Freeform and precise irradiance tailoring in arbitrarily oriented planes

Abstract

Freeform and precise irradiance tailoring in arbitrarily oriented planes is an ultimate goal of nonimaging optics and has not been well addressed. In this paper, we develop a general formulation for arbitrary and precise irradiance tailoring in three-dimensional (3D) space using freeform lenses. This method breaks any symmetric constraints imposed on the geometrical arrangement of conventional beam shaping systems, yielding high-performance beam shaping systems with new functions and flexible geometrical arrangements in 3D space. This method paves a way for the broad application of freeform optics. The robustness and effectiveness of the method is demonstrated by two interesting but challenging designs.

Fresnel reflections in inverse freeform lens design

“…As mentioned, most inverse methods for freeform optical design do not take into account Fresnel reflections. There are some methods that aim to minimize the total loss due to Fresnel effects [10][11][12]. However, the authors only try to minimize the reflectance, and do not take into account the effect of the Fresnel reflections on the outgoing intensity or irradiance.…”

Supporting Quadric Method for Designing Freeform Mirrors That Generate Prescribed Near-Field Irradiance Distributions

“…The problem of designing a reflecting or refracting optical surface that can generate a required irradiance distribution in a certain domain belongs to the inverse problems of nonimaging optics and is extremely complex. In the geometrical optics approximation, this inverse problem can be reduced to finding a solution to a nonlinear differential equation (NDE) of an elliptic type [1][2][3][4][5][6][7][8][9][10]. Although several finite difference methods have been proposed for solving such NDEs [1][2][3][4][5][6][7][8][9][10], the design of optical elements using this approach is sophisticated and has significant limitations.…”

“…In the geometrical optics approximation, this inverse problem can be reduced to finding a solution to a nonlinear differential equation (NDE) of an elliptic type [1][2][3][4][5][6][7][8][9][10]. Although several finite difference methods have been proposed for solving such NDEs [1][2][3][4][5][6][7][8][9][10], the design of optical elements using this approach is sophisticated and has significant limitations. In particular, the formulation of the problem of the calculation of an optical element as an NDE assumes that the optical surfaces of the element are smooth.…”

“…In this case, the known methods based on The presented example demonstrates one of the advantages of the proposed method, which consists of the capability to calculate continuous piecewise smooth surfaces for implementing discontinuous ray mappings. In this case, the known methods based on numerical solution of NDEs of an elliptic type [1][2][3][4][5][6][7][8][9][10] are either inapplicable or numerically unstable.…”

Fresnel reflections in inverse freeform lens design

“…As mentioned, most inverse methods for freeform optical design do not take into account Fresnel reflections. There are some methods that aim to minimize the total loss due to Fresnel effects [10][11][12][13]. However, the authors only try to minimize the reflectance, and do not take into account the effect of the Fresnel reflections on the outgoing intensity or irradiance.…”