifting speckle interferometric setups for maximum accuracy of phase measurement

Negative exponentially distributed intensities of speckle fields seem unfavorable in terms of precision metrology, if interferometric setups are involved with a saturable photodetector and an analog-to-digital converter that imposes a finite resolution. By spatial integration, extended detector apertures modify the intensity distribution toward a less awkward function. However, because the detector aperture also integrates over points of rapidly changing speckle phases, this is done at the expense of a lower modulation of measured intensity during phase shift. An optimum set of parameters is calculated here, consisting of values for the lens aperture, the mean speckle intensity, and the beam ratio. The remaining phase-measurement error assumes its minimum of 10.6 mrad when the space-bandwidth product of the lens-detector system (thus concerning the lens aperture) is 0.31, the mean speckle intensity is 1/11 of the saturation intensity, and the reference intensity is four times higher than the mean speckle intensity. The 90 degrees phase-shift algorithms with either three, four, or five frames turned out to be quite powerful, even with interference signals of rather poor modulation. Not needing a very small lens aperture is interesting, because stopping down the lens is a trade-off with the limited power of the laser.     

Considerations of aperture configuration in focal modulation microscopy from the standpoint of modulation depth

Focal modulation microscopy (FMM) is a simple, yet efficient, method to preserve image quality in terms of signal-to-background ratio by selecting ballistic photons for image formation. The aim of this paper is to investigate the effect of the various aperture configurations of the spatial phase modulator on the modulation depth of the FMM signal. The definition of modulation depth in FMM and its calculation method are introduced. According to two brief principles of choosing aperture configuration, three types of configurations with different numbers of zones ranging from two to six (totaling eight aperture configurations) are selected, and their corresponding modulation depths and attainable spatial resolutions are simulated. The results show that the modulation depth increases significantly when the number of zones varies from two to six, with a slight or no sacrifice in resolution. In summary, the annular configuration is superior to the fan- and stripe-shaped configurations in modulation depth and spatial resolution.     

Focal shifts in focused nonuniformly polarized beams.

We present a simple formula to evaluate the relative focal shift in a circular-aperture lens system illuminated by a nonuniformly polarized (NUP) light wave. Specifically, it is shown that the relative focal shift is determined by the effective Fresnel number. The effective Fresnel number is equal to the product of the Fresnel number of the lens aperture and the parameter sigma, which describes the uniformity of the polarization distribution of the NUP beam across the lens aperture. Some examples are given to illustrate the use of this approach. The influence of the polarization distribution of the incident NUP light wave on the polarization distribution in the axial points of the focused field is also presented.     

Fundamental diffraction limitations in a paraxial 4-f imaging system with coherent and incoherent illumination

In the usual model of an imaging system, only the effects of the aperture stop are considered in determining diffraction-limited system performance. In fact, diffraction at other stops--those associated with different lens elements, for example--can also affect system performance and cause the imaging to be space variant, even in the absence of vignetting in the conventional ray optics sense. For the 4-f imaging system investigated in this paper, the severity of the space variance depends on the relative sizes of the two lens stops and the aperture stops. If the diameters of the lenses are equal, the aperture of the first lens has a greater effect on system performance than does that of the second.     

Experimental observation of the effect of astigmatic aperture lens on the spectral switches of polychromatic Gaussian beam

Experimental results of a study, conducted to investigate the effect of an astigmatic aperture lens on the spectral switches observed with spatially coherent polychromatic light, are reported. It is found that the spectrum at the observation plane exhibits anomalous behavior after passing through the astigmatic aperture lens. It is shown that at a particular position of the aperture, the spectrum splits into two halves, while at other positions the spectrum either shifts towards lower frequencies (red shift) or shifts towards higher frequencies (blue shift). These spectral changes take place in the vicinity of the dark region of the diffraction pattern. Experimental observations show that the behavior of the spectral switch is affected by the astigmatism of the lens. It is found that the spectral minimum value and the transition height of the spectral switch change as the astigmatism of the lens changes. Moreover, the critical position of the aperture where spectral switch occurs also changes with the astigmatism of the lens. The results are consistent with the theoretical predictions [Pan, L.; Lü, B. Opt. Commun. 2004, 234, 13–22].     

Minimum variance beamforming applied to ultrasound imaging with a partially shaded aperture

Shadowing of an imaging aperture occurs when ultrasound beams are partially obstructed by an acoustically hard tissue, e.g., bone tissue. This effect leads to reduced resolution and, in some cases, geometrical distortion. In this paper, we initially introduce a binary apodization model to simulate effects of the shadowing on the point scatterers located close to a bone structure. Further, in a simulation study and an in vitro experiment, the minimum variance (MV) beamforming method is employed to image scatterers partly located in the shadow of bone. We show that the MV beamformer can result in a distorted image when the imaging aperture is highly obstructed by the bone structure. This distortion can be seen as an apparent lateral shift of the point spread function and a decrease in the sensitivity. Based on the signal power across the aperture, we adaptively determine the shadowed elements and discard their corresponding data from the covariance matrix to improve the MV beamformer performance. This modified MV beamformer can retain the resolution and compensate for the apparent lateral shifting and signal attenuation for the shadowed point scatterers.     

三维重构视觉系统的标定

文章基于改进两步法的标定思想,在三维重构中提出了一种新的视觉系统参数标定与镜头畸变修正方法.该方法根据图像中心附近点畸变量较小的性质,利用中心附近点和全场视点对CCD相机和DLP投影仪的内外部参数标定和镜头畸变修正进行分离.在标定过程中,所设计的带标准圆阵列的靶标和伪随机连续方形编码可以实现特征点的自动识别和匹配.实验表明,该方法能快速、方便地对视觉系统参数进行标定和镜头畸变修正.     

Incorporating lens distortion into the design of undistorted catadioptric omnidirectional cameras

An improved approach for design of the catadioptric omnidirectional camera with horizontal scene undistorted imaging is described. In the proposed approach, the influence of the lens distortion on the imaging quality of the omnidirectional camera is taken into account. We establish a radial distortion model for an image pickup lens and retain some opposite distortion in the mirror to correct the distortion existing in the image pickup lens. A horizontal scene undistorted catadioptric omnidirectional camera is designed with an off-the-shelf TV short focus lens using our approach; the numerical simulation shows that the distortion introduced by the imaging lens is eliminated effectively.     

Self-consistent way to determine relative distortion of axial symmetric lens systems

We present a simple method to determine the relative distortion of axially symmetric lens systems. This method uses graphs to determine every parametric value instead of nonlinear minimization computation and is composed of an LCD screen to display a square grid pattern of pixel-wide spots and a set of analyzing processes for the spots in the image. The two Cartesian components of the spot locations are processed by a two-step linear least-square fitting to third-order polynomials. The graphs for the coefficients enable us to determine the amount of decentering of the camera lens axis with respect to the center of the image array and the tip/tilt of the screen, which in turn gives the relative distortion coefficient. We present experimental results to demonstrate the utility of the method by comparing our results with the corresponding values determined by open source software available online.     

Programmable array microscopy with a ferroelectric liquid-crystal spatial light modulator

We present a programmable array microscope that uses a ferroelectric liquid-crystal spatial light modulator (SLM) for dynamic generation of scanning apertures. A single SLM serves as both the source and the detector aperture array in a double-pass confocal system. Successive aperture frames scan the array across the viewing area for complete imaging of a sample while preserving depth discrimination. Integration of the microscope output across all aperture frames produces a confocal image.     

Depth resolution and displayable depth of a scene in three-dimensional images

The depth resolution and the recordable object depth range, obtainable with parallel, toed-in and sliding aperture camera configurations for multiview image acquisition in the three-dimensional imaging systems, are found by assuming that the camera lens resolution is diffraction limited and the resolution of the recorded image is limited by a pixel pitch of the imaging sensor. The depth resolution for the holographic image is calculated and compared with that of the multiview images for the same parameter values. The influence of the viewer's eye resolution limit on the depth resolution of the multiview images and hologram is also found.     

A Study of Electric Charging Using Low-Magnification Electron Holography

As experimentally found by low-magnification holography, both the size of the condenser aperture and the excitation of the objective lens strongly modify the object wavefunction of an electron wave. For example, the phase by electrically charged polystyrene latex spheres attached to a copper grid increases with decreasing excitation of the objective lens and/or decreasing diameter of the condenser aperture. It was also found that a smaller diameter of the condenser aperture increases the phase shift by a carbon foil or magnetic memory cells. In addition, the phase of the image wave is modified by the lateral position of the aperture, whereas different electron densities of the imaging beam have only minor influence on the detected phase shifts.     

Optical and Photographic Problems In the Development and Use of an .f/l .0 Streak Camera Transparent to the Ultra-violet

The early stages of the high-voltage spark discharge in air are faintly luminous, most of the emission lying in the ultra-violet. For the purpose of obtaining time-resolved photographs of this growth, a lens consisting of a pair of monocentric spherical mirrors was designed. The system was of aperture f/1 .0 and focal length 2.4 in, and included a rotating-mirror to give an image velocity of O.14 in./μsec. The lens produced an image of spherical curvature of radius 2.4 in. The technique which was developed to produce films moulded to this curvature is described. The image distortion which is introduced by the system in both space and time is calculated. It is shown that relaxation of the film after removal from the camera reduced such errors considerably. Stationary photographs were used to obtain the co-ordinates of the three-dimensional spark track. Techniques for obtaining accurate time measurement and the elimination of perspective effects are described. Some examples of spark photography and quantitative measurements obtained with this camera are presented.     

Multipoint phase calibration for improved compensation of inherent wavefront distortion in parallel aligned liquid crystal on silicon displays

The inherent distortion of a reflective parallel aligned spatial light modulator (SLM) may need compensation not only for the backplane curvature but also for other possible nonuniformities caused by thickness variations of the liquid crystal layer across the aperture. First, we build a global look-up table (LUT) of phase modulation versus the addressed gray level for the whole device aperture. Second, when a lack of spatial uniformity is observed, we define a grid of cells onto the SLM aperture and develop a multipoint calibration. The relative phase variations between neighboring cells for a uniform gray level lead us to build a multi-LUT for improved compensation. Multipoint calibration can be done using either phase-shift interferometry or Fourier diffraction pattern analysis of binary phase gratings. Experimental results show the compensation progress in diffractive optical elements displayed on two SLMs.     

现场勘察中广角镜头相机快速标定算法及实现

基于摄影资料的图像测距技术已广泛应用于交通事故、考古等不可复原的现场勘察工作中,利用普通相机进行摄影测量也日趋成熟。但是普通相机没有广角镜头相机的取景优势,现场分析也比较局限,因此广角镜头相机逐渐取代普通相机。而广角镜头相机容易产生图像畸变效应。为此,本文基于相机成像原理,通过精确网格模板标定图像,利用相机参数间物理关系计算出相机内参和畸变参数,提出了一种广角镜头相机的快速标定算法,结合拍摄现场图像,精确定位参考模板标志牌在照片中的成像结果,计算出广角镜头相机的外参,建立广角镜头相机摄影测量系统。现场实验应用表明,本算法标定快速、简单、测量精度高,可以应用于交通事故现场勘测。     

激光探测告警光学系统设计

为满足激光探测告警光学系统对大视场和光学增益的要求,提出了宽视场有增益光学系统。该系统工作波长范围1.06~1.54μm,全视场角60°,最大口径28mm,PIN光电探测器光敏面直径2mm。物镜采用二片式反远距结构,增大了视场和后工作距离。弯月型负透镜在前,具有平衡像差和棱镜的偏向作用;物镜后放置高折射率标准超半球型浸没透镜,满足小光敏面探测器接收。分析结果表明,系统像高0.99mm,光学增益达15.33,结构简单,可有效降低激光辐射源功率、增强探测距离。     

Modulation light efficiency of diffractive lenses displayed in a restricted phase-mostly modulation display

We present an analysis of the diffraction efficiency of diffractive lenses displayed on spatial light modulators that depends on the modulation response of the display. An ideal display would produce continuous phase-only modulation, reaching a maximum phase-modulation depth of 2pi. We introduce the concept of modulation diffraction efficiency that accounts for the effect of nonlinearities only in the phase modulation of the display. We review a diffractive model with which to evaluate this modulation efficiency, including modulation defects such as nonlinear phase modulation, coupled amplitude modulation, phase quantization, and a limited modulation depth. We apply this diffractive model to Fresnel lenses and show that these modulation defects produce a lens multiplex effect. Finally we demonstrate that the application of a minimum Euclidean projection principle leads to high modulation diffraction efficiency even if the phase-modulation depth is much less than 2pi. We demonstrate that the modulation efficiency can exceed 90% for a modulation depth of 1.4pi and can exceed 40% (the equivalent for a binary phase element) for a modulation depth of only 0.7pi. Experimental results from use of a twisted nematic liquid-crystal display are presented to confirm these conclusions.     

Digital refraction distortion correction with an astigmatic coherence sensor

We demonstrate the sensing and correction of an isoplanatic refractive distortion (not lens aberrations), using the complete measurement of the partially coherent field in an aperture that the previously described astigmatic coherence sensor provides. Isoplanatic distortions, and in general distortions that do not cause energy loss, maintain the orthogonality of the coherent modes. We use the fact that a common distortion will occur to all coherent modes to separate the distortion from the source behind it, rather than requiring a reference source at a different wavelength. Digital deconvolution was performed on the full four-dimensional partially coherent field for simultaneously computing the distortion and the source intensity distribution.