The aberrations of reflective optical systems with planar symmetry are investigated in the most general case, with freeform surfaces and possibly different locations of the tangential and sagittal object and image. In this second and last paper, closed-form expressions are derived for the aberrations created by an individual mirror. We study two-mirror off-axis telescopes and establish a new family of designs that we show is simultaneously free of constant coma, linear astigmatism, and quadratic distortions (including smile and keystone). Analytical expressions for the intrinsic aberrations of an astigmatic beam are also derived.

Off-axis systems with freeform mirrors is a design approach of increasing importance for space instruments. While the off-axis reflective approach allows simple, versatile and obstruction free designs, the use of freeform surfaces allows to achieve better optical performance and/or compactness. In recent years, many such instruments have been designed and manufactured at TNO. Some important examples are the Tropomi (S5/precursor) and TSBOA (Sentinel-5) telescopes and several pushbroom spectrometers of the Spectrolite family. Despite the recognized potential of these systems, there is to our knowledge no available theory that allows to describe and predict the aberrations of plane symmetrical (off-axis) systems with freeform mirrors. In this context, an effort has been started 4 years ago at TNO to develop an approach that can describe and explore systematically off-axis freeform mirror systems with an arbitrary geometry. Since then the developed theory has been proven to be very useful in scanning the solution space for better starting designs, folding geometries and correction of lower aberrations in an early design phase. To circumvent difficulties linked to a wavefront formalism, generalized ray-tracing equations were derived, that include aberration terms up to 3rd order in X/Y object and pupil coordinates. These equations were recently published in two papers for the case of pure mirror systems [1,2]. The theory was also expanded to describe flat reflective gratings, opening a way to a complete description of reflective freeform spectrometers. In the present paper, after providing a high-level description and introduction to the aberration theory for freeform mirror systems, we will report some of its outcomes that have some practical relevance for space instruments. In particular: - two-mirror telescope designs for slit spectrometers (thus having a 1D field along the slit) that are inherently corrected for spatial smile will be presented. For these designs the slit projection in object space is exactly straight. - a new family of mirror spectrometers will be introduced that uses flat gratings and no collimator. In a collimator-less spectrometer, the aberrations induced by the grating under diverging light are corrected with freeform mirrors. The presented designs are entirely calculated from theory, with only optimization of the higher order freeform terms. A simpler architecture than traditional designs is obtained, with less optical surfaces. - finally we present a systematic classification of distortions in imaging slit spectrometers. The difference between distortions originating in the collimator and at the grating or in the imager is clarified and described mathematically. We discuss aberration-induced non-linear dispersion, as well as distortions from the keystone and smile families. The proposed classification also applies to catadioptric and refractive systems, the only requirement being to have a plane of symmetry.

In this invited paper, a simple and efficient matrix formalism is presented for computing aberrations in plane-parallel freeform mirror systems. The approach is flexible and can be easily generalized to arbitrary aberration orders and/or to systems with different symmetries. As an illustration, we derive analytical expressions for all 2nd and 3rd order image and pupil aberrations in plane-parallel confocal N-mirror systems. Some design examples are also presented and discussed.

High-index dielectric metasurfaces featuring Mie-type electric and magnetic resonances have been of great interest in a variety of applications such as imaging, sensing, photovoltaics, and others, which led to the necessity of an efficient large-scale fabrication technique. To address this, here we demonstrate the use of single-pulse laser interference for direct patterning of an amorphous silicon film into an array of Mie resonators a few hundred nanometers in diameter. The proposed technique is based on laser-interference-induced dewetting. A precise control of the laser pulse energy enables the fabrication of ordered dielectric metasurfaces in areas spanning tens of micrometers and consisting of thousands of hemispherical nanoparticles with a single laser shot. The fabricated nanoparticles exhibit a wavelength-dependent optical response with a strong electric dipole signature. Variation of the predeposited silicon film thickness allows tailoring of the resonances in the targeted visible and infrared spectral ranges. Such direct and high-throughput fabrication is a step toward a simple realization of spatially invariant metasurface-based devices.

Optically resonant high-index dielectric metasurfaces featuring Mie-type electric and magnetic resonances are usually fabricated by means of planar technologies, which limit the degrees of freedom in tunability and scalability of the fabricated systems. Therefore, we propose a complimentary post-processing technique based on ultrashort (≤ 10 ps) laser pulses. The process involves thermal effects: crystallization and reshaping, while the heat is localized by a high-precision positioning of the focused laser beam. Moreover, for the first time, the resonant behavior of dielectric metasurface elements is exploited to engineer a specific absorption profile, which leads to a spatially-selective heating and a customized modification. Such technique has the potential to reduce the complexity in the fabrication of non-uniform metasurface-based optical elements. Two distinct cases, a spatial pixelation of a large-scale metasurface and a height modification of metasurface elements, are explicitly demonstrated.

We present a planar spectro-polarimeter based on Fabry-Pérot cavities with embedded polarization-sensitive high-index nanostructures. A 7 µm-thick spectro-polarimetric system for 3 spectral bands and 2 linear polarization states is experimentally demonstrated. Furthermore, an optimal design is theoretically proposed, estimating that a system with a bandwidth of 127 nm and a spectral resolution of 1 nm is able to reconstruct the first three Stokes parameters with a signal-to-noise ratio of -13.14 dB with respect to the the shot noise limited SNR. The pixelated spectro-polarimetric system can be directly integrated on a sensor, thus enabling applicability in a variety of miniaturized optical devices, including but not limited to satellites for Earth observation.

The health and environmental effects of particulate matter (PM) in the air depend on several parameters. Besides particle size, shape, and concentration, the chemical nature of the PM is also of great importance. State-of-the-art PM sensors only detect the particle size and concentration. Small, low-cost sensors only identify PM according to PM2.5 and PM10 standards. Larger detectors measure the complete particle size distribution. However, the chemical composition of PM is not often assessed. The current paper presents the initial stages of the development of an infrared-based detector for the inline assessment of the chemistry of PM in the air. By combining a mini cyclone that is able to concentrate the particles at least a thousand fold and a hollow waveguide that aligns the flow of particles with infrared light, the feasibility of the concept was shown in this study. A clear differentiation between amorphous and crystalline silica was demonstrated at outdoor PM levels of lower than 1 mg per cubic meter.

The aberrations of reflective optical systems with one plane of symmetry are investigated in the most general case, with freeform surfaces and possibly different locations of the tangential and sagittal object and image. In this first paper in a series of two, we establish generalized ray-tracing equations including transverse aberrations up to the third order in ray coordinates. The ray-tracing treatment allows us to overcome difficulties linked to the non-existence of a suitable astigmatic wavefront reference. The obtained expressions can describe multi-mirror systems and include all induced aberration terms. As an illustration, a simple freeform off-axis mirror is analyzed.

Digital color imaging relies on spectral filters on top of a pixelated sensor, such as a CMOS image sensor. An important parameter of imaging devices is their resolution, which depends on the size of the pixels. For many applications, a high resolution is desirable, consequently requiring small spectral filters. Dielectric nanostructures, due to their resonant behavior and its tunability, offer the possibility to be assembled into flexible and miniature spectral filters, which could potentially replace conventional pigmented and dye-based color filters. In this paper, we demonstrate the generation of transmissive structural colors based on uniform-height amorphous silicon nanostructures. We optimize the structures for the primary RGB colors and report the construction of submicrometer RGB filter arrays for a pixel size down to 0.5 μm.

A superoscillatory lens (SOL) is known to produce a sub-diffraction hotspot that is useful for high-resolution imaging. SOLs have not yet been directly used in a confocal reflection setup, as the SOL suffers from poor imaging properties. Additionally, the illuminating intensity distribution of the SOL still has high-intensity rings called sidelobes coexisting with the central hotspot. By means of a reflection setup, which does not have the SOL in the detection chain, thereby mitigating the poor imaging properties, we assessed the resolution capabilities of a SOL. This was done for different objects, whose dimensions were both above and below the SOL field-of-view (FOV). We found that the sidelobe illumination degrades the imaging properties in the case of extended objects, limiting the applicability of a SOL system.

Optically resonant high-index dielectric metasurfaces featuring Mie-type electric and magnetic resonances are usually fabricated by means of planar technologies, which limit the degrees of freedom in tunability and scalability of the fabricated systems. Therefore, we propose a complimentary post-processing technique based on ultrashort ($\leq$ 10 ps) laser pulses. The process involves thermal effects: crystallization and reshaping, while the heat is localized by a high-precision positioning of the focused laser beam. Moreover, for the first time, the resonant behavior of dielectric metasurface elements is exploited to engineer a specific absorption profile, which leads to a spatially-selective heating and a customized modification. Such technique has a potential to reduce the complexity in the fabrication of non-uniform metasurface-based optical elements. Two distinct cases, a spatial pixelation of a large-scale metasurface and a height modification of metasurface elements, are explicitly demonstrated.

With the introduction of the NXE:3400B scanner, ASML has brought EUV to High-Volume Manufacturing for sub-10nm node lithography. And work has already been started on a successor high-NA system with NA=0.55. For both these systems, node resolution will go down faster than NA increases, resulting in decreasing k(1)-factors and tightening of aberration requirements. A crucial component for measuring and controlling aberrations in-situ is a diffuser to fill the full pupil of the projection optics appropriately. This paper presents several new diffuser concepts, both reflective as well as transmissive, with their respective key performance metrics for both NA= 0.33 and NA= 0.55 EUV projection optics. These concepts can be used for measuring wavefront quality from dedicated fiducial plates, or for measuring directly from the imaging reticle. The latter would enable a combination of reticle alignment with lens aberration control without throughput penalty. It will be shown that with these diffuser concepts, we have a solution for in-situ aberration control for 5nm nodes and below.

Optical systems for space applications face challenges that are very different from those known for terrestrial conditions, which we are all too familiar with. First of all, there is the launch, which shakes delicate systems to a degree that our common optics would jump out of their mechanical mounts or break apart. Next, the space environment imposes thermal conditions that are extremely demanding. We are faced with an extremely cold background on the side that is looking away from the sun, while at the same time other areas of the space craft suffer from a very high thermal load. To make things worse, the situation typically is not stable in time, due to orbital or operational variations. The varying temperature gradients would certainly create nightmares for designers of earth-bound optical systems. And then there is the vacuum environment, which has a huge impact on thermal management, but also creates huge challenges related to the propagation of (outgassing) contaminants, which are likely to deposit on exactly those places you do not want to have them: on the optics, causing stray light, or on the detectors, deteriorating the efficiency and possibly creating artificial spectral features. Finally, after the launch you cannot repair your highly expensive equipment; a Hubble repair mission, aside from the enormous cost, is simply not always possible. The issues mentioned above should be kept in mind when one reads the articles in this Space Optics issue of Advanced Optical Technologies (AOT). If you think about this, you really start to appreciate the near-impossible task one has to fulfil when designing and building an extremely accurate instrument like the James Webb Space Telescope (JWST) with its four state of the art instruments. This issue of AOT contains a detailed description of two of JWST’s optical instruments, the near infrared spectrograph and the mid-infrared instrument. These somewhat boring names do no justice to the fabulous technology behind them. Thinking about the ground-breaking scientific discoveries to be made with JWST makes every astronomer’s heart beat faster, and not only theirs. Next to space telescopes like the JWST a different class of space missions is being developed in our quest to understand the universe and its fundamental laws a lot better. Gravitational waves have only recently been observed in incredibly sensitive experiments on Earth. In order to understand their full dynamics, there is a need of a space-based observatory, which will complement the earth-bound experiments. First, concepts of an instrument design for this very important science mission are discussed in the article on the telescope of the Laser Interferometer Space Antenna (LISA). The JWST is, as we all know, a highly complex and extremely expensive instrument. On the other side of the complexity/price spectrum we have space systems that are meant to be far easier to be built and a lot cheaper. It all depends on what you have to do with it. For instance, a constellation of many cheap and small satellites with limited field of view allows Earth observations with a high spatial and temporal resolution. Also there, we might want to gather as much light as possible and increase the optical resolution. If space instruments can be designed such that they unfold to their full size and capability only after being launched into space, the size of the satellite could become smaller and the cost of launching such a volume would be a lot cheaper. A deployable space telescope, as is described in this issue, allows doing just that. When talking about Earth observation special attention should be paid to the Earth’s atmosphere. In view of global warming, detailed knowledge of atmospheric chemistry and radiative properties is crucial. While a lot is known already, thanks to several Earth orbiting instruments like TROPOMI making detailed maps of our Earth atmosphere, more knowledge is required on the impact of aerosols. This is a topic of worldwide interest, as shown by the contribution from China about their Aerosol Sensor to be launched on the GaoFen-5B satellite. Many earth observation instruments are spectroscopic instruments. An essential part of these units are the dispersive elements – most of the time – the gratings. Therefore, it is of great importance to understand the performance of the grating and especially all the artefacts *Corresponding author: Stefan Bäumer, TNO, Optics, Delft, The Netherlands, e-mail: stefan.baumer@tno.nl Henri Werij: Technische Universiteit Delft, Faculty of Aerospace Engineering, Delft, The Netherlands

Digital imaging has been steadily improving over the past decades and we are moving towards a wide use of multi- and hyperspectral cameras. A key component of such imaging systems are color filter arrays, which define the spectrum of light detected by each camera pixel. Hence, it is essential to develop a variable, robust and scalable way for controlling the transmission of light. Nanostructured surfaces, also known as metasurfaces, offer a promising solution as their transmission spectra can be controlled by shaping the wavelength-dependent scattering properties of their constituting elements. Here we present, metasurfaces based on silicon nanodisks, which provide filter functions with amplitudes reaching 70-90% of transmission, and well suitable for RGB and CMY color filter arrays, the initial stage towards the further development of hyperspectral filters. We suggest and discuss possible ways to expand the color gamut and improve the color values of such optical filters.

Due to its potential for high resolution and three-dimensional imaging, soft x-ray ptychography has received interest for nanometrology applications. We have analyzed the measurement time per unit area when using soft x-ray ptychography for various nanometrology applications including mask inspection and wafer inspection, and are thus able to predict (order of magnitude) throughput figures. Here we show that for a typical measurement system, using a typical sampling strategy, and when aiming for 10-15 nm resolution, it is expected that a wafer-based topology (2.5D) measurement takes approximately 4 minutes per μm2 , and a full three-dimensional measurement takes roughly 6 hours per μm2 . Due to their much higher reflectivity EUV masks can be measured considerably faster; a measurement speed of 0.1 seconds per μm2 is expected. However, such speeds do not allow for full wafer or mask inspection at industrially relevant throughput.

In the last years, much interest has grown around the concept of optical surfaces employing high contrast dielectric resonators. However, a systematic approach for the design of this optical surfaces under particular requirements has never been proposed. In this contribution, we describe this approach applied to the robust design of an array of microlenses characterized by a numerical aperture of NA=0.19 with a field of view of FOV = ±60 mrad in a bandwidth of 20 nm. Typically, dielectric resonators are engineered in such a way to have almost full transmissive surfaces with locally tunable phase. However, considering the multiple wavelengths and angles under which the lenses may work, it is difficult to get uniform transmission characteristics for all the dielectric resonators employed. The design strategy, here proposed, uses a particle swarm optimization routine to find the best resonator distribution able to meet the requirements considering the amplitude and phase dispersive characteristics of the resonators surfaces. In the optimization process, also the effects of possible manufacturing inaccuracies, such as variations of resonators radii, are taken into account, allowing a robust design of the structure, within the given manufacturing tolerances. Different designs, operating at 405 nm and 635 nm, are presented and their performances are discussed.

In this paper, we present a design strategy for single layer metasurface lenses based on dielectric resonators. This strategy is based on a robust optimization procedure for the resonator distribution in order to meet required performances (e.g. encircled energy, bandwidth, field of view, etc.). Possible deviations due to manufacturing errors are taken into account in the design procedure. This is applied to the design of array of microlenses for maskless lithography applications. The final design shows more uniform focusing performances (bandwidth 20 nm at 395 nm - 415 nm, field of view ±60 mrad) and increased robustness against manufacturing errors, compared to designs based on analytic phase projections.

Optics is a truly enabling technology of the 21st century.Looking around us, there are many devices in our daily lives, which we use to share our experiences, gain knowledge, or explore virtual worlds: smart phones with their cameras, tablets, computers with their cameras and screens and virtual or augmented reality glasses are increasing in ever larger numbers.There are also many optics based sensors which make our lives safer or just easier -think of cameras with various functions in a car: from lane assistance to parking aids or of the many security cameras helping in preventing crime.And as solid state lighting gains increasing importance, beam shaping optics are needed to direct the light precisely into the direction we want.The internet of things (IOT) will need 'ears and eyes'.There is a good possibility, that optical sensor systems will play a large role in enabling the IOT.All of these applications and many more that we can think of are in need of affordable optics with sufficient quality and availability in large volumes.When these three criteria come together it is very likely that polymer optics will play an important role.The technology of injection molding optics has matured and can be regarded as a standard technology for the production of optical elements and systems.It is widely accepted in the market and discussions on the quality of plastic optics in general are not held anymore.It is only discussed, if plastic optics is fit for a certain application.Furthermore in most cases it is the method of choice for (large) volume production of optics and can be very cost effective.Plastic optics have come a long way!What is ahead for plastic optics?Where are the new developments advancing the field?

Hyperbolic metamaterials (HMMs) are anisotropic materials with a permittivity tensor that has both positive and negative eigenvalues. Here we report that by using a type II HMM as a cladding material, a waveguide that only supports higher-order modes can be achieved, while the lower-order modes become leaky and are absorbed in the HMM cladding. This counter-intuitive property can lead to novel application in optical communications and photonic integrated circuits. The loss in our HMM insulator-HMM (HIH) waveguide is smaller than that of similar guided modes in a metal-insulator-metal (MIM) waveguide.

This paper presents the use of optical antennas in metrology scenarios. Two design concepts are presented: dielectric nanoresonator arrays and plasmonic nanoantennas arrays. The first ones are able to focus an incident light beam at an arbitrary focal plane. The nanoantennas arrays can be employed for collecting the high-spatial frequencies of any scattering environment and redirecting into far-field information. The first concept can be employed in the manufacturing of custom holographic surfaces for free-form optics characterization. The second concept is attractive for the development of high-resolution, high-efficiency optical metrology instruments.