Reflective dual field-of-view optical system based on the Alvarez principle.

A novel, to the best of our knowledge, dual-state reflective optical relay system based on the Alvarez system is proposed, which can be used for remote sensing applications. By keeping the image and pupil positions constant, it can be combined with a telescope to achieve two different magnifications. As a compact structure with only two moving parts, freeform optical mirrors and a nearly diffraction limited performance for the infrared wavelength 8 µm make it an attractive subsystem for space applications. Different design tradeoffs and the preferred layout properties are discussed in detail.

Design and test of a rigid endomicroscopic system for multimodal imaging and femtosecond laser ablation.

Significance: Conventional diagnosis of laryngeal cancer is normally made by a combination of endoscopic examination, a subsequent biopsy, and histopathology, but this requires several days and unnecessary biopsies can increase pathologist workload. Nonlinear imaging implemented through endoscopy can shorten this diagnosis time, and localize the margin of the cancerous area with high resolution. Aim: Develop a rigid endomicroscope for the head and neck region, aiming for in-vivo multimodal imaging with a large field of view (FOV) and tissue ablation. Approach: Three nonlinear imaging modalities, which are coherent anti-Stokes Raman scattering, two-photon excitation fluorescence, and second harmonic generation, as well as the single photon fluorescence of indocyanine green, are applied for multimodal endomicroscopic imaging. High-energy femtosecond laser pulses are transmitted for tissue ablation. Results: This endomicroscopic system consists of two major parts, one is the rigid endomicroscopic tube 250 mm in length and 6 mm in diameter, and the other is the scan-head (10×12×6 cm3 in size) for quasi-static scanning imaging. The final multimodal image accomplishes a maximum FOV up to 650 µm, and a resolution of 1 µm is achieved over 560 µm FOV. The optics can easily guide sub-picosecond pulses for ablation. Conclusions: The system exhibits large potential for helping real-time tissue diagnosis in surgery, by providing histological tissue information with a large FOV and high resolution, label-free. By guiding high-energy fs laser pulses, the system is even able to remove suspicious tissue areas, as has been shown for thin tissue sections in this study.

Field curvature reduction in miniaturized high numerical aperture and large field-of-view objective lenses with sub 1 µm lateral resolution.

In this paper the development of a miniaturized endoscopic objective lens for various biophotonics applications is presented. While limiting the mechanical dimensions to 2.2 mm diameter and 13 mm total length, a numerical aperture of 0.7 in water and a field-of-view (FOV) diameter of 282 µm are achieved. To enable multimodal usage a wavelength range of 488 nm to 632 nm was considered. The performed broad design study aimed for field curvature reduction when maintaining the sub 1 µm resolution over a large FOV. Moreover, the usage of GRadient-INdex (GRIN) lenses was investigated. The resolution, field curvature improvement and chromatic performance of the novel device were validated by means of a confocal laser-scanning-microscope.

Material-specific high-resolution table-top extreme ultraviolet microscopy.

Microscopy with extreme ultraviolet (EUV) radiation holds promise for high-resolution imaging with excellent material contrast, due to the short wavelength and numerous element-specific absorption edges available in this spectral range. At the same time, EUV radiation has significantly larger penetration depths than electrons. It thus enables a nano-scale view into complex three-dimensional structures that are important for material science, semiconductor metrology, and next-generation nano-devices. Here, we present high-resolution and material-specific microscopy at 13.5 nm wavelength. We combine a highly stable, high photon-flux, table-top EUV source with an interferometrically stabilized ptychography setup. By utilizing structured EUV illumination, we overcome the limitations of conventional EUV focusing optics and demonstrate high-resolution microscopy at a half-pitch lateral resolution of 16 nm. Moreover, we propose mixed-state orthogonal probe relaxation ptychography, enabling robust phase-contrast imaging over wide fields of view and long acquisition times. In this way, the complex transmission of an integrated circuit is precisely reconstructed, allowing for the classification of the material composition of mesoscopic semiconductor systems.

Extended aberration analysis in symmetry-free optical systems - part I: method of calculation.

The imaging performance evaluation of symmetry-free optical systems is of great importance during the correction process of optical design. However, due to the complexity and limitations of the available tools, the higher-order aberrations in the system cannot be well analyzed and are hard to control. In this paper, the theoretical background and the mathematical approach of a quantitative analysis method for surface-decomposed transverse aberration in the symmetry-free systems are introduced. With the mixed ray-tracing calculation in both real and paraxial cases, the implementations of full-order intrinsic/induced aberration, as well as the surface-additive Zernike coefficient fitting method are demonstrated. The applications of this method help assess the correction performance considering the relatively critical surfaces in an arbitrary off-axis system. The reliability and the accuracy of the method will be evaluated in part II with a test system. And as an illustration of the practical usage of the method for optical design, the corresponding applications on a group of lithographic systems will also be demonstrated.

Generalized chromatic aberrations in non-rotationally symmetric optical systems-Part I: mathematical approach.

In non-rotationally symmetric optical systems, chromatic aberrations must be defined in a generalized way with reference to the optical axis ray and optimal tilted parabasal image plane of the central wavelength. In this paper, the definition of generalized chromatic aberrations is clarified. The mathematical calculation in optical systems with arbitrary symmetry and surface shape is realized by ray- and wavefront-based methods, respectively, that are originally identical. The additivity of wavefront after each surface ensures the surface decomposition of chromatic aberrations. In the end, the influence of pupil aberration, which is of a higher order, is discussed. The consistency of our methods with Seidel aberrations in the lowest aberration order of the rotationally symmetric system and the application of our methods in diverse non-rotationally symmetric refractive systems will be addressed in detail in Part II.

Generalized chromatic aberrations in non-rotationally symmetric optical systems-Part II: applications.

In this paper, as a supplement to Part I, three examples will be provided to verify our methods. In the first example of a double Gauss system, the chromatic aberrations calculated by our methods and those given by the Seidel aberrations are compared. Then we will present two examples analyzing the generalized chromatic aberrations in refractive system with freeform surfaces by our methods. The stereomicroscope is utilized to demonstrate the feasibility and consistency of both ray- and wavefront-based methods. The anamorphic imaging objective lens proves that it is necessary to consider the pupil aberration when it cannot be neglected. In both examples, the surface decomposed a full-field display of the chromatic aberrations shows us that it is a convenient and powerful tool to analyze the generalized chromatic aberrations in nonrotationally symmetric refractive optical systems.

Wigner function-based modeling and propagation of partially coherent light in optical systems with scattering surfaces.

Light scattering from residual manufacturing errors of optical surfaces has a large impact on the image quality of optical systems. Classical ray-based methods to simulate surface scattering in optical systems depend on statistical models of surface errors and neglect the wave properties of light, which prohibit the integration of statistical surface error models with beam propagation methods. Additionally, the impact of multiple scattering from different frequency components of surface errors cannot be easily modelled by existing methods. Here we analyze the impact of different frequency components of surface errors induced by diamond-turned surface grinding on image quality, and we propose a Wigner function-based approach in which light is modelled as partially coherent. In this unified model, by selecting the proper definition of light coherence, we can combine the statistical and deterministic models of surface errors, enabling efficient, simultaneous simulation of multiple scattering from high- and mid-spatial frequency (HSF and MSF, respectively) surface errors, as well as the interference and edge diffraction of light.

Flexible, fast, and benchmarked vectorial model for focused laser beams.

In-bulk processing of materials by laser radiation has largely evolved over the last decades and still opens up new scientific and industrial potentials. The development of any in-bulk processing application relies on the knowledge of laser propagation and especially the volumetric field distribution near the focus. Many commercial programs can simulate this, but, to adapt them, or to develop new methods, one usually must create a specific software. Besides, most of the time people also need to measure the actual field distribution near the focus to evaluate their assumptions in the simulation. To easily get access to this knowledge, we present our high-precision field distribution measuring method and release our in-house software InFocus [https://github.com/QF06/InFocus], under the Creative Commons 4.0 license. Our measurements provide 300 nm longitudinal resolution and diffraction limited lateral resolution. The in-house software allows fast vectorial analysis of the focused volumetric field distribution in bulk. Simulations of the linear propagation of light under different conditions (focusing optics, wavelength, spatial shape, and propagation medium) are in excellent agreement with propagation imaging experiments. The aberrations provoked by the refractive index mismatch as well as those induced by the focusing optics are both taken into account. The results indicate that our proposed model is suitable for the precise evaluation of energy deposition.

Improved correction by freeform surfaces in prism spectrometer concepts.

The correction of spatial resolution and distortion in imaging spectrometer systems is of great importance due to their significant impact on efficiency and quality. In this study, we analyze the corrective power of freeforms added at different positions in various spectrometer systems for high-performance requirements. The results show that the combination of a freeform prism and a second freeform close to the image has the best correction of distortion while preserving spot size.

Efficient simulation of surface scattering in symmetry-free optical systems.

Simulation of scattering from optical surfaces is usually based on Monte Carlo methods in which the bidirectional scattering distribution function (BSDF) of the optical surfaces are sampled randomly by many rays, resulting in long calculation times. In order to accelerate the simulation, a quasi-analytical phase space model is proposed. In this model, few rays are traced from the object and image space to the target surface to determine the illumination and acceptance areas in phase space, where these areas can be conveniently coupled simultaneously in the spatial and angular domain. Since no random sampling is involved in the phase space model, no statistical noise perturbs the result and the surface scattering simulation can be greatly accelerated. Additionally, due to the use of real raytracing, the phase space model removes the limitation of paraxial approximation, which usually limits the accuracy of deterministic stray light analysis models. Meanwhile, by the discretization of the optical surfaces into subareas, this new approach is able to model freeform surfaces with arbitrary geometries, and space-variant BRDFs can be applied for different subareas of the optical surface.

Beam characterization by phase retrieval solving the transport-of-intensity-equation.

A new method for the characterization of coherent laser beams is proposed. It is based on the non-iterative solution of the transport-of-intensity-equation. The phase to recover is decomposed into paraxial properties of laser beams and a set of lateral shifted radial basis functions, which allows for the derivation of a direct solution of the phase by a least-squares fit without the need of an initial guess. The method is tested with synthetic data to deduce an accuracy metric. Additionally, two real laser beams are characterized. Including the real light source in terms of the reconstructed field allows for a more holistic simulation of optical systems.

Application of Gaussian pulsed beam decomposition in modeling optical systems with diffraction grating.

A diffraction grating is one of the most commonly used components in ultrafast optical systems such as pulse stretchers and compressors. Hence, modeling the temporal dispersion and spatiotemporal distortions associated with the angular dispersion of a diffraction grating is very crucial for wave optical modeling of such systems. In this paper, the Gaussian pulsed beam decomposition (GPBD) method is extended to handle the propagation of ultrashort pulses, with arbitrary spatial and spectral profiles, through complex ultrashort pulse shaping systems containing diffraction gratings. Although the diffraction efficiencies are not rigorously computed, the GPBD method enables modeling of the large angular dispersion of idealized diffraction gratings without running into an impractically large number of spectral samples as in the case of Fourier-transform-based methods. The application of the extended method is demonstrated by performing the wave optical propagation of an ultrashort pulse through a single diffraction grating and then through a Treacy compressor system. By combining the Treacy compressor with the Martinez grating pair stretcher with internal lenses, the pulse shaping through a complete chirped pulse amplification (CPA) setup is modeled. Finally, the effects of using real dispersive lenses in the Martinez stretcher on the output pulse of the CPA setup are presented. For analysis of the output pulses, methods of computing the spatiotemporal and spatio-spectral amplitudes of the output pulse from the phase correct superposition of individual Gaussian pulsed beams are presented.

Gaussian pulsed beam decomposition for propagation of ultrashort pulses through optical systems.

Many applications of ultrashort laser pulses require manipulation and control of the pulse parameters by propagating them through different optical components before the target. This requires methods of simulating the pulse propagation taking into account all effects of dispersion, diffraction, and system aberrations. In this paper, we propose a method of propagating ultrashort pulses through a real optical system by using the Gaussian pulsed beam decomposition. An input pulse with arbitrary spatial and temporal (spectral) profiles is decomposed into a set of elementary Gaussian pulsed beams in the spatiospectral domain. The final scalar electric field of the ultrashort pulse after propagation is then obtained by performing the phase correct superposition of the electric fields all-Gaussian pulsed beams, which are propagated independently through the optical system. We demonstrate the application of the method by propagating an ultrashort pulse through a focusing aspherical lens with large chromatic aberration and a Bessel-X pulse generating axicon lens.

Cascaded diffraction in optical systems. Part I: simulation model.

In every real optical system, the light beam or ray bundle is laterally limited by diaphragms or lens boundaries. Therefore, from a rigorous point of view, a diffraction calculation of the point spread function by assuming a truncation at the exit pupil is a simplification. If several boundaries at different $z$z positions inside a system truncate the rays, cascaded diffraction occurs and the field in the exit pupil is modified in amplitude and phase by the edge diffraction effects at all relevant boundaries. A simple model for a fast estimation of these effects and a rule of thumb for real optical systems are worked out in this work.

Cascaded diffraction in optical systems. Part II: example calculations.

Real imaging optical systems are in any case finite in diameter and therefore limit the ray cones coming from the various object points. The truncation of the ray cones generates edge diffraction effects, which have an impact on the point spread function and therefore on the resolution of the system. Traditionally real calculations of the diffraction effects are mostly simplified by assuming a truncation in the exit pupil only. In this hybrid approach, the light propagation therefore can be calculated by raytrace first, and the more cumbersome diffraction calculated is only performed between exit pupil and image plane. To come to a better quantitative understanding of the validity of this approximation, a more refined model is developed in an adjacent publication. Some example calculations for real setups and an overview about the order of magnitude of the cascaded diffraction effects are worked out in this contribution.

Spatially truncated Gaussian pulsed beam and its application in modeling diffraction of ultrashort pulses from hard apertures.

A new kind of pulsed beam, which we call a spatially truncated Gaussian pulsed beam, is defined to represent a Gaussian pulsed beam that is diffracted from a semi-infinite hard aperture. The analytical equations for the propagation of the spatially truncated Gaussian pulsed beam through a nonrotationally symmetric paraxial system with second-order dispersion is derived starting from the generalized spatiotemporal Huygens integral. The spatially truncated Gaussian pulsed beam is then combined with the conventional Gaussian pulsed beam decomposition method to enable the modeling of diffraction of a general ultrashort pulse from an arbitrarily shaped hard aperture. The accuracy of the analytical propagation equation derived for the propagation of the truncated Gaussian pulsed beam is evaluated by a numerical comparison with diffraction results obtained using the conventional pulse propagation method based on the Fourier transform algorithm. The application of the modified Gaussian pulsed beam decomposition method is demonstrated by propagating an ultrashort pulse after a circular aperture through a dispersive medium and a focusing aspherical lens with large chromatic aberration.

Correction of 2D-telecentric scan systems with freeform surfaces.

For scanning systems the resolution, distortion as well as the telecentricity are important performance criteria. For two-dimensional scanning systems, scan mirrors deflecting in only one transverse direction are not allowing for telecentricity in x and y simultaneously in case of an axisymmetric system. It is possible to achieve two-dimensional telecentricity by splitting the pupils in x- and y-direction and shifting the principal planes in one dimension by changing the focal power using an anamorphic setup. However, for higher specifications concerning a large aperture and wide scanning angle, using cylindrical lenses are not enough to achieve a good system quality. It has been proved in many researches that freeform surfaces are effective to improve the resolution of systems without rotational symmetry. In this work, a systematic case study is presented to investigate the potential of freeform surfaces to improve the resolution, telecentricity, and distortion simultaneously. It is shown as a result that freeform surfaces offer large correction ability in all the three aspects concerning high specifications of 2D-telecentric anamorphic scan systems. This contribution provides the insight into the application of freeform surfaces in non-rotationally symmetric optical systems with refractive components.

Fast computation and characterization of perturbed Bessel-Gauss beams.

In this paper, an extended definition of the Strehl ratio is introduced for Bessel-Gauss (BGB) beams, which, in contrast to classical beams, are not defined at a single point but along the optical axis. For that purpose, the Fresnel diffraction integral is solved analytically to calculate the on-axis field of a BGB that is perturbed by spherical aberration, astigmatism, and coma. Certain approximations are introduced, discussed, and tested against a rigorous propagation method. The derived expression is applied to tolerancing of an example system.

General analysis and optimization strategy to suppress autofluorescence in microscope lenses.

With the development of fluorescence microcopy, the autofluorescence effect of optical glass in microscope lenses has become an important source of stray light which decreases the contrast of the image. However, the autofluorescence effect of various types of microscope lenses has not been thoroughly discussed and the dominant factors of this effect are not clear. Currently, the most commonly used analysis method of the autofluorescence effect is based on the volume scattering model and Monte Carlo raytracing, which is extremely time-consuming due to the large number of rays that need to be traced. In our previous work, we have presented an efficient phase-space-based simulation method, which significantly accelerates the simulation of the autofluorescence effect [Appl. Opt.58, 3589 (2019)APOPAI0003-693510.1364/AO.58.003589]. Here we apply this new method on different types of microscope lenses and perform a systematic analysis of the autofluorescence effect based on the simulation results. In order to obtain an overview of the autofluorescence effect of different types of microscope lenses, more than 100 microscope lenses with different numerical aperture (NA), magnification, working distance, and immersion medium are selected and the corresponding autofluorescence contribution from each element in the lenses is calculated. Following a systematic analysis of the simulation result, we find that the autofluorescence effect of a lens is dependent on the etendue and complexity of the system, while the most critical elements are usually found in the front and rear groups. After the origins of the autofluorescence contribution from these critical lens groups have been found, possibilities to reduce the autofluorescence intensity have been investigated. Finally, effective methods to reduce the autofluorescence effect are presented and compared. The major contribution of this work is a detailed analysis of the impact of different factors on the autofluorescence effect, based on which a guideline is provided for the optical designers as well as the users to design or to select an appropriate microscope lens with low autofluorescence intensity.