Large Optical Path Difference Research Articles

Three-Dimensional Printed Diffraction Gratings Drop Coated by Different Resins and Their Mechanism

Abstract 3D-printed blocks with drop coating could work as diffraction gratings while the layer stepping serves as the grooves of the gratings. This paper reports 3D-printed diffraction gratings coated with different resins. A collimated laser with a wavelength of 520 nm passed through the gratings and generated diffraction patterns. Optical path differences and surface profiles of the samples were measured to analyze the mechanism of the diffraction phenomenon. The as-printed samples had a grating height of about 8 µm induced by layer stepping, which could not generate clear diffraction patterns because of too large optical path difference. After being coated with different resins on the surfaces, the printed samples generated diffraction patterns. We experimentally showed that the magnitude of optical path differences became close to the wavelength of the laser and that the diffraction phenomenon was mainly caused by the difference in the refractive indices between the as-printed part and the drop-coated part. This novel method enables low-cost 3D printers to fabricate diffractive optical elements for visible light.

On-chip monolithic Fourier transform spectrometers assisted by cGAN spectral prediction.

Silicon photonic spatial heterodyne Fourier transform spectrometers (SH-FTSs) are attractive with chip-scale monolithic arrays of imbalanced Mach-Zehnder interferometers; however, there exist optical path difference (OPD) errors from the inevitable fabrication imperfection, which will severely distort the retrieved spectra. In this Letter, we propose that a predictive model can be created for rapid and accurate spectral recovery based on the conditional generative adversarial network (cGAN) featuring strong input-on-output supervision, instead of both complicated physical OPD modification and time-consuming iterative spectral calculation. As a demonstration, cGAN spectral prediction was performed for our previously presented dual-polarized SH-FTS with large OPD errors [Opt. Lett.44, 2923 (2019)OPLEDP0146-959210.1364/OL.44.002923]. Due to the strong noise-resistant capability, the cGAN-predicted spectra can stay reliable, even though the signal-to-noise ratio of acquired interferograms dramatically drops from 1000 to 100, implying a lower limit of detection.

Research Progress on On‐Chip Fourier Transform Spectrometer

AbstractA Fourier transform spectrometer (FTS) is recognized as a highly precise analytical instrument for analyzing the constituent elements of matter in the fields of physics, chemistry, aerospace, and so on. With the emergence and development of miniaturized and portable devices in numerous scientific and technological fields, there has been an urgent need for on‐chip FTSs due to their benefits of small size, portability, low energy consumption, and robustness. However, the small size of on‐chip FTSs hinders the acquisition of a large optical path difference, resulting in a low resolution of the spectrometer. In addition, the sampler spacing is not sufficiently small to satisfy Nyquist's sampling theorem, directly influencing the bandwidth of the spectrometer. Therefore, studies have been performed to investigate the trade‐off between the reduced size and performance of spectrometers. This paper aims to systematically review the progress in on‐chip FTSs, especially in on‐chip static FTSs, including spatially modulated, temporally modulated, and space‐time comodulated FTSs, from the aspects of theories, implementations, and performance indicators. Finally, the paper ends with a discussion of the challenges and a view of the prospective development of this exciting field.

Optimization-based optical diffraction tomography using iODT initialization.

Optical diffraction tomography (ODT) is a label-free and noninvasive technique for biological imaging. However, ODT is only applicable to weakly scattering objects. To extend ODT to the multiple-scattering regime, more advanced inversion algorithms have been developed, including optimization-based ODT (Opti-ODT) and iterative ODT (iODT). In this paper, we propose a combined strategy, namely, an iODT initialization for Opti-ODT, based on the observed complementarity of their individual advantages. This study numerically demonstrates that under this combined strategy, the reconstruction can accurately converge to a better local minimum, especially in the case of multiply scattering objects with large optical path differences.

Modified Sagnac imaging spectropolarimeter for full linear Stokes parameters

A modified Sagnac imaging spectropolarimeter is conceptually described. It consists of a spectral-polarimetric modulator, a modified Sagnac interferometer with large optical path difference, and a CCD camera. This design modulates the Stokes components of the input light into different wave numbers and obtains the modulated interferogram in snapshot mode, and the spectra of the Stokes components can be separated and demodulated from the interferogram. The performance of the system is demonstrated through a numerical simulation, and a novel method is proposed to detect the polarization parameters including the degree of polarization and polarization direction for eliminating the aliasing effects between linear Stokes parameters. Compared with the existing imaging spectrometers, the modified Sagnac imaging spectropolarimeter can acquire one-dimensional spatial information and its full linear spectropolarimetric information in one exposure, and some other spatial information can be obtained by push-broom mode.

Optical Fiber Refractive Index Profiling by Iterative Optical Diffraction Tomography

A non-destructive iterative interferometric tomographic technique is proposed for imaging fibers with high refractive index contrast, complex structures, and/or large optical path differences. Both simulation and experimental results demonstrate that this technique enables the reconstruction of fiber refractive index profiles accurately and robustly with sub-wavelength resolution.

The Influence of Fiber Cross-Section on Fabric Far-Infrared Properties.

Far-infrared radiation (FIR) possesses various promising properties that are beneficial to an individuals’ health. Exploring the interaction between fiber shapes and FIR performance is thought to be a significant means to develop highly-efficient FIR textile products. In this study, a non-additive triangular polyamide (PA) fiber showed excellent FIR properties in both theoretical simulation and experimental verification aspects. The triangular PA fiber affords a higher probability to facilitate large optical path difference, improving both FIR absorption and emission. Textiles woven with the specific triangular PA fiber achieved a remarkable emissivity of 91.85% and temperature difference of 2.11 Celsius, which is obviously superior to the reference circular fiber (86.72%, 1.52 Celsius). Considering the low cost, environmental stability, facile fabrication, as well as being environmentally friendly, this non-additive triangular PA fiber has great potential for high-performance and cost-effective FIR textiles in the future.

Design of a large aperture tunable refractive Fresnel liquid crystal lens.

A large aperture tunable lens based on liquid crystals, which is considered for near-to-eye applications, is designed, built, and characterized. Large liquid crystal lenses with high quality are limited by very slow switching speeds due to the large optical path difference (OPD) required. To reduce the switching time of the lens, the thickness is controlled through the application of several phase resets, similar to the design of a Fresnel lens. A main point of the paper is the design of the Fresnel structure to have a minimal effect on the image quality. Our modeling and experimental results demonstrate that minimal image degradation due to the phase resets is observable when the segment spacing is chosen by taking into account human eye resolution. Such lenses have applications related to presbyopia and, in virtual reality systems, to solve the well-known issue of accommodation-convergence mismatch.

A novel Sagnac imaging polarization spectrometer

A novel Sagnac imaging polarization spectrometer based on a modified Sagnac interferometer (MSI) with a moving wedge prism is proposed in this paper, and it is a framing instrument with the advantages of miniaturization, variable optical path difference (OPD) and large field of view. The construction and split-beam principle of the system are described detailedly, and the exact expressions of the OPD and lateral displacement changing with different parameters are obtained. The variations of the OPD and lateral displacement as a function of the wedge angle and moving displacement are simulated, and the influences of the wedge angle on the OPD and lateral displacement are very small, while most effects come from the moving displacement. In order to obtain a larger OPD and lateral displacement, the wedge angle is controlled in a range of [45°,50°]. In addition, the influences of the dispersion effect of the glass plate on the OPD and lateral displacement are analyzed and discussed, and the suitable material choice for the MSI can reduce the influence of the dispersion effect on the OPD, which also allows the system construction spanning the spectral range of [480nm, 960nm]. In comparison with the conventional Sagnac interferometer with a large optical path difference (LOPDSI), the spectral resolution of the MSI can be made much higher if choosing suitable parameters. This study provides a theoretical and practical guidance for the design and engineering of the Sagnac imaging polarization spectrometer.

Optical path squeezing interferometry: boosting the resolution for Fourier transform imaging spectrometers.

We present an optical path squeezing interferometer dedicated to high-spectral-resolution Fourier transform imaging spectrometry. By incorporating a pair of gratings into a Sagnac interferometer, the short-wavelength light has a larger optical path difference (OPD) than the long-wavelength light. Interference fringes with different OPDs are squeezed into the same sampling window in data acquisition. As a result, the spectral resolution is greatly enhanced without large OPD scanning. The experimental results demonstrate that the proposed method is a promising technology for high-resolution spectral imaging.

WINDII on UARS in the context of SCISAT and Odin

The fundamental elements of the atmosphere are its energy input, composition, temperature and dynamics. Of these the dynamics have had the least observational investigation because of the difficulty of the measurement of winds through optical remote sensing. This article reviews one approach to this topic, the application of the Doppler Michelson Interferometer, focusing on one particular instrument, the Wind Imaging Interferometer (WINDII) flown on NASA׳s Upper Atmosphere Research Satellite (UARS) from 1991 to 2003. With this concept, the wind is measured through the phase shifts of a single fringe from a Michelson interferometer set to an appropriately large optical path difference, determined by phase stepping over that fringe. This configuration allows the implementation of field-widening, allowing the measurements to be made over a wide field, providing wind images extending from roughly 80km to 300km altitude. The Doppler target is the day and night airglow of the upper atmosphere, whose emission rates provide valuable information about the composition of the atmosphere and whose wavelength shifts provide the Doppler information. The primary result, not fully predicted, was the observation of the influence of the dynamics on the composition of the atmosphere. This review provides a minimal instrumentation description, but adequate references, and concentrates on the larger picture of how these data contribute to understanding the interactions of composition, temperature and dynamics, in the context of the SCISAT and Odin measurements. Some new results presented indicate future directions, yet to be explored in full.

The mechanical and thermal setup of the GLORIA spectrometer

Abstract. The novel airborne Gimballed Limb Observer for Radiance Imaging of the Atmosphere (GLORIA) measures infrared emission of atmospheric trace constituents. GLORIA comprises a cooled imaging Fourier transform spectrometer, which is operated in unpressurized aircraft compartments at ambient temperature. The whole spectrometer is pointed by the gimbal towards the atmospheric target. In order to reach the required sensitivity for atmospheric emission measurements, the spectrometer optics needs to operate at a temperature below 220 K. A lightweight and compact design is mandatory due to limited space and high agility requirements. The cooled optical system needs to withstand high pressure and temperature gradients, humidity, and vibrations. A new cooling system based on carbon dioxide and liquid nitrogen combined with high-performance insulation has been developed to meet the mechanical, thermal, and logistical demands. The challenging mechanical and spatial requirements lead to the development of a novel rigid linear slide design in order to achieve the large optical path difference for high spectral resolution. This paper describes the mechanical and thermal setup of GLORIA and presents the performance results on two different research aircrafts.

Modulation transfer function of a modified spatially modulated imaging interferometer

The modulation transfer function (MTF) is one of the main criteria for judging the image quality of an imaging system. Together with the well-known optical transfer function, the MTF can be regarded as an objective basis reflecting the comprehensive performance of an imaging interferometer. In order to improve the imaging quality of a modified spatially modulated imaging interferometer (MSMII) with large optical path difference, the boundary conditions of an incident ray, at full field of view, along the x and y directions, respectively, are first calculated by the method of prism expansion, and then the exact expression of the pupil function of the MSMII is given. The two-dimensional MTF of the MSMII is obtained by the Fourier transform. Compared with previous studies, this work gives the two-dimensional MTF for the MSMII, and analyzes the effects of various parameters on the MTF. The optimal values of the incident angle i together with the acute angels and are chosen as and , respectively. If so, a high MTF is obtained, i.e. the imaging quality of the MSMII can satisfy the need of detecting upper atmospheric wind fields.

Optical path difference and lateral displacement of Sagnac lateral shearing interferometer

The basic principle of the Sagnac lateral shearing interferometer with a large optical path difference (OPD) is explained. Using the method of prism expansion, the exact expressions of the OPD and the lateral displacement as a function of different parameters are obtained. In order to analyze and discuss the influences of the incident angle, , the angle between the incident plane and the bottom plane of the Sagnac lateral shearing interferometer, along with the acute angles and on the OPD and the lateral displacement, computer simulations were carried out. To ensure a large OPD and lateral displacement, the incident angle is controlled in the range while the angle has minimal impact on the OPD and the lateral displacement. Moreover, if the relative error of the OPD is required to be less than 2%, the deviations of and relative to the ideal situation () must be in the ranges and , respectively. The result provides a theoretical and practical guidance for improving the spectral resolution of the Sagnac lateral shearing interferometer together with its engineering realization.

Optical throughput of the Sagnac interferometer with a modified large optical path difference

The basic principle of Sagnac interferometer with modified large optical path difference is expounded on in this paper. According to the Fresnel formula, electromagnetic field energy, and energy flux, the transmittance and reflectance of each interface of a Sagnac interferometer are calculated, respectively, and then the exact expressions of the optical throughput changing with the incident angle, the angle of the incident plane, and paper plane (the bottom plane of Sagnac interferometer) and Sagnac interferometer acute angles are given. Furthermore, we analyze the effects of various parameters on the optical throughput by computer simulation, and some important conclusions are obtained. This work is of great scientific significance to the static, real-time simultaneous detection of upper atmospheric wind field.

Exact calculation of the minimal thickness of the large optical path difference wind imaging interferometer

This paper gives the relation between spatial ray and its projection on paper plane based on the vector form of reflective law. Using the method of prism expansion, it obtains the exact expression of the exit height. The exit height can ensure that the incident rays, at arbitrary direction and arbitrary angle, after several transmission and reflection in the two right-angle reflectors, finally pass through the exit surface. Furthermore, it analyses the effects of different parameters on the exit height through computer simulation, and some important conclusions are obtained. The physical meaning of the sign of exit height is described, and the exact expression of the minimal thickness of the large optical path difference wind imaging interferometer is gained. This work is of great scientific significance to the static, realtime simultaneous detection of atmospheric wind field, and it will provide a theoretical and practical guidance for the miniaturization design and engineering realization of wind imaging interferometer.

Attenuation of mirror image and enhancement of the signal-to-noise ratio in a Talbot bands optical coherence tomography system

A Fourier domain optical coherence tomography setup is presented built around an optical configuration that exhibits Talbot bands. A low astigmatism spectrometer is used, employing a spherical mirror and a cylindrical lens between a diffraction grating and a linear CCD camera. To produce Talbot bands, the two interferometer beams--object and reference--are laterally shifted in respect to each other in their way toward the diffraction grating. This allows attenuation of mirror terms and optimization of the sensitivity profile. We evaluate the optimization of the sensitivity profile with depth, in respect to its overall strength and its position peak, which can be shifted toward a larger optical path difference in the interferometer. We demonstrate the efficiency of such a configuration at large depths by imaging a thick phantom and human skin in vivo for different values of the lateral distance between the two beams.

An interferometric method for determining the mean refractive indices of highly birefringent fibres

An interferometric method with its mathematical derivation is suggested to determine the mean refractive indices and birefringence of highly birefringent fibres using multiple-beam Fizeau fringes in transmission. The application of this method depends on measuring the cross-sectional area of the fibre and the area enclosed under the fringe shift. It is very difficult to measure the area enclosed under the fringe shift in case of highly birefringent fibres, as these fibres have a relatively large optical path difference and a bad connection with the surrounding medium fringe. This difficulty is solved using the suggested method. Poly(aryel ether ether ketone) (PEEK) and poly(ethylene 2,6-naphthalene-dicarboxylate) (PEN) were used as applied examples of highly birefringent fibres for the suggested method. The refractive indices and birefringence of polypropylene fibre with draw ratio 4 are determined using the suggested and conventional methods. The results of the two methods are compared and it is found to be in agreement with the previously published data. The diffraction of He–Ne laser beam was used to determine the mean value of cross-sectional areas of fibres. Microinterferograms and tables are given for illustrations.

Principle of the moving-mirror-pair interferometer and the tilt tolerance of the double moving mirror

A novel type of interferometer, the moving-mirror-pair interferometer, is presented, and its principle and properties are studied. The new interferometer is built with three flat mirrors, which include two flat moving mirrors fixed as a single moving part by a rigid structure and one flat fixed mirror. The optical path difference (OPD) is obtained by the straight reciprocating motion of the double moving mirror, and the OPD value is four times the physical shift value of the double moving mirror. The tilt tolerance of the double moving mirror of the novel interferometer is systematically analyzed by means of modulation depth and phase error. Where the square aperture is concerned, the formulas of the tilt tolerance were derived. Due to the novel interferometer's large OPD value and low cost, it is very applicable to the high-spectral-resolution Fourier-transform spectrometers for any wavenumber region from the far infrared to the ultraviolet.

An electromagnetically driven lamellar grating based Fourier transform microspectrometer

A lamellar grating based Fourier transform micro-spectrometer is presented in this paper in which an electromagnetic actuator is used to drive the mobile facets of the lamellar grating to move bi-directionally. This configuration allows double-sided interferograms to be recorded, thus avoiding problems associated with zero optical path difference (OPD) identification and at the same time satisfying the requirements for large OPD scans. Based on the experimental results, a large deflection of ±62.5 µm is achieved when the electromagnetic microactuator is driven by a current of ±129 mA. To demonstrate the system performance, the spectrum of the combined light beam of a He–Ne laser and a diode-pumped solid-state (DPSS) laser was measured. The two different wavelength components introduced were distinguished with a full width at half maximum (FWHM) spectral resolution around 3.8 nm at 632.8 nm and 3.44 nm at 532 nm.