On the complex three-dimensional amplitude point spread function of lenses and microscope objectives: theoretical aspects, simulations and measurements by digital holography

The point spread function is widely used to characterize the three-dimensional imaging capabilities of an optical system. Usually, attention is paid only to the intensity point spread function, whereas the phase point spread function is most often neglected because the phase information is not retrieved in noninterferometric imaging systems. However, phase point spread functions are needed to evaluate phase-sensitive imaging systems and we believe that phase data can play an essential role in the full aberrations' characterization. In this paper, standard diffraction models have been used for the computation of the complex amplitude point spread function. In particular, the Debye vectorial model has been used to compute the amplitude point spread function of ×63/0.85 and ×100/1.3 microscope objectives, exemplifying the phase point spread function specific for each polarization component of the electromagnetic field. The effect of aberrations on the phase point spread function is then analyzed for a microscope objective used under nondesigned conditions, by developing the Gibson model (Gibson & Lanni, 1991), modified to compute the three-dimensional amplitude point spread function in amplitude and phase. The results have revealed a novel anomalous phase behaviour in the presence of spherical aberration, providing access to the quantification of the aberrations. This work mainly proposes a method to measure the complex three-dimensional amplitude point spread function of an optical imaging system. The approach consists in measuring and interpreting the amplitude point spread function by evaluating in amplitude and phase the image of a single emitting point, a 60-nm-diameter tip of a Near Field Scanning Optical Microscopy fibre, with an original digital holographic experimental setup. A single hologram gives access to the transverse amplitude point spread function. The three-dimensional amplitude point spread function is obtained by performing an axial scan of the Near Field Scanning Optical Microscopy fibre. The phase measurements accuracy is equivalent to λ/60 when the measurement is performed in air. The method capability is demonstrated on an Achroplan ×20 microscope objective with 0.4 numerical aperture. A more complete study on a ×100 microscope objective with 1.3 numerical aperture is also presented, in which measurements performed with our setup are compared with the prediction of an analytical aberrations model.

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

Correction of spherical surface measurements by confocal microscopy

Jeremy Béguelin, Wilfried Noell, Toralf Scharf

Refractive microlenses are nowadays widely used in optical systems. Characterizing their surface is essential to ensure their quality and to optimize their fabrication process. This is realized by optical surface profilers thanks to their vertical resolution, short measurement time and areal information. However, when measuring non-flat surfaces, errors appear caused by aberrations of the microscope objective used in such systems, which significantly limit the achievable quality of the manufactured spherical surfaces. Approaches have been proposed to tackle these errors, but none of them demonstrated its validity for measurements of high quality microlenses. In this work, we demonstrate that the surface error depends on the surface position within the field of view of the microscope objective and on the surface slope. We then explain how to record the value of this error experimentally: this can be done by measuring a reference ball placed at different positions in the field of view. We finally use a machine learning algorithm to fit the experimental data in order to correct subsequent measurements. We apply this approach to measurements performed by a 20x numerical aperture 0.6 microscope objective of a confocal microscope. The effectiveness of the proposed method is demonstrated by showing that the surface error corresponds to a RMS wavefront error of lambda/7 before correction and of lambda/50 after correction for glass microlenses used in the visible range. This method thus allows the use of high numerical aperture microscope objectives for an accurate characterization of microlenses. Likewise, the fabrication capability of microlenses in terms of slope and quality is greatly extended, which is especially important for aspheres or freeforms.

2020

Numerical reconstruction of digital holograms

Etienne Cuche

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.