Physical Optics Propagation Research Articles

Arbitrary wavefront uncertainty evaluation for the Shack–Hartmann wavefront sensor using physical optics propagation

The Shack–Hartmann wavefront sensor (SHWS) is a common option to characterize optical fields, due to its noninterference, high accuracy, and high-speed advantages. However, the current methods for evaluating measurement accuracy can only work for predefined standard wavefronts and cannot provide the error estimate for an arbitrary wavefront. Here, we propose an SHWS uncertainty evaluation approach for specific wavefronts based on the physical optics propagation. Our approach constructs a comprehensive SHWS model that incorporates twelve error sources. We analyzed the influence of different error sources on the measurement accuracy under the diffraction effect and reported that our model could achieve an accuracy of λ/559 under the ideal condition. In the experiment, we measured three different wavefronts and confined their uncertainty down to λ/65, λ/260, and λ/40, respectively. Our work may offer an effective solution for evaluating measurement errors in the high-accuracy wavefront measurement and provide a reliable, unbiased evaluation criterion.

Design Simulation of Czerny–Turner Configuration-Based Raman Spectrometer Using Physical Optics Propagation Algorithm

We report the design simulation of the Raman spectrometer using Zemax optical system design software. The design is based on the Czerny–Turner configuration, which includes an optical system consisting of an entrance slit, two concave mirrors, reflecting type diffraction grating and an image detector. The system’s modeling approach is suggested by introducing the corresponding relationship between detector pixels and wavelength, linear CCD receiving surface length and image surface dimension. The simulations were carried out using the POP (physical optics propagation) algorithm. Spot diagram, relative illumination, irradiance plot, modulation transfer function (MTF), geometric and encircled energy were simulated for designing the Raman spectrometer. The simulation results of the Raman spectrometer using a 527 nm wavelength laser as an excitation light source are presented. The present optical system was designed in sequential mode and a Raman spectrum was observed from 530 nm to 630 nm. The analysis shows that the system’s image efficiency was quite good, predicting that it could build an efficient and cost-effective Raman spectrometer for optical diagnostics.

Optical design of the laser launch telescope via physical optics theorem for laser guide star facility

The Laser Guide Star Facility (LGSF), as the most important part of the adaptive optics system of the large ground-based telescope, is aimed to generate multiple laser guide stars at the sodium layer. Laser Launch Telescope is employed to implement this requirement by projecting the Gauss beam to the sodium layer with a small beam size in LGSF system. As the diffraction and interference effects of laser’s long-distance transmission, the conventional optical design based on the geometrical optics mechanism cannot achieve the expected laser propagation. In this paper, we propose a method to design optical system for laser launch telescope based on the physical optics theorem to generate an acceptable light spot at the sodium layer in the atmosphere. Besides, a tolerance analysis method based on physical optics propagation is also demonstrated to be necessitated to optimize the system’s instrumentation performance. The numerical results show that the optical design considering physical optics propagation is highly rewarding and even necessitated in many occasions, especially for laser beam propagation systems.

Studying the impact of optical aberrations on diffraction-limited radial velocity instruments

Spectrographs nominally contain a degree of quasistatic optical aberrations resulting from the quality of manufactured component surfaces, imperfect alignment, design residuals, thermal effects, and other other associated phenomena involved in the design and construction process. Aberrations that change over time can mimic the line centroid motion of a Doppler shift, introducing radial velocity (RV) uncertainty that increases time-series variability. Even when instrument drifts are tracked using a precise wavelength calibration source, the barycentric motion of the Earth leads to a wavelength shift of stellar light, which causes a translation of the spectrum across the focal plane array by many pixels. The wavelength shift allows absorption lines to experience different optical propagation paths and aberrations over observing epochs. We use physical optics propagation simulations to study the impact of aberrations on precise Doppler measurements made by diffraction-limited, high-resolution spectrographs. Using the optical model of the iLocater spectrograph, we quantify the uncertainties that cross-correlation techniques introduce in the presence of aberrations and barycentric RV shifts. We find that aberrations that shift the point-spread-function photocenter in the dispersion direction, in particular primary horizontal coma and trefoil, are the most concerning. To maintain aberration-induced RV errors <10 cm / s, phase errors for these particular aberrations must be held well below 0.05 waves at the instrument operating wavelength. Our simulations further show that wavelength calibration only partially compensates for instrumental drifts, owing to a behavioral difference between how cross-correlation techniques handle aberrations between starlight versus calibration light. Identifying subtle physical effects that influence RV errors will help to ensure that diffraction-limited planet-finding spectrographs are able to reach their full scientific potential.

Investigation of the influence of optical turbulence on DIRCM laser’s jamming effectiveness: A wave-optics approach

Due to their exceptionally large jam-to-signal ratios (J/S), Directed Infrared Countermeasure (DIRCM) systems are the most efficient means for defeating heat seeking missiles. Although many studies have investigated DIRCM systems, the influence of optical turbulence on the jamming code effectiveness is mostly ignored. However, due to optical turbulence caused by the exhaust plume of the air platform and the atmosphere, a DIRCM laser’s beam may be exposed to time-varying intensity fluctuations, which may dramatically reduce the effective J/S at the seeker’s aperture compared to the one at the platform. In addition, previous studies have generally focused on the signal processing stages of seeker heads while ignoring diffractive and aberrative properties of the missile optics. In this study, we employ a wave-optics approach for estimating the jamming code effectiveness under turbulence. Specifically, we investigate time-varying influence of several degrees of optical turbulence on DIRCM laser beams with specified beam quality factors (M2) that are modulated with various jamming patterns. In our model, the DIRCM laser beam first passes through a highly turbulent region, which is caused by the rotor downwash of the exhaust plume of a rotary-wing platform. Next, the DIRCM laser beam propagates in an atmospheric turbulence region for much longer distances (on the order of few km’s) until it reaches the missile. Laser beam propagation in both turbulence regimes is simulated using the split-step method. Subsequently, using the ZEMAX software and its wave-optics-based Physical Optics Propagation (POP) package, we employ a generic model for the optical system of a first-generation spin-scan seeker and obtain the time-dependent intensity profiles of the laser beam at the focal point. Generic models for an uncooled lead-sulfide detector and the following signal processing stages have also been included in the model.

Sharper $N$-D Heisenberg's Uncertainty Principle

A sharper uncertainty inequality which exhibits a lower bound tighter than that in the classical N-dimensional Heisenberg's uncertainty principle is obtained. The condition that reaches an equality relation of the uncertainty inequality is deduced. Example and simulations are carried out to illustrate that the newly derived uncertainty principle is truly sharper than the classical one. The new proposal's applications in time-frequency analysis, optical signal processing and physical optics propagation are also given.

Physical-optics propagation through curved surfaces.

Curved surfaces are the basic elements of various optical components and systems such as microscopy systems, diffractive optical elements, freeform components, microlens arrays, etc. In order to model the propagation through curved surfaces fully vectorially and fast, the local plane interface approximation (LPIA) [Appl. Opt.39, 3304 (2000)APOPAI0003-693510.1364/AO.39.003304] is often used. However, the evaluation of the validity and accuracy of this method has, to our knowledge, not yet been fully addressed in the literature. In this work, we compare the field on the curved surface obtained by LPIA with that obtained with the finite element method. We find it is highly accurate even when the size of the curved surface is on the scale of micrometers. We further evaluate the limitation of LPIA in the cases of multi-reflection/transmission and internal resonance.

Analytical and practical implementation of anamorphic beam shaping in polar coordinates, Spinner system

In recent years, Diode lasers with a few kilowatts of power in the Near IR spectrum, or hundreds of watts in the UV spectrum have become available. In spite of the very high power of these lasers, they are not applicable for micro processing due to their low coherence characteristics (highly multimode), limiting their energy density. To overcome this limitation, it is possible to apply tailored beam shaping techniques to optimize the intensity distribution for specific applications to benefit from high power and to achieve performance similar to a laser with much better coherence. Specifically, in this article, a novel method of anamorphic ring shaping with polar coordinates will be demonstrated and compared to ring beam shaping by use of an Axicon optical element, the standard practice in the field. High power laser beams shaped into a ring are widely used in a variety of laser applications, including corneal surgery, material processing and laser micro-drilling.The theoretical model for anamorphic beam shaping using polar coordinates has been developed from established formalism in Cartesian coordinates, using the beam quality factor term M2. An incident multimode beam is split into radial segments (sub-beams). These sub-beams are then redirected in azimuthal coordinates using a special optical element (Spinner element), and focused by a lens, creating a diffraction limited ring with a significantly narrower width than a ring created by an Axicon. The proposed concept is confirmed in both geometrical raytracing and physical optics propagation methods. A practical optical system is proposed, taking into considerations both input and output parameters. A simulation of the system in geometrical ray tracing achieved much higher intensity in comparison to that achieved by a ring-shaped beam using an Axicon element.

Effect of slope errors on the performance of mirrors for x-ray free electron laser applications.

In this work we point out that slope errors play only a minor role in the performance of a certain class of x-ray optics for X-ray Free Electron Laser (XFEL) applications. Using physical optics propagation simulations and the formalism of Church and Takacs [Opt. Eng. 34, 353 (1995)], we show that diffraction limited optics commonly found at XFEL facilities posses a critical spatial wavelength that makes them less sensitive to slope errors, and more sensitive to height error. Given the number of XFELs currently operating or under construction across the world, we hope that this simple observation will help to correctly define specifications for x-ray optics to be deployed at XFELs, possibly reducing the budget and the timeframe needed to complete the optical manufacturing and metrology.

Single-mode fiber-to-single-mode fiber coupling efficiency and tolerance analysis: comparative study for ball, conic and GRIN rod lens coupling schemes using Zemax Huygen's integration and physical optics calculations

In this work, numerical coupling efficiency calculations comparing single-mode fiber (SMF) to SMF coupling schemes using uncoated single ball, conic and graded-index (GRIN) rod lenses are discussed. The reported fiber coupling efficiency (FCE) calculations were performed using Huygens integral and Gaussian beam physical optics propagation (GBPOP) features in Zemax®. The Huygens integral method results indicate that the FCE for ball, conic and GRIN rod single uncoated lenses (without accounting for Fresnel reflection and bulk absorption effects) can reach with the optimal lens and fiber parameters 91.11% (N-BK7 glass), 99.68% (N-BK7 glass) and 96.58%, respectively. In comparison, the calculated FCE for uncoated N-BK7 glass ball lens using the GBPOP method was 87.22% (without accounting for Fresnel reflections and bulk absorption effects). Furthermore, FCE calculations for ball lenses made out of sapphire, fused silica, S-LAH79 and N-LASF9 glass are given. The calculated deviation between the GBPOP and Huygens integral methods is <0.5%. Finally, tolerance analysis for each lens coupling scheme relating FCE to the tilts and the decentering of the lens and the two fibers is provided. The tolerance analysis calculations indicate that decentering of fibers and the single lens has the highest impact on the FCE values. Finally, FCE results suggest that the GRIN lens coupling scheme is the most sensitive scheme to misalignment and the ball lens scheme is the least sensitive to misalignment.

Co2amp: a software program for modeling the dynamics of ultrashort pulses in optical systems with CO(2) amplifiers.

A computer code for simulating the amplification of ultrashort mid-infrared laser pulses in CO2 amplifiers and their propagation through arbitrary optical systems is described. The code is based on a comprehensive model that includes an accurate consideration of the CO2 active medium and a physical optics propagation algorithm, and takes into account the interaction of the laser pulse with the material of the optical elements. The application of the code for optimizing an isotopic regenerative amplifier is described.

Advanced simulations of optical transition and diffraction radiation

Charged particle beam diagnostics is a key task in modern and future accelerator installations. The diagnostic tools are practically the ``eyes'' of the operators. The precision and resolution of the diagnostic equipment are crucial to define the performance of the accelerator. Transition and diffraction radiation (TR and DR) are widely used for electron beam parameter monitoring. However, the precision and resolution of those devices are determined by how well the production, transport and detection of these radiation types are understood. This paper reports on simulations of TR and DR spatial-spectral characteristics using the physical optics propagation (POP) mode of the Zemax advanced optics simulation software. A good consistency with theory is demonstrated. Also, realistic optical system alignment issues are discussed.

High-resolution through-focus metric with two-pitch grating target

Through-focus focus-metric is a method that is used to analyze images on a fixed plane with the help of focus-metric values when the target moves through the focus. In this study, an optical microscope having a magnification of 250× is constructed. A two-pitch grating target is imaged on a CCD detector and through-focus image data are measured. In addition, the optical field on the CCD detector is simulated using the boundary element method and physical optics propagation. By comparing the measured focus-metric signatures with the simulated signatures, information regarding the linewidth is obtained. The results show that the through-focus focus-metric method is a very sensitive method that can be used for measuring parameters such as the linewidth. Thus, a nanoscale resolution can be achieved.

Synthesis of gyrotron phase-correcting mirrors using irradiance moments

A new approach using the moments of field amplitudes has been applied for phase-correcting mirror synthesis of a 110-GHz gyrotron internal mode converter. The synthesized mirrors have smooth profiles in contrast to the mirrors synthesized using the previously employed iteration method. The design has been checked using a physical optics propagation code with the result of a Gaussian output amplitude at the gyrotron window position.

Fast method for physical optics propagation of high-numerical-aperture beams

A method is presented that expands the scheme of physical optics propagation beyond the Fresnel approximation to include beams that are nonparaxial. The formalism retains most of the calculation advantages of the Fresnel approach; i.e., it is based on a single Fourier transform step. The kernel of the new transformation is no longer separable in Cartesian coordinates; thus the formalism can account for astigmatic coupling effects originating purely from diffraction. The validity limits of the proposed algorithm are explored. Analytical expressions, numerical simulation results, and experimental data are compared.

Gaussian Fitting Parameters of the ESA PLANCK HFI Beams

We present Gaussian fitting parameters of simulated beams of the High Frequency Instrument (HFI) of the ESA PLANCK mission. This space probe is designed for measuring the anisotropy of temperature and polarization of the Cosmic Microwave Background (CMB). The six HFI spectral bands cover the frequency range 0.1 - 1 THz with 52 bolometers. Their beams are computed by multi-mode physical optics propagation of the source field from the apertures of the horns simulated by the scattering matrix approach. Computed power patterns are fitted by the elliptical Gaussian beams minimizing the peak difference between the two power distributions within the beam. This approximation is generally considered as acceptable from the scientific viewpoint, although we show that induced errors are far from negligible.

Whispering gallery effects in the troposphere

Experimental data that recorded higher‐than‐expected signals at 3087.7 MHz far beyond the horizon in the presence of an elevated duct are examined and compared to results from the radio physical optics (RPO) propagation model. RPO is a range‐dependent hybrid model that combines ray optics and parabolic equation methods. Previous modeling of this same case study using waveguide methods for both the measured elevated duct and hypothetical evaporation ducts has been disappointing. However, when the elevated duct is allowed to rise slowly with increasing range, the RPO results closely match the observed signal levels, indicating that weakly attenuated Earth‐detached, or whispering gallery, modes were the dominant propagation mechanism.

Influence of a thermally bloomed atmosphere on target image quality

An assessment is made of the impact of a thermally bloomed atmosphere on target image quality. The steady-state phase perturbations due to blooming and the effects of the distortion on return wave fronts are determined using a physical optics propagation code. Return target images for several realistic scenarios are reconstructed based on the incoherent point spread function for each isoplanatic region of the object (target) plane. The behavior of the images is discussed with respect to wavelength sensitivity, blur, distortion, and degradation in peak irradiance. The wave-optics approach is shown to agree with published experimental results.