Undersampled digital holography

Abstract

Acceptable signal recovery of the band-pass signals typically used in the off-axis digital holography systems is possible in the undersampling conditions. A typical system is considered in which the angle between two beams represents a variable parameter. For the given signal bandwidth and experimental conditions the hologram reconstruction is constrained by the sampling frequency of the array photo-detector. Reconstructions from the undersampled digital holograms are analyzed both theoretically and experimentally. It is shown how increasing the angle values beyond the Nyquist limits leads to repeatedly folding and inverting the reconstructed object image until the fading of the image. The phase point at the image fading and the non-overlapping intervals for correctly preserving the useful information are defined and evaluated. Amplitude distributions are analyzed on the example of the time-averaged holograms acquired for an oscillating membrane. Based on removing the zeroth-order reconstruction term, significant extensions of these intervals are also demonstrated.

Digital Fresnel holography beyond the Shannon limits

“…1 and theoretical basics. Note that the results are in contradiction with [22], in which the object direction may be inverted. For each object shift, the phase changes are extracted from the two recordings without and with tilt.…”

“…The Shannon theorem applied to off-axis digital holography, resulting in the spatial separation of the three diffraction orders, leads to the optimal recording distance. Practically, the spatial frequencies can be adjusted following this method: the reference beam is perpendicular to the recording plane but the object is laterally shifted [22,24]. We consider here that the spatial Shannon limits are given by the maximum lateral shift, as long as that the center of the object fulfills the Shannon theorem.…”

“…In their paper, Xu et al proposed an imaging analysis of digital holography, in which they demonstrated that the pixel has a multiplicative sinc effect on the reconstructed field [21]. In 2009, Demoli et al [22] proposed experimental results exhibiting the effect of under sampling in digital Fourier holography. They showed the appearance of aliasing frequencies.…”

Digital holographic recording and reconstruction of large scale objects for metrology and display

“…However, in special cases with additional effort, it is possible to recover the signal even for angle values beyond the Nyquist limits. 14 The sampling theorem requires sampling of the period p with more than two pixels, thus…”

Fiber optics sensor for sub-nanometric displacement and wide bandwidth systems

“…Nowadays, performances have evolved since then with resolutions below the nanometer and bandwidths beyond the MHz. Digital holography is another optic solution for applications in modal analysis of MEMS (micro-electromechanical systems) [9] and dynamic endoscopy [10] for instance, with a sub-micrometric resolution and a bandwidth of a few kHz. Another noncontact solution is the capacitive gauge; nowadays commercial systems report resolution as good as 0.01 nm over a 100 µm range in static case and 0.02 nm with a 10 kHz bandwidth in dynamic case [11], after software correction of mechanical errors and non-linearities.…”