Common-path phase-shifting interferometer with binary grating

An experimental setup for phase extraction of 2D phase distributions is presented. The system uses a common-path interferometer consisting of two windows in the input plane and a translating grating as spatial filter. In the output, interference of the fields associated with replicated images of the input windows is achieved by a proper choice of the windows spacing with respect to the grating period, the focal length of the transforming lens and the wavelength of the coherent illumination employed. Because in this type of grating interferometer a grating is placed as a spatial filter, the phase changes which are needed for phase-shifting interferometry can be easily performed with translations of the grating driven by a linear actuator. Some experimental results are shown.     

Semiderivative real filter for microoptical elements quality control

The article presents a proposal for a new method of automatic quality control of microlenses arrays, which is based on a semiderivative real filter. The use of the semiderivative filter for examining pure-phase objects involves modifying the spatial frequency. The basis of the proposed setup is a 4f correlator setup with coherent light. The phase object examined is placed in the input plane of the correlator. Next, the light passes through a filter located in the frequency plane, which gives an intensity signal. In the output plane a charge-coupled device (CCD) camera registers the light intensity, the range of which informs the shape of the phase object. The proposed method is shift invariant, so it allows for examination of single elements or a set of micro-optical elements simultaneously. Additionally, the same setup allows for measuring the phase of objects whose thickness is either considerably smaller or much bigger than 2π.     

Spatial frequency pseudo-coloring with binary filters

Spatial frequency pseudo-coloring is performed by simply inserting a binary filter in the Fourier plane of a spatially coherent, white light optical processing system. The range of encoded spatial frequencies can be extended by using multiple filters or by using sampled input objects.     

Weighting iterative Fourier transform algorithm of the kinoform synthesis

Two object-dependent filters (an amplitude and a phase filter) are used in the object plane on the iterative calculation of a kinoform instead of a single (phase) filter as usual. The amplitude filter is a system of weight coefficients that vary in the process of iterations and control the amplitude of an input object. The advantages of the proposed method over other ones are confirmed by computer-based experiments. It is found that the method is most efficient for binary objects.     

Optical rotation invariant corner detector

In this work we introduce a new approach for corner extraction with rotation invariance. The method is based on an optical processor where the filter in the frequency plane is composed by a spiral phase function and a binary amplitude. The output image of the optical setup presents intensity peaks in each square corner location. The performance of the proposed method was tested on synthetic scenes by numerical simulations and by optical measurements. The presented results show that the method allows the corner extraction, even with rotated scenes.     

Common-path interferometer with a tri-window

A common-path interferometer is proposed with a tri-window. It is built using a 4f optical system with Ronchi ruling as a spatial filter. The input rectangular aperture is formed by three windows; the central window supports a phase object, and the other two are used for reference beams. Using an appropriate grating period relative to input aperture size, an interferogram containing three patterns can be obtained in the output plane. The object phase can then be reconstructed from the three patterns using just one interferogram. The experiments are carried out to demonstrate the feasibility and reliability of the proposed scheme.     

Enhanced deterministic phase retrieval using a partially developed speckle field

A technique for enhanced deterministic phase retrieval using a partially developed speckle field (PDSF) and a spatial light modulator (SLM) is demonstrated experimentally. A smooth test wavefront impinges on a phase diffuser, forming a PDSF that is directed to a 4f setup. Two defocused speckle intensity measurements are recorded at the output plane corresponding to axially-propagated representations of the PDSF in the input plane. The speckle intensity measurements are then used in a conventional transport of intensity equation (TIE) to reconstruct directly the test wavefront. The PDSF in our technique increases the dynamic range of the axial intensity derivative for smooth phase objects, resulting in a more robust solution to the TIE. The SLM setup enables a fast and accurate recording of speckle intensity. Experimental results are in good agreement with those obtained using the iterative phase retrieval and digital holographic methods of wavefront reconstruction.     

Real-time recognition of microscopic phase objects

A method of image enhancement and real-time input of 3-D, microscopic phase objects into a coherent optical pattern recognition system is described. The method consists of directing a low-power laser beam into a microscope objective to produce a real, magnified, coherent image of the specimen under test. The image plane is followed by two successive Fourier transform (FT) planes. In the first FT plane, low and high frequency spatial filters, one of which is photographically produced, are used as pre-processing filters to enhance the image quality. The enhanced signal is imaged from the first FT plane to the second FT plane which contains a matched spatial filter used for specimen identification. The system does not require an expensive incoherent-to-coherent light transducer and in addition, is capable of utilizing both phase and amplitude information from 3-D objects. Examples of results are given.     

Self adaptive high pass filtering using photochromic glass

We describe an auto programmable spatial-filtering system using photochromic glass plate as a programmable spatial light modulator, SLM, illuminated by a single wavelength of light. The proposed setup is a conventional 4f coherent optical system. At Fourier plane the filter function is written on the SLM as negative copy of the power spectrum of the input image. The method does not involve numerical processing, and thus, it could be potentially useful for processing large images. Validation experiments are presented.     

Generation of optical vortices with arbitrary shape and array via helical phase spatial filtering

We report a method for generation of arbitrary shape and array of optical vortices by use of a superposition of coherent elementary vortices based on helical phase spatial filtering in spatial frequency domain. In this method, a helical phase spatial filter (HPSF) is placed in the spatial frequency plane of a 4-f imaging processing system. We demonstrated that the output field distribution represents the convolution between the input field and an elementary vortex field introduced by the HPSF, which results in a special shape or array of optical vortices determined by the “degenerate” properties of coherent elementary vortices and the distribution formats of the input field.     

Diffraction and scattering of TM plane waves from a binary periodic random surface

This paper deals with the diffraction and scattering of a TM plane wave from a binary periodic random surface generated by a stationary binary sequence using the stochastic functional approach. The scattered wave is represented by a product of an exponential phase factor and a periodic stationary process. Such a periodic stationary process is regarded as a stochastic functional of the binary sequence and is expressed by an orthogonal binary functional expansion with band-limited binary kernels. Then, hierarchical equations for the binary kernels are derived from the boundary condition without approximation. We point out that binary kernels obtained by a single scattering approximation diverge unphysically when the periodic random surface is zero on average, thus the effects of multiple scattering should be taken into account. The expressions of such binary kernels are obtained using the multiply renormalizing approximation. Then, statistical properties such as differential scattering cross-section and the optical theorem are numerically calculated with the first two order binary kernels and illustrated in the figures. It is found that the incoherent Wood's anomaly appears in the angular distribution of scattering even when the surface has zero average.     

Special phase mask and related data format for page-based holographic data storage systems

Random phase masks in object and reference beam of page-based holographic storage systems suppress the DC-peak and improve the overlap of both beams inside the storage material. Furthermore, they allow for a narrow shift-selectivity. In a holographic setup the phase mask has to be introduced at a conjugate image plane of the spatial light modulator (SLM), if it is not fixed directly on the SLM itself. A binary phase mask with cells generating 0 and π phase shifts has to be aligned very accurately with respect to the SLM pixels, otherwise image artifacts disturb the received data page. We present a phase mask, where the phase cells have the size of a data block which consists of a rectangular set of SLM pixels. Additionally, the corresponding data page has no data at the position of phase jumps and thus relaxes the alignment tolerance significantly.     

Influence of finite spatial resolution on single- and double-pass femtosecond pulse shapers

We investigate the influence of the finite spatial resolution of a typical 4f pulse-shaping setup in a single- and double-pass configuration on the shaped waveforms. Specifically, we calculate and measure the space-frequency distribution at the focal plane of a lens following the shaping setup and show that steep amplitude or phase jumps, as they appear with pixelated spatial light modulators, are affected by a finite spatial resolution.     

Optical implementation of the Banyan network using the Wigner distribution approach

A new optical processor is proposed for implementing the Banyan interconnection network. The optical system is simple and compact since it only employs a phase filter to permute the data input. Based on a relation between the space-spatial frequency information of the input plane and that of the output plane, the required local phase variation of the filter is determined by means of the Wigner distribution function. Experimental verifications are presented for a one-stage four-channel interconnection.     

A two-dimensional diffraction pattern sampling system for determining the optimum parameters of a matched spatial filter

The synthesis of a matched spatial filter based on holographic methods requires that the spatial frequency band in which the holographic fringe pattern with the best modulation is formed be tuned to the appropriate weighting at the Fourier transform plane of the spatial frequencies of the input object to be studied. For this purpose both the spectral intensity distribution of an input object at the Fourier transform plane and the intensity distribution of a reference beam at that plane must be accurately known beforehand. A two-dimensional diffraction pattern sampling system has been constructed which enables the Fourier spectral intensity distribution of the input object and the reference beam intensity distribution to be faithfully recorded. A preliminary experimental study shows the usefulness of this system.     

Wave scattering from a periodic random surface generated by a stationary binary sequence

This paper studies the scattering of a TE plane wave from a periodic random surface generated by a stochastic binary sequence using a stochastic functional method. The scattered wave is first expressed as a product of an exponential phase factor and a periodic stationary process. The periodic stationary process is then expressed by a harmonic series representation, that is a 'Fourier series' with 'Fourier coefficients' given by mutually correlated stationary processes. These stationary processes are regarded as stochastic functionals of the binary sequence and they are represented by orthogonal binary functional expansions with band-limited binary kernels. The binary kernels are determined up to the second order from the boundary condition. Then, several statistical properties of the scattering are calculated numerically and illustrated in figures. It is found that, in the binary case, the second-order scattering cross section has a subtractive term and becomes much smaller than the first-order one.     

Enhanced Optical Image Verification Based on Joint Transform Correlator Adopting Fourier Hologram

In this paper two new architectures for optical image verification are proposed. Both architectures are based on conventional joint transform correlators (JTCs) adopting a Fourier hologram and can significantly improve the recovered image quality. First, an input phase-only function is Fourier transformed and then interferes with a reference wave that is diffracted from a plane wave incident on another random phase mask. Second, two phase-only functions are placed at the two input sides of a beamsplitter such that the interference pattern of their Fourier transforms can be detected. To obtain a predefined target image in the output plane, one of the input phase functions is iteratively retrieved by the use of the projection onto constraint sets algorithm. Simulation results show that the less mean squared error and better image quality are obtained for both the binary and grayscale images.     

Image differentiation with the aid of a phase knife

A scheme for optical differentiation of images based on spatial filtering is proposed. A phase knife—a glass plate consisting of two halves, whose thicknesses are chosen so that the optical path difference between the light waves passed through them makes up half the wavelength—serves as a filter. The linearity of the transformation and the sensitivity of the system to noise are investigated theoretically. The scheme was experimentally implemented on the basis of a liquid-crystal light valve. The experimental results confirm that such a setup can be efficiently used for processing images with a narrow-band spatial spectrum and for visualization of phase objects.     

Simultaneous Determination of the Amplitude-Phase Structure of an Optical Signal and a Transfer Function with the Influence of the Medium Given by a Modulation Function

We consider a solution to the phase problem in optics as applied to registering and analyzing amplitude-phase structures of 1) d optical fields that form or transfer images and 2) transfer or spread functions of the medium where optically inhomogeneous fields propagate or those of the systems forming fields and producing distortions. The influence of the medium is characterized by the modulation function and is described by the operation of multiplication. In order to measure the amplitude and phase field characteristics and transfer or spread functions, we use an original development of the modulation-spectral method proposed earlier by the authors. There are two variants of optical schemes considered. They include identical parts designed to form the light field to be processed. Using the first optical system, one forms the spectrum of spatial frequencies and introduces the first additional space modulation in the plane of spatial frequencies. The second optical system is placed in the same plane to form the image of the investigated field in the input plane of the developing scheme after passing the transmitting medium. In the first variant, the second part of the scheme contains at the input the third optical system forming the spatial spectrum in the registration plane. At the input of this scheme, the second additional spatial modulation is introduced. In the second variant, the third optical system forms the image of the developing scheme input plane in the registration plane. The second additional spatial modulator is placed in the spatial frequency plane of the third optical system. In the output, in both cases four independent two-dimensional intensity distributions are registered, which allow one to solve the formulated problem.     

Phase-Only Encryption and Single Path Decryption System Using Phase-Encoded Exclusive-OR Rules in Fourier Domain

A phase-only encryption scheme using phase-encoded exclusive-OR (XOR) rules in a Fourier plane and a single path decryption system are presented. To generate phase-only encrypted data, a zero-padded original image, multiplied by a random phase image, is Fourier transformed and its real-valued data is encrypted with key data by using phase-encoded XOR rules. Since the original information is encrypted on the Fourier plane, the proposed encryption is more tolerant to loss of key information by scratching or cutting than previous XOR encryption in a space domain. A decryption is simply performed based on 2-f setup with spatial filter by Fourier transform for multiplication phase-only encrypted data with phase-only key data. Due to single path architecture without a reference wave, the proposed system is resistant to mechanical vibrations and fluctuation. Numerical simulations have confirmed the validity of the proposed encryption scheme and simple decryption architecture.