• Proceedings of the Optical Society of Korea Conference
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• 2000.08a
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• pp.40-41
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• 2000

광학설계의 최적화에서는 최소자승법과 감쇠최소자승법이 주로 사용되고 있다. 최소자승법은 error의 제곱의 합을 최소화하는 방법으로, 이 방법은 최적점 부근에서의 불안정성이 발생하는 문제점이 있다. 감쇠최소자자승법은 최소자승법에 적절한 감쇠항을 부가함으로써 최적점 부근에서의 불안정성을 줄여주고 있다. 본 연구에서는 광학설계의 제한조건을 Lagrange 부정승수$^{(1)}$ 를 사용하여 감쇠최소자승법의 정규방정식에 결합하여 제한조건을 유지하면서 merit function을 줄이는 방법에 대하여 연구하였다. 이 방법에서는 제한조건이 merit function의 error 함수보다 우선적으로 보정되며, 이를 이용하여 매 iteration 마다 merit function에서 절대값이 큰 error를 감쇠최소자승법의 정규방정식에서 제거하고 이 보정조건을 제한조건에 추가함으로서 다른 error항 보다 우선적으로 보정되도록 하였다. 이 때 이 error를 한번에 보정하는 경우에는 merit function의 진동이 심하고 광학계가 사용불가능한 형태로 변화하는 경우가 많아 적절한 target ratio를 설정하여 반복과정을 통하여 점진적으로 보정되도록 하였으며, 이를 통하여 최적화의 안정성을 개선할 수 있었다. (중략)

• Korean Journal of Optics and Photonics
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• v.4 no.4
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• pp.363-372
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• 1993

An optimization technique with variable orthogonalization and SVD(singular value decomposition) is examined in a double-Gauss type photographic lens design and its convergence and stability are compared with ordinary least squares and DLS(damped least squares) method. It is known that there are close relationship between the stability of optimization and condition number of nomal equation, the ratio between maximum and minimum of eigenvalues. In this study, the stability is greatly improved by limiting the condition number, the SVD, as expeded. The case of DLS with small damping, orthogonalization and SVD shows the most rapid convergence and stability. It means that the unstability of DLS method with small damping is overcome by using the variable orthogonalization and SVD.

• Korean Journal of Optics and Photonics
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• v.8 no.2
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• pp.88-94
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• 1997

Photographic lenses and an aspheric optical pickup-lens are designed by using damped least-squares(DLS) method. We start optimization with arbitrary initial damping factor. To improve the rate of convergence and the stability in optimization, we apply the special procedure that estimates numerical adequacy of derivative increments of variables to the DLS method. When the initial damping factor is almost equal to the median of series of eigenvalues, the convergence and the stability of the method significantly are improved. Optimized lenses have the performance of each target.

• Proceedings of the KSEEG Conference
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• 1999.04a
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• pp.100-102
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• 1999

• Journal of Korean Ophthalmic Optics Society
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• v.6 no.2
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• pp.121-127
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• 2001

While SVD and Gaussian elimination method were applied to the additive damped least squares(DLS), the convergence and the stability of the optimization process were examined in a triplet-type camera lens-system where the condition number is well conditioned. DLS with SVD method generated a suitable merit function but this merit function may be trapped in a local minimum by the nonlinearity of error function. Therefore, the least camera lens-system was further designed by the global optimization method is grid method, and this method is adopted to get merit function that convergent to global minimum without local minimum trapping.

• Geophysics and Geophysical Exploration
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• v.1 no.3
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• pp.155-160
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• 1998

EM tomography technique has been developed. The algorithm used the extended Born approximations for forward modeling and reconstructed a conductivity image by a smoothness constraint least squares inversion method. Observed data, the vertical components of secondary magnetic fields, were simulated with the 3-D integral equation code. The results showed that the location of anomalous body could be imaged very well, but conductivity of the body was lower than real one and the vertical resolution was much higher than the horizontal resolution.

• Korean Journal of Optics and Photonics
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• v.6 no.3
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• pp.178-187
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• 1995

The method that determines the appropriate damping factor is studied for a lens design. When suitable damping factor is applied to the additive damped least-squares (DLS) method, the convergence and the stability of the optimization process are examined in a triplet-type photographic lens design. We calculate eigenvalues of the product of the Jacobian matrix of error functions by using the singular value decomposition (SVD) method. We adopt the median of eigenvalues as an appropriate damping factor. The convergence and the stability of the optimization process are improved by choosing the adequate damping factor for the optimization of a photographic lens. It is known that the numerical inaccuracy in the calculation of normal equation is overcome by using the orthogonal transformations of the Jacobian matrix. Therefore, a combination of the method for setting a proper damping factor and the orthogonal transformations of the Jacobian matrix is good for application to the design of an aspheric lens with high-order terms. terms.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.20 no.4
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• pp.489-496
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• 2019

This paper is a study on the evaluation of loss factor of damping treatment materials to reduce the noise and vibration for panels of railway vehicles and automobiles. In order to determine the modal parameters of damping materials, beam excitation tests were carried out using different type PVC coated aluminum and steel base beam specimens. The specimens were excited from 10 Hz to 1000 Hz frequency range using sinusoidal force, and transfer mobility data were measured by using an accelerometer. The loss factors were determined by using integrated program, based on theories of Half Power Method, Minimum Tangent Error Method, Minimum Angle Error Method and Phase Change Method, which enable to evaluate the parameters using modal circle fit and least squares error method. In the case of lower loss factor and data of linear characteristics, any method could be applied for evaluation of parameters, however the case of higher loss factor or data including non-linear characteristics, the minimum angle error method could reduce the loss factor evaluation. The obtained dynamic properties of the coating material could be used for application of Finite Element Method analyzing the noise control effects of complex structures such as carbody or under-floor boxes of rolling stock. The damping material will be very useful to control the structural noise, because the obtained modal loss factors of each mode show very good effect on over $2^{nd}$ mode frequency range.

• Proceedings of the Optical Society of Korea Conference
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• 1991.06a
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• pp.162-167
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• 1991

홀로그램 광학소자(holographic optical element)의 일종인 holographic collimating lens(HCL)를 최적 설계하였으며, 중크롬산 젤라틴 필름을 사용하기 최적 설계치에 따라 HCL을 제작하였고 그 성능을 평가하였다. off-axis 방식의 holographic zone plate (HZP) 구조를 채택하였으며, 기록광과 재생광의 파장 차이에 의한 색수차를 최소화시키기 위해 유한 광선 추적법과 감쇠 최소자승법으로 최적 설계하였다. Dipping 법으로 제작된 중크롬산 젤라틴(Dichromated Gelatin, DCG) 필름을 기록 매질로 사용하여 HCL을 제작하였으며 회절광의 집적도를 측정하여 그 성능을 평가하였다.

• Geophysics and Geophysical Exploration
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• v.8 no.2
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• pp.129-136
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• 2005

The damped least-squares inversion has become a most popular method in finding the solution in geophysical problems. Generally, the least-squares inversion is to minimize the object function which consists of data misfits and model constraints. Although both the data misfit and the model constraint take an important part in the least-squares inversion, most of the studies are concentrated on what kind of model constraint is imposed and how to select an optimum regularization parameter. Despite that each datum is recommended to be weighted according to its uncertainty or error in the data acquisition, the uncertainty is usually not available. Thus, the data weighting matrix is inevitably regarded as the identity matrix in the inversion. We present a new inversion scheme, in which the data weighting matrix is automatically obtained from the analysis of the data resolution matrix and its spread function. This approach, named 'extended active constraint balancing (EACB)', assigns a great weighting on the datum having a high resolution and vice versa. We demonstrate that by applying EACB to a two-dimensional resistivity tomography problem, the EACB approach helps to enhance both the resolution and the stability of the inversion process.