Ray Spot Research Articles

Third-Order Intrinsic Aberration Modification with Second-Order Accuracy Transfer of Pupil Coordinates and Extrinsic Aberration of Plane-Symmetric Optical System with a Two-Dimensional Field Light Source

A plane-symmetric optical system with a two-dimensional field light source, such as a soft X-ray and vacuum ultraviolet optical system, is widely used for synchrotron radiation source devices, microscopes and so on. Therefore, this paper studied third-order intrinsic aberration modification with second-order accuracy transfer of pupil coordinates and extrinsic aberration of these kinds of optical systems. First, we discuss the extrinsic aberration calculation method and derive the corresponding aberration expressions; in addition, we apply optical geometric relations and the polynomial fitting method to obtain a second-order accuracy transfer relationship expression of the pupil coordinates between adjacent optical surfaces and derived the modification calculation expressions of the intrinsic aberration caused by the above factor. Finally, the third-order intrinsic aberration modification with second-order accuracy transfer of pupil coordinates and extrinsic aberration expressions derived in this paper are applied to calculate ray spot diagrams of two soft X-ray and vacuum ultraviolet optical systems with meridional and sagittal field angle light sources, and these results are compared with those obtained from the ray-tracing software Shadow; this showed that the calculation accuracy of the aberration expressions is sufficient.

Optimized design of a gravitational wave telescope system based on pupil aberration.

The telescope is vital for accurate gravitational wave detection in the TianQin project. It must meet criteria like a geometric tilt-to-length (TTL) coupling noise c o e f f i c i e n t≤0.02√2n m/µr a d and wavefront R M S≤λ/30. Analyzing the pupil aberration's impact on geometric TTL noise, we devised an optimization method using the chief ray spot diagram's standard deviation. Implementing this in Zemax with a ZPL macro, we designed an optical system meeting TianQin's requirements. The system has a maximum geometric TTL noise coefficient of 0.0250nm/µrad over the science FOV and a wavefront RMS of 0.0111λ, confirming the method's feasibility.

Performance analysis of wavefront coding system with spherical aberration by using ray aberration approach

Imaging characteristics of wavefront coding systems in the presence of spherical aberration are analyzed by using ray aberration approach. The analytical expressions for ray aberration, the boundary of ray map and the size of spot diagram of a wavefront coding system in the presence of defocus and spherical aberration are obtained by wave aberration theory. The effect of spherical aberration on imaging performance of wavefront coding systems with a cubic phase mask is presented by ray aberration and spot diagram. The results show that the wavefront coding systems have a high tolerance to spherical aberration through a given defocus range.

Comparison of geometrical and diffraction imaging in the space and frequency domains.

The geometrical and diffraction point-spread functions of an optical imaging system have been reviewed and compared in the past [Proc. SPIE3729, 434 (1999)PSISDG0277-786X10.1117/12.346821]. In this paper, we review and compare corresponding optical transfer functions. While the truth lies with the diffraction optical-transfer functions (OTF), it is considered easier and quicker to calculate the geometrical OTF, especially for large aberrations. We describe the theory of the two OTFs and explore the range of spatial frequencies and the magnitude of the primary aberrations over which the geometrical OTF may provide a reasonable approximation of the diffraction OTF. Moreover, balancing of spherical aberration with defocus for optimum diffraction OTF is studied as a function of both the aberration value as well as the spatial frequency. How to gauge the progress of an optical design in the frequency domain based on the geometrical OTF is outlined as the ray spot size is used in the space domain.

Third-order aberration analysis of an off-axial optical system

The aberration theory applied to co-axial optical systems is extended to off-axial systems, for which third-order aberration coefficients are considered. The derived aberrations are analyzed using three-dimensional ray bundles, spot diagrams, and image charts, and classified in relation to the system symmetry. This theory is very useful for optical designers, allowing them to clarify the relationship between the structures of off-axial optical systems and the corresponding off-axial aberrations.

Null Ronchi Gratings as a function of period

In this work is presented in a simple manner, a method to generate null Ronchi gratings. This method consider the period of the Ronchi grating as a function of the x and y positions over the grating, compared to the currently known methods which utilize ray tracing or spot diagrams for the null Ronchi gratings calculus. We compare null Ronchi gratings reported in the literature against gratings calculated with our method. We have found that our method can calculate the Ronchi gratings for any conical surface in a satisfactory way.

Wave theories of non-laminar charged particle beams: from quantum to thermal regime

AbstractThe standard classical description of non-laminar charged particle beams in paraxial approximation is extended to the context of two wave theories. The first theory that we discuss (Fedele R. and Shukla, P. K. 1992 Phys. Rev. A45, 4045. Tanjia, F. et al. 2011 Proceedings of the 38th EPS Conference on Plasma Physics, Vol. 35G. Strasbourg, France: European Physical Society) is based on the Thermal Wave Model (TWM) (Fedele, R. and Miele, G. 1991 Nuovo Cim. D13, 1527.) that interprets the paraxial thermal spreading of beam particles as the analog of quantum diffraction. The other theory is based on a recently developed model (Fedele, R. et al. 2012a Phys. Plasmas19, 102106; Fedele, R. et al. 2012b AIP Conf. Proc.1421, 212), hereafter called Quantum Wave Model (QWM), that takes into account the individual quantum nature of single beam particle (uncertainty principle and spin) and provides collective description of beam transport in the presence of quantum paraxial diffraction. Both in quantum and quantum-like regimes, the beam transport is governed by a 2D non-local Schrödinger equation, with self-interaction coming from the nonlinear charge- and current-densities. An envelope equation of the Ermakov–Pinney type, which includes collective effects, is derived for both TWM and QWM regimes. In TWM, such description recovers the well-known Sacherer's equation (Sacherer, F. J. 1971 IEEE Trans. Nucl. Sci.NS-18, 1105). Conversely, in the quantum regime and in Hartree's mean field approximation, one recovers the evolution equation for a single-particle spot size, i.e. for a single quantum ray spot in the transverse plane (Compton regime). We demonstrate that such quantum evolution equation contains the same information as the evolution equation for the beam spot size that describes the beam as a whole. This is done heuristically by defining the lowest QWM state accessible by a system of non-overlapping fermions. The latter are associated with temperature values that are sufficiently low to make the single-particle quantum effects visible on the beam scale, but sufficiently high to make the overlapping of the single-particle wave functions negligible. This lowest QWM state constitutes the border between the fundamental single-particle Compton regime and the collective quantum and thermal regimes at larger (nano- to micro-) scales. Comparing it with the beam parameters in the existing accelerators, we find that it is feasible to achieve nano-sized beams in advanced compact machines.

Customized Aspheric IOL Design by Raytracing through the Eye Containing Quadric Surfaces

Purpose: The purpose of the present study was to demonstrate a method of how to calculate intraocular lenses with a customized asphericity and how to apply this strategy to clinical examples in cases where biometric data of the cornea (front and back surface topography) as well as distances in the eye are known.Methods: (1) we demonstrated an algebraic method for tracing a bundle of rays through a schematic eye containing surfaces which can be represented by 2nd order surfaces (quadric surfaces), and (2) we introduced a strategy for customization of the lens’ back surface for compensating the optical path length differences of the rays from object to image in terms of a wave front correction while predefining the lens front surface.Results: The presented method was applied to three working examples: example 1 referred to a centered optical system with a spherical cornea (front and back surfaces) and a predefined spherical lens front surface, example 2 referred to a centered optical system with aspherical surfaces for the corneal front and back surfaces and a predefined spherical lens front surface, and example 3 referrred to a non-centered system with a decentered aspherical cornea (front and back surface), and a predefined spherical lens front surface. The parameterized ray intersection points with the lens back surface were optimized in terms of equalizing the ray path lengths and a quadric surface was fitted to these ray intersection points to characterize the customized lens. The fitting error, ray spot diagram, and the optical path length of the rays are provided.Conclusion: This simple calculation strategy may be the first step in developing individual aspherical lenses, which have the potential to fully compensate spherical aberrations based on individual measures of the eye.

A 200kV Comprehensive Analytical Electron Microscope

With the use of a high-brightness electron source, the performance of the analytical electron microscope (AEM) has significantly improved. It features a variety of sophisticated analytical functions, such as X- ray spot analysis, area analysis, electron beam energy analysis, electron diffraction, and phase analysis using a biprism for holography. Here, we report the results of our analysis using a 200kV comprehensive AEM which has an integrated ZrO/W emitter as its optic source. The AEM (JEM- 2010F) is equipped with an X-ray energy dispersive spectrometer (EDS), scanning image observation device (ASID), parallel detection electron energy loss spectrometer (PEELS), and TV camera.(1) X-ray mapping using EDS and ASID With FEG, the probe current in a 1 nm probe is increased by two-order orders of magnitude, and the background noise generated near the sample and in the illumination system is minimized. As a result, EDS analysis features high sensitivity at a minimum detection of 1% weight fraction from an ultra-micro area of lnm diameter.

Cathode Ray Film Scanner

A spark chamber film reader has been developed which uses a computer directed cathode ray spot as the scanning light source. The equipment features data processing speed of 20 000 points per second while achieving position resolution of 4 μ. Search modes and film areas covered are controlled by the computer software giving wide flexibility.

New Instrument for Assessing Lens Quality by Pupil Scanning (Spot Diagram Generation)

An instrument has been constructed which can be used to assess the quality of infrared imaging systems (0.6 µm and 1.8 µm) by forming a picture on a cathode ray tube of the ray intersection pattern or spot diagram. Image analysis is carried out using a SIRA position-sensitive photocell. A complete diagram containing up to 400 points can be presented in 4 seconds with a magnification up to ×2,500 and with a noise equivalent spot diameter or 1 µm. Examples of the diagrams produced by good quality lenses and by lenses with residual astigmatism, spherical aberration and coma are shown. The present work is being extended to the construction of a system for converting spot diagrams to wavefront shapes and by the introduction of a range of transducers with a spectral sensitivity extending from the ultra-violet to the infra-red.

Model Experiments Relating to Sound Propagation in Shallow Seas

The object of model experiments on sound transmission in the sea is to supplement the somewhat empirical approach to the subject on a full scale. One serious difficulty in transmission research in the sea is that the conditions of the experiment are frequently not under our control—various perturbing factors are present which may mask the effect it is required to detect. The paper deals with the design of tanks, sound absorbers, transducers, etc., for small-scale work at frequencies of the order of 0.5 to l Mc/sec. This equipment has been used to record amplitude and phase of the received signal and to study the following factors influencing sound transmission: (1) nature of the bottom, (2) mean temperature and temperature gradients, (3) surface waves, and (4) depth of water. A study has also been made by visual observations of the sound distribution on the bottom and surface using (a) chemical methods, (b) abrasive methods, and (c) photography of “wedge” interference fringes on the water surface. These experiments reveal the complex nature of the interference phenomena occurring in the water. A new scanning technique has also been developed which gives a picture of a vertical section of the sound field (longitudinal or transverse) in the “model” tank. In this method the sound received is used to modulate the brightness of a cathode ray spot, and a “picture” record is made of the sound-intensity variations of the sound-field in the water. Comparisons have been made in this way between rocky and sand/mud bottoms.