Study On The Methods For Fast And High Resolution Measurement Of Wavefront And Diffractive Imaging Based On Digital Holography

Fast reconstruction and high resolution imaging are two basic research problems in the field of digital holography. According to the angle that the reference beam departs from the object beam, digital holography can be divided into two categories: on-axis digital holography and off-axis digital holography. The frequency bandwidth of on-axis digital hologram is two times the bandwidth of object wave while the frequency bandwidth of off-axis digital hologram is generally more than four times the frequency bandwidth of object wave which makes higher request to the resolution of the image sensor in off-axis digital holography. But there is a unique advantage for off-axis holography that it allows retrieval of the wavefront information of object recorded in the hologram only by one exposure because of the spectrum of object departing from the spectra of autorelation item and of conjugate item. So off-axis digital holography plays an important role in fast reconstrucition of holograms. From another perspective, the reconstructed image can get higher lateral resolution in on-axis digital holography than that in off-axis digital holography under the same condition that satisfies the sampling theorem, but on-axial holography requires complex algorithm, for example phase shift method to eliminate the influence of noises introduced by the conjugate and autoralation items. Off-axis digital holography can be also subdivided into the slightly off-axis digital holography which has the characters of on-axis digital holography and off-axis digital holography.This paper focuses on the methods for fast reconstruction of off-axis digital hologram and the methods for high resolution imaging of on-axis digital holograms and slightly off-axis digital holographm. The main research contents of this dissertation include:1. The characteristics of digital holographic imaging were studied. We derived thepoint spread function of digital holographic imaging system from which the expression of lateral resolution of reconstructed images was drawn out. And the influence of each pixel of the image sensor on the resolution of the reconstructed images was further studied. We deduced the distance requirement for recording digital holograms, and according to which the judgment that the resolution of the reconstructed images is generally lower than the resolution of the image sensor was obtained.2. Proposed a fast reconstrucion algorithm of off-axis digital hologram based on digital spatial multiplexing—the spatial multiplexing(SM) algorithm. Based mainly on the characteristic that the bandwidth of the off-axis hologram is generally more than or equal to four times the bandwidth of object wave, the SM algorithm first encodes a SM hologram by adding four holograms, each of which was multiplied by a plane wave tilted in y direction(orthogonal to the tilt direction x of the reference beam in holographic recording). Different angles that the four holograms translate make the spectra of the four holograms apart from each other and full of the spectrum space of the SM hologram.Then the four separate spectra of object waves can be obtained only by performing one1.25-dimensional Fourier transform(1.25D-FT) on the SM hologram. Finally, the wavefronts of the four objects can be retrived, respectively, by four two-dimensional inverse Fourier transform(2D-IFT) on each of the four spectra.The SM algorithm greatly reduces the amount of calculation because of geting four spectra information of four holograms only through one 1.25D-FT. So the reconstruction efficiency of hologram can be speeded up.3. Proposed a fast reconstruction algorithm of off-axis digital hologram based on a combination of complex encoding(CE) and spatial multiplexing(SM).—the complex spatial multiplexing(CSM) algorithm. The CSM algorithm is the further development of the SM algorithm. It can obtain eight spectra of eight object waves only through one 2D- FT. The detailed steps are the following. Every two of off-axis holograms recorded in sequence are firstly assembled into a CE hologram through one hologram as the real part, and the other as the imaginarypart. And then each four of the CE holograms are again encoded into one complex spatial multiplexing(CSM) hologram based on the SM algorithm. Next,performing 2D-FT on the CSM hologram, the four complex spectra information of the four CE holograms were first obtained; then the eight spectra of eight holograms would be worked out by analytical formula. Finaly, the eight original wavefronts of the objects recorded could be retrieved by eight 2D-IFTs on the eight spectra. Eight spectra of objects were gotten only using one 2D-FT in the CSM algorithm, so the CSM algorithm further reduced the amount of calculation and improved the reconstruction efficiency than the SM algorithm.4. Proposed a wavefront reconstruction algorithm of slightly off-axis digital hologram based on phase derivative—phase derivative(PD) algorithm. Based on the peculiarity in the off-axis digital holography(including slightly off-axis situation), that the first order derivative of the object wave’s relative phase to space is always less than or equal to zero, the PD algorithm derives a relationship between the signs of the first order derivative of the absolute value of the object wave’s relative phase and the object wave’s relative phase. According to the relationship, the object wave’s relative phase can be retrieved. This method adopts the phase derivation to the space which only involvs the local operation and do not use the integral or iteration calculation, so it is especially suitable for the reconstruction of large size of the off-axis digital hologram.5. Proposed a wavefront reconstruction algorithm of on-axis digital hologram---zero difference(ZD) algorithm. In the ZD algorithm, first two holograms before and after a phase shift whose value is unknown are record. In the two holograms,there are always some points whose light intensities are invariant through that the ZD algorithm works out the value of phase shift. Then the wavefront amplitude and relative phase information are worked out according to the value of phase shift. This ZD method avoids the requirement of accurate phase shift which makes wider adaptability of phase shift algorithm.The feasibility and accuracy of the algorithms mentioned above have been given detailed theoretical analysis and experimental verification.