Behnam Tayebi

Dual-wavelength diffraction phase microscopy for simultaneous measurement of refractive index and thickness

We present a quantitative phase microscopy scheme that simultaneously acquires two phase images at different wavelengths. The simultaneous dual-wavelength measurement was performed with a diffraction phase microscope (DPM) based on a transmission grating and a spatial filter that form a common-path imaging interferometer. With a combined laser source that generates two-color light continuously, a different diffraction order of the grating was utilized for each wavelength component so that the dual-wavelength interference pattern could be distinguished by the distinct fringe frequencies. Our dual-wavelength phase imaging allowed us to extract information on the physical thickness and the refractive index for a specimen immersed in a highly dispersive surrounding medium. We found that our dual-wavelength DPM (DW-DPM) provides an accurate measurement of the volume and the refractive index of a microscopy sample with good measurement stability that results from the common-path geometry.

Reduced-phase dual-illumination interferometer for measuring large stepped objects

We present a reduced-phase dual-illumination interferometer (RPDII) that measures the topography of a sample with large step height variation. We experimentally demonstrate the basic principle and the feasibility of this novel single-shot quantitative phase imaging. Two beams of this interferometer illuminate a sample at different incident angles, and two phases of the different incident angles and their phase difference are simultaneously recorded using three spatial frequencies. The relative phase difference between two beams of an RPDII can be controlled by adjusting the angle such that the maximum phase difference is smaller than 2π, and thus there is no phase wrapping ambiguity in the reconstructed phase. One 4f optical system with a transmission grating is used to illuminate the sample with two collimated beams incident at different angles. The feasibility of this technique is demonstrated by measuring the thicknesses of two stepped metal layers with heights of 150 and 660 μm. Although the change in stepped height is more than 1000 times the wavelength of the laser used in our interferometer, the thicknesses of these two metal layers are successfully obtained without the use of an unwrapping algorithm.

Large step-phase measurement by a reduced-phase triple-illumination interferometer.

We present a reduced-phase triple-illumination interferometer (RPTII) as a novel single-shot technique to increase the precision of dual-illumination optical phase unwrapping techniques. The technique employs two measurement ranges to record both low-precision unwrapped and high-precision wrapped phases. To unwrap the high-precision phase, a hierarchical optical phase unwrapping algorithm is used with the low-precision unwrapped phase. The feasibility of this technique is demonstrated by measuring a stepped object with a height 2100 times greater than the wavelength of the source. The phase is reconstructed without applying any numerical unwrapping algorithms, and its noise level is decreased by a factor of ten.

Optimum phase shift for quantitative phase microscopy in volume measurement.

Volume measurement of a phase object is one of the most distinctive capabilities of quantitative phase microscopy (QPM). However, the accuracy of a measured volume is limited by the different noises of a measurement system and the finite bandpass filter used in the phase extraction algorithm. In this paper, we analyze the inherent errors in volume measurement with QPM and propose the optimum condition that can minimize these errors. We find that phase information of a sample in the frequency domain nonlinearly oscillates as a function of the phase shift corresponding to the sample and its medium, and that the phase information of a sample inside the bandpass filter can be maximized by a proper phase shift. Through numerical simulations and actual experiments, we demonstrate that the error in phase volume measurement can be effectively reduced by the enhancement of the phase signal inside the bandpass region using an optimum amount of phase, which can be controlled by changing either the medium index or the wavelength of illumination.

Double-field-of-view, quasi-common-path interferometer using Fourier domain multiplexing

We present a quasi-common-path interferometer with a double field of view (FOV). The laser beam of an imaging system is separated into three parts using three mirrors; the first and second beams are used to image two different areas of a sample, while the third beam functions as a reference beam. The reference beam is prepared by making clear area in a sample and projecting it on an image sensor. A double FOV is obtained by Fourier domain multiplexing, whereby two interferometric images corresponding to two different areas of a sample are modulated with two different spatial carrier frequencies. The feasibility of this technique is experimentally demonstrated by imaging two different areas of a test target with a single image sensor.

Transparent stepped phase measurement using two illuminating beams

We propose a single shot and single wavelength phase imaging technique for measuring phase of the transparent objects without using unwrapping process. A grating between a laser and the object is used to make beams with different angle, which determines the measurement range of the microscope. The grating pitch and magnification of the lens system before the sample affect the angle. The angle inside the object is changed according to Snell’s law; therefore, final angle is related to the refractive index of the object. Magnification of the lens system after sample will control the modulation frequency of microscope. The interference pattern is constructed at CCD plane and convey information of the sample. For a phase below the measurement range of the microscope, the reconstructed phase is not wrapped. By increasing the measurement range accuracy of the system will drop; therefore the magnification of the lenses must choose carefully to obtain optimal phase. The ability of this technique is demonstrated by reconstructing phases of two transparent step objects with 150 and 510 μm height. Their refractive indexes for red light are 1.515 and 1.508 , respectively. Therefore, total optical path length difference is 336 micrometers that is 500 times more than the laser wavelength. The phase is successfully reconstructed without using unwrapping algorithms.

Dual-wavelength diffraction phase microscopy for real-time dispersion measurement

We present a dual-wavelength diffraction phase microscopy (DW-DPM) that obtains the wavelength-differentiated dual phase images in a single shot of interference fringe acquisition. For this, the diffraction phase microscopy (DPM) system was constructed with a transmission grating and a spatial filter that form a common-path interferometer. With a light source of two spectral components, a different diffraction order of the grating was utilized for each. This resulted in a combined but distinguishable interference pattern to be acquired by a single image sensor. In this research, our dualwavelength phase imaging scheme was applied to simultaneously measure dispersion of a sample. Stable and reliable measurements could be performed in a single shot due to the robust structure of our DW-DPM system.

Compact single-shot four-wavelength quantitative phase microscopy with polarization- and frequency-division demultiplexing

We present a novel single-shot four-wavelength quantitative phase microscopy (FW-QPM). Four lasers operating at different wavelengths are multiplexed with a pair of dichroic mirrors and a polarization beam splitter in a three-mirror quasi-common-path interferometer. After a single-shot interference pattern is obtained with a monochrome camera, four holograms of different wavelengths were demultiplexed from it in the frequency domain with polarization- and frequency-division multiplexing. Polarization-division demultiplexing scheme uses polarization dependent visibility changes in an interference pattern, and it plays a critical role in making only two interference patterns exist within a single quadrant in the frequency domain. We have used a single-mode optical fiber as a phase object sample and demonstrated that a measured single-shot interference pattern can be successfully demultiplexed into four different interferograms of different wavelengths with our proposed scheme.

Dispersion measurement of optical fiber using dual wavelength diffraction phase microscope

Various quantitative phase microscopy (QPM) techniques for noninvasive and quantitative analysis of samples proposed based on imaging interferometry techniques over the last decade [1-4]. A phase image can be obtained with a single set of interference data in some types of phase microscopes such as diffraction phase microscope [5, 6]. They are suitable for studying rapidly varying phenomena with reduced concern for systematic and sample variations that may occur during the acquisition of the raw data. Dispersion measurements of a sample carry more information than refractive index of measurements at a single wavelength [7]. Knowledge of the optical dispersion for phase objects such as optical fibers, biological cells and micro-particles can provide very useful information about their property. In this work, we report on a common-path and dual wavelength quantitative phase microscope that simultaneously acquires two phase images at different wavelengths. The simultaneous dual-wavelength measurement was performed with a diffraction phase microscope based on a transmission grating and a spatial filter that form a common-path imaging interferometer. With a combined laser source that generates two-color light continuously, a different diffraction order of the grating was utilized for each wavelength component so that the dual-wavelength interference pattern could be distinguished by the distinct fringe frequencies. The refractive index profiles of fiber in both wavelengths were measured adequately by our DW-DPM system.

Reduction of phase volume error in off-axis quantitative phase microscopy using optimum phase-shift

We present a method to reduce the inherent errors caused by band-pass filter in off-axis quantitative phase microscopy and propose the optimum condition that can minimize these errors. We found that phase information of a sample in frequency domain nonlinearly oscillates as a function of the phase-shift correspond to the sample and its medium and the phase information of a sample inside the band-pass filter can be maximized by a proper phase-shift. Through numerical simulations and actual experiments, we demonstrate that the error in phase volume measurement can be effectively reduced by the enhancement of phase signal inside band-pass region using an optimum amount of phase that can be controlled by either changing medium index or wavelength of illumination.