Linear-wavenumber swept source based on an acousto-optic device for optical coherence tomography.

Linear-wavenumber swept-source optical coherence tomography (SS-OCT) enables real-time, high-quality OCT imaging by eliminating the need for data resampling, as required in conventional SS-OCT. In this study, we introduced a high-performance linear-wavenumber swept source (k-SS) with a broad scanning range and high output power. The linear k-SS is an acousto-optic-modulator-based external-cavity laser diode analogous to the Littrow configuration. The k-SS exhibits strong linearity in the 1.3 µm region, justified by a high goodness of fit R2 value of 0.9998. Additionally, its scanning range, output power, and linewidth are 120 nm, more than 43 mW, and approximately 1.6 nm, respectively. The sweep rate is 280 Hz after the linear k compensation of the experimental equipment. We demonstrated the effectiveness of the linear k-SS by applying it to measure a sample distribution without k-domain resampling before the Fourier transform. This successful implementation indicates that the linear k-SS has practical potential for application in SS-OCT systems.

External-cavity laser diode using acousto-optic deflector as tunable grating.

In this study, a novel, to the best of our knowledge, external-cavity laser diode (ECLD) without a diffraction grating is proposed and demonstrated. In the proposed configuration, an acousto-optic deflector (AOD) acts not only as a deflector but also as a diffraction grating. Thus, the AOD functions as a wavelength-selective device, which helps improve the overall performance of the ECLD. In fact, the proposed configuration realizes a wide range of wavelength scanning with a simple configuration, highly efficient optical feedback, and a steady optical resonator with a constant cavity length. We confirm that the wavelengths scanned with the proposed ECLD agree well with theoretical calculations. The scanning range and maximum frequency response reached approximately 60 nm and 50 kHz, respectively. Moreover, reproducible measurements of the three-dimensional thickness distribution of a thin glass plate indicates that the proposed ECLD can be used for optical coherence tomography imaging systems.

Measurement of phase refractive index directly from phase distributions detected with a spectrally resolved interferometer.

A phase refractive index is measured directly from an unwrapped spectral phase distribution whose 2π ambiguity is determined by fitting the spectral phase distribution with functions based on Cauchy's equation. The phase refractive index of a quartz glass with 20 µm thickness is measured exactly from three spectral phase distributions detected in two different configurations of a spectrally resolved interferometer. Since there is a high possibility that the 2π ambiguity cannot be correctly determined when there is a large difference between a function of the real refractive index and Cauchy's equation, characteristics of the fitting are examined.

Signal correction by detection of scanning position in a white-light interferometer for exact surface profile measurement.

In order to perform an exact surface profile measurement with a white-light scanning interferometer (WLSI), an actual optical path difference (OPD) changing with time is detected with an additional interferometer in which the light source of the WLSI and an optical band-pass filter are used. This interferometer is simply equipped in the WLSI and does not negatively influence the WLSI. The real OPD is easily calculated from an interference signal with the same signal processing as that in the WLSI. The interference signal of the WLSI is corrected with the real OPD values or the real scanning position values. The corrected interference signal with a constant sampling interval is obtained with an interpolation method. With this correction method, a surface profile with a step shape of 3-µm height is measured accurately with an error less than 2 nm.

Tight focusing properties of a circular partially coherent Gaussian beam.

Tight focusing properties of a circular partially coherent Gaussian (CPCG) beam with linear polarization have been studied based on vectorial Debye theory. Expressions for the intensity distribution and degree of coherence near the focus are derived. Numerical calculations are performed to show the intensity distribution and degree of coherence of the CPCG beam in the focal region. It is interesting to find that after focusing the CPCG beam through a high numerical-aperture objective we can obtain a super-length optical needle (>12λ) with homogeneous intensity along the propagation axis and wavelength beam size (∼λ). Moreover, the numerical calculations of coherence illustrate that, in the range of full width at half-maximum of the optical needle, for any two of the parallel electric field components of the optical needle the coherence is close to 1, but for any two of orthometric electric field components the value of coherence is between 0.4 and 0.9. Such a non-diffracting optical needle may have potential applications in atom optical experiments, such as in atom traps and atom switches.

Topological charge measurement of vortex beams by phase-shifting digital hologram technology.

We propose a direct measurement method that is applicable to both integral and fractional vortex beams. In this approach, the phase distribution of the vortex beam is visualized via the phase-shifting digital holography technique. The least square method is initiatively employed to improve the measurement precision. The maximal error of the experimental results is below 4.8%.

Exact surface profile measurement without subtracting dispersion phase through Fourier transform in a white-light scanning interferometer.

A new signal processing is proposed in which the dispersion phase is not subtracted from the detected spectral phase distribution. The linear and bias components in the spectral phase distribution are used to calculate the complex-valued interference signal (CVIS). The simulations verify that the dispersion phase generates an inclination in the measured surface profile along one direction in which the magnitude of the dispersion phase changes linearly. The simulations also show that the position of zero phase nearest the position of amplitude maximum in the CVIS almost does not change due to the bias component, although the random phase noise contained in the interference signal changes the slope of the linear component. Measured surface profiles show that the new signal processing achieves highly accurate measurement by the CVIS.

Utilization of complex-valued signals in a white-light scanning interferometer for accurate measurement of a surface profile.

Complex-valued interference signals (CVISs) of a white-light scanning interferometer (WLSI) and a spectrally resolved interferometer (SRI) are obtained from their real-valued interference signals through Fourier transform. First the phase distribution in the CVIS of the SRI indicates a dispersion phase caused by two sides of unequal length in a cubic beam splitter, and the magnitude of the dispersion phase changes linearly along a horizontal direction of the beam splitter. Next the dispersion phase with a different magnitude is subtracted from the spectral phase in Fourier transform of the CVIS of the WLSI. Through inverse Fourier transform of this spectral distribution, a dispersion-free CVIS is obtained, and the position of zero phase nearest to the position of amplitude maximum provides a surface profile measured accurately with an error less than 4 nm after 2π corrections, while a position calculated by the linear component of the spectral phase causes measurement error less than 12 nm.

Nonsubsampled contourlet transform method for optical fringe pattern analysis in profilometry and interferometry.

A method based on a nonsubsampled contourlet transform, which is an overcomplete transform with multiresolution, directionality, and shift-invariance properties, is proposed to extract the fundamental frequency component of an optical fringe pattern in profilometry and interferometry. The nonsubsampled contourlet transform method overcomes the disadvantages of the original contourlet transform method, which lacks the shift-invariance property. Besides, it improves the frequency selectivity. A strategy is developed to automatically determine the optimal decomposition scale for removing the background intensity and suppressing the noise of the fringe pattern. The proposed method is precise, effective, and possesses a strong noise immune ability. Simulations and experiments verify the validity, and show the superiorities of the proposed method.

Multifrequency swept common-path en-face OCT for wide-field measurement of interior surface vibrations in thick biological tissues.

Microvibrations that occur in bio-tissues are considered to play pivotal roles in organ function; however techniques for their measurement have remained underdeveloped. To address this issue, in the present study we have developed a novel optical coherence tomography (OCT) method that utilizes multifrequency swept interferometry. The OCT volume data can be acquired by sweeping the multifrequency modes produced by combining a tunable Fabry-Perot filter and an 840 nm super-luminescent diode with a bandwidth of 160 nm. The system employing the wide-field heterodyne method does not require mechanical scanning probes, which are usually incorporated in conventional Doppler OCTs and heterodyne-type interferometers. These arrangements allow obtaining not only 3D tomographic images but also various vibration parameters such as spatial amplitude, phase, and frequency, with high temporal and transverse resolutions over a wide field. Indeed, our OCT achieved the axial resolution of ~2.5 µm when scanning the surface of a glass plate. Moreover, when examining a mechanically resonant multilayered bio-tissue in full-field configuration, we captured 22 nm vibrations of its internal surfaces at 1 kHz by reconstructing temporal phase variations. This so-called "multifrequency swept common-path en-face OCT" can be applied for measuring microdynamics of a variety of biological samples, thus contributing to the progress in life sciences research.

Orthonormal polynomials for annular pupil including a cross-shaped obstruction.

By nonrecursive matrix method using the Zernike circle polynomials as the basis functions, we derived a set of polynomials up to fourth order which is approximately orthonormal for optical systems with an annular pupil having a cross-shaped obstruction. The performance of the polynomials is compared with the strictly orthonormal polynomials with some numerical examples.

Full-range Fourier domain Doppler optical coherence tomography based on sinusoidal phase modulation.

A novel full-range Fourier domain Doppler optical coherence tomography (full-range FD-DOCT) using sinusoidal phase modulation for B-M scan is proposed. In this sinusoidal B-M scan, zero optical path difference (OPD) position does not move corresponding to lateral scanning points in contrast to linear B-M scan. Since high phase sensitivity arises around the zero OPD position, the proposed full-range FD-DOCT can achieve easily high velocity sensitivity without mirror image around the zero OPD position. Velocity sensitivity dependent on the OPD and the interval of scanning points is examined, and flow velocity detection capability is verified through Doppler imaging of a flow phantom and an in vivo biological sample.

Generation of stochastic electromagnetic beams based on modified degenerate cavity lasers.

This study introduces a technique for generating stochastic electromagnetic (SEM) beams using a modified degenerate cavity laser in which one mirror is substituted with a spatial light modulator (SLM). We propose two methods to manipulate the spatial coherence of SEM beams: the first involves adjusting the size of a spatial filter within the laser cavity, which alters the number of oscillating transverse modes and thus varies the spatial coherence. The second method employs phase modulation by applying a dynamic random phase to the SLM. This dual approach allows for precise control over the spatial coherence properties of SEM beams. Experimental results demonstrate the generation of SEM beams using an SLM within a modified degenerate cavity laser and reveal a correlation between two orthogonal polarization components of the beams.

Profile measurement of glass sheet using multiple wavelength backpropagation interferometry.

Multiple-wavelength backpropagation interferometry based on a spectral interferometer is proposed for measuring thin glass sheets with nanometer accuracy. The multiwavelength backpropagation method introduced to the spectral interferometer eliminates time-encoded wavelength sweeping and mechanical scanning, which enables high-speed profile measurements. The applicability of the proposed method is experimentally demonstrated through cross-sectional profile and vibrating surface displacement measurements of a glass sheet.

High spatial resolution zonal wavefront reconstruction with improved initial value determination scheme for lateral shearing interferometry.

In a recent paper [J. Opt. Soc. Am. A 29, 2038 (2012)], we proposed a generalized high spatial resolution zonal wavefront reconstruction method for lateral shearing interferometry. The test wavefront can be reconstructed with high spatial resolution by using linear interpolation on a subgrid for initial values estimation. In the current paper, we utilize the difference between the Zernike polynomial fitting method and linear interpolation in determining the subgrid initial values. The validity of the proposed method is investigated through comparison with the previous high spatial resolution zonal method. Simulation results show that the proposed method is more accurate and more stable to shear ratios compared with the previous method. A comprehensive comparison of the properties of the proposed method, the previous high spatial resolution zonal method, and the modal method is performed.

Use of numerical orthogonal transformation for the Zernike analysis of lateral shearing interferograms.

A numerical orthogonal transformation method for reconstructing a wavefront by use of Zernike polynomials in lateral shearing interferometry is proposed. The difference fronts data in two perpendicular directions are fitted to numerical orthonormal polynomials instead of Zernike polynomials, and then the orthonormal coefficients are used to evaluate the Zernike coefficients of the original wavefront by use of a numerical shear matrix. Due to the fact that the dimensions of the shear matrix are finite, the high-order terms of the original wavefront above a certain order have to be neglected. One of advantages of the proposed method is that the impact of the neglected high-order terms on the outcomes of the lower-order terms can be decreased, which leads to a more accurate reconstruction result. Another advantage is that the proposed method can be applied to reconstruct a wavefront on an aperture of arbitrary shape from its difference fronts. Theoretical analysis and numerical simulations shows that the proposed method is correct and its reconstruction error is obviously smaller than that of Rimmer-Wyant method.

Generalized zonal wavefront reconstruction for high spatial resolution in lateral shearing interferometry.

A new zonal wavefront reconstruction method for lateral shearing interferometry was presented. The proposed algorithm allows shear amounts equal to arbitrary integral multiple of the sample intervals. High spatial resolution reconstruction is achieved with only two difference wavefronts measured in orthogonal shear directions. The presented algorithm was generalized to be applicable for general aperture shape by using zero padding and Gerchberg-type iterative methods. The capability of the presented algorithm was demonstrated by some numerical examples. Also, the reconstruction error was analyzed theoretically and numerically.

Sinusoidal phase-modulating interferometer insensitive to intensity modulation of a laser diode for displacement measurement.

In sinusoidal phase-modulating laser diode interferometers, an injection current of a laser diode is sinusoidally modulated to scan the laser wavelength. However, the modulation of the injection current also involves an intensity modulation of the light, which increases the measurement error if a conventional signal processing is used. A novel signal processing for displacement measurement is proposed to eliminate the influence of the intensity modulation. Numerical simulation results and experimental results make it clear that an optimal depth of the sinusoidal phase modulation exists that can reduce the measurement error to a few nanometers.

Utilization of frequency information in a linear wavenumber-scanning interferometer for profile measurement of a thin film.

The positions of the front and rear surfaces of a silicon dioxide film with 4 µm thickness is measured with a novel and simple method in which both amplitude and phase of a sinusoidal wave signal corresponding to one optical path difference of a reflecting surface is utilized in a linear wavenumber-scanning interferometer. For this utilization, the scanning width and the position of the reference mirror are adjusted exactly to distinguish the two sinusoidal waves corresponding to the two surfaces of the film. The scanning width of the wavenumber and wavelength of the light source are 0.326×10(-3) nm(-1) and 140 nm, respectively.

Phase-shifting laser diode interferometer using pulse modulation.

A phase-shifting laser diode interferometer that uses direct pulse modulation is proposed and demonstrated. We found that a laser beam with a wide range of wavelength variation at constant optical power could be generated when a pulsed current was injected into the laser diode. We constructed a highly accurate interferometer by using a pair of interferometers. Several experiments, such as observations of temporal interference signals and spatial interferograms, measurement of a concave mirror, and duplicate measurements, confirmed the characteristics of pulse modulation and demonstrated the effectiveness of our technique.