Object Wavefront Research Articles

Infrared holography using a microbolometer array

We describe a series of experiments to demonstrate holography at far-infrared wavelengths using an uncooled microbolometer array. Simple interference patterns and Fresnel zone holograms are recorded with a 10 W cw CO(2) laser illumination in a Mach-Zehnder interferometer setup. A sparse-sampling method is used to sample the hologram at a rate dependent on the bandwidth of the object wavefront rather than the carrier frequency. The samples are then used to reconstruct the complex object wavefront in the hologram plane, which is Fresnel backpropagated for image reconstruction. Uncooled microbolometer arrays are most commonly used in passive mode to image the thermal-blackbody radiation. Their technology has matured to include the wavelength range of far-infrared to submillimeter radiation. The use of microbolometers with active illumination for holography, as described in this paper, suggests their interesting future applications.

Submicrometer optical tomography by multiple-wavelength digital holographic microscopy

We present a method for submicrometer tomographic imaging using multiple wavelengths in digital holographic microscopy. This method is based on the recording, at different wavelengths equally separated in the k domain, in off-axis geometry, of the interference between a reference wave and an object wave reflected by a microscopic specimen and magnified by a microscope objective. A CCD camera records the holograms consecutively, which are then numerically reconstructed following the convolution formulation to obtain each corresponding complex object wavefront. Their relative phases are adjusted to be equal in a given plane of interest and the resulting complex wavefronts are summed. The result of this operation is a constructive addition of complex waves in the selected plane and destructive addition in the others. Tomography is thus obtained by the attenuation of the amplitude out of the plane of interest. Numerical variation of the plane of interest enables one to scan the object in depth. For the presented simulations and experiments, 20 wavelengths are used in the 480-700 nm range. The result is a sectioning of the object in slices 725 nm thick.

Achromatic optical elements

The principles of wavefront reconstruction by means of a geometric-optical reflection of radiation from surfaces of interference fringe maxima are discussed. The optical elements based on these principles should be achromatic. Two methods of the optical elements design are proposed. The first method is a direct holographic recording of the interference fringe structure containing only a few periods, and the second method is a combination of the measurement of the object wavefront shape with digital holography methods.

Application of eliminating zero-order diffraction light in wavefront reconstruction of inverse diffraction computation

According to the Collins formula and its inverse diffraction computation, this paper presents an algorithm for reconstructing the object wavefront of a numerical holograph. To improve the quality of wavefront reconstruction, a technique of eliminating the zero-order diffraction light is introduced, which is achieved by subtraction of two intensities of the interference patterns. The computer simulation and image processing show that the method of eliminating the zero-order diffraction beam can be applied to the wavefront reconstruction of inverse diffraction computation.

Phase-shifting digital holography with a phase difference between orthogonal polarizations

Phase-shifting digital holography with a phase difference between orthogonal polarizations is proposed. The use of orthogonal polarizations can make it possible to record two phase-shifted holograms simultaneously. By combining the holograms with the distributions of a reference wave and an object wave, the complex field of the object's wavefront can be obtained. Preliminary experimental results are shown to confirm the proposed method.

Visualization of domain inversion region characteristics in RuO2:LiNbO3 crystal by digital holographic interferometry

In order to obtain the two dimensional distribution of the refractive index changes due to the domain inversion in the RuO2:LiNbO3 crystal, we make use of the Mach-Zehnder interferometer and 4f optical lens system to record holograms, with the object light transmitting through the poled RuO2:LiNbO3 crystal, and then filter the spectrum in the frequency domain to get the object light spectrum for numerically reconstructing the object wavefront. The results confirm that the electro-chromic effect region well coincides with the domain inversion region in RuO2:LiNbO3 crystal. Digital holographic interferometry has the merits of being nondestructive and it provides a prospective way to in-situ visualization, monitoring and analysis of the domain inversion in LiNbO3 crystal.

Two-dimensional wave-front reconstruction from lateral shearing interferograms

An algorithm is proposed to reconstruct two-dimensional wave-front from phase differences measured by lateral shearing interferometer. Two one-dimensional phase profiles of object wave-front are computed using Fourier transform from phase differences, and then the two-dimensional wave-front distribution is retrieved by use of least-square fitting. The algorithm allows large shear amount and works fast based on fast Fourier transform. Investigations into reconstruction accuracy and reliability are carried out by numerical experiments, in which effects of different shear amounts and noises on reconstruction accuracy are evaluated. Optical measurement is made in a lateral shearing interferometer based on double-grating.

Active, LCoS based laser interferometer for microelements studies

The modification of classical Twyman-Green interferometer by implementation of Liquid Crystal on Silicon (LCoS) spatial light modulator as the reference mirror allows introducing arbitrary phase in the reference wavefront. This special capability is applied to facilitate the measurements of shape and deformation of active microelements and extend the range of such measurement. This can be realized by introducing linear or circular spatial carrier frequency into interferogram or by compensating object wavefront deformation. Moreover LCoS display can be used as an accurate phase shifter if the proper calibration is introduced. The analysis of sources of measurement errors introduced by LCoS display is presented and the ways of their elimination are discussed. The possible application of LCoS based laser interferometer for initial microelement shape determination and transient deformation monitoring as well as active reference phase modification are shown and experimentally confirmed during silicon micromembranes studies.

Virtual shearing interferometry by digital holography

A novel method of virtual shearing interferometry (VSI) is proposed. In this method, the shearogram is obtained by interference of a real object wave-front and a virtual object wave-front. The former is optically recorded and then digitally reconstructed; and the latter is introduced digitally by repositioning or reforming the former. The obvious advantages of VSI over conventional shearing interferometry (SI) are its versatility, accuracy, and simplicity. Only one real field is necessary to produce shearogram; there is no need of any real shearing device or even the phase unwrapping computation; and the digital shear can take any possible form according to different purposes. Both the optical experiments and computer simulations with lateral shearing, 180° rotational shearing and double lateral shearing for evaluation of lens aberrations in the general case including spherical aberration, coma, astigmatism, defocus, and tilts based on phase-shifting interferometry are given to verify the effectiveness of this method.

Extended object wavefront sensing based on the correlation spectrum phase

In this paper we investigate the performance of a Fourier based algorithm for fast subpixel shift determination of two mutually shifted images subjected to noise. The algorithm will be used for Shack-Hartmann based adaptive optics correction of images of an extended object subjected to dynamical atmospheric fluctuations. The performance of the algorithm is investigated both analytically and by Monte Carlo simulations. Good agreement is achieved in relation to how the precision of the shift estimate depends on image parameters such as contrast, photon counts and readout noise, as well as the dependence on sampling format, zero-padding and field of view. Compared to the conventional method for extended object wavefront sensing, a reduction of the computational cost is gained at a marginal expense of precision.

Phase extraction from three and more interferograms registered with different unknown wavefront tilts

We propose phase retrieval from three or more interferograms corresponding to different tilts of an object wavefront. The algorithm uses the information contained in the interferogram differences to reduce the problem to phase shifting. Three interferograms is the minimum for restoring the phase over most of the image. Four or more interferograms are needed to restore the phase over the whole image. The method works with images including open and closed fringes in any combination.

Temporal speckle pattern interferometry for measuring micron-order surface motion of a liquid bridge

This paper presents a technique based on temporal speckle pattern interferometry (TSPI), a new version of electronic speckle pattern interferometry (ESPI), for measuring micron-order motion of a deformable surface of a quasi-cylindrical liquid bridge. The time sequence phase method (TSPM) proposed recently has been extended to develop automated and robust procedures for temporal phase recovering of specklegrams. The performance of the procedures is verified through computer simulations made in a range of parameters involved. The technique is implemented into a TSPI system utilizing a ground glass for generating speckles from non-speckled reference and object wavefronts. The validity and accuracy of the technique are examined in the measurement of dynamic displacement of both a flat mirror and a cylindrical glass rod, where detailed comparison is made with the simultaneous measurement taken with the laser focusing displacement meter. The capability of the present technique is demonstrated by some experimental results obtained from dynamic surface displacement of a liquid bridge of silicone oil.

Correction of wave-front errors caused by the slight tilt of a reference beam in phase-shifting interferometry.

In standard phase-shifting interferometry the reference beam is supposed to be a plane wave exactly normal to the recording plane. A slight tilt of the reference beam, however, may occur in practice, and it will introduce phase distortion for the reconstructed object wave front. The effects of reference wave tilt on the wave reconstruction are analyzed, and a novel method is proposed to correct the errors caused by this tilt. This method is simple and convenient without the need of any additional optical devices and measurements, and it can be used for both the smooth and the diffuse object surfaces. The effectiveness of this method is verified by a series of computer simulations.

Rapid high spatial resolution imaging of ground vibration for buried landmine detection using ESPI

Recent work has shown that many landmines exhibit a multimode vibration pattern. To fully map the vibration pattern of these modes requires spatial resolutions on the order of millimeters. Any practical field instrument to detect landmines that cues on such modal patterns must take advantage of parallel optical processing. An optical technique that lends itself to such vibration sensing is an electronic speckle pattern interferometer (ESPI). The double-pulsed ESPI system has been used for the vibration measurement of the ground surface. The first and second laser pulses synchronized with the vibration peak and the vibration valley, respectively, illuminate the object. The imaged object wavefronts are combined with a reference wavefront and recorded in two video frames by using a CCD camera. The spatial distribution of the 2D vibration amplitude is obtained by subtracting two speckle patterns and processing the corresponding fringe pattern. The displacement sensitivity of the ESPI is about 30 nm. Here, we not only consider airborne sound sources to excite vibrations in the ground, but also a mechanical shaker to significantly increase the vibration amplitudes at the spot of interest. The vibrational pattern at the surface of the ground over buried antitank and antipersonnel landmines is studied.

Simultaneous digital correction of amplitude and phase errors of retrieved wave-front in phase-shifting interferometry with arbitrary phase shift errors

Both the amplitude error and phase error retrieved in the recording plane in phase-shifting interferometry (PSI) have effects on the reconstructed wave-front in original object plane placed a distance away. We have proposed a simple and effective algorithm, which can simultaneously correct both kinds of wave errors caused by arbitrary and unequal phase shift errors in PSI for an off-lying object and then greatly improve the reconstructed object wave-front by digital image processing based on the statistic nature of diffraction field. The principles are explained, and a series of computer simulations are made to verify its feasibility.

Generalized phase-shifting interferometry with arbitrary unknown phase steps for diffraction objects.

A general method of extracting the arbitrary unknown and unequal phase steps in phase-shift interferometry from interferograms recorded on the diffraction field of an object and then reconstructing the object wave front digitally with our derived formulas is proposed. The phase steps are first calculated based on the statistical nature of the diffraction field and are further improved by an iterative approach. This method is simple, highly accurate, and usable for any frame number N (N > or = 3) and for both smooth and diffusing objects, as is verified by a series of computer simulations.

Phase-shift extraction and wave-front reconstruction in phase-shifting interferometry with arbitrary phase steps.

A new approach to reconstructing the object wave front in phase-shifting interferometry with arbitrary unknown phase steps is proposed. With this method the actual phase steps are first determined from measured intensities with an algorithm based on the statistic property of the object phase distribution in the recording plane. Then the original object field is calculated digitally with a derived formula. This method is simple, accurate, and capable of retrieving the original object field, including its amplitude and phase distributions simultaneously, with arbitrary and unequal phase steps in a three- or four-frame method. The effectiveness and correctness of this approach are verified by a series of computer simulations for both smooth and diffusing surfaces.

Experimental demonstration of the longitudinal image shift in digital holography

In digital holography, it is necessary to know the distance of the object from the recording charge-coupled device camera to obtain a correct numerical reconstruction process. The presence of a plane parallel plate along the path of the object beam, such as a beamsplitter cube, often used in interferometers, affects the actual reconstruction distance. This effect, to our knowledge, has never been discussed in the literature despite the fact that it adds a contribution that cannot be ignored in the reconstruction process. We evaluate the effect for a spherical object wavefront as well as in the case of an extended object.

Digital holographic aberration compensation in electron holography

This paper proposes a new digital method to compensate for the aberration of an electron objective lens in electron holography. In this method, the object wavefront in the exit pupil plane is numerically reconstructed from a digitized electron hologram, and is corrected by multiplying it with the conjugated phase-error function. Then, an aberration-free image can be obtained by calculating the Fresnel integral of this corrected wavefront. In comparison with traditional methods, this method is much more convenient and accurate. Some verifying experiments are also presented in this paper. (C) 2003 Society of Photo-optical Instrumentation Engineers.

Method and apparatus for detecting internal structures of bulk objects using acoustic imaging

Apparatus for producing an acoustic image of an object according to the present invention may comprise an excitation source for vibrating the object to produce at least one acoustic wave therein. The acoustic wave results in the formation of at least one surface displacement on the surface of the object. A light source produces an optical object wavefront and an optical reference wavefront and directs the optical object wavefront toward the surface of the object to produce a modulated optical object wavefront. A modulator operatively associated with the optical reference wavefront modulates the optical reference wavefront in synchronization with the acoustic wave to produce a modulated optical reference wavefront. A sensing medium positioned to receive the modulated optical object wavefront and the modulated optical reference wavefront combines the modulated optical object and reference wavefronts to produce an image related to the surface displacement on the surface of the object. A detector detects the image related to the surface displacement produced by the sensing medium. A processing system operatively associated with the detector constructs an acoustic image of interior features of the object based on the phase and amplitude of the surface displacement on the surface of the object.