Caojin Yuan

Resolution improvement in digital holography by angular and polarization multiplexing

Angular and polarization multiplexing techniques are utilized in both object and reference arms in the digital holographic microscopy system to improve its resolution. The angular multiplexing provides on-axis and off-axis illumination and reference beams with different carrier frequencies. Polarization multiplexing prohibits the occurrence of interference between low and high object spatial frequencies and reference beams. The proposed system does not require special light sources or filtering masks. Experimental results show that the resolution of the synthesized image exceeds the resolution determined by the numerical aperture of the imaging microscope objective.

Fast autofocusing in digital holography using the magnitude differential

Typical methods of automatic estimation of focusing in digital holography calculate every single reconstructed frame to get a critical function and then ascertain the focal plane by finding the extreme value of that function. Here, we propose a digital holographic autofocusing method that computes the focused distance using the first longitudinal difference of the magnitude of the reconstructed image. We demonstrate the proposed method with both numerical simulations and optical experiments of amplitude-contrast and phase-contrast objects. The results suggest that the proposed method performs better than other existing methods, in terms of applicability and computation efficiency, with potential applications in industrial and biomedical inspections where automatic focus tracking is necessary.

An absolute test for axicon surfaces.

We present a method for absolute testing of axicon surfaces in a null test setup. The absolute test exploits the symmetry of axicons, which allows us to introduce a shift of the surface under test in both the axial and rotational directions while still maintaining the null test condition. With two shifts of the surface under test and four measurements, the interferometer and null optics error can be removed. The absolute surface local deviation can be obtained by wavefront reconstruction with a double-side spiral-path direct integration method. A simulation of the method, including typical systematic as well as statistical errors as input, is presented to estimate the error propagation. Experimental absolute test results of a 90° axicon surface are given.

Systematic analysis of the measurement of cone angles using high line density computer-generated holograms

Computer-generated holograms (CGHs) allow to transfer the high 2D-positioning accuracy of modern lithography equipment into high precision 3D-shape measurements, e.g. in CGH asphere metrology. In this contribution, we give a detailed look into the characterization of steep topologies with CGHs on the example of a 90 deg axicon surface, requiring rather high line densities in the hologram. Several aspects gain importance with increasing CGH line densities when measuring dimensional quantities such as the cone angle of the surface: misalignment of the setup, fabrication effects of the CGH rigorous effects of the high density grating, and effects due to wavelength variations of the interferometer. This paper presents the experimental approach for the cone angle measurement and a systematic analysis of its measurement uncertainty, focusing on the specifics of this null test CGH measurement.

Generation of optical vortex array along arbitrary curvilinear arrangement

We propose an approach for creating optical vortex array (OVA) arranged along arbitrary curvilinear path, based on the coaxial interference of two width-controllable component curves calculated by modified holographic beam shaping technique. The two component curve beams have different radial dimensions as well as phase gradients along each beam such that the number of phase singularity in the curvilinear arranged optical vortex array (CA-OVA) is freely tunable on demand. Hybrid CA-OVA that comprises of multiple OVA structures along different respective curves is also discussed and demonstrated. Furthermore, we study the conversion of CA-OVA into vector mode that comprises of polarization vortex array with varied polarization state distribution. Both simulation and experimental results prove the performance of the proposed method of generating a complex structured vortex array, which is of significance for potential applications including multiple trapping of micro-sized particles.

Axicon metrology using high line density computer-generated holograms

Axicon surfaces are widely used in nowadays optical engineering, requiring accurate metrology for these highly aspheric surfaces. In this contribution, we present a complete approach to determine the shape deviation of axicons in an absolute manner. The setup is an interferometric null configuration using a computer generated hologram (CGH) as null optics. We demonstrate an absolute shifting method and the calibration issues connected with measuring the absolute cone angle. Experimental results are shown for the metrology of a 90° cone angle sample.

Anisotropic edge enhancement with spiral zone plate under femtosecond laser illumination

Fractional and de-centered phase spiral zone plates (SZPs) are proposed for anisotropic edge enhancement using a femtosecond laser. The transmission functions of the two types of phase SZPs are deduced and the diffraction distributions are theoretically analyzed and simulated as well. By setting the fractional topological charge p and the orientation angle ϑ of a fractional SZP (FSZP), the intensity and the direction of the anisotropic edge enhancement can be controlled. A de-centered SZP (DSZP) can be obtained by shifting the coordinates of the traditional phase SZP while the topological charge equals to 1. The intensity and direction of the anisotropic edge enhancement can be controlled by setting the displacement distance r0 and the azimuthal angle φ0 of a DSZP. The anisotropic edge enhancement of the two phase SZPs was experimentally demonstrated with a phase pattern and living biological cells under femtosecond laser illumination.

Phase-shifting-free resolution enhancement in digital holographic microscopy under structured illumination

In this paper, we present a phase-shifting-free method to improve the resolution of digital holographic microscopy (DHM) under the structured illumination (SI). The SI used in the system is different from the traditional SI for it is free of the visible structure due to two illumination lights with orthogonal polarization states. To separate the recorded information and also retrieve the object phase, two reference beams with different carrier frequencies and orthogonal polarization states are adopted. The principle component analysis (PCA) algorithm is introduced in the reconstruction process. It is found that the modulated frequency of SI besides the quadratic phases of the imaging system can be easily removed with help of PCA. Therefore, phase-shifting is not required both in recording and reconstruction process. The simulation is performed to validate our method, while the proposed method is applied to the resolution enhancement for amplitude-contrast and phase-contrast objects imaging in experiments. The resolution is doubled in the simulation, and it shows 78% resolution improvement in the experiments.

Generation of elliptic perfect optical vortex and elliptic perfect vector beam by modulating the dynamic and geometric phase

We propose a method for generating an elliptic perfect vector beam (EPVB) by modulating the dynamic and geometric phases. It is theoretically demonstrated that the shape of the beam can be changed from circle to ellipse by setting the scale factor m of the dynamic phase, but the diameter of it is independent on the topological charge and the polarization order. Since the geometric phases provided by the dialectic Q-plate vary with the polarization state of the illumination beam, EPVB can be converted to the elliptic perfect optical vortex (EPOV) beam by changing the polarization state of the illuminating beam. Therefore, we also provide an alternative method to generate the EPOV beam. The experimental results agree well with the theoretical expectations.

Absolute test using the conjugate differential method

The conjugate differential method has been applied to the absolute test of flat, cylindrical, and axicon surfaces. In the previous work, simulations and correspond experiments have been carried out to verify the feasibility of the method. To analyze the influences of different factors upon the measurement result, the conjugate differential method is discussed in detail. Considering the characteristics of the test surface such as surface types and surface profiles, the application ranges of the conjugate differential method are discussed into three parts. According to the three surface types using the conjugate differential method, the method can be extended to the absolute test of the spherical surfaces based on spherical coordinate system. The reconstructed errors caused by different aberrations expressed as Zernike polynomial terms show that they are more sensitive to high order aberration terms of the surface under test. And for surfaces with different frequency distributions, the surface with less mid-spatial frequency information is less sensitive to the sampling frequency. The influence from the other factors in interferometric test are also discussed into three parts. The influences from the uncertainty of shifts are correlated with the increased aperture diameters, since the integration error caused by the shift error increases gradually with the expanding of the integration path. The integration error changes by the influences from the coherent noise and pixel noise related to pixel deviations. The reconstructed deviations get increased while the peak pixel deviation is increasing. For the balance of the differential deviation and integration error, the optimization of sampling resolution should take considered for accuracy improvement.