Inverse symmetric Dammann grating is a special grating, whose transition points are reflection symmetric about the midpoint with inverse phase offset in one period. It can produce even-numbered or odd-numbered array illumination when the phase modulations are pi or a specific value. Numerical solutions optimized by the steepest-descent algorithm for binary phase and multilevel phases with splitting ratio from 1 X 4 to 1 X 14 are given. Fabrication of 1 X 6 array without the zero-order intensity and 1 X 7 array with the zero-order intensity are made from the same amplitude mask. A 6 X 6 output without the crossed zero-orders was achieved by crossing two one-dimensional 1 X 6 inverse symmetric Dammann gratings. This grating may have potential value for practical applications.
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机译：逆对称达曼光栅是一种特殊的光栅，其过渡点围绕中点反射对称，并且在一个周期内具有逆相位偏移。当相位调制为pi或特定值时，它可以产生偶数或奇数阵列照明。给出了用最速下降算法对分相比为1 X 4到1 X 14的二元相和多能相进行优化的数值解。用相同的振幅掩模制造没有零阶强度的1 X 6阵列和没有零阶强度的1 X 7阵列。通过交叉两个一维1 X 6逆对称Dammann光栅，可以实现没有交叉零阶的6 X 6输出。该光栅对于实际应用可能具有潜在价值。
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