Signal reconstruction algorithm based on a single intensity in the Fresnel domain

Abstract

A novel algorithm that can reconstruct a symmetrical signal (both the amplitude and the phase information) with only a single Fresnel transform intensity is proposed. A new complex-convolution method is introduced, which is needed in the algorithm. The essential properties of the discrete Fresnel transform are presented as well. Numerical results show that this method can successfully rebuild the signal from one signal intensity, which is more advantageous in speed and efficiency than the conventional method that requires two intensities to accomplish this task.

Signal Reconstruction Algorithm Based on a Single Intensity in the Fresnel Domain

“…The recovered magnitude and phase information are indicated in Figure 3a and 3b, respectively. The solid curves in Figure Hwang and Han, 2007. ) recovered by our recursive method.…”

“…Figure 5a and 5b show that the recovered signal is good for signal to noise ratio (SNR) equal to 10, but it Hwang and Han, 2007. ) would have larger errors when the SNR is equal to 3.…”

“…Based on these advantages in the Fresnel domain, we introduce an improved version of Cong's method, which uses only one intensity in the Fresnel domain to retrieve the phase and the amplitude of the object (Hwang and Han, 2007). A new relation called complex convolution is proposed that plays an important role in our work.…”

Iterative Noise Reduction in Digital Holographic Microscopy

“…A conventional setup in DHM is based on the use of an external reference wave (RW), which interferes with the field generated by the object, forming an intensity pattern which is known as hologram of the field (Takeda et al, 1982;Kreis, 1986;Yamaguchi-Zhang, 1997;Yamaguchi et al, 2001;Arrizón-Sanchez, 2004;Liebling, 2004;Quian, 2006;Meneses-Fabian, 2006;Guo, 2007;Cruz et al, 2009). Alternately, it is possible to omit the external RW, with a consequent simplification of the optical setup (Pedrini, 1998;Xu, 2002;Morlens, 2006;Garcia-Sucerquia, 2006;Hwang-Han, 2007;Singh-Asundi, 2009). In any case, either the object hologram or the intensity of the field scattered by object are recorded with an electronic intensity meter, such as a charge-coupled device (CCD).…”

“…However, if DHM is used to study microscopic samples of large BW, the isolation of the object field component, in the hologram, cannot be realized by this simple spatial filtering procedure. In this case, one of the useful procedures is to perform the elimination of non desired hologram components by iterative procedures (Fienup, 1987;Cederquist et al, 1989;Wu, 2004;Denis et al, 2005;Hwang-Han, 2007;Nakamura, 2007). In this chapter we describe an iterative method that effectively recovers the object field component from the recorded hologram, in both the LOADH and RLOADH setups.…”