The output of physical systems, such as the scrambled pattern formed by shining the spot of a laser pointer through fog, is often easily accessible by direct measurements. However, selection of the input of such a system to obtain a desired output is difficult, because it is an ill-posed problem; that is, there are multiple inputs yielding the same output. Information transmission through scattering media is an example of this problem. Machine learning approaches for imaging have been implemented very successfully in photonics to recover the original input phase and amplitude objects of the scattering system from the distorted intensity diffraction pattern outputs. However, controlling the output of such a system, without having examples of inputs that can produce outputs in the class of the output objects the user wants to produce, is a challenging problem. Here, we propose an online learning approach for the projection of arbitrary shapes through a multimode fibre when a sample of intensity-only measurements is taken at the output. This projection system is nonlinear, because the intensity, not the complex amplitude, is detected. We show an image projection fidelity as high as ~90%, which is on par with the gold-standard methods that characterize the system fully by phase and amplitude measurements. The generality and simplicity of the proposed approach could potentially provide a new way of target-oriented control in real-world applications when only partial measurements are available.

物理系统的输出，例如通过雾中照亮激光指示器的点而形成的加扰图案，通常可以通过直接测量轻松获得。然而，选择这样的系统的输入以获得期望的输出是困难的，因为这是一个不适的问题。也就是说，有多个输入产生相同的输出。通过散射介质的信息传输就是这个问题的一个例子。用于成像的机器学习方法已在光子学中非常成功地实现，以从变形的强度衍射图输出中恢复散射系统的原始输入相位和幅度对象。但是，在没有这样的输入示例的情况下控制这种系统的输出，该示例可以产生用户想要产生的输出对象类别的输出，是一个具有挑战性的问题。在这里，我们提出了一种在线学习方法，当在输出端仅进行强度测量时，可以通过多模光纤投影任意形状。该投影系统是非线性的，因为可以检测到强度而不是复振幅。我们显示的图像投影保真度高达〜90％，这与通过相位和幅度测量完全表征系统的金标准方法相当。当只有部分测量可用时，所提出方法的一般性和简单性可能会为现实应用中的面向目标的控制提供一种新方法。该投影系统是非线性的，因为可以检测到强度而不是复振幅。我们显示的图像投影保真度高达〜90％，这与通过相位和幅度测量完全表征系统的金标准方法相当。当只有部分测量可用时，所提出方法的通用性和简单性可能会为现实应用中的面向目标的控制提供一种新方法。该投影系统是非线性的，因为可以检测到强度而不是复振幅。我们显示的图像投影保真度高达〜90％，这与通过相位和幅度测量完全表征系统的金标准方法相当。当只有部分测量可用时，所提出方法的通用性和简单性可能会为现实应用中的面向目标的控制提供一种新方法。