Simplex optimization method for illumination design

Koshel, R. John

doi:10.1364/ol.30.000649

Cited by 54 publications

(28 citation statements)

References 4 publications

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“…4(b). The first 37 orthogonal Zernike standard polynomials were employed to fit the surface errors and the downhill simplex method [22,23] was applied to optimize the geometrical parameter GP . Figure 6 shows the change of the testing result on the surface error in the reverse optimization process, the testing result converged after three optimization cycles.…”

Section: Numerical Simulation Resultsmentioning

confidence: 99%

Computer-aided high-accuracy testing of reflective surface with reverse Hartmann test

Wang

Zhang

et al. 2016

Opt. Express

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Abstract:The deflectometry provides a feasible way for surface testing with a high dynamic range, and the calibration is a key issue in the testing. A computer-aided testing method based on reverse Hartmann test, a fringe-illumination deflectometry, is proposed for high-accuracy testing of reflective surfaces. The virtual "null" testing of surface error is achieved based on ray tracing of the modeled test system. Due to the off-axis configuration in the test system, it places ultra-high requirement on the calibration of system geometry. The system modeling error can introduce significant residual systematic error in the testing results, especially in the cases of convex surface and small working distance. A calibration method based on the computer-aided reverse optimization with iterative ray tracing is proposed for the highaccuracy testing of reflective surface. Both the computer simulation and experiments have been carried out to demonstrate the feasibility of the proposed measurement method, and good measurement accuracy has been achieved. The proposed method can achieve the measurement accuracy comparable to the interferometric method, even with the large system geometry calibration error, providing a feasible way to address the uncertainty on the calibration of system geometry.

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Section: Numerical Simulation Resultsmentioning

confidence: 99%

Computer-aided high-accuracy testing of reflective surface with reverse Hartmann test

Wang

Zhang

et al. 2016

Opt. Express

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“…For a nonimaging design, the most prevalent objectives to be optimized are efficiency, uniformity, angular emission, concentration factor, etc., 7,9 and as a rule, all of them must be optimized at the same time. In this paper, efficiency and uniformity are selected as the objectives of the MF as they conform to two of the most typical parameters involved in nonimaging systems.…”

Section: Dynamic Merit Functionmentioning

confidence: 99%

“…Equation (1) shows the direct influence of the weight factors on the MF and, therefore, on the optimization procedure. Commonly, the weights' factors fw i g are manually adjusted by a trial and error procedure; 7 this nonoptimal situation suggests the need to study methods for automatic adjustments of the weight factors fw i g. In this paper, we propose a new type of merit function, dynamic merit function (DMF), which automatically adjusts the weight factors fw i g during the progress of the optimization procedure. The variation of weight factors modifies the optimization problem, and DMF becomes an effective optimization method.…”

Section: Introductionmentioning

confidence: 99%

Application of dynamic merit function to nonimaging systems optimization

et al. 2015

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Abstract. Automatic optimization algorithms have been recently introduced as nonimaging optics design techniques. Unlike optimization of imaging systems, nonsequential ray tracing simulations and complex noncentered systems design must be considered, adding complexity to the problem. The merit function is a key element in the automatic optimization algorithm; nevertheless, the selection of each objective's weight, fw i g, inside the merit function needs a prior trial and error process for each optimization. The problem then is to determine appropriate weights' values for each objective. We propose a new dynamic merit function with variable weight factors fw i ðnÞg. The proposed algorithm automatically adapts weight factors during the evolution of the optimization process. This dynamic merit function avoids the previous trial and error procedure by selecting the right merit function and provides better results than conventional merit functions.

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“…The simplex method and its variants have been shown to provide satisfying results in nonimaging optics design optimization [14][15][16]. However, their capabilities for nonlinear or high dimensional problems are limited [12,[17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Augmented design and analysis of computer experiments: a novel tolerance embedded global optimization approach applied to SWIR hyperspectral illumination design

et al. 2016

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A novel meta-heuristic approach for minimizing nonlinear constrained problems is proposed, which offers tolerance information during the search for the global optimum. The method is based on the concept of design and analysis of computer experiments combined with a novel two phase design augmentation (DACEDA), which models the entire merit space using a Gaussian process, with iteratively increased resolution around the optimum. The algorithm is introduced through a series of cases studies with increasing complexity for optimizing uniformity of a short-wave infrared (SWIR) hyperspectral imaging (HSI) illumination system (IS). The method is first demonstrated for a two-dimensional problem consisting of the positioning of analytical isotropic point sources. The method is further applied to two-dimensional (2D) and five-dimensional (5D) SWIR HSI IS versions using close-and far-field measured source models applied within the non-sequential ray-tracing software FRED, including inherent stochastic noise. The proposed method is compared to other heuristic approaches such as simplex and simulated annealing (SA). It is shown that DACEDA converges towards a minimum with 1 % improvement compared to simplex and SA, and more importantly requiring only half the number of simulations. Finally, a concurrent tolerance analysis is done within DACEDA for to the five-dimensional case such that further simulations are not required.

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Simplex optimization method for illumination design

Cited by 54 publications

References 4 publications

Computer-aided high-accuracy testing of reflective surface with reverse Hartmann test

Computer-aided high-accuracy testing of reflective surface with reverse Hartmann test

Application of dynamic merit function to nonimaging systems optimization

Augmented design and analysis of computer experiments: a novel tolerance embedded global optimization approach applied to SWIR hyperspectral illumination design

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