Review of Fresnel Incoherent Correlation Holography with Linear and Non-Linear Correlations

Abstract

Fresnel incoherent correlation holography (FINCH) is a well-established incoherent imaging technique. In FINCH, three self-interference holograms are recorded with calculated phase differences between the two interfering, differently modulated object waves and projected into a complex hologram. The object is reconstructed without the twin image and bias terms by a numerical Fresnel back propagation of the complex hologram. A modified approach to implement FINCH by a single camera shot by pre-calibrating the system involving recording of the point spread function library and reconstruction by a non-linear cross-correlation has been introduced recently. The expression of the imaging characteristics from the modulation functions in original FINCH and the modified approach by pre-calibration in spatial and polarization multiplexing schemes are reviewed. The study reveals that a reconstructing function completely independent of the function of the phase mask is required for the faithful expression of the characteristics of the modulating function in the image reconstruction. In polarization multiplexing method by cross-correlation, a partial expression was observed, while in spatial multiplexing method by cross-correlation, the imaging characteristics converged towards a uniform behavior.

Roadmap on Recent Progress in FINCH Technology

“…Furthermore, the beam characteristics of the two interfering beams were not manifested in the imaging characteristics in this correlation approach. A recent simulative study revealed that the performance of FINCH in the pattern recognition approach was nearly independent of the characteristics of the interfering beams [36]. Therefore, the methods developed by Bouchal and Bouchal using vortex filter could not applied for edge enhancement [38] in this case.…”

“…FINCH was proposed as a correlation between the object and Fresnel zone plates (FZP). It is based on a single on-axis interferometer and does not require any movement or multiplexing image of the scene [36,39]. So, the FINCH system is widely applied in microscope and imaging methods with a synthetic aperture.…”

“…Recently, Anand et al proposed a pattern recognition approach of FINCH in which the point spread hologram (PSH) of FINCH was recorded and cross-correlated with the object hologram. In this study, the beam modulator was randomly multiplexed Fresnel zone lenses fabricated using electron beam lithography [14,36]. In 2020, FINCH was demonstrated for the first time using flat bifocal metalens by Zhou et al [37].…”

Advanced Imaging Methods Using Coded Aperture Digital Holography

“…Fresnel incoherent correlation holography (FINCH), published in 2007 [23], was a return to the principle of self-interference and was proposed as an alternative to the scanning-based holography methods mentioned above. Following the first FINCH, many other incoherent digital holograms were proposed, with most of them based on the self-interference principle [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. Fourier incoherent single-channel holography (FISCH) [39] is a typical example of using the self-interference principle, but the obtained hologram, in this case, is a 2D cosine Fourier transform of the object.…”

Fresnel Incoherent Correlation Holography using Lucy-Richardson-Rosen Algorithm

“…Most recently, a two-step phase-shift FINCH was developed utilizing the mathematical model of self-interference holography and implemented FINCH with two camera shots [7]. A radically different approach of single shot FINCH was demonstrated by prerecording the point spread hologram (PSH) and correlating it with the FINCH hologram of an object using non-linear reconstruction [8][9][10]. In that approach, the optical modulator of FINCH was designed based on the configuration of the first version of FINCH by randomly multiplexing two quadratic phase functions and manufactured as a passive optical element using electron beam lithography.…”