## 1 Introduction  
With the development of electronic array sensors as CCD (Charge Coupled Device), or CMOS (Complementary Metal Oxide Semiconductor), with sufficiently small pixels to fulfill the Shannon conditions, Digital Holography has expanded rapidly [1]. This technique now has applications in a large number of domains from investigation of particles in flows [2; 3; 4; 5; 6; 7], to visualization of cells in biology or medicine, to phase contrast metrology, or to detection of nanoparticles without being exhaustive [8; 9; 10; 11; 12; 13; 14]. Research activities in this field have many orientations: some articles treat the elaboration of models to compute and predict holograms. Others emphasize on the development of new image processing techniques for object reconstruction, estimation of ultimate sensitivity of the set-up, or design of specific configurations for _in situ_ applications [15; 16; 17; 18; 19; 20]. In digital holography, the in-line configuration allows the design of a simple set-up with a relatively low number of optical elements. Depending on the application (visualization of bubbles in a cavitation tunnel, visualization of droplets through a transparent engine), the set-up has to be carefully designed. In order to optimize the design, we have developed analytical models that calculate theoretically in-line holograms generated by various kinds of spherical opaque or transparent particles [19; 21; 22; 23; 24]. Our analytical models allow to determine precisely reconstruction parameters from parameters of the set-up, through estimation of the coefficients of its optical transfer matrix. Nevertheless, these previous models are limited to the description of relatively simple circular particles, located in the center of the optical axis of the incident laser beam. There is no simulator that can predict the in-line holograms generated by objects that are arbitrarily-shaped and arbitrarily positioned in the field of the incident laser beam. In this paper, a numerical model that can calculate in-line holograms generated by arbitrarily-shaped arbitrarily-located objects is described. It is based on the scalar diffraction theory. Objects can be either opaque, transparent or semi-transparent. They are described by a 2-Dimensional transmission function. The whole set-up is described by optical transfer matrices of all elements. This formalism allows the description of _in situ_ set-ups, that combine beam shaping, protection windows, different kinds of spherical or cylindrical lenses and objectives. Digital reconstruction of opaque and phase objects using the 2D-fractional Fourier transform is then shown to illustrate the potentiality of the simulator.  
Section 2 will present the principle of the simulator. Attention will be focused on the description of the optical system by its own optical transfer matrix, and the definition of the objects (irregularly-shaped, arbitrarily-located, opaque or phase objects). The method to evaluate the intensity pattern in the plane of the electronic array sensor will be described in section 3: it is based on the use of generalized Huygens-Fresnel integrals. We will finally introduce in section 4 two main applications of our simulator: detection of inclusions in droplets for detection of nanoparticles, and analysis of ice-particles for calibration of airborne instruments that can detect and measure the size of ice crystals in the atmosphere.