Analysis of speckle reduction based on theory of optical eigenfunction

The principle of optical eigenfunction is used in the analysis of speckle reduction in laser projection display.When the moving diffiuser is used in the speckle reduction approach,the speckle contrast is decided by both the degree of freedom (DOF) of the projector and the area of resolving cell of the eyes on the screen.It can gain high DOF of the projector by increasing the space-bandwidth product,i.e.,adopting a projection lens with a high numerical aperture or a large viewing field.The best scheme is equalizing the DOF of the scattering wave from a moving diffiuser to that of the projection lens.The experimental results are in accordance with the conclusion drawn by optical eigenfunction.     

Understanding the exposure-time effect on speckle contrast measurements for laser displays

To evaluate the influence of exposure time on speckle noise for laser displays, speckle contrast measurement method was developed observable at a human eye response time using a high-sensitivity camera which has a signal multiplying function. The nonlinearity of camera light sensitivity was calibrated to measure accurate speckle contrasts, and the measuring lower limit noise of speckle contrast was improved by applying spatial-frequency low pass filter to the captured images. Three commercially available laser displays were measured over a wide range of exposure times from tens of milliseconds to several seconds without adjusting the brightness of laser displays. The speckle contrast of raster-scanned mobile projector without any speckle-reduction device was nearly constant over various exposure times. On the contrary to this, in full-frame projection type laser displays equipped with a temporally-averaging speckle-reduction device, some of their speckle contrasts close to the lower limits noise were slightly increased at the shorter exposure time due to the noise. As a result, the exposure-time effect of speckle contrast could not be observed in our measurements, although it is more reasonable to think that the speckle contrasts of laser displays, which are equipped with the temporally-averaging speckle-reduction device, are dependent on the exposure time. This discrepancy may be attributed to the underestimation of temporal averaging factor. We expected that this method is useful for evaluating various laser displays and clarify the relationship between the speckle noise and the exposure time for a further verification of speckle reduction.     

Reduction of speckle in an image by a moving aperture - second order statistics

In an earlier paper the second-order statistics of time-averaged speckle were investigated for the case of speckle formed in the Fraunhofer plane when an aperture was moved over the surface of a uniformly illuminated diffuse object. In this paper it is the intention to substantiate a claim that was made in that paper that the same treatment will also apply to time-averaged speckle in an image plane when an aperture is moved in the pupil plane of the imaging lens. The optical system is allowed to have aberrations of any degree of severity, and the object is allowed to have non-uniform brightness, subject to the condition that the brightness variations are slow in comparison to the size of the (aberrated) point spread function. The treatment makes use of the usual assumption that a very large number of independent scattering points in the object contributes to any one point in the image: for this assumption to be realistic, however, it will be shown that the point spread function of the lens must be of a size that restricts us either to systems where the numerical aperture in object space is low or, alternatively, to systems where the aberrations are severe.     

Nonuniform intensity distribution of the scattered light by moving diffuser across projection lens pupil and its influence in speckle reduction

The measurement of the nonuniform intensity distribution of scattered light by a moving diffuser using an integrating sphere, which lowers the effective numerical aperture of the projection lens and affects the lowest speckle contrast, is reported. A comparison of the effective numerical apertures realized by several diffusers revealed that JIS #600 or #800 diffusers are most appropriate for efficient speckle reduction     

Measurement of contrast of speckle in and near the image plane

The contrast of a speckle pattern formed by a conventional imaging system has been experimentally investigated. A dip in contrast of the speckle pattern produced near the focal plane and the image plane has been observed. It is also found that the variation of contrast along the optical axis of the imaging system with a hard-edged aperture differs considerably from that with a soft aperture.     

Detection properties of an optical fiber probe for laser speckle velocimetry

Temporal power spectra of the speckle signal detected by a simple optical fiber probe are analyzed as a function of the laser spot size at a moving scatter plate, the velocity of the plate, the core diameter of the detecting fiber and the numerical aperture of it. The fiber probe is shown to be useful for velocity measurements of the moving scatter plate.     

Speckle reduction by a rotating aperture at the fourier transform plane

Statistical properties of the time-averaged speckle-reduced pattern at the image plane of a coherently illuminated uniform diffuse object are theoretically and experimentally studied. The diffuse object is assumed to be approximated by a deep random phase screen and zero-mean circular complex Gaussian statistics is also assumed to hold for the formation of speckles. The time-averaging process is performed by using a rotating aperture at the Fourier transform plane of the object. A theoretical study of the speckle reduction is conducted for a rotating Gaussian soft aperture at the Fourier transform plane. Expressions are analytically derived for the mean, autocorrelation function, power spectrum, and contrast of the time-averaged speckle pattern at the image plane. In particular, the contrast of the time-averaged speckle pattern is theoretically evaluated and its characteristics are discussed in detail. The theoretical results for the contrast are experimentally confirmed using a TV/film recording system. Excellent agreement between theoretical and experimental results is obtained.     

散斑自相关分辨率测量和修正

散斑相关是许多基于散斑的光学测量和成像技术的基础,决定了光学系统的分辨率。当前散斑尺寸（颗粒度或分辨率）的理论描述不够精确,也缺乏实验验证。探究了散斑图样自相关尺寸的影响因素,与相同数值孔径物镜聚焦进行比对,揭示薄散射介质的“散射透镜”性质。通过散斑自相关和透镜聚焦尺寸的多组测量,结果表明,截趾函数会影响其分辨率,需要根据具体光路对阿贝判据做修正。对基于散斑的测量和成像技术具有一定的参考价值。     

Velocity measurement by the laser speckle method using optical fibres

An optical device for in-plane velocity measurement is described. Laser light is focused by the use of an optical fibre onto the object, and the device utilizes the dynamic sparkle effect for velocity determination. The influence of different optical fibres on the speckle formation is investigated with special respect to fibre movement, and as the diameter of the aperture used for speckle detection also affects the measuring signal, an optimum value is found. A simple electronic circuit processes the measuring value proportional to the object velocity.     

The influence of hologram aperture on speckle noise in the reconstructed image of digital holography and its reduction

Based on the whole process of the recording and reconstruction of digital holography, we study the formation cause of speckle noise in its reconstructed image and acquire the conclusion that the small size of hologram aperture diffraction aggravates the speckle noise of reconstructed image and the speckle noise has been one of primary noise sources in the reconstruction process. In order to reduce the speckle noise resulting from little hologram aperture diffraction, we set an appropriate aperture function matching the recording parameter and aperture size of hologram and deconvolve the reconstructed image with it. The validity has been proved in theory and experiment. Therefore, it offers a brand-new thought and practical way to reduce the speckle noise in the reconstructed image of digital holography.     

Dynamic behaviour of speckle cluster formation

In this work, we analyse the speckle cluster structure generated when a coherently illuminated diffuser is imaged by introducing a multiple aperture pupil mask in front of the lens plane. We demonstrate that the speckle cluster originates from the complex speckle modulation generated by multiple interferences among the wavefront passing through each aperture. The auto-correlation function of the intensity distribution when using a multiple aperture pupil arrangement is calculated. Besides, we demonstrate that the autocorrelation function and the intensity corresponding to a single scattering element of the input are coincident. This result allows interpretation of the dynamics behaviour of the speckle cluster formation by considering the result obtained by a single scattering element. Then, we determine the pupil mask geometrical parameters that control the cluster behaviour and therefore the condition for obtaining a highly repetitive cluster structure that we define as a 'regular cluster'. The theoretical simulations based on the random walk model are in agreement with the experimental results supporting the validity of our approach.     

Experimental study of the angular correlation function in the double passage of waves through a one-dimensional random phase screen

Abstract

Experimental results are presented for the angular correlation function of far-field speckle patterns scattered in the double passage of waves through a one-dimensional random phase screen. The experiment for the correlation measurement was set up to use a CCD camera to obtain the image of the speckle patterns in the scattering directions for each given angle of incidence; the cross-correlation function is then calculated from the digitized images. The theoretical analysis of the motion of the speckle as the source is moved, as given by Escamilla, is verified experimentally. It is found that in contrast with the memory effect line of speckle motion, the speckle pattern produced in the region of observation tracks the backscattering direction.     

数值孔径与数字剪切散斑干涉条纹亮度的关系

分析了数字剪切散斑干涉条纹图的形成理论，并获得了条纹亮度与摄象机数值孔径等参数的精确关系式，从理论分析和实验验证均得出在采用小的摄象机数值孔径和３ｍＷ Ｈｅ－Ｎｅ激光器的情况下，仍可获得比较满意的数字剪切散斑干涉条纹图，理论工作及其结论对于进行数字剪切散斑干涉实验的最佳参数选择具有指导作用。     

Longitudinal Correlation Properties of Speckles Produced by Ring-Slit Illumination

Spatial correlation properties are studied for speckle patterns produced in the diffraction region behind a lens which is located at a focal distance from a diffuser with an aperture under illumination of the coherent plane-wave light. It is shown theoretically that, if a ring-slit aperture of a negligible slit width is used, the speckle field produced has a perfect correlation in the longitudinal direction. An experiment was performed using a circular aperture and ring-slit apertures having different ratios of the inner to the outer radius and the speckle pattern produced using the ring-slit aperture with the smallest slit width had the longest longitudinal correlation in all cases examined. The statistical stationarity and symmetry of the speckle field, as well as variation in the speckle size, are also discussed.     

Variation of the speckle patterns in graded-index fibres with a misaligned joint

The intensity variation of a speckle pattern on the exit end face of graded-index multimode fibres with a misaligned fibre-to-fibre joint is experimentally studied from its first-order statistics of the average contrast and the probability density function for two different kinds of longitudinal and axial misalignments. It is found that the speckle contrast varies as a function of the radial position with a peak which shifts towards the periphery of the speckle pattern with an increase of the joint loss. A varying form of the speckle contrast also depends on the type of misalignment. The probability density function of the speckle intensity variation is also found to vary as a function of the radial position but to scarcely vary as a function of the joint loss.     

Reduction of speckle noise in the reconstructed image of digital holography

Based on the whole process of recording and reconstruction of digital holography, we study the formation causes of speckle noise in the reconstructed image and its characteristics. And we reach the conclusions that the little hologram aperture diffraction aggravates the speckle noise and the speckle noise in the reconstructed image is a kind of multiplicative noise. Serving as the basis of these features, we propose the reduction technique for speckle noise. Firstly, we set an appropriate aperture function matching the recording parameter and an aperture size of hologram and deconvolve the reconstructed image of the hologram with it. Secondly, we converted the multiplicative noise into additive noise by means of homomorphic transform and realize the separation of signal and noise. Thirdly, we applied the Wiener filtering to reduce the additive noise. Finally, we carried out the inverse transformation. The proposed reduction technique is illustrated with experimental results. Therefore, the paper offers a brand-new thought and practical way of reducing the speckle noise in the reconstructed image of digital holography.     

Analysis of reflection speckle holograms in a BSO crystal

A theoretical and experimental study of speckle registering in photorefractive BSO crystals through reflection hologram geometry is implemented. The three-dimensional speckle nature is considered in the diffraction efficiency calculations. The interference process produces index-of-refraction gratings in the speckle volume via the photorefractive effect. It is demonstrated that the coupled-wave theory for reflection geometry allows explaining the diffraction efficiency behavior when the interaction length is properly taken into account. It means that the speckle depth is related with the interaction length. The speckle depth can be controlled by the imaging system pupil aperture diameter. Under this condition, the influence of the speckle depth on the diffraction efficiency is analyzed. An agreement between the numerical model based on the coupled-wave theory and the experimental results is obtained.     

Spatial coherence measurement of a scanning laser system and applicability of the Zernike’s approximation to the exit pupil on the scan mirror

Spatial coherence of the scanning laser beam was observed on the Young??s experimental set up using 50-??m-wide, 200-??m-separation double slits, which measured the less than unity fringe visibility in the Fraunhofer diffraction pattern of the double slits illuminated by the scanning laser beam at horizontal scan frequency 21 kHz, while approximately unity in case of the illumination by the laser beam at rest. This fact allow us to use the Zernike??s approximation when applying the van Cittert Zernike theorem to the scanning laser system such as the laser pico-projectors in order to estimate its speckle contrast in the projected image on the screen diffuser. The predicted and measured speckle contrasts showed excellent agreement on the screen illuminated by the laser projector.     

Speckle Effects on Statistical Performance of Optical Radar

The statistical performance of optical radar using energy detection techniques has been studied in this paper. The analytical expressions of the speckle number subtended by the receiving aperture are derived. The results show that the speckle number is only determined by the relative size of the speckle cell and the area of the entrance pupil. The receiving aperture will integrate a considerable number of speckle cells when the beam expander is not adopted in the transmitting optical system. Few speckle cells will be intercepted by the aperture when the beam expander is employed and the laser speckle is expected to be the dominant noise source. The detection performance of airborne and space-based optical radar has been analyzed based on two critical parameters--the speckle number and the average photoelectron counts. The probability density function of photoelectrons and the detection probability are derived for a number of occasions.     

压电薄膜变形镜响应函数计算及参数优化

 针对方口径压电薄膜变形镜,采用傅里叶级数法推导了其机电行为的数学解析式。并利用该表达式对该类变形镜的交联值、使用口径等性能指标进行了研究。结果表明：交联值随电极尺寸呈线性变化关系,在可用范围内保持在0.6以上,压电薄膜变形镜大的交联值保证了其对低阶像差强的校正能力;变形镜的校正能力与通光口径密切相关,其最佳使用口径比约为0.8。