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

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.

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