Wavefront shaping is a technique that uses phase or amplitude modulation to create desired wavefronts on light in optical systems. Wavefronts which are properly conjugated will refocus after reflection from a rough surface. This refocusing effect is called reflective inverse diffusion. There currently are two different wavefront shaping techniques used to achieve reflective inverse diffusion: iterative methods and matrix methods. Iterative methods find one phase front which allows for reflected light to be focused at a single, specific position, with results that are immediately available and continuously improving. Matrix methods calculate the complex matrix which describes the rough surface and allow for reflected light to be be refocused at many positions after reflective inverse diffusion and at multiple spots simultaneously. However, matrix methods are susceptible to decreased performance in a noisy system, and their results are not available until the entire matrix is measured. A new alternative method for reflective inverse diffusion combines non-mechanical beam steering principles with an iterative method’s phase front, giving it the multiple-spot capabilities of matrix methods. Utilizing an optical Fourier transform relationship in the reflective inverse diffusion setup, the shift theorem of Fourier transforms creates phase tilts at the sample on top of the conjugating phasefront when the phasefront from the SLM is translated in position. The phase tilts at the sample steer the reflected focused beam. Translations of an iterative method’s phase front using circular shifts steer the reflected spot at the cost of decreased enhancement with a larger shift.
The reflection matrix (RM) measured from a rough-surface reflector contains the phase information of the light from each spatial light modulator (SLM) segment to every segment in the observation plane. This phase infor- mation can be used to produce phase maps that can refocus light to any segment in the observation plane. The measurement of an RM requires the optical system to be completely static; any disturbances result in degraded ability to refocus light. Diffraction based simulations show that RMs contain redundant phase information that can be exploited. A method is presented that allows control of the refocused light in the observation plane from a single reference phase map. This allows for the continuous optimization of the reference phase map, that compensates for system disturbances, while preserving the ability to control the location of the refocused light and eliminate the need to measure the entire RM.
Reflective inverse diffusion is a method of refocusing light scattered by a rough surface. An SLM is used to shape the wavefront of a HeNe laser at 632.8-nm wavelength to produce a converging phase front after reflection. Iterative methods previously demonstrated intensity enhancements of the focused spot over 100 times greater than the surrounding background speckle. This proof-of-concept method was very time consuming and the algorithm started over each time the desired location of the focus spot in the observation plane was moved.
Transmission matrices have been developed to control light scattered by transmission through a turbid media. Time varying phase maps are applied to an SLM and used to interrogate the phase scattering properties of the material. For each phase map, the resultant speckle intensity pattern is recorded less than 1 mm from the material surface and represents an observation plane of less than 0.02 mm2. Fourier transforms are used to extract the phase scattering properties of the material from the intensity measurements. We investigate the effectiveness this method for constructing the reflection matrix (RM) of a diffuse reflecting medium where the propagation distances and observation plane are almost 1,000 times greater than the previous work based on transmissive scatter. The RM performance is based on its ability to refocus reflectively scattered light to a single focused spot or multiple foci in the observation plane. Diffraction-based simulations are used to corroborate experimental results.