A fast and effective shape reconstruction method of large aspheric specular surfaces with high order terms is proposed in fringe reflection technique, which combines modal estimation with high-order finite- difference...A fast and effective shape reconstruction method of large aspheric specular surfaces with high order terms is proposed in fringe reflection technique, which combines modal estimation with high-order finite- difference algorithm. The iterative equation with high- order truncation errors is derived for calculating the specular surface with large aperture based on high-order finite-difference algorithm. To achieve the wavefront estimation and improve convergence speed, the numerical orthogonal transformation method based on Zemike polynomials is implemented to obtain the initial iteration value. The reconstruction results of simulated surface identified the advantages of the proposed method. Furthermore, a freeform in illuminating system has been used to demonstrate the validity of the improved method in practical measurement. The results show that the proposed method has the advantages of making the reconstruction of different shape apertures accurate and rapid. In general, this method performs well in measuring large complex objects with high frequency information in practical measurement.展开更多
We present a freeform lens for application to light-emitting diodes （LED） road lighting. We propose a simple source-target luminous intensity mapping method based on Snell＇s law and geometric-optics analysis. We ca...We present a freeform lens for application to light-emitting diodes （LED） road lighting. We propose a simple source-target luminous intensity mapping method based on Snell＇s law and geometric-optics analysis. We calculated different contours of cross-sections to construct a freeform lens with a smooth surface. The computer simulation results show that the lighting performance of a single freeform lens is not sufficient for road lighting. For the road lamp simulation, we adopted an oval arrangement of freeform lenses on a printed circuit board. In addition, we performed tolerance analysis to determine the tolerance limits of manufacturing and installation errors. A road lamp at a height of 12 m can create rectangular illumination with an area of 40 m ~ 12 m, 69.7% uniformity, and average illuminance of 24.6 lux. This lighting performance can fully comply with the urban road lighting design standard.展开更多
Subaperture stitching （SAS） provides us with an attractive way of extending the effective aperture and dynamic range of phase measuring interferometers. Accuracy of stitching algorithm becomes the key factor in the ...Subaperture stitching （SAS） provides us with an attractive way of extending the effective aperture and dynamic range of phase measuring interferometers. Accuracy of stitching algorithm becomes the key factor in the SAS technology. In this paper, the basic principle of SAS was introduced and four modes of SAS were discussed. The stitching experiments were done through the SSI-300 workstation designed and developed indepen- dently. There were several comparisons between the four different stitching methods and the measurement of full aperture. The results suggest that the global error averaging mode with reference of subaperture near optic axis is of high precision.展开更多
This study presents a strategy which integrates extra polishing path （EPP） and error map extension to weaken the edge effect in the ultraprecise optical surfacing process. Different data extension algorithms were pr...This study presents a strategy which integrates extra polishing path （EPP） and error map extension to weaken the edge effect in the ultraprecise optical surfacing process. Different data extension algorithms were pre- sented and analyzed. The neighbor-hood average can be selected as the frequently-used method, as it has not bad precision and time-saving performance for most surface forms through the simulation results and practical experi- ment. The final error map was obtained, its peak-to-valley （PV） was 0.2732 and root mean square （RMS） was 0.0282 （2 = 632.8nm）. The edge effect was weakened and suppressed well through the experiment.展开更多
Three-dimensional （3D） profile measurement is an indispensable process for assisting the manufacture of various optic, especially aspheric surfaces. This work presents the measurement error calibration of a 3D profi...Three-dimensional （3D） profile measurement is an indispensable process for assisting the manufacture of various optic, especially aspheric surfaces. This work presents the measurement error calibration of a 3D profile measurement system, namely PMI700. Measurement errors induced by measuring tool radius, alignment error and the temperature variation were analyzed through geometry analysis and simulation. A quantitative method for the compensation of tool radius and an alignment error compensation model based on the least square method were proposed to reduce the measurement error. To verify the feasibility of PMI700, a plane and a non-uniform hyperboloidal mirror were measured by PMI700 and interferometer, respectively. The data provided by two systems were high coincident. The direct subtractions of results from two systems indicate RMS deviations for both segments were less than 0.22.展开更多
This paper focuses on the process of electrorheological （ER） finishing optical surfaces. Experiments on K9 mirrors were conducted. In one experiment, the operating distance was varied over 0.5-0.8 mm with the voltag...This paper focuses on the process of electrorheological （ER） finishing optical surfaces. Experiments on K9 mirrors were conducted. In one experiment, the operating distance was varied over 0.5-0.8 mm with the voltage at 2000 V. The maximum peak-to-valley （PV） reduction was obtained at the distance of 0.5 ram, where the PV value was reduced from 58.71 to 25.03nm. In another experiment, the voltage was varied over 1500- 3000V with operating distance at 0.5mm. The final surface roughness （Ra） achieved was as low as 2.5 rim. A higher voltage produced a higher relative reduction of the Ra. These experimental results validated the process.展开更多
In this paper, the principle of subaperture stitching interferometry was introduced. A testing stage with five degrees of freedom for stitching interferometry was built. A model based on least-squares method and error...In this paper, the principle of subaperture stitching interferometry was introduced. A testing stage with five degrees of freedom for stitching interferometry was built. A model based on least-squares method and error averaging method for data processing was estab- lished, which could reduce error accumulation and improve the precision. A 100ram plane mirror was measured with a 50mm aperture interferometer by means of stitching interferometry. Compared with the results by a 100 mm interferometer, peak to valley （PV） and root mean square （RMS） of the phase distribution residual are 0.00382 and 0.00042, respectively. It proved that the model and method are helpful for large optical measurement.展开更多
文摘A fast and effective shape reconstruction method of large aspheric specular surfaces with high order terms is proposed in fringe reflection technique, which combines modal estimation with high-order finite- difference algorithm. The iterative equation with high- order truncation errors is derived for calculating the specular surface with large aperture based on high-order finite-difference algorithm. To achieve the wavefront estimation and improve convergence speed, the numerical orthogonal transformation method based on Zemike polynomials is implemented to obtain the initial iteration value. The reconstruction results of simulated surface identified the advantages of the proposed method. Furthermore, a freeform in illuminating system has been used to demonstrate the validity of the improved method in practical measurement. The results show that the proposed method has the advantages of making the reconstruction of different shape apertures accurate and rapid. In general, this method performs well in measuring large complex objects with high frequency information in practical measurement.
文摘We present a freeform lens for application to light-emitting diodes （LED） road lighting. We propose a simple source-target luminous intensity mapping method based on Snell＇s law and geometric-optics analysis. We calculated different contours of cross-sections to construct a freeform lens with a smooth surface. The computer simulation results show that the lighting performance of a single freeform lens is not sufficient for road lighting. For the road lamp simulation, we adopted an oval arrangement of freeform lenses on a printed circuit board. In addition, we performed tolerance analysis to determine the tolerance limits of manufacturing and installation errors. A road lamp at a height of 12 m can create rectangular illumination with an area of 40 m ~ 12 m, 69.7% uniformity, and average illuminance of 24.6 lux. This lighting performance can fully comply with the urban road lighting design standard.
基金This work was supported by the National Natural Science Foundation of China （Grant Nos. 60978043, 61128012, 610611 60503, and 61222506）.
文摘Subaperture stitching （SAS） provides us with an attractive way of extending the effective aperture and dynamic range of phase measuring interferometers. Accuracy of stitching algorithm becomes the key factor in the SAS technology. In this paper, the basic principle of SAS was introduced and four modes of SAS were discussed. The stitching experiments were done through the SSI-300 workstation designed and developed indepen- dently. There were several comparisons between the four different stitching methods and the measurement of full aperture. The results suggest that the global error averaging mode with reference of subaperture near optic axis is of high precision.
文摘This study presents a strategy which integrates extra polishing path （EPP） and error map extension to weaken the edge effect in the ultraprecise optical surfacing process. Different data extension algorithms were pre- sented and analyzed. The neighbor-hood average can be selected as the frequently-used method, as it has not bad precision and time-saving performance for most surface forms through the simulation results and practical experi- ment. The final error map was obtained, its peak-to-valley （PV） was 0.2732 and root mean square （RMS） was 0.0282 （2 = 632.8nm）. The edge effect was weakened and suppressed well through the experiment.
基金Acknowledgements This work was supported by the National Natural Science Foundation of China （Grant Nos. 61128012, 61061160503 and 61222506）, the Key Laboratory of Photoelectronic Imaging Technology and System, BIT, Ministry of Education of China （No. 2013OEIOF06）.
文摘Three-dimensional （3D） profile measurement is an indispensable process for assisting the manufacture of various optic, especially aspheric surfaces. This work presents the measurement error calibration of a 3D profile measurement system, namely PMI700. Measurement errors induced by measuring tool radius, alignment error and the temperature variation were analyzed through geometry analysis and simulation. A quantitative method for the compensation of tool radius and an alignment error compensation model based on the least square method were proposed to reduce the measurement error. To verify the feasibility of PMI700, a plane and a non-uniform hyperboloidal mirror were measured by PMI700 and interferometer, respectively. The data provided by two systems were high coincident. The direct subtractions of results from two systems indicate RMS deviations for both segments were less than 0.22.
文摘This paper focuses on the process of electrorheological （ER） finishing optical surfaces. Experiments on K9 mirrors were conducted. In one experiment, the operating distance was varied over 0.5-0.8 mm with the voltage at 2000 V. The maximum peak-to-valley （PV） reduction was obtained at the distance of 0.5 ram, where the PV value was reduced from 58.71 to 25.03nm. In another experiment, the voltage was varied over 1500- 3000V with operating distance at 0.5mm. The final surface roughness （Ra） achieved was as low as 2.5 rim. A higher voltage produced a higher relative reduction of the Ra. These experimental results validated the process.
基金This work was supported by the National Natural Science Foundation of China （Grant No. 61128012） and the Research Grants Council of the Hong Kong Special Administrative Region （No. 9041577）.
文摘In this paper, the principle of subaperture stitching interferometry was introduced. A testing stage with five degrees of freedom for stitching interferometry was built. A model based on least-squares method and error averaging method for data processing was estab- lished, which could reduce error accumulation and improve the precision. A 100ram plane mirror was measured with a 50mm aperture interferometer by means of stitching interferometry. Compared with the results by a 100 mm interferometer, peak to valley （PV） and root mean square （RMS） of the phase distribution residual are 0.00382 and 0.00042, respectively. It proved that the model and method are helpful for large optical measurement.
