Fucai Zhang

Phase retrieval using multiple illumination wavelengths.

An iterative phase retrieval method is proposed, which uses a sequence of diffraction intensity patterns recorded at different wavelengths. This method has a rapid convergence, and a high immunity to noise and environmental disturbance. The wrap-free phase measurement range is also extended based on the principle of two-wavelength interferometry. Simulation and experimental results are presented to demonstrate the approach.

Reconstruction algorithm for high-numerical-aperture holograms with diffraction-limited resolution.

A fast algorithm is proposed for the reconstruction of digital holograms that are recorded at high numerical aperture. The method directly evaluates the Rayleigh-Sommerfeld diffraction integral by use of a fast convolution algorithm. A shift parameter that accounts for the coordinate systems transverse displacement of the object plane and the hologram plane is introduced in a discrete representation of the diffraction kernel. Combination of the samplings reconstructed with different shift values yields diffraction-limited resolution over the full field of view. The algorithm is suitable for various applications such as holographic microscopy and metrology. Simulation and experimental results are presented.

High-fidelity numerical realization of multiple-step Fresnel propagation for the reconstruction of digital holograms

A cascaded Fresnel algorithm for the flexible reconstruction of digital holograms is proposed. Since the fast-Fourier-transform-based numerical realization of the Fresnel integral shows a dependency of its pixel resolution and its computation window size on the propagation distance different from that of the corresponding physical system, the computation window can be smaller than the actual physical diffraction field in the intermediate plane. Consequently, distortions in the final reconstruction may occur. A method is proposed to eliminate such distortion. The validity of this method is shown by both numerical simulations and experimental results.

Characterization of a spatial light modulator and its application in phase retrieval

Recently a phase retrieval method using a movable phase plate as modulator has been proposed [Phys. Rev. A75, 043805 (2007)]. This method is applicable to general complex-valued fields and exhibits rapid convergence and high robustness to noise. In this paper, we demonstrate how to use this technique to characterize the phase shifting properties of a liquid-crystal modulator, and in turn we use the characterized modulator as the modulation device in the presented phase retrieval method. The adoption of a dynamic modulator gives a much more robust and flexible setup.

Digital holographic microscopy in the deep (193 nm) ultraviolet

We present a system based on digital holography suitable for the investigation of microscopic objects. To increase the resolution of the system a deep (193 nm) UV laser source has been used. A method for compensating aberrations due to the non-perfect optical elements used for the recording has been developed. The system allows the investigation of reflecting and transmitting samples.

Phase retrieval by pinhole scanning

We describe a method where phase and amplitude of a wavefront are obtained by processing a sequence of pattern produced by the interference between the light transmitted by a scanning pinhole (which is sequentially shifted) and a reference pinhole. Simulations and experimental results are presented.

Image formation in digital holography

In this study we investigate the imaging mechanism of digital holography. The imaging process is separated into three steps: hologram recording, phase retrieval, and object field reconstruction. For hologram recording, the average effect due to the sensor pixel aperture and the role of the physical reference beam are addressed particularly. The average effect of pixel aperture is equivalent to a low pass filter, which acts on the interference term between the object field and the reference wavefront. An optimal physical reference beam is then to minimize the bandwidth of the interference term so that more object information can pass through the filter. For the reconstruction of object field, emphasis is paid on the correspondence between the underlying physical process and the discrete system represented by the reconstruction algorithms. The implication of sampling theory on each reconstruction algorithm is discussed in detail. The sampling requirement imposes a limitation only on the maximum extension of object field. Our analysis indicates that the achievable spatial resolution by digital holography is determined by the recording numerical aperture and wavelength of light, the same as the conventional microscopy. The independent analysis of each part illumines the way to optimize the system performance.

Aberration-free reconstruction algorithm for high numerical aperture digital hologram

In digital holographic microscopy, a high numerical aperture object lens of good quality is required in order to achieve high lateral resolution. As well known, such lenses usually have large aberrations and are difficult to fabricate, especially in the ultra-violet and infrared spectral regions. In these circumstances, a system without objective lens is highly preferred. According to imaging theory, this means that the hologram should be recorded with a high numerical aperture (NA). For the reconstruction of high NA holograms, the Rayleigh-Sommerfeld diffraction integral without approximation must be evaluated. However the current mostly used three algorithms, namely, the Fresnel algorithm, the angular spectrum algorithm, and the convolution algorithm are not suitable. In this paper, the properties of these algorithms are presented. Then a modified convolution algorithm is proposed. In this method, a shift parameter is introduced in the discrete representation of diffraction kernel and then reconstructions with different shift values are combined. The modified convolution method is able to give samplings of diffraction-limited resolution for the full field of view. The simulation results of point field with different reconstruction algorithm are presented. Experimental results of a test dot array are also given.

Wrap-free phase retrieval using a series of intensity measurements produced by tuning the illumination wavelength

In this paper, we present a phase retrieval method where a sequence of diffraction speckle intensities, recorded by tuning the illumination wavelength, is used. These recordings, combined with an iterative calculation method, allow the reconstruction of the amplitude and the phase of the wavefront. The main advantages of this method are: simple optical setup and high immunity to noise and environmental disturbance, since no reference beam or additional moving parts are needed. Furthermore, this method allows for an extended wrap-free phase measurement range by using synthetic wavelengths. The technique shows great potential in some fields of micro-metrology, such as lensless phase contrast imaging and wavefront sensing.

Phase retrieval based on wavefront modulation

A practical method is proposed for the wavefront measurement of arbitrary complex-valued fields. A mask having random phase is placed in the path between the object and the image sensor. Three or more diffraction patterns are collected, as the mask translated in the direction parallel to the sensor. Phase retrieval is performed by propagating the wave field back and forth between the sensor and the mask plane and making the following change on the calculated wavefront: at the sensor plane, the modulus of calculated wavefront is replaced with the square root of recorded intensity; while at the mask plane, the modulation phase is updated to the one corresponding to the next mask position for next iteration. This process starts from a random estimate of the object field falling on the mask and ends when the change of the amplitude of two successively retrieved object fields before the mask is below a given threshold. Further propagation of the retrieved field from mask to object plane yields the original object field. Results from both simulated data and experimental data show that this method works quite well in terms of its absence of stagnation, suitability for complex-valued field, and high immunity to the noise in recordings. The technique is believed to find wide applications, such as aspherical lens testing, and diffraction imaging of micro-objects.