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

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.

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

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

Tristan Colomb, Etienne Cuche, Christian Depeursinge

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.

SPIE2006

Shot noise, refractive index tomography and aberrations estimation in digital holographic microscopy

Florian Charrière

The present thesis develops some specific aspects of digital holographic microscopy (DHM), namely the effect of shot noise on the phase image accuracy, the use of DHM in micro-tomography and in aberrations evaluation of a microscope objective (MO). DHM is an imaging technique, allowing to measure quantitatively the wavefront transmitted through or reflected by a specimen seen through a MO. A hologram, composed by the interference of the wave coming from the object with a reference wave, is recorded with a camera and then numerically processed to extract both amplitude and phase information. Thanks to its interferometric nature, DHM provides phase images, corresponding to a nanometric accuracy along the optical axis of the microscope, revealing extremely detailed information about the specimen surface in reflection configuration or its internal structure in transmission configuration. DHM has proven its efficiency on numerous applications fields going from cells biology to MEMS-MOEMS devices. In a first part, the use of DHM as metrological tools in the field of micro-optics testing is demonstrated. DHM measurement principle is compared with techniques employed in Twyman-Green, Mach-Zehnder, and white-light interferometers. Refractive microlenses are characterized with reflection DHM and the data are confronted with data obtained with standard interferometers. Specific features of DHM such as digital focussing, measurement of shape differences with respect to a perfect model, surface roughness measurements, and evaluation of a lens optical performance are discussed. The capability to image nonspherical lenses without modification of the optical setup, a key advantage of DHM against conventional interferometers, is demonstrated on a cylindrical mircrolens and a square lenses array. A second part treats the effect of shot noise in DHM. DHM is a single shot imaging technique, and its short hologram acquisition time (down to microseconds) offers a reduced sensitivity to vibrations. Real time observation is achievable, thanks to present performances of personal computers and digital camera. Fast dynamic imaging at low-light level involves few photons, requiring proper settings of the system (integration time and gain of the camera; power of the light source) to minimize the influence of shot noise on the hologram when the highest phase accuracy is aimed. With simulated and experimental data, a systematic analysis of the fundamental shot noise influence on phase accuracy in DHM is presented. Different configurations of the reference wave and the object wave intensities are also discussed, illustrating the detection limit and the coherent amplification of the object wave. In a third part, DHM has for the first time been applied to perform optical diffraction tomography of biological specimens: a pollen grain and living amoebas. Quantitative 2D phase images are acquired for regularly-spaced angular positions of the specimen covering a total angle of π, allowing to build 3D quantitative refractive index distributions by an inverse Radon transform. A precision of 0.01 for the refractive index estimation and a spatial resolution in the micron range are shown. For the amoebas, morphometric measurements are extracted from the tomographic reconstructions. The fourth part presents a DHM technique to determine the integral refractive index and morphology of cells. As the refractive index is a function of the cell dry mass, depending on the intra-cellular concentration and the organelles arrangement, the optical phase shift induced by the specimen on the transmitted wave can be regarded as a powerful endogenous contrast agent. The dual-wavelengths technique proposed in this thesis exploits the dispersion of the perfusion medium to obtain a set of equations, allowing decoupling the contributions of the refractive index and the cellular thickness to the total phase signal. The two wavelengths are chosen in the vicinity of the absorption peak of a dye added to the perfusion medium, where the absorption is accompanied by a strong variation of the refractive index as a function of the wavelength. The technique is demonstrated on yeasts. The last part exposes two methods capable of measuring the complex 3D amplitude point spread function (APSF) of an optical imaging system. The first approach consists in evaluating in amplitude and phase the image of a single emitting point, a 60 nm diameter tip of a Scanning Near Field Optical Microscopy (SNOM) fiber, with an original digital holographic setup. A single hologram giving access to the transverse APSF, the 3D APSF is obtained by performing an axial scan of the SNOM fiber. The method is demonstrated on an 20x 0.4 NA MO. For a 100x 1.3 NA MO, measurements performed with the new setup are compared with the prediction of an analytical aberrations model. The second method allows measuring the APSF of a MO with a single holographic acquisition of its pupil wavefront. The aberration function is extracted from this pupil measurement and then inserted in a scalar model of diffraction allowing to calculate the distribution of the complex wavefront propagated around the focal point. The results are compared with a direct measurement of the APSF achieved with the first proposed approach.