Huaying Wang

Simple and robust digital holography for high-resolution imaging

Based on the point spread function of holographic system, the lateral resolution of digital holographic imaging system without any pre-magnification is studied. The expression of resolution limitation of holographic imaging system is thus presented. We investigate the possibilities to improve the lateral resolution. The simple experimental setup with an off-axis arrangement is built. By using a U.S. Air Force (USAF) test target as microscopic object, the recorded holograms are reconstructed digitally based on the principle of Fresnel diffraction. The lateral resolution of 2.76 micron without any pre-magnification is demonstrated experimentally, which matches the theoretical prediction well.

Imaging technique for three-dimensional microstructure by digital holography

Digital holography is a whole-field, non-contact, and highly sensitive interferometric imaging and testing technology. It is more suitable for microscopic measurement owing to digitalization and flexibility in holograms recording, storage, reconstruction and transmittance. This paper analyzes the factors which lead to the phase aberrations in the off-axis lensless Fourier transform digital holography firstly. Then a method, which is obtained by borrowing ideas from T. Colomb, is presented to correct the phase aberrations automatically during the numerical reconstruction. This is implemented by multiplying a phase mask directly with the reconstructed wave field. The phase mask is obtained by an iterative procedure computing automatically without the pre-knowledge of the physical parameters, such as the off-set of the reference point source and the recording distance. This method enables one to reconstruct the relative correct and accurate phase-contrast image, even in the presence of the noise, which is needed to be smoothed by a median filter. In order to achieve an accurate phase image, the procedure described here is applied iteratively, starting from the initial values provided by the first evaluation. We present and analyze the simulation results of the phase images based on a special three-dimensional micro object. The results show that for a weak noise the above method is very effective; while for strong noise the common phase-unwrapping method must be applied. This indicates that it is very important to record high quality hologram and to suppress the noise in phase data.

Recording conditions of digital holography

Based on Fresnel diffraction formula, the spatial frequency distribution of the holograms recorded with plane and spherical reference wave are analyzed. Using the sampling theorem and the condition of spectrum separation, the general recording conditions of the digital hologram are deduced. The minimum recording distances and the offsets of the reference wave for some practical recording configurations are given. The deduced recording conditions about off-axis Fresnel hologram are different from others, which are different each other. The separating condition of the frequency spectrum for Fourier transform holography is applied directly in their derivation. Moreover, they have applied different other approximations in their derivation. No approximation is applied to our deduction. Therefore, the results derived from our proposed method are accurate. The recording conditions of digital holography with general spherical reference wave are presented firstly on our knowledge. The recording conditions of in-line and off-axis lensless Fourier can be gotten directly as special case. The simulations and the experiments demonstrate that the method and the results are valid. The results also show that only the sampling and separation conditions are met simultaneously, the reconstructed image with high quality can be obtained.

Comparison of reconstruction algorithms in lens-less Fourier transform digital holography

The different reconstruction algorithms are investigated and the reconstructed images are presented in lensless Fourier transform digital holography. The most employed three algorithms, all based on the fast-Fourier-transform, are: the convolution algorithm, the angular spectrum algorithm, and the Fresnel algorithm. With the convolution algorithm and angular spectrum algorithm, there is an optimal reconstruction distance where the pass-band range of the transfer function is the largest. Then the whole reconstructed image with the highest resolution can be acquired. When the distance is different from the optimal distance, the size of the reconstructed image may vary with the distance and may disappear from the field of view in some cases. In order to obtain the whole image, two methods are proposed. However, at this time the resolution of the reconstructed image becomes lower. When the distance is smaller than the optimal distance, the whole image can be obtained, but the resolution of the image also decreases. The Fresnel algorithm is performed by using a single fast-Fourier-transform. With Fresnel algorithm, the same reconstructed images can be obtained with the different reconstruction distances and the reconstruction is better than with the convolution algorithm and the angular spectrum algorithm.

High-resolution digital holography for shape measurement of microscopic object

Digital holography is particularly well suited for characterization of microstructure such as surface shape, surface nanostructures and surface roughness. The direct availability of both amplitude and phase information offers a range of versatile processing techniques that can be applied to complex field data, including phase imaging, which is particularly straightforward in digital holography. Based on digital off-axis lensless Fourier transform holographic configuration, the principle of topography by digital holography is analyzed. The wavefront deformation created by numerical Fresnel reconstruction is then studied. Thus the model of phase mask which is a parabolic function and related to the recording parameters is built. The phase mask can be obtained automatically by using digital hologram itself to evaluate automatically and accurately the values of the parameters involved by a curve-fitting procedures applied to the phase data extracted along two profiles, which are defined in the region where sample contributions are constant. The reconstructed wave field can be simply obtained by multiplying the phase mask with Fourier transform of the hologram. Both theoretical analysis and the simulation results show that the procedure proposed by Colomb is more suitable for phase reconstruction of digital off-axis lensless Fourier transform holography. Moreover, the correcting procedure can be applied to compensate high-order aberrations.

Imaging and measurement techniques for three-dimensional microstructure by digital holographic microscopy

Digital holography is an emergent imaging technique which provides complete three-dimensional information of an object. An off-axis Fresnel digital holographic system with pre-magnification is built. Experimental investigations have been performed for a USAF test target. By using four autofocusing algorithms the optimal recording distance of the recorded hologram is determined accurately. The experimental results show that the variance algorithm is the most effective one for digital holographic microscopy. Based on the obtained recording distance, the phase image of the investigated microscopic object is reconstructed accurately by associated applying the automatic phase aberration compensation procedure proposed by T.Colomb with the manual adjustment method. The lateral resolution with better than 2.38 μm and the axial resolution of 10nm has been achieved experimentally.

Automatic compensation for phase aberration in digital holographic microscopy

Based on the point spread function of the off-axis Fresnel digital holographic system with pre-magnification, the phase aberration introduced by microscope objective is obtained. Using a collimated light as reconstructing wave, the phase aberration introduced by the difference between the reconstructing wave and the reference recording wave is analyzed. This method is very simple, and it is very different from the one proposed by T. Colomb et al. The phase mask that can be used to compensate automatically the phase aberration in the phase reconstruction is obtained. According to the principle of digital holography, it must be pointed out that for Fresnel digital holography, the recording distance must be determined accurately before compensating automatically the phase aberration. This is done by an automatic focusing procedure, which is based on image-gray-entropy-method. The simulation result for a special three-dimensional micro object, which is polluted by a random noise, is presented. The percentage error of the reconstructing distance obtained by the focusing procedure is below 0.6 for SNR = 25. Then an automatic aberration compensation procedure, which is the same as that one proposed by T. Colomb et al., is applied to reconstruct the phase image. The results show that for a weak noise the above method is very effective; for a stronger noise the procedure described here is applied iteratively, starting from the initial values provided by the first evaluation; while for a very strong noise the procedure fails at all. Moreover, after applying a median filter to the primary reconstructed phase image, the aberration of the phase image obtained by further iteration decreases, at the same time the noise is strengthen.

Lateral resolution of digital holographic system

Based on Fresnel diffraction theory, the point spread function (PSF) of the off-axis lensless Fourier transform digital holographic system with pre-magnification is deduced for the first time to the best of our knowledge. The limited lateral resolutions of the digital holographic systems with and without pre-magnification are analyzed in detail. For lensless Fourier digital holography, the expression of the limit resolution is obtained by use of Rayleigh resolution criterion and the PSF of this system. The obtained resolution is different from others in coefficient. Moreover, we propose new recording conditions with which the higher resolution can be achieved. The experimental results of a USAF test target demonstrate the correctness of the theoretical analysis about the lensless Fourier digital holography. For digital holography with pre-magnification, the limit resolution is also analyzed in detail. The results show that the imaging resolution is associated with the parameters of MO and CCD, the recording condition and the light wavelength. If the imaging resolution of CCD is higher than that of MO, the resolution of the whole system is dependent on the numerical aperture of MO. On the contrary, the resolution is dependent on the imaging resolution of the CCD. It is best to make the imaging resolution of MO approach the resolution limitation and the imaging resolution of CCD equal to or higher than the resolution of MO slightly, which can be implemented by decreasing the distance between the object and MO and decreasing the recording distance properly. The simulation results indicate the correctness of the theoretical analysis.

Depths of view and focus of digital holographic imaging system

There exist some ambiguities about the depth of view (DOV) and depth of focus (DOF) of digital holographic imaging system (DHIS). Based on the principle of digital holography, the DOV and the DOF of the DHIS is analyzed in detail for the first time to the best of our knowledge. For the four common configurations for recording digital holograms, the axial complex amplitude and the intensity distributions of the reconstructed optical field of a point object are deduced respectively using Fresnel diffraction formula. According to the same criterion in common coherent imaging system of the lens (CCISL), the DOF of the DHIS is obtained. The results show that the DOV and the DOF of the DHIS are related not only to the optical wavelength and the numerical aperture of the CCD camera but also to the offset of the reference light wave. The DOF of the CCISL is found larger than that of the digital in-line holographic system. But the DOF of the digital off-axis lensless Fourier transform holographic imaging system, which is depended strongly on the offset of the reference point source, may be larger or smaller than that of the CCISL. The computer simulation results confirm the validity of the theoretical analysis.

Imaging resolution of digital holographic microscopy with premagnification

The pre-magnification digital holography with a microscopic objective (MO) has become an important mean for imaging and measuring of microscopic objects. Based on Fresnel diffraction theory, the point spread function of digital off-axis Fresnel holographic system with pre-magnification is firstly deduced in detail. The lateral resolution of this imaging system is then analyzed. The amplitude distributions of the point spread functions of the MO, the holographic CCD and the whole imaging system are simulated respectively. Then, the matching requirements between MO and the holographic CCD are discussed. Some ambiguities about the resolution limitation in existing literatures are clarified. The results show that only when the image resolution of the holographic CCD is not below the imaging resolution of the MO, the resolution of overall system is dependent on the numerical aperture of the MO. Otherwise, it is dependent on the numerical aperture of the CCD. It is optimum to make the imaging resolution of the MO approach its limitation and be equal to or less than the resolution of the holographic CCD a little. The simulation results verify the validities of the theoretical analysis.