Created by sebastien.popoff on 13/06/2013

Tutorials Digital holography

Phase Measurement: Introduction


Most exciting phenomenons that occur in complex media arises from interference effects. Controlling the phase of an incident field with a spatial light modulator is what made the field of wavefront shaping possible. Nevertheless, the measurement of the phase is a crucial step for many applications. In particular, recording both the amplitude and the phase for a set of input wavefront is necessary to record the transmission matrix of a linear medium. The knowledge of the transmission matrix of a scattering medium allows, for example, to use it as a lens [1], a controllable phase plate [2,3] or polarizer [4,5].

In such experiments, the phase of the output optical field for different input illuminations has to be recorded with the same phase reference. For this reason, one uses interferometric methods to measure the complex field; Phase Shifting Digital Holography (tutorial to come) or Off-Axis Holography (tutorial to come). In both cases, the unknown optical field interferes with a reference wavefront. The intensity of the interference is measured using a CCD to reconstruct the phase image. Phase Shifting Digital Holography requires 4 different measurements to obtain one phase image, leading to longer acquisition times and making the method more sensitive to interferometric instabilities. Off-Axis Holography allows us to measure the complex field in one shot but at the cost of a loss of resolution.

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Created by sebastien.popoff on 13/05/2013


Subwavelength light focusing through a scattering medium

[J. H. Park et al., Nat. Photon., (2013)]

After the first experiment of light focusing through a scattering medium using wavefront shaping (see A pioneer experiment), the same group demonstrated in [I. M. Vellekoop et al., Nat. Photon., 4, 320, (2010)] that a random medium can improve the sharpness of the focus. The scattering in a medium behind a lens randomizes the direction of the light. The speckle pattern shows high spatial frequencies not allowed by the lens alone because of its finite numerical aperture. After optimization of the input wavefront, the focus spot obtained is sharper than the resolution limit of the lens. In these experiments, the intensity profile was always measured in the far field, i.e. at least several wavelengths away from the surface, where only the propagating waves contribute to the optical field. In the present paper, J. H. Park and his colleagues optimize the input wavefront impinging on turbid media to increase the intensity measured in the near field at a given position. Subwavelength focusing is achieved thanks to the contributions of the evanescent waves.

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Created by sebastien.popoff on 04/05/2013

Tutorials Spatial Light Modulators

How to characterize and calibrate a phase-only SLM

For most applications in complex media, spatial light modulators are used for their ability to control the phase of a laser beam. Whereas deformable mirrors are insensitive to the input polarization, liquid crystal based SLMs need to work with a given input polarization or sometimes a precise combination of input and output polarizations. It is then necessary for LC SLMs to carefully characterize the modulation to find the setup conditions where amplitude variations are minimal and for which the phase range is at least 2π. In any case, for a given wavelength, it is necessary to know the relation between the value given to a pixel on the SLM and the relative phase shift associated. I present here a typical way to characterize the complex modulation of an SLM.

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Created by sebastien.popoff on 28/04/2013


From the bimodal distribution to the quarter circle law

[A. Goetschy and A. D. Stone, Phys. Rev. Lett., 1304.5562, (2013)]

Almost thirty years ago, theoreticians predicted that the distribution of the transmission values of a multiple scattering sample should follow a 'bimodal distribution'.  Physically, that means that, in the diffusive regime, there is a large number of strongly reflected channels - the closed channels - and a small number of channels of transmission close to one - the open channels. The existence of these open channels regardless of the thickness of the medium is of big interest for researchers, especially for imaging or communication applications. Nevertheless, such channels have not yet been directly observed. A investigation on those channels requires a measurement of the entire transmission matrix of a lossless scattering medium. For practical reasons (open geometry, limited numerical aperture, noise...) one usually has access to a subpart of the total transmission matrix. In recent experimental measures of the transmission matrix in optics [S.M. Popoff et al., Phys. Rev. Lett., 104, 100601, (2010)] the distribution of the transmission values follows a 'quarter circle law', characteristic of totally uncorrelated systems. This means that the fraction of the transmission matrix measured shows no effect of the correlations at the origin of the bimodal distribution due to the loss of information. In this paper, A. Goetschy and D. Stone theoretically study the effect of the loss of information or the imperfect control on the statistics of the transmission matrix of a scattering system.

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