The recent history of optical design saw a progressive trend of also designing without rotational symmetry, especially spectrometers due to the use of reflective and diffractive elements in their designs. A freeform hyperspectral imager design in CubeSat format is presented in this work, which has large deviation from rotational symmetry. Based on a generalization of paraxial optics and wavefront aberration expansion applicable to plane-symmetric systems, in this dissertation we derived the aberration coefficients of aberration types in the third group for plane-symmetric systems that include the second order effects of the light beam footprint on optical surfaces. We also expanded the theory to include the contributions from freeform surfaces and induced aberrations. For the application to plane-symmetric spectrometers, the aberration coefficients related to distortion are of special interest. Comparisons between the distortion results predicted by the aberration coefficients and simulated from real raytracing show good consistency in example systems of a Dyson spectrometer and freeform spectrometers that share the three-mirror double-pass structure, which is similar to the spectrometer component of the hyperspectral imager we designed. In comparison to real raytracing, results of the theory applied to the spectrometer of the hyperspectral imager we designed show the limits of the theory that is limited to the third group of aberrations, while in this design, high-order groups also significantly contribute. In all cases, the analytical formulae of the aberration coefficients contain the information on surface contributions, induced aberrations, and the relation between the aberration behavior and system parameters, which provide valuable insights in the analysis of plane-symmetric systems.
An analytical closed-form formula for the design of freeform lenses free of spherical aberration is presented. Given the equation of the freeform input surface, the formula gives the equation of the second surface in order to correct the spherical aberration. The derivation is based on the formal application of the variational Fermat principle under the standard geometrical optics approximation.
In their article -Appl. Opt. 58, 1010_1015 (2019)- González-Acuña et al claimed:"an analytical closed-form formula for the design of freeform lenses free of spherical aberration and astigmatism." However, as we show here, their formula can only be applied when the object and image are both real and the image is inversed, additionally, the refractive index in the object and image media is the same. Here, we present the complete solution of this particular formula.
For more than 150 years, scientists have advanced aberration theory to describe, analyse, and eliminate imperfections that disturb the imaging quality of optical components and systems. Simultaneously, they have developed optical design methods for and manufacturing techniques of imaging systems with ever-increasing complexity and performance up to the point where they are now including optical elements that are unrestricted in their surface shape. These so-called optical freeform elements offer degrees of freedom that can greatly extend the functionalities and further boost the specifications…
We apply the Lie algebraic method to reflecting optical systems with plane-symmetric freeform mirrors. Using analytical ray-tracing equations we construct an optical map. The expansion of this map gives us the aberration coefficients in terms of initial ray coordinates. The Lie algebraic method is applied to treat aberrations up to arbitrary order. The presented method provides a systematic and rigorous approach to the derivation, treatment and composition of aberrations in plane-symmetric systems. We give the results for second- and third-order aberrations and apply them to three single-mirro…
With the development in freeform technology, it has now become more and more feasible to use freeform surfaces in real system designs. While the freeform surfaces helping optical designers achieve more and more challenging system features, the methods for multiple freeform implementations are still underdeveloped. We therefore investigate strategies to use freeform surfaces properly in imaging optical systems with one Scheimpflug system and one lithographic system. Based on the studies of the influences of the freeform normalization radius, freeform order and system eccentricity, the methods o…
Lens design uses a calculation of the lens' surfaces that permit to obtain an image from a given object. A set of general rules and laws permits to calculate the essential points of the optical system such as distances, thickness, pupils, and focal distance among others. Now, the theory on which the classical lens design is based changes radically as our theoretical foundations do not rely on the classical ray tracing rules. We show that with the rules expressed in a reduced vector analytical solution set of equations, we can take into account all optical elements, i.e. refractive, reflective,…
The performance of electron energy-loss spectrometers can often be limited by their electron-optical aberrations. Due to recent developments in high energy-resolution and momentum-resolved electron energy loss spectroscopy (EELS), there is renewed interest in optimizing the performance of such spectrometers. For example, the "ω-q" mode of momentum-resolved EELS, which uses a small convergence angle and requires aligning diffraction spots with a slot aperture, presents a challenge for realigning the spectrometer after adjusting the projection lenses. Automated and robust alignment can greatly b…
Reflective imaging systems form an important part of photonic devices such as spectrometers, telescopes, augmented and virtual reality headsets or lithography platforms. Reflective optics provide unparalleled spectral performance and can be used to reduce overall volume and weight. So far, most reflective designs have focused on two or three reflections, while four-reflection freeform designs can deliver a higher light throughput (faster F-number) as well as a larger field-of-view (FOV). However, advanced optical design strategies for four-reflection freeform systems have been rarely reported …
Brillouin spectroscopy is a powerful optical technique for viscoelastic characterization of samples without contact. However, like all optical systems, Brillouin spectroscopy performances are degraded by optical aberrations, and have therefore been limited to homogenous transparent samples. To correct for aberrations, adaptive optics (AO) methods have been previously integrated into a variety of optical modalities ranging from ground-based telescopes to super-resolution microscopes. In this work, we developed an adaptive optics configuration designed for Brillouin scattering spectral analysis.…
The optical design of a novel spectrometer is present, combining a cylindrically convex pre-mirror with a cylindrically concave VLS grating (both in meridional) to deliver a resolving power of 100,000-200,000 in 'water window' (2-5nm). More remarkably, unlike a typical RIXS spectrometer to obtain such high resolution by tight focusing or tiny confinement slit (<1μm), here the resolution could be achieved for an effective meridional source size of 50μm (r.m.s.). The overall optical aberrations of the system are well analysed and compensated, providing an excellent flat field at the detector dom…
We present a modified $8f$ geometry for time domain terahertz (THz) spectroscopy (TDTS) experiments. We show, through simulations and data, that a simple rearranging of the off-axis parabolic mirrors, which are typically used to focus and direct THz radiation in TDTS experiments, results in a nearly 40% reduction in the THz focal spot diameter. This effect stems from significant reduction of the principle optical aberrations which are enhanced in the conventional $8f$ geometry but partially compensated in the modified $8f$ experimental setup. We compare data from our home-built TDTS spectromet…
Using Fisher information and the Cramér-Rao lower bound, we analyse fundamental precision limits in the determination of spectral parameters in inelastic optical scattering. General analytic formulae are derived which account for the instrument response functions of the dispersive element and relay optics found in practical Raman and Brillouin spectrometers. Limiting cases of dispersion and diffraction limited spectrometers, corresponding to measurement of Lorentzian and Voigt lineshapes respectively, are discussed in detail allowing optimal configurations to be identified. Effects of defocus,…
