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.     

Multiplexing encryption-decryption via lateral shifting of a random phase mask

We present an holographic memory optical arrangement based on the successive shifting of a random pure-phase mask to achieve encrypted images multiplexing. The input images are encrypted to a stationary white noise using the usual double random encoding in the Fresnel domain. The encrypted information is imaged in a photorefractive crystal where also a reference beam impinges. In the holographic memory, a BSO crystal is used to provide both a recording medium and a phase conjugate mirror. The combination of these two features supplies at the same time the necessary exact cancellation of the random pure-phase mask as well as allows a real-time decryption process. Successive images are encrypted and position-encoded by speckle patterns arising from the random pure-phase mask in-plane shifting between exposures. We include experimental results to corroborate the multiplexing capability and the read-out fidelity of the proposed arrangement.     

Cluster speckle structures through multiple apertures forming a closed curve

In this work, cluster-like speckle patterns are analyzed. These patterns are generated when a diffuser illuminated by coherent light is imaged by a lens having a pupil mask with multiple apertures forming a closed curve. We show that the cluster structure results from the complex modulation produced inside each speckle which is generated by multiple interferences of light through the apertures. In particular, when the apertures are uniformly distributed along a closed curve, the resulting image speckle cluster replicates the pupil aperture distribution. Experimental results and theoretical simulations show that cluster features depend on the apertures distribution and the size of the closed curves.     

A clustered speckle approach to optical trapping

An in situ study of the clustered speckle 3D structure using an optical tweezer setup is presented. Clustered speckles appear when a coherently illuminated diffuser is imaged through a pupil mask with several apertures, properly distributed over a closed path, which is placed before the objective lens of a standard optical trapping system. Thus, light volumes are reduced several times when compared with standard speckles, being even smaller than the focus volume of a Gaussian beam commonly used to trap. Moreover, clustered speckles have odd statistical properties which differentiated it from standard speckles. Then, geometrically ordered multiple trapping arrays, with statistical random distribution of intensities, can be created with this technique. This fact could enable different studies concerning optical binding or new developments in coherent matter wave transport where Optical Trapping has been proven with standard speckles. In this work, a qualitative analysis of clustered speckles in an optical tweezer setup relative to the number of apertures in the mask and their size is carried on. Besides, in the Rayleigh regime, a general quantitative method to characterize the trapping capability of an optical field is proposed. Then, it is applied to clustered speckles. As a result, a relation between aperture size and the maximum size of the particles that could be trapped is found. This fact opens the possibility of engineering the statistic of the trapped particles by properly selecting the pupil mask.     

Multiple-aperture speckle method applied to local displacement measurements

The goal of this work is to analyze the measurement capability of the modified speckle photography technique that uses different multiple aperture pupils in a multiple exposure scheme. In particular, the rotation case is considered. A point-wise analysis procedure is utilized to obtain the fringes required to access to the local displacement measurements. The proposed arrangement allows simultaneous displaying in the Fourier plane several fringes system each one associated with different rotations. We experimentally verified that the local displacement measurements can be determined with a high precision and accuracy.     

Code retrieval via undercover multiplexing

The purpose of this research is to develop an undercover multiplexing technique to give additional protection for optical information encryption. We employ the double random phase mask as our basic optical encryption system. The holographic storage medium of choice is a photorefractive crystal. To achieve the multiplexing we use the aperture size of the pupil in the optical system, as it governs the speckle size. We introduce such variation in order to produce a decorrelation between two consecutively stored speckle patterns. Each stored speckle pattern is associated to an input encrypted image, thus producing a multiplexing of the encrypted information. We implement this operation without altering the setup architecture and the random phase masks. This multiplexing is our undercover operation to encipher a true code behind a fake code. Under this approach, the user can only recover the bulk information stored in the volume hologram. However, he cannot recover the true code without the additional information on the pupil size key, even if accessed in position of the original decoding mask.     

Polarization phase in aberration compensation

A phase/amplitude mask on the aperture of an imaging system results in a pupil function that is multiplicative with the lens function, resulting in a morphological transformation of the imaging wavefront. It was shown that such amplitude and phase functions can be implemented using polarization masks, with the advantage that the phase and amplitude can be controlled in real time and in some cases, independently of each other. The phase and amplitude variation over the mask can be controlled either by changing the polarization of the mask or by changing the input beam parameters. Wavefront tailoring using polarization-masked apertures is therefore feasible and may be utilized for focal shift and partial aberration compensation. For complete compensation of aberration, the phase distribution over the mask should be conjugate to that of the phase error of the aberrant wavefront, which necessitates the use of a continuously variable polarization mask. Since such a mask is difficult to implement, we have considered polarizing masks consisting of discrete polarized zones on the lens aperture, leading to polarization phase steps on the exit pupil of the imaging system. The simulation results presented in this paper show that effects of focal shift, partial compensation of primary spherical aberration and astigmatism can indeed be achieved by the proper use of polarization masked apertures.     

Influence of the volume speckle on fiber specklegram sensors based on four-wave mixing in photorefractive materials

In this work, the dependence on the speckle size in the performance of a micro displacement sensor based on fiber specklegrams stored in a photorefractive BSO (Bi₁₂SiO₂₀) crystal is experimentally demonstrated. In our experimental setup, a plastic optical fiber (POF) was used to generate a subjective speckle pattern which was recorded in the crystal by using a four-wave mixing arrangement in transmission geometry. The speckle size was controlled by modifying the diameter of a pupil aperture adjacent to a lens producing the image of the speckle. The signal speckle beam was mixed into the crystal with two counter propagating pump beams to generate a fourth beam which is proportional to the conjugate of the original speckle beam. Real time fringe patterns were obtained at the output of the system by producing micro displacements of the fiber output end. Increases of the phase conjugation reflectivity and the visibility of the fringe patterns were appreciated when the speckle length was increased by decreasing the pupil aperture diameter. This behavior allowed recovering the autocorrelation functions of fringe patterns associated to micro displacements that initially led to decorrelation, and therefore, to improve the dynamic range of the metrological system. Until the best of our knowledge this is the first report about the influence of the speckle size on fiber specklegrams sensors recorded on photorefractive materials by four-wave mixing.     

Optimal key mask design for optical encryption based on joint transform correlator architecture

We examine perfect recovery in the optical encryption system based on joint transform correlator architecture, which requires the key mask to be space-limited and phase-only in the frequency domain. Accordingly, a discrete sinc function interpolation is used to generate a binary phase difference mask for image encryption and decryption. Furthermore, the optimal binary phase difference mask is derived from the interpolation process best approximating the ideal sinc function interpolation. The simulation results confirm better recovery of the decrypted image for applying the proposed key masks to the optical encryption system. Especially, the optimal binary phase difference mask significantly enhances the recovery performance.     

Improvement of the dynamic range of a fiber specklegram sensor based on volume speckle recording in photorefractive materials

In this work, the improvement of the dynamic range of a micro displacement sensor based on fiber specklegrams holographically stored in a photorefractive BSO (Bi₁₂SiO₂₀) crystal is reported. In our experimental setup, a plastic optical fiber (POF) was used to generate a subjective speckle pattern that was recorded in the crystal using a two-wave mixing arrangement. The speckle size was controlled by modifying the diameter of a pupil aperture adjacent to a lens producing the image of the speckle. Fringe patterns were obtained at the output of the system by producing micro displacements of the fiber output end. An increase in the visibility of the fringe patterns was appreciated when the pupil aperture diameter decreased even without controlling the average modulation of the intensity of the light pattern, i.e. when the speckle length increased and the average light modulation simultaneously decreased. This behavior allowed recovering the autocorrelation functions of fringe patterns associated with displacements that initially led to decorrelation, and therefore, significantly to improve the dynamic range of the metrological system. To the best of our knowledge this is the first report about the influence of speckle size on the dynamic range of fiber specklegrams sensors recorded on photorefractive materials.     

Speckle interferometric technique to assess soap films

An speckle interferometric technique to monitor the thinning process of vertical soap film before the film rupture is presented. The interferometric arrangement consists in a double aperture pupil optical system which images an input diffuser. In a first step, a reference specklegram is stored in the computer buffer memory. Afterwards, the soap film is located in front of one pupil aperture, an uniform displacement of the diffuser is produced and a new speckle pattern is stored. The soap film status is characterized in terms of the changes that this dynamic phase object introduces in the correlation fringes obtained by applying a FFT algorithm to the resulting summed specklegram. This procedure is done in real time as far as the soap film evolves in the successive status. It is experimentally demonstrated that the soap film during drawing acts as a variable wedge. The correlation fringes behavior becomes an important tool to establish the wedge shaped soap film angle and the thickness variations.     

波前编码系统相位板视场效应的消除

通过在光学系统的光阑面上加入一个非球面相位板,使得光学系统的成像对离焦不敏感.但当入射视场角较大时,图像的边缘发生变形且难以恢复.针对此问题,提出了两种解决方案,方案一是把相位板移至光路中光线较为平缓的区域,但不是系统的光阑位置;方案二是保持相位板位置不变,优化整个光学系统,使相位板前的光线能够平缓地入射到相位板.实验中对一个EFL=12.5 mm,F/#=1.3,半视场角为13.5°的波前编码实际系统进行仿真比较,得出方案二可以有效地消除波前编码相位板引入的视场效应.     

High resolution optical image restoration for ground-based large telescope using phase diversity speckle

Phase diversity speckle (PDS) is an image restoration technique which is based on the idea of phase diversity (PD). It uses multi-frame short-exposure image sequence to calculate their corresponding wave-front information. Each image pair consists of two images collected by two cameras at the same time with one in focus and the other with known defocus value. Multi-frame processing can significantly improve the target signal to noise ratio, and decrease noise influence. In this paper, based on the principle of pupil Fourier imaging, by adjusting the pupil size, we get different scales of the optical point spread function (PSF). Also, we analysis different camera noise distribution channels, location differences and other factors to optimize the objective evaluation function, and this can reduce the computational complexity and improve the processing speed of image restoration. In the indoor environment, we build optical platform, and use multi-frame phase diversity speckle to make experiment under different turbulence conditions. The experimental results show that the image restoration effect of the proposed method is close to the diffraction limit.     

Fabrication of double-aperture hololens imaging system: application to mechanics

Duffy suggested the use of double-aperture imaging system for the measurement of in-plane displacement component. In this arrangement, twin apertures are placed symmetrically over the imaging lens. This imaging system is used in speckle metrology to measure component of displacement parallel to the line joining the two apertures. The imaging lens used in such configuration need not be diffraction limited over the entire lens aperture, but only over the two small areas encompassed by the two apertures. In present work, compact holographic lenses have been used to generate the two apertures of Duffy's double-aperture interferometer. This imaging system has been used in speckle metrology to measure crack mouth opening displacement (CMOD) in an aluminium beam specimen having central edge crack subjected to three point bending. Experimental results are in good agreement with theoretical predictions. Present experimental investigation reveals that compact holographic lenses can be used advantageously to generate apertures of double-aperture speckle interferometer for its use in the measurement of in-plane displacement component.     

High depth of focus by combining annular lenses

In some technological applications, optical systems that produce a high depth of focus and superresolving transversal responses are required. In this paper we present a pupil design consisting in a phase pupil with binary amplitude, that added to a conventional optical system, can accomplish these goals. The pupil function is characterized by a complex amplitude that consists basically in combining two annular lenses with different focal length. Meanwhile the central portion of the pupil has an amplitude equal to 0, the external portion is modulated with two quadratic phases each one covering an annular zone. One of the phases corresponds to a convergent lens and the other to a divergent lens. The effect on the incident wavefront is to redirect the light in front of and behind the best image plane (BIP) producing a widened focus. The evolution of the transverse gain for the extended focus is also studied. Experimental results are given, and they confirm the extended focus and the superresolving behavior of the proposed pupil function.     

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.     

Multichanneled puzzle-like encryption

In order to increase data security transmission we propose a multichanneled puzzle-like encryption method. The basic principle relies on the input information decomposition, in the same way as the pieces of a puzzle. Each decomposed part of the input object is encrypted separately in a 4f double random phase mask architecture, by setting the optical parameters in a determined status. Each parameter set defines a channel. In order to retrieve the whole information it is necessary to properly decrypt and compose all channels. Computer simulations that confirm our proposal are presented.     

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.     

Adaptive optics interferometer using superspeckles for high resolution deformation measurement

Digital speckle pattern interferometry (DSPI) is a well-known technique for measuring deformations, but it is limited in range by speckle decorrelation. We developed an adaptive interferometer with increased measurement range by combining the DSPI set-up with a pupil filter that generates optical superresolution. As a result, a decrease in the transverse speckle size is observed accompanied with a substantial increase in the longitudinal speckle size. The increase in the speckle correlation length along the optical axis allows for obtaining an out-of-plane deformation measurement over a significantly extended depth. An experimental verification of this concept of superspeckles is presented with an intensity-only LCD spatial light modulator (SLM) acting as a pupil filter. Comparison of speckle correlation fringes with and without the superresolution filter confirms the proposed concept. The present work demonstrates a doubling of the measurement range when using the superresolution interferometer. A standard set-up in which the speckle length is comparably elongated by stopping down the lens has a similar loss of intensity, but its lateral resolution is only half as good.     

Triple image encryption scheme in fractional Fourier transform domains

We proposed a triple image encryption scheme by use of fractional Fourier transform. In this algorithm, an original image is encoded in amplitude part and other two images are encoded into phase information. The key of encryption algorithm is obtained from the difference between the third image and the output phase of transform. In general case, random phase encoding technology is not required in the proposed algorithm. Moreover, all information of images is preserved in theory when image are decrypted with correct key. The optical implementation of the algorithm is presented with an electro-optical hybrid structure. Numerical simulations have demonstrated the efficiency and the security of this algorithm. Based on this scheme a multiple image algorithm is expanded and designed.