Measurement of the M² beam propagation factor using a focus-tunable liquid lens

M2 factor estimation in few-mode fibers based on a shallow neural network

A high-accuracy, high-speed, and low-cost M² factor estimation method for few-mode fibers based on a shallow neural network is presented in this work. Benefiting from the dimensionality reduction technique, which transforms the two-dimension near-field image into a one-dimension vector, a neural network with only two hidden layers can estimate the M² factor directly. In the simulation, the mean estimation error is smaller than 3% even when the mode number increases to 10. The estimation time of 10000 simulation test samples is around 0.16s, which indicates a high potential for real-time applications. The experiment results of 50 samples from the 3-mode fiber have a mean estimation error of 0.86%. The strategies involved in this method can be easily extended to other applications related to laser characterization.

High-speed coherent diffraction imaging by varying curvature of illumination with a focus tunable lens

A high-speed coherent diffraction imaging method is proposed by varying the curvature of illumination with a focus tunable lens. The imaging setup is free of conventional mechanical translation and takes only milliseconds to refocus by changing the electric signal applied on the lens. It is more compact and also an inexpensive alternative to coherent diffraction imaging with computerized translational stages. A detector that is kept at a fixed distance from the sample records diffraction patterns each time the spherical wavefront illuminations on the sample is changed with a control current. The complex wavefront of the object is then quantitatively recovered from the diffraction intensity measurements using an iterative phase retrieval algorithm. The feasibility of the proposed method is experimentally verified using various samples. Extremely short response time of the focus tunable lens makes the proposed method highly suitable for applications that requires high speed imaging.

Optical performance evaluation and chromatic aberration correction of a focus tunable lens used for 3D microscopy

Recently, the development of motion-free 3D microscopy utilizing focus tunable lenses (FTL) has been rapid. However, the downgrade of optical performance due to FTL and its gravity effect are rarely discussed in detail. Also, color dispersion is usually maintained purely depending on the FTL material without further correction. In this manuscript, we provide a quantitative evaluation of the impact of FTL on the optical performance of the microscope. The evaluation is based on both optical ray tracing simulations and lab experiments. In addition, we derive the first order conditions to correct axial color aberration of FTL through its entire power tuning range. Secondary spectrum correction is also possible and an apochromatic motion-free 3D microscope with 2 additional doublets is demonstrated. This study will serve a guidance in utilizing FTL as a motion-free element for 3D microscopy.

Deep learning enabled superfast and accurate M2 evaluation for fiber beams

We introduce deep learning technique to predict the beam propagation factor M² of the laser beams emitting from few-mode fiber for the first time, to the best of our knowledge. The deep convolutional neural network (CNN) is trained with paired data of simulated near-field beam patterns and their calculated M² value, aiming at learning a fast and accurate mapping from the former to the latter. The trained deep CNN can then be utilized to evaluate M² of the fiber beams from single beam patterns. The results of simulated testing samples have shown that our scheme can achieve an averaged prediction error smaller than 2% even when up to 10 eigenmodes are involved in the fiber. The error becomes slightly larger when heavy noises are added into the input beam patterns but still smaller than 2.5%, which further proves the accuracy and robustness of our method. Furthermore, the M² estimation takes only about 5 ms for a prepared beam pattern with one forward pass, which can be adopted for real-time M² determination with only one supporting Charge-Coupled Device (CCD). The experimental results further prove the feasibility of our scheme. Moreover, the method we proposed can be confidently extended to other kinds of beams provided that adequate training samples are accessible. Deep learning paves the way to superfast and accurate M² evaluation with very low experimental efforts.

Fast measurement of the laser beam quality factor based on phase retrieval with a liquid lens

In this paper, a new method for measuring the beam quality (M²) of lasers based on phase retrieval with a liquid lens is proposed. With intensity profiles obtained under different focal lengths in a certain position, a variable-focus iterative retrieval algorithm is established for the reconstruction of the complex amplitude. Then M² can be calculated with the angular spectrum theory. Feasibility of the proposed method is demonstrated with single- and multimode lasers through both simulations and experiments. Compared with the traditional liquid lens method, the M² of lasers can be measured faster with the proposed method.

Regression-based technique for improved optical rangefinding using tunable focus lenses

In this paper, we present a novel method of target range estimation by tuning the spot size of a Gaussian beam at the plane of a reflective target. The beam spot size tuning is achieved through the use of a tunable focus lens (TFL). Using a carefully aligned sensor assembly, the diameter of the reflected beam is recorded at the plane of an imaging detector for different TFL focal length settings. This dataset is then used to estimate the distance of the target from the TFL. The proposed rangefinder is compact and requires minimal post-data-acquisition signal processing resulting in a fast response time compared to other spatial signal processing-based sensor designs. The estimation of target distance through a multiple data-point measurement dataset also ensures that the proposed method is robust to errors associated with obtaining range estimates from a single measurement data point. Experimental results demonstrate an excellent agreement with theory. With our proposed estimation method, we show a significant improvement in the measurement dynamic range of the sensor as well as its resolution compared to similar sensing schemes in prior art. We also experimentally demonstrate the possibility to extend the measurement dynamic range by incorporating a bias lens of a fixed focal length with the sensor module. The proposed sensor module is electronically controlled and consequently can be fully automated and compactly packaged with the use of commercially available miniature optical components.

Suppressing the influence of charge-coupled device vertical blooming on the measurement of laser beam quality factor (M2) of a near-infrared laser

In this paper, a new method, which is based on reconstructing the original intensity distribution of a laser with images captured by a charge-coupled device (CCD) in two orthogonal directions, is proposed for suppressing the influence of CCD vertical blooming on the measurement of the laser beam quality factor (M²). A simplified theoretical model for the distribution of CCD blooming is also proposed. With the proposed method and model, the influence of CCD vertical blooming on the measurement of M² is simulated. The experimental results demonstrate that the new method can be an effective means to measure the M² of a near-infrared laser with a silicon CCD camera. The proposed method can be applied to a beam quality analyzer in order to suppress the influence of blooming on the measurement of M².

Determination of the laser beam quality factor (M2) by stitching quadriwave lateral shearing interferograms with different exposures

A complete complex amplitude reconstruction method for the determination of the laser beam quality factor M² based on the multiple exposure of a quadriwave lateral shearing interferometer (QWLSI) is presented. The theoretical analysis and simulation of the influence of the information in the small signal area on the calculation of the M² factor is provided. The experimental results demonstrate that the new method can be an accurate means to measure the M² factor. The proposed method can avoid the influence of phase inaccuracy in the small signal area of the interferogram, during the measurement of the M² factor.

Real-time complex amplitude reconstruction method for beam quality M2 factor measurement

We present a real-time complex amplitude reconstruction method for determining the beam propagation ratio M² of laser beams based on the transport of intensity equation (TIE). In this work, a synchronous acquisition system consisting of two identical CCDs is established. Once two beam intensity images at different cross-section positions along the optical axis are captured simultaneously by the system, the complex amplitude of the laser beam can be rapidly reconstructed using TIE algorithm. Then the beam intensity distribution at any section position along its propagation direction can be obtained by using angular spectrum (AS) theory. The beam quality M² factor is therefore calculated utilizing the second-order moments and hyperbola fitting methods, which conform to the ISO standard. The suitability of this method is verified by the numerical analysis and experiments with the He-Ne and high-power fiber laser sources, respectively. The experimental technique is simple and fast, which allows to investigate laser beams under conditions inaccessible to other methods.

Robust motion-free and error-correcting method of estimating the focal length of a lens

This paper presents a motion-free technique to characterize the focal length of any spherical convex or concave lens. The measurement test-bench uses a Gaussian laser beam, an electronically controlled variable focus lens (ECVFL), a digital micro-mirror device (DMD), and a standard photo-detector (PD). The method requires measuring beam spot sizes for different focal length settings of the ECVFL and using the measurement data to obtain a focal length estimate through an iterative least-squares-based curve-fitting algorithm. The method is also shown to overcome potential measurement errors that arise due to inaccurate placement of optical components on the test-bench as well as unknown principal plane locations of asymmetric lens samples such as plano-convex lenses. Contrary to the commercially deployed and other proposed methods of focal length characterization, this method does not involve any bulk mechanical motion of optical elements. This approach eliminates measurement errors due to gradual mechanical wear and tear and improves measurement repeatability by minimizing mechanical hysteresis. The compact and fully automated method delivers fast, repeatable, and reliable measurements, which we believe makes it ideal for deployment in industrial lens production units and characterizing lenses used in sensitive imaging systems and various other optical experiments and systems. Measured focal lengths are within the 1% manufacturer-provided tolerance values showing excellent agreement between theory and experiments. We also demonstrate measurement robustness by rectifying discrepancies between known and actual separation distances on the measurement test bench.

Complex amplitude reconstruction for dynamic beam quality M2 factor measurement with self-referencing interferometer wavefront sensor

A real-time complex amplitude reconstruction method for determining the dynamic beam quality M² factor based on a Mach-Zehnder self-referencing interferometer wavefront sensor is developed. By using the proposed complex amplitude reconstruction method, full characterization of the laser beam, including amplitude (intensity profile) and phase information, can be reconstructed from a single interference pattern with the Fourier fringe pattern analysis method in a one-shot measurement. With the reconstructed complex amplitude, the beam fields at any position z along its propagation direction can be obtained by first utilizing the diffraction integral theory. Then the beam quality M² factor of the dynamic beam is calculated according to the specified method of the Standard ISO11146. The feasibility of the proposed method is demonstrated with the theoretical analysis and experiment, including the static and dynamic beam process. The experimental method is simple, fast, and operates without movable parts and is allowed in order to investigate the laser beam in inaccessible conditions using existing methods.

Quantitative measurement of the orbital angular momentum of light with a single, stationary lens

We show that the average orbital angular momentum (OAM) of twisted light can be measured simply and robustly with a single stationary cylindrical lens and a camera. Theoretical motivation is provided, along with self-consistent optical modeling and experimental results. In contrast to qualitative interference techniques for measuring OAM, we quantitatively measure non-integer average OAM in mode superpositions.

Continuously tunable orbital angular momentum generation using a polarization-maintaining fiber

We demonstrate the generation of orbital angular momentum (OAM) in a two-mode polarization-maintaining (PM) optical fiber. We combine two linearly polarized modes of PM fiber to generate linearly polarized optical vortex beams with OAM. The average OAM can be finely varied by changing the phase between modes. We have quantitatively measured the resulting OAM to vary between ±1ℏ per photon while varying the relative phase between the LP_11e- and LP_11o-like fiber modes. The modal purity is 97%.

Simulation, fabrication, and characterization of a tunable electrowetting-based lens with a wedge-shaped PDMS dielectric layer

Microlenses with tunable focal length have wide applications in optofluidic devices. This work presents a numerical and experimental investigation on a tunable electrowetting-based concave lens. Optical properties such as focal length of the lens and visibility of images were investigated numerically and experimentally. A finite element analysis and a ZEMAX simulation were used for determination of surface profile and focal length of the lens. The results show that the theoretical surface profile and focal length of the lens are in good agreement with the experimental ones. The lens has a wide tuning focal length equal to 6.5 (cm). Because the polydimethylsiloxane (PDMS) layer is wedge shaped (as both the dielectric and hydrophobic layers), lower applied voltage is needed. A commercial program was used to find the focal length of the lens from maximum visibility value by tuning the applied voltage.

Scattered light imaging method (SLIM) for characterization of arbitrary laser beam intensity profiles

A laser beam characterization method is reported, which is applicable to arbitrary and ideal laser beam intensity profiles. This method, called the scattered light imaging method (SLIM), is based on scattered light imaging of a laser beam and provides a complete visualization of it in the region of interest. The method was applied to characterize an arbitrary pedestal-shaped beam and compared with a conventional method (camera scanning). The results we presented show that, for arbitrary beams, it seems much more meaningful to know the intensity profile evolution than to determine an M2 value. Therefore the SLIM is a powerful tool for a new and more complete type of laser beam characterization.