Simultaneous Phase-shifting Interferometry Research Articles

Fresnel incoherent compressive holography toward 3D videography via dual-channel simultaneous phase-shifting interferometry.

Fresnel incoherent correlation holography (FINCH) enables high-resolution 3D imaging of objects from several 2D holograms under incoherent light and has many attractive applications in motionless 3D fluorescence imaging. However, FINCH has difficulty implementing 3D imaging of dynamic scenes since multiple phase-shifting holograms need to be recorded for removing the bias term and twin image in the reconstructed scene, which requires the object to remain static during this progress. Here, we propose a dual-channel Fresnel noncoherent compressive holography method. First, a pair of holograms with π phase shifts obtained in a single shot are used for removing the bias term noise. Then, a physic-driven compressive sensing (CS) algorithm is used to achieve twin-image-free reconstruction. In addition, we analyze the reconstruction effect and suitability of the CS algorithm and two-step phase-shift filtering algorithm for objects with different complexities. The experimental results show that the proposed method can record hologram videos of 3D dynamic objects and scenes without sacrificing the imaging field of view or resolution. Moreover, the system refocuses images at arbitrary depth positions via computation, hence providing a new method for fast high-throughput incoherent 3D imaging.

Phase Shifting Approaches and Multi-Channel Interferograms Position Registration for Simultaneous Phase-Shifting Interferometry: A Review

Simultaneous phase-shifting interferometry (SPSI) can simultaneously obtain multiple phase-shifted interferograms and can realize the dynamic wavefront measurement with the use of a phase-shifting algorithm. From the respect of a beam-splitting technique and phase shift achievement of the phase-shifting units, research progress on spatial phase shifting approaches for SPSI systems are classified and summarized, and the key problem affecting SPSI technology is discussed. To ensure the measurement accuracy, it is necessary to perform accurate position registration for multi-channel phase-shifted interferograms before the implementation of a phase-shifting algorithm, and so, the methods of position registration for multi-channel interferograms are also reviewed. This review is expected to prompt research on related fields of phase-shifting interferometry.

Parameter mismatch phase extraction method for spatial phase-shifting interferograms

Mismatch of interferogram parameters, such as the contrast and the fringe frequency inconsistency, can lead to phase error in simultaneous phase-shifting interferometry. In the dynamic Fizeau interferometer (DFI) based on the lateral displacements of light sources, an extended light source is used to suppress coherent noise. Aiming at the contrast mismatch generated by the extended light source and the inherent fringe frequency mismatch of the DFI, We propose a phase-extraction method to solve these problems. Based on this dynamic interferogram model, a linear relationship is constructed between the tilt angle and interferogram contrast, carrier frequency error, phase-shift error. Use the two steps of initial estimation and fine iterations to extract the phase. The RMS of the residuals was better than 1.5 × 10–5λ for the simulation and 0.004 λ for the experimental calculation, which demonstrates that the ripple error was suppressed during phase extraction.

Oblique incidence dynamic phase-shifting interferometer based on inclination angle deflection

An oblique incidence dynamic phase-shifting interferometer based on inclination angle deflection is proposed to quickly obtain the surface distribution of optical surface with flatness of micron dimension. A 2×2 point source array is introduced into a Michelson interference system, and the incidence angle of each point source on the interferometer cavity is adjusted precisely to induce equal phase shift. Spatial separation is realized in combination with a lens array. The four phase-shifting interferograms are captured simultaneously on a single CCD, thereby realizing dynamic measurement. The flatness of a 35 mm aperture silicon wafer is measured at oblique incidence angle of 68°, the root mean square (RMS) is 1.631 μm and peak-to-valley (PV) is 9.082 μm. The experimental results indicate that the proposed interferometer overcomes the disturbance of vibration environment and extends the measurement range of interferometer with high precision by introducing the simultaneous phase-shifting interferometry based on inclination angle deflection into the oblique incidence interference system.

Correction of errors due to uneven intensity distribution and inaccurate phase shifts in prism-based simultaneous phase-shifting interferometry.

Simultaneous phase-shifting interferometry (SPSI) is a suitable technique for dynamic surface measurement due to its rapid measurement capability. Based on whether there are obvious multiple phase-shifting channels in the setup, it can be divided into the multi-channel type and the pixelated phase-mask type. For the former type, two important error sources are the uneven intensity distribution among different phase-shifting channels and inaccurate phase shifts in each phase-shifting channel. In order to diminish the influence of these two error sources, several methods have been proposed. However, in some of these methods, only one error source of the two was considered and corrected. In the methods where the two error sources were both considered, some assumptions such as the uniform background intensity and fringe contrast are needed, so a complete and universal suppression method for both error sources is still needed in actual applications. In this paper, for a prism-based SPSI, we proposed such an error-correction method that mainly contains the following contributions. First, the intrinsic parameters of the system, including intensity distribution coefficients and relative phase shifts among phase-shifting channels, are calibrated in advance. We also checked the uniformity of phase shifts in each phase-shifting channel. Second, based on the obtained parameters, a corrected four-step phase-shifting algorithm is deduced to recover the more accurate measured phase. Results of both simulation and experiment verify the effectiveness of the proposed method.

Dynamic refractive index distribution measurement of dynamic process by combining dual-channel simultaneous phase-shifting interferometry and total internal reflection

We propose and demonstrate a novel method to measure dynamic refractive index distributions using a combination of total internal reflection (TIR) and dual-channel simultaneous phase-shifting interferometry (DCSPSI). First, a right-angle prism is introduced into the DCSPSI system, the reflection phase variation induced by TIR, which contains the refractive index information of tested sample, can be achieved by the spatial carrier-frequency phase-shifting algorithm from a pair of interferograms with the phase shifts of π/2 captured by DCSPSI system. Second, based on the relationship between the reflection phase variation and the refractive index, the 2D refractive index distribution can be calculated easily. Importantly, the proposed TIR-DCSPSI method will supply a useful tool for dynamic refractive index distribution measurement of dynamic process, such as the droplet evaporation, mutual solubilization and diffusion of different droplets, cell culture, colloid curing, etc.

Simultaneous phase-shifting dual-wavelength interferometry based on independent component analysis.

An independent component analysis-based simultaneous phase-shifting dual-wavelength interferometry approach is proposed. By using a one-time phase-shifting procedure, the simultaneous phase-shifting operation of two illumination wavelengths can be implemented, and then the background intensity and two orthogonal independent components of each single wavelength can be separated from a sequence of simultaneous phase-shifting dual-wavelength interferograms with random phase shifts. Subsequently, the wrapped phases of single wavelength can be calculated by above two orthogonal independent components; thus the unambiguous phase of synthetic wavelength can be achieved. Both the simulation and experimental results show that the proposed approach reveals the advantages of high accuracy, rapid speed, high stability, and good adaptability for arbitrary phase shifts.

Optical image hiding based on dual-channel simultaneous phase-shifting interferometry and compressive sensing

We propose an optical image hiding method based on dual-channel simultaneous phase-shifting interferometry (DCSPSI) and compressive sensing (CS) in all-optical domain. In the DCSPSI architecture, a secret image is firstly embedded in the host image without destroying the original host’s form, and a pair of interferograms with the phase shifts of π/2 is simultaneously generated by the polarization components and captured by two CCDs. Then, the holograms are further compressed sampling to the less data by CS. The proposed strategy will provide a useful solution for the real-time optical image security transmission and largely reducing data volume of interferogram. The experimental result demonstrates the validity and feasibility of the proposed method.

Phase retrieval based on temporal and spatial hybrid matching in simultaneous phase-shifting dual-wavelength interferometry.

In simultaneous phase-shifting dual-wavelength interferometry, by matching both the phase-shifting period number and the fringe number in interferogram of two wavelengths to the integers, the phase with high accuracy can be retrieved through combining the principle component analysis (PCA) and least-squares iterative algorithm (LSIA). First, by using the approximate ratio of two wavelengths, we can match both the temporal phase-shifting period number and the spatial fringe number in interferogram of two wavelengths to the integers. Second, using above temporal and spatial hybrid matching condition, we can achieve accurate phase shifts of single-wavelength of phase-shifting interferograms through using PCA algorithm. Third, using above phase shifts to perform the iterative calculation with the LSIA method, the wrapped phases of single-wavelength can be determined. Both simulation calculation and experimental research demonstrate that by using the temporal and spatial hybrid matching condition, the PCA + LSIA based phase retrieval method possesses significant advantages in accuracy, stability and processing time.

Simultaneous phase-shifting interferometry: immune to azimuth error of fast-axes in retarder array.

Simultaneous phase-shifting interferometry based on a 2×2 retarder array with random fast-axes (RARF-SPSI) is proposed for real-time wavefront measurements. The retarder array is used as the phase-shift component, where the phase retardances are π/2, π, 3π/2, and 2π and the four fast-axes of the four retarders can be somewhat random. In this paper, the mathematical model of RARF-SPSI is built by using a Stokes vector and a Mueller matrix, the phase demodulation method through solving equations is derived, and the coefficient matrix of the equations that is associated with the azimuth of the fast-axes is calculated by Fourier analysis. Then the corresponding simulation analysis is executed. In the experiment, four simultaneous phase-shifting interferograms are captured and the phase distribution under test is demodulated through the proposed method. Compared with the four-bucket phase-shifting algorithm adopted in traditional simultaneous phase-shifting interferometry, the ripple error is suppressed well. The advantage of the proposed RARF-SPSI is that there is no need to calibrate the fast-axes of the phase-shift component before measuring; in other words, the phase demodulation error caused by the azimuth error of fast-axes is eliminated.

Visual measurement of the evaporation process of a sessile droplet by dual-channel simultaneous phase-shifting interferometry.

To perform the visual measurement of the evaporation process of a sessile droplet, a dual-channel simultaneous phase-shifting interferometry (DCSPSI) method is proposed. Based on polarization components to simultaneously generate a pair of orthogonal interferograms with the phase shifts of π/2, the real-time phase of a dynamic process can be retrieved with two-step phase-shifting algorithm. Using this proposed DCSPSI system, the transient mass (TM) of the evaporation process of a sessile droplet with different initial mass were presented through measuring the real-time 3D shape of a droplet. Moreover, the mass flux density (MFD) of the evaporating droplet and its regional distribution were also calculated and analyzed. The experimental results show that the proposed DCSPSI will supply a visual, accurate, noncontact, nondestructive, global tool for the real-time multi-parameter measurement of the droplet evaporation.

Simultaneous phase-shifting dual-wavelength interferometry based on two-step demodulation algorithm.

A simultaneous phase-shifting dual-wavelength interferometry based on two-step demodulation algorithm is proposed in this Letter. First, two lasers with different wavelengths go through the same inline phase-shifting interference system simultaneously, and a sequence of five frames of simultaneous phase-shifting dual-wavelength interferograms (SPSDWIs) with the special phase shifts are captured by a monochrome CCD. Subsequently, using the subtraction between the first SPSDWI and the other SPSDWI, each wavelength of two frames of single-wavelength interference images (SWIIs) without the background can be achieved. Finally, using two-step demodulation algorithm, the wrapped phase of each single-wavelength can be determined easily and quickly with high accuracy.

Spatial mismatch calibration using circular carrier technique in the simultaneous phase shifting interferometry

In most simultaneous phase shifting interferometry (SPSI) systems, a group of phase shifting interferograms are captured simultaneously at the different physical locations to retrieve the phase. The data of different interferograms should be spatially matched correctly, which is hard to realize by existing methods or this spatial mismatch will lead to phase retrieving error. In this paper, a spatial mismatch calibration method is proposed, where the circular carrier is introduced in the interferograms of the SPSI system, and the modulating phases of any two interferograms can be retrieved by the demodulation technique of circular carrier interferogram. The slope of the difference between these two phases is proportional to the mismatch value, so this error can be extracted and the experiment setup calibrated. The main error sources of the proposed method are analyzed with the conclusion that its match precision can be achieved up to 0.5 pixel. In addition, the simulated interferograms and actual interferograms captured in a SPSI system are processed to validate our proposed method.

Single-shot polarization-imaging digital holography based on simultaneous phase-shifting interferometry

We propose single-shot digital holography which is capable of simultaneously capturing both the information of multiple phase-shifted holograms and the distribution of the polarization. In this technique, a single image sensor records both the information required for phase-shifting interferometry and that of the polarization states of objects using an array of polarizers. The essence of the technique is the capability of imaging the distribution of the polarization of three-dimensional objects with a single-shot exposure by using the space-division multiplexing of holograms. The validity of the proposed technique was confirmed by the preliminary experiments.

Confocal simultaneous phase-shifting interferometry

In order to implement the ultraprecise measurement with large range and long working distance in confocal microscopy, confocal simultaneous phase-shifting interferometry (C-SPSI) has been presented. Four channel interference signals, with π/2 phase shift between each other, are detected simultaneously in C-SPSI. The actual surface height is then calculated by combining the optical sectioning with the phase unwrapping in the main cycle of the interference phase response, and the main cycle is determined using the bipolar property of differential confocal microscopy. Experimental results showed that 1 nm of axial depth resolution was achieved for either low- or high-NA objective lenses. The reflectivity disturbance resistibility of C-SPSI was demonstrated by imaging a typical microcircuit specimen. C-SPSI breaks through the restriction of low NA on the axial depth resolution of confocal microscopy effectively.

On-line detecting and controlling conception for time-delay measurement in ultrafast laser pulse pump-probe

A novel optical system for detecting and controlling the time-delay value of probe light in the femtosecond pulse pump-probe measurements is presented based on the simultaneous phase-shifting interferometry scheme. The intensity distributions of interference pattern are calculated based on the Jones theory to optimize the optical system, by which the analytical expressions for phase-shifting length between the neighboring interferograms and the relevant phase-delay value are derived. To meet the requirement of practical application, possible latent errors in the process of detecting time-delay are analyzed. In particular, a minimum time-resolution with attosecond level at 800 nm wavelength was achieved. The results show that this system satisfies the requirement of femtosecond pulse pump-probe high-precision measurement.