Frédéric Montfort

Cell refractive index tomography by digital holographic microscopy

For what we believe to be the first time, digital holographic microscopy is applied to perform optical diffraction tomography of a pollen grain. Transmission phase images with nanometric axial accuracy are numerically reconstructed from holograms acquired for different orientations of the rotating sample; then the three-dimensional refractive index spatial distribution is computed by inverse radon transform. A precision of 0.01 for the refractive index estimation and a spatial resolution in the micrometer range are demonstrated.

Real-time dual-wavelength digital holographic microscopy with a single hologram acquisition.

A technique to perform two-wavelengths digital holographic microscopy (DHM) measurements with a single hologram acquisition is presented. The vertical measurement range without phase ambiguity is extended to the micron-range, thanks to the resulting synthetic wavelength defined by the beating of two wavelengths with a separation of about 80nm. Real-time dual-wavelength imaging is made possible by using two reference waves having different wavelengths and propagation directions for the hologram recording. The principle of the method is exposed and experimental results concerning a 1.2μm m high test sample as well as a moving micro-mirror are presented. To the extent of our knowledge, this is the first time that real-time synthetic beat-wavelength digital holography measurements are reported.

Automatic procedure for aberration compensation in digital holographic microscopy and applications to specimen shape compensation

We present a procedure that compensates for phase aberrations in digital holographic microscopy by computing a polynomial phase mask directly from the hologram. The phase-mask parameters are computed automatically without knowledge of physical values such as wave vectors, focal lengths, or distances. This method enables one to reconstruct correct and accurate phase distributions, even in the presence of strong and high-order aberrations. Examples of applications are shown for microlens imaging and for compensating for the deformations associated with a tilted thick plate. Finally we show that this method allows compensation for the curvature of the specimen, revealing its surface defects and roughness. Examples of applications are shown for microlenses and metallic sphere imaging.

Numerical parametric lens for shifting, magnification and complete aberration compensation in digital holographic microscopy

The concept of numerical parametric lenses (NPL) is introduced to achieve wavefront reconstruction in digital holography. It is shown that operations usually performed by optical components and described in ray geometrical optics, such as image shifting, magnification, and especially complete aberration compensation (phase aberrations and image distortion), can be mimicked by numerical computation of a NPL. Furthermore, we demonstrate that automatic one-dimensional or two-dimensional fitting procedures allow adjustment of the NPL parameters as expressed in terms of standard or Zernike polynomial coefficients. These coefficients can provide a quantitative evaluation of the aberrations generated by the specimen. Demonstration is given of the reconstruction of the topology of a microlens.

Characterization of microlenses by digital holographic microscopy

We demonstrate the use of digital holographic microscopy (DHM) as a metrological tool in micro-optics testing. Measurement principles are compared with those performed with Twyman-Green, Mach-Zehnder, and white-light interferometers. Measurements performed on refractive microlenses with reflection DHM are compared with measurements performed with standard interferometers. Key features of DHM such as digital focusing, measurement of shape differences with respect to a perfect model, surface roughness measurements, and optical performance evaluation are discussed. The capability of imaging nonspherical lenses without any modification of the optomechanical setup is a key advantage of DHM compared with conventional measurement tools and is demonstrated on a cylindrical microlens and a square lens array.

Axial sub-nanometer accuracy in digital holographic microscopy

We present state-of-the-art dual-wavelength digital holographic microscopy (DHM) measurement on a calibrated 8.9 nm high chromium thin step sample and demonstrate sub-nanometer axial accuracy. By using a modified DHM reference calibrated hologram (RCH) reconstruction method, a temporal averaging procedure and a specific dual-wavelength DHM arrangement, it is shown that specimen topography can be measured with an accuracy, defined as the axial standard deviation, reduced to at least 0.9 nm. Indeed for the first time to the best of our knowledge, it is reported that averaging each of the two wavefronts recorded with real-time dual-wavelength DHM can provide up to 30% spatial noise reduction for the given configuration. Moreover, the presented experimental configuration achieves a temporal stability below 0.8 nm, thus paving the way to Angstrom range for dual-wavelength DHM.

Submicrometer optical tomography by multiple-wavelength digital holographic microscopy

We present a method for submicrometer tomographic imaging using multiple wavelengths in digital holographic microscopy. This method is based on the recording, at different wavelengths equally separated in the k domain, 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 CCD camera records the holograms consecutively, which are then numerically reconstructed following the convolution formulation to obtain each corresponding complex object wavefront. Their relative phases are adjusted to be equal in a given plane of interest and the resulting complex wavefronts are summed. The result of this operation is a constructive addition of complex waves in the selected plane and destructive addition in the others. Tomography is thus obtained by the attenuation of the amplitude out of the plane of interest. Numerical variation of the plane of interest enables one to scan the object in depth. For the presented simulations and experiments, 20 wavelengths are used in the 480-700 nm range. The result is a sectioning of the object in slices 725 nm thick.

Submicrometer tomography of cells by multiple-wavelength digital holographic microscopy in reflection

We present first results on a method enabling mechanical scanning-free tomography with submicrometer axial resolution by multiple-wavelength digital holographic microscopy. By sequentially acquiring reflection holograms and summing 20 wavefronts equally spaced in spatial frequency in the 485-670 nm range, we are able to achieve a slice-by-slice tomographic reconstruction with a 0.6-1 microm axial resolution in a biological medium. The method is applied to erythrocytes investigation to retrieve the cellular membrane profile in three dimensions.

Purely numerical compensation for microscope objective phase curvature in digital holographic microscopy: influence of digital phase mask position

Introducing a microscope objective in an interferometric setup induces a phase curvature on the resulting wavefront. In digital holography, the compensation of this curvature is often done by introducing an identical curvature in the reference arm and the hologram is then processed using a plane wave in the reconstruction. This physical compensation can be avoided, and several numerical methods exist to retrieve phase contrast images in which the microscope curvature is compensated. Usually, a digital array of complex numbers is introduced in the reconstruction process to perform this curvature correction. Different corrections are discussed in terms of their influence on the reconstructed image size and location in space. The results are presented according to two different expressions of the Fresnel transform, the single Fourier transform and convolution approaches, used to propagate the reconstructed wavefront from the hologram plane to the final image plane.

Shot-noise influence on the reconstructed phase image signal-to-noise ratio 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.