Polarization digital holographic microscope: A single acquisition for a complete determination of polarization state

In this paper, we present a transmission polarization digital holographic microscope (Pol-DHM) that allows for imaging the state of polarization of a wave front with the acquisition of a single hologram. This apparatus records, using a CCD camera, the interference in off-axis geometry between two orthogonally polarized reference waves and an object wave transmitted through a microscopic sample and magnified by a microscope objective. Since the reference waves have orthogonal polarizations, they do not interfere and the hologram results in two different fringes patterns, which can be separately filtered in the spatial Fourier domain and reconstructed separately to compute the amplitude and phase of two wave fronts. These four images allow computing the polarization ellipse azimuth and the phase difference associated with the polarization state of the object wave. The method is illustrated by imaging the strain induced in a polymethylmethacrylate (PMMA) sample and in a bended optical fiber.

Birefringence measurement by use of digital holographic microscopy: examples with fiber optics and concrete samples

Tristan Colomb, Etienne Cuche, Christian Depeursinge

In this paper, we present a modified transmission digital holographic microscope that can be used to image the state of polarization. The resulting device, called polarization digital holographic microscope (Pol-DHM), records in off-axis geometry the interference between two orthogonally polarized reference waves and the object wave transmitted by a microscopic sample and magnified by a microscope objective. A CCD camera records the resulting hologram. Using a single hologram, we reconstruct separately the amplitude and phase of two wave fronts, which are used to represent the object wave's state of polarization, represented by the azimuth and the phase difference associated to the polarization ellipse. ne proposed method is illustrated with two applications. The first application is to use a 10-times magnification microscope objective to measure the bireftingence induced by internal stresses in transparent materials such as a bended optical fiber. The second application is to use a 20-times microscope objective to image the state of polarization of a thin concrete sample and reveals birefringent properties of the different aggregates found in the concrete.

SPIE2005

Numerical aberrations compensation and polarization imaging in digital holographic microscopy

Tristan Colomb

In this thesis, we describe a method for the numerical reconstruction of the complete wavefront properties from a single digital hologram: the amplitude, the phase and the polarization state. For this purpose, we present the principle of digital holographic microscopy (DHM) and the numerical reconstruction process which consists of propagating numerically a wavefront from the hologram plane to the reconstruction plane. We then define the different parameters of a Numerical Parametric Lens (NPL) introduced in the reconstruction plane that should be precisely adjusted to achieve a correct reconstruction. We demonstrate that automatic procedures not only allow to adjust these parameters, but in addition, to completely compensate for the phase aberrations. The method consists in computing directly from the hologram a NPL defined by standard or Zernike polynomials without prior knowledge of physical setup values (microscope objective focal length, distance between the object and the objective...). This method enables to reconstruct correct and accurate phase distributions, even in the presence of strong and high order aberrations. Furthermore, we show that this method allows to compensate for the curvature of specimen. The NPL parameters obtained by Zernike polynomial fit give quantitative measurements of micro-optics aberrations and the reconstructed images reveal their surface defects and roughness. Examples with micro-lenses and a metallic sphere are presented. Then, this NPL is introduced in the hologram plane and allows, as a system of optical lenses, numerical magnification, complete aberration compensation in DHM (correction of image distortions and phase aberrations) and shifting. This NPL can be automatically computed by polynomial fit, but it can also be defined by a calibration method called Reference Conjugated Hologram (RCH). We demonstrate the power of the method by the reconstruction of non-aberrated wavefronts from holograms recorded specifically with high orders aberrations introduced by a tilted thick plate, or by a cylindrical lens or by a lens ball used instead of the microscope objective. Finally, we present a modified digital holographic microscope permitting the reconstruction of the polarization state of a wavefront. The principle consists in using two reference waves polarized orthogonally that interfere with an object wave. Then, the two wavefronts are reconstructed separately from the same hologram and are processed to image the polarization state in terms of Jones vector components. Simulated and experimental data are compared to a theoretical model in order to evaluate the precision limit of the method for different polarization states of the object wave. We apply this technique to image the birefringence and the dichroism induced in a stressed polymethylmethacrylate sample (PMMA), in a bent optical fiber and in a thin concrete specimen. To evaluate the precision of the phase difference measurement in DHM design, the birefringence induced by internal stress in an optical fiber is measured and compared to the birefringence profile captured by a standard method, which had been developed to obtain high-resolution birefringence profiles of optical fibers. A 6 degrees phase difference resolution is obtained, comparable with standard imaging polariscope, but with the advantage of a single acquisition allowing real-time reconstruction.

EPFL2006

Numerical reconstruction of digital holograms

Etienne Cuche

This thesis presents a new method for the numerical reconstruction of digital holograms recorded in the off-axis configuration using a CCD camera. The propagation of the reconstructed wave front, from the hologram plane to an observation plane, is achieved by a calculation of scalar diffraction in the Fresnel approximation. An image representing the distribution of intensity at the surface of the object can be obtained by calculating the intensity of the reconstructed wave front. The focusing of this image is performed digitally by adjusting a parameter which defines the distance between the hologram and the observation plane. A second image representing the phase distribution at the surface of the object can be obtained from the same hologram by calculating the argument of the reconstructed wave front. We show here that for getting a phase distribution that represents only the contribution of the object wave, the hologram or the reconstructed wave front must be multiplied by a computed replica of the complex conjugate of the wave used as reference during the recording. For a plane reference wave, the reconstruction of the phase distribution requires a precise adjustment of two digital parameters defining its propagation direction. An application to surface profilometry has demonstrated the quantitative nature of the obtained phase distribution which gives access to the topography of the object. A vertical resolution of λ/100 has been estimated on the basis of a preliminary study. The introduction of a microscope objective along the optical path of the object wave enhances the transverse resolution of the method. In this case, the wave front deformation produced by the microscope objective can be digitally compensated. Under the assumption of a paraboloidal deformation, we show that the wave front curvature can be numerically corrected by multiplication with an array of complex numbers computed using the complex conjugate of the analytical expression describing the defocusing aberration. A preliminary study indicates that the transverse resolution of the method approaches that of classical optical microscopy (diffraction limit). The application of a digital technique of spatial filtering allows for the elimination of the zero order of diffraction and of the twin image. This operation enhances the signal to background ratio. We show also that the influence of diffraction effects associated to the numerical reconstruction method can be reduced by apodization of the hologram aperture. This operation is performed digitally by means of a procedure which defines the transmission of the hologram aperture using a cubic spline interpolation.