# Incoherent Digital Holography: A Review
## 1 Introduction  
The demand for three-dimensional (3D) imaging [1; 2] has been increasing more and more in recent years. The acquisition of 3D information is important, particularly in the fields of life science [1] and information science [2]. To record the 3D position, shape, and image of an object, many types of methods, such as dual focus-plane imaging [1], integral imaging with a lens array [2], scanning and nonlinear optics [3], coherent diffraction imaging [4], and holography [5], have been actively researched. However, as a result of advanced computer and photonic devices, digital holography (DH) [6; 7] can record a hologram of a real 3D object on a two-dimensional (2D) plane and reconstruct its image digitally, which has given a promising 3D technique in the last decade. DH is an interference technique, and the light source should be both spatially and temporally coherent to guarantee the success of the interference. In practice, there is no perfect coherent source, and thus holographic recording is always performed by a partially coherent source. For a source with a high spatial coherence but low temporal coherence, interference can be performed when the time delay between the object light and the reference light is smaller than the coherence time. This is also the fundamental concept of \"low-coherence DH\", which has been applied to perform 3D imaging and sectional reconstruction [8; 9; 10; 11; 12]. On the other hand, holographic recording by using a source with a high temporal coherence but low spatial coherence is more difficult, because it is difficult to generate a mutually coherent reference light from such a light source. This is the case that we are interested in for this paper, and it is referred to as \"incoherent DH\" henceforth. There are two different kinds of techniques to realize incoherent DH. The first technique is optical scanning holography (OSH) [13], which was first proposed in 1979 by [PERSON] and [PERSON] and was pioneered by [PERSON] [14; 15; 16]. OSH does not perform interference between the object light and the reference light. Instead, a heterodyne interference fringe pattern without the information of the object is first generated, and the object target is raster scanned by this interference pattern. The scattered light from the object is then detected and demodulated to obtain a resulting hologram. So far, OSH has been applied to remotessing [17; 18], cryptography [19; 20; 21], microscopy [22; 23; 24; 25; 26; 27; 28; 29] and 3D display [30; 31; 32]. However, the most important feature of OSH is the ability to record incoherent holograms. In OSH, although the light source is always highly coherent spatially and temporally, the recorded hologram can be either spatially coherent or incoherent. The reason is that the spatial coherence of OSH depends on the recording geometry. If the active area of the detector is large enough, the hologram is formed by the superposition of the irradiance response of the object target, resulting in an incoherent hologram. Therefore, OSH can record incoherent holograms at the wavelength of the light source. Subsequently, OSH can also record fluorescence holograms [22; 26], which is an incoherent holographic technique of single-wavelength excitation and continuous-spectrum emission and detection. The second technique of incoherent DH is Fresnel incoherent correlation holography (FINCH) [33]. FINCH is based on a single-path and self-interference interferometer, which generates an incoherent hologram that is composed of the summation of Fresnel zone plate (FZP) patterns. [PERSON] and [PERSON] initially presented a single-path and self-interference holography setup adopting a spatial light modulator (SLM) [33; 34]. In the optical path, an optical element converts an object wave into two wavefronts that have different curvature radii from each other. A birefringent crystal, SLM, or double-focus lens is typically selected as the optical element to generate the two waves. FINCH has been applied to color 3D imaging [34] and microscopy [35; 36; 37; 38].