# Fast Computational Ghost Imaging with Laser Array Modulation
## 1 Introduction  
Ghost imaging (GI) differs from conventional optical imaging in several important aspects. One of them is that object signals are detected not with imaging optics and an image sensor, but with collecting optics and a single photo-detector. Theoretically, GI is based on correlation of optical properties.  
In the first GI proposal [1] and experimental verification [2], quantum entanglement was utilized for imaging. Therefore, a specific quantum light source was required. In Ref. [3; 4; 5], it was shown that GI can be implemented not only with a quantum source but also with a thermal one. In thermal GI, random illumination patterns generated by speckle phenomena illuminate the target. A two-dimensional image is then reconstructed from a measured data set. Signal processing for image reconstruction is conducted in accordance with the second order statistical properties of the speckle [4].  
According to Ref. [4], GI is suitable for measuring weak signals. In GI, the signals measured from the target correspond to spatial integrals of the optical intensity. Therefore, the effects of noise components caused by the dark current of the photo-detector are reduced. Consequently, the signal-to-noise ratio (SNR) of the reconstructed images obtained by GI is high in comparison with camera imaging. GI based X-ray imaging has been reported in Ref. [6]. As shown in that study, GI can effectively reduce radiation damage to biological targets.  
For thermal GI, several methods of signal processing for improving the image quality have been reported. Differential ghost imaging [7] can effectively improve the signal-to-noise ratio of the reconstructed images. In [8], normalized ghost imaging (NGI) has been proposed. NGI is considered to be useful for experimental systems. Further, some iterative algorithms [9; 10] and those employing compressed sensing [11; 12] have been applied to signal reconstruction in GI.  
Later, computational GI (CGI) has been developed [13; 14]. CGI is considered to be suitable for practical use because the associated optical setup is much simpler than that of conventional GI. Several techniques based on CGI have been proposed. In Ref. [15], CGI was applied to image encryption. In addition, methods for remote sensing with CGI were reported in Refs. [16; 17].  
In CGI, a spatial light modulator (SLM) with phase modulation is generally utilized to generate speckle patterns. For optical measurements to reconstruct one image, the phase patterns on the SLM should be updated more than thousand times such that different speckle patterns illuminate the target object. Therefore, reducing the optical measurement time is one of the most important issues in CGI. In Refs. [18; 19], some methods to solve the issue have been proposed. These methods, however, treat only less than \(100\times 100\) pixels because of device specifications.  
We propose a novel method to solve this issue. The key device employed in the proposed method is an array of laser diodes (LDs). LDs provide a broad bandwidth for modulation. Optical signals emitted by each element of the array are scattered by a phase modulator. As a result, specific speckle patterns illuminate the target object. The method is suitable for both higher speed measurement and high definition imaging.