论文标题
Hadamard和规范底座的比较，用于原位波前校正以及压缩感中排序的效果
Comparison between Hadamard and canonical bases for in-situ wavefront correction and the effect of ordering in compressive sensing
论文作者
论文摘要
在这项工作中，我们比较了使用空间光调制器（SLM）对聚焦高斯光束的原位波前校正的规范和Hadamard底座进行比较。光束被透明的光学元件（稀疏）或随机散射器（都阻止聚焦在单个位置）。相位校正以不同的基础大小（$ n = 64、256、1024、4096 $）实现，并且每个基元元素的相位贡献都通过3步干涉测量测量。该字段是从完整的$ 3N $测量值重建的，并且通过在SLM上投影共轭阶段来实现校正。我们的实验表明，通常，Hadamard基量测量结果会产生更好的校正，因为每个元素都跨越SLM的相关区域，从而减少了干涉图中的噪声。相比之下，规范基础具有基本限制，即元素的面积与$ 1/n $成比例，并且需要与光栅空间时期兼容的尺寸。在随机散射器的情况下，我们只能以哈达姆的基础进行合理的校正，而校正点的强度则与$ n $单调增加，这与小空间尺度上的相位快速随机变化是一致的。我们还探索了Hadamard基础的压缩感测，发现实现与使用完整测量的质量相似的校正所需的最小压缩率取决于基础排序。在Hadamard-Walsh和Cake Cutter Orderings的情况下，取得了最好的效果。出乎意料的是，在随机散射器的情况下，我们发现$ 10-20 \％$（$ n = 4096 $）的中等压缩比允许恢复重点的斑点，尽管如预期的那样，最大强度随着信号的非稀疏性而单调的数量增加。
In this work we compare the Canonical and Hadamard bases for in-situ wavefront correction of a focused Gaussian beam using a spatial light modulator (SLM). The beam is perturbed with a transparent optical element (sparse) or a random scatterer (both prevent focusing at a single spot). The phase corrections are implemented with different basis sizes ($N=64, 256, 1024, 4096$) and the phase contribution of each basis element is measured with 3 step interferometry. The field is reconstructed from the complete $3N$ measurements and the correction is implemented by projecting the conjugate phase at the SLM. Our experiments show that in general, the Hadamard basis measurements yield better corrections because every element spans the relevant area of the SLM, reducing the noise in the interferograms. % In contrast, the canonical basis has the fundamental limitation that the area of the elements is proportional to $1/N$, and requires dimensions that are compatible with the spatial period of the grating. In the case of the random scatterer, we were only able to get reasonable corrections with the Hadamard basis and the intensity of the corrected spot increased monotonically with $N$, which is consistent with fast random changes in phase over small spatial scales. We also explore compressive sensing with the Hadamard basis and find that the minimum compression ratio needed to achieve corrections with similar quality to those that use the complete measurements depend on the basis ordering. The best results are reached in the case of the Hadamard-Walsh and cake cutting orderings. Surprisingly, in the case of the random scatterer we find that moderate compression ratios on the order of $10-20\%$ ($N=4096$) allow to recover focused spots, although as expected, the maximum intensities increase monotonically with the number of measurements due to the non sparsity of the signal.
