Point spread function and two-point resolution in Fresnel incoherent correlation holography

Abstract

Fresnel Incoherent Correlation Holography (FINCH) allows digital reconstruction of incoherently illuminated objects from intensity records acquired by a Spatial Light Modulator (SLM). The article presents wave optics model of FINCH, which allows analytical calculation of the Point Spread Function (PSF) for both the optical and digital part of imaging and takes into account Gaussian aperture for a spatial bounding of light waves. The 3D PSF is used to determine diffraction limits of the lateral and longitudinal size of a point image created in the FINCH set-up. Lateral and longitudinal resolution is investigated both theoretically and experimentally using quantitative measures introduced for two-point imaging. Dependence of the resolving power on the system parameters is studied and optimal geometry of the set-up is designed with regard to the best lateral and longitudinal resolution. Theoretical results are confirmed by experiments in which the light emitting diode (LED) is used as a spatially incoherent source to create object holograms using the SLM.

Enhanced-resolution using modified configuration of Fresnel incoherent holographic recorder with synthetic aperture

“…where f 1 and f 2 are real constants representing the focal distances of the two converging spherical waves (relative to the SLM plane), C 1 and C 2 are constants, θ is one of the three angles used in phase shifting in order to eliminate the twin image and the bias terms from the final hologram, in accordance with Refs [11][12][13][14][15]. The limiting function of each physical aperture is a rectangular function defined by …”

“…A different approach to analyzing the FINCH resolution is via the violation of the Lagrange invariant, as was indicated by Refs [13,20]. Any conventional imaging system in homogeneous space satisfies the condition T in out M NA NA  , which is known as a form of the Lagrange invariant.…”

“…The two waves interfere on the camera plane, where their interferogram encodes the 3D location and intensity value of each point source. Summing the interferograms of the total spherical beam couples creates a Fresnel hologram of the entire observed 3D scene [11][12][13]. Thus, in FINCH, the object itself serves as the only light source for each of the interfered waves and, therefore, no external active coherent illumination (i.e., laser beam) is needed.…”

“…The early studies of FINCH [11][12][13] presented a method of interfering between plane and spherical waves. Later on [14,15], it was demonstrated, theoretically and experimentally, that the imaging resolution of FINCH is beyond the Rayleigh resolution limit when compared to conventional incoherent and coherent imaging systems with the same NA.…”

Improved axial resolution of FINCH fluorescence microscopy when combined with spinning disk confocal microscopy

“…Self-referenced holographic techniques [1][2][3][4][5] such as FINCH [1,[3][4][5][6][7][8][9][10][11][12] offer advantages over standard coherent holographic techniques, including the lack or requirement for use of a laser in the recording process, suitability for any illumination technique, and, for FINCH and similar techniques, inherent super-resolving capability for objects located away from the focal plane of the entry lens into the system. Thus, since the FINCH concept provides a platform for flexible and adaptable methods with the ability to offer high resolution 3D fluorescent images with little additional difficulty beyond standard imaging techniques, they are increasingly studied as techniques for improving microscopy performance.…”