Fresnel incoherent correlation holography with Lucy-Richardson-Rosen algorithm and modified Gerchberg-Saxton algorithm

Fresnel incoherent correlation holography (FINCH) is a well-established incoherent digital holography technique for imaging objects with an enhanced transverse resolution. In FINCH, light from an object point is split into two and modulated using two different quadratic phase masks and interfered to obtain the self-interference hologram. The two beams can be generated either by spatial random multiplexing or polarization multiplexing, with the former being power efficient and the latter exhibits a high signal to noise ratio. At least three such holograms are recorded with phase shifts 0, 2π/3 and 4π/3 radians and combined to obtain a complex hologram. This complex hologram can be numerically propagated to reconstruct any plane of the object. Under special beam matching condition, FINCH can exhibit a transverse resolution that is 1.5 times better than incoherent lens-based direct imaging systems with the same numerical aperture. To summarize, FINCH records 3D information with a high resolution at the expense of reduced temporal resolution. Several techniques have been developed in the past to improve the temporal resolution of FINCH by sacrificing transverse resolution and field of view. In this study, a recently developed phase mask design algorithm called Transport of Amplitude into Phase based Gerchberg-Saxton Algorithm (TAP-GSA) and reconstruction algorithm called Lucy-Richardson-Rosen algorithm (LR²A) has been implemented in FINCH. The modified approach with the TAP-GSA and LR²A significantly improved the performance of FINCH with an improved temporal resolution, light throughput and signal to noise ratio.