Experimental Ray Tracing Research Articles

Multi-parameter identification of gratings measurement by Experimental Ray Tracing

A simple method for measuring grating groove density as well as its position and orientation is proposed based on the idea of ERT (Experimental Ray Tracing). Conventional methods only measure grating groove density with accuracy limited by its rotary stage and goniometer. The method proposed in the paper utilizes linear guides which could be calibrated to much higher accuracy. It is applicable to gratings of arbitrary surface profile or mosaic of a group of various gratings. Various measurement error sources are simulated by the Monte Carlo method and the results show high accuracy capability of grating parameters identification. A verification testing is performed. The accuracy dependency on main configuration parameters is evaluated. A method to expand measurement range by double wavelength is also discussed.

Characterization of specular freeform surfaces from reflected ray directions using experimental ray tracing

Abstract. The applications of freeform surfaces in optical components and systems are increasing more and more. Therefore, appropriate measurement techniques are needed to measure these freeform surfaces for verification. This task is still a challenge for most measurement techniques. In this paper, we propose a measurement technique for optical and other specular freeform surfaces based on experimental ray tracing. This technique is able to measure form and mid-spatial-frequency deviations simultaneously. The focus will be set on the sensing technique and the measurement uncertainties in the setup. As the measurement technique is described, an estimation of the influence of different uncertainties based on simulations is given. The result from an experimental measurement is evaluated in relation to the influence of the uncertainties. A comparison measurement for evaluation is given.

Experimental ray-tracing with point diffraction interferometry and its application in focal length measurement.

A novel method that could experimentally trace the ray propagation of an optical system based on point diffraction interferometry (PDI) is presented. The ray represented by the line connecting two point light sources (PLS) intersects with two parallel photographic planes, which are separated at a distance. The intersections of the ray defined by the PLSs with the planes occur where the optical path difference is a maximum and can be determined from interferograms on the photographic planes. The ray is determined by connecting the two intersections. Using fibers as the PLSs and CCD arrays as the photographic planes, we demonstrate its principle and its application in focal length measurement through experiments.

Fitting discrete aspherical surface sag data using orthonormal polynomials.

Characterizing real-life optical surfaces usually involves finding the best-fit of an appropriate surface model to a set of discrete measurement data. This process can be greatly simplified by choosing orthonormal polynomials for the surface description. In case of rotationally symmetric aspherical surfaces, new sets of orthogonal polynomials were introduced by Forbes to replace the numerical unstable standard description. From these, for the application of surface retrieval using experimental ray tracing, the sag orthogonal Q(con)-polynomials are of particular interest. However, these are by definition orthogonal over continuous data and may not be orthogonal for discrete data. In this case, the simplified solution is not valid. Hence, a Gram-Schmidt orthonormalization of these polynomials over the discrete data set is proposed to solve this problem. The resulting difference will be presented by a performance analysis and comparison to the direct matrix inversion method.

Experimental ray-tracing – a precise and accurate method for the determination of the properties of optical systems

We developed a new technique to determine the impact position of single pencil beams in the image plane with an accuracy of 0.2 μm. This technique bases on the overlapping of secondary electron images from a 1000 mesh grid. The measurements themselves can be obtained without any change in the routine setup if a secondary electron counter is installed. By choosing different object positions (x0, y0) and divergence angles (θ0, ϕ0) for the pencil beam the characteristics of the used lens system can be analysed and the lens errors can be calculated with high precision. Results for the Heidelberg quadrupole doublet will be reported.

Experimental test of an achromatic quadrupole lens doublet — Aberration coefficients of second degree in ion energy at the operating point

Experimental tests of the focusing behaviour of an achromatic quadrupole lens doublet are made using protons of energy 350 < E < 800 keV. The procedure of experimental ray tracing is used, in which aberrations of a finely focused beam at the focal plane are measured as the location ( x 2, y 2) of the input ray within the lens aperture is varied. In general, the aberration is a linear function of the convergence angles a, b measured from the center of the image into the lens aperture. The magnitude of the linear slope, which indicates defocus, depends on the energy deviation e = dE E 0 , where E 0 is the achromatic operating energy. In both principal sections the slope decreases to a minimum at E 0, where the 1st-order, 1st-degree aberration coefficients are 〈 x, ae〉 = 0, and 〈 y, be〉 = 0. A quadratic dependence of the slope upon e 2 is fitted to the data, and experimental 1st-order, 2nd-degree coefficients 〈 x ae 2 〉 = 14 cm , 〈 y be 2 〉 = 2.7 cm are determined, in agreement with theory.

Experimental compensation of parasitic octopole aberrations in small-bore quadrupole lenses

Using a procedure of experimental ray tracing, measurements of the aberrations of an achromatic quadrupole lens are made, from which 3rd-order coefficients such as 〈 x a 2b 〉 = − 0.6 km and 〈 y ab 2 〉 = 5 km may be estimated. Both these coefficients would be zero in a lens with perfect quadrupole symmetry, so that they must arise from parasitic effects. Theory predicts that the first coefficient can be compensated by electric excitation of the eight lens poles, while the second coefficient arises from parasitic octopole fields inclined at an angle of 22.5° to the principal sections of the quadrupoles. Since the quadrupoles contain no pole at this azimuth, we have added an inclined electric octopole corrector upstream of the doublet. It is found that the inclined octopole can be used to set 〈 y ab 2 〉 = 0 within the accuracy of the experimental measurements.

Testing optics by experimental ray tracing with a lateral effect photodiode

We demonstrate a method for testing optics (spherical and aspheric) and other reflecting or transmitting objects. We call this experimental ray tracing. A laser beam is sent through the sample, and its propagation is determined with a lateral effect photodiode. A modified Hartmann test can be performed by measurement of beam location within two planes. Measurement in one plane close to the focus delivers a spot diagram. The method is well suited for testing even strong aspheric optics. As a further use we demonstrate 3-D shape measurement of nonplanar glass plates, e.g., car windshields.

The ion optical properties of the Munich Q3D-spectrograph investigated by means of a special experimental ray tracing method

The ion optical properties of the Munich Q3D-spectrograph were investigated using a special experimental ray tracing method. Cs +-ions produced in a thermal ion source were accelerated by means of a very stable dc-voltage and focused on the object point of the spectrograph (spot size 0.2 × 2 mm 2). From this ion beam a set of rays corresponding to those used in ray tracing calculations was obtained by a special collimator system. The positions of these rays were measured in the region of the focal plane with an accuracy of about 0.15 mm. From these measurements we have been able to determine the ion optical properties of the spectrograph including aberration coefficients up to 4th order. The results are compared to ray tracing calculations for the spectrograph. Within the accuracy of both the ray tracing calculations (due to uncertainties in field boundaries), and the measurements reasonable agreement is found.