Spatial bandwidth extended reconstruction for digital color Fresnel holograms

Abstract

This paper presents a reconstruction algorithm based on the convolution formula of diffraction which uses the Fresnel impulse response of free space propagation. The bandwidth of the reconstructing convolution kernel is extended to the one of the object in order to allow the direct reconstruction of objects with size quite larger than the recording area. The spatial bandwidth extension is made possible by the use of a numerical spherical wave as a virtual reconstructing wave, thus modifying the virtual reconstruction distance and increasing the kernel bandwidth. Experimental results confirm the suitability of the proposed method in the case of the simultaneous recording of two-color digital holograms by using a spatial color multiplexing scheme.

Measurement of density fluctuations using digital holographic interferometry in a standing wave thermoacoustic oscillator

“…This is achieved by multiplying C by e À2ipður xþvr yÞ . Note that if the image of the test section is not in focus, the refocusing can be performed using the angular spectrum transfer function to get an in-focus image [37,38]. After the reconstruction process, both the optical phase and the amplitude can be estimated from Eq.…”

Design of the spatial filter window for digital holographic convolution reconstruction of object beam field

“…In reference [3], we have researched the relationship between the object shape and its spectrum distribution in the computation of convolution reconstruction using the impulse response of free space propagation, and the filter windows of different outlines according to the shape of the object can be easily designed. For example, in this paper, the shape of the experimentally studied object is circular.…”

“…Recently, the convolution reconstruction method with an adjustable magnification has been introduced based on the angular spectrum theory of diffraction [2] when the projection dimension of the object is quite greater than the recording area of the CCD. Actually, this method is not only convenient for the above situation, but has also applications in digital color holography or multi-wavelength illumination [3]. However, in order to integrate the information of the different wavelengths for the latter situation, not only do the object fields need to be well reconstructed with the same magnification, but the reconstructed images also need to be accurately superimposed.…”

Simultaneous full-field 3-D vibrometry of the human eardrum using spatial-bandwidth multiplexed holography

“…16,17 The spatial bandwidth of the convolution kernel can be determined by taking a partial derivative of the convolution kernel with respect to the two directions and can be calculated with NΔx∕λd and NΔy∕λd, where N 2 is the number of pixels in the hologram plane, Δx and Δy are the pixel sizes in the x and y directions, and d is the reconstruction distance. On the other hand, it can be geometrically shown that the maximum bandwidth of the object can be calculated from L x ∕λd and L y ∕λd, where L x and L y are the dimensions of the object in the horizontal and vertical directions.…”