By Ulf Schnars, Claas Falldorf, John Watson, Werner Jüptner
This e-book offers a self-contained remedy of the foundations and significant functions of electronic hologram recording and numerical reconstruction (Digital Holography). This moment version has been considerably revised and enlarged. The authors have prolonged the bankruptcy on electronic Holographic Microscopy to include new sections on particle sizing, particle picture velocimetry and underwater holography. a brand new bankruptcy now offers comprehensively and largely with computational wave box sensing. those ideas characterize a desirable substitute to straightforward interferometry and electronic Holography. they permit wave box sensing with out the requirement of a selected reference wave, hence permitting using low brilliance gentle resources or even liquid-crystal screens (LCD) for interferometric applications.
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Extra resources for Digital Holography and Wavefront Sensing: Principles, Techniques and Applications
The terms~ s1 and~ s2 are unit vectors from b1 and ~ b2 are the illumination source point S to P1, and P2 respectively. Similarly, ~ unit vectors from P1 to the observation point B, and from P2 to B, respectively. The optical path difference between a ray from S to B via P1 and a ray from S to B via P2 is therefore given by, À Á d ¼ SP1 þ P1 B À SP2 þ P2 B ! ! ! ! ! ¼! s1 SP1 þ b1 P1 B À ! 7 Holographic Interferometry 29 Fig. 18 Calculation of the interference phase Illumination point s2 S s1 P2 d b2 P1 b1 Hologram B Observation point Object The lengths SP1=2 and P1=2 B are in the range of metres, while ~ d is in the range of several micrometres.
It represents the non-diffracted wave passing through the hologram (zero diffraction order). The second term is the reconstructed object wave and forms the virtual image. The real factor bsa2R only inﬂuences the brightness of the image. The third term generates a distorted real image of the object. For off-axis holography the virtual image, the real image and the non-diffracted wave are spatially separated. The reason for the distortion of the real image is the spatially varying complex factor ER2 , which modulates the image forming conjugate object wave EOÃ .
The original object wave is reconstructed by illuminating the hologram with the reference wave, Fig. 13. An observer sees a virtual image, which is optically indistinguishable from the original object. The reconstructed image exhibits all effects of perspective, parallax and depth-of-ﬁeld. The holographic process is described mathematically using the formalism of Sect. 2. Across the extent of the photographic plate, the complex amplitude of the object wave is described by EO ðx;yÞ ¼ aO ðx;yÞ expðiuO ðx;yÞÞ ð2:58Þ with real amplitude aO and phase uO .