Optical tomography by means of a numerical low-coherence holographic technique

Etienne Cuche, Christian Depeursinge
1997
Journal paper

Abstract

Digital holograms are recorded by a CCD camera and are numerically reconstructed, in intensity and phase, by means of an algorithm which calculates their discrete Fresnel transform. By using a low-coherence source, the tomography of a 3D scene can be performed without lateral scanning with a depth resolution equal to the coherence length and a lateral resolution equal to the diffraction limit of the microscope objective used

Official source

https://infoscience.epfl.ch/record/139598?ln=en

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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.

EPFL2000

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

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