Showing papers in "Journal of Optics in 2015"

Design of a low F-number freeform off-axis three-mirror system with rectangular field-of-view

Abstract: In this paper, a low F-number freeform off-axis three-mirror system with rectangular field-of-view (FOV) is presented, and the system has an integrated configuration that can be aligned with ordinary methods. The initial structure is solved analytically, and the optimization process is described in detail. This F/1.38 freeform system with a 4° × 5° FOV provides good imaging performance, especially in middle-wave and long-wave infrared bands. The primary mirror and the tertiary mirror are approximately tangent, so these two freeform mirrors can be fabricated on a single substrate. This configuration provides a solution to the practical application of freeform off-axis three-mirror systems. Additionally, a prototype of this system is demonstrated, and the imaging performance of the prototype is tested experimentally. The actual performance of the prototype is discussed and analyzed.

Mitigating of modal instabilities in linearly-polarized fiber amplifiers by shifting pump wavelength

Abstract: We investigated the effect of pump wavelength on the modal instabilities (MI) in high-power linearly polarized Yb-doped fiber amplifiers. We built a novel semi-analytical model to determine the frequency coupling characteristics and power threshold of MI, which indicates promising MI suppression through pumping at an appropriate wavelength. By pumping at 915 nm, the threshold can be enhanced by a factor of 2.1 as compared to that pumped at 976 nm. Based on a high-power linearly polarized fiber amplifier platform, we studied the influence of pump wavelength experimentally. A maximal enhancement factor of 1.9 has been achieved when pumped at 915 nm, which agrees with the theoretical calculation and verified our theoretical model. Furthermore, we show that MI suppression by detuning the pump wavelength is weakened for fiber with a large core-to-cladding ratio.

Critical coupling to Tamm plasmons

Abstract: The conditions of critical coupling of light to Tamm plasmons are investigated with comprehensive numerical simulations, highlighting the parameters that maximize absorption of incident light in the metal layer. The asymmetric response in reflection and absorption with respect to the direction of incidence is discussed, the two cases yielding different optimal coupling conditions. These findings are relevant for the design of optimized Tamm structures, particularly in applications such as narrow-band thermal emitters, field-enhanced spectroscopy and refractive-index sensing.

Measuring the self-healing of the spatially inhomogeneous states of polarization of vector Bessel beams

Abstract: We experimentally measured the self-healing of the spatially inhomogeneous states of polarization of vector Bessel beams. Radially and azimuthally polarized vector Bessel beams were experimentally generated via a digital version of Durnin's method, using a spatial light modulator in concert with a liquid crystal q-plate. As a proof of principle, their intensities and spatially inhomogeneous states of polarization were experimentally measured using Stokes polarimetry as they propagated through two disparate obstructions. It was found, similar to their intensities, that their spatially inhomogeneous states of polarization self-healed. The self-healing can be understood via geometric optics, i.e., the interference of the unobstructed conical rays in the shadow region of the obstruction, and may have applications in, for example, optical trapping.

Gold-based SERS tags for biomedical imaging

Abstract: The use of SERS tags in biomedical imaging is described. SERS tags are a novel entity that has recently emerged in the SERS community, mainly spurred by the necessity of carrying out experiments in the biomedical and clinical fields, where the heterogeneity and constant evolution of the environment hamper the application of direct SERS sensing concepts. Direct sensing would in fact require the use of nanoparticles with bare metallic surfaces to allow for intense signal responses; however, the high salt contents typical of physiological conditions and issues such as fouling lead the nanoparticles to aggregate and precipitate out of solution, thus limiting reproducibility and quantitative target identification. As a consequence, the concept of indirect detection has gained importance, in which the SERS signal provided by the SERS tag indirectly provides identification and localization of the target. In this brief review, aimed both at the expert scientist and the novice, the anatomy of a SERS tag is first described, which includes the gold nanoparticle, Raman reporter molecules, a coating layer, and targeting moieties, and the concept of hot spot is explained. A brief overview of the most recent imaging applications in vitro, ex vivo, and in vivo is also provided, along with specific recommendations toward the synthesis of effective SERS tags that could find application in the biomedical field, and meet specific needs of the clinical community. Major emphasis is placed on the concept of multiplexing, which is perhaps the most important feature of SERS tags that could render their clinical application a reality.

Generation of cylindrical vector beams of high orders using uniaxial crystals

Abstract: The generation of cylindrical vector beams in birefringent crystals is studied analytically and experimentally in paraxial and non-paraxial regimes. At sharp focusing (in the non-paraxial case), two foci corresponding ordinary and extraordinary beams are formed along the crystal’s axis. There is the radially polarized distribution in one focus and the azimuthally polarized distribution in the other focus when the incident beam has the vortex phase of the first order and circular polarization of the opposite direction. The results are extended to the generation of higher-order radially and azimuthally polarized laser beams. The physical experiments with an Iceland spar crystal have been conducted.

Iterative phase-amplitude retrieval with multiple intensity images at output plane of gyrator transforms

Abstract: For the iterative phase retrieval, multiple measured intensity images in output plane are only considered for accelerating the convergence. The amplitude and phase at the observed object plane of measurement system are unknown in this research. The observing system is composed of gyrator transform, in which several images are recorded by using several transform angles for the same input image. An amplitude-phase retrieval scheme is designed and tested. The numerical simulations have demonstrated that the amplitude and phase pattern within a very small error (less than 0.04 and 0.0005 for an 8-bit two-dimensional data) can be recovered after 1000 iterations.

Ultra-thin optical vortex phase plate based on the metasurface and the angular momentum transformation

Abstract: The ultra-thin optical vortex phase plate (VPP) has been designed and investigated based on the metasurface of the metal rectangular split-ring resonators (MRSRRs) array. The circularly polarized incident light can convert into corresponding cross-polarization transmission light, and the phase and the amplitude of cross-polarization transmission light can be simultaneously governed by modulating two arms of the MRSRR. The MRSRR has been arranged in a special order for forming an ultra-thin optical VPP that can covert a plane wave into a vortex beam with a variety of the topological charges, and the transformation between spin angular momentum (SAM) and orbital angular momentum (OAM) has been discussed in detail. The multi-spectral characteristics of the VPP have also been investigated, and the operating bandwidth of the designed VPP is 190 nm (in the range of 710–900 nm), which enable a potential implication for integrated optics and vortex optics.

Half Pearcey laser beams

Abstract: We obtain a new solution of the paraxial Helmholtz equation that describes a family of three-dimensional and two-dimensional form-invariant half-Pearcey beams (HP-beams). HP-beams generalize Pearcey beams obtained in Ring et al (2012) Opt. Express 20 18955, since these Pearcey beams can be considered as the sum of two first-order HP-beams. Three-dimensional HP-beams have angular spectra of plane waves, which are non-zero at a half parabola. For functions of HP-beam complex amplitudes, the orthogonality properties have been revealed. Using a spatial phase modulator, we generated superposition of HP-beams. For two-dimensional HP-beam acceleration and deceleration of trajectory has been shown for areas before and beyond the focal plane respectively.

Tunable plasmonic enhancement of light scattering and absorption in graphene-coated subwavelength wires

Abstract: Fil: Riso, Maximo. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Oficina de Coordinacion Administrativa Ciudad Universitaria. Instituto de Fisica de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Fisica de Buenos Aires; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Fisica. Grupo de Electromagnetismo Aplicado; Argentina

Optimizing gold nanostars as a colloid-based surface-enhanced Raman scattering (SERS) substrate

Abstract: The one-pot seedless protocol provides a facile approach in the synthesis of gold nanostars (AuNS) that involves only three reagents, gold (III) chloride (HAuCl4), silver nitrate (AgNO3) and ascorbic acid (C6H8O6). While studies correlating the synthesis parameters of the seed-mediated protocol to surface-enhance Raman scattering (SERS) enhancement is well reported, the same understanding of the one-pot seedless protocol is limited. Here, we aim to elucidate how the synthesis parameters of AuNS from the one-pot seedless protocol, the AuNS concentration, surface passivation and aggregation level affect the colloidal SERS enhancement. Using crystal violet (CV) as a Raman probe molecule, we found that the SERS enhancement increases with Au3+/C6H8O6 molar ratio up to 0.60 and Au3+/Ag+ molar ratio up to 18. Although the surfactant, cetyltrimethylammonium bromide (CTAB) maintained colloidal stability, it reduced the SERS enhancement. Interestingly, the SERS enhancement did not increase monotonically with AuNS concentration, but decreased when AuNS concentration was beyond 15 pM. The SERS enhancement also increased with the increasing level of salt-induced aggregation of AuNS, but only within a few minutes. While the concept of SERS with colloidal nanostructures is not new, we have shown for the first time, a detailed systematic study of various parameters that affect the SERS enhancement of AuNS synthesized using a one-pot seedless protocol. This study enables us to optimize the SERS enhancement of AuNS at the synthesis level to make them effective colloid-based SERS substrates for potential use in intracellular biosensing.

Scattering and absorption of terahertz waves by a free-standing infinite grating of graphene strips: analytical regularization analysis

Abstract: The plane wave scattering and absorption by an infinite flat graphene strip grating in the free space are studied in the THz range in the H- and E-polarization regimes. Accurate numerical treatment is based on the dual series equations and the analytical regularization technique. The resulting numerical algorithm possesses guaranteed convergence and controlled accuracy of computations. Reflectance, transmittance and absorbance by the graphene-strip gratings are studied as a function of various parameters. In the H-polarization case, the dominant feature is the excitation of the surface plasmon resonances on each strip. In the E-polarization case, Rayleigh anomalies are the only observable features.

Propagation of Airy–Gaussian beam in Kerr medium

Abstract: By using the method of moments, the critical power of the Airy–Gaussian (AiG) beam is given for different decay factors and different distribution factors numerically. The critical power Pcr of the AiG beam decreases as the distribution factor increases. Using the split-step Fourier method, the propagations of the AiG beam in the free space and in the Kerr medium are shown. It has been found that the self-acceleration effect becomes weaker when the distribution factor increases. As the initial input power increases, we can observe the quasi-breather finally. From the root mean square (rms) beam width and the peak intensity figures, one can see that the beam with large distribution factor is more sensitive to the change of the initial input power.

Optical image encryption via photon-counting imaging and compressive sensing based ptychography

Abstract: In this study, we investigate the integration of compressive sensing (CS) and photon-counting imaging (PCI) techniques with a ptychography-based optical image encryption system. Primarily, the plaintext real-valued image is optically encrypted and recorded via a classical ptychography technique. Further, the sparse-based representations of the original encrypted complex data can be produced by combining CS and PCI techniques with the primary encrypted image. Such a combination takes an advantage of reduced encrypted samples (i.e., linearly projected random compressive complex samples and photon-counted complex samples) that can be exploited to realize optical decryption, which inherently serves as a secret key (i.e., independent to encryption phase keys) and makes an intruder attack futile. In addition to this, recording fewer encrypted samples provides a substantial bandwidth reduction in online transmission. We demonstrate that the fewer sparse-based complex samples have adequate information to realize decryption. To the best of our knowledge, this is the first report on integrating CS and PCI with conventional ptychography-based optical image encryption.

OPCPA front end and contrast optimization for the OMEGA EP kilojoule, picosecond laser

Abstract: OMEGA EP is a large-scale laser system that combines optical parametric amplification and solid-state laser amplification on two beamlines to deliver high-intensity, high-energy optical pulses. The temporal contrast of the output pulse is limited by the front-end parametric fluorescence and other features that are specific to parametric amplification. The impact of the two-crystal parametric preamplifier, pump-intensity noise, and pump-signal timing is experimentally studied. The implementation of a parametric amplifier pumped by a short pump pulse before stretching, further amplification, and recompression to enhance the temporal contrast of the high-energy short pulse is described.

Near video-rate linear Stokes imaging with single-pixel detectors

Abstract: In this work we demonstrate a polarization sensitive computational imaging system based on a digital micro-mirror device (DMD) and several single-pixel photodetectors. By taking advantage of computational imaging techniques, the light measured by each single-pixel detector can reconstruct a 2D image for a specific linear polarization state. Using the rapid frame-rate of the DMD to continuously project a series of spatially orthogonal illumination patterns, near video-rate reconstructions can be achieved. In addition we extend this approach to provide full-colour images through a process of sequential colour selection (RGB). Taking the difference between photodetector signals from orthogonal linear polarization states, we obtain images corresponding to the linear Stokes parameters. We apply this rapid polarization sensitive imaging system to inert and biological material. Since the spatial information in the images reconstructed by this approach are determined by the projection system, rather than the detectors, the approach provides perfect pixel registration between the various polarization selective images and associated Stokes parameters. Furthermore, the use of single-pixel detectors and the large operational bandwidth afforded by DMDʼs means that the approach can readily be extended for imaging at wavelengths where detector arrays are unavailable or limited.

Standing waves on two-dimensional periodic dielectric waveguides

Abstract: Guided modes of a periodic waveguide usually exist below the light line, if the minimum period of the waveguide is used in the definition, but for some periodic waveguides, there are standing waves with the same period as the waveguide. These non-propagating waves localized around the waveguide core are special guided modes above the light line with a zero wavenumber, and they are related to transmission anomalies and other resonant phenomena. In this paper, we analyze the standing waves on two periodic waveguides: a periodic array of circular dielectric cylinders, and a dielectric slab with a periodic array of circular air-holes. Based on an efficient semi-analytic method, the frequencies of standing waves are calculated as functions of the dielectric constant and the radius of cylinders. Our work provides a basis for further studies on these waves and for realizing their potential applications.

Implementation of a spatial light modulator for intracavity beam shaping

Abstract: In this paper we outline the steps necessary to create a laser with an intra-cavity spatial light modulator (SLM) for transverse mode control. We employ a commercial SLM as the back reflector in an otherwise conventional diode-pumped solid state laser. We show that the geometry of the liquid crystal (LC) arrangement strongly influences the operating regime of the laser, from nominally amplitude-only mode control for twisted nematic LCs to nominally phase-only mode control for parallel-aligned LCs. We demonstrate both operating regimes experimentally and discuss the potential advantages of and improvements to this new technology.

First principles approach to the Abraham-Minkowski controversy for the momentum of light in general linear non-dispersive media

Abstract: We study the problem of the definition of the energy?momentum tensor of light in general moving non-dispersive media with linear constitutive law. Using the basic principles of classical field theory, we show that for the correct understanding of the problem, one needs to carefully distinguish situations when the material medium is modeled either as a background on which light propagates or as a dynamical part of the total system. In the former case, we prove that the (generalized) Belinfante?Rosenfeld (BR) tensor for the electromagnetic field coincides with the Minkowski tensor. We derive a complete set of balance equations for this open system and show that the symmetries of the background medium are directly related to the conservation of the Minkowski quantities. In particular, for isotropic media, the angular momentum of light is conserved despite of the fact that the Minkowski tensor is non-symmetric. For the closed system of light interacting with matter, we model the material medium as a relativistic non-dissipative fluid and we prove that it is always possible to express the total BR tensor of the closed system either in the Abraham or in the Minkowski separation. However, in the case of dynamical media, the balance equations have a particularly convenient form in terms of the Abraham tensor. Our results generalize previous attempts and provide a first principles basis for a unified understanding of the long-standing Abraham?Minkowski controversy without ad hoc arguments.

Four-step phase-shifting digital holography simultaneously sensing dual-wavelength information using a monochromatic image sensor

Abstract: Four-step phase-shifting digital holography simultaneously sensing dual-wavelength information from wavelength-multiplexed holograms is presented. Specific phase shifts for respective wavelengths are introduced to remove the crosstalk components and extract only the object wave at the desired wavelength from the holograms. Object waves at multiple wavelengths are selectively extracted by utilizing 2π ambiguity and the subtraction procedures based on phase-shifting interferometry. Two-step phase-shifting interferometry is merged into the procedures to decrease the number of the recorded holograms. The proposed technique is numerically investigated and experimentally demonstrated. The applicability to the case where the number of wavelengths is more than two and possible noise when using two-step phase-shifting interferometry are discussed.

Harmonic nanoparticles: noncentrosymmetric metal oxides for nonlinear optics

Abstract: response, often referred to as harmonicnanoparticles (HNPs). HNPs feature a series of properties which distinguish them from otherphotonics nanoprobes (quantum dots, up-conversion nanoparticles, noble metal particles). HNPsemission is inherently nonlinear and based on the efficient generation of harmonics as opposed tofluorescence or surface plasmon scattering. In addition, the fully coherent signal emitted byHNPs together with their polarization sensitive response and absence of resonant interactionmake them appealing for several applications ranging from multi-photon (infrared) microscopyand holography, to cell tracking and sensing.Keywords: multiphoton microscopy, second harmonic generation, third harmonic generation,nonlinear optics, nanophotonics, perovskites(Some figures may appear in colour only in the online journal)1. IntroductionSince the advent of ultrafast lasers in the early nineties andrelated availability of high peak power pulses at compara-tively low energies, the investigation of nonlinear opticalresponse have become a widespread activity resulting ininnovative applications. In particular, in the field of imagingthis has led to the introduction of multi-photon microscopy byW Webb [1]. This technique, as compared to one-photonexcited fluorescence microscopy, features increased imagingdepth, no out-of-focus bleaching, and spatial resolutioncomparable to confocal techniques without compromise insensitivity. The latest technological advancements in this fieldare related to its extension towards longer wavelengths,facilitated by the timely introduction of novel tunable sourcesin the 0.7–1.3 μm spectral range and new optical componentswith optimized performances in this region (microscopeobjectives, acousto-optic modulators, ...). Although these newinfrared tunable devices are supposedly more adapted forimaging through thick (living) samples because of reducedscattering [2–4], the available choice of imaging targets(fluorescent molecules, dyes) with two-photon absorptionbands >1200nm is very limited.Nanoparticle-based labelling, which is sometimes pre-ferred over other approaches for its superior photo-stability,brightness, and chemical selectivity usually requires two-photon interactions in the 700–900nm range, with a fewnotable exceptions [5]. However most optically active labelsmay suffer from bleaching and blinking and their use inbiological research might be prevented because of low bio-compatibility. For these reasons, since 2006, several researchgroups worldwide have proposed a complementary approach,

High concentration Yb-Er co-doped phosphate glass for optical fiber amplification

Abstract: We present the fabrication and characterization of two high concentration Yb3+-Er3+ co-doped double clad phosphate glass optical fibers (named A and B for short) manufactured by preform drawing, with the preform being obtained by the rod-in-tube technique. Optical amplification was demonstrated by core pumping 27 mm of fiber A (7/25/70 µm and NA = 0.17 between core and inner cladding) with a laser diode at 976 nm, achieving a 10.7 dB internal gain, i.e., 4.0 dB cm-1, for small signal input at 1535 nm. Amplification was also demonstrated in a cladding-pumped counter propagating configuration using both fibers A and B (12/48/140 µm and NA = 0.08). A maximum internal gain of 18.5 dB was achieved with 8 cm of fiber B, corresponding to an amplification of 2.3 dB cm-1, for small signal input at 1535 nm.

Comparison of adhesion layers of gold on silicate glasses for SERS detection

Abstract: Gold is one of the most widely used metals for building up plasmonic devices. Although slightly less efficient than silver for producing sharp resonance, its chemical properties make it one of the best choices for designing sensors. Sticking gold on a silicate glass substrate requires an adhesion layer, whose effect has to be taken into account. Traditionally, metals (Cr or Ti) or dielectric materials (TiO2 or Cr2O3) are deposited between the glass and the nanoparticle. Recently, indium tin oxide and (3-mercaptopropyl)trimethoxysilane (MPTMS) were used as a new adhesion layer. The aim of this work is to compare these six adhesion layers for surface-enhanced Raman scattering sensors by numerical modeling. The near-field and the far-field optical responses of gold nanocylinders on the different adhesion layers are then calculated. It is shown that MPTMS leads to the highest field enhancement, slightly larger than other dielectric materials. We attributed this effect to the lower refractive index of MPTMS compared with the others.

Blocking-assisted infrared transmission of subwavelength metallic gratings by graphene

Abstract: The transmittance of simple one-dimensional gratings and two-dimensional pillar arrays is usually broadband with poor selectivity in the infrared region. In this paper, it is demonstrated that covering graphene on top of a Ag grating will improve both the magnitude and coherence of the transmitted infrared radiation. The underlying mechanism of this anomalous blocking-assisted transmission is attributed to the excitation of localized magnetic resonances. Quantitative predictions of the resonance wavelength for different geometric parameters and graphene chemical potentials are provided based on the equivalent-circuit model. The enhancement is alignment-free and actively tunable. Such graphene-covered gratings may help improve the performance and robustness of optical devices, such as polarizers, color filters, lab-on-chip sensors, and transparent conductors.

SERS efficiencies of micrometric polystyrene beads coated with gold and silver nanoparticles: the effect of nanoparticle size

Abstract: Rapid advances in nanofabrication techniques of reproducibly manufacturing plasmonic substrates with well-defined nanometric scale features and very large electromagnetic enhancements paved the way for the final translation of the analytical potential of surface-enhanced Raman scattering (SERS) to real applications. A vast number of different SERS substrates have been reported in the literature. Among others, discrete particles consisting of an inorganic micrometric or sub-micrometric core homogeneously coated with plasmonic nanoparticles stand out for their ease of fabrication, excellent SERS enhancing properties, long-term optical stability and remarkable experimental flexibility (manipulation, storage etc). In this article, we performed a systematic experimental study of the correlation between the size of quasi-spherical gold and silver nanoparticle and the final optical property of their corresponding assembles onto micrometric polystyrene (PS) beads. The size and composition of nanoparticles play a key role in tuning the SERS efficiency of the hybrid material at a given excitation wavelength. This study provides valuable information for the selection and optimization of the appropriate PS@NPs substrates for the desired applications.

Enhanced absorption of thin-film photovoltaic cells using an optical cavity

Abstract: We show via numerical simulations that the absorption and solar energy conversion efficiency of a thin-film photovoltaic (PV) cell can be significantly enhanced by embedding it into an optical cavity. A reflective hemi-ellipsoid with an aperture for sunlight placed over a tilted PV cell reflects unabsorbed photons back to the cell, allowing for multiple opportunities for absorption. Ray tracing simulations predict that with the proposed cavity a textured thin-film silicon cell can exceed the Yablonovitch (Lambertian) limit for absorption across a broad wavelength range, while the performance of the cavity-embedded planar PV cell approaches that of the cell with the surface texturing.

Scattering of surface plasmons on graphene by a discontinuity in surface conductivity

Abstract: The scattering of graphene surface plasmons from an arbitrary, one-dimensional discontinuity in graphene surface conductivity is treated analytically by an exact solution of the quasi-static integral equation for surface current density in the spectral domain. It is found that the reflection and transmission coefficients are not governed by the Fresnel formulas obtained by means of the effective medium approach. Furthermore, the reflection coefficient generally exhibits an anomalous reflection phase, which has so far only been reported for the particular case of reflection from abrupt edges. This anomalous phase becomes frequency-independent in the regime where the effect of inter-band transitions on graphene conductivity is negligible. The results are in excellent agreement with full-wave electromagnetic simulations, and can serve as a basis for the analysis of inhomogeneous graphene layers with a piecewise-constant conductivity profile.

Producing any desired far-field mean irradiance pattern using a partially-coherent Schell-model source

Abstract: A new technique is presented to produce any desired mean far-field irradiance pattern using a partially-coherent Schell-model source. The new method differs from similar approaches in the literature by requiring only phase control. This permits the proposed approach to be easily implemented in the laboratory using a single spatial light modulator. The analytical development of the phase-only method is presented and discussed. Simulation and experimental results are presented to validate the proposed method. Applications for the new technique include free-space optical communications, material processing/manufacture, and particle trapping.

Manipulating ellipsoidal micro-particles by femtosecond vortex tweezers

Abstract: We study the manipulation of the ellipsoidal micro-particles by the femtosecond vortex tweezer experimentally and theoretically. In our setup the micro-particles can be rotated stably by means of optical torque induced by the femtosecond optical whirl. In order to give insight into observed effects, we establish two adequate theoretical models: one is based upon assumption of full absorption and the other uses the ray tracing method. The numerical simulations agree well with the experimental results.

Construction method through forward and reverse ray tracing for a design of ultra-wide linear field-of-view off-axis freeform imaging systems

Abstract: In this paper, a construction method through forward and reverse ray tracing for a design of ultra-wide linear field-of-view (FOV) off-axis freeform systems is proposed. The freeform initial system is numerically constructed by a point-by-point calculation. This method begins with a spherical system solved by the paraxial optical theory. In this method, the primary mirror is calculated through the reverse ray tracing; hence, the size and position of the aperture stop is not affected by the changes of mirrors. The fields in the reverse system are selected to cause certain beam overlaps on the primary mirror between adjacent fields. These overlaps offer a more uniform distribution of data points, improving the calculation of this mirror. As an example, an off-axis freeform system with an ultra-wide linear field-of-view of 70? is designed by this method. The effective focal length of the system is 75 mm, and the F-number is 5.8. The diffraction-limited performance of this freeform system in the visible band and the near infrared and near ultraviolet bands validate the construction method presented in this paper.