Shot noise influence in reconstructed phase image SNR in digital holographic microscopy

In digital holographic microscopy, shot noise is an intrinsic part of the recording process with the digital camera. We present a study based on simulations and real measurements describing the shot-noise influence in the quality of the reconstructed phase images. Different configurations of the reference wave and the object wave intensities will be discussed, illustrating the detection limit and the coherent amplification of the object wave. The signal-to-noise ratio (SNR) calculation of the reconstructed phase images based on the decision statistical theory is derived from a model for image quality estimation proposed by Wagner and Brown [Phys. Med. Biol. 30, 489 (1985)]. It will be shown that a phase image with a SNR above 10 can be obtained with a mean intensity lower than 10 photons per pixel and per hologram coming from the observed object. Experimental measurements on a glass-chrome probe will be presented to illustrate the main results of the simulations.

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.

EPFL2007

Tomography using multiple wavelengths in digital holographic microscopy

Frédéric Montfort

This thesis presents a new tomographic imaging method using multiple wavelengths in digital holographic microscopy. It is based on the addition of several reconstructed wavefronts measured at different wavelengths. The resulting diffraction tomographic visibility is then enhanced and the position of the interfaces is determined with ultrahigh precision. Digital holographic microscopy is a method enabling the recording of complex wavefronts and its numerical reconstruction. In our case, it is based on the recording, in off-axis geometry, of the interference between a reference wave and an object wave reflected by a microscopic specimen and magnified by a microscope objective. A couple charged device (CCD) camera records consecutively the resulting holograms at several wavelengths equally separated in the frequency domain. An adapted reconstruction algorithm has been developed to perform an achromatic reconstruction of the different wavefronts. Tomography is then performed by adding the reconstructed wavefronts. Each wavefront phase is individually adjusted to be equal in a given plane of interest. The result of this operation is a constructive addition of complex waves in the selected plane and destructive addition in the others. The amplitude image is attenuated according to a function, called filter function. For perfectly constructive phases no attenuation is present. Varying the plane of interest enables the scan of the object in depth. The obtained diffraction tomographic resolution is better than the one obtained in OCT, with an equivalent spectral width, in low-coherence or short-pulse lasers in optical coherence tomography. Nevertheless, no axial scanning is needed and the shape of the spectrum can be post acquisition tailored. A method is then proposed to enhance the visibility and to precisely determine the position of the interfaces. An axial scan allows the extraction of depth profiles. The maxima detection and a least square fit algorithm are used to perform this enhancement. Moreover, weights are introduced in the addition of the wavefronts, in order to tailor the filter function. Different weights distributions are discussed in terms of separation limit and precision on the interface position. It is shown that position resolution increases for higher separation limit. Finally, the tomographic method has been simplified for cases of a total reflective surface to perform topography. This allows measurements on specimen of several microns high without phase ambiguities. The results are directly measured in optical pathlengths. Experimental measurements have been performed on a specifically designed and homemade target, as well as on a multilayer specimen. Twenty wavelengths in the range of 480-700 nm have been used, resulting in tomographic sections of 725 nm. It is shown that the experimental results perfectly correspond the simulations. Enhanced tomographic results show a separation limit of 725 nm with a position resolution under 130 nm. Measures performed using the Kaiser weight distribution allow a position resolution of a few nanometers, for an increasing separation limit to 3 µm.

EPFL2006

Biological cell (pollen grain) refractive index tomography with digital holographic microscopy

Florian Charrière, Etienne Cuche, Christian Depeursinge, Pierre Marquet

This paper present a novel approach to perform the tomography of biological specimen based on Digital Holographic Microscopy (DHM). A hologram results from the interference between a reference wave and an object wave reflected from or transmitted through a sample. In the hologram, both amplitude and phase of the field transmitted through the object are registered. In DHM, the object field is recovered when the hologram is processed by a digitally computed replica of the reference wave, allowing quantitative measurement of both phase and amplitude. Phase measurements provide high accuracy optical path length measurements across the specimen along the optical axis. To proceed to a tomographic reconstruction of the refractive index of the sample based on this quantitative phase measurement, such 2-dimentionnal data must be recorded for different sample orientations covering an angle of 180 degrees to cover all the object spatial frequencies in the reciprocal space. The representation of the data in function of the angle is known as a sinogram. The 3-dimentionnal refractive index can then be reconstructed from the sinograms by a filtered backprojection algorithm. In our system, the specimen is inserted in a glass micropipette to permit its rotation. To our knowledge, a quantitative tomography of the refractive index of a pollen cell with a resolution in the micron range is presented for the first time.