Magnified reconstruction of digitally recorded holograms by Fresnel–Bluestein transform

Abstract

A method for numerical reconstruction of digitally recorded holograms with variable magnification is presented. The proposed strategy allows for smaller, equal, or larger magnification than that achieved with Fresnel transform by introducing the Bluestein substitution into the Fresnel kernel. The magnification is obtained independent of distance, wavelength, and number of pixels, which enables the method to be applied in color digital holography and metrological applications. The approach is supported by experimental and simulation results in digital holography of objects of comparable dimensions with the recording device and in the reconstruction of holograms from digital in-line holographic microscopy.

Digital Inline Holographic Microscopy (DIHM) of Weakly-scattering Subjects

“…In the limit of monochromatic illumination, the resolution of a DIHM system is ultimately set by the numerical aperture of the objective lens (NA) and the wavelength of illumination (λ) 23,24 . Laterally separated points should lie at least a distance Δ lat ='λ'/2NA apart if they are to be separately resolved.…”

Phase retrieval for object and probe in the optical near-field

“…A slightly different formulation of the discrete Fresnel-Kirchhoff integral helps to overcome this drawback and allows scaling of input and output pixel sizes that is not restricted by equation 3.153 [39]. To this end, the complex exponential function of the discrete Fourier transform (see equation 3.152) is modified as proposed by L. I. Bluestein [43]:…”

“…It is essential, since it contains the fundamentals of wave optics necessary for digital holography. Here, four different implementations of near-field propagation shall be introduced: the single Fourier transform method [37,38], the transfer function and the impulse response propagation [37] as well as the Fresnel-Bluestein transform [39,40]. Extensive literature and practical implementation techniques of Fresnel diffraction can be found in the textbooks of D. G. Voelz [41] and J. D. Schmidt [42].…”

“…However, at least approximately correct sampling of C FB2 and C FB3 is important. Fresnel-Bluestein propagation does not require a fixed relation between input and output pixel sizes (like relation 3.153 for the Fresnel integral formulation): 193) where M in principal can take any value [39]. When inserting equation 3.193 in C FB2 , one finds…”

A Study on Two-wavelength Digital Holography Using the Fresnel-Bluestein Transform

“…[12,13] . [14,15] . 본 연구에서는 2π 모호함 (2π ambiguity)을 해결하기 위하 여 2-파장 홀로그래픽 시스템을 구성하고 재생상을 구성 할 때 프레즈넬-불루스타인 변환을 이용하여 위상 재생상을 만 들고, 이를 이용하여 정확한 측정이 가능함을 실험적으로 연 구하였다.…”