# Speckle Noise Reduction in Digital Holography Using a DMD and Multi-Hologram Resampling
## 1 Introduction  
Robust and versatile imaging techniques are always at the forefront of development in engineering and sciences. Digital Holography (DH) provides an interesting alternative as it allows retrieving the three-dimensional information from a scene. Its potential has given rise to different applications in imaging objects [1], microscopy [2], quantitative phase estimation [3], and many others. Using coherent illumination, a holographic register is made by the light interference of the reference beam and object beam coming from the transmission or reflection of an object. The holograms are recorded digitally to be numerically reconstructed, retrieving the amplitude and phase information. When coherent light strikes an object with rough surfaces scaled to the visible wavelength range, a coherent noise or speckle appears. The hologram stores this noise along with the object information, and its presence extends to the reconstructed image deteriorating its quality. Multiple strategies to reduce the speckle noise on DH have been proposed. They can be categorized, according to the number of holograms registered, into multiple and single-shot strategies. According to their approach, they can be divided into two categories: optical and numerical operations. Optical techniques tend to require multiple registers, as a specific property is modified between measurements to produce uncorrelated noise. Some examples of existing strategies include recording holograms with different wavelengths [4], polarization states [5], rotating diffuser [6], lateral shifting of the camera [7], lateral shifting of the object [8], and time multiplexing [9]. The multiple registers are expected to have a differently behaved noise, which implies that a simple averaging operation can produce a new intensity image with less coherent noise. The drawbacks inherent for these techniques come from the complexity of the optical set-ups and the inability to register dynamic events provided multiple registers are needed. Numerical techniques, on the other hand, tend to achieve the noise reduction based on a single hologram. There are approaches with traditional image processing techniques [10; 11] where the reconstructed intensity is processed to improve its quality. Other techniques try to obtain multiple reconstructions from a single hologram, by rectangular segment subdivision [12] or grid-like subdivision [13] of the recorded hologram. These generated registers are consequently reconstructedand the resulting intensities averaged. As the resolution of a holographic reconstruction is affected by the size of the hologram, these techniques suffer from an increasing loss of resolution when increasing the subdivisions. Random non-Bayesian complementary masks have been proposed [14], where a multiplication with the original hologram produces multiple new registers with an expected different noise. The randomness of the sampling consequently affects the resolution of the reconstructed image. In this paper, we propose a combination of a numerical and optical approach to reduce the speckle noise. We introduce a Digital Micromirror Device (DMD) into the holographic set-up that allows varying the phase of the illumination hitting the object. Multiple holograms are recorded with varying illumination. Similar techniques have been proposed in the past, albeit based on physically rotating a mirror [15; 16] or a spatial light modulator [17]. Here, we propose the use of a DMD which is known to be a more robust and experimentally approachable device that offers a high speed of operation as it has been documented in the past [18] with its adaptation to a holographic setup. This feature allows us to implement synchronous registering with the camera at high frame rates reducing the constraints of this approach for dynamic applications. Furthermore, we present a numerical resampling of the recorded holograms, producing new synthetic holograms with more varying coherent noise.