Synthetic Wavelength Research Articles

Line-scan phase-resolved synthetic wavelength LiDAR using an off-axis holographic approach.

We demonstrate a novel, to our knowledge, approach for phase-resolved coherent 3D surface imaging that utilizes synthetic wavelength phase-based ranging and line-scan off-axis holography. Our proof-of-concept system employs an akinetic tunable laser to perform fast wavelength switching and a galvanometer mirror for slow-axis mechanical scanning. Quantitative depth measurements of an anodized aluminum plate and 3D-printed depth calibration targets and a printed circuit board are demonstrated. Analyses of both shot-noise limited system performance and speckle noise are also presented. The proof-of-concept system achieves micron-scale depth precision with a FOV of 12.8 mm × 34 mm and a 50 ms image acquisition time.

Impact of Cyclic Error on Absolute Distance Measurement Based on Optical Frequency Combs.

Absolute distance measurements based on optical frequency combs (OFCs) have greatly promoted advances in both science and technology, owing to the high precision, large non-ambiguity range (NAR), and a high update rate. However, cyclic error, which is extremely difficult to eliminate, reduces the linearity of measurement results. In this study, we quantitatively investigated the impact of cyclic error on absolute distance measurement using OFCs based on two types of interferometry: synthetic wavelength interferometry and single-wavelength interferometry. The numerical calculations indicate that selecting a suitable reference path length can minimize the impact of cyclic error when combining the two types of interferometry. Recommendations for selecting an appropriate synthetic wavelength to address the tradeoff between achieving a large NAR and minimizing the risk of failure when combining the two methods are provided. The results of this study are applicable not only in absolute distance measurements but also in other applications based on OFCs, such as surface profile, vibration analysis, etc.

Single-shot synthetic wavelength imaging: Sub-mm precision ToF sensing with conventional CMOS sensors

We present a novel single-shot interferometric ToF camera targeted for precise 3D measurements of dynamic objects. The camera concept is based on Synthetic Wavelength Interferometry, a technique that allows retrieval of depth maps of objects with optically rough surfaces at submillimeter depth precision. In contrast to conventional ToF cameras, our device uses only off-the-shelf CCD/CMOS detectors and works at their native chip resolution (as of today, theoretically up to 20 Mp and beyond). Moreover, we can obtain a full 3D model of the object in single-shot, meaning that no temporal sequence of exposures or temporal illumination modulation (such as amplitude or frequency modulation) is necessary, which makes our camera robust against object motion.In this paper, we introduce the novel camera concept and show the first measurements that demonstrate the capabilities of our system. We present 3D measurements of small (cm-sized) objects with > 2 Mp point cloud resolution (the native pixel resolution of our used detector) and up to sub-mm depth precision. We also report a “single-shot 3D video” acquisition and a first single-shot “Non-Line-of-Sight” measurement. Our technique has great potential for high-precision applications with dynamic object movement, e.g., in AR/VR, industrial inspection, medical imaging, and imaging through scattering media like fog or human tissue.

Multi-wavelength pinhole point diffraction interferometry for optics metrology with interferometric intensity based phase retrieval method

In this paper, we propose a multi-wavelength pinhole point diffraction interferometry (MPPDI) and a two-step phase extraction method based on the interferometric intensity information. MPPDI is mainly used to extend the dynamic measurement range of traditional pinhole point diffraction interferometry (PPDI) to realize the measurement of large-aperture and high-order aspheric surface. Spherical/aspherical optics will be test under three different wavelengths, and the corresponding interferograms are recoded by 3CMOS detector at the same moment. By combining different wavelengths, MPPDI can obtain a synthetic wavelength with a larger measuring range and greater flexibility. In interferometry, the choice of the wavelength of the light source has a great influence on the measurement range and accuracy. In MPPDI, we can choose different wavelength combinations to select the most suitable synthetic wavelength according to the asphericity of the tested mirror. To enhance efficiency and reduce the impact of air disturbances during phase shifts, we propose a new phase extraction method based on interferometric intensity to interpret the phase map of surface information. The background intensity of diffraction wavefront is firstly pre-recorded by 3CMOS, then phase-shift interferograms of test mirror is acquired with two-step piezoelectric ceramic driver (PZT) movement. From the analysis, it can be found that fringe modulation has tiny influence on the interferograms intensity. Therefore, based on global intensity distribution of fringe pattern and grayscale information, phase map can be retrieval using proposed two-step processing method (only single phase-shift). The two-step phase extraction method can reduce the number of phase shifts from 9 to 3, which improves the efficiency and reduces errors due to multiple phase shifts. MPPDI and two-step phase extraction we proposed have a larger measurement while reducing the number of phase shifts and avoiding error accumulation due to too many phase shifts. Suitable for large-aperture and high-order aspheric surface measurement.

Phase Unwrapping Based on Large Dynamic Range Synthetic Wavelength for Phase-Sensitive SD-OCT

Phase Unwrapping Based on Large Dynamic Range Synthetic Wavelength for Phase-Sensitive SD-OCT

Towards Mixed-State Coded Diffraction Imaging.

Coherent diffraction imaging (CDI) is a computational technique for reconstructing a complex-valued optical field from an intensity measurement. The approach is to illuminate an object with a coherent beam of light to form a diffraction pattern, and use a phase retrieval algorithm to reconstruct the object's complex transmittance from the measurement. However, as the name implies, conventional CDI assumes highly coherent illumination. Recent works therefore extend CDI to account for partial coherence and imperfect detection, by modeling light as an incoherent mixture of multiple fields (e.g., multiple wavelengths) and recovering each field simultaneously. In this work, we make strides towards the practical implementation and usage of multi-wavelength diffraction imaging. In particular, we provide novel analysis of the noise characteristics of multi-wavelength diffraction imaging, and show that it is preferable to coherent diffraction imaging under high signal-independent noise. Additionally, we present a compact coded diffraction imaging system and corresponding phase retrieval algorithms to robustly and simultaneously recover complex fields representing multiple wavelengths. Using a novel mixed-norm color prior, our prototype system reconstructs a larger number of multi-wavelength fields from fewer measurements than existing methods, and supports applications such as micron-scale optical path difference measurement via synthetic wavelength holography.

Phase space analysis of two-wavelength interferometry.

Multiple wavelength phase shifting interferometry is widely used to extend the unambiguous range (UR) beyond that of a single wavelength. Towards this end, many algorithms have been developed to calculate the optical path difference (OPD) from the phase measurements of multiple wavelengths. These algorithms fail when phase error exceeds a specific threshold. In this paper, we examine this failure condition. We introduce a "phase-space" view of multi-wavelength algorithms and demonstrate how this view may be used to understand an algorithm's robustness to phase measurement error. In particular, we show that the robustness of the synthetic wavelength algorithm deteriorates near the edges of its UR. We show that the robustness of de Groot's extended range algorithm [Appl. Opt.33, 5948 (1994)APOPAI0003-693510.1364/AO.33.005948] depends on both wavelength and OPD in a non-trivial manner. Further, we demonstrate that the algorithm developed by Houairi and Cassaing (HC) [J. Opt. Soc. Am. A26, 2503 (2009)JOAOD60740-323210.1364/JOSAA.26.002503] results in uniform robustness across the entire UR. Finally, we explore the effect that wavelength error has on the robustness of the HC algorithm.

Six-pack holography for dynamic profiling of thick and extended objects by simultaneous three-wavelength phase unwrapping with doubled field of view

Dynamic holographic profiling of thick samples is limited due to the reduced field of view (FOV) of off-axis holography. We present an improved six-pack holography system for the simultaneous acquisition of six complex wavefronts in a single camera exposure from two fields of view (FOVs) and three wavelengths, for quantitative phase unwrapping of thick and extended transparent objects. By dynamically generating three synthetic wavelength quantitative phase maps for each of the two FOVs, with the longest wavelength being 6207 nm, hierarchical phase unwrapping can be used to reduce noise while maintaining the improvements in the 2π phase ambiguity due to the longer synthetic wavelength. The system was tested on a 7 μm tall PDMS microchannel and is shown to produce quantitative phase maps with 96% accuracy, while the hierarchical unwrapping reduces noise by 93%. A monolayer of live onion epidermal tissue was also successfully scanned, demonstrating the potential of the system to dynamically decrease scanning time of optically thick and extended samples.

Interval-locked dual-frequency φ-OFDR with an enhanced strain dynamic range and a long-term stability.

We report on an interval-locked dual-frequency phase-sensitive optical frequency-domain reflectometry relying on a common-reference optical phase-locked loop. With a shared unbalanced interferometry, this design allows for synchronizing the frequency drift of two lasers, leading to a steadily stabilized dual frequency with an arbitrary interval. Equivalently to a longer synthetic wavelength, their phase difference is utilized to demodulate the ambient changes of interest with an enhanced dynamic range and long-term stability. With a stabilized interval of 1 THz, it allows for an enhancement in a strain measurement range of up to 193-fold in theory. Demonstration in terms of distributed strain sensing covering a distance of 500 m with a 10 cm spatial resolution has been verified, showing a significant extension in the achievable strain dynamic range with a preserved sensitivity over 1 h.

Simultaneous dual-wavelength digital holographic microscopy as a tool for the analysis of keratoacanthoma skin samples

A keratoacanthoma (KA) skin tumor is usually caused by sun exposure and may be an alert sign prior to the development of a more aggressive tumor or skin cancer. Studying the shape of the KA cells and their 3D rendering visualization are important parameters to prevent its evolution to higher stages of tumor cells or skin cancer. KA cells shape can be obtained through digital holographic microscopy; for that purpose, a setup with two illumination wavelengths (532 and 638 nm) is implemented to render a synthetic wavelength of 3.2 μm that avoids wrapping the optical phase of the processed holograms and increases measurement range. To recover the optical phase, two off-axis digital holograms are simultaneously recorded at each wavelength. From the processed hologram height variations, the shape and length of KA cells, as well as the stratum corneum epidermal layer, are obtained as phase images. The results achieved aid to discriminate healthy from malignant cells.

Micrometer-precision absolute distance measurement with a repetition-rate-locked soliton microcomb.

The soliton microcomb has sparked interest in high-precision distance measurement, owing to its ultrahigh repetition rate and chip-integrated scale. We report absolute distance measurements based on synthetic wavelength interferometry with a soliton microcomb. We stabilized the repetition rate of 48.98 GHz through injection locking, with fluctuations below 0.25 Hz. Distance measurements up to 64 mm were demonstrated, presenting residuals below 2.7 μm compared with a referenced laser interferometer. Long-term distance measurements were made at two fixed positions of approximately 0.2 m and 1.4 m, resulting in a minimum Allan deviation as low as 56.2 nm at an average time of 0.05 s. The dynamic demonstration illustrated that the proposed system could track round-trip motion of 3 mm at speeds up to 100 mm/s. The proposed distance measurement system is, to our knowledge, the first microcomb-based synthetic wavelength interferometer and achieves a ranging precision of tens of nanometers, with potential applications in the fields of satellite formation flying, high-end manufacturing, and micro-nano processing.

Phase-Locked Synthetic Wavelength Interferometer Using a Femtosecond Laser for Absolute Distance Measurement without Cyclic Error.

We present a phase-locked synthetic wavelength interferometer that enables a complete elimination of cyclic errors in absolute distance measurements. With this method, the phase difference between the reference and measurement paths is fed back into a phase lock-in system, which is then used to control the synthetic wavelength and set the phase difference to zero using an external cavity acousto-optic modulator. We validated the cyclic error removal of the proposed phase-locked method by comparing it with the conventional phase-measuring method of the synthetic wavelength interferometer. By analyzing the locked error signal, we achieved a precision of 0.6 mrad in phase without any observed cyclic errors.

Nanometer-precision surface metrology of millimeter-sized stepped objects using full-cascade-linked synthetic-wavelength digital holography using a line-by-line full-mode-extracted optical frequency comb.

Digital holography (DH) is a powerful tool for the surface profilometry of objects with sub-wavelength precision. In this article, we demonstrate full-cascade-linked synthetic-wavelength DH for nanometer-precision surface metrology of millimeter-sized stepped objects. 300 modes of optical frequency comb (OFC) with different wavelengths are sequentially extracted at a step of mode spacing from a 10GHz-spacing, 3.72THz-spanning electro-optic modulator OFC. The resulting 299 synthetic wavelengths and a single optical wavelength are used to generate a fine-step wide-range cascade link covering within a wavelength range of 1.54 µm to 29.7 mm. We determine the sub-millimeter and millimeter step differences with axial uncertainty of 6.1 nm within the maximum axial range of 14.85 mm.

The phase range extension and accuracy improvement in Fresnel biprism-based digital holography microscopy

We report a highly stable and affordable dual-wavelength digital holographic microscopy system based on common-path geometry. A Fresnel biprism is used to create an off-axis geometry, and two diode laser sources with different wavelengths λ1 = 532nm and λ2 = 650nm generate the dual-wavelength compound hologram. In order to extend the measurement range, the phase distribution is obtained using a synthetic wavelength Λ1 = 2930.5nm. Furthermore, to improve the system's temporal stability and reduce speckle noise, a shorter wavelength (Λ2 = 292.5nm) is used. The feasibility of the proposed configuration is validated by the experimental results obtained with Molybdenum trioxide, Paramecium, and red blood cell specimens.

Multi-heterodyne interferometric absolute distance measurements based on dual dynamic electro-optic frequency combs.

In multi-heterodyne interferometry, the non-ambiguous range (NAR) and measurement accuracy are limited by the generation of synthetic wavelengths. In this paper, we propose a multi-heterodyne interferometric absolute distance measurement based on dual dynamic electro-optic frequency combs (EOCs) to realize high-accuracy distance measurement with large scale. The modulation frequencies of the EOCs are synchronously and quickly controlled to perform dynamic frequency hopping with the same frequency variation. Therefore, variable synthetic wavelengths range from tens of kilometer to millimeter can be flexibly constructed, and traced to an atomic frequency standard. Besides, a phase-parallel demodulation method of multi-heterodyne interference signal is implemented based on FPGA. Experimental setup was constructed and absolute distance measurements were performed. Comparison experiments with He-Ne interferometers demonstrate an agreement within 8.6 µm for a range up to 45 m, with a standard deviation of 0.8 µm and a resolution better than 2 µm at 45 m. The proposed method can provide sufficient precision with large scale for many science and industrial applications, such as precision equipment manufacturing, space mission, length metrology.

Advances of Research on Dual-Frequency Solid-State Lasers for Synthetic-Wave Absolute-Distance Interferometry.

Frequency-difference-stabilized dual-frequency solid-state lasers with tunable and large frequency difference have become an ideal light source for the high-accuracy absolute-distance interferometric system due to their stable multistage synthetic wavelengths. In this work, the advances in research on oscillation principles and key technologies of the different kinds of dual-frequency solid-state lasers are reviewed, including birefringent dual-frequency solid-state lasers, biaxial and two-cavity dual-frequency solid-state lasers. The system composition, operating principle, and some main experimental results are briefly introduced. Several typical frequency-difference stabilizing systems for dual-frequency solid-state lasers are introduced and analyzed. The main development trends of research on dual-frequency solid-state lasers are predicted.

Synthetic wavelength scanning interferometry for 3D surface profilometry with extended range of height measurement using multi-colour LED light sources

We report three-dimensional surface profilometry with extended range of height measurements using synthetic wavelength scanning interferometry without tunable filters, wavelength-tuning lasers, grating elements. We have used inexpensive multiple colour light emitting diodes (LEDs) and operate them sequentially one by one or combination of two or more colours simultaneously to visualize synthetic wavelength light source. Multiple colour LED light source was synthesized and entire visible range from violet to deep red colour was covered. A wide range of synthetic wavelengths were obtained. Five step phase shifting algorithm was used to recover phase maps with Mirau type interferometer which can be further utilized for 3D height measurements. A simple phase subtraction method was used to reconstruct the phase map at synthetic wavelength. The present system provides extended range of height measurements from sub-wavelength to tens of wavelengths. Experimental results of 3D-surface profile measurements of Si-IC chip and standard step object are presented.

Two-wavelength digital holography through fog

Interferometric detection enables the acquisition of the amplitude and phase of the optical field. By making use of the synthetic wavelength as a computational construct arising from digital processing of two off-axis digital holograms, it is possible to identify the shape of an object obscured by fog and further increase the imaging range due to the increased sensitivity in coherent detection. Experiments have been conducted inside a 27 m long fog tube filled with ultrasonically generated fog. We show the improved capabilities of synthetic phase imaging through fog and compare this technique with conventional active laser illumination imaging.

Quantitative phase reconstruction method based on an infrared-like single wave conversion in dual-wavelength phase-shift digital holography

Dual-wavelength digital holography has recently become a promising tool for achieving higher axial measurement ranges in microscopy. However, digital filtering, such as Fourier transform, or a separate hologram acquisition process is essential for retrieving the quantitative phase information of each respective wavelength. In this paper, a quantitative phase reconstruction method based on an infrared-like single wave conversion in dual-wavelength phase-shift digital holography, which does not require any of the processes mentioned above, has been proposed. Based on the proposed method, the quantitative phase information on the axial measurement specimen was simply obtained by only a phase-shift of a quarter of an infrared-like single wave which has the same magnitude of the synthetic wavelength. This approach simplifies not only the hologram acquisition process but also the numerical reconstruction process. The newly proposed theory is verified and evaluated using simulations and experimental validation.

Binocular phase retrieval based on the transport of intensity equation under multiwavelength illumination

In view of the limitation that the transport of intensity equation method can only be used at a single wavelength, we propose a binocular phase retrieval algorithm based on multiwavelength illumination. First, we solve for the corresponding single-phase results at different wavelengths and then calculate the surface height of the object by combining the obtained synthetic wavelengths and synthetic phases, in order to reconstruct the initial phase results at different wavelengths. To solve the problem of amplification of traditional noise and surface profile noise in the phase diagram in the phase synthesis step, we introduce a step-by-step noise reduction method that can reduce the noise in the initial phase results to the level for a single wavelength and finally obtain the corresponding high-precision phase results at different wavelengths. The intensity images collected by the proposed dual-microscope system verify the correctness and effectiveness of the algorithm.