We present SLIM, a new optical method measuring optical pathlength changes of 0.3 nm spatially and 0.03nm temporally. SLIM combines two classic ideas in light imaging: Zernike’s phase contrast microscopyand Gabor’s holography.

Spatial light interference microscopy (SLIM)

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Robust phase unwrapping in the presence of high noise remains an open issue. Especially, when both noise and fringe densities are high, pre-filtering may lead to phase dislocations and smoothing that complicate even more unwrapping. In this paper an approach to deal with high noise and to unwrap successfully phase data is proposed. Taking into account influence of noise in wrapped data, a calibration method of the 1st order spatial phase derivative is proposed and an iterative approach is presented. We demonstrate that the proposed method is able to process holographic phase data corrupted by non-Gaussian speckle decorrelation noise. The algorithm is validated by realistic numerical simulations in which the fringe density and noise standard deviation is progressively increased. Comparison with other established algorithms shows that the proposed algorithm exhibits better accuracy and shorter computation time, whereas others may fail to unwrap. The proposed algorithm is applied to phase data from digital holographic metrology and the unwrapped results demonstrate its practical effectiveness. The realistic simulations and experiments demonstrate that the proposed unwrapping algorithm is robust and fast in the presence of strong speckle decorrelation noise.

Phase calibration unwrapping algorithm for phase data corrupted by strong decorrelation speckle noise.

Off-axis holographic multiplexing involves capturing several complex wavefronts, each encoded into off-axis holograms with different interference fringe orientations, simultaneously, with a single camera acquisition. Thus, the multiplexed off-axis hologram can capture several wavefronts at once, where each one encodes different information from the sample, using the same number of pixels typically required for acquiring a single conventional off-axis hologram encoding only one sample wavefront. This gives rise to many possible applications, with focus on acquisition of dynamic samples, with hundreds of scientific papers already published in the last decade. These include field-of-view multiplexing, depth-of-field multiplexing, angular perspective multiplexing for tomographic phase microscopy for 3-D refractive index imaging, multiple wavelength multiplexing for multiwavelength phase unwrapping or for spectroscopy, performing super-resolution holographic imaging with synthetic aperture with simultaneous acquisition, holographic imaging of ultrafast events by encoding different temporal events into the parallel channels using laser pulses, measuring the Jones matrix and the birefringence of the sample from a single multiplexed hologram, and measuring several fluorescent microscopy channels and quantitative phase profiles together, among others. Each of the multiplexing techniques opens new perspectives for applying holography to efficiently measure challenging biological and metrological samples. Furthermore, even if the multiplexing is done digitally, off-axis holographic multiplexing is useful for rapid processing of the wavefront, for holographic compression, and for visualization purposes. Although each of these applications typically requires a different optical system or processing, they all share the same theoretical background. We therefore review the theory, various optical systems, applications, and perspectives of the field of off-axis holographic multiplexing, with the goal of stimulating its further development.

Off-axis digital holographic multiplexing for rapid wavefront acquisition and processing

Two dual-wavelength operation regimes of a diode-pumped Nd:YVO4 laser were demonstrated at 1064.1 & 1073.1 and 1064.1 & 1085.3 nm with two intracavity birefringent plates. The output power ratio of the dual-wavelength output could be freely adjusted. The highest total output power was 1.44 W under the dual-wavelength condition with 1:1 power ratio for both wavelength pairs. The slope efficiency was more than 16% and optical-to-optical efficiency more than 13% with respect to the absorbed pump power.

Dual-wavelength operation of a diode-pumped Nd:YVO 4 laser at the 1064.1 & 1073.1 nm and 1064.1 & 1085.3 nm wavelength pairs

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.

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

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.

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

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.

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

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.

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

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.

Mohammad Reza Jafarfard

Papers

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

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

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

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

Optimum phase shift for quantitative phase microscopy in volume measurement