Optical micro-manipulation has seen a resurgence of interest in recent years which has been due in part to new application areas and the use of tailored forms of light beams particularly intereference patterns of light. Particle dynamics in 2D and 3D light patterns and the transport properties therein are of interest. As examples, I show the ability to sort and separate biological matter in a three dimensional optical lattice and also dynamics in a Bessel light beam which can be considered as a set of concentric rings created by interference.

We present the results from a non-diffracting optical beam experiment that utilizes extremely low power levels (single-photon). The non-diffracting beam has a Bessel spatial distribution and demonstrates interesting single-photon self-interference effects such as spatial confinement. The single-photon Bessel beam is generated using two means: (1) an attenuated HeNe laser beam that statistically provides a single photon flux through the optical system, and (2) one photon from a pair of quantum entangled twin photons produced by spontaneous parametric down-conversion (SPDC) in a Beta Barium Borate (BBO) crystal pumped by a UV laser. The entangled nature of the single-photon Bessel beam using the SPDC source provides a high level of discrimination from ambient background noise photons that would otherwise severely limit the utility of such a technique to dark enclosures. The HeNe laser on the other hand, provides higher photon count rates and is more convenient to work with in contrast to the entangled photon source. We verify that a single-photon Bessel beam reforms itself beyond a circular obscuration by measuring the transmitted spatial distribution.

A two-color quantum-entangled photon source is used to produce fourth-order interference. Because the period of the interference is produced by the frequency difference of the entangled photons, problems associated with counting fringes can be avoided. This also permits measurements at a virtual wavelength, which can prevent problems associated with transmission or absorption when such a longer wavelength may be needed. The interference wavelength can be varied with a geometry change in the beam path without any change in the source wavelength. The entangled photons are produced using an argon ion laser at 351 nanometers and a type I BBO crystal. The interference is detected in coincidence using four photomultiplier tubes.

Dynamic interferometry is a highly sensitive means of obtaining phase information that can determine phase at rates of a few measurements per second. The sensitivity of these phase-measurement instruments is on the order of thousandths of a wavelength at visible wavelengths enabling the measurement of small temperature changes and thermal fields surrounding living biological objects. Temperature differences are clearly noticeable using a visible wavelength source because of subtle changes in the refractive index of air due to thermal variations between an object and the ambient room temperature. Living objects can also easily be measured over a period of time to monitor changes as a function of time. This technique has many promising applications in biological and medical sciences for studying thermal fields around living objects. In this paper we compare differences in thermal fields measured with dynamic phase-measuring interferometry surrounding room temperature and body temperature inanimate objects as well as living biological objects at data rates of many measurements per second.

Absolute metrology measures the actual distance between two optical fiducials. A number of methods have been employed, including pulsed time-of-flight, intensity-modulated optical beam, and two-color interferometry. The rms accuracy is currently limited to ~5 microns. Resolving the integer number of wavelengths requires a 1-sigma range accuracy of ~0.1 microns. Closing this gap has a large pay-off: the range (length measurement) accuracy can be increased substantially using the unambiguous optical phase. The MSTAR sensor (Modulation Sideband Technology for Absolute Ranging) is a new system for measuring absolute distance, capable of resolving the integer cycle ambiguity of standard interferometers, and making it possible to measure distance with sub-nanometer accuracy. In this paper, we present recent experiments that use dispersed white light interferometry to independently validate the zero-point of the system. We also describe progress towards reducing the size of optics, and stabilizing the laser wavelength for operation over larger target ranges. MSTAR is a general-purpose tool for conveniently measuring length with much greater accuracy than was previously possible, and has a wide range of possible applications.

We present two novel multi-frequency techniques for absolute range measurement in interferometry. The first employs a generalised optimum multi-frequency technique for maximising the measurement range by careful selection of the measurement frequencies. Furthermore, the approach utilises the minimum number of measurement wavelengths and hence reduces the complexity of an interferometer for a given application. The second technique uses the same measurement frequency selection approach as in the well-known technique of excess fractions, but introduces a novel algorithm based on the Chinese remainder theorem to produce reliable fringe order information in the presence of phase measurement noise. A comparison of these techniques with the method of excess fractions has been performed by computer simulation showing that the generalised optimum multi-frequency approach offers the best combination of process speed and measurement reliability. The new techniques have been successfully applied to data from coherent and incoherent fringe projection systems to produce shape data. The results from an initial investigation into a fibre interferometer for high speed single point ranging with 2 measurement frequencies is also presented.

In this paper, advances in our study and characterization of a MEMS micromirror device are presented. The micromirror device, of 510 mm characteristic length, operates in a dynamic mode with a maximum displacement on the order of 10 mm along its principal optical axis and oscillation frequencies of up to 1.3 kHz. Developments are carried on by analytical, computational, and experimental methods. Analytical and computational nonlinear geometrical models are developed in order to determine the optimal loading-displacement operational characteristics of the micromirror. Due to the operational mode of the micromirror, the experimental characterization of its loading-displacement transfer function requires utilization of advanced optical metrology methods. Optoelectronic holography (OEH) methodologies based on multiple wavelengths that we are developing to perform such characterization are described. It is shown that the analytical, computational, and experimental approach is effective in our developments.

The benefits of using two-wavelength measurements to extend the dynamic range of an interferometric measurement are well known. We present a new multi-wavelength interferometer that uses two successive single frame measurements obtained rapidly in time to significantly reduce sensitivity to vibration. At each wavelength, four phase-shifted interferograms are captured in a single image. The total acquisition time for both wavelengths is 100 microseconds, over three orders of magnitude shorter than conventional interferometers. Consequently, the measurements do not suffer from the fringe contrast reduction and measurement errors that plague temporal phase-shifting interferometers in the presence of vibration. In this paper we will discuss the basic operating principle of the interferometer, analyze its performance and show some interesting measurements.

Wavelength scanned interferometry can distinguish in frequency space interference signals from different surfaces , and therefore allows the measurement of optical thickness variation between several quasi-parallel surfaces of a composite transparent object. Discrete Fourier analysis of the signal spectrum with a suitable sampling window can then detect the phase of the individual signals. The actual frequencies of the various signals can deviate from their nominal detection frequencies because of refractive index dispersion of the material and/or nonlinearities in the wavelength scanning. This creates problems for conventional sampling window functions, such as the von Hann window, because they are sensitive to detuning of the signal frequency. Therefore we have derived an error-compensating algorithm (with 2N-1 samples and individual phase steps of 2p/N) with a modified triangular window that allows some frequency detuning and can determine the phase of any specific harmonic order within the frequency range of the detected signal. A composite object consisting of four reflecting surfaces was measured using the new algorithm in a Fizeau interferometer. Experimental results show that the new algorithm measured the front surface and the optical thickness variations in a glass-air-glass cavity with an error of 10 nm rms over a 90 mm diameter aperture.

One of the ways to achieve 3D objects visualization is holography. The recent progress of CCD/CMOS cameras provides quick development of digital holographic recording. Optoelectronic reconstruction of digital holograms can be realized by means of variety of spatial light modulators, however each of them suffers several limitations due to big pixel size, low diffraction efficiency and noise. In the paper high efficiency liquid crystal on silicon (LCOS) spatial light modulator is proposed as the novel solution for optoelectronic holographic reconstruction. The system for holograms reconstruction based on LCOS is presented. The results of initial experiments on reconstruction of computer generated and digital holograms of different classes of 2D and 3D objects are shown and discussed. The problems connected with limited resolution of the recording (CCD) and reconstruction (LCOS) devices are considered. The comparison of the results obtained by numerical and optoelectronic reconstruction of digital holograms is presented, together with a discussion of the limitations and further possibilities of these techniques.

Digital holography is widely used as a fast, simple and robust method for the field of non-destruction and non-contact testing, especially in deformation measurement. In this paper, an in-line digital holographic interferometry setup is described, which is based on phase-shifting digital holography. Taking advantage of digital holography, the setup is able to measure the deformation of an object. In addition, two theoretical methods are briefly described: two-exposure technique and phase-shifting digital holography, which can both realize deformation measurement. This paper utilizes the whole information of the object in two different states in the hologram plane which can respectively be reconstructed onto the image plane with two different methods: two-exposure digital holographic interferometry and phase shifting digital holography interferometry, which are derived from the computer reconstruction of single hologram and reconstruction technique combined with phase shifting technique. Then the interference fringe pattern and the phase difference map between the two reconstructed images can both be obtained, which indicate the deformation of the tested object by analyzing some kind of quantitative mapping relationship. In this paper, practical measurement results are presented to verify the metrology. High precision is obtained simultaneously. Several error factors are analyzed and some corresponding suppression methods are described.

In digital holography the imaging process consists of physical registration using CCD camera and digital image reconstruction with specialized software. Amplitude gradients of the reconstruction field at the hologram plane influence significantly the phase reconstruction quality. The field truncation by hologram edges is of particular concern. The image reconstruction process can be software repeated several times using various apodization functions. Basing on phase imaging changes introduced by different apodization functions a decrease of phase errors can be achieved for some object types. Basing on the results received from experimental measurements and computer simulations for some object examples the advantages and disadvantages of the proposed method will be presented.

We present a method for in-situ visualization of electric field domain reversal in congruent lithium niobate (LN) through an electro-optic interferometric technique. The crystal refractive index n changes by the linear electro-optic and piezoelectric effects along the z crystal axis, due to the external electric field. This variation depends on the domain orientation so that two adjacent antiparallel domains present a refractive index difference equal to 2Dn which is used for in-situ visualization of the reversed domain pattern during formation. A digital holographic (DH) technique is employed for a two-dimensional (2D) reconstruction of the wavefield transmitted by the sample in amplitude and phase during the process. The corresponding amplitude-map and phase-map movies are presented. The amplitude-map gives qualitative information about the spatial evolution of the domain boundaries while the phase-map provides measurement of the 2D distribution of the phase shift induced along the z axis. The phase-map movies provide unequivocal information about the spatial distribution of the reversed domain regions. This technique can be used as in-situ monitoring method alternative to the measurement of the poling current which provides information only about the amount of charge delivered to the sample, ignoring the spatial distribution of the domain boundaries.

A new technique, called spatio-spectral digital holography, is proposed. The technique is based on the combination of the principles of a spectral interference microscope and digital holography, where the spectral interferometry provides the function of full-field tomographic imaging, and digital holography gives a microscope objective the function of adaptive numerical focusing. Experimental results are presented that demonstrate the validity of the proposed principle.

We evaluate the application of the Wigner-Ville distribution (WVD) to measure phase gradient maps in digital speckle pattern interferometry (DSPI), when the generated correlation fringes present phase discontinuities. The performance of the WVD method is evaluated using computer-simulated fringes. The influence of the filtering process to smooth DSPI fringes and additional drawbacks that emerge when this method is applied are discussed. A comparison with the conventional method based on the continuous wavelet transform in the stationary phase approximation is also presented.

The ordinary fringe analysis method based on Fourier transform cannot analyze a closed fringes using only single specklegram produced with two sheets of speckle patterns before and after deformation. On the basis of this discussion, the novel fringe analysis method is proposed in this paper. In the proposed method, not a specklegram but speckle patterns that produce the specklgram are directly analyzed using Fourier transform technology. Then, the ordinary problems can be solved by the proposed method. In the experiment, it is confirmed that the new proposed method can analyze an out-of-plane displacement using only two sheets of speckle patterns before and after deformation.

Under the assumption of Gaussian random process, we discuss the first and the second order statistical properties of the complex amplitude of analytic signal of the white-light speckle pattern. We derive the autocorrelation function of the pseudo phase. Based on these results, we show mathematically that the proposed signal domain phase-only correlation (SD-POC) has advantage over the conventional intensity-based correlation techniques in its performance of micro-displacement measurement. We also present experimental results that support the theory.

Short-range speckle correlation techniques were used to measure the refractive index of turbid biological media. The refractive index depends on the cell content, which is about 80% water and 15% protein. The variation in water or protein content produced various small shifts in the oscillatory features of the speckle intensity spatial correlation function for correlation distances shorter than the transport mean free path. Optical diffusion profiles in transmission, and long range speckle intensity correlation techniques were used to measure the transport mean free path. The optical system was calibrated with a porous silicate slab, and live yeast was the biological system studied. It is found that the techniques employed could serve as markers for the cell's water and protein contents. Consistent results were also found for chicken tissue and a combined yeast sample. Extension to abnormal cell detection, and the application to in-situ refractive index mapping are also discussed.

We describe a novel method of measuring absolute distances by using a two-point diffraction source specially devised to generate two high quality spherical waves simultaneously with a small lateral offset. Interference of the generated two spherical waves produces a unique ellipsoidal phase distribution in the measurement space. A partial map of the resulted interference phase field is sampled and fitted to a geometric model of multilateration that allows absolute-distance measurements to be performed without 2π-ambiguity. The partial phase map may be obtained by use of either homodyne or heterodyne phase measuring technique. Test results demonstrate that high precision with 1 part in 10⁶ uncertainty can be achieved over 1 meter distance range.

Because the single-mode optical fiber keeps spatial coherence in fiber cross-section and the selected interferometric configuration also the temporal one, the coherence aspect in optical-fiber interference phenomenon can be omitted. Basing on this fact and taking into consideration the anisotropic properties of optical fiber, the fiber-optic interferometer gives a possibility for direct analysis of polarization role in the interference phenomenon as well as possibilities of their practical use. Such idea is presented in this paper where the theoretical as well as experimental investigation base on fiber-optic loop interferometer configuration is presented. The practical aspect of this analysis is developed in the systems described in this paper and designed for: slow-speed platform investigation, detection of rotational seismic waves, fiber-optic element investigation, and polarization parameters analysis.

In this paper we present recent work about the application of digital phase detection for accurate wavelength measurement using two beam interferometry (lambdametry). The advantage of two beam interferometry is the sinusoidal fringe signal for which precise phase detection algorithms exist. Modern algorithms can cope with different sources of errors, and correct them. We recall the principle of the Michelson-type lambdameter using temporal interference and we introduce the Young-type lambdameter using spatial interference. The Young-type lambdameter is based on the acquisition of the interference pattern from two point sources (e.g. two ends of monomode optical fibers) projected onto a CCD camera. The measurement of an unknown wavelength can be achieved by comparison with a reference wavelength. Accurate interference phase maps can be calculated using spatial phase-shifting. In this way, each small group of contiguous pixels acts as a single interferometer, and the whole set of pixels corresponds to a massively parallel interferometric measurement system (up to many hundreds of thousands units). The major advantage of our method is its structural simplicity and the possibility of full optical integration. The final goal is to achieve a relative uncertainty of the order of some 10^-8 with a measurement duration of the order of some minutes. Preliminary results are presented.

A new technique of double-source interferometry is proposed, which can suppress spurious noise fringes arising from the interference with unwanted lights reflected from a surface that is not under test. Two collimated beams from a pair of mutually incoherent monochromatic sources are introduced into an interferometer to generate two sets of interference fringes, each of which is a superposition of signal fringes and noise fringes. The key idea is to choose the angle between the two beams in such a manner that the noise fringes generated by one beam become 180 degree out of phase from those generated by the other beam; thereby the noise fringes are canceled out while the signal fringes are maintained. The technique is also suited to the measurement of an optical parallel plate where noise fringes are unavoidable because of reflection from the rear surface. Experimental results are presented that demonstrate the validity of the proposed principle.

Phase unwrapping remains a challenging problem in optical interferometry. In this paper we only deal with noisy phase maps. The noise is removed by a windowed Fourier transform and then the sequential line scanning method is adopted for phase unwrapping. This simple approach is verified to be effective.

The processing of low-coherence interferometric signals in the frequency domain generates multiple images of an object surface, each image corresponding to a distinct wavelength or illumination angle. The detection of the motion of object features between images provides a direct measure of the net effect of chromatic and some geometric imaging aberrations. The data are presented as vector plots showing the motion of the centroid of imaging ray bundles as a function of wavelength or illumination angle, and as a function of field position. The correlation technique developed for this application resolves feature motions smaller than the optical resolution of the imaging system. The approach is applied to the characterization of high and low numerical aperture interference microscope objectives. The information can be used to minimize misalignments of an interferometer, compare the performance of lenses and offer objective means of assessing the potential lateral resolution of an instrument.

A longitude coherence control system needs a source that is temporally coherent and yet spatially incoherent. For this reason, a zone plate-like pattern is imaged onto a rotating ground glass. Generally the ground glass exhibits a strong directivity. It is far from an ideal uniform diffuser that is implicitly assumed in the theory. To solve this problem, we propose a new illumination system. In our system, the beam illuminating the zone plate-like pattern is focused on the test surface. We measured the longitudinal coherence functions in our optical system. The result shows that the longitude coherent function is better controlled in our interferometer.

Interference microscopes use quasi-monochromatic, broad band, and white light illumination for surface topography measurement. Fringe spacing for quasi-monochromatic illumination changes with the numerical aperture of system, and these changes have been previously examined by others. In this article we compare changes in fringe spacing for white light and broad band illumination for objectives with a numerical aperture of 0.13 and 0.55. We find that white light fringe spacing changes with tilt of the object much faster than for monochromatic illumination. We also investigate the influence of reference mirror tilt on changes in white light fringe spacing.

We address the basic issue of the observation condition in a synthetic coherence function applied to optical tomography and profilometry, which has not been made clear in previous papers. We present a more general theory for interference fringe formation for spatial coherence control with a synthetic source. The generalized theory predicts the existence of the observation condition that can make the measurement insensitive to the tilt of the object, which will open the new possibility of measuring objects with rough surfaces. We present experimental results that quantitatively verify the validity of the principle and the prediction.

A new profiling algorithm is proposed for the scanning white-light interferometry. A series of white-light interferograms are acquired by traditional vertical scanning process. The collected intensity data of the interferograms are then Fourier-Transformed with respect to the ordinate, or the scanning axis, into the wave number domain, where two or more wave numbers are selected for further calculation. The multi-wavelength phase-unwrapping technique is then used to solve for the surface profile. Preliminary experiment has been carried out with a Mirau-type white-light interferometer on two sets of step-height standards. The proposed algorithm works as well even when the spectrum of the white-light source is not Gaussian distributed, while the conventional peak sensing algorithms do not.

This paper will illustrate several approaches to retrieving the shape of aspherical reflective surfaces as used in EUV Lithography, from measurements from a previously reported angstrom-accuracy interferometer. First, the working principles of the interferometer will be reviewed, and typical measurement data expected from the instrument will be presented. Several methods will then be introduced for retrieving the reflector shape from such measurements. These methods will include approaches based on ray tracing, approximate diffraction calculations, and linearization of rigorous diffraction calculations which use a novel numerical scheme to reduce calculation time of the diffraction integral. The methods will be compared on the basis of accuracy, calculation time and extendibility.

We demonstrate a phase-shifting, point diffraction interferometer that achieves high accuracy and is capable of measuring a single pulse of light. The measurement system utilizes a polarizing point diffraction plate to generate a synthetic reference beam that is orthogonally polarized to the transmitted test beam. The plate has very high polarization contrast, works over an extremely broad angular and spectral range, and is only 100 nanometers thick. The unique features of the polarizing element make the system amenable to measuring strongly convergent light from high numerical aperture optics without the need to use a point reference source to calibrate the system. Results of measuring optics with numerical apertures as high as NA 0.8 are presented.

We describe new techniques of synthesizing three types of computer-generated hologram (CGH); Fourier, Fresnel and image CGHs. These holograms, aimed to reconstruct three-dimensional (3-D) objects, are synthesized by means of a unique algorithm of fusing multiple perspective views of the observed scene. The hologram is initially generated in the computer as a Fourier hologram. Then, it can be converted to either Fresnel or image holograms by computing the desired wave propagation and the interference process. By illuminating the ready-to-use CGHs with a collimated plane wave, a 3-D image of the objects is reconstructed. Diffraction efficiency enhancement of the above algorithm by superimposing a random phase on the object during the CGH formation is also presented. Computer simulation and experimental results of the constructed 3-D objects demonstrate the suggested technique

We describe an application of artificial neural networks (ANN) for solving of inverse and direct problems of optics. Using the ANN we calculate local and integral characteristics of object by means of incomplete set of data that characterize optical images. Possibilities of usage the only one value of a function of signal intensity distributionn in a plane of a registration for full determination of distribution of local characteristics in an object are shown. It is very important for optical fiber sensors, smart sensors and MEMS. Examples of ANN usage for a case of object with a cylindrical symmetry in a field of interferometry are presented. Results obtained show that determination of object local and integral characteristics can be perform very much simpler than by means of standard procedures and numerical approaches for signal processing, reduction and analysis. The ANN can allow also to solve number of tasks that could not be solved by means of usual approaches. In prospects, this method can be used for creation of automated systems for diagnostics, testing and control in various fields of scientific and applied research as well as in industry.

Spatial heterodyning is an interferometric technique that allows a full complex optical wavefront to be recorded and quickly reconstructed with a single image capture. Oak Ridge National Laboratory (ORNL) has combined a high-speed, image capture technique with a Fourier reconstruction algorithm to produce a method for recovery of both the phase and magnitude of the optical wavefront. Single frame spatial heterodyne interferometry (SHI) enables high-speed inspection applications such as those needed in the semiconductor industry. While the wide range of materials on wafers make literal interpretation of surface topology difficult, the wafers contain multiple copies of the same die and die-to-die comparisons are used to locate defects in high-aspect-ratio structures such as contacts, vias, and trenches that are difficult to detect with other optical techniques. Metrology with SHI has also been investigated by ORNL, in particular the use of SHI to perform metrology of line widths and heights on photolithographic masks for semiconductor wafer production. Several types of masks are currently in use with phase shifting techniques being employed to extend the wafer printing resolution. With the ability to measure the phase of the wavefront, SHI allows a more complete inspection and measurement of the phase shifting regions.

The Fourier method of interferogram analysis requires the introduction of a constant tilt into the interferogram to serve as a 'carrier signal' for information on the figure of the surface under test. This tilt is usually removed in the first steps of analysis and ignored thereafter. However, in the problem of aligning optical components and systems, knowledge of part orientation is crucial to proper instrument performance. This paper outlines an algorithm which uses the normally ignored carrier signal in Fourier analysis to compute an absolute tilt (orientation) of the test surface. We also provide a brief outline of how this technique, incorporated in a rotating Twyman-Green interferometer, can be used in alignment and metrology of optical systems.

We demonstrate a new type of spatial phase-shifting, dynamic interferometer that can acquire phase-shifted interferograms in a single camera frame. The interferometer is constructed with a pixelated phase-mask aligned to a detector array. The phase-mask encodes a high-frequency spatial interference pattern on two collinear and orthogonally polarized reference and test beams. The phase-difference between the two beams can be calculated using conventional N-bucket algorithms or by spatial convolution. The wide spectral response of the mask and true common-path design permits operation with a wide variety of interferometer front ends, and with virtually any light source including white-light.

Microelectromechanical systems (MEMS) are under development as radio-frequency (RF) switches for a broad range of applications, where active and passive components can be switched into or out of RF circuits. Optical interferometry is well-suited to the characterization of MEMS structures due to its wide dynamic range, its fine resolution, and its non-invasive qualities. However, RF MEMS operate at frequencies ranging from a few megahertz to tens of gigahertz. These high operating frequencies offer challenges in the demodulation of the interferometric system. Our demodulation system consists of photodetecting the optical interferometric signal, converting the analog electronic signal to a digital signal, and digitally processing the signal to compute the MEMS structure's vibration amplitude. In this paper, we present a digital signal processing algorithm for demodulating an interferometer developed for characterizing RF MEMS. Our algorithm is based on a phase-generated carrier modulation system and assumes that the target structure is oscillating at a fixed frequency. A key feature of our algorithm is that it permits determination of a structure’s vibration amplitude, where the structure's vibration frequency is greater than the analog-to-digital converter's (ADC's) sample frequency. Therefore, commercially-available low-cost ADCs and microprocessor systems may be used for real-time demodulation. Both simulation and experimental results will be presented.

We describe a new method to keep an electrically isolated Mach-Zehnder electro-optic modulator biased in quadrature despite changes in temperature and optical coupling efficiency. The modulator is part of a system to measure electromagnetic waves in an outdoor environment. All data and control signals between the modulator and electronics control module are carried by analog optical-fiber links, and all of the bias signals and control procedures are implemented with an onboard computer and digital signal-processing unit. Our method compares the average DC optical power in the complementary outputs of the modulator and adjusts the bias point by controlling the optical power to small photocells in the sensor head. A second control loop balances responses from a small dither signal applied to the modulator, consequently balancing the optical losses in each of the complementary outputs by way of a variable optical attenuator. This control system allows us to maintain the bias to within ±2 degrees of the quadrature point. The response time of the control loop is about 10 ms.

Digital holography technique is the numerical version of conventional holography technique. It is widely applied in computer reconstruction for the object image, opt-electronic reconstruction and the object information measurement, in which the computer reconstruction is the basis of the others. In this paper, the computer reconstruction technique combined with digital holography is researched. It puts forward reverse transform method to realize the digital reconstruction and applies focusing function to determine the exact registering/reconstruction distance. Finally the experimental results are shown.

Phase shifting error is a major error source in phase-shifting digital holography. It affects the quality of the reconstructed object and causes errors in its phase and amplitude calculation. This paper presents a simple method to accurately retrieve the actual phase-shifting value used in practical hologram recording. It therefore provides the possibility of completely eliminating the phase-shifting error in digital hologram. The proposed method is based on solving the object wave reconstruction equation. The effectiveness of the proposed method is verified by both mathematical analysis and computer simulation.

A fiber optic interferometer for a novel application is proposed in this paper. This new configuration and decoding scheme is in particular suitable for an AFM-tip tailoring system. A theoretical analysis method for simulating the relation of displacement and interfering intensity from the fiber optic sensor is thoroughly discussed. Experimental data for evaluating interfering efficiency agree well with simulation results. Higher resolution becomes achievable with the help of the two-channel interferometer decoding scheme. Moreover, the properties of the piezoelectric actuator used in this system are characterized by the optical sensor. This compact sensor exhibits satisfactory performance for the nanometer-resolution requirement of the developing AFM tip tailoring system.

In this work we present a polarimetric method that uses a polarization description based on the Poincare sphere. The erbium fiber is modeled assuming that it is uniform and behaves as a distributed retarder with linear and circular birefringences. We show that taking advantage of the geometric properties of the Poincare sphere it is possible to separate the linear birefringence contribution from that of the circular birefringence while the measurement precision is optimized. The experimental procedure here presented provides reproducible results for the measurement of the linear and circular distributed birefringences in erbium-doped fibers.

We describe in this paper a special polarimeter for measuring linear birefringence in transparent optical samples. The polarimeter employs two photoelastic modulators that operate at different frequencies (50 KHz and 60 KHz). The resulting electronic signal at the detector is processed using two methods: demodulation by lock-in amplifiers or using Fourier analysis of a digitized waveform. We compare the results obtained by using the two signal processing methods in this special polarimeter and discuss how each method benefits selected applications.

Recently, frequency-domain (FD) -optical-coherence-tomography (OCT) methods have been investigated extensively as more efficient and sensitive system compared with conventional time-domain (TD) -OCT. Superstructure-grating-distributed-Bragg-reflector (SSG-DBR) lasers are particularly suited for optical-frequency-domain-reflectometry (OFDR) -OCT with its wide wavelength tunability and frequency agility. We have made a discrete frequency OFDR-OCT system with an SSG-DBR laser, which can tune the wavelength from 1533 to 1574 nm with tuning speed of 10μs per 0.1 nm step. The theoretical expression of the discrete frequency OFDR-OCT is given. Utilizing near-transparent nature of enamel of teeth in the wavelength region of the SSG-DBR laser and long object range of the OFDR-OCT, we have carried out OCT measurements on teeth. Experimental OCT imaging of a canine are reported here.

The phase-shifting diffraction-grating interferometer uses a diffraction grating that performs manifold functions of beam splitting, beam recombining, and phase shifting. The reference and measurement waves generated by means of diffraction have different amplitudes depending on their orders of diffraction, so the interference fringe pattern resulting from the two waves tends to yield poor visibility. In this investigation, we select a phase grating of reflection type and attempt to improve the interference visibility with optimization of the groove shape of the grating through numerical analysis. And we apply the proposed analytic method to the CGH null system for testing a large-scale aspheric mirror, which adopt a binary amplitude CGH and a new phase-shifting diffraction-grating interferometer.

In this paper we are going to review two interferometric techniques to demodulate a single fringe pattern containing closed fringes. It is well known that analyzing a single interferogram with spatial carrier is relatively easy [1]. That is, whenever the modulating phase of the interferogram contains a linear component large enough to guarantee that the total modulating phase would remain an increasing function in a given direction of the two dimensional space. Why it is interesting to demodulate a single or a series of interferograms in which there is no spatial or temporal carrier ?, knowing that this is a substantially more difficult task ?. The answer is that although one always tries to obtain a single or a series of interferograms with spatial and/or temporal carrier [2], sometimes the very nature of the experimental set-up do not permit to obtain them. One reason could be that one is studying fast transient phenomena where there is no time to introduce a carrier. In these cases one still wants to demodulate the interferograms to evaluate quantitatively the physical variable under study.

In this paper, a set of polynomials are calculated to approximate the phase from a single closed fringe pattern image or interferogram. A scanning window is used to carry out the demodulation process. A polynomial function is fitted over the sub-image obtained from each scanning window. Then, the scanning window is moved on an overlapped neighbourhood of the previous one and the process is repeated. The coefficient polynomial optimization is achieved by multiple application of a genetic algorithm (GA). The GA optimizes a cost function which considers the irradiance similitude between original interferogram and fringes generated by the polynomial obtained from chromosome decodification, the smoothness of the phase being demodulated, and the phase similitude between the overlapped area of actual and previous scanning window. Closed fringe patterns with broad bandwidth can be demodulated. Preliminary results are presented.

Temporal fringe pattern analysis is gaining prominence in interferometry; in particular for transient phenomena studies. This form of analysis, nevertheless, necessitates large data storage. Current compression schemes do not facilitate efficient data retrival and may even result in important data loss. Here, we describe a novel compression scheme that does not result in crucial data loss and allows the efficient retrieval of data for temporal fringe analysis. In sample tests using digital speckle inferometry or fringe patterns of a plate and of a cantilever beam subjected to temporal phase and load evolution respectively, a compression ratio of 1.6 was achieved without filtering out any data from discontinuous and low fringe modulation spatial points. By eliminating 38% of the data from discontinuous and low fringe modulation special points, a very significant compression ratio of 2.4 was attained.

In order to test aspheric optical elements, wedge plate lateral shearing interferometer is used. In a wedge plate the thickness varies along the wedge direction. Because of this thickness varying characteristic, the optical path difference between the original wavefront and the sheared wavefront in wedge plate lateral shearing interferometer is changed according to the incident position of the ray. Simply moving the wedge plate in-parallel to the wedge direction gives the phase shift quantity required for phase shifting interferometry. In typical phase shifting methods, piezoelectric transducer(PZT) is mainly used to give phase shifting quantity. But this method requires only one additional linear translator to move the wedge plate. The required moving distance for the phase shift of wavefront in this method is an order of millimeter, whereas the typical moving distance in the other method using a piezoelectric transducer is an order of wavelength. This method has an advantage in the moving distance precision compared with the other methods. Using this wedge plate lateral shearing interferometer, optical wavefront is measured and reconstructed.

This paper presents a novel least squares calibration approach for fringe projection profilometry. This approach is based on a simple nonlinear function, which is deduced by analyzing the geometry of measurement system and perfectly describes the mapping relationship between the depth map and phase distribution. The calibration is implemented by translating a target plane to a sequence of given positions with known depths, and measuring its phase distributions. Based on least squares estimation, an algorithm with linear computation is deduced to retrieve the related parameters, by which the burden of computational complexity is effectively alleviated. In experiment, a plaster statue is measured to demonstrate the validity of the principle.

The support schemes and thermoelastic deformation of 460-mm diameter interferometer mirrors are studied by means of finite element method. The surface deformation and stress distribution in a variety of support schemes are analyzed. By comparison, the band support with 180°wrap angle and a dentiform rubber-lined strip is accepted to be the optimum. In the optimal support scheme, the thermoelastic deformation analyses for mirrors are carried out at specified thermal gradients (axial, radial, circumferential temperature differences). The contours of surface deformation and the transmitted wavefront distortion are presented respectively. According to the results, it is clear that the influence of thermal effects is much greater than the ones of mechanical forces. Lastly, some suggestions are given to eliminate the effects of thermal turbulence.

In reality, the duration of all light sources (oscillators) is finite. So, effectively, light is always pulsed, whether it is of nano second or of giga second durations. This paper develops a conceptually congruent model of propagating the carrier frequency of a generic pulse directly in the time domain through traditional instruments and media. The modeling approach covers all spectrometers like multi-beam Fabry-Perots and gratings, and two-beam Fourier transform spectrometers. The established approach uses a non-causal Fourier integral to generate Fourier decomposed frequencies of the pulse, which exist in all time, and find their steady state delays through instruments and media. This frequency domain approach gives correct results when appropriately used, but encounters contradictions under some situations that are discussed. In contrast, the time-domain analysis, while mathematically less elegant, always makes correct predictions, besides giving us a deeper and better understanding of the physical processes of temporal evolution of the pulse through various instruments.