Phase-shifting shearing interferometer

Nanoscale surface metrology with a liquid crystal-based phase-shifting angular shearing interferometer

In this Letter, a phase-shifting angular shearing interferometer has been proposed for the application in optical surface metrology (SM) by using a combination of a wedge-shaped liquid crystal (LC) cell and a polarization phase shifter. The demonstration of this angular shearing interferometer for step height measurement is accomplished with the help of a phase-shifting technique. Four phase-shifted interferograms produced by a geometrical phase shifter are subjected to a simplified Wiener deconvolution method, which resembles a simple analysis technique for shearing interferograms in comparison to alternative approaches. A simulation study has been conducted to validate the proposed technique. The experimental results show an accuracy of 5.56% for determining the step height, which also agrees with the results obtained by atomic force microscopy. Owing to the tunability of birefringence, the proposed LC-based angular shearing interferometry technique will be useful to control spatial resolution in optical metrology.

Double-frequency grating shearing interferometer with built-in phase-shifting function for robust multi-level phase retrieval

In this paper, we propose and demonstrate a novel interferometer and signal process to retrieve two-dimensional signals with multilevel phases. The interferometer is based on a shearing interferometry with double-frequency grating, and phase-shifting interferometry is derived as a built-in function of the lateral displacement of the grating. The interferometer not only retrieves the multilevel phase signals but also eliminates slow-varying phase errors wherever they occur. Owing to the common path algorithm, the new interferometer is more robust in dynamic circumstances for optical testing and data processing. We propose a pre-integral signal process for two-dimensional (2D) data processing to prevent post-phase-integral due to shearing interferometry. The simulation and experiment showed that the proposed interferometer with a pre-integral process has various advantages in signal processing for multilevel phase retrieval, and will be useful for higher data rates in optical data storage and free-space communication.

Phase Retardation Analysis in a Rotated Plane-Parallel Plate for Phase-Shifting Digital Holography

In this paper, we detail a phase-shift implementation in a rotated plane-parallel plate (PPP). Considering the phase-shifting digital holography application, we provide a more precise phase-shift estimation based on PPP thickness, rotation, and mutual inclination of reference and object wavefronts. We show that phase retardation uncertainty implemented by the rotated PPP in a simple configuration is less than the uncertainty of a traditionally used piezoelectric translator. Physical experiments on a phase test target verify the high quality of phase reconstruction.

Phase-shifting radial-shearing digital holography with Greek-ladder zone plates

Holography has been widely applied in fields of imaging and measurement, but the optical setup of traditional phase-shifting holography is complicated. Here, a kind of phase-shifting radial-shearing holography with Greek-ladder zone plates is presented, which largely simplifies the optical configuration for holographic recording and enhances the stability of system. A 1951 U.S. Air Force resolution test target is measured by experiment to verify the validity of our proposed method. Benefiting from amplitude-only diffractive lenses and high stability of the common path, the phase-shifting radial-shearing interference with Greek-ladder zone plates has great potential in biological imaging and x-ray holography for the next generation of synchrotron light sources.

Phase-shifting lensless Fourier-transform holography with a Chinese Taiji lens

Compared to off-axis holography, phase-shifting technology takes full use of the space-bandwidth product of the detector array. Here we introduce the Chinese Taiji into diffractive lenses and generate the phase-shifting focal spots, which not only can be used for a spherical reference wave, but also make it possible to realize the lensless Fourier-transform holography. The experimental results of a 1951 U.S. Air Force resolution test target verify the validity of the above theory in the optical region. Owing to the amplitude-only diffractive lenses, these kinds of lenses will have great potential in x-ray holography or biochemical microscopy for the next generation of synchrotron radiation and free electron lasers in the future.

Tunable angular shearing interferometer based on wedged liquid crystal cells

The concept of a liquid crystal wedge as a tunable angular shearing interferometer is introduced and demonstrated to combine both high stability and high tunability. Different wedges are fabricated from planar aligned nematic liquid crystal cells with thickness gradients. These wedges are shown to produce stable interferograms from the polarization interference between the ordinary and extraordinary waves propagating in different directions at the output of the cell. The fringe periods, ranging from 70 μm to 1.25 mm, can be precisely controlled by a low voltage. Despite the wedge-shaped structure, no inhomogeneity has been detected when the wedge is driven adiabatically and the interferograms are uniform over regions as large as 5×5  mm. Moreover, dynamical measurements show that the wedges behave as a succession of multiple cells with different thickness, giving rise to a moving front of stabilizing fringes when driven dynamically. All the observations show that the device is suitable for large beam size and tunable shearing interferometry, with attractive features for applications such as phase sensing, photoalignment or photolithography.

Shape measurement with modified phase-shift lateral shearing interferometry illumination and radial basis function

Three-dimensional shapes of objects were evaluated with modified phase-shift lateral shearing interferometry illumination and radial basis function. A simple optical system was developed to create the fringe pattern based on the Murty interferometer. The phase shift was generated only by moving a plane-parallel plate along an in-plane parallel direction. A novel moving radial basis function method was presented to improve the quality of fringe patterns. And the proper calculation window size was given based on numerical simulation. Three-dimensional shapes of two kinds of objects were determined to verify the feasibility and effectiveness of the proposed method, and the reconstructed height distributions were in good accordance with the referenced data.

Scientific developments of liquid crystal-based optical memory: a review

The memory behavior in liquid crystals (LCs), although rarely observed, has made very significant headway over the past three decades since their discovery in nematic type LCs. It has gone from a mere scientific curiosity to application in variety of commodities. The memory element formed by numerous LCs have been protected by patents, and some commercialized, and used as compensation to non-volatile memory devices, and as memory in personal computers and digital cameras. They also have the low cost, large area, high speed, and high density memory needed for advanced computers and digital electronics. Short and long duration memory behavior for industrial applications have been obtained from several LC materials, and an LC memory with interesting features and applications has been demonstrated using numerous LCs. However, considerable challenges still exist in searching for highly efficient, stable, and long-lifespan materials and methods so that the development of useful memory devices is possible. This review focuses on the scientific and technological approach of fascinating applications of LC-based memory. We address the introduction, development status, novel design and engineering principles, and parameters of LC memory. We also address how the amalgamation of LCs could bring significant change/improvement in memory effects in the emerging field of nanotechnology, and the application of LC memory as the active component for futuristic and interesting memory devices.

Generalized phase-shifting for three-wave shearing interferometry

A generalized phase-shifting method for three-wave shearing interferometry is proposed. The phase-shifting algorithm is derived by an optimal process based on least-squares fitting. With this generalized algorithm, the steps of phase-shifting can be reduced to five, which greatly simplifies the measurement and decreases the burden of computation. Both the numerical simulation and the optical experiment are carried out to demonstrate the adaptability of the method.

Phase-shifting lateral shearing interferometry using wedge-plate and interferometric grating

A simple and robust method for introducing a phase-shifting test procedure in a wedge-plate shearing interferometer is proposed. The output of the wedge-plate lateral shearing interferometer (LSI) is superposed onto a sinusoidal grating, forming a moiré pattern. The in-plane translation of grating perpendicular to the grating lines is used for introducing a known amount of phase shifts in the interferometer. Direct measurement of phase using a four-step phase-shifting method is undertaken. The applicability of this devised phase-shifting wedge-plate LSI has been successfully tested for setting the collimation position of optical beams. Good accuracy and precision are achieved.

Liquid-crystal phase-shifting lateral shearing interferometer with improved fringe contrast for 3D surface profilometry

We report the development of a common-path and nonmechanical scanning phase-shifting lateral shearing interferometer based on a homogeneous gap and wedge-shaped gap liquid-crystal (LC) cell. The modified cell consists of semi-reflecting and fully reflecting glass plates with LC material sandwiched between them so that the amount of reflected light from both the surfaces is nearly equal, thus generating high contrast interference fringes. The thickness of the LC cell was maintained at ~3 μm uniformly for a homogeneous gap and a varying wedge gap was also introduced between two glass plates. Phase-shifting linear fringe patterns of high contrast were generated. The phase-shifted interferograms were projected onto an object and the distorted interferograms were recorded by a CCD camera. The phase-shifting fringe analysis technique was used to reconstruct the 3D shape of the object. The present system is compact and low cost.

Adaptive optics technology for high-resolution retinal imaging

Adaptive optics (AO) is a technology used to improve the performance of optical systems by reducing the effects of optical aberrations. The direct visualization of the photoreceptor cells, capillaries and nerve fiber bundles represents the major benefit of adding AO to retinal imaging. Adaptive optics is opening a new frontier for clinical research in ophthalmology, providing new information on the early pathological changes of the retinal microstructures in various retinal diseases. We have reviewed AO technology for retinal imaging, providing information on the core components of an AO retinal camera. The most commonly used wavefront sensing and correcting elements are discussed. Furthermore, we discuss current applications of AO imaging to a population of healthy adults and to the most frequent causes of blindness, including diabetic retinopathy, age-related macular degeneration and glaucoma. We conclude our work with a discussion on future clinical prospects for AO retinal imaging.

Broadband light source shearing interferometer using Savart plate and angular scanning technique

A shearing interferometer based on using broadband light source, Savart plate, and angular scanning technique is proposed for slope contour measurements in this Letter. Of which, the Savart plate divides the wavefront reflected from the detected surface into two laterally displaced ones, the interference pattern generated by the interference of the divided wavefronts is modulated by an envelope function, and the slope contour of the detected surface is determined by examining the shifting of the darkest fringe as the shear plate is angularly scanned. A setup for realizing the interferometer is constructed. The experimental results of using this setup agree the validity and feasibility of the proposed interferometer.

Three-wave shearing interferometer based on spatial light modulator

The use of a SLM for the three-wave lateral shearing interference is proposed, and an eight-step phase-shifting scheme is developed for extracting phase information from three-wave interferograms. The two-dimensional phase of object is reconstructed from two phase differences which are calculated from two orthogonal sheared interferograms. The flexibility of SLM can be fully utilized in the sense of dynamical controlling of the direction and amount of shear, as well as phase shift. The numerical simulation and optical experiment are carried out to demonstrate the feasibility and reliability of the proposed scheme.

Adaptive-optics system with liquid-crystal phase-shift interferometer

We develop an adaptive-optics system based on a Mach-Zehnder radial shearing interferometer with liquid-crystal-device (LCD) phase-shift interferometry (PSI). Using accurate phase calibration and transient nematic driving of the LCD, the developed three-step PSI procedure can be achieved in a time of 5 ms. The proposed Mach-Zehnder radial shearing PSI method reconstructs the phase information using a digital signal processor (DSP). The DSP then computes appropriate control signals to drive a deformable mirror in such a way as to eliminate the wavefront distortion. The current adaptive-optics system is capable of suppressing low-frequency thermal disturbances with a signal-to-noise ratio improvement of more than 20 dB and a steady-state phase error of less than 0.02pi root mean square when the control loop is operated at a frequency of 30 Hz.

Simple multifrequency and phase-shifting fringe-projection system based on two-wavelength lateral shearing interferometry for three-dimensional profilometry

We propose a simple multifrequency spatial-carrier and phase-shifting fringe-projection system based on two-wavelength lateral shearing interferometry (LSI). In this system a wedge-shaped plate lateral shearing interferometer is used and, owing to the presence of tilt, a finite number of fringes parallel to the direction of the shear appears; hence a significant spatial-carrier frequency is generated at the focus position. We further enhance the spatial-carrier frequency either by changing the wavelength of the laser light or by slight defocusing. A synthetic interferogram with low spatial-carrier frequency is obtained by use of laser light of two wavelengths simultaneously in the lateral shear interferometer. We obtain the phase-shifted fringe patterns from the same setup by simply moving the wedge plate in an in-plane parallel direction, using a linear translator. The fringe projection system was tested for measurement of the three-dimensional shape of a discontinuous object. The present system has many advantages; e.g., it is a common-path interferometry and hence is insensitive to external vibrations, is compact in size, and is relatively inexpensive.

Optical phase shifting with acousto-optic devices

A novel optical phase-shifting method based on a well-known acousto-optic interaction is proposed. By using a pair of acousto-optic modulators (AOMs) and properly aligning them, we construct an optical phase shifter that can directly control the phase of a collimated beam. The proposed phase shifter is insensitive to the polarization of the incident beam when polarization-insensitive AOMs are used, and no calibration is necessary. The proposed approach is confirmed with experimental results.

Simple phase-shifting method in a wedge-plate lateral-shearing interferometer

A simple phase-shifting method in a wedge-plate lateral shearing interferometer is described. Simply moving the wedge plate in an in-plane parallel direction gives the amount of phase shift required for phase-shifting interferometry because the thickness of a wedge plate is not constant and varies along the wedge direction. This method requires only one additional linear translator to move the wedge plate. The required moving distance for a phase shift of the wave front with this method is of the order of a millimeter, whereas the typical moving distance for another method that uses a piezoelectric transducer is of the order of a wavelength. This method yields better precision in controlling the moving distance than do the other methods.

Phase modulation by polarization recording in bacteriorhodopsin: application to phase-shifting interferometry

A novel phase-control method with application to phase-shifting interferometry is presented. The linear polarization state of an external (green) light beam is recorded on a bacteriorhodopsin film, and this polarization state is read by a circular polarized (red) laser beam. By reading the bacteriorhodopsin film, the original (red) wave reverses its circularity and becomes phase shifted by an amount that is dependent on the polarization of the external (green) beam. This method of phase control can be applied in a two-beam interferometer in which the test and reference waves are orthogonally polarized, which allows one to obtain phase modulation without moving parts inside the interferometer.

Phase-shifting lateral shearing interferometer with two pairs of wedge plates

We present a compact and robust phase-shifting lateral shearing interferometer that produces shearing fringes in orthogonal directions without any mechanical rotation or precise alignment. It consists of two pairs of wedge plates, a beam splitter, and a single CCD camera. Both phase-shifting and tilt for lateral shearing are achieved with two pairs of wedge plates, which can reduce systematic errors caused by external vibration and atmospheric disturbance.

Comment on "Phase-shifting shearing interferometer"

The role of the liquid-crystal layer in the phase-shifting shearing interferometer that was proposed by Griffin [Opt. Lett. 26, 140 (2001)] is analyzed. An extra voltage-dependent phase difference is produced when the phase retarder is oriented at an angle from the optical axis of the laser beam such that the interferogram will not repeat itself after a 2pi phase change of the liquid-crystal retarder in either the common Mach-Zehnder interferometer or the phase-shifting shearing interferometer.

Measurement of the induced refractive index in a photothermorefractive glass by a liquid-cell shearing interferometer

A liquid-cell shearing interferometer was developed to measure refractive-index variations (delta n) in transparent materials. The cell was filled with a liquid having a matched refractive index. The achieved resolution was better than 1/1000 of a fringe shift and resulted in a delta n measurement sensitivity down to 10(-7) for 1-mm-thick samples. A refractive-index increment in photothermorefractive glass of up to 5 x 10(-6) was observed after UV exposure at 325 nm. A refractive-index decrement of up to 1 x 10(-3) was observed after thermal development of the exposed sample. It was proved that photothermorefractive glass obeys the reciprocity law; i.e., delta n depends on the UV dosage but does not depend on the irradiance.