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.

A complete digital optics applied to digital holographic microscopy: Application to chromatic aberration compensation

Florian Charrière, Tristan Colomb, Christian Depeursinge, Jonas Kühn, Frédéric Montfort

In optics, optical elements are used to transform, to filter or to process physical wavefronts in order to magnify images, compensate for aberration or to suppress unwanted diffracted order for example. Because digital holography provides numerical wavefronts, we developed a digital optics, involving numerical elements such as numerical lenses and pinholes, to mimic numerically what is usually done physically, with the advantage to be able to define any shape for these elements and to place them everywhere without obstruction problems. We demonstrate that automatic and non-automatic procedures allow diffracted order or parasitic interferences filtering, compensation for aberration and image distortion, and control of position and magnification of reconstructed wavefront. We apply this digital optics to compensate for chromatic aberration in multi-wavelength holography in order to have perfect superposition between wavefronts reconstructed from digital hologram recorded with different wavelengths. This has a great importance for synthetic wavelength digital holography or tomographic digital holography that use multiple wavelengths.

SPIE2007

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

Automatic procedure for aberrations compensation in digital holographic microscopy

Nicolas Aspert, Florian Charrière, Tristan Colomb, Etienne Cuche, Christian Depeursinge, Jonas Kühn, Mihaela Marian, Pierre Marquet, Frédéric Montfort

Digital Holographic Microscopy (DHM) is a powerful imaging technique allowing, from a single amplitude image (amplitude and phase), reflected acquisition (hologram), the reconstruction of the entire complex wave front by or transmitted through an object. Because holography is an interferometric technique, the reconstructed phase leads to a sub-wavelength axial accuracy (below lambda/100). Nevertheless, this accuracy is difficult to obtain from a single hologram. Indeed, the reconstruction process consisting to process the hologram with a digital reference wave (similar to classical holographic reconstruction) seems to need a-priori knowledge about the physical values of the setup. Furthermore, the introduction of a microscope objective (MO), used to improve the lateral resolution, introduces a wave front curvature in the object wave front. Finally, the optics of the set-up can introduce different aberrations that decrease the quality and the accuracy of the phase images. We propose here an automatic procedure allowing the adjustment of the physical values and the compensation for the phase aberrations. The method is based on the extraction of reconstructed phase values, along line profiles, located on or around the sample, in assumed to be flat area, and which serve as reference surfaces. The phase reconstruction parameters are then automatically adjusted by applying curve-fitting procedures on the extracted phase profiles. An example of a mirror and a USAF test target recorded with high order aberrations (introduced by a thick tilted plate placed in the set- up) shows that our procedure reduces the phase standard deviation from 45 degrees to 5 degrees.

SPIE2006

Numerical aberrations compensation and polarization imaging in digital holographic microscopy

Tristan Colomb

EPFL2006