The measurement of optical components using Experimental Ray Tracing (ERT) has proven its abilities in numerous applications. In this paper, we show how the measurement speed can be boosted by using a position sensitive detector (PSD). The results are compared with the measurement results using a camera. The idea of ERT is based on the linear propagation of a beam’s centroid through a homogenous medium. Therewith, detecting the centroid position of a beam in two parallel planes with a known distance leads to the beams direction. By introducing narrow laser beams at known positions and directions into an optical component or system and measuring the direction of the beams behind the component or systems as described above, the optical function of the component or system can be determined. To get this measurement technique working accurately, we used a movable camera chip as detector in two parallel planes. This brings the advantage of a good linearity and repeatability of the centroid detection. However, in contrast with a PSD, a camera chip is slow due to the generation and processing of many unused data. A PSD can achieve a measurement rate 20 times faster than a camera chip. Although, a good calibration is needed to achieve the same linearity and repeatability as a camera chip. In this paper we show the advantages and disadvantages of the use of a camera chip and a PSD in ERT. By measuring the same optical component, the detectors characteristics can be compared.
The manufacturing of optical components introduces varying surface errors with diverse impact to the optical performance. In this paper we propose a measurement technique to detect form and mid-spatial-frequency errors of specular freeform surfaces. Results from simulation and experimental measurements are presented. The aim of a manufacturer of optical components is to produce its products as precise as possible according to the given parameters of the designer. However, errors due to the manufacturing process are not avoidable. Regarding surface deviations, one distinguishes between form deviations, mid-spatial-frequency errors and roughness. The proposed measurement technique in this paper is able to detect form and mid-spatial-frequency errors in one measurement. Therefore, the investigated surface is scanned with a single laser beam. The direction if the reflected beam is measured using Experimental Ray Tracing. From the direction of the incident and the reflected beam, the surface gradient at the investigated position can be determined. Proper integration methods lead to the reconstruction of the surface. Knowing the model of the investigated optical components, the form deviations and the mid-spatial-frequency errors can be calculated. Considering the model as unknown, the mid-spatial frequency-errors can still be determined, by separating the mid-spatial-frequency components from the low-frequency form information of the reconstructed surface. In this paper we propose a measurement technique for the measurement of form and mid-spatial-frequency errors of specular freeform surfaces. The measurement principle as well as results from simulation and experimental measurements of freeform surfaces are shown and evaluated.
Lenses and mirrors with freeform surfaces are the latest step in the evolution of optical components. However, the measurement of these components still challenges metrology. We have developed a gradient-based measurement technique that is able to measure freeform specular surfaces either if their form is known or not. The measurement of freeform surfaces is a challenge for every measurement system. Especially if the form of the surface is not known in advance. Our measurement system can measure continuous freeform surfaces with up to 10° deviation from a plane surface even if the surface model is not known in advance. Therefore, a ray, represented by a narrow laser beam, is targeted on the surface under test (SUT) under a certain angle. Affected by its slope, the surface reflects the ray in a new direction. This direction is measured by using a variation of Experimental Ray Tracing (ERT). This includes the measurement of the position of the reflected ray in two parallel planes. Calculating the difference of the position on these planes, the direction of the ray in relation to them can be calculated. Having the direction of the reflected ray, as well as the direction of the incident ray, one can determine the surface normal at the point of reflection. By moving the SUT, the incident ray targets on a different point on the SUT. Therewith, various points are investigated. Using appropriate integration methods, the surface can be reconstructed. Although, with the introduction of the incident ray under a certain angle comes the issue, that the point of reflection changes with the sag of the SUT. This leads to an unequal distant measurement grid of points of reflection even if the SUT has been moved to equal distant sample points. This shift has to be considered for the reconstruction of the surface. This issue is solved in different ways for known or unknown surfaces. For an unknown surface, the investigated sample points are transferred into a coordinate system where they are equal distant. This is the coordinate system of the incident beam. Performing the integration here and transferring the reconstructed surface back into the coordinate system of the SUT leads to the expected shift of the sample points. For a known surface, the expected surface form is taken into account to determine the sample point shift. Therewith, the difference between the measured surface normals and the expected normals can be calculated and the integration can be performed only on the normal residuals. By adding the residuals to the model, the surface can be reconstructed. The measurement technique described above has been implemented in an experimental setup. To show the abilities of this technique, we will show the process of the measurement of a known and an unknown surface using the same sample. The results will be evaluated and compared.
New methods enabling the production of custom-tailored Gradient Index (GRIN) optical components brings the next challenge to the lens manufacturers. Simultaneously, for testing these optics, metrology has to evolve to accommodate new optics. In this paper, we describe how Experimental Ray Tracing (ERT) can be used to test GRIN optics produced using additive manufacturing. To evaluate this technique, we compare the results to those obtained using Phase Shifting Diffraction Interferometry (PSDI). The common way of lens manufacturers to verify their products is the measurement of the surface, e.g. using surface profilers or reflective interferometry. Determination of optical performance solely from surface topography includes the assumption of a completely homogeneous structure inside the lens. Since GRIN lenses introduce material inhomogeneity on purpose, these measurement techniques exceed their limits, as surface measurement techniques cannot see the material structure inside the lens. To overcome this problem, we propose the measurement of GRIN lenses using ERT. This reference free measurement technique measures the device under test in transmission. A narrow laser beam is introduced into the device under test (DUT) at a known position. By measuring the direction of the beam behind the DUT, its optical function at this position can be determined. Evaluating these local measurements to an optical powermap over the full aperture, details of the inside structure of the DUT can be seen. The results of the proposed measurement technique show good agreement with the results from measurements using PSDI. However, differences can be seen between the two techniques. Therefore, the results of both measurement techniques are evaluated and compared and the advantages and disadvantages of both techniques are presented.
Several investigations have been performed in the field of designing a lens-array for LED signal lighting applications. Solving the parabolic Monge-Ampere (PMA) equation to design the required lens-array leads to problems in matching the boundaries of the lens-lets. Therefore, considerations should be taken into account while generating the mapping adaptive grids. In this paper, we focus on the mathematical investigations of the numerical solution of the PMA equation for the steady state solution, as it is one of the state of the art methods. The first objective is to use the solution of PMA equation for generating the adaptive grid. The second objective is to test the quality of the light-energy mapping by applying the Monte-Carlo simulation to the generated adaptive mesh grid. The last objective is to use the resulting mesh grids in designing a lens-array for signal lighting applications. The paper starts by presenting the difference between signal lighting and optical illumination. Then, an explanation of the advantages of using the beam-let transformation concept in the optical systems designs which is the motivation for us to investigate the solutions of the PMA equation. After that, procedures of generating the adaptive grid are discussed. Also, results of the Monte-Carlo simulation are presented to evaluate the quality of the generated grid. Finally, the problems of using the generated grid for designing a lens-array are discussed, including an approach to control the light-energy mapping to design the boundaries of the optical surfaces as a part of our future investigations.
The design of a secondary optical lens for light beam shaping using the transformation method is performed by transforming the light source energy distribution using the concepts of energy conservation and light energy mapping. Using these concepts creates a dependency relation between the output optical performance and the luminous intensity distribution of the light source. This relation leads to errors on the optical performance due to the fabrication misalignment between the light source and the secondary optical lens. On the other hand, in the illumination applications, the integration method has been proved to be an efficient method for achieving a high degree of homogenized luminous intensity distribution by integrating and superimposing the light source energy over the illuminated objects. In signal lighting applications, the luminous intensity distribution must meet the requirements regarding the brightness perception of users over the spatial angular distribution, not the illumination of objects. In this paper, the integration method is combined with the transformation method to design a refractive lens-array for signal lighting applications. The difference between the two methods is described, presenting the advantages of the combination process. Design procedures are explained in detail including the lens-array modeling. The optical performance is investigated using an optical ray tracing. Finally, the influence of the misalignment between the light source and the refractive lens-array is measured.
Freeform optical systems are playing an important role in the field of illumination engineering for redistributing the light intensity, because of its capability of achieving accurate and efficient results. The authors have presented the basic idea of the freeform lens design method at the 117th annual meeting of the German Society of Applied Optics (DGAOProceedings). Now, we demonstrate the feasibility of the design method by designing and evaluating a freeform lens. The concepts of luminous intensity mapping, energy conservation and differential equation are combined in designing a lens for non-imaging applications. The required procedures to design a lens including the simulations are explained in detail. The optical performance is investigated by using a numerical simulation of optical ray tracing. For evaluation, the results are compared with another recently published design method, showing the accurate performance of the proposed method using a reduced number of mapping angles. As a part of the tolerance analyses of the fabrication processes, the influence of the light source misalignments (translation and orientation) on the beam-shaping performance is presented. Finally, the importance of considering the extended light source while designing a freeform lens using the proposed method is discussed.
KEYWORDS: Ray tracing, 3D metrology, Channel projecting optics, Information theory, Sensors, Reflection, Error analysis, Optical components, Tolerancing, 3D modeling
Optical deflectometric methods with their inherent potential of high channel capacity with regard to information theory has been of great interest for specular surface topography measurement, where the limited dynamic range needs to be considered in the detection plane. Achieving a final smooth reconstructed surface is the next challenge, because the 2Dintegration methods for the interpolation of the derived data from such sensors are prone to various sources of error such as path dependency, large data sets and secondary reflections. On the other hand, Radial Basis Functions have been studied in this respect for the last years and their characteristics have been widely discussed. In this paper, we introduce our approach for the 3D measurement of specular surfaces by means of Experimental Ray Tracing and Radial Basis Functions integration. We present simulations and discuss the reconstructed surface and the resulting reconstruction error results.
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