## 1 Introduction  
The majority of surfaces can be considered rough when compared to the wavelength of visible light. The microscopic surface-height variations of the rough surface cause incident light to diffusely scatter. The scattering surface can be treated as a complex field that interferes with incident light to produce reflected speckle patterns. If the complex field of the rough surface were known, a properly modified incident beam could be used to eliminate the scattering effects of the rough surface and even cause the light to refocus after reflection [1].  
Transmissive inverse diffusion used phase modulation to shape the wavefront of incident light, causing it to refocus after transmission through a turbid media [2; 3; 4; 5; 6]. These methods were also demonstrated to work in controlling reflective scatter [7]. Reflective inverse diffusion is an iterative process with intensity feedback from a CCD (charged-coupled device) detector to search for the SLM (spatial light modulator) phase map that produced the brightest target spot in the observation plane. This requires tens of thousands of intensity measurements and limits the phase map to a small subset of available values.  
Transmission matrices have been developed to map the effect of the complex field of the scatterer on the incident light. These matrices provide the phase information required to control the resultant light scatter [8; 9; 10; 11]. These transmission matrices were measured with microscopic objectives and thin films of turbid media, resulting in a propagation distance of less than 1 mm and an observation plane field of view of a few hundred microns. The complex field representation is not limited to transmissive scattering, but the reflective case represents a \(10^{3}\) increase in propagation distance and observation plane size. Initial work in reflective inverse diffusion always placed the rough-surface reflector at the focus of a positive lens, rather than in the image plane of a demagnifying microscope objective as in the transmissive case [7]. This paper continues to examine the enhancement capabilities of the RM (reflection matrix) with the rough-surface reflector at lens focus. Additionally, the RM will be measured with the lens producing a demagnified image of the SLM at the rough-surface reflector.  
Previous work in the transmissive scattering case shows enhancements (\(\eta\)) ranging from 50 to 1000 using both iterative and transmission matrix methods [3; 5; 8; 10; 12]. The cause of this wide range of enhancement values is still currently being investigated, with some of the disparity likely caused by noise [12]. Enhancement capabilities of the RM in laboratory experiments and diffraction-based simulations are compared with surface roughness, correlation length, and slope to provide initial insight into surface characteristics that effect enhancement. The simulations examined the effect on enhancement of simplified device measurement error for the SLM and CCD along minute mechanical vibrations that cause microscopic shifts in the optical setup.  
Imaging around corners using reflectively scattered light has tremendous application in remote sensing. Previous work in this area has always required the occluded scene to be illuminated by a light source either in the scene or with direct line of sight of the scene [13; 14]. This presents an application problem since access to the occluded scene may not be possible. The goal of this RM research is to provide a method of illuminating the occluded target scene without access or direct line of sight.